Brown UniversityECON 1210

������������������Lectures Notes: Intermediate

Macroeconomics������������������

Christian Roessler

Spring 2011

Contents

1 Sizing Up the Economy 21.1 Macroeconomic Issues . . . . . . . . . . . . . . . . . . . . . . 21.2 Measurement of Aggregate Output . . . . . . . . . . . . . . . 31.3 GDP Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 Long-Run Growth 122.1 Aggregate Production and Productivity . . . . . . . . . . . . . 122.2 The Solow Model . . . . . . . . . . . . . . . . . . . . . . . . . 142.3 Saving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4 Innovation: the Romer Model . . . . . . . . . . . . . . . . . . 202.5 Quantifying the Role of Technology . . . . . . . . . . . . . . . 24

3 Frictions 273.1 Income Inequality and Unemployment . . . . . . . . . . . . . 273.2 Natural Rate of Unemployment . . . . . . . . . . . . . . . . . 303.3 Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.4 The Aggregate Price Level . . . . . . . . . . . . . . . . . . . . 373.5 Costs of In�ation . . . . . . . . . . . . . . . . . . . . . . . . . 403.6 In�ation and Interest Rates . . . . . . . . . . . . . . . . . . . 42

4 Short-Run Fluctuations 434.1 Cyclical Component of GDP . . . . . . . . . . . . . . . . . . . 434.2 Investment-Saving Equilibrium . . . . . . . . . . . . . . . . . 464.3 Multiplier E¤ect . . . . . . . . . . . . . . . . . . . . . . . . . . 484.4 Fed Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.5 Interest Rate Targeting and the Money Supply . . . . . . . . . 594.6 Aggregate Demand and Supply . . . . . . . . . . . . . . . . . 624.7 Real Business Cycle Theory . . . . . . . . . . . . . . . . . . . 694.8 The Financial Crisis of 2008 . . . . . . . . . . . . . . . . . . . 794.9 The Fed Response . . . . . . . . . . . . . . . . . . . . . . . . . 83

5 Public Finance 885.1 Tax Revenue . . . . . . . . . . . . . . . . . . . . . . . . . . . . 885.2 Budget De�cits and the Federal Debt . . . . . . . . . . . . . . 915.3 Entitlement Programs . . . . . . . . . . . . . . . . . . . . . . 97

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6 The International Dimension 1026.1 Relationship between Budget De�cit and Trade De�cit . . . . 1026.2 Exchange Rates vs. In�ation and Interest Rates . . . . . . . . 1066.3 Exchange Rate Regimes . . . . . . . . . . . . . . . . . . . . . 1116.4 Business Cycle in an Open Economy . . . . . . . . . . . . . . 1136.5 The Asian Crisis of 1997 . . . . . . . . . . . . . . . . . . . . . 115

1 Sizing Up the Economy

1.1 Macroeconomic Issues

� Some facts we want to explain: US GDP per capita now �fty timeshigher than Ethiopia�s; divergent trends in the unemployment rate be-tween US and Europe. In�ation in wealthy countries was high in theseventies, dropped in the eighties; US trade de�cit and budget de�cithave tended to increase.

� US GDP per capita has been increasing at roughly 2% on average, butthere are �uctuations (notably Great Depression)

� Long-run trend dominates short-run �uctuations, 15-fold increase inGDP per capita for US between 1870 ($ 2,500) and 2004 ($ 37,000)

� Nobel laureate Robert Lucas, in 1987, calculated how much consump-tion people would be willing to give up each year in order to havesmooth consumption (essentially a full insurance), rather than the vari-able pattern of consumption that we observe in practice.

� This exercise involves assuming a level of risk aversion (which can beinferred, for example, from the interest rate people require in orderto save when income is expected to increase in the future - savingmore means more uneven, i.e. "riskier," consumption). But even forthe highest measures of risk aversion, the price people would pay onaverage to eliminate business cycles is tiny - Lucas estimates 0.06% ofincome, or $ 30 for someone earns $ 50,000 per year.

� Is this plausible? The value of such insurance would seem much higherwhen people stand to lose all their income by becoming unemployed(rather than just the standard deviation in consumption, which is about

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1.5%). Of course, unemployment insurance o¤sets this potentially dev-astating loss.

� Elements of a model: exogenous (given) vs. endogenous (determined).Could refer to values of variables, functional forms etc. Exogenousvalues also called parameters, may be interested in comparing outcomesof the model for di¤erent values.

� Example: demand, supply functions are exogenous, price is endoge-nous. Alternatively: preference relations, technologies are exogenous,demand and supply functions are endogenous.

� Distinction between long run (what happens inequilibrium, with allvariables fully adjusted) and short run (some variables are �xed, forexample the price and supply of labor).

1.2 Measurement of Aggregate Output

� Simon Kuznets got the 1971 Nobel for inventing Gross Domestic Prod-uct, aggregate measure of all goods (including physical products andservices) created within a country�s borders in a given year (note thisis not the output of the country�s citizens: excludes citizens abroad,includes foreign nationals living here).

� GDP aggregates the value-added from each productive activity in theeconomy to arrive at the total value produced.

� For example, value-added from car assembly is the factory cost of thecar less the procurement cost of the individual parts. Then the dealeradds value when the car is sold above factory cost; the di¤erence be-tween the �nal purchase price and the factory cost is the value-addedfrom selling.

� GDP is equal to the value of all expenditures:

GDP = C + I +G+NX

where C are consumer spending, I is the value of investments (primarilyby �rms), G is government purchases, and NX is net exports (domesticproducts bought by foreigners, less foreign products bought by localresidents).

3

� For the US, the largest component (about 70%) is consumption spend-ing on �nal goods and services (not used in the production of furthergoods and services). The next largest components (respectively about15% and 20%) are investments in buildings (o¢ ce and residential),equipment and inventory as well as government outlays on schools,highways, research and defense. The smallest component (negative5%) is net exports (the trade balance): since imports recently exceedexports in the US since the mid-1970s, this entry is negative.

� Note that business expenditures on intermediate goods are not includedanywhere in the expenditure approach, so there is no double counting.Investment goods are by de�nition not used up in production.

� Transfer payments are not included, e.g. stock purchases and welfarebene�ts, since these simply shift wealth (do not create anything new)and are used by recipients to make purchases, which are recorded inother categories.

� There was a large increase in consumption, at the expense of invest-ment, during the Great Depression, and a large reduction in both con-sumption and investment during WW II, as the government expandeddefense spending.

� The expenditure shares have been fairly stable since WWII, but notethe increasing trend in consumption, which is matched by a decreasein net exports (and, to a lesser extent, government purchases).

� GDP is also equal to the aggregate income of the economy�s resources,namely capital and labor. This consists of pro�ts on the one hand, andsalaries and bene�ts on the other.

� But not all business income that is generated is received in the form ofpro�ts. Firms use up and replace capital (and therefore charge depre-ciation against their pro�ts). They must also pay certain taxes to thegovernment that do not come out of pro�t. Income must be generatedto cover these additional expenses, and this income should be counted.

� Note that gross salaries and pro�ts include taxes that will be paid"directly" out of earned income to the government. But there arealso indirect taxes, such as the sales tax which businesses collect from

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consumers, which is not counted under either salaries or pro�ts. Thesemust be added in, since they re�ect value the economy created.

� Moreover, some income must be reinvested in order to maintain thecapital stock. Again, the business income that covers depreciation isvalue that we should count.

� An important fact is that the share of labor (i.e. salaries and bene�ts)in total income is roughly constant at 2/3. If resource markets arecompetitive, this means labor contributes about 2/3 of the value theeconomy creates, and production functions we use in modeling shouldre�ect this.

� Compensation of employees is actually only a little more than half ofGDP in 2005. But have to keep in mind that pro�ts include compensa-tion for business owners�labor, which needs to be separated out whenmeasuring labor and capital shares.

� The national income identity

Y = C + I +G+NX

says that total income Y must equal total expenditure (and both equalGDP). An identity is true by de�nition - any deviations in practicere�ect measurement errors or incorrect accounting.

� Some of the omissions in GDP are what is produced outside the market(cooking and cleaning at home, volunteer work) and the exhaustion ofnatural resources (oil, clean air). This can be an issue in comparingGDP across countries, where some have a large informal sector or growon depletion of resources, pollution or unhealthy lifestyles.

� When we look at total output of an economy, we have to literally ag-gregate apples and oranges - quantities of products and services thatcannot be directly compared. What does it mean that a million carsand three million hours of hospital care were provided in a year? Hastotal output increased or decreased if the number of cars goes downand the number of hours of care goes up?

� GDP solves this by weighting quantities by prices - supposedly theyre�ect the value of the products and services.

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� This isn�t quite correct, even with perfectly competitive markets. Whatis true is that prices re�ect the marginal value of products and services,i.e. the value of the last unit sold. They contain no information aboutthe value of non-marginal units. (Think about pain reliever - it�s cheap,but clearly worth much more than its price to some individuals!) How-ever, such information would be di¢ cult or impossible to obtain, soweighting units by prices is the best we can do.

� Prices are quoted in terms of money, which varies in supply and there-fore can become more abundant or more scarce. More on this later, buttwo reasons why it becomes more abundant is that the Fed constantlyreleases more bills into circulation and that a given bill might get spentmore often in a given year.

� Abundant money - more bills chasing the same quantity of goods -means that goods get on average more expensive. In comparing GDPover time, we must account for in�ation to isolate the change in valuethat is created.

� Distinguish between nominal GDP (total value of �nal goods and ser-vices, weighted by their current prices) and real GDP (nominal GDPadjusted for change in the average price level). Various approaches toadjusting for in�ation.

� One idea is to keep prices constant: to compare GDP at two di¤erenttimes, t and t+1, use either the prices at time t or at time t+1. Thiswas the traditional way to measure real GDP in the US until the 1990s.

� Fixing at time t prices,

NGDPt = RGDPt =nXi=1

pitqit

where pi is the price of good i, and qi is the quantity of good i (herewe are using the expenditure approach to GDP). Holding prices �xed,we have

RGDPt+1 =

nXi=1

pitqit+1:

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� Implicitly, at time t the price level is 1, but it may change by time t+1.

NGDPt+1 =nXi=1

pit+1qit+1 = PP �RGDPt+1

where

PP =

Pni=1 p

it+1q

it+1Pn

i=1 pitqit+1

is the price index. This is a so-called Paasche price index, based onquantities consumed at time t + 1. (In general, a Paasche index holdsa variable constant at its �nal level.)

� Note that changes in nominal GDP from t to t+1 can be driven eitherby changes in prices or by changes in real GDP.

� The increase in real GDP is

rP =RGDPt+1RGDPt

=1

PP

Pni=1 p

it+1q

it+1Pn

i=1 pitqit

:

� Fixing at t+ 1 prices, we have

RGDPt =nXi=1

pit+1qit

and

NGDPt+1 = RGDPt+1 =nXi=1

pit+1qit+1:

� NowNGDPt =

RGDPtPL

=

nXi=1

pitqit

and

PL =

Pni=1 p

it+1q

itPn

i=1 pitqit

is the price index. This is a Laspeyres index, based on quantities con-sumed at time t. (In general, a Laspeyres index holds a variable con-stant at its initial level.).

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� The increase in real GDP according to this de�nition is

rL =RGDPt+1RGDPt

=1

PL

Pni=1 p

it+1q

it+1Pn

i=1 pitqit

:

� Problem is, in comparing across longer periods, have to keep holdingprices constant (for example, at the level of 1960 when comparing realGDP in 2010 to 1960). This may give an unrealistic picture, sincesome prices change greatly over time. This became especially clear inthe early 1990s, as computer prices fell rapidly, even from year to year.

� Hence national income accountants began to adjust the price indexgradually, using a Fisher, or chain-weighted, index:

PC =pPL � PP :

� If the Fisher index is bechmarked to time t,

NGDPt = RGDPt =nXi=1

pitqit

NGDPt+1 = PC �RGDPt+1 =nXi=1

pit+1qit+1

and therefore the increase in real GDP is

rC =RGDPt+1RGDPt

=1

PC

Pni=1 p

it+1q

it+1Pn

i=1 pitqit

=prP rL:

� If the Fisher index is bechmarked to time t+ 1,

NGDPt =RGDPtPC

=

nXi=1

pitqit

NGDPt+1 = RGDPt+1 =

nXi=1

pit+1qit+1

and again

rC =RGDPt+1RGDPt

=1

PC

Pni=1 p

it+1q

it+1Pn

i=1 pitqit

=prP rL:

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� The reason it�s called chain-weighted is that, for multi-year periods, say2008 to 2010, we would calculate PC =

pPL � PP �rst for 2009 to 2010,

an average of prices �xed at the 2009 and 2010 levels, then calculate PCfor 2008 to 2009, an average opf prices �xed at 2008 and 2009 levels.So it�s a moving average, like a chain.

� The price indices are called GDP de�ators, since they are used to ad-just nominal GDP for in�ation to recover real GDP, which is what weultimately care about.

� When we compare GDP across countries to see how well o¤ the averagecitizen is, it is also important to hold prices �xed. Exchange rates aredetermined by many factors and do not necessarily re�ect the pricesof consumer goods. So, we might compare GDP by keeping pricesconstant at the level of US prices in a given year.

� Laspeyres and Paasche are names from index theory that refer, respec-tively, to holding something �xed at the initial level (Laspeyres) vs.�nal (Paasche). But when we calculate real variables in macro, thatsomething might refer either to prices or quantities, and that�s how theusage of the terms can be confusing or seemingly contradictory.

� In calculating in�ation, we factor out any increases in quantities andimplicitly �x them at some level. If real GDP is de�ned in terms of�nal prices (a Paasche index), quantities are e¤ectively �xed at theinitial level, and in that sense the price index is Laspeyres. If real GDPis de�ned in terms of initial prices (a Laspeyres index), quantities areimplicitly �xed at the �nal level, and in that sense the price index isPaasche.

� To see this, you only need to realize that, with the Paasche de�nitionof real GDP, real GDP is equal to nominal GDP in the �nal period,so the price level is one. When you work out the growth in the priceindex, it�s a function of nominal vs. real GDP in the initial period,which is based on initial quantities. So the price level is a Laspeyres

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index:

NGDP =nXi=1

pit+1qit = P �RGDP;RGDP =

nXi=1

pit+1qit

Pt =NGDPtRGDPt

=

Pni=1 p

itqitPn

i=1 pit+1q

it

; Pt+1 =NGDPt+1RGDPt+1

= 1

Pt+1 � PtPt

=

Pni=1 p

it+1q

it �Pn

i=1 pitqitPn

i=1 pitqit

:

1.3 GDP Facts

� There�s been little change in wealth for two-thousand years, since theemergence of agriculture and cities, then a dramatic rise from the 18thcentury, spread unequally across countries (from roughly $500 per per-son to $30,000 per person in the richest countries).

� Evidence of conversion: wealthier US states in 1880 grew slower thanpoorer states, e.g. theWest (wealthy due to mining boom) had markedlyslower growth than the South (initially poor due to civil war).

� Within the Northeast, relatively poor Maine and Vermont caught upwith relatively rich Massachusetts and Rhode Island.

� On average, half the di¤erence in wealth was eliminated every 35 years.

� Quantitatively very similar observations for regions in Western Eu-rope from 1950, while the rate of convergence is slower across OECDcountries since 1960 (di¤erences halve every 70 years) and there is notendency of conversion when we look at all countries of the world from1960.

� Growth rates from 1960-2000 versus wealth relative to US in 2000:higher growth rates were actually associated with higher initial wealth.

� Empirically, we have conditional convergence: poorer countries growfaster if they are otherwise similar. Most important characteristics(that correlate with higher growth, given current wealth) are: rule oflaw / property rights protection, openness to international trade, lowshare of government consumption purchases in GDP, high saving rate,low population growth, better education and health.

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� As mentioned before, US average growth rate per capita has beenaround 2% for a long time. Total GDP grew even more, but so didpopulation.

� Detrended �uctuations (cyclical component of real GDP) has standarddeviation of about 1.7%. (I.e. growth is on average 1.7% above orbelow trend of 2% at any given time.)

� Can also look at cyclical components of items in real GDP (i.e. theirdeviations from trend) as it relates to cyclical component of GDP.

� Low standard deviation relative to real GDP (half): consumption ofnon-durables and services, net exports. High standard deviation rela-tive to real GDP (three to �ve times): consumption of durables andgross private investment. Similar standard deviation: government pur-chases.

� Thus much of volatility comes from behavior of investment, broadlyde�ned.

� Correlation coe¢ cient cov (X; Y ) =pvar (X) var (Y ) is a normalization

of the covariance E [(X � E (Y )) (Y � E (Y ))], a measure of whethervariables tend to be large / small at the same time or not (i.e. towhat extent they move together or in opposite directions, or are notsystematically related). Falls between 1 and �1.

� Variables that move in the same direction as real GDP are procyclical,variables that move in the opposite direction are countercyclical. Vari-ables that do not systematically move with or against real GDP areacyclical.

� Procyclical: consumption, investment. Countercyclical: net exports(more is imported in boom periods). Acyclical: government purchases.

� Thus, the big story in �uctuations is that investment expands in goodtimes, contracts in bad times, and this accounts for most of the expan-sion and contraction in real GDP.

� Employment and average worker hours are procyclical, hence we seeunemployment and underemployment when investment and real GDPcontract.

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� Output per worker and output per worker hour are procyclical (the �rstmore so than the second), i.e. worker productivity is higher in boomsand hours expand at a greater rate than employment.

� So it seems that investment expands in response to an increase in workerproductivity (sources of which are not clear). Formalizing these rela-tionships is the focus of one approach to �uctuations (real businesscycles, where shocks to labor productivity are taken to be exogenous).Another (Keynesian) takes as its starting point �uctuations in demand(which appears to have less empirical support, but o¤ers more guidanceto policy).

2 Long-Run Growth

2.1 Aggregate Production and Productivity

� Cobb-Douglas production function:

Y = AK�L�:

� Interpretation of � and �: elasticity of output with respect to inputs,

@Y

@K

K

Y= �AK��1L�

K

AK�L�= �

@Y

@L

L

Y= �AK�L��1

L

AK�L�= �:

� Note that@Y

@K

K

Y=MPK �K

Yand

@Y

@L

L

Y=MPL � L

Y:

� Since MPK = r (marginal product of capital equals the price of cap-ital) and MPL = w (marginal product of labor equals the price oflabor) in competitive factor markets, we have � = (r �K) =Y and� = (w � L) =Y , i.e. � and � correspond to the income shares of capitaland labor. Since these are empirically 1=3 and 2=3, it is reasonable toset � = 1=3 and � = 2=3.

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� Then we have constant returns to scale (scaling all inputs by factor �scales output by factor �):

A (�K)1=3 (�L)2=3 = �1=3�2=3A (K)1=3 (�L)2=3

= �1=3+2=3AK1=3L2=3

= �AK1=3L2=3 = �Y:

� On the other hand, marginal products of each individual factor is di-minishing:

MPK =@Y

@K=1

3A

�L

K

�2=3is declining in capital, and

MPL =@Y

@L=2

3A

�K

L

�1=3is declining in labor.

� Note that marginal products increase in A as well as the quantity ofthe other factor.

� Per capita GDP is

y � Y

L= AK1=3L

2=3

L= A

�K

L

�1=3� Ak1=3:

� Suppose A is constant across countries, then the only source of dif-ferences should be capital stocks per person. From the size of capitalstock per person relative to the US (data from 2000) we can predictGDP per capita relative to the US (�1=3 where � is ki=kUS). The pre-dicted di¤erences in GDP per capita tend to fall short of the actualdi¤erences. So A seems to be a signi�cant source of di¤erences too.

� Large di¤erences in capital stock per person translate into smaller dif-ferences in predicted GDP per capita because of diminishing MPK.

� There is a positive relationship between predicted and actual GDP,but the �t is far from perfect (i.e. deviates strongly and systematicallyfrom the 45 degree line, along which predicted and actual GDP wouldbe equal).

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� The implied value of A, which can be interpreted either as total factorproductivity (TFP) if we trust the model, or as the residual (deviationfrom reality) if we don�t.

� Di¤erences in A put countries on di¤erent growth trajectories as kincreases. If China had the same TFP as the US, the it would lie onthe high path, but as estimated, its lower TFP puts it on the low path.

� Calculating TFP for di¤erent countries and mapping against GDP percapita, we see that wealthier countries tend to have higher TFP.

� How important is A relative to k? Comparing Ai=AUS to ki=kUS empir-ically (where TFP is imputed so as obtain the correct GDP per capita,given the capital per person), we �nd that Ai=AUS is typically twice aslarge as ki=kUS, so it accounts for 2=3 of the di¤erences in GDP percapita. You could either say that most of the di¤erences are attribut-able to productivity or unexplained, which really amounts to the samething.

� What might account for di¤erences in A? As the empirical results Imentioned in the previous lecture suggest, di¤erences in growth can belinked to di¤erences in rule of law / enforcement of property rights,government policy on things like spending and trade barriers ("institu-tions"), or health and education ("human capital"). Another possiblefactor would be di¤erences in technological know-how.

2.2 The Solow Model

� Solow model endogenizes the size of the capital stock in a dynamicmodel. Capital accumulates if investment exceeds depreciation:

Kt+1 = Kt + It � �Kt:

Depreciation is a constant that is typically thought to be around 10%or slightly lower. In di¤erence notation,

4Kt � Kt+1 �Kt = It � �Kt:

� The capital stock keeps increasing while investment is greater than de-preciation, but depreciation also increases (since it�s a �xed percentage

14

of an increasing quantity) - if investment is constant, the addition tothe capital stock gets smaller and smaller.

� We have no government or trade in this model, so expenditure on GDPis

Yt = Ct + It:

In this context the expenditure equation is referred to as the resourceconstraint.

� LetIt = sYt;

i.e. a constant fraction of output is saved and invested (where s 2[0; 1]). Then

Ct = (1� s)Yt:

� Production function at time t is

Yt = AK1=3t L2=3:

For the moment, think of A and L as �xed parameters.

� Starting level of capital K0 at time 0 must be positive - why? (Elsenothing ever gets produced and accumulated.)

� Capital accumulation is driving everything, we want to express it as afunction of the present capital stock (or of Yt, which depends directlyon Kt):

4Kt = It � �Kt = sYt � �Kt:

� For given constants A and L, as well as s and �, we can now workout the size of the capital stock at any point t by starting from K0

and adding net investment 4K1, 4K2 and so forth. The interestingquestion is: will capital forever increase in this fashion?

� Since Yt is concave in Kt (increasing at a diminishing rate) and �Kt islinear in Kt (increasing at a constant rate) a point K� will eventuallybe reached where sYt = �Kt, i.e. saving just o¤sets depreciation. Butthen 4Kt = 0 (net investment is nil), so the capital stock does notgrow any further and will stay �xed at that level.

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� If Kt > K� initially, depreciation exceeds investment, and the capital

stock declines.

� Thus, for a given production function, saving and depreciation rate,regardless of what they are, the capital stock is �xed in the long run.We say the system is in its steady state, once K� has been reached,and because the steady state is reached regardless of the initial level ofcapital K0, we say that it is (globally) stable.

� Since K� has the property that 4K� = 0, i.e. Kt+1 = Kt, we have

sY �t � �K� = 0

and, substituting for Y � and rearranging,

sAK�1=3L2=3 � �K� = 0

and

K� =�s�A�3=2

L:

� At K�, output is Y �, the associated steady-state level of production.Note that ouput grows while capital is below its steady-state level andthen ceases to grow. Similarly, in the steady state, investment is �xedat sY �, consumption at (1� s)Y �. similarly.

� We have

Y � = AK�1=3L2=3

= A

��s�A�3=2

L

�1=3L2=3

=�s�

�1=2A3=2L:

� Per capita output in the steady state is therefore

y� =Y �

L=�s�

�1=2A3=2:

It increases in the productivity parameter A and in the saving rate.

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2.3 Saving

� What determines the saving rate? The return to investment is �xedhere by � = 1=3 (remember, this is the elasticity of output with re-spect to capital). Somewhere in the background, though not explicitlymodeled, you can imagine a market where savers lend funds or rent outcapital to �rms, and if that market is competitive, the price of capitalwill be its marginal product, so this is what savers get.

� People have to decide whether they want to consume immediately orwait till later and bene�t from returns to investment. Diminishingreturns to capital means MPK is high when the capital stock is small,and MPK is low when the capital stock is large. So there is a strongincentive to save when investment is currently low and a weak incentivewhen investment is currently high.

� The saving rate is likely to be positive but not one. Ultimately, timepreference determines the precise level. The more patient consumersare, i.e. the more output they are willing to set aside so that morecan be produced in the future, the higher will the saving rate be. Thispreference / cultural explanation is frequently given for the high savingrates in Asia relative to Western countries.

� Capital-to-output ratios (K=Y ) against saving rates for di¤erent coun-tries in 2000: positive relationship is predicted by the steady stateequation sY � = �K� or

K�

Y �=s

�

and borne out by the data.

� To quantify the role of saving in explaining di¤erences in GDP percapita, notice that high-saver countries like Japan had about a 30%saving rate, whereas low-saver countries like Ethiopia saved around5%. So, except for the most extreme cases, saving rates vary at mostbe a factor of 6.

� Since the Solow model implies that

y�Jy�E=

�sJ�

�1=2A3=2J�

sE�

�1=2A3=2E

=

�sJsE

�1=2�AJAE

�3=2;

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and sJ=sE � 6, while y�J=y�E � 45, we have

AJAE

=(y�J=y

�E)2=3

(sJ=sE)1=3� 12:6

1:8= 7:

� But, even though this di¤erence in productivity is not much di¤erentfrom that in saving, its implied impact on GDP per capita is muchlarger:

(AJ=AE)3=2

(sJ=sE)1=2

=y�J=y

�E

sJ=sE� 45

6= 7:5:

� Hence it appears that most of the di¤erences in GDP per capita must beattributed to di¤erences in productivity, rather than saving behavior.

� Moreover, the Solow model implies that long-rung growth is not possi-ble through capital accumulation alone - eventually, the economy set-tles down to a steady state. Higher saving implies that the steady stateGDP per capita is higher (and perhaps grows faster during the tran-sition, depending on how far the initial GDP is from the steady statelevel). However, it cannot change the fact that there is no growth oncecapital has reached its steady state level.

� E¤ect of an increase in the saving rate on the steady state: igher savingand investment at all levels of capital implies steady-state capital K�

increases.

� As a result, steady-state GDP Y � also increases. Transition dynam-ics: when the saving rate increases, there is at �rst a sharp increasein GDP (since the capital stock is far below its new steady-state level,and therefore investment far exceeds depreciation), followed by dimin-ishing increases (as depreciation approaches the level of investment)and ultimately stagnation.

� An increase in the depreciation rate causes steady-state capital to fall.Steady-state output decreases, at �rst rapidly as depreciation far ex-ceeds the level of investment, then more slowly and ultimately thesystem comes to a rest point again.

18

� Since4Kt

Kt

= sYtKt

� �

= sYtKt

� s Y�

K�

(recall 4K� = sY � � �K� = 0), we have

4Kt

Kt

= sY �

K�

�Yt=Kt

Y �t =K�t

� 1�

= sY �

K�

�K�t

Kt

�2=3� 1!;

which implies that the growth rate of the capital stock increases inK�t =Kt, i.e. the distance from the steady-state level of capital (note

that Y �=K� is just a constant).

� Similarly, GDP and GDP per capita grow faster when they are fartherfrom their steady-state levels.

� Current OECD countries that were poorest in 1960 tended to havethe highest growth rates. Why is this not really convincing evidence?(OECD is a non-random sample: we are looking at the richest countriestoday and conclude that those that were poorest in 1960, but endedup being rich today, had high growth rates. There is a selection bias -what about countries that were poor in 1960, but did not make it intothe OECD?)

� No such correlation when we expand the set of countries beyond theOECD. Similar growth rates for poor and rich countries suggests thatmany countries were close to their steady states in 1960 and grew forother reasons than catch-up, i.e. they experienced steady-state growththat was unrelated to their level of wealth.

� Growth experience of the Philippines to that of Korea: Philippine in-vestment rate was nearly constant since 1950, much like the US, so itmay have been near its steady state initially. Korea saw constant in-vestment from 1950 to 1960, and then a big increase right up to 2000,thus in 1960, its steady state appears to have shifted.

19

� Once in steady state,y� =

�s�

�1=2A3=2

can only grow if there is growth in one of the parameters (s, � or A).In the steady state, where MPK (and therefore the interest rate) isconstant, saving could only change due to changes in time preference.We do not have a good story for this or for a persistent decline ofdepreciation. So the implication of the Solow model is that economistsmust focus on changes in productivity to explain sustained long-rungrowth.

� Note that y� does not depend on L, therefore population growth cannotlead to growth in GDP per capita. Equivalently, if everything else isconstant, GDP grows exactly at the rate of population growth.

� Suppose a poor country like Ethiopia receives aid in the form of ma-chinery. Will this contribute to long-run growth? (No, if Ethiopia isin steady state, this will only lead to a temporary increase in GDP;because depreciation exceeds future investment, the capital stock willdwindle down and eventually go back to the old level, as does GDP.)

2.4 Innovation: the Romer Model

� It�s clear that we need to focus on total factor productivity to explainlong-term growth, but how can we model productivity growth? PaulRomer�s insight was to treat "ideas" as another input in the productionfunction, with some unique properties, and to model the creation ofideas through division of labor into production and research.

� Ideas are non-rivalrous goods: once produced, they can be used overand over again. Thus, if A represents the stock of ideas in the Cobb-Douglas function, it makes sense that there are constant returns toscale with respect to K and L (rather than all three factors): we candouble K and L and double output without increasing A at all. It�slike building another plant that follows the same blueprint as the �rst.

� But then we have increasing returns to scale with respect to K, L andA:

(�A) (�K)1=3 (�L)2=3 = �2AK1=3L2=3 = �2Y:

20

� We now imagine that the economy can produce goods Y as well as ideasA. Labor has to be allocated to these two sectors. LY is the amountof labor the economy uses to manufacture Y , and LA is the labor thatis involved in creating A, where

L = LY + LA:

� Hence we have two production functions:

Yt = AtK1=3t L

2=3Y

and4At � At+1 � At = AtLA:

� Ideas being non-rivalrous, they can simultaneously contribute to theproduction of goods and of new ideas, so At shows up in both produc-tion functions. What is key to the Romer model is that there are nodiminishing returns to ideas in either production function. Ideas leadto further ideas at the same rate in perpetuity. These ideas add thesame amount of productivity in the goods sector in perpetuity.

� Unlike in the Solow model, it is not clear whether a steady state, wherethe capital stock stops growing, exists. Therefore, we focus on a solu-tion where the capital stock grows at a constant rate instead - calleda "balanced growth path" (steady state is a special case where theconstant growth rate is zero).

� If capital stock grows at a constant rate, then4Kt

Kt

= sYtKt

� �

is constant, and thus Yt=Kt is constant, which implies

4Kt

Kt

=4YtYt:

� The quickest way to calculate the growth of a function is by taking thetime derivative of its natural log

@ lnYt@t

=1

Yt

@Yt@t

=4YtYt:

21

� Applying this to the production function, we have

4YtYt

=@ lnYt@t

=@

@t

�lnAt +

1

3lnKt +

2

3lnLY

�=

4AtAt

+1

3

4Kt

Kt

:

� Substituting 4Kt=Kt = 4Yt=Yt, we can solve for

4YtYt

=3

2

4AtAt

:

Note that output grows faster than productivity - the reason is that thecapital stock keeps expanding as productivity increases (more outputis produced and available for investment at a constant saving rate, soinvestment always stays ahead of depreciation). So part of the increasein output comes from productivity growth, and part comes from posi-tive net investment. (Recall: we are de�ning a balanced growth pathsolution as one where net investment is proportional to Kt, which isonly possible here if net investment is positive.)

� Since ideas grow at the rate

4AtAt

= LA;

we have4YtYt

=3

2LA =

4Kt

Kt

:

� So the capital stock and output are now growing at a rate that increasesin the productivity of the idea-generating sector and the amount oflabor that is involved in research.

� The stock of ideas at time t, assuming an initial level A0, is

At = A0

�1 +

4AtAt

�t= A0 (1 + LA)

t :

(It would be A1 = A0 (1 + g) at time 1, A2 = A1 (1 + g) = A0 (1 + g)2

at time 2, and so forth, where g = 4At=At.)

22

� Similarly for capital:

Kt = K0

�1 +

4Kt

Kt

�t= K0

�1 +

3

2LA

�t:

� Therefore,

Yt = AtK1=3t L

2=3Y = A0K

1=30 L

2=3Y (1 + LA)

t

�1 +

3

2LA

�t=3along the balanced growth path.

� Romer argued that, because of the positive externalities inherent tothe production of ideas, �rms engaged in research could not absorb thefull bene�ts in pro�ts and therefore would tend to employ less thanthe e¢ cient amount of the labor. (I.e. only very bene�cial and prof-itable ideas would be created, because the fraction of the value thatresearchers could pocket would be large enough to justify the costs.Other ideas might have a positive value for society, but are not prof-itable to develop.)

� Nevertheless, the Romer model delivers permanent growth. And it tellsus that incentives for research (i.e. to raise LA), e.g. through patentprotection, are a vehicle for long-run growth.

� We need to qualify this �nding a bit: knowledge is likely to spill overfrom the most advanced countries to others, so it may not make sensefor the latter to invest in research. Growth in all countries is thendriven by knowledge creation in the most advanced countries, and it isthey who must ensure the incentives are in place.

� In the basic Romer model without capital accumulation, adjustment tothe equilibrium level of capital is not an issue, so the economy is neverin transition. (This is a simpli�cation, not a substantive assumption.We could explicitly model capital stock dynamics.) The growth rateadjusts instantaneously when parameters change.

� An increase in population (more of LA and LY ) raises productivity andoutput growth.

23

� An increase in the fraction of workers assigned to idea generation (moreof LA, less of LY ) leads to an initial reduction in output (since the laboris taken out of goods production), but eventually to an increase, asproductivity growth increases from research. Why not assign all laborto research? (Because then output jumps to zero, since manufacturingrequires labor too. The more we cut output at time t, the more growththe economy needs to get back to the old level. If people want some levelof consumption now, they can�t neglect production even temporarily.)

� An increase in the saving rate s leads to transition dynamics as in theSolow model, i.e. rapid initial growth as the capital stock adjusts (in-vestment far exceeds depreciation). But now the economy does notend up in a no-growth steady state, it goes back to the constant bal-anced growth, the "normal" growth rate, once increasing depreciationand diminishing returns to capital return the economy to a state whereproductivity improvements are the sole source of growth again.

2.5 Quantifying the Role of Technology

� If we allow that, in principle, all factors in the production functioncould be growing (i.e. Yt = AtK

1=3t L

2=3Y t , where LY now has a time

subscript), GDP per capita can be written as follows:

yt =YtLt= At

�Kt

Lt

�1=3�LY tLt

�2=3= Atk

1=3t �

2=3t ;

where �t = LY t=Lt denotes the fraction of labor allocated to manufac-turing goods and services.

� The growth rate of GDP divides into factor growth rates as follows:

4ytyt

=@ ln yt@t

=4AtAt

+1

3

4ktkt

+2

3

4�t�t:

� This equation can be used to determine the relative contributions ofthe factors to GDP growth: just plug in the observable growth ratesof GDP, capital per (non-research) worker and growth in the share ofnon-research labor, and the remainder is productivity growth.

24

� The decomposition for the US, �rst for the 1948-2002 period and thenfor three subintervals. Note how GDP per capita (or, more precisely,per hour) dropped temporarily from 1973-1995, then picked up again.This pattern is mimicked by productivity, and to a lesser extent cap-ital per worker - they fell and then recovered to an extent. From thenumbers, it�s apparent that productivity changes played the key role.

� 1973 is of course associated with the explosion of crude oil prices thatwas triggered by the Yom Kippur war between Israel and its neighborsSyria and Egypt. The initial attack on Israel occurred on October 5,1973, and OPEC (which had already been founded in 1960, mostlyby Arab countries) responded to support for Israel from the UnitedStates and other western countries with an embargo (i.e. a cut in oilproduction for export). This quadrupled the price of crude oil by 1974.

� The Iranian revolution at the end of the decade and the subsequent in-vasion by Iraq further reduced the crude oil supply and led to anothertripling of oil prices by 1981. The US government instituted price con-trols that caused domestic producers to also cut back their productionand led to a shortage. When they were lifted, consumers had to facethe reality of permanently higher oil prices.

� Over time, consumers invested in more fuel-e¢ cient cars, insulation forhome etc.; oil companies in non-OPEC countries increased exploratione¤orts and oil production. This ultimately reduced prices, despiteOPEC�s e¤orts to maintain them through the mid-1980s. However,OPEC had become su¢ ciently in�uential to sustain oil prices abovethe 1970 level. They spiked up again in the early 1990s, after Iraq�sinvasion of Kuwait started the �rst Gulf War. (More recently, the crudeoil price went through cycles where it tended to hit lows during majorcrises, such as Asia at the end of the 1990s and September 11, rising inbetween to meet the increased demand from the growing economies inAsia and elsewhere.)

� There would have been an impact on productivity on many levels, butmost directly productivity as we use it here comes in part from theavailability of resources other than capital and labor - such as energy.In other words, if energy is needed to produce goods and services, andit�s in short supply, capital and labor can�t generate as much output.

25

The production function changes, and the only place where that can beaccounted for with Cobb-Douglas is At. Hence, it is not surprising thatthe rising oil price - which re�ected a relative oil shortage - coincidedwith low productivity measures and lower growth.

� Another reason to believe that the productivity slowdown of 1973-1995had to do with oil is that it also occurred in other advanced economies- the main exception being the UK, which started to extract North Seaoil in the early 1970s (and deregulated its economy under the Thatcheradministration during part of this period).

� Computers appeared in the 1980s: the �rst PC in 1981, the �rst Macin 1984. By the late 1980s, fax and e-mail were part of our lives. Sowhy did productivity not recover until the mid-1990s? Experience withother technologies has shown that it takes time, after the initial appear-ance, for the technology to improve and for businesses to learn how toapply it. Adoption involves an initial diversion of resources: infor-mation must be gathered, choices made between competing platforms,employees must be trained, processes adjusted and optimized.

� Harvard economist Dale Jorgensen studied the impact of IT technolo-gies on productivity growth in-depth, and he estimates that it alreadyaccounted for most of the TFP growth that did happen in 1973-1990(in other words, there would have been no growth at all, had it not beenfor the advent of computer). Between 1990 and 1995, it accounted forall TFP growth (in fact, TFP would have grown at a slightly negativerate otherwise), and afterwards - when TFP growth picked up again -IT was responsible for two thirds of that growth (and the rest is ba-sically investment in hardware, which is attributed to capital). So ittook time for the full impact to be felt, but IT is what got us out ofthe productivity slowdown and into the mid-1990s economic boom.

� This corresponds quite closely to the "ideas" Romer had in mind: theever-improving chip designs and software kept making capital moreproductive, and therefore �rms accumulate machinery more rapidlyand produce more value that is partly reinvested. Software is a classicexample of something that is essentially non-rivalrous and makes iteasier to create more and more advanced software.

26

� People who work in software programming or chip design are the "re-search labor" of the Romer model. Think about whether software �rmsare able to appropriate all the value they create for society. One issueis piracy - it�s hard to protect a good that can be so easily transferred.Then there is competition between software developers - it constrainsthe prices they might charge. As a result, the industry�s pro�tability,while high, is probably far from its actual social value, and that meansthat some applications for which there might be adequate demand cannever repay their development costs and are therefore not undertaken- too few "research jobs" are created.

3 Frictions

3.1 Income Inequality and Unemployment

� Growth is about what happens to the GDP of a country. This is an im-portant measure of overall well-being, but how this value is distributedalso matters. A large part of GDP is paid out in wages to employees,and as we know wages can di¤er very substantially. What causes thesedi¤erences?

� Even as the supply of college-educated workers in the US and elsewhereis growing, the return to college education (in terms of additional ex-pected lifetime income) has been increasing since the 1960s. It�s hard toput an exact number on this return, since we would have to account forself-selection (more talented people getting an education - they wouldnot necessarily earn the same without their college degree as those whoactually start working after high school). But it�s clear that the dividebetween low- and high-skill labor income is widening.

� Some popular explanations are IT revolution that creates a larger de-mand for educated workers, and globalization, which has contributedto the demand for high-end service exports from countries like the US.In any case, these developments imply a more unequal income distrib-ution, which subtracts from the social value of GDP growth. It is noaccident that welfare systems are expanding, i.e. some of the additionalwealth is used to address inequality.

27

� In growth theory, the labor force is fully employed, since we are lookingat the long run, where prices (such as�wages) are fully �exible andmarkets have ironed out any shortages or surpluses.The long run is ananalytical device - what would happen if we could keep various thingsconstant, so that we can isolate the e¤ects of capital accumulation andproductivity change. In reality, we live in the short run, where somepeople are always unemployed.

� Employment in the US over time vs. GDP (recession intervals). Overthe post-war period of economic growth, there has been continuous netentry into the labor force, as women increasingly sought careers. Thesocial transformation underlying this phenomenon in the US began inWorld War II, when women were needed as workers while men weredrafted for military service overseas. Note how temporary reductionsin GDP (recessions) coincided with reductions in employment.

� Involuntary unemployment carries signi�cant costs beyond the loss ofoutput. This is because an increase in the unemployment rate does nota¤ect everyone the same: it entails a dramatic drop in the quality oflife for a small subset of the population, and we all face a personal riskof being a¤ected.

� Both the resulting inequality in incomes and the risk are costly from asocial perspective. This has to do with the way incomes translate intoutility, i.e. actual preferences. If we are risk averse, marginal utilityof income is diminishing. Inequality means that the poor, who have arelatively high marginal bene�t from income, have too little. Moreover,if income is risky because we might get unemployed, it is less valuablein utility terms. So what causes unemployment?

� A person is o¢ cial unemployed if (i) currently available to work, (ii)actively looking for jobs within the past four weeks. Most unemploy-ment spells are brief, a few weeks or months - on average, 25% of theunemployed �nd a job each month. About 20% of the unemployed tendto be long-term unemployed: out of a job for more than six months.

� US civilian population (16 and older) in 2005: those in the labor force(employed and unemployed) account for about 2/3 of the population;those not in the labor force (not looking for a job) for about 1/3.

28

� In 2005, unemployment was at about 5%, which is on the low side his-torically (close to 10% in 1982, 25% during the Great Depression). Ofcourse, now we�re back at almost 10%, which is very much on the highside. European economies traditionally have much higher unemploy-ment, and this di¤erence has to be explained.

� Wages are determined by supply (from prospective workers) and de-mand (from prospective employers) in the labor market. Generally,supply is higher and demand is lower at higher wages.

� Income taxes shift labor supply in (workers demand higher pay). Else,they are likely to exit the labor market, in which case they should notbe counted as unemployed (since they are no longer actively looking).However, in Europe where unemployment bene�ts last longer and after-tax wages are substantially lower than in the US, there is a greaterincentive to keep looking "reluctantly," i.e. be o¢ cially unemployedbut unwilling to accept some of the available jobs.

� European legislation that makes it di¢ cult to �re people, and raisesnon-wage expenses to the employer, reduces labor demand. With laborsupply �xed, this is another factor that increases unemployment.

� Wage rigidity refers to the tendency of wages to remain �xed as de-mand conditions change. This is what underlies the Keynesian theoryof �uctuations, which can certainly explain labor surplus (unemploy-ment). But these rigidities are quite controversial as an assumption.One has to keep in mind that we are talking about real wages - to keepthem �xed, nominal wages have to actually increase (assuming there issome in�ation). It is not clear what would cause nominal wages to riseduring recessions.

� A possible reason is union power (since traditionally union workers aremore di¢ cult to �re, unions might have a smaller incentive to protectjobs than to protect incomes of the employed). So greater wage rigidi-ties may be another reason why Europe sees higher unemployment, inparticular during recessions.

29

3.2 Natural Rate of Unemployment

� A recent focus in labor economics on "normal unemployment" thatarises from transitions in and out of jobs as the sectoral allocation oflabor changes (industries rise and fall, people look for careers elsewhere)led to the distinction between a long-term trend in unemployment andcyclical �uctuations that are driven by booms and recessions.

� The trend is determined by (i) the frequency with with jobs get cre-ated and destroyed over industry lifecycles, forcing workers to searchfor new jobs (frictional unemployment) and (ii) systemic constraintsand incentives that cause people to remain unemployed (structural un-employment). Most of the di¤erence between the US and Europe istraditionally structural: labor laws, unemployment bene�ts.

� Relative to the US and Japan, the unemployment rate in Europe (France,Germany, Italy and the United Kingdom) rose dramatically and per-manently after the productivity slowdown of the early 1970s. Note how�uctuations are closely correlated between the US and Europe, but thelong-term di¤erence in unemployment rates persists.

� Change in the hours work per person, relative to the US: from 1970-1974 to 1993-96, all other countries had experienced a relative reduc-tion, and all European countries worked fewer hours. Some of this maybe due to lifestyle preferences, but a good part is likely to re�ect lowerlabor demand for structural reasons.

� Together, frictional and structural unemployment make up what iscalled the natural rate of unemployment. This is calculated as theten-year moving average (a period long enough to cancel out the busi-ness cycle). A reduction in unemployment bene�ts is an example ofa policy that is expected to lower the natural rate of unemployment,regardless of the state of business cycle.

� The actual unemployment rate is the natural rate plus the cyclicalcomponent, which is positive in a recession and negative during a boom.

� The microeconomics of unemployment. Workers have, and jobs require,di¤erent skills and characteristics, therefore the labor market needs tomatch the right workers with the right jobs. This takes time and leads

30

to temporary (in most cases) unemployment when someone loses ajob (say because the �rm�s needs or worker�s preferences change, orprevious matches turn out to be poor).

� Denote the fraction of the labor force that is employed by e, the fractionthat is unemployed by u (so e + u = 1). The job-separation rate � isthe percentage of employed individuals who lose their jobs in a period(say 1% of e). The job-�nding rate � is the percentage of unemployedindividuals who accept jobs in the same period (say 9% of u).

� Then4e = �u� �e = 0

ifu =

�

�+ �

since e = 1 � u. (With � = 0:01 and � = 0:09, we would have 10%unemployment.)

� u is the natural rate of unemployment. Not surprisingly, it increases inthe job-separation rate, for a given job-�nding rate; and it decreases inthe job-�nding rate, for a given job-separation rate. We can think ofjob separation as driving frictional unemployment and job �nding asre�ecting structural unemployment (low � indicates not many jobs arebeing created, or few individuals are accepting o¤ers).

� Business cycles can temporarily change � and �: for example, a re-cession is likely to increase job separation as labor demand from �rmsfalls, while decreasing job �nding. This would increase unemployment.After the recession ends and labor demand is back to the old level, un-employment drops (4e > 0) because u has increased and e decreasedrelative to the natural levels. Still, it takes some time for the old un-employment rate to be restored.

� Job separation rates tend to be higher for younger employees, whichcan be explained in that they have had less time to �nd an optimalmatch. This means that a younger employee is more willing to leave ajob and also that a �rm is more likely to lay o¤ a younger employee.Seasonal and other temporary jobs often require less experience, and

31

this may also account for higher job separation among younger em-ployees. Because of this, we see more unemployment among youngpeople.

� The job-�nding rate is a¤ected by policies such as minimum wage andunemployment insurance. Minimum wage legislation causes some jobsto disappear and therefore permanently reduces the number of job of-fers, increases unemployment. A more subtle e¤ect of minimum wageis that, in the teenage labor market where it matters most (McDonaldsetc.), higher wages bring new workers into the labor market (middle-class kids) who displace the more disadvantaged groups (minority kids)that were willing to work for low pay. So no only do minimum wagesincrease unemployment, they also cause jobs to be less e¢ ciently allo-cated.

� Unemployment bene�ts encourage job seekers to turn more o¤ers down.Suppose there is a distribution of job o¤ers the job seeker is likelyto get at any given time. If pay determines the value of a job (asimpli�cation, but a harmless one), there will be a threshold level w,so that a particular job seeker will accept jobs that pay more than thislevel and reject jobs that pay less.

� The threshold will lie somewhere above w0, the level of unemploymentbene�ts. Rejecting an o¤er w means that the job seeker foregoes earn-ing of w � w0 in the current period, in order to attract a better o¤erw0 > w. Just how high the threshold is will depend on the (known)distribution of jobs out there, the better the o¤ers you can expect, thehigher your standard for acceptance. It also depends on w0, the higherw0, the smaller are the wages foregone by continuing to search.

� What happens if unemployment bene�ts (w0) increase? Then you areguaranteed a better income, w � w0 declines for all o¤ers. You shouldincrease your threshold, since you are exposed to a smaller risk (po-tential income loss). With the higher threshold, you are less likely toaccept o¤ers and likely to be unemployed longer. Thus, better andlonger-lasting bene�ts imply more unemployment.

32

3.3 Money

� One aspect of GDP that we have not explicitly modeled is that it in-cludes many di¤erent goods, and that individual workers tend to spe-cialize in producing a few speci�c things that they have a comparativeadvantage at. In fact, the division of labor contributes greatly to theproductivity of modern economies, as Adam Smith already emphasized.

� But this is only possible if goods can easily be traded. Money replacesbarter to eliminate the need for a "double coincidence of wants": that,in order to purchase a good from someone, you need to have a goodof similar value that they desire and will accept in exchange. Whena commodity in �xed supply, such as gold coins or certain types ofprinted paper, is universally accepted in trade, it acts as a promisefrom the whole economy (rather just one individual) to deliver goodsin the future.

� A further advantage of coin or paper money is that, unlike most goods,it is almost in�nitely divisible, so that it�s easy to exchange goods fora quantity of money of similar value. Thus, money greatly facilitatesexchange and increases the value that production can generate becauseit allows for a more e¢ cient allocation of consumption goods throughtrading.

� Early forms of money had intrinsic value: e.g. coins were made fromprecious metals, gold being the most common. Later, governmentsissued more convenient paper currency, but promised to exchange itfor gold etc. at a �xed rate at the bearer�s request.

� In the 20th century, countries began to abandon the gold standardand paper currency became "�at" money (�at means "by decree" -the government simply declares the paper to be "legal tender"). Thisis possible because, over time, a mutual expectation has evolved thatpaper bills will be accepted for purchases. We accept our salary indollars as long as we believe the grocer will accept dollars for food.The grocer accepts dollars as long as she can pay her employees indollars.

� We now insert money in a little general equilibrium model to see how ita¤ects the price level. In this economy, there are two individuals who

33

each specialize in the production of a good and then trade.

� Person 1 supplies X units of the �rst good to the market and haspreferences represented by

u1 (x1; y1) = x1=21 y

1=21 :

1�s budget constraintpxx1 + pyy1 = pxX

reduces topyy1 = px (X � x1) ;

we can substitute for y1 and write the utility function in terms of onevariable:

u1 (x1) = x1=21

�pxpy(X � x1)

�1=2:

� Maximizing with respect to x1, we have �rst-order condition

@u1 (x1)

@x1=

1

2

1

x1=21

�pxpy(X � x1)

�1=2� 12

pxpyx1=21

1�pxpy(X � x1)

�1=2 = 0()

x1 =1

2X:

Theny1 =

pxpy(X � x1) =

1

2

pxpyX:

� Person 2 supplies Y units of the second good to the market and haspreferences represented by

u2 (x2; y2) = x1=32 y

2=32 :

2�s budget constraintpxx2 + pyy2 = pyY

reduces topxx2 = py (Y � y2) ;

we can substitute for x2 and write the utility function in terms of onevariable:

u2 (y2) =

�pypx(Y � y2)

�1=3y2=32 :

34

� Maximizing with respect to y2, we have �rst-order condition

@u2 (y2)

@y2= �1

3

pypx

1�pypx(Y � y2)

�2=3y2=32 +2

3

�pypx(Y � y2)

�1=31

y1=32

= 0

()y2 =

2

3Y:

Thenx2 =

pypx(Y � y2) =

1

3

pypxY:

� The market for Y clears,

Y = y1 + y2 =1

2

pxpyX +

2

3Y;

at relative pricespxpy=2

3

Y

X:

(The same conclusion would be reached if we set x1 + x2 = X andsolved for px=py. This is known as Walras�law: if one market clears,then so must the other.)

� The price ratio solves the general equilibrium model in the sense that,any prices in this proportion clear the markets for both goods. Wecannot pin down both prices: the usual practice is to declare py theprice of the "numeraire" (reference good) and just assume that it�spy = 1. The "price level" is meaningless, since an increase in px and pywould, on the one hand, make things more expensive but, on the other,provide more income to 1 and 2; they could still a¤ord (and would stillchoose) exactly the same quantities. Nothing happened in real terms.

� But this is a barter economy, where we assume direct trades (y1 for x2)are possible. Now suppose when 1 wants to buy y1 from 2, 2 will onlyaccept money, and likewise 1 will only accept money for x2.

� Say, both 1 and 2 have just enough money to purchase what they wish,i.e. the money supply is

M = pyy1 + pxx2

= py (Y � y2) +pxpypy (X � x1) =

2

3pyY:

35

� Note that pyy1+pxx2 is GDP in this simple economy; assuming that x1and y2, the quantities that 1 and 2 keep for themselves, are not traded.We have

py =3

2

M

Y

and

px =2

3

Y

Xpy =

M

X:

� Now the prices are both pinned down by the further constraint that isimposed by the money market equilibrium (money supply equals moneydemand, i.e. GDP). Prices are increasing in the money supply anddecreasing in X and Y . The latter re�ects that more goods "chasing"the same amount of money must get cheaper - there just isn�t enoughcurrency to purchase them otherwise.

� What would happen if 1 and 2 sold all their produce to "the market"and then bought back what they wish to consume? Now GDP is pxX+pyY , and money supply and demand are equal if

M =pxpypyX + pyY

=5

3pyY;

implying

py =3

5

M

Y

and

px =2

5

M

X:

� Prices have dropped (speci�cally, the price level; relative prices remainthe same). Why? Essentially for the reason we just gave: there arenow more goods traded, so at a given money supply the prices mustcome down.

� Finally, what if money is initially not allocated in the right quantities?Say 2 has all the money. In order to sell y1 to 1, 2 must lend money to1. Let�s suppose 1 charges an interest rate r for this (we�ll learn laterhow the interest rate is in fact determined).

36

� E¤ectively then, 1 pays (1 + r) py for each unit of 2�s good: every dollarhas to be borrowed and repaid with interest. Since x1 is not sensitiveto py (a special property of demand functions that arise from Cobb-Douglas utility), we can simply multiply py by 1 + r everywhere. So 1will consume x1 = X=2 and

y1 =1

2

1

1 + r

pxpyX:

� 2 receives extra income and gets to consume y2 = 2Y=3 and

x2 =1

3(1 + r)

pypxY:

� This means that (with everything traded)

py =3

5

1

1 + r

M

Y

and

px =2

5

1

1 + r

M

X:

� Hence a higher interest rate is associated with a lower price level. Ingeneral, this is true because the interest rate represents a cost of holdingmoney - the better the terms at which it can be lent out, the less moneyis demanded. At �xed supply, this means the price level at which moneysupply equals demand drops.

3.4 The Aggregate Price Level

� So far we expressed the equilibrium in the market for money as M =GDP (money supply equals money demanded in order to purchase theGDP at current prices). Aggregating the various outputs and prices,we can write nominal GDP as P � Y , where P is the price level.

� What we neglected so far is that a dollar bill might be spent severaltimes over in the relevant period, e¤ectively increasing the money sup-ply. The frequency with which currency is spent on average is called"velocity" and denoted by the letter V . We have therefore

MV = PY

(where, in the previous example, we implicitly assumed V = 1).

37

� Can velocity be measured? Well, we can measure GDP, and the Fedknows (roughly) how much currency it has in circulation (some moneygets destroyed or lost each year). According to the formula, velocity issimply PY=M .

� If we view velocity and output as independent of the money supply, wehave the quantity theory of money: the price level is mainly determinedby how much money the Fed prints. Everything except the price levelis exogenous, but M is a matter of policy. (It is exogenous in the sensethat the model does not explain how the policy is determined. We willconsider the question later on.)

� We can calculate the rate of in�ation, i.e. the growth in the price level

Pt � Pt�1Pt�1

;

from the equilibrium equation: since

Pt =MtV

Yt;

we have

4PtPt

=@

@t(lnMt + lnV � lnYt) =

4Mt

Mt

� 4YtYt

(because lnV is a constant, its time derivative is zero).

� As we discussed earlier, there are various ways to de�ne the aggregateprice level. One might aggregate the value of all goods in the economyand compare it to a base year (or a moving average): these are GDPde�ators. Or one might focus on a selected set of goods that are relevantto a particular agent.

� Examples are investment or export goods, but the best-known of theseis the consumer price index (CPI), which compares the prices of a"typical" basket of consumption goods over time. (The CPI keepsquantities �xed at the initial level, so it is a Laspeyres index.)

� In the US, we had relatively high rates of in�ation in the 1970s, andsustained moderate rates around 3% since then.

38

� This is re�ected in the CPI benchmarked to the year 2005. It doublesin the 1970s, then grows more slowly.

� According to the quantity theory, we get in�ation when the growth inthe money supply outpaces growth in real output. This conclusion de-pends on real GDP Yt being in fact unrelated to Pt, an idea known asthe "neutrality of money." While it makes intuitive sense, since incen-tives to produce should only depend on relative prices (not the pricelevel), there may be imperfect adjustment to an increase in the moneysupply in the short run: businesses need some time to �gure out thatthere is more money around and prices should increase. In that case,relative prices could be (temporarily) a¤ected, and then also what isproduced.

� Generally, the money supply includes "highly liquid assets." There arevarious de�nitions of what that includes, depending on the standardof liquidity. The strictest would be what we conventionally think of ascurrency - i.e. dollar bills in circulation.

� The "monetary base" is currency plus the reserves that commercialbanks are required to hold with the Federal Reserve Bank (to coverwithdrawals from bank accounts). Although reserves aren�t actuallyin circulation, they can be drawn on immediately if needed and paidout to people as cash. In fact, the Fed will provide short-term cashto banks at the "discount rate" (set as part of its management of themoney supply) so that they can maintain their reserves when they runshort.

� M1 is the monetary base plus demand deposits, which are accountsthat, while not actually cash, can immediately be converted into cash,such as when you draw on your checking account with a debit card.

� M2 is M1 plus savings and money market accounts (i.e. bank depositswith some withdrawal limitations, but this does not include time de-posits). Savings accounts yield a �xed interest rate. Money marketaccounts are accounts with commercial banks or money market fundsthat are invested in the money market and pay an interest rate tied tothe going money market rate. While a savings account imposes somecosts on withdrawals (you may have to go to the bank or transfer funds

39

online), a money market account typically gives convenient access to aportion of your funds (it may let you write checks, but only in limitedamounts).

� The money market trades securities that banks, government (municipalpaper, treasury bills) and corporations (commercial paper, repurchaseagreements) issue in order to manage their cash �ows. For example,a town needs to pay its employees while waiting for tax receipts. Itmight issue municipal paper to raise the cash immediately. A tradingcompany pays a supplier with a banker�s acceptance (bank guaranteeto pay a certain amount at a certain date, i.e. upon receipt of thegoods). Because these instruments are repaid quickly and backed byanticipated earnings, they are considered very safe and interest ratesare similar.

� In�ation in the US against the rate of (M2) money growth: the rela-tionship is positive, as predicted by the quantity theory, higher moneygrowth is associated with higher in�ation. The same is true acrosscountries, for the average money growth and in�ation rates from 1990to 2003.

3.5 Costs of In�ation

� German hyperin�ation: in 1919, a loaf of bread cost 25 Pfennige (theequivalent of "penny"; one dollar was worth about �ve Mark at thetime); four years later, the loaf of bread cost 80 billion Mark (theequivalent of dollars; by then, a dollar was worth one trillion Mark).

� Two episodes from the time: a German lawyer bought a 20-year lifeinsurance policy in 1903 and, when it came due in 1923, used it allto purchase one loaf of bread. A German cook received a one-dollartip from an American tourist: he decided to start a trust fund for hisfamily.

� In�ation progress so quickly that people were paid every day and wouldimmediately buy whatever was sold, or had relatives stand by to do itfor them. You bought a cup of co¤ee at one price, and by the time youordered another, the price might have doubled.

40

� Reasons included that Germany abandoned the gold standard in 1914on the eve of World War I in order to �nance the war machine. Afterthe war, Germany had massive reparations to pay to France, leavingthe government scrambling to �nance its normal operation, and on topof it, unfolding political unrest (murder of the foreign minister) un-dermined faith in the state. A spiral began where citizens sought toconvert currency into real assets and increasingly bartered, so the de-mand for money dwindled. The central bank printed money to �nancethe government. The value of money dropped, and the more pricesincreased, the more money had to be printed. Once in�ation was fullyunderway, it was self-reinforcing and seemingly nothing could stop it.

� In 1923, the central bank introduced a new currency that was backedby real goods (i.e. it stood in a �xed proportion to output by farmsand factories and was independent of government needs). But peoplehad lost their savings, and the extreme experience of the hyperin�ationwas blamed by some for a culture that had become demoralized andpassive in the face of "fate," giving birth to the Nazi regime. (ThomasMann: "The market woman who without batting an eyelash demanded100 million for an egg lost the capacity for surprise. And nothing thathas happened since has been insane or cruel enough to surprise her.")

� Other hyperin�ations occurred during times of trouble, such as Yu-goslavia and Russia during transition from socialism in the early 1990s,Latin America during the debt crisis in the 1980s, Hungary after WorldWar II in the 1940s, and the confederate states during the Americancivil war.

� Hyperin�ations are usually de�ned as increases in the price level at amonthly rate exceeding 50%. All hyperin�ations are associated withmoney printing. This yields immediate cash for the government, butthe growing prices devalue citizens�savings. In this sense, it is like ahidden tax on money holders. The temptation for governments to raiserevenue in this manner is why countries like the US and Germany havetraditionally emphasized central bank independence.

� While the costs of hyperin�ation are obvious, even moderate levels ofin�ation cause problems: businesses rely on being able to roll over loans(i.e. get a new loan in order to pay o¤ old loans). Rising interest rates,

41

associated with in�ation, can make this di¢ cult. They can also catchhome owners o¤ guard who have variable-rate mortgages, and whoseincomes may not be growing at the rate of in�ation.

� In general, in�ation bene�ts those who have long-term debts at �xedrates, and it harms creditors, because it devalues debt. Creditors in-clude banks and employees with pensions. Without in�ation-adjusted("indexed") interest rates (which only came into use after the expe-rience with high interest rates in the 1970s), the value of what theyinitially paid out (as loans or deposits into the pension system) mighteven exceed the value, in real terms, of what they get back.

3.6 In�ation and Interest Rates

� The nominal interest rate can be decomposed into the rate of in�ationand the real interest rate. Suppose you borrow an amount x0 and agreeto repay x1, a year later.

� The implicit (nominal) interest rate is i such that (1 + i)x0 = x1, so

i =x1x0� 1:

� But what is repaid in real terms is x1=P1, where P1 is the eventual pricelevel (assuming it is benchmarked to the present, so that P0 = 1). Inreal terms, the interest rate is r such that x0 + rx0=P1 = x1=P1, so

r =x1x0� P1:

(We have to divide rx0 by P1 since it is received in the future, whenthe price level has changed to P1.)

� Hence

r =

�x1x0� 1�� (P1 � 1)

= i� �

where

� =P1 � P0P0

= P1 � 1

is the rate of in�ation.

42

� The nominal interest rate i is the interest you would actually pay on aloan (assuming default risk is negligible). If this is �xed, at some level,then the real interest rate (what your payment is worth in terms ofgoods) depends on the rate of in�ation: it falls when in�ation is higher.This is why in�ation enriches debtors at the expense of creditors.

� In general equilibrum, the real interest rate is the marginal product ofcapital (re�ects the cost of renting capital). This is another version ofmoney neutrality: in the long run, after full adjustment, the nominalinterest rate will simply increase with the rate of in�ation. But in theshort run, when adjustment is imperfect and in�ation is not alwayspredictable, the real interest rate can be sensitive to in�ation.

4 Short-Run Fluctuations

4.1 Cyclical Component of GDP

� At any given point in time, the economy is in the short run - i.e. realoutput is not necessarily the long-run capacity (what growth theorypredicts), but rather �uctuates around it while adjusting to some cur-rent shock.

� Trend line of real GDP ("potential output"), determined by the econ-omy�s capacity to produce if resources are optimally allocated, contrastswith a curve that depicts the measured real GDP ("actual output"),which is more volatile. Actual output can be detrended (i.e. poten-tial GDP �Y at each point in time subtracted), so that we isolate thedeviation, the cyclical component (or "short run component") ~Y .

� The cyclical component is de�ned by

Yt = �Yt + ~Yt;

where Yt is observed real GDP (de�ated nominal GDP).

� There are various techniques for detrending real GDP, called "�lters."All involve averaging real GDP growth over a period of time, so thattemporary deviations are "�ltered out."

43

� The most popular is the HP-�lter (Hodrick-Prescott), which picks thesmoothed (trend) series �Y1; �Y2; :::; YT such that the function

TXt=1

�Yt � �Yt

�2+ �

T�1Xt=2

��Yt+1 � �Yt �

��Yt � �Yt�1

��2is minimized for some �. The parameter � weights deviations fromthe trendline (captured by the �rst term) against changes in the trendgrowth (captured by the second term), i.e. it determines how the dualobjectives of "good �t" and "smoothness" of the trend line are bal-anced. (The HP-�lter is often applied to the logarithms of the Yt series.GDP data are available quarterly, and in that case the suggested valuefor � is 1600.)

� The solution to the minimization problem can be stated in matrix no-tation as

�Y = [I + �M 0M ]�1Y;

where �Y =��Y1; �Y2; :::; YT

�is the vector of trend values, Y = (Y1; Y2; : : : ; YT )

are the observed GDP data, I is the identity matrix (where all non-diagonal entries are zero, and diagonal entries are 1), andM is a specialmatrix (starting with the identity matrix, replace each zero immedi-ately to the right of a diagonal entry with �2, and the zero immediatelyto the right of that entry, i.e. two positions from the diagonal entry,with 1). For example�e.g.2664�Y1�Y2�Y3�Y4

3775 =266426641 0 0 00 1 0 00 0 1 00 0 0 1

3775+ �0BB@26641 0 0 0�2 1 0 01 �2 1 00 1 �2 1

3775�26641 �2 1 00 1 �2 10 0 1 �20 0 0 1

37751CCA3775�1 2664

Y1Y1Y1Y1

3775(where the superscript �1 refers to matrix inversion).

� As previously remarked, when we compare actual output against thelong run trend, �uctuations do not seem severe (between -5% and +5%of real GDP), except at times like the Great Depression, but much of thecost lies in individual exposure to extreme events like unemployment.

� The di¤erence, ~Yt, is - roughly speaking - positive in a boom (whenGDP temporarily exceeds long-run capacity) and negative in a reces-sion. In practice, whether the economy is in an o¢ cial recession or not

44

is determined by the Business Cycle Dating Committee of the NBER,a panel of prominent macroeconomists. They take various indicators,such as employment and output in leading sectors, like wholesale, re-tail and manufacturing, into account. As a simple rule of thumb, arecession is called when real GDP has been below potential for abouta year.

� A regularity of short-run �uctuations is that in�ation falls during arecession.

� The positive relationship between changes in in�ation and the cyclicalcomponent of output is re�ected in a stylized fashion by the Phillipscurve, named after a New Zealand economist who �rst noticed it. Ex-plaining it is one of the tasks of macroeconomic theory.

� Comparing in�ation growth and detrended output growth over timein the US, we can see the Phillips curve in the data: for every per-cent increase in in�ation, the detrended output grows by about 2%.The correlation is far from perfect, but the tendency is something ourmodeling will have to re�ect.

� One way to rationalize this relationship is as follows: suppose peopleexpect a certain amount of in�ation each year, and wages tend to growaccordingly. Now, due to some shock (e.g. an increase in money supplygrowth), goods prices rise faster than anticipated. Then �rms �nd theirpro�t margin increasing and may expand production. If the economywere in equilibrium, wages would have risen, and the relative prices ofgoods and labor would be una¤ected. But, for a while, wages mightfall in real terms, and it becomes feasible for �rms to pay workers forovertime and expand output beyond long-run capacity. I.e. the priceincrease triggers a boom in production.

� On the other hand, suppose in�ation slowed (because of a decreasein money supply growth). Then wages rise in real terms, and �rms -unable to raise prices for their output, but stuck with increasing wages- want to scale back production, lay o¤ people. Then the economymight enter a recession.

� Another regularity of short-term �uctuations is the negative relation-ship between output and unemployment. Over time in the US, a 1%

45

increase in cyclical unemployment (the di¤erence between actual unem-ployment and the natural rate) has been associated with a 2% reductionin the short-term component of GDP.

� This is known as Okun�s law (after a member of the Council of Eco-nomic Advisors during the Kennedy administration).

� Unemployment and in�ation a¤ect the livelihoods and life satisfactionof voters. Not surprisingly, they can help predict the outcomes of presi-dential elections in the US. Predicted popular vote shares of the incum-bent based on a model by Yale economist Ray Fair (which mainly usesin�ation and unemployment, but controls for incumbency advantage)are quite close to the actuals.

4.2 Investment-Saving Equilibrium

� The Phillips curve captured that an unexpected increase in in�ation isassociated with an increase in cyclical GDP. We saw previously thathigher in�ation reduces the real interest rate that lenders earn andborrowers pay. Now we make the connection by modeling the negativerelationship between the real interest rate and cyclical GDP.

� This relationship is called the IS curve, for investment = saving. If werearrange the national income identity,

Yt = Ct + It +Gt +NXt;

toIt = Yt � Ct �Gt �NXt

and add and subtract taxes Tt, we have investment on the left andsaving from various sources on the right:

It = (Yt � Tt � Ct) + (Tt �Gt) + (�NXt) :

� Namely, Yt � Tt � Ct is saving by consumers (after-tax income notconsumed), Tt �Gt is government saving (tax revenue not spent), and�NXt is saving by foreigners (imports net of exports, which must cor-respond to domestic assets held by foreigners).

46

� That investment will equal saving in this sense is true because thenational income identity must hold. The IS curve re�ects that thenational income identity implies a negative relationship between thereal interest rate and cyclical output.

� Dividing by the potential output Y , we have

YtY=CtY+ItY+GtY+NXtY:

We treat Ct=Y = aC , Gt=Y = aG and NXt=Y = aNX as exogenous.

� Investment becomes more attractive when the real interest rate Rt issmall relative to the marginal return to capital r that businesses mustpay on loans. Hence, let

I = aIY � b (Rt � r)Y:

� Thus,

~Yt =Yt � YY

=CtY+ItY+GtY+NXtY

� 1

= aC + aI � b (Rt � r) + aG + aNX � 1= a� b (Rt � r)

where a � aC + aI + aG + aNX � 1.

� This is the IS curve in its algebraic form: note that cyclical output ~Ytdecreases in the real interest rate Rt and increases in a (the spendingpropensity in the various sectors) as well as r (the marginal return tocapital).

� Note that, when Rt = r, i.e. the real interest rate is the marginal returnto capital (as it would be in the long run), output is at its potential(since deviations of Rt from r are the only source of change here), sowe must have ~Yt = a = 0.

� Since the IS curve re�ects ~Yt at each value for the real interest rate Rt,any changes in the real interest rate involve movement along the curve.The important thing to keep in mind is that the relationship has notchanged in this case, the curve is still in place.

47

� If a (spending propensity) or r (marginal return to capital) increase,~Yt is higher at any interest rate. The curve, i.e. the values of ~Yt atdi¤erent Rt, has shifted out.

� Examples include: an invention (raises r), an increase in consumeror investor con�dence (raises a through aC or aI), a new governmentinitiative (raises a through aG) and an increase in exports due to aneconomic boom abroad (raises a through aNX).

� Conversely, the IS curve might shift in if a new computer virus reducesthe marginal return to capital, consumers and businesses anticipateslower growth, the government cuts spending and foreign economiesare faring poorly and import less.

� Changes in potential output do not directly a¤ect the IS curve, if theyare neutral with respect to a and r. Though we can think of events thatwould shift both potential output and the IS curve, we must identifyhow they alter a or r. For example, a new management approach mightmake the economy more productive and increases the marginal returnto capital. Potential GDP increases for the �rst reason, and the IScurve shifts for the second.

4.3 Multiplier E¤ect

� In the derivation of the IS curve, we have treated the spending propen-sities (a) as exogenous, i.e. uncorrelated with the state of the economy~Yt. This seems a bit unrealistic, and we will take a closer look at theissue in this lecture. Speci�cally, if they depend on ~Yt, what happensto the IS curve?

� Milton Friedman�s permanent income hypothesis says that consumerswill base their spending not on their current income, but on the netpresent value of their expected lifetime income:

TXt=0

�twt;

where wt is income at time t, and � is the discount factor.

48

� Note that �w1 is the time-0 value of w1, �w2 is the time-1 value of w2,so � (�w2) = �

2w2 is the time-0 value of w2 ... In general, �twt is the

current (time-0) value of receiving income wt at time t.

� Individuals who are risk-averse (exhibit diminishing marginal utilityof income) will want to smooth their consumption over time, sinceit is welfare-improving to allocate a dollar from times when they arerelatively wealthy to times when they are relatively poor.

� Hence, students and retirees overspend relative to their current incomes(students "borrow" from their parents, retirees live down their savingsand bene�ts), professionals underspend (save, e.g. through programslike retirement contributions). This implication of the permanent in-come hypothesis is known as the life-cycle theory of consumption.

� If consumption stands in a �xed proportion to expected lifetime in-come, then it should not be responsive to short-term �uctuations, andtherefore aC = Ct=Y would be approximately constant.

� In reality, consumption smoothing is a bit more intricate: you can�tforesee every event that a¤ects your future income, such as promotions,winning the lottery etc. Hence, your expected lifetime income, andtherefore consumption, will in fact �uctuate when you learn somethingnew about what your future looks like. But the logic of the permanentincome hypothesis implies that, at each time, consumption choices arebased on your best current forecast of lifetime income - any futurechanges in consumption are in response to "surprises." Technically,this means that consumption is a "random walk" (a stochastic processwhere the expected value in the next period is the same as the currentvalue).

� Moreover, risk averse consumers will engage in "precautionary saving"to insure themselves against adverse events. Even someone who ispoor relative to expected future income would therefore not necessarilyborrow to consume. Others, who might wish to borrow, cannot do sobecause banks will not lend to them if they have no collateral to o¤erand future income is uncertain.

� Even if income were perfectly predictable, consumption smoothing doesnot imply that spending on consumption will be constant, since e.g.

49

the availability of time varies over one�s lifetime. Once you retire, youcan more easily cook yourself, so you can maintain a given standardof eating without the expense of going to restaurants all the time.Anticipating this change in resources (time), your income might haveto be higher while you are working and earning, in order to keep yourconsumption smooth.

� If you think about these points carefully, you will notice that they allimply that consumption is somewhat sensitive to short-term �uctua-tions in GDP: higher current income is likely to increase your estimatedlifetime income, reduce the "worst case scenario" and preference for in-surance, relieve borrowing constraints, and perhaps cause you to workovertime so that you will spend more on services. The fact that thegovernment �nds it necessary to mandate some saving (retirement ac-counts) moreover suggests that individuals don�t necessarily conformperfectly to the incentive to smooth consumption. We will build thedependence of consumption on short-term GDP into the model shortly.

� Investor income is exposed to progressive taxation (higher income istaxed at a higher rate). This provides an incentive to smooth receiptsby maintaining a relatively stable investment volume.

� But there are also reasons why investment might �uctuate with GDP:if �rms have less cash on hand, they must borrow more in order toundertake investments, and this involves paying risk premia that arisefrom moral hazard (borrowers have an incentive to take excessive risk)and adverse selection (�rms that have private knowledge that they areat risk are more likely to �nance investment with debt rather thanequity). Thus, the cost of borrowing is usually substantially higherthan the risk-free real interest rate, and in a downturn, when incomesare low and funds must be sourced in the capital market, investing isless attractive, even if the real interest rate does not change.

� Government spending is, to some extent, constrained by the tax rev-enue, which would suggest that it is fairly stable. On the other hand,government can borrow in the bond market on attractive terms, andmay want to use �scal policy to stimulate the economy in a recession,or cool it during a boom.

50

� However, since additional government spending must be �nanced throughloans that will necessitate higher future taxes, it lowers consumers�expected lifetime income and investors� expected returns. Thoughtthrough to its conclusion, this suggests that �scal policy cannot af-fect total spending in the economy - since consumers and investors willscale back their spending in response to higher government spending,in anticipation of future tax increases. Economists refer to this idea as"Ricardian equivalence." In practice, Ricardian equivalence does notappear to hold perfectly: the e¤ects of �scal expansion are tempered,but not fully cancelled, by reductions in consumer and investor spend-ing.

� Net exports re�ect economic conditions overseas, which are correlatedwith domestic GDP. Hence imports and exports are likely to movetogether, but shocks arising from resource prices, government policyetc. will make the relationship imperfect and net exports somewhatresponsive to ~Yt.

� So what if the fraction of GDP that is spent on consumer, investment,government and overseas purchases varies with the short-term �uctu-ations in the economy? Suppose that they actually take the followingform:

CtY

= �aC + xC ~Yt

ItY

= �aI + xI ~Yt � �b (Rt � r)GtY

= �aG + xG ~Yt

NXtY

= �aNX + xNX ~Yt:

� Let �a � �aC + �aI + �aG + �aNX � 1 and x � xC + xI + xG + xNX . Then

~Yt =Yt � YY

=CtY+ItY+GtY+NXtY

� 1

= �a+ x ~Yt � �b (Rt � r)

=1

1� x��a� �b (Rt � r)

�:

51

� We recover our original IS equality ~Yt = a� b (Rt � r) if we let

a � �a

1� xand

b ��b

1� x:

� The term 1= (1� x) is the famous "multiplier." It re�ects the dominoe¤ect of an increase or reduction in spending propensity: if a downturncauses ~Yt to fall by 1%, everybody spends x cents less of each dollarthey receive in income. This causes ~Yt to drop by another x% (total1 + x). But for each of these additional x%, everybody lowers theirspending again by x%, so there is a further reduction in ~Yt by x2%,and so forth. Overall ~Yt falls by 1 + x + x2 + x3 + � � �%, and this is ageometric series, so it can be written as 1= (1� x).

� The way to think of the multiplier is as follows: "one person�s cutbackin spending is another person�s loss of income, which induces anothercutback in spending." If you decide to put another dollar aside becausetimes are bad, that means the grocer has a dollar less and may ulti-mately need to cut sta¤, which forces the laid o¤ employee to spendless, and so forth.

� Of course, it works opposite when there is an exogenous increase in~Yt: the economy actually expands by a greater amount because theadditional income is spent several times over.

� While the multiplier does not really a¤ect the qualitative logic of theIS curve, it magni�es volatility ~Yt (greater a) and makes investmentmore sensitive to the real interest rate (greater b). If a decrease in ~Ytcauses the some of the economy�s agents to reduce their spending, then~Yt decreases further, triggering another round of spending reductionsand another decrease in ~Yt ... Clearly, this mechanism ampli�es anychange in ~Yt that the real interest rate might induce.

4.4 Fed Policy

� The Federal Reserve System consists of 12 regional federal reserve banksand the federal reserve board of governors. There are seven governors,

52

appointed by the president to 14-year terms, including the chair (whoseterm is four years), currently Ben Bernanke. The Federal Reserve Bankcontrols the money supply and can therefore lend unlimited amounts.It can use this power in order to e¤ectively set interest rates, since itis able to lend any amount at the desired interest rate to commercialbanks, or to borrow.any amount at the same rate. (Managing theinterest rate is only one of the Fed�s roles. It also auctions governmentsecurities in order to raise cash for the treasury.)

� For example, if the target rate is lower than the current interest rate,the Fed wants to increase the money supply: by o¤ering to buy bonds(and thereby releasing new currency to borrowers), or by lowering thereserve requirement and / or the discount rate.

� If the target rate is higher than the current interest rate, the Fed tight-ens the money supply by issueing bonds (thereby taking the currencyof lenders out of circulation), or by raising the reserve requirement and/ or the discount rate.

� Banks borrow from each other when their reserves with the Fed tem-porarily fall below the required level (a bank in need of a loan will lookfor a bank with excess reserves). This might happen when Bank Aattracts additional deposits while Bank B lost some deposits. Bank Aneeds to increase its reserve account with the Fed by 10% of the newdeposits. Bank B could lower its reserve account by 10% of the lostdeposits. It might cash those reserves in for currency (which it couldthen loan to anybody), or it might lend its excess reserves to Bank Ain the "federal funds market."

� The interest rate on such short-term interbank loans is called the federalfunds rate. (If needed, banks can also borrow from the Fed at thediscount window, but they tend to be cautious about it, since the Fedwill monitor them, especially if they seem to need help repeatedly.)

� The Fed targets a particular federal funds rate through open markettransactions (sales and purchases of bills and bonds). Interest ratepolicy is set by the Federal Open Market Committee within te Fed,which has twelve members: the governors, the president of the NewYork Fed, and four other presidents of regional Feds that rotate.

53

� Here is how an open market operation might work. At any given time,the private sector holds a quantity of US treasury bills and governmentbonds of di¤erent maturities. The Fed also holds some of this debt.If the Fed wants to raise the interest rate, it will tighten the moneysupply by selling some of its government securities, say three-monthtreasury bills, to banks.

� In practice, it will use a repo ("repurchase agreement") with one of18 banks ("primary dealers"): the bank buys the bills for a speci�edperiod of time (typically, one day to a week) and agrees to resell them(at a higher price) to the Fed at the end of the period. Essentially, thebank loans money to the Fed: the di¤erence in the sales and repurchaseprice re�ects the interest rate that the Fed is implicitly paying.

� The bank that purchases the bills will have a reserve account with theFed. The Fed debits the reserve account for the price of the bills. If thebank did not have su¢ cient excess reserves, it falls below its reserverequirement at this point and will most likely borrow in the federalfunds market to make up the di¤erence. Hence the Fed�s sale of T-billsled to an increase in demand for federal funds, and therefore upwardpressure on interest rates in the federal funds market.

� Similarly, if the Fed wants to lower the federal funds rate, it purchasesgovernment securities from banks (through a reverse repo, with anagreed date on which it sells them back) and credits their reserve ac-counts. The excess reserves reduce demand and increase supply in thefederal funds market, which puts downward pressure on the interestrate.

� Once the Fed is borrowing at a particular interest rate, this is theminimal rate at which banks will loan out money, since there would beno point in setting a lower rate in the open market: they could lendthose same funds to the Fed (we will see in the next lecture how thisworks exactly) and earn a higher interest rate. (One has to qualify thisstatement a bit, since loan terms di¤er. However, if the expectation isthat the Fed�s target rate will persist for some time, banks can get thesame rate for a longer period by rolling loans over, hence the e¤ect ofchanges in the target rate should show up in the whole term structureof commercial interest rates.)

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� It also means that all banks can obtain loanable funds at the samecost, and competition should ensure that they charge relatively similarinterest rates on their loans. Interest rates on business and consumerloans will generally be higher than the Fed�s target rate, since theymust include service charge and risk premia and account for the loanperiod for the bank to stay viable. Nevertheless, the real interest ratesthat borrowers pay are largely determined by the federal funds rate. Inthis sense, the Fed controls the (nominal) interest rate.

� Federal funds rate over time in the US: normally falls during recessions(re�ecting how the Fed uses the interest rate to counteract the businesscycle) - except in the early 1980s, when Fed chairman Paul Volcker wascombating in�ation and intentionally induced a recession.

� Since there is very little risk involved in federal funds transactions,and volumes are large (the service component is negligible), the federalfunds rate is essentially the real interest rate plus in�ation.

� Recall the Fisher equation: the (risk-free) nominal interest rate it isthe sum of the real interest rate Rt and the rate of in�ation �t. Hencethe real interest rate is

Rt = it � �t:

� If an increase in the nominal interest rate is always accompanied bya corresponding increase in in�ation, the Fed has no control over thereal interest rate, it would be stable. In the present context, we assumethat in�ation is in fact �xed in the short run (any upward or downwardpressures induced by Fed policy take time to materialize - people do notimmediately adjust their expectations about the future rate of in�ationand continue to raise prices at the same rate for a while).

� One way to justify this idea is that people do not observe all prices atthe same time. If I run a business and I see demand for my productsincrease, there are two possibilities: a positive demand shock that isspeci�c to my industry, or an overall price increase. In the �rst case,I want to expand output (even if I notice that my costs have goneup proportionately), since my pro�t has increased in real terms (fromp � c > 0 to (1 +4) p � (1 +4) c = (1 +4) (p� c) per unit). Inthe second case, my pro�t is unchanged (the extra 4 (p� c) merely

55

compensates for in�ation). So there is temporary confusing about thesource of the price increase, and it would then be rational for �rms tocautiously expand production (and reduce it later if they discover theprice increase was universal).

� If in�ation is momentarily �xed, then the Fed e¤ectively controls thereal interest rate through the nominal target rate. The monetary policy"curve" horizontal to re�ect that the interest rate is exogenous to short-run GDP, it is whatever the Fed decides it should be.

� An increase in the real interest rate shifts the line up..

� Example of how the Fed might �ght a recession. A housing marketbubble comes to an end, and consumers and investors reduce theirspending, fearing an economic downturn. This shifts the IS curve in(left panel). The interest rate is una¤ected, since that is set by theFed, but cyclical GDP declines.

� The Fed responds by lowering the target rate, inducing a reduction inthe real interest rate (right panel). We move along the new IS curve to- if the interest rate cut is properly targeted - the old level of cyclicalGDP.

� Behind this is a spending increase by investors in response to the lowerrate at which they can now borrow. In practice, it takes 6 to 18 monthsfor a rate cut to make itself felt, and the Fed often cuts the interestrate repeatedly - �rst cautiously, then more boldly - to �gure out justhow much is needed.

� If the Fed sets interest rates in order to steer cyclical GDP, what is thee¤ect on in�ation? The Phillips curve described how in�ation increaseswith cyclical GDP. Expressed as a function,

�t = o+ �et + v ~Yt;

where o is an exogenous shock to in�ation and �et is the expected rate ofin�ation, i.e. the price increase that people anticipate at the beginningof the period, before they observe the actual rate of in�ation �t. Forexample, it seems reasonable that �et = �t�1; people believe that, absentany unforeseen shocks, the previous rate of in�ation will persist. (There

56

are other theories as to how these expectations are formed; this one isreferred to as "adaptive expectations.")

� Hence, with adaptive expectations,

4�t = �t � �t�1 = o+ v ~Yt:

� When �uctuations in GDP cause deviations from the expected rateof in�ation, we speak of "demand-pull" in�ation. Speci�cally, duringa boom in�ation increases, and during a recession in�ation decreases.The rationale lies in how �rm-level pricing responds to changes in de-mand. If the economy is contracting, �rms have trouble selling theiroutput and therefore increase prices by less than the typical rate. Ifthe economy is expanding, and �rms are approaching capacity as they�ll their many orders, they raise prices faster than typical.

� An increase in ~Yt leads to a movement along the Phillips curve and4�t > 0 because of "demand-pull" in�ation. Notice that ~Yt = 0(no �uctuations), absent a shock, leaves the rate of in�ation constant:4�t = 0.

� If o increases, perhaps due to a positive oil price shock or an increasein wages negotiated by a large union, the Phillips curve shifts upward,and we get "cost-push" in�ation. Makes sense because any in�ationthat does not involve a change in ~Yt cannot be attributed to changesin demand (~Yt includes the demand from each agent in the economy).

� A notable success of Fed policy was the ending of the "Great In�ation"of the 1970s. This sustained in�ation through the 1970s was partlycaused by the rise in oil prices we have already discussed.

� But it is now also attributed to a misguided monetary policy. TheFed wanted to thwart what they perceived as a coming recession bystimulating the economy. It did not recognize that potential output,not cyclical output, was in decline (the productivity slowdown, causedby the permanently reduction in oil supply after OPEC got active).By keeping GDP above trend, i.e. ~Yt > 0 (mistakenly believing that~Yt = 0), the Fed allowed in�ation to keep growing. (This relationshipwas also not clearly understood at the time, the Philipps curve used to

57

have in�ation, not change in in�ation, on the y-axis, so that a sustainedboom would have left in�ation constant. The experience of rising in�a-tion despite little growth in GDP, "stag�ation," was a puzzle that ledto the reexamination of the Phillips curve.)

� When Paul Volcker became chairman of the Fed in 1979, he faced adecade of high in�ation. By raising interest rates, the Fed induced areduction in cyclical output, i.e. a recession (moving from point A topoint B in the diagram). The contraction would have come from fallinginvestments.

� Banks raised their prime lending rates (for the most creditworthy clients)from under 5% in 1979 to 19% in 1981. Housing purchases dropped asmortgage rates rose to over 20%. With these drastic reductions in in-vestment spending, income in the economy fell (including for consumerswho are, ultimately, the recipients of returns to investment), and �rmsresponded to lower demand for their products with price cuts.

� In the Phillips curve diagram, we have the e¤ect of cyclical output onin�ation: we can see that the recession (which was the worst since theGreat Depression) caused the rate of in�ation to fall.

� What happened to the real interest rate, real GDP and in�ation dy-namically. Soaring oil prices delivered an external shock to in�ation.Initially, Rt might have been at the marginal product of capital r (leftpanel) and GDP on trend (middle panel), but in�ation was high be-cause of the shock (right panel). (This isn�t quite historically accurate,the economy was probably above trend, and Rt below the true mar-ginal return to capital r during the Great In�ation, causing in�ationto grow.)

� At time 0, Volcker raised Rt above r, which caused GDP to fall belowtrend, and this induced the slowdown in in�ation. At time t�, oil pricedhad eased and expected in�ation was lower (since people knew the Fedwas committed to reigning in in�ation), so Rt could be lowered back tor, so that GDP jumped back to trend. Absent any in�ationary pressurefrom output, in�ation remained low.

� This does not yet explain why the lower rate of in�ation became sus-tained into the present. But for this we have the quantitative theory

58

of money: responsible management of the money supply (keeping it atthe rate that is necessary to maintain prices given output growth) willkeep in�ation constant, if there are no further in�ationary shocks thatrequire a response like the one we just discussed (OPEC only raised oilprices "once," so it was a permanent shock to prices, but a temporaryshock to in�ation).

� Development of GDP and employment through the 2001 recession,which was brought about by the burst of the dot-com bubble (and,at the tail end, a¤ected by the September 11 attacks). The interest-ing, and as yet not fully explained, aspect of the recession is that thesubsequent recovery was associated with a continued increase in unem-ployment.

� Just like stag�ation caused macroeconomists to rethink the Phillipscurve, the "jobless recovery" has called the current version of Okun�slaw into question. It is important to keep in mind that these are "em-pirical laws," not logical theories. They are accepted only until we runinto contrary evidence.

4.5 Interest Rate Targeting and the Money Supply

� The federal funds rate that Fed policy targets is in reality determinedby the supply and demand for money faced by commercial banks. Themoney supply is the side the Fed can directly control.

� The money demand curve slopes down: money holdings decrease in thenominal interest rate, which is the opportunity cost of keeping currencyon hand, rather than invested in an interest-bearing asset. The nominalinterest rate is such that money demand equals the money supply, henceit is determined by the demand for liquidity (unless the Fed intervenesand adjusts the money supply through open market operations).

� Recall that, according to the quantity theory of money,

M =PY

V:

With money supply, price level and output �xed in the short run, theonly thing that can change in response to the nominal interest rate is

59

the velocity of money: people want to keep less currency in their walletsif the return on savings and money market accounts is higher, so eachbill gets spent less often. The nominal interest rate that we see in theshort run is the one where the (�xed number of) bills in circulationcover the (�xed) cost of the produced goods.

� Tightening the money supply makes money more scarce. The result isa higher interest rate and decreased velocity. This is how the Fed canraise the interest rate through monetary policy.

� With interest rate targeting, the money supply is horizontal at thenominal interest rate the Fed is setting. It will adjust in whateverdirection is necessary to establish this interest rate.

� The Fed used to target the money supply (M1), rather than the inter-est rate. Even if the relationship between the money supply and theinterest rate were perfectly predictable, a problem with such a policyis that the growth in checkable deposits (the largest component of M1)is not so easy to manage. The Fed�s open market operations directlya¤ect the monetary base (it credits and debits banks�reserve accounts).While a greater stock of reserves would allow the commercial bankingsystem to make additional loans, that would create additional deposits,the precise change in M1 depends on consumer choices as to how theywant to hold their money.

� An open market operation has a "money multiplier" e¤ect: as a bank�sreserves with the Fed increase by an amount X, it can loan out 90%of X, and if those 90% are deposited with another bank, that bankcan loan out 81% (90% of 90%) of X, and so on. Ultimately (if every-thing gets re-deposited and nothing is held as currency), deposits in the�nancial system increase by X=0:1 = 10X. Conversely, if the Fed tem-porarily sold securities and debited reserves by X, checkable depositswould decrease by a multiple of X.

� However, if each borrower decided to keep 10% of the loan in cash, thenonly 81% of X (the 90% less 10% of it) is deposited with the secondbank, which needs to keep 8.1% on reserve, and only 65.52% (72.8%less 10% of it) reaches the third bank, etc. The multiplier is in this

60

case

0:9 � (1� 0:1) + (0:9 � (1� 0:1))2 + � � �= (0:9)2 + (0:9)4 + � � �

=1

1� (0:9)2� 5;

i.e. only half. Since the interest rate is easily and instantaneouslyobservable, the Fed can target it with more precision.

� When the Fed wants to change the interest rate, it most commonlyengages in open market transactions: it buys and sells treasury billsand bonds to adjust the currency in circulation. In principle, the Fedhas two other options: it could alter the reserve requirement, allowingcommercial banks to loan out more of their funds, or the discount rate,making it cheaper to replenish reserves.

� Since a reduction in the discount rate would make it less costly for banksto fall below their reserve requirements, it would encourage them tokeep fewer excess reserves and lend more money. This would increasesupply in the federal funds market and lower the federal funds rate.Conversely, raising the discount rate would increase the federal fundsrate, by decreasing supply in the federal funds market as banks keeplarger reserves.

� However, unless the Fed intends to compete directly with the federalfunds market and become a large-scale lender to commercial banks,the discount rate is not as e¤ective a tool as open market operations:currently, banks use it as a last resort and borrow almost exclusivelyfrom other banks.

� Even though the reserve requirement has been stable for a long timenow, the Fed can use (and has in the past used) it to manage theinterest rate. Currently, �nancial institutions must hold 10% of theircheckable deposits in reserve (3% if they have less than $ 50 million incheckable deposits)

� If the reserve requirement were lowered, commercial banks could loanout a larger fraction of their deposits, so they would be willing to paya higher interest rate on accounts to their customers (at a given federal

61

funds rate). This will encourage individuals to hold more money incheckable deposits, so it ultimately reduces the monetary base andincreases M1.

� The federal funds rate would fall because bank balances are less likely tofall beneath a lower reserve requirement, and if they did, other bankswould have more funds available to loan out on a short-term basis.Conversely, raising the reserve requirement would increase the federalfunds rate, by increasing demand and decreasing supply in the federalfunds market.

� Reserve requirements have a secondary role to play as "insurance"against sudden increases in demand for currency (bank runs), so theFed is reluctant to lower them as a monetary policy instrument.

4.6 Aggregate Demand and Supply

� Monetary policy rule: a principle the central bank uses to determinewhat the money supply should be. It might be tied to cyclical GDP ~Ytor the rate of in�ation �t or cyclical unemployment, depending in thecentral bank�s objectives.

� The Fed primarily tries to manage the rate of in�ation. Recall fromthe Phillips curve that cyclical GDP is related to changes in the rate ofin�ation, so by keeping in�ation stable, the Fed is implicitly also reign-ing in the business cycle. In a boom, in�ation is higher than expected(i.e. prices grow faster than usual), lowering the rate of in�ation backto a target rate depresses output growth.

� The Fed�s monetary policy rule might be described as follows:

Rt � r = m (�t � ��) ;

where �� is the target rate of in�ation. The parameter m describes howsharply the Fed will adjust the interest rate Rt if in�ation �t deviatesfrom the target rate.

� By substituting for Rt � r in the IS curve equation,~Yt = a� b (Rt � r) = a� bm (�t � ��) ;

we have ~Yt as a function of in�ation.

62

� This is referred to as the aggregate demand (AD) function, since it isa downward-sloping relationship between overall output and the pricelevel. Actually, in our approach, a change in the price level, but tra-ditionally Keynesian analysis links the interest rate to the price level,not in�ation, to derive the AD curve. This connection can be made viathe quantity theory of money: P =Mv=Y .

� The AD curve slopes down because, when in�ation �t rises, the centralbank responds by raising the interest rate Rt, which reduces investmentand thereby ~Yt.

� Recall that, at ~Yt = 0 we have a = 0 (which is to say, aC + aI + aG +aNX = 1). Thus, �t = �� means ~Yt = 0.

� A change in the rate of in�ation, due to some price shock, would inducea movement along the AD curve to a lower cyclical GDP. Any otherchange (spending propensity a, target in�ation rate �� etc.) would implya shift.

� Higher m means that the Fed �ghts unintended in�ation more aggres-sively (by raising or lowering the target interest rate more). In thiscase, the AD curve gets �atter: a given change in �t creates a greaterchange in ~Yt under the policy rule.

� In the last lecture, we introduced a function for the Phillips curve:�t � �t�1 = o + v ~Yt (this assumes adaptive expectations, �e = �t�1).This implies

~Yt =1

v(�t � �t�1)�

o

v:

� Because output increases in the price level (more directly, change inthe price level), the Phillips curve in this form is called the aggregatesupply (AS) curve.

� The AS curve slopes up. When in�ation increases, �rms produce more,given our maintained assumption that prices change unevenly, and inparticular �nal goods prices initially rise faster than business costs(wages, intermediate goods).

� Recall that, at ~Yt = 0 we have o = 0 (no shocks to in�ation). Thus,�t = �t�1 = �

e (in�ation is as expected) means ~Yt = 0.

63

� Here, a change in �t is a movement along the AD curve, and a changein �t�1 constitutes a shift. Thus, a movement along the curve in thecurrent period implies a shift in the next.

� In this context, �t = �t�1 (and the absence of demand or price shocks,a = 0 and o = 0) is the de�nition of the steady state. Thus, from theAS curve, ~Yt = 0 in the steady state, and, from the AD curve, �t = ��(which means that �e = �t�1 = ��, i.e. the target level of in�ation isexpected).

� Overlaying the AS curve on the AD curve, they intersect in steady stateat �t = �� and ~Yt = 0. I.e., in the absence of shocks, the Fed�s targetinterest rate will be attained and GDP will be at potential.

� In predicting the dynamics induced by a shock, it is important to keepin mind that the economy will eventually, after temporary shocks havesubsided, return to steady state. Note that only two things can changethe steady state: (1) the central bank might adjust �� (so the newsteady state is at ~Yt = 0 and the new ��), or (2) permanent "shocks"might alter the de�nition of ~Yt (which is relative to potential GDP),but this would not a¤ect AD-AS analysis (since we are only talkingabout deviations from potential GDP, we do not need to know whatpotential GDP is).

� Consider a shock to the in�ation rate, i.e. o > 0. This shifts the AScurve up: now in�ation is higher at any level of GDP. But the impacton ~Yt is softened by the monetary policy response, which is re�ected inthe move along the AD curve: the Fed will raise the interest rate anddiscourage investment, forcing ~Yt to fall. The equilibrium changes fromA to B.

� What happens next? Even though the shock is temporary, there is anincrease in expected in�ation, so �t increases at any ~Yt (and the ADcurve shifts out again) relative to the initial AD curve, but by less thanbefore. (Since the actual rate of in�ation �t�1 after the policy responsewas less than what it would have been purely on account of the shock,so the increase in �t�1 is smaller than o.). The short-run equilibriumchanges from B to C.

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� The same pattern continues. Since the rate of in�ation has declined,�t < �t�1, there is a further shift inward in the next period as �e falls.

� In this fashion, the rate of in�ation continues to decline (and ~Yt grad-ually recovers) toward the target rate (and potential output).

� It takes time for the economy to adjust after the temporary shock;typically, monetary policy will not immediately return the economy toits steady state. As in the principle of transition dynamics in growththeory, convergence toward the steady state is strongest initially, whenthe economy is at its farthest from it. Later, interest rates adjust moregradually, and the e¤ect on ~Yt is less pronounced.

� Note that, even though the book relates this to stag�ation experience ofthe 1970s, that was triggered by a change in potential output, whereashere we are looking at a short-term deviation from trend. A change inthe long-term trend would not shift the AS curve relative to the ADcurve, ~Yt would remain zero at the expected rate of in�ation.

� Consider an attempt to set a new target rate of in�ation within theAD-AS framework. This is what Volcker implicitly did in the early1980s.

� Since �� enters positively into the AD equation ~Yt = a� bm (�t � ��), adecrease would shift the AD curve in: at any level of in�ation, cyclicaloutput ~Yt will be reduced (since the Fed is taking a more aggressivestance against in�ation). Initially, the equilibrium changes from pointA to B, moving down the AS curve because falling in�ation means �nalgoods prices drop faster than costs of production, so �rms scale backtheir output. The economy is in recession.

� But as in�ation starts to drop, the expected rate of in�ation �e = �t�1also changes from period to period, and we see successive downwardshifts of the AS curve, ~Yt = (�t � �t�1) =v � o=v. Eventually, the ADcurve will be at the point where ��0 (the new target rate of in�ation) isassociated with potential output, ~Yt = 0. During transition, in�ationdrops gradually and output gradually recovers.

� Earlier we considered a one-time supply-side shock to in�ation andfound that it left the interest rate ultimately unchanged. What if the

65

shock persists for some time? (If the demand shock were permanent, itwould amount to a one-time in�ationary shock, which we have alreadyconsidered.)

� Suppose a increases in the AD equation, perhaps due to a boom inEurope. Then net exports increase beyond their long-run level, and~Yt > 0 at the current interest rate �t. This implies a shift up of the ADschedule, and the economy moves from A to B to higher output and ahigher in�ation rate.

� For GDP to transition back to potential, ~Yt = 0, the AS curve mustshift up as well, which implies a new equilibrium at C, where ~Yt = 0but �t > ��. How does this happen? Initially, the rise in in�ation isunexpected and moderated by the fact that �rms expand their output(while input prices aren�t keeping up). But over time, everyone adjuststheir expectations of the in�ation rate upward. As input prices catchup, �rms scale back their output at every level of in�ation - that is, theAS curve goes through a series of upward shifts.

� Now the economy is at potential but the in�ation rate di¤ers fromthe target. Speci�cally, the equation for the AD curve tells us that�t = �� + a= (bm) since a� bm (�t � ��) = ~Yt = 0.

� When the shock ends, AD shifts back to its old place. Unexpectedde�ation leads the economy into a recession, since �rms see their outputprices drop faster than their costs. So ~Yt is reduced at any given levelof in�ation: the AS curve shifts in. Eventually, the economy returns tothe original steady state.

� What we are left with, after the temporary shock to demand, is theboom-recession cycle in between the departure and return to steadystate. As we have previously discussed, these �uctuations are costlyto the economy, since they are. for example, associated with cyclicalunemployment. If the central bank had not adjusted the interest rateaccording to its monetary policy rule (movements along the AD curve),the swings would have been more severe.

� Since we have been presuming that Fed policy follows the rule Rt�r =m (�t � ��) in targeting the federal funds rate, we should stop to seewhether we can verify this in the data. Of course, the observable federal

66

funds rate is a nominal rate, but we can apply our theory to nominalinterest targeting via the Fisher equation:

it = Rt + �t = m (�t � ��) + r + �t:

� The in�ation rate �t is observable, the marginal return to capital ris usually taken to be 2%. For the policy parameters, �� = 2% andm = 1=2 have been suggested as providing a good approximation toFed behavior.

� This is a simple version of the Taylor rule for targeting the nominalinterest rate, named after John Taylor, who suggested it. The fullTaylor rule also takes deviation from potential output into account,

it =1

2(�t � 0:02) + 0:02 + �t +

1

2

�lnYt � ln �Yt

�so that the Fed �ghts both in�ations and cyclicality in GDP. Withthese values for the (simple) Taylor rule, we get a reasonably good �tto the actual federal funds rate.

� In�ation rates have fallen since the 1980s in developed countries through-out the world. This is support for the assumption that monetary policyreacts to the rate of in�ation. Some central banks (not the US Fed)announce o¢ cial in�ation targets these days.

� When the central bank exercises "discretionary" policy, i.e. takes adhoc decisions to target what appears to be the best interest rate, it canintroduce "time inconsistency" (deviating from previously announcedpolicies, say in order to create unexpected in�ation in a recession).Ultimately, such behavior (or even just the possibility of it) increasesuncertainty in the economy, and adjustment to a new policy targettakes longer.

� By acquiring a reputation for following a particular policy rule, centralbanks can in�uence expectations about the in�ation rate and achievefaster adjustment. In the model so far, people predicted - rather naively- that the previous rate of in�ation will persist, no matter what. Theyshould use the best information available (including the central bank�strack record and announcements) in forming such views.

67

� Even though we have a theory that "perfectly" predicts the changesin the in�ation rate induced by a shock, we are arguing that people inthe economy are "surprised" by these changes, which is what causesoutput to increase according to the AS curve. Why don�t they learnsome macroeconomics? Money could be made in the stock market ifyou buy when the economy starts to expand and sell when it contracts.Sellers of intermediate goods could raise their prices in anticipation ofincreased demand during a boom. Workers could demand intermittentpay raises while their labor is in short supply.

� To some extent they do: think about industries that pay bonuses basedon �rm performance - these schemes implicitly adapt the real wage tothe business cycle. Suppliers are certainly not systematically blindto foreseeable events, they do try to maximize their pro�ts and raiseprices when they can. These are the kinds of conceptual issues modernmacroeconomics is trying to sort out.

� In what became known as the "Lucas Critique," Robert Lucas madethis point in 1976. Rational expectations - the idea that people acton the best forecast possible from a statistical point of view - has be-come widely accepted as a standard that economic modeling shouldmeet (even if economists privately argue over whether individuals areindeed approximately rational). Adaptive expectations are thereforean oversimpli�cation.

� When the central bank has a strict policy of implementing a certaintarget level of in�ation through its management of the interest rate,the rational expectation would be for the interest rate to remain closeto target.

� If a lower target rate is announced, the AD curve shifts in (since �� enterspositively), but the AS curve immediately shifts out (because �e = ��replaces �t�1, which enters negatively). In theory, the in�ation rateadjusts immediately, and there is no recession (unlike with adaptiveexpectations).

� This is why macroeconomists today support a predictable and con-sistent Fed policy, with explicit targets - with approximately rationalexpectations, this will minimize the cyclical variations in GDP that the

68

economy has to go through when the Fed intervenes. And it will keepin�ation stable in the �rst place, since everyone acts on the assumptionthat the Fed will restore the target rate of in�ation swiftly, so there islittle pressure for unexpected price increases.

4.7 Real Business Cycle Theory

� The main empirical problem with the Keynesian approach is that itsuggests labor productivity falls during a boom (�rms hire more labortime because wages do not keep up with output prices, so the marginalproduct of labor declines), which is contradicted by the data. The mainalternative model �xes this �aw, but is analytically much more di¢ cult.

� The natural extension of the Solow-Romer model to short-term be-havior is a so-called real business cycle model. In this model, pricesstill adjust perfectly, so in�ation has no real e¤ects. In fact, money isnot needed in order generate short-term �uctuations in real variables.The �uctuations arise from productivity shocks that might re�ect any-thing from natural disaster to oil discovery, from tax increases to newbusiness practices and inventions, from foreign wars to growth miraclesoverseas. It�s a catch-all concept, and that is a strength as well as aweakness.

� While we can �t many scenarios into the model and do not need to im-pose assumptions like price rigidity, the productivity shocks themselvesremain unexplained, and government (which does not even feature insimple real business cycle models) is mostly powerless against down-turns. Policy makers have been hesitant to adopt these models for suchreasons, yet they form the basis for much of modern macroeconomicresearch.

� As usual, the economy�s output is given by the Cobb-Douglas produc-tion function

Yt = AtK1=3t L

2=3t :

In the long run, productivity At may be determined by Romer-styleidea generation, but in the short run, we now think of

At = ezt

as driven by a shock.

69

� In the real business cycle literature, zt is typically speci�ed as an au-toregressive process of the form

zt+1 = �zt + "t+1;

which is at each point in time a normally distributed random variable:"t+1 � N (0; �2). Such models ultimately produce the best �t with thedata, but they do not have closed-form solutions. In calibrating thiskind of process to the data, shocks are found to be quite persistent: areasonable value for � is about 0:95, so that much of a shock in periodt carries over to period t+ 1.

� For our purposes, we will consider a process

zt+1 = �2

3ln

1

(ezt)3=2+ "t+1

!that is a random walk with drift: the expectation of zt+1 is positiveand increasing one-for-one in zt.

� E.g. suppose the distribution of "t+1 (conditional on zt) is as follows:Pr ("t+1 = 0) = 1=2 and

Pr

"t+1 = �

1

2

1

(ezt)3=2

!= Pr

"t+1 =

1

2

1

(ezt)3=2

!=1

4:

Then

Et [zt+1] =1

4

�23ln

1

2

1

(ezt)3=2

!!+1

2

�23ln

1

(ezt)3=2

!!+1

4

�23ln

3

2

1

(ezt)3=2

!!= zt +

1

3ln2p3:

The constant re�ects technological progress.

� The representative agent is assumed to act according to instantaneousutility function

u (Ct; Lt) = lnCt � 'Lt;where Ct is individual consumption and Lt is time worked. Note thatthe marginal utility from consumption is diminishing, which entails apreference for consumption smoothing.

70

� If labor supply is indivisible (i.e. you either have a job and work 9-5or you don�t have a job and thus work no hours), you can think of ' isre�ecting the probability of being employed in a given period (where, ifyou were unemployed, you would receive unemployment bene�ts equalto the market wage). In that type of economy, everyone is paid the mar-ginal product of labor, and however many people are actually neededto work are selected by lottery, the others get to take a nap. The im-portant thing is that the representative agent dislikes working if income(consumption) is given.

� The representative agent is in�nitely lived (e.g. we care equally aboutour children�s welfare as about our own) and maximizes expected utilityover time:

Et

" 1Xt=0

�tu (Ct; Lt)

#;

subject to the budget constraint

Ct +Kt+1 = Yt + (1� �)Kt:

In more elaborate real business cycle models, we may have �nancialassets, money, government spending etc.

� At any point in time, there are three independent choice variables (Ct,Lt and Kt+1). Why is Kt not a choice variable? (It�s determined byconsumption and previous saving and work e¤ort, which �x Yt). In agraduate class, you would learn how to solve this problem by dynamicprogramming methods. But, with a little care, we can treat it as aLagrangean:

� (Ct; Lt; Kt+1) = Et

" 1Xt=0

�t�lnCt � 'Lt + �t

�eztK

1=3t L

2=3t + (1� �)Kt � Ct �Kt+1

��#:

� To simplify notation, de�ne the marginal returns to labor and capital:

wt =@Yt@Lt

=2

3

YtLt=2

3ezt�Kt

Lt

�1=3rt =

@Yt@Kt

=1

3

YtKt

=1

3ezt

1�Kt

Lt

�2=3 = 1

2

1Kt

Lt

wt:

Note that they are sensitive to the shock zt.

71

� We have �rst-order conditions

(1)@�

@Ct=1

Ct� �t = 0 () �t =

1

Ct

(2)@�

@Lt= �'+ �twt = 0 () �t = '

1

wt

(3)@�

@Kt+1

= ��t�t + Et��t+1�t+1 (rt+1 + 1� �)

�= 0 () �t = Et [��t+1 (rt+1 + 1� �)] ;

plus the budget constraint (which can be thought of as a fourth �rst-order condition, where we di¤erentiate � by �t). It can be written asfollows:

(4) 3rtKt + (1� �)Kt = Ct +Kt+1:

� Note that the realization of the random element zt, and therefore Yt,is known at time t; we have Et [Yt] = Yt and Et [Ct] = Ct. But in the�rst-order (3) condition for Kt+1 we must di¤erentiate two terms: Kt+1

appears in

�t�lnCt � 'Lt + �t

�eztK

1=3t L

2=3t + (1� �)Kt � Ct �Kt+1

��as well as in

Et

h�t+1

�lnCt+1 � 'Lt+1 + �t+1

�ezt+1K

1=3t+1L

2=3t+1 + (1� �)Kt+1 � Ct+1 �Kt+2

��i:

The latter includes Yt+1 = ezt+1K1=3t+1L

2=3t+1, which is not known at time

t (since the realization of the shock zt+1 has not been observed yet).Hence we must retain the expectation operator in this case.

� From (1), (2), (4):

(1), (2) Ct =1

'wt

(4) Ct = (3rt + 1� �)Kt �Kt+1;

henceKt+1 = (3rt + 1� �)Kt �

1

'wt:

This is the equation of motion for the capital stock, familiar (in slightlydi¤erent form) from the Solow model.

72

� It re�ects the budget constraint, as well as intertemporal substitution:a higher rate of return to capital increases capital accumulation, but ahigher wage today increases consumption and reduces capital accumu-lation.

� From (2), (3):

wt =1

�

1

Et

h1

wt+1(rt+1 + 1� �)

i :� This relationship is known as an Euler equation. It re�ects how therepresentative agent takes into account how current choices a¤ect futurequantities (wt+1 and rt+1). This is where rational expectations are builtinto the model, unlike in Keynesian analysis. Once we understand thisrelationship, we can predict the motion of the capital stock and howit will react to a shock (to wt and rt). Then we will also know whathappens to labor and GDP.

� We set up a real business cycle model and derived two optimality con-ditions for the representative agent�s choices. One is the motion of thecapital stock,

Kt+1 = (3rt + 1� �)Kt �1

'wt;

the other is the Euluer equation,

wt =1

�

1

Et

h1

wt+1(rt+1 + 1� �)

i :� The marginal return to capital and labor had the form

wt =2

3ezt�Kt

Lt

�1=3rt =

1

3ezt

1�Kt

Lt

�2=3 = 1

2

1Kt

Lt

wt:

� We are assuming a shock

zt+1 = �2

3ln

1

(ezt)3=2+ "t+1

!;

73

with Et ["t+1] = 0.

� The expectation of zt+1 is Et [zt+1] = zt + �, where �:is a constantthat depends on the distribution of "t+1 (conditional on zt). The keypoint is that this process entails persistence of a shock "t 6= 0, unlikethe standard real business cycle, where shocks eventually vanish. Wewill see in a moment that persistence leads to counterfactual results(and thus it becomes clear why the real business cycle literature goesthrough the trouble of working with models that have no closed-formsolutions).

� Suppose (subject to veri�cation) that the capital-labor ratio dependson the shock in the following way:

Kt

Lt= (xezt)3=2 ;

where x is a constant. Then

wt =2

3x1=2 (ezt)3=2

rt =1

3

1

x:

� We can now rewrite

Et

�1

wt+1(rt+1 + 1� �)

�=1

2

1 + 3x (1� �)x3=2

Et

"1

(ezt+1)3=2

#:

Rearranging the equation for zt+1, and taking the expectation, yields

Et

"1

(ezt+1)3=2

#= E

"1

(ezt)3=2+ "t+1

#=

1

(ezt)3=2:

� Substituting these expressions into the Euler equation, we can deter-mine the value of x:

wt =2

9

1

�

x3=2

1 + 3x (1� �) (ezt)3=2

andwt =

2

3x1=2 (ezt)3=2 ;

74

imply

x =1

3

�

1� � (1� �) :

Since this is a constant, we have veri�ed the assumed functional formfor Kt=Lt.

� Substituting for the marginal products in the motion of the capitalstock,

Kt+1 = (3rt + 1� �)Kt �1

'wt

=

�1

x+ 1� �

�Kt �

2

3

1

'x1=2 (ezt)3=2 :

Notice that Kt+1 is reduced by an increase in productivity zt.

� Writing Yt asYt = e

zt1�

Kt

Lt

�2=3Kt =1

xKt;

we have

Yt+1 =1

xKt+1 =

1

x

��1

x+ 1� �

�Kt �

2

3

1

'x1=2 (ezt)3=2

�=

�1

x+ 1� �

�Yt �

2

3

1

'

1

x1=2(ezt)3=2

(sinceKt = xYt by the same token). Again, Yt+1 falls when productivityzt increases.

� Let�s try to understand the strange behavior of GDP in this model.A kind of potential GDP can be isolated by keeping capital and laborconstant in the absence of a new shock, i.e. "t+1 = 0 and so zt+1 = zt.The capital stock is constant (at given zt) if

Kt+1 =

�1

x+ 1� �

�Kt �

2

3

1

'x1=2 (ezt)3=2 = Kt;

hence

Kt =2

3

1

'

x1=2

1x� �

(ezt)3=2 � �Kt:

75

(Since the capital to labor ratio is determined by zt, labor is implicitlyalso constant if capital is.)

� We see that potential GDP

�Yt =1

x�Kt =

2

3

1

'

x1=2

1� x� (ezt)3=2 :

is increasing in productivity zt.

� What is going on? Consumption, which from the �rst-order conditionsof the Lagrangean problem was

Ct =1

'wt =

2

3

1

'x1=2 (ezt)3=2 ;

increases in zt as one would expect. Since the representative agent�sutility is concave in consumption, she wants to smooth consumptionover time. Given that a positive shock permanently increases expectedproductivity, consumption is permanently higher (at least, that is theplan at time t: unexpected negative shocks later on could reverse this).

� SinceKt

Lt= (xezt)3=2 ;

labor e¤ort isLt =

1

(xezt)3=2Kt;

which is decreasing in zt (of course, Kt is �xed at time t, it does notchange in response to zt).

� Why would individuals work less when they become more productive?The reason is that the productivity increase (in this oversimpli�ed ver-sion of a real business cycle) is permanent, so the representative agentexpects to be able to produce more with less e¤ort now and in thefuture. Since labor enters negatively into the utility function, she takesadvantage of the positive shock by raising consumption a bit and re-ducing work hours a bit.

76

� Think about how this conclusion would change if the shock only hada temporary e¤ect on productivity. Then it would make sense to workmore today, when time spent working yields more output than tomor-row. This seems more realistic: employment and hours worked increasewhen labor productivity is high (which is typically the case during aboom).

� Since a positive shock makes the representative agent�s labor more pro-ductive, she can maintain a su¢ ciently high long-run output with asmaller capital stock. The saving rate in our model is

st = 1� CtYt= 1� 1

'wtx

1

Kt

= 1� 23

1

'x3=2 (ezt)3=2

1

Kt

:

This decreases in zt. Similarly, gross investment

It = Kt+1 � (1� �)Kt =1

xKt �

2

3

1

'x1=2 (ezt)3=2

and net investment

Kt+1 �Kt =1� �xx

Kt �2

3

1

'x1=2 (ezt)3=2

decline in zt.

� Hence, the representative agent here divests over time in response to aproductivity increase: she works less, but permanently consumes more- this can only come at the expense of capital accumulation. Overtime, the increase in consumption is funded less from new productionand more by running down the capital stock.

� Again, it does not accord with reality that investment falls when laborproductivity rises. If productivity increases due to a positive shock weretemporary, the representative agent would use periods of high produc-tivity to work more, save more and thereby perpetuate the increase inwealth through capital accumulation. This would smooth the increasein consumption over time.

77

� The present model shares with the Keynesian model the mistaken impli-cation that labor productivity is countercyclical. In Keynesian analysis,this was because sticky wages made it pro�table for businesses to hiremore workers (or make them work longer, lowering marginal productiv-ity) when there was unexpected in�ation (resulting in a boom). Here,the productivity increase is primary, but the anticipation of higher fu-ture productivity induces people to work and save less, causing GDPto fall below potential.

� Clearly, real business cycle models with temporary shocks are neededto mimic the basic facts of macroeconomic �uctuations: labor produc-tivity, hours worked, investment and consumption are all procyclical.

� Moreover, they should - and can - re�ect that investment is morevolatile than consumption. Keynesian analysis achieves this throughmonetary policy, which is designed to expand and contract investment.In real business cycle theory, the Fed cannot easily do this, because realinterest rates are taken to be independent of in�ation (nominal interestrates adjust fully and quickly to any predictable change in in�ation).Thus, investment volatility must arise from the optimal reaction ofthe representative agent to productivity shocks, i.e. from consumptionsmoothing.

� You might ask yourself how proponents of real business cycles wouldexplain the empirically observed Phillips curve, which links booms toin�ation. After all, real business cycles do not allow for temporarymisalignment in prices, which explains the Phillips curve in Keynesiananalysis.

� More sophisticated real business cycle models do include money andgovernment. Although they maintain "money neutrality" - that theprice level cannot cause changes in real GDP - they are consistent withthe possibility that changes in real GDP cause changes in the pricelevel, directly or as a result of Fed policy.

� During a boom, the quantity theory of money predicts that, with con-stant money supply, prices decrease. (But, unlike Keynesians, real busi-ness cycle theorists expect all prices to adjust fully, instantaneously.)Because demand for loans (by businesses and consumers) grows (as a

78

result of higher productivity and expected future incomes), there is up-ward pressure on the real interest rate. If the Fed seeks to stabilizethe interest rate, it has to expand the money supply, which might pushthe economy into in�ation, and this would imply the Phillips curverelationship.

� However, the primary e¤ect is in the wrong direction, and it is not clearwhy the Fed would overreact to de�ationary pressure, nor is interestrate stabilization (rather than in�ation and business cycle smoothing)consistent with the Fed�s actual policy stance. This is one of the prob-lems of real business cycle theory: it does not have a very plausibleexplanation for the Phillips curve, which is clearly observable in thedata.

4.8 The Financial Crisis of 2008

� Crises that hit Latin America, East Asia and Russia in the 1990s depre-ciated foreign currencies against the dollar and reduced demand for USproducts. As a result, developing countries held increasing amounts ofUS currency (paid by US �rms for goods imported to the US or in ex-change for foreign currency that was needed to pay for imports). Thesedollar reserves did not sit idly in a vault somewhere, but were loanedback to the US economy in one way or another. They contributed torecord low interest rates in the United States.

� As a result, credit was in ample supply and �nancial institutions relaxedlending standards for businesses as well as individuals. As debt becamecheaper and more readily available, businesses, especially �nancial in-stitutions, increased their leverage. Leverage refers to the ratio of debtto equity (equity is the net worth of the �rm: assets minus debt).

� High leverage implies that small percentage changes in the value ofinvestments translate into large amounts relative to the �rm�s equity.Hence, a modest loss on all investments might wipe out any positivenet worth. Normally, such losses are not supposed to happen because�nancial institutions hold diversi�ed portfolios that are calculated toyield predictable gains. But when an event causes many investments togo bad at the same time, the �rm can no longer pay o¤ its short-termdebt, unless it �nds an unsuspecting lender.

79

� Thus, increasing leverage made the survival of �nancial institutions(and other businesses) more sensitive to such an event. Moreover, sincemany �nancial institutions hold signi�cant debt of other �nancial in-stitutions, the failure of one could quickly lead to the failure of others,a condition known as "systemic risk." Essentially, each bank was notonly relying on the wisdom of its own investment decisions, but onthose of all other banks as well.

� Fannie Mae and Freddie Mac are companies operating under govern-ment charter that purchase mortgages from banks, pool them and resellthem to investors (including banks). Their role is to increase liquidityin the primary mortgage market (i.e. for the institutions that originatethe mortgages). At a premium, they guarantee principal and interest,and these guarantees were perceived in the �nancial community to beimplicitly backed by the government.

� In the mid-1990s, the Clinton administration had paved the way forso-called subprime mortgages: home buyer loans for relatively high-risk borrowers. Fannie Mae and Freddie Mac were encouraged tobuy lower-quality mortgages, which gave banks an incentive to issuesuch mortgages, given that they could resell them and avoid the risk.(The government�s objective was to increase home ownership for poorerAmericans at a time when defaults did not seem to be a big threat.)

� In the decade prior to 2006, house prices tripled on average as newbuyers entered the market, and by 2006 a �fth of new mortgages weresubprime.

� What caused the housing market bubble to burst? If we look at thedevelopment of the federal funds rate, we see that the Fed sharply raisedthe target interest rate starting in 2004, to �ght in�ationary pressures.This cooled the demand for new mortgages and brought house pricesdown.

� Many of the new mortgages carried low introductory interest rates thatwere �xed ("teaser rates"), followed by a high variable interest rate afew years later. When interest rates increased, subprime borrowers,who could barely a¤ord their mortgages, were suddenly in trouble.Moreover, falling house prices meant in some cases that the home was

80

now worth less than the value of the outstanding mortgage. As homeowners defaulted and their houses went back on the market, prices fellfurther, causing even more homes to be vacated. This downward spiralexplains why house prices dropped so dramatically.

� Like Fannie Mae and Freddie Mac, banks "securitize" mortgages (andother types of debt, such as credit card debt) by bundling them togetherto create a new instrument that is sold to investors at a discount. Ifthe loans perform, the proceeds are paid to the investors, who arebasically betting against default (counting on the portfolio e¤ect thatthe number of individual defaults will be predictable and small). Manybuyers of such mortgage-backed securities are other banks.

� The fact that banks were so heavily invested in mortgages, many ofwhich were subprime, caused additional problems when it became clearthat many mortgages were in danger of default. Interbank lending isnormally at a slight premium over the T-bill rate (which is consideredalmost riskless). By 2007, banks perceived a greater risk in lending toeach other, since one bank could not know exactly how much of anotherbank�s assets was invested in subprime mortgages, and therefore whatits short-term default risk really was.

� The spread between the interest rate on three-month interbank loans(LIBOR is the London Interbank O¤ered Rate) and the interest rate onT-bills grew from less than half a percent to, eventually, almost 3.5%.

� This greatly increased the cost to banks of falling below their reserverequirements (in which case they would have to borrow in the interbankmarket) and forced them to issue fewer loans to consumers and busi-nesses - a phenomenon that became known as the "liquidity crisis" or"credit crunch." The sudden high cost or unavailability of loans wors-ened defaults on mortgages as well as businesses, both of whom dependon being able to cover short-term �uctuations in income by borrowingfrom commercial banks.

� The S&P 500 stock price index fell by almost 50% between 2007 and2009, re�ecting a risk evaluation in response to the liquidity crisis aswell as a huge increase in the price of oil: the price of a barrel went fromabout $20 in 2002 to $140 in July 2008, a six-fold rise in real terms.

81

This development had very di¤erent causes (increase in demand for oiland other basic commodities from growing economies like China andIndia, and speculation on that), but further undermined the viabilityof businesses across industries, increased the need for credit while itwas tight, and ultimately devalued investor portfolios.

� In September 2008, it became clear that major �nancial institutions hadso many non-performing assets on their books that they were worthlessand could no longer repay their short-term debts: Lehman Brotherscollapsed, AIG was bailed out, Merrill Lynch had to be sold to Bank ofAmerica. Fannie Mae and Freddie Mac were taken over by the federalgovernment.

� By 2009, GDPwas below trend and continued to fall sharply for anotheryear. Somewhat earlier, in 2007, the unemployment rate began to climbfrom under 5% toward 10%. By either measure, decline in GDP or risein unemployment, the 2009 recession is far worse than typical recessionsin the US since 1950. This table is based on April 2009 values, beforethe recession reached its trough.

� Note the drop in consumption, which suggests people expect incomegrowth to slow in the long run or face binding wealth constraints thatforce them to adjust their standard of living. Usually, consumptioncontinues to grow during recessions, since it should be based on per-manent income.

� But this is not an ordinary recession that arises from normal demandor productivity shocks (depending on which theory of �uctuations yousubscribe to). It has its origin in a breakdown of the �nancial system, sowe should compare it to other crises that were associated with failuresof �nancial institutions - the Great Depression, the Asian crisis in 1997,etc.

� Comparing with average changes in economic variables, from start to�nish, for 20th century �nancial crises around the world. The largedrops in asset prices (housing and stocks) are typical, as are severereductions in output, employment. Governments greatly increase theirdebt in �ghting these crises.

82

� As capital markets are increasingly interlinked, banks and investorshold foreign assets, it is not surprising that the current �nancial cri-sis is global in scope, a¤ecting developed and developing economiesalike. This means, unfortunately, that reductions in consumption leadto reduced demand for exports, which exacerbates the decline in GDP.

� In summary, what caused the crisis were �nancial innovations, suchas subprime mortgages, that took advantage of overabundant creditand poor monitoring (non-transparent risks of securitized instruments,the government shouldering risk through Fannie Mae and Freddie Mac,which it implicitly backed). Sooner or later, in�ated asset markets hadto implode; the immediate trigger was probably the Fed�s decision toraise interest rates. High leverage of �nancial institutions increasedsensitivity to such events and created systemic risk.

� Oil price increases coincided with these developments, slowing produc-tivity The global nature of capital markets exposed other economiesto the crisis and, by pulling them down alongside the US, worsened therecession further.

4.9 The Fed Response

� How can we understand the Fed and US government response to thecrisis within our short-run model? The reduction in asset values andliquidity translates into a reduction in aggregate demand: at any in-terest rate, consumers would buy fewer products and businesses wouldinvest less money; in addition, because of the global dimension of thecrisis, foreigners could a¤ord fewer exports.

� Normally, the Fed would want to cut the federal funds rate in order toinduce in�ation and stimulate the economy. It would do so by borrow-ing government debt in the open market from banks at very low in-terest, thereby increasing the money supply. Indeed, the federal fundsrate basically went to zero, which provided the needed short-term cashto �nancial institutions.

� However, this does not mean that banks will automatically lend atlow rates to commercial customers. When there is heightened defaultrisk, they demand a higher risk premium or may decline to lend at

83

all. (This scenario is called a "liquidity trap," money is available butremains trapped in the bank vaults.) The actual real interest rate facedby borrowers becomes Rt + pt, where Rt is the risk-free rate (managedby the Fed) and pt is the risk premium.

� Troubled businesses are especially in need of long-term loans. Thewedge between the rate on ten-year treasury bonds and ten-year cor-porate BAA-rated bonds was increasing, causing the latter to increaseeven as the former fell. (On the Standard & Poor�s scale, investmentgrade bonds are bonds with at least a BBB- rating. Bonds with lowerratings than that are "junk bonds.")

� What happens when the interest rate reduction targeted by the Fed isinsu¢ cient to bring the risk-adjusted interest rate down. The economyslides farther into recession to point D (panel b) instead of C (panela). Once the federal funds rate reaches zero, the Feds�hands are tied,it cannot reduce interest rates further.

� Recall that the IS curve

~Yt = a� b�RISt � r

�and the monetary policy rule

RMPt � r = m (�t � ��)

together constitute the aggregate demand curve.

� Now, in the IS curve, Rt refers to the interest rate at which businessescan borrow (it drives the investment component of GDP). In the MPrule, Rt refers to the interest rate the Fed targets: the (largely) risk-free federal funds rate. If investors face a risk premium, then RISt =RMPt + pt. Hence the monetary policy can be rewritten as

RISt � r = pt +m (�t � ��) :

� Then the AD curve has the form

~Yt = a� bpt � bm (�t � ��) ;

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and we can see that an increase in the risk premium reduces ~Yt atevery rate of in�ation. The reduction in investment comes on top of thedemand reductions caused by the asset devaluation (which are re�ectedin a).

� In the AD-AS diagram, the downward shift of the AD curve triggers aseries of downward shifts in the AS curve

~Yt =1

v(�t � ��t)�

o

v

leading to an ever lower rate of in�ation while the increased risk premia(and asset devaluation) persist.

� The problem is that, when the in�ation rate is already low initially, afurther drop might lead to de�ation. De�ation is costly because, withimperfectly adjusted prices, it causes output prices to fall more slowlythan input prices and therefore leads to layo¤s, further reductions indemand, more layo¤s etc., the de�ationary spiral. Since the Fed cannotpush the nominal interest rate below zero (you wouldn�t leave yourmoney in the bank if you had to pay interest on your deposits), it cannote¤ectively �ght a real interest rate that is rising above the nominal ratedue to de�ation (recall the Fisher equation it = Rt+�t, in other wordsRt � it if �t � 0).

� Given the limitations on managing liquidity through the interest rate,the Fed took extraordinary measures. It started loaning money directlyto the private sector (previously, the Fed only held public debt), e.g.through the purchase of commercial paper This injects cash into theeconomy where it is needed and where commercial lenders perceive toomuch risk or uncertainty to play this role.

� How did the Fed come up with the money to do this? For the most part,it didn�t print it. Instead, the Fed o¤ered interest on federal reserveaccounts. In other words, it attracted deposits from banks far in excessof the o¢ cial reserve requirement (which banks where, of course, happyto supply, since it seemed too risky to loan the money to the privatesector). These excess reserves where then channeled into the economyvia private debt purchases.

85

� Compare the Fed�s balance sheet in 2007 and 2009. Note the (private-sector) loans that appear under assets in 2009, and the large increasein reserves under liability. The Fed also borrowed funds from the trea-sury that the treasury had raised from the public by issuing new debt(these obligations to the treasury are entered under treasury accounts).Overall, Fed assets and liabilities more than doubled.

� Composition of non-government debt held by the Fed since 2008. Cen-tral bank liquidity swaps are instruments through which the Fed pro-vides dollars to foreign central banks (in exchange for foreign currency)over a period of time. The other items are loans to the US private sec-tor and US banks (term auction credit refers to direct loans the Fedauctions o¤ to �nancial institutions).

� The crux to this strategy is that the Fed can lend money to the privatesector on better terms than commercial banks because partly controlsthe systemic risk. Where a commercial bank needs to charge a highrisk premium (or deny loans) to stay viable in a risky economy, theFed is reducing the risk by the very act of purchasing the debt, and ithopes that it can ultimately save many of the borrowers and get thedebt repaid. If this does not happen, then the Fed will be left withnegative equity that has to be covered through either direct or indirecttaxation (printing money) in the future.

� In addition to the Fed�s interest policies and loans, the governmenttook actions designed to clean up the portfolios of �nancial institutions(the Troubled Asset Relief Program, or TARP) and increase demand(the stimulus packages). TARP took assets o¤ the books of �rms and�nancial institutions that were in trouble and thereby allowed them toliquidate those assets at full value, rather than the heavy discounts theprivate sector would demand, given the associated risks. The sellers ofthese assets were able to repay their short-term debt and survive.

� To the extent that �nancial institutions are bailed out (their "toxic,"i.e. nonperforming, assets are bought above value), there is a poten-tially large long-term cost, because �nancial institutions will expectsimilar rescues in the future. Since they will fully bene�t from theupside of a risky investment, but believe they can share failures withthe public (since the government uses taxpayer money to subsidize the

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losses), they have an incentive to take excessive risk even against betterjudgement. The debate about whether banks should be allowed to failweighs the costs of an even more severe liquidity crisis against the costsof perpetuating bad incentives.

� The stimulus packages re�ect the Keynesian logic that recessions thatoriginate with demand shocks can be �xed if the government increasesspending enough to o¤set temporary reductions in consumer and in-vestor spending. The idea is that this will induce increases in in�ationthat lead �rms to hire and expand output.

� Classical economic reasoning that does not acknowledge sticky pricesdisagrees with this view. Rational expectations imply that people fore-see correctly that increases in government spending today must be �-nanced with tax increases in the future, hence decreases permanentincome. Therefore, consumers would cut back their own consumption(which has in fact happened in the current crisis, as we have seen).

� The 2008 stimulus, which involved tax credits for low- and middle-income earners, raised current incomes and was expected to raise con-sumer spending. This has not occurred, consistent with the permanentincome hypothesis: people realized that the increase in income is tem-porary and therefore saved it, smoothing consumption over time. Inthe graph, the spike in disposable income (after the disbursements) didnot lead to an increase in personal consumption expenditures.

� It is impossible to know what would have happened if �nancial in-stitutions had been allowed to collapse. The immediate e¤ect wouldlikely have been sharp. While the Fed has avoided unraveling, it facesa di¢ cult challenge to regulate the system in a way that discouragesexcessive risk-taking despite a demonstrated willingness to bail failingbanks out at the expense of the public.

� The e¤ect of the recent, much larger stimulus packages remains to beseen. Whether they work depends on whether prices are indeed sticky,i.e. wages are slow to adjust to increasing in�ation. E¤orts to increaseconsumer spending via tax credits appear not to have succeeded, whichgives some validation to the rational expectations hypothesis.

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5 Public Finance

5.1 Tax Revenue

� The major sources of income for the federal government are currentlypersonal income taxes and social insurance contributions, followed bycorporate pro�t taxes, then customs and excise duties, and �nallymoney creation by the Fed (newly printed money is used by the trea-sury for its purchases).

� Historically, the government used to be �nanced almost entirely bycustoms and excise duties before World War I, until corporate andpersonal incomes taxes were established, respectively, in 1909 and 1913.Their shares in total revenue rose to 25% and 40% by the end of WorldWar II. While the share of personal income taxes has remained fairlyconstant since then, the shares of corporate and customs / excise taxeshave been declining.to about 10%.

� Unemployment insurance and social security started on a small scale in1936 and 1937 as part of FDR�s "new deal." Today, social and healthinsurance contributions make up more than 40% of tax revenue, andthe share continues to increase.

� State and local tax revenues are about half the size of federal incomeState and local governments used to rely primarily on the propertytax, but at this point sales taxes, local income taxes and federal aid(transfers for social programs like welfare, medical care, transportation,education etc.) are roughly equally important sources of income, eachaccounting for about a �fth. The remainder includes local school andpro�t tax, social insurance levies and revenues from toll and such.

� Any tax that is tied to income (as virtually all taxes are in one way oranother) ultimately discourages income-generating activities, such aswork and investment, and encourages leisure and consumption. (Theidea behind the earned income tax credit, which supplements incomesof the working poor, was to make their marginal tax rate negative, todiscourage voluntary unemployment. Introduced in 1996 under Clin-ton, the EITC indeed raised work hours among this group.) In somecases, taxes direct people away from legal activities, that are reported

88

and taxed, toward the black market (or at least informal exchange),where no taxes are paid. This is why tax increases, other things equal,reduce measured GDP and the tax base.

� A long-standing debate is over the point where tax increases will resultin a reduction in tax revenue. In theory, it is clear that the point existswhere the tax base shrinks so much that the increase in percentage doesnot translate into an absolute increase. In fact, every tax increase leadsto a smaller incremental increase in tax revenue. This relationship isknown as the La¤er curve and played an important role in motivatingthe Reagan tax cuts of 1981.

� Speci�cally, an increase in the tax rate from � to � 0 implies a decreasein the fraction of the marginal return (to work or capital, dependingon what is taxed) that the taxpayer gets to keep, from 1� � to 1� � 0.If � > 0:5, the percentage reduction in 1 � � exceeds the percentageincrease in � if the tax rate is raised. Depending on how responsive,for example, labor supply is to wages, the tax revenue might rise or fallin response to a tax increase, and the higher the initial tax rate, themore likely it is to fall.

� Most economists believe that the tax rates we see in practice are nothigh enough to cause tax revenue to fall. However, when Reagan cameto power, marginal tax rates were signi�cantly higher than now, 70%.The Reagan administration lowered taxes across the income spectrum,expecting an increase in revenue. So what happened? (Even the factsare still hotly debated and frequently in misleading ways.)

� The initial Reagan tax cut reduced the maximum marginal tax rate onpersonal income from 70% to 50%, and later in 1986 to 28%. (Reaganalso eliminated tax loopholes, raised the corporate tax rate and so-cial security contributions during his presidency, but one overall e¤ectwas a signi�cant tax cut for high-income earners.) Overall, tax revenuedeclined and the debt soared in the early 1980s.

� However, if we focus on the top range of the income distribution, thepicture is di¤erent. Those with adjusted gross income over 200K paid23% more in 1984 than in 1981. The economy was booming over thisperiod, so an absolute increase in tax collection is not so surprising.

89

Yet, the share in tax revenue of those in the top 0.5% of the incomedistribution also rose from 14% in 1981 to 18% in 1984. (After thefurther tax cut in 1986, it climbed again temporarily, but this can beattributed to the increase in the capital gains tax rate that followedin 1987, which caused the wealthy to make planned asset sales. Later,the share fell back to about 18%, so this tax cut did not change theirrelative contribution.)

� What we can conclude is that low and middle income brackets werecertainly not on the declining portion of the La¤er curve, they paidlower taxes absolutely and relatively as a result of the Reagan cuts.The highest income bracket appears to have been close, but it mayhave paid lower taxes, had it not been for the boom and the closing ofloopholes. The Clinton administration later raised marginal tax ratesat the top to over 40%, and the tax revenue from the richest 0.5%increased as a result. Perhaps tax revenue is maximized at a marginaltax rate somewhere between 40% and 50% in the US. (In Sweden,where the top marginal tax rate was temporarily at 80% in the early1970s, tax revenues were actually below the maximum, and a series ofreductions showed that the maximum occurred at a marginal tax rateof about 70%.)

� Even though politicians debate whether or not the e¤ect of a tax in-crease on revenues is negative, it should be emphasied that maximizingthe tax revenue is not a reasonable goal. Being on the downward-sloping portion of the La¤er curve would be blatantly ine¢ cient (highertaxes reduce output and do not even increase tax revenue). On theupward-sloping portion, tax increases may still reduce output notice-ably while yielding little in extra tax revenue.

� The progressive character of most taxes (i.e. the wealthy pay more inabsolute terms, and mostly also in percentage terms) means that theyredistribute income from the wealthy to the poor. (This is certainlytrue for money spent on welfare programs, but also more generally, tothe extent that everyone has the same access to goods provided by thegovernment, such as defense and transportation.) If the wealthy savemore than the poor (because their marginal utility from consumptionis smaller), this redistribution lowers saving and, via the interest rate,

90

investment. (The income tax is most progressive and therefore has thegreatest e¤ect on saving.)

5.2 Budget De�cits and the Federal Debt

� In recent years, the government has more or less consistently spentmore than it took in. 2005 US government spending (federal, state,local combined) was more than $15,000 per person.

� Federal spending accounted for 20% of GDP in 2005. Health care,social security and defense were the largest items. There is a budgetde�cit - expenditures exceed revenues.

� Budget de�cits must be �nanced by borrowing (the federal governmentissued more than $1,000 per person in bonds in 2005), and debt musteventually be repaid, at which point the government has to run a budgetsurplus. If it does not reduce spending, it must raise taxes in the future.

� If we think of G as government spending in this context (not just "pur-chases," as in the discussion of GDP; the main di¤erence is that spend-ing also includes transfer payments), the budget constraint for the gov-ernment at time t is

Bt+1 = (1 + it)Bt +Gt � Tt

(where Bt are borrowed funds at time t, Tt is tax revenue, it is thenominal interest paid on bonds). In principle, the government mightalso print money to �nance its operations, but this is like an implicittax and is not a sustainable strategy in the long run.

� Above, we see that new debt (Bt+1) must be incurred if the budgetsurplus (Tt�Gt) is not large enough to over interest obligations on theoutstanding debt (Bt).

� Applying this equation repeatedly, and supposing that the budget de�citand the nominal interest rate stay the same through time, we have

Bt+2 = (1 + i)Bt+1 +G� T= (1 + i)2Bt + (1 + 1 + i) (G� T )

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and

Bt+3 = (1 + i)Bt+2 +G� T= (1 + i)3Bt +

�1 + 1 + i+ (1 + i)2

�(G� T ) ;

i.e. in general:

Bt+n+1 = (1 + i)n+1Bt +

nXk=0

(1 + i)k (G� T )

= (1 + i)n+1Bt +(1 + i)n+1 � 1

i(G� T )

by the geometric series identity:Pn

k=0 xk = (1� xn+1) = (1� x).

� Rearranging, we have

(1 + i)n+1 � 1i

G+ (1 + i)n+1Bt =(1 + i)n+1 � 1

iT +Bt+n+1:

This says that the present value of future government spending andinterest obligations has to equal the present value of future taxes andborrowing.

� If G consistently exceeds T , we need Bt+n+1 � (1 + i)n+1Bt, whichbecomes ever larger over time (as n increases).

� How large will creditors allow the outstanding debt to become beforethe government needs to start paying it down? When US and foreigninvestors are no longer willing to lend to the US government (at present,US debt is owed about equally to domestic and foreign citizens), thedebt must be paid o¤ by running a budget surplus - or by printingmoney.

� The incentive to do the latter can create a dangerous cycle, wherelenders anticipate seignorage that leads to in�ation. If they requirea higher interest rate to compensate, which forces the government toprint more money, the expectation of in�ation can be a self-ful�llingprophecy, and ultimately we may get a hyperin�ation.

92

� Hence, lenders will be cautious of governments that have trouble ser-vicing their debt through tax revenues. An important criterion of cred-itworthiness is how large debt is as a share of GDP, i.e. the tax base.(Much in the same way as your bank will consider your annual incomein determining your credit line.)

� De�cits were very large during World War II, as the government �-nanced the war e¤ort. Then budget de�cits and surpluses alternateduntil the 1970s, at which point the federal government began to runlasting de�cits (with the exception of a brief interval in the late 1990s,the second term of the Clinton administration). However, because GDPhas been increasing over time, the debt to GDP ratio has not risen atthe same pace and remains at about 40%.

� In the US and other advanced economies, the debt to GDP ratio tendsto increase during wars and recessions and decrease during peace-timebooms. In recessions, we see both an increase in debt-�nanced gov-ernment spending and a decrease in output; the opposite is true forbooms.

� Compared to other major economies, the US debt-to-GDP ratio is notespecially large.

� It might be argued that growth in GDP is a consequence of investmentsbeing made by the current generation into science, infrastructure etc.so that future generations can be better o¤. Perhaps it is appropriatethat our wealthier descendants shoulder some of the expenses by payinghigher taxes.

� However, many economists believe that an increase in government spend-ing, which is not necessarily productive, actually "crowds out" privateinvestment. Borrowing by the government is in direct competition withborrowing by the private sector and raises the interest rate.

� On the other hand, the permanent income hypothesis would suggestthat budget de�cits cause people to reduce consumption, since theyknow they will be taxed higher someday. This means the de�cit wouldbe o¤set by increasing private saving.

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� This is what economists call Ricardian equivalence. Consider a rep-resentative agent who receives income from wages, which are equal tooutput Yt, and from interest on government bonds Bt. He spends thisincome on taxes Tt due to the government, consumption Ct, and gov-ernment bonds held into the next period Bt+1. Hence, he faces budgetconstraint

Tt + Ct +Bt+1 = Yt + (1 + i)Bt

in each period.

� SinceTt+1 + Ct+1 +Bt+2 = Yt+1 + (1 + i)Bt+1;

this implies.

Bt+1 = �1

1 + i(Yt+1 � Tt+1 � Ct+1 �Bt+2) ;

Recursively,

C0 = Y0 � T0 + (1 + i)B0 �B1= Y0 � T0 + (1 + i)B0 +

1

1 + i(Y1 � T1 � C1 �B2)

= Y0 � T0 + (1 + i)B0 +1

1 + i

�Y1 � T1 � C1 +

1

1 + i(Y2 � T2 � C2 �B3)

�...

=1Xt=0

1

(1 + i)t(Yt � Tt)�

1Xt=1

1

(1 + i)tCt + (1 + i)B0 �

1

(1 + i)1B1

or1Xt=0

1

(1 + i)tCt =

1Xt=0

1

(1 + i)t(Yt � Tt) :

if B0 = 0. This says that the present value of consumption must equalthe present value of disposable income.

� The government�s budget constraint is:

Tt +Bt+1 = Gt + (1 + i)Bt;

since income from taxes and bonds issued must equal spending Gtand interest payments on outstanding bonds. Combining this with

94

the representative agent�s budget constraint (which can be writtenTt +Bt+1 � (1 + i)Bt = Yt � Ct), we get

Yt � Ct = Gt

and thus1Xt=0

1

(1 + i)tGt =

1Xt=0

1

(1 + i)tTt;

the present value of government spending must equal the present valueof taxes.

� Alternatively then,1Xt=0

1

(1 + i)tCt =

1Xt=0

1

(1 + i)t(Yt �Gt) :

� The timing of consumption does not depend on the timing of taxes orgovernment spending. Suppose the representative agent�s preferencescorrespond to instantaneous utility u (Ct) = lnCt, so that he wants tomaximize intertemporal utility

1Xt=0

�t lnCt:

� Since Ct = Yt�Tt+(1 + i)Bt�Bt+1 according to the personal budgetconstraint,

1Xt=0

�t lnCt =

1Xt=0

�t ln (Yt � Tt + (1 + i)Bt �Bt+1) ;

which has �rst-order condition (with respect to Bt+1)

��t 1Ct+ �t+1

1 + i

Ct+1= 0;

orCt+1 = � (1 + i)Ct:

95

� The consumption sequence is now determined by the intertemporalbudget constraint:

C0 = Y0 � T0 �B1C1 = � (1 + i) (Y0 � T0 �B1)C2 = �2 (1 + i)2 (Y0 � T0 �B1)

...

Ct = �t (1 + i)t (Y0 � T0 �B1) :

� The value of B1 is determined by the government�s budget constraint,which yields

B1 = G0 � T0 + (1 + i)B0 = G0 � T0;

soCt = �

t (1 + i)t (Y0 �G0) :

� The interpretation of this consumption rule, which does not dependat all on taxes and future government spending, is quite simple: agovernment de�cit creates a future tax liability for the representativeagent, but it also increases the representative agent�s wealth today(either substitutes for planned consumption or reduces taxes), and theagent invests this additional wealth in a bond that �nances the de�citand earns interest from which future taxes are paid.

� In this fashion, consumption decisions are completely uncoupled from�scal decisions. Consumption does not increase in response to a taxreduction or an increase in government spending, nor is overall (publicand private) investment a¤ected. If the government dissaves (issuesnew bonds), the private sector saves (purchases the bonds). Hencethere is no crowding out.

� Incidentally, this does not mean that the government cannot raise out-put by reducing taxes. Lower taxes imply higher marginal after-taxincome from working or investing, so they encourage productive activi-ties. But if taxes are raised again in the future, there is a correspondingdrop in output as people work and invest less.

96

� The empirical evidence that more government spending is associatedwith less private investment is mixed. While the investment and bud-get surplus series are positively correlated (suggesting crowding out),the trend toward sustained de�cits is not re�ected in investment - thereis no systematic drop in private investment (consistent with the per-manent income hypothesis).

� During the major wars, WWI, WWII, the Korean and Vietnam wars,sharp increases in government spending were accompanied by very no-ticeable reductions in private investment (crowding out). Israel expe-rienced a large budget de�cit in 1984 followed by a balanced budget in1985. Again, private saving rose suddenly when the de�cit appearedand dropped just as quickly when the de�cit disappeared again, keepingnational saving nearly constant.

� One may also be worried that the current generation is making sel�shconsumption choices, living o¤ future tax revenues, that reduce livingstandards tomorrow relative to ours. (Unfairly, future generations can-not vote on current spending.) But the strongest indication of thatwould be a rising debt to GDP ratio, which so far has not occurredover long periods of time.

5.3 Entitlement Programs

� The earliest known welfare state was the Islamic caliphate of the 7thcentury. The �rst modern welfare system was introduced by Bismarckin Germany in the late 19th century. In the United States, socialsecurity commenced during the �rst Roosevelt presidency. While theIslamic welfare state was created in a time of unprecedented prosperity,the German and American programs were reactions to severe economiccrisis and uncertainty (both episodes were in their day known as "GreatDepressions").

� The Islamic caliphate was established by the prophet Muhammad in the7th century. Its capital was Medina in western Saudi Arabia. Muham-mad�s �rst successor (caliph) subdued the tribes on the Arab penin-sula and recommitted them to the Islamic faith. Under the second andthird caliphs, Umar and Uthman, the remainder of the Middle East

97

and Egypt were conquered, and a �ourishing market economy devel-oped after the introduction of currency (the dinar), debt instruments,and property rights to land, which could be bought and mortgaged byanyone.

� The Quran requires Muslims to practice charity by giving zakat (2.5% oftheir unused wealth) to the needy. Non-muslim citizens of the caliphatehad to pay jizya, a form of tribute, and could freely practice theirlifestyles and religions in exchange. As a result of the military suc-cesses, receipts multiplied, and Umar founded a central treasury tohouse them. The treasury began to collect zakat, jizya and other taxeson land, imports and spoils and administered the provision of incometo the poor, elderly and disabled. After victories in war generated largesurpluses, a system of allowances, based on religious merit, was intro-duced. Hence, the riches the caliphate amassed through warfare andfrom taxes on the wealth of increasingly prosperous citizens created ademand for public insurance that was met through this earliest form ofthe welfare state.

� Bismarck was prime minister of Prussia from 1862 until 1890 and �rstchancellor of the uni�ed German empire, which he had engineered mil-itarily and diplomatically, from 1871 to 1890. The Long Depression(known at the time as "the Great Depression") began in 1873 with theVienna Stock Exchange crash, at the tail end of an industrial boom,which was fueled further by cheap capital from the reparations imposedon France at the conclusion of the Franco-Prussian war in 1871 and con-�dence in the new industries, such as railroads, all of which led to aninvestment bubble. The crash ushered in a period of de�ation until theend in 1879. The Long Depression was an unprecedented event, thelongest depression in history and the �rst international crisis.

� By the end of the 1870s, Bismarck was increasingly concerned with aswell of support for the socialist movement and introduced both anti-socialist laws and social programs to stem the tide. In 1883 and 1884,health and accident insurance for workers were enacted, in 1889 pen-sions and disability insurance followed. Employers or the government(which taxed land and property) contributed to each type of insurance.Bismarck even considered establishing unemployment insurance, but itdid not actually appear in Germany until 1927. These programs were

98

in fact responible for a signi�cant decline in German emigration to theUnited States in the 1880s.

� The Great Depression began, in the United States, in September 1929as stock prices headed downward toward the "Black Tuesday" crash onOctober 29, 1929. A gradual recovery began in 1933, helped along byRoosevelt�s New Deal policies and rearmement following the outbreakof World War II, but was interrupted by another recession in 1937 afterthe government raised taxes to control its ballooning debt. The �rstNew Deal, i.e. laws passed directly after Roosevelt�s election in 1932,regulated the economy more tightly and introduced stimulus programs.The second New Deal brought on Social Security in 1935 and measuresaimed at generating employment and promoting unions, most of whichwere revoked by a conservative congress in 1938 when the economy wasback on track.

� The Social Security Act of 1935 provided for retirement and unem-ployment bene�ts, �nanced in equal parts through a payroll tax onworkers and employer contributions. These were collected for the �rsttime in 1937 and were meant to build up a reserve from which re-tirement bene�ts would be paid beginning in 1942 (a so-called "fullyfunded" system). A 1939 amendment advanced the payouts to 1940,turning the system into a "pay-as-you-go" scheme (where the paymentsof the current working generation are used to fund bene�ts for the cur-rent retired generation), in response to concerns that the reserve wouldwithdraw too many funds from the economy. The �rst recipient, IdaMay Fuller of Vermont, paid a total of $25 into the system until sheretired in 1940, and had drawn $23,000 in bene�ts by the time she diedat the age of 100.

� The Social Security Act of 1965 added health insurance for the el-derly (Medicare, which is funded by an additional tax) and the poor(Medicaid). Still under the Johnson administration, another signi�cantexpansion of bene�ts was passed in 1972. In unadjusted dollars, bene-�ts rose steadily from $35 million in 1940 to over $650 billion in 2009,roughly a 1,800-fold increase, while nominal GDP grew about 140-foldover the same period, and the number of bene�ciaries increased 200-foldfrom under 250,000 to over 50 million. The share of welfare payouts inGDP rose 130-fold from 0.035% to 4.6%. Because the social security

99

tax is a percentage of income (federal payroll taxes are typically 7.65%of wages for both employee and employer, i.e. 15.3% in total), andmoreover payouts in excess of certain levels are taxable since 1983, itis clearly redistributive.

� Even though social security is �nanced by contributions, people workever fewer years relative to the period over which they expect to collectretirement bene�ts (due to increased life expectancy and longer educa-tion). The child birth rate has also declined: all in all, there are moreand more old people per young adults who are working and payinginto the system. Hence, government spending on social security is ona predictable path of growth.

� But the bigger problem is health care. Increasing availability of, anddemand for, expensive treatments is continually raising the cost of cov-erage. Of course, the increasing life expectancy is another complication,since more people qualify for Medicare for longer periods.

� Social security and health care have expanded (and are projected docontinue expanding) drastically as a share of GDP, accounting for muchof the growth in federal spending. Meanwhile, tax revenues, as a per-centage of GDP, have remained roughly constant.

� Much of the growth in entitlement spending is projected to come fromhealth care, rather than social security.

� Health care spending has also been increasing in other advanced economies,although somewhat less so than in the US.

� The alarming �scal picture hides some �ner points. Perhaps it is nat-ural that individuals choose to spend an increasing portion of theirincome on health care, given longer life expectancy. Unlike other con-sumption goods, health insurance is so essential that it is providedpublically, rather than privately, for those who are at risk of not beingable to a¤ord it. In this sense, the increase in government spendingmerely re�ects a change in consumption patterns, and it makes senseto cover it through higher taxes.

� A less optimistic view would point to the special problems associatedwith health care provision (doctors may have poor incentives to pre-scribe moderated and less costly treatments) and attribute rising costs

100

at least in part to ine¢ ciencies. The focus would then be on designinga better health care market, and public administration of health careis conceivably one of the reasons why incentives are distorted, so thatthe de�cit could be reduced through privatization (and any increasesin health care costs would show up in private spending, not in highertaxes).

� The Health Care Reform Act that was passed in the US in 2010 aimsto cut costs in various ways. By requiring coverage for everyone, pre-ventive health care is supposed to be universally accessible and lowerlong-run treatment costs. Part of the increase in insurance costs fromcovering the formerly uninsured is o¤set by reductions in Medicare pay-ments (some of which are now absorbed by providers out of their sav-ings from no longer having to treat uninsured patients) and levies andtaxes on drug manufacturers, insurance companies (for high-premium,so-called "cadillac plans") and high-income earners.

� Except for the doubtful savings from expanded preventive care, and theimplicit penalty on cadillac plans, none of this works against the risein health care costs, however. The basic issues are malpractice laws(doctors have an incentive perform too many tests and treatments),asymmetric information (patients cannot well determine what is essen-tial) and intransparent costs (arising from the multitude of providersand complicated billing practices). Since patients cannot accurately de-termine needs and costs when they make choices, providers have littlereason to compete on price.

� It may be inherently di¢ cult to enable patients to make more informedchoices regarding their health care, so solutions probably need to focuson the incentives of providers. Ultimately, doctors should be rewardedfor treatment outcomes, rather than treatment costs, so that they �ndit in their interest to monitor costs themselves. As our knowledge ofhow to measure health improves, it becomes easier to evaluate outcomesand understand the price-quality trade-o¤s, so that price competitionbetween providers of comparable services will hopefully become feasi-ble.

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6 The International Dimension

6.1 Relationship between Budget De�cit and TradeDe�cit

� About half of the US public debt is held by foreigners. The sustain-ability of the debt is therefore closely related to the demand for dollarsoverseas. To understand this demand, we need to take a closer look atthe net exports part of GDP.

� There are several reasons why trade has become more important. Freightcharges, both at sea and airborne, have dropped sharply, as have longdistance communication costs (e.g. via telephone). In 1930, a three-minute call from New York to London cost $250!

� Tari¤s have also been cut and quotas lifted through international nego-tiations under the umbrella of the World Trade Organization (WTO).Average tari¤ on manufacturing goods was 14% in the early 1960s, butonly 4% in 2000.

� The share of export and imports in GDP has increased steadily sincethe 1970s, and since the 1980s imports have risen faster than exports.Currently, imports account for 15% of GDP and exports for about10%. Hence, there is a trade de�cit (negative net exports) of 5% ofGDP. Since the 1990s, the trade de�cit has been rapidly growing.

� Since the trade balance must be zero worldwide, this means that thatthe rest of the world runs a trade surplus. Major trading partnersare shown in this graph: the blue bars measure these countries�tradesurplus as a share of US GDP. (Note: these do not directly re�ect theshare of the US trade de�cit the country accounts for. We are lookinghere at the trade surplus with the rest of the world.) China and Japanrun the biggest trade surpluses, followed by France and Germany. TheUK has a trade de�cit, like the US.

� Note that even China�s trade surplus is much smaller than the UStrade de�cit. This contrasts with the fact that exports and importsare a larger share in most countries�GDP compared to the US. Thedi¤erence is that other countries (inlcuding China) import closer to the

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amount that they export, whereas the US imports much more than itexports.

� How should we evaluate a trade de�cit - is it a bad thing? Trade occursvoluntarily: it makes the trading partners better o¤. In that sense, itmust be a good thing. It exploits comparative advantage - just likeindividuals in the US economy are better o¤ specializing in productivetasks, so do countries bene�t from doing what they can do better ofmore cheaply than other countries.

� Clearly, you would not want to have to make every good you consumeyourself - you can live much more comfortably by learning a professionand acquiring goods with the income it generates for you. Similarly, itwould be ine¢ cient for every country to produce everything.

� This is even true when one country can produce every good at lowercost - maybe because its workers are more educated - it is still in thatcountry�s interest to specialize in what it does best. What matters isthe opportunity cost of producing a good, which is the best alternativeuse of the resources.

� If I need three hours to make x and two hours to make y, and you needtwo hours to make x and one hour to make y, your opportunity costof producing x is greater than mine, since you can make two units ofy for each unit of x and I can only make 1.5 units of y for each unitof x. At the same time your opportunity cost of producing y is lowerthan mine, since you can only make half a unit of x for each y, while Ican make two thirds of unit of x. So I should specialize in x and youshould specialize in y.

� Each country has a comparative advantage at something, regardless ofhow productive it is. Hence there should absolutely be trade. (Notwith-standing certain adjustment costs that can arise when trade opens upand workers have to be reallocated to new sectors. Those costs are con-centrated among a few, and they engage in political advocacy for tradebarriers, while the bene�ts from lower prices and higher consumptionare spread over the whole population. However generally it is safe tosay that the overall bene�ts from trade exceed the costs; and as jobs inan importing industry move overseas, more valuable jobs are createdin an exporting industry.)

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� A trade de�cit arises when trade is unbalanced, and while it re�ectsoptimal consumption choices, there is certainly a cost.

� When US �rms import goods, one of three things must occur. (1)The importer may be required to pay in foreign currency and thereforeneeds to exchange dollars. Or the importer might be allowed to payin dollars, and then the supplier would either (2) exchange the dollarsinto foreign currency or (3) acquire a US asset, such as a bond, stockor piece of real estate.

� In case (1) and (2), somebody accepts dollars in exchange for foreigncurrency. Either there is a corresponding demand for dollars from �rmsabroad that wish to import US goods, or - if the US has a trade de�cit- the dollars remain in the hands of foreigners. They will invest thosedollars in US assets. Either way then, a trade de�cit is matched bya transfer of real or �nancial US assets to foreign owners. If they runtrade de�cits with the US in the future, they can sell those assets o¤and use the dollars to pay for imports in excess of exports.

� This is precisely what�s been happening: a lot of West Coast real estate,in particular, belongs to Chinese citizens. Half of the public debt isowed to foreign citizens all over the world.

� Of course, someday, foreigners will want to use the income from dollar-denominated assets to increase their consumption, i.e. to purchase USgoods. At that time, the US will have to run a trade surplus. A tradede�cit today is an implicit commitment to export more than you importin the future and accept a reduction in consumption then.

� From the point of view of the permanent-income hypothesis, a tradede�cit would thus make sense for a country that expects its consump-tion to increase relatively quickly, while a trade surplus should occurwhen a country expects slower than typical consumption growth.

� If we look at the fastest-growing economies between 1980 and 2000,this relationship is not borne out at all. Of the top six, only Mauri-tius had a trade de�cit on average during this period. For some reasonthat might have to do with time preferences or government policies,fast-growing economies like China show greater restraint in their con-sumption relative to the US.

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� Using the national income accounting identity,

Y = C + I +G+NX;

we can make a direct connection between a trade de�cit and the out�owof assets from the US. Since Y � C � T (private saving) and G � T(government saving) together constitute domestic saving S, we have

NX = (Y � C � T )� (G� T )� I = S � I:

� In other words, a positive trade balance implies that the country�sresidents save more than they invest domestically (and are thereforenet investors overseas), whereas a negative trade balance means thatthe country is receiving investments from abroad.

� Net saving is also called the "current account" balance (this includes,besides net domestic saving S�I, net income from foreign investments,i.e. interest earned abroad by domestic residents minus interest paidto foreign residents). The "capital account" balance is the resultingchange in asset ownership: foreign assets acquired by domestic residentsminus assets acquired by foreigners. The current account and capitalaccount balances add to the balance of payments, which must be zero.

� In the US private investment was recently roughly equal to privatesaving. If I = Y � C � T , then NX = � (G� T ). I.e. the currentaccount de�cit tracked the budget de�cit, a phenomenon sometimesreferred to as the "twin de�cits."

� While domestic investment has �uctuated around 15% of GDP, notshowing a long-term trend, the budget and trade de�cits have risentogether after 2000. The relationship between the current account andthe capital account implies that the US is currently paying for thebudget de�cit with assets that are being transferred to foreigners.

� In the mid-1980s, the US ceased to be a net creditor in the world capitalmarket and accumulated an increasing net debt through regular tradede�cits that were counterbalanced by asset transfers (remember thisincludes debt instruments like bonds, but also property such as stockand real estate).

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6.2 Exchange Rates vs. In�ation and Interest Rates

� Imports and exports respond to cost di¤erences in goods across coun-tries, which are, at the most fundamental level, re�ected in the realexchange rate. The pound-to-dollar real exchange rate is

RER =qUKqUS

;

where qUS is the quantity of a good that a dollar buys in the US, andqUK is the quantity of the same good that a dollar buys in the UK ifthe dollar is exchanged for pounds at the prevailing nominal exchangerate.

� To reconcile this de�nition of the "real" exchange rate with the notionof "real" GDP, remember that real GDP is nominal GDP (GDP atcurrent price) adjusted for in�ation, i.e. changes in the overall pricelevel. If we had only one good, then real GDP would be output of thegood at a price that is held constant over time, so that all variationis due to changes in output. In fact, we might as well hold the priceconstant at 1 and equate real GDP to physical output (this is notpossible when there are multiple goods, hence the actual de�nition ofreal GDP is more complicated than that).

� So the pound-to-dollar real exchange rate is the number of goods apound can buy relative to the number of goods a dollar can buy. Thenominal exchange rate is the price of dollars in terms of the face value ofanother currency, unadjusted for in�ation in that country. The pound-to-dollar nominal exchange rate re�ects how many pounds a dollar canbuy, where the value of a pound in terms of goods (its "purchasingpower") might be �uctuating.

� A related concept are the "terms of trade": a country�s export priceindex divided by its import price index. These are average prices for�xed baskets of export and import goods from a common base year.Roughly, the terms of trade tell us how much the US needs to exportto pay for what it imports - but unlike the real exchange rate, this hasunits of di¤erent goods in the numerator and denominator.

� Let PUS be the US price (in dollars), PUK the overseas price (in pounds)and E the nominal exchange rate of pounds per dollar. (To keep things

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consistent, we will always de�ne nominal exchange rates as foreign cur-rency per dollar, not the other way around.) Then qUS is equal to1=PUS (e.g. if a unit costs $2, one dollar buys half a unit). Extendingthat logic to the UK, qUK is equal to (1=PUK)E, since you would getE pounds for a dollar and 1=PUK units per pound. Hence

RER =PUSPUK

E:

� At given price levels, the nominal exchange rate therefore determinesthe real exchange rate, and we can predict that a higher nominal ex-change rate would reduce US exports and increase US imports, sincetraders can get more units of the same good in the UK than in the USfor a given dollar outlay.

� We might also expect that arbitrage must eventually balance qUK andqUS, i.e. the real exchange rate must tend toward 1. This situation iswhat economists call "purchasing power parity": a dollar buys the samequantity of goods in all countries. It is an example of the "law of oneprice": valued in dollars at the current exchange rate, things should costapproximately the same everywhere.(after adjusting for freight costs,tari¤s and di¤erences in tax, and absent trade restrictions).

� How does arbitrage lead to purchasing power parity? If EPUS > PUK ,then the good costs more pounds in the US than in the UK, and some-one could make money buy shipping it from the UK to the US. Even-tually, this would increase supply in the US, and decrease supply in theUK, to a point where the price (denominated in either currency) is thesame. Similarly, if EPUS < PUK , shipping the good from the US to theUK is pro�table and should bring the price down in the latter. Thus

EPUS = PUK ;

and it follows that RER = 1.

� We should keep in mind that the absence of arbitrage opportunities(purchasing power parity) does not imply that there is no reason totrade. Trade arises from comparative advantage and causes the goodto be supplied by the least-cost producer to other countries with higheropportunity costs. This is consistent with a single world price. But if

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there is a temporary di¤erence in prices between countries, we shouldexpect additional trade �ows from where it is relatively cheap to whereit is expensive - until the real exchange rate is back at 1.

� In the long run, the quantity theory of money (MV = PY ) applies,and the price level in each country is pinned down by the money sup-ply, which is a matter of local central bank policy. Under purchasingpower parity, the nominal exchange rate is the only free variable thatcan bring the demand and supply for tradable goods into equilibrium.In a single-currency area like the US, price di¤erences aren�t sustain-able. In a world with multiple currencies, there can be multiple pricesdenominated in their respective currencies, but the nominal exchangerate (in the long run) must be such that prices are the same in terms ofa single currency like the dollar. It balances world demand with worldsupply for goods whose relevant market is global and for currenciesused to purchase these goods.

� Since purchasing power parity implies that

E =PUKPUS

;

we would expect that the nominal exchange rate correlates with in�a-tion rates. An increase in the US money supply expands the relativesupply of dollars and, other things equal, should bring the price of down- depreciate the dollar. According to the quantity theory, it raises pricesin the US, hence decreases PUK=PUS for any tradable good we chooseto consider, so the nominal exchange rate indeed falls.

� What is the connection between in�ation and the market for dollars?As prices rise in the US relative to the UK, arbitrageurs seek to sourcefrom the UK and therefore want to exchange dollars for pounds. Thisreduces the price of the dollar - it will buy fewer pounds.

� The yen tended to appreciate against the dollar since the 1970s (adollar bought fewer and fewer yens over time). Over much of thatperiod, the Japanese in�ation rate was below the US in�ation rate, butthe relationship is not perfect.

� The Economist�s Big Mac index regularly compares the price of a BigMac across countries in dollar terms (at the given exchange rate). There

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is substantial variation. Why? A burger is not a tradable good - to alarge extent, its cost is determined by the local price of produce andlabor. And at least labor cannot easily be shipped.

� The Big Mac is one case where the law of one price will not hold.What are others? (Mainly services, goods that are customized for eachcountry - such as instructions in the local language - and branded /unique goods where the seller can control distribution and price dis-criminates across countries, e.g. fashion is much cheaper in the USthan elsewhere.) We must also bear in mind that tari¤s and taxesmake a di¤erence: e.g. higher sales tax and corporate pro�t tax in-crease the price sellers must charge in order to earn the same return asin other countries.

� Trade in goods is not the only thing that a¤ects exchange rates. De-mand for currency also arises from trade in �nancial assets, and giventhe instantaneous operation of, and information �ow in, �nancial mar-kets, arbitrage there is more immediate. It also accounts for the bulkof currency trade, which is more then twelve times of world GDP invalue.

� A key part of this market is debt denominated in foreign currency. If in-terest rates increase in the US, bonds and other debt instruments in theUS become more attractive investment assets. But they cost dollars,and foreigners who want to purchase them must �rst acquire dollarsin the foreign exchange market. The demand for dollars increases, andthe dollar appreciates as a result.

� This leads us to another form of the law of one price: interest paidon a dollar in the US must be worth the same as interest paid on theequivalent of a dollar in the UK:

(1 + iUS)� 1 = (1 + iUK)E

E 0� 1:

On the left, we have the return in the US: one dollar invested pays backthe dollar with interest iUS. On the right, we have the return that isavailable to the US investor in the UK: she exchanges the dollar for Epounds, earns interest iUK on these and changes them back into dollarsat the future exchange rate E 0.

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� The equation simpli�es to

iUK � iUS = (1 + iUS)E 0 � EE

� E 0 � EE

:

Any positive di¤erence between the UK and US nominal interest ratesmust correspond to the capital gain the investor can realize from anappreciation in the dollar over the period. This relationship is referredto as nominal interest rate parity. (There are some reasons why itneed not hold exactly: risk premia, di¤erences in taxation of interestpayments, restrictions on capital �ows ...)

� In the long run, when purchasing power parity leads to full adjustmentin exchange rates, we must have E 0 = E and iUK = iUS. In fact,when currencies buy the same quantities of goods everywhere, nominalinterest rate parity implies real interest parity. But how might investorsexpect the nominal exchange rate to vary in the short run, so thatnominal interest rates would di¤er from country to country?

� Perhaps investors anticipate a change in monetary policy in the futurethat alters the rate of in�ation. A future increase in the US nominalinterest rate will slow in�ation and cause the long-run exchange rateto rise, in accordance with purchasing power parity. Hence, investorsexpect a capital gain from buying the US asset with cheap dollars todayand changing more valuable dollars back tomorrow. To compensatethose who invest in the UK asset, the UK interest rate must be highertoday.

� In combination with nominal interest rate parity, purchasing powerparity (E = PUK=PUS) yields

E 0 � EE

=P 0UK=P

0US

PUK=PUS� 1 = P 0UK=PUK

P 0US=PUS� 1 = 1 + �UK

1 + �US� 1

(note that P 0US=PUS = 1+ (P0US � PUS) =PUS = 1+ �US), and thus the

growth of nominal exchange rates re�ects the in�ation rates.

� Arbitrage in �nancial assets determines the nominal exchange rate inthe short run. In the long run, the trend of the nominal interest ratealso re�ects arbitrage in goods that takes longer and is less perfect, dueto the inherent informational and physical barriers. I.e. we get nominal

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interest rate parity in the short run and a tendency toward purchasingpower parity in the long run (which means that international di¤erencesin exchange rates ultimately re�ect di¤erences in in�ation rates).

� In the long run, real interest rates around the world approach parity.This implies that the real interest rate in an integrated world is ul-timately determined by the global return to capital r, since domesticresidents have access to the global capital market both for lending andborrowing purposes and would arbitrage away any local di¤erences inthe price of funds. The global return is determined by the global de-mand and supply of capital, which depend on investment opportunitiesand the desire for consumption smoothing.

� Some examples where countries borrowed on the world credit marketto smooth their consumption are Poland after harvest failures in 1978-1981 and Mexico when oil was discovered in the early 1970s. TheUnited States in the 19th century and Brazil during its boom in the1970s borrowed in order to �nance their high levels of investment in arapidly growing economy. In each case, substantial debt was amassed.

� On the other hand, many of the industrialized countries were untilrecently net lenders (including the US until the 1980s). Besides theEast Asian economies that apparently discount future income less thanWestern countries, oil-producing nations like Saudi Arabia are creditorsin order to preserve their �nite income into the future.

� Events in a small country like Poland will only have a negligible e¤ect onthe world capital market, so its real interest rate is beyond its control.A large economy like the US, however, does a¤ect the real interestrate. The real interest rate is somewhat procyclical (and the currentaccount somewhat countercyclical) in the US, re�ecting that investmentdemand exceeds saving in a good business climate.

6.3 Exchange Rate Regimes

� Through the 19th century up until World War I, the major currencieslike the British pound were on the gold standard (or a gold and silverstandard in the case of the US until 1879, when it switched to goldonly). I.e. countries maintained gold reserves and o¤ered to trade

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domestic currency for gold at a �xed price. You could literally walkinto a bank and purchase or sell a bar of gold at a price that remainedstable. This served as assurance that paper money indeed had a value.

� One implication is that the exchange rates between di¤erent currenciesalso had to be stable: after all, you could always buy gold in one countryat a �xed price and resell it in another at a �xed price, no one had anincentive to trade currency at anything other than the implied ratio.

� One result of World War I was that this regime fell apart as countrieshad to resort to printing money. Since they did not have enough goldreserves to sell for all the currency that came into circulation, they couldno longer o¤er to trade gold at a �xed price and therefore abandonedthe gold standard.

� In�ation was rampant in the aftermath of World War I, we alreadytalked about the German hyperin�ation. In 1944, asWorldWar II cameto close, a meeting took place in Bretton Woods, NH, with the goalto restore stability to exchange rates. The US committed to trade USdollars for gold at a �xed rate ($35 per ounce) with other central banks,thus guaranteeing the stability of the dollar. Other major currencieswere pegged to the dollar, i.e. they committed to trade their currencyfor the dollar at a �xed rate.

� Bretton Woods fell apart in the 1970s, when price increases in the USdevalued the dollar in real terms and the Fed was running its goldreserves down as central banks around the world wanted to exchangedollars for gold (probably because they anticipated a nominal devalu-ation). Since then, countries have used various exchange rate regimesat the same time, including voluntary pegs to major currencies like thedollar and limited or full �oats.

� The purest form of a peg is a currency board, as practiced by Ar-gentina in the 1990s. It requires the central bank to hold enough dol-lars to exchange all outstanding domestic currency at the proclaimedrate (else, speculators might "attack" by buying dollars in the hopethat the domestic currency will be devalued, so that it can be boughtback cheaply). (What eventually forced Argentina to give up the pegwas mounting government debt, to the point where it defaulted, aftera depreciation of Brazil�s currency led to a large trade de�cit.)

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� Once the currency is pegged, the central bank loses the option to pursueother objectives through monetary policy, since the money supply mustbe adjusted to maintain the exchange rate. This can be a good thing,if the central bank wants to assure citizens that it will not print moneyto �nance government debt and thereby create in�ation. But it alsorenders it powerless to respond to recessions.

� Capital controls, as practiced by China in the 1990s, limit the amountof trading and therefore require fewer dollar reserves. (You could onlybuy dollars from the Bank of China at the time, and only up to acertain amount.) But capital controls prevent a country from takingfull advantage of the �nancial system, which can channel funds to theirmost e¢ cient uses. For China, this is perhaps less of a problem becauseof its very high domestic saving rate that can fund the investmentopportunities.

� Many central banks today commit not to a �xed rate, but to a bandwithin which they allow the exchange rate to �uctuate. If the bandapplies to the dollar exchange rate, they usually adjust their interestrates in the same direction as US interest rates, hence will typicallyfollow Fed actions. But they reserve discretion to deviate on a smallscale to manage the domestic business cycle.

6.4 Business Cycle in an Open Economy

� In the long-run, exchange rates re�ect price levels in accordance withpurchasing power parity. Hence they depend on how much currency thecentral banks issue relative to the economy�s output. This makes nodi¤erence to relative prices and economic decisions. In the short run,however, exchange rates can �uctuate as we have seen, to maintainnominal interest parity.

� How do exchange rates enter into our short-run analysis? An increasein the real interest rate makes dollar-denominated assets more valuable.Hence the exchange rate appreciates, both in nominal and in real terms(given sticky in�ation), and net exports fall as imports get cheaper (andexports more expensive from the point of view of foreigners).

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� Our model should therefore account for the fact that net exports de-pend negatively on the real interest rate. More speci�cally, if the long-term fraction of GDP spent on net exports is aNX , net exports shoulddecrease when the domestic real interest rate exceeds the world realinterest rate. (Recall that, in the long run, it is equal to the world realinterest rate.) Thus:

NXtYt

= aNX � bNX (Rt �RW )

= aNX � bNX (Rt � r) + bNX (RW � r) :

� The IS equation can now be rewritten

~Yt = a� b (Rt � r)

wherea = aC + aI + aG + aNX + bNX (RW � r)� 1

andb = bI + bNX :

� The IS curve has exactly the same form and shape as before; only thede�nitions of the parameters have changed (and therefore the types ofshocks that can change them). Now the relationship between short-runoutput and the real interest rate is negative not only because investmentfalls when the interest rate increases, but also because the currencyappreciates and net exports fall.

� When the money supply is tightened overseas and the interest rate in-creased, the parameter a now increases, shifting the IS curve out, i.e.~Yt is higher at each Rt. The reason is that the pound appreciates, andtherefore American goods become cheaper for UK residents, which in-creases US exports (at the same time, imports from the UK becomemore expensive and decline). Thus, the NXt component of GDP ex-pands. (Assuming the interest rate increase does not also depress theUK economy and reduce demand for imports there ...).

� In the AS-AD diagram, the AD curve (which combines the IS curvewith the monetary policy rule) shifts out and induces an increase inin�ation and a temporary boom, point B. The Fed raises the interest

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rate in the process to discourage investment and avoid overheating. Asexpected in�ation increases, �rms see their costs increase faster andwant to produce less at any given actual rate of in�ation, so that theAS curve shifts in, point C. At this point, the Fed lowers the interestrate to avoid a deep recession, and this increases in�ation further.

� When the shock vanishes (because interest rates in the UK have fallenback to their old level), the AD curve shifts back to the old level, causinga recession, point D. Now, in�ation is dropping and the AS curve shiftsout as expected in�ation falls over time, so that costs slow and �rmswant to produce more at any given in�ation rate. Eventually, the oldequilibrium is reestablished.

6.5 The Asian Crisis of 1997

� In the �nal lectures, we take a closer look at the Asian growth miracleand the Asian crisis of the late 1990s. The discussion will touch onmany of the issues we have encountered in growth theory, short-runanalysis and international macroeconomics. While we will identify theshocks that activated the Asian crisis in the summer of 1997, the focusis on why the Asian economies could not e¤ectively respond.

� Taking an aerial view �rst, we consider the place of the crisis yearsin the long run growth history of Asia, and identify the main threadsin the story we will explore in some detail. Then, we follow threemajor developments of the 1990s that rendered the Asian economiesvulnerable to macroeconomic disruption and discuss why. Finally, wechronicle the events of the crisis itself and consider the policy issuesand options that arose.

� The growth of the East Asian economies since the 1960s (with a few ex-ceptions, where political arrangements were unfavorable) was an episodewithout parallels. Never had a single country, much less a group ofcountries, grown so much in so little time. Over 40 years (1960-1999),the US economy expanded by a factor of 3.5 (which is remarkable initself), but many East Asian economies were between 10 and 20 timeswealthier than 30 years earlier!

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� In the scheme of things, the Asian crisis was a small dent (and almostdidn�t a¤ect China at all) �but it was also the �rst such setback: eventhe oil crises didn�t stop the region from expanding . . . And for a groupof countries that�s used to high positive annual growth rates, swinginginto the negative for two years was certainly perplexing and disturbing.A shaken con�dence in the future (more cautious consumption, morerisk-conscious investment) added to the real costs (corporate and bankfailures, a signi�cant increase in unemployment).

� Compared to the other recent currency crisis, that of Mexico in 1994and 1995, Asia�s was also more serious in two ways: it spread throughthe region and beyond. Mexico�s crisis was not contagious (Latin Amer-ican countries maintained their pegs): the peso depreciated in realterms against the currencies of export competitors, improving the cur-rent account quickly. While Mexico bene�ted from a vigorous US econ-omy (the main export market), and recovered fully after nine months,the global environment was less friendly at the end of the 1990s (USslowing, Japan stagnant, EU weak), o¤ering no such boost to Asia.

� Among economists, an old debate about the feasibility of �saving our-selves rich�was rekindled. On one side were those who said Asia hadblindly and unproductively invested for years, and was now paying theprice in the form of bankruptcies and defaults. On the other side, opti-mists argued that Asia was merely undergoing a structural transition,and that speculation had blown the problems out of proportion. Wehave, thus, a long-term and a short-term argument, with di¤erent im-plications: one says, Asia was on the wrong track with its developmentstrategy of encouraging massive investments; the other says, Asia�s suc-cessful expansion came to a temporary halt due to a charred psyche andsome necessary corrections.

� The fact is that Asia did regain strength in 1999 and 2000, but the re-gion soon labored under a new global malaise that had largely unrelatedreasons: the weak electronics market, the US slowdown, the terroristattack. But before we dismiss too rashly the Alwyn Youngs and PaulKrugmans (who had predicted an Asian slip in the early 1990s, basedon low estimates of productivity growth, especially for Singapore), let�sconsider how troublesome the long-term picture is.

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� An economy cannot grow forever in per capita terms (given savingand labor force participation rates) unless there is some kind of e¢ -ciency improvement. The capital stock (per e¤ective worker) will onlygrow until a steady-state is reached, where capital is just su¢ cientlyproductive to replace itself, making up for depreciation and the capi-tal requirements of labor force entrants. Alwyn Young published twoarticles with such melodramatic titles as �A Tale of Two Cities�and�The Tyranny of Numbers�, which attracted much publicity, and wherehe calculated that Singapore had virtually no productivity growth fordecades. It�s one of those results that strike everyone as funny (afterall, does the excellent public transport network not add to e¢ ciency?;don�t Singaporeans have computers?; doesn�t Singapore have excellentschools?), but that have to be addressed anyhow.

� One explanation is that Young�s technique imputes productivity changeinto his �factor contributions�(he basically subtracts labor force andcapital stock growth from output growth and calls the rest productivitygrowth, but he weights labor force growth according to the wage rate,which rises with productivity). Another objection is that he just usedweird data, and his results haven�t often been replicated in follow-upstudies (they sometimes �nd that Singapore ranks among the economieswith the highest e¢ ciency growth).

� Generally, it would be wrong to speak of a single �Asian developmentmodel.�Some countries in the region invest like there�s no today (Tai-wan, Singapore, Korea, Japan); some are primarily catching up througheducation (China, Indonesia); some are doing a bit of both and don�tlook so di¤erent from the US in this respect (Hong Kong, Thailand).

� But the typical return to capital (by the crude measure of the capital-output ratio) is indeed far below that in the US. Even though I don�tbelieve that Asia had insigni�cant productivity growth, I�m sympa-thetic to the idea that there has been overinvestment in the region,with relatively low returns as a consequence. If we calculate the in-cremental capital-output ratio (by how much the capital stock grewwith each 1% increase in output), and compare the 1987-1992 aver-age with the average for 1993-1996, we get additional con�rmation forthe hypothesis: most Asian countries�capital stocks are becoming lessproductive.

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� You might ask: why are investors still investing? There are severalexplanations: (1) The government is a big investor in some of thesecountries, and the government isn�t necessarily guided by returns. (2)A lot of investments �ow into projects that don�t contribute to futureoutput, but hold potential for lucrative reselling (think residential prop-erty and stocks). (3) It has been argued that there is signi�cant reversecausality from GDP growth to investment. Investors form exuberantexpectations about prospects in an economy that has been doing well inthe past. Let�s not forget that there is much uncertainty about returnsin practice and that practitioners do use simple rules of thumb.

� As we proceed to a medium- and short-run view of the crisis, let�s keepin mind that a tradition of overinvestment in Asia may have loweredthe real returns to economic activity �despite what most people wereperceiving at the time. This would increase �rms�exposure during adownturn and limit the amount of debt they can shoulder.

� While the conditions that led to the crisis were not identical aroundAsia, the trigger was in all cases an unexpected currency depreciation,increase in the real value of international debt, defaults that spreadfrom �rms to banks, further depreciation as investors tried to sell theirlocal assets, and the cycle over again, several times.

� Why had �rms and banks been able to borrow until they were notresilient to shocks? That�s where my opening point about systemic�aws comes in. This is what the Asian crisis, and any crisis, is primarilyabout. In many Asian countries, the �nancial sector lacked incentiveto monitor because (1) governments seemed willing to support ailingbanks and conglomerates and (2) central banks were committed to �xedexchange rates. Investments in the region appeared essentially risk-freeand could be justi�ed even if nominal returns were relatively low.

� Why did currencies suddenly depreciate? Exchange rates are prone to�uctuate in response to sentiments, and sentiments tend to build andcollectively overreact to real events. (Sounds irrational, but it reallyisn�t in an environment characterized by uncertainty.) And a centralbank can only stem a limited amount of pressure on a currency . . .

� The initial spark was a minor capital �ow out of Thailand in response toan everyday event (we�ll get to speci�cs later), but as the central bank

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stepped in to support the baht, it became clear that its depleted forexreserves could not sustain the peg (to the US dollar) in the event of amajor movement. The perceived risk caused just such a major move-ment, and Thailand had to give up the peg. Then attention shifted toother regional economies, like the Philippines, Indonesia and Malaysia(and a bit later Korea) that seemed to have some of the same problems,and by then the sheer magnitude of the capital �ow reversals unhingedevery one of the targeted currencies. Even intact economies like Singa-pore, Hong Kong and Taiwan eventually experienced pressure as theircurrencies had undergone real appreciation relative to those of theircompetitors in export markets.

� While this is how the crisis came to fruition, I want to emphasizethe fundamental misalignments that had, over years, nourished theprospect of a crisis. We look at medium-term developments of the1990s now that set the stage for July 1997.

� Through the 1990s, Asian economies were overheated. Factual evidencecomes from high in�ation rates. In a period during which US pricesrose by 20%, Chinese and Philippine prices doubled, and those of otherAsian economies (except depressed Japan) tended to rise faster, bymultiples.

� Rapid money growth powered these expansions in an ironic race againstrising prices (to avoid a liquidity crunch). Malaysian in�ation wasrelatively low only because of price controls. In fact, large-scale publicinfrastructure projects fueled overheating in the Malaysian economy inthe mid-1990s. (The price controls were a factor in Malaysia�s wideningcurrent account de�cit: if the exchange rate is �xed and regulationscause a domestic shortage, imports close the gap.)

� A consequence were deteriorating trade balances due to rising importsand also weakening exports. Exports su¤ered from (1) the Japaneseslowdown: stagnant till 1995 and growing brie�y in 1996, Japan wasback in a slump in 1997 after an increase in the consumption tax �Japan received 30% of regional exports; (2) the electronics sector down-turn in 1996: demand for semiconductors, a major export item of re-gional economies, fell signi�cantly; (3) the increasing weight of China inAsian exports: a 50% nominal devaluation of the RMB in 1994 implied

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a sharp real depreciation and large trade surpluses at the expense ofAsian competitors; (4) worsening terms of trade (more on that later).

� The seeming lack of exchange rate risk also enticed private foreigninvestors to buy high-interest Asian bonds and seemingly high-yieldAsian equity. Particularly in Thailand and the Philippines, interestrates were signi�cantly higher than abroad (for example in the US),driven ultimately by unrealistic expectations of capital gains in prop-erty and equity markets.

� Driven by import demands and readily �nanced by capital in�ows,current account de�cits in Korea, Indonesia, Malaysia, and especiallyThailand surged above 5% of GDP. These countries saw the most dras-tic currency depreciations in 1997 (and the won and baht were underattack from 1996).

� Importers need dollars, which they acquire from banks, and if exportersand foreign investors don�t supply enough dollars to banks, banks bor-row o¤shore. This amounts to a reduction in the country�s net foreignassets (as the banks are selling domestic debt ��nancial assets �to for-eigners), in line with the external balance requirement that net exportequal net foreign investment.

� Not surprisingly, an increase in foreign-currency denominated debt ac-companied the trade de�cits of the 1990s. In Indonesia and Thailand,debt exceeded the combined value of forex reserves and annual exports.We�ll have more to say about the nature of that debt later on, but willfocus for the moment on the conditions under which a current accountis thought to be sustainable. (Of course, if economists think it unsus-tainable, so will investors over short or long, translating into actualspeculative attacks and collapse.)

� Current account de�cits are acceptable and healthy at an early stageof development if the economy is growing on a solid foundation andcreates the wealth from which to repay the debt in the future. Ideallya developing country would import investment goods that contributeto growth in export sectors.

� A bad sign would be that a current account de�cit coincides with areduction in domestic saving. In this case, foreign investment e¤ec-

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tively �nances current consumption and does not provide the meansfor repayment. This is what led to the Mexican peso crisis in 1994:Mexico was unable to meet its short-term interest obligations becausethe foreign loans had been used unproductively. The data show thatsomething like it happened in Thailand in the 1990s. In some otherAsian countries, �forced saving�(such as CPF contributions in Singa-pore) prevented the problem.

� Another bad sign is usually that a current account de�cit coincideswith persistent �scal de�cits. The reason is, again, that governmentspending goes mostly into consumption (public services), not invest-ment. The Latin American debt crisis in 1980 was primarily causedby budget de�cits �nanced abroad �but Asian governments (exceptChina�s) ran surpluses in the 1990s.

� The good news is that what Asia borrowed tended to get invested. Thebad news is that returns were low by the 1990s (for reasons we havealready touched on) and that a good deal of investment took place innon-traded sectors (construction and internal services). Troubled Ko-rean and Indonesian companies borrowed abroad to �nance marginallypro�table operations and projects of dubious quality. Thailand andMalaysia, especially, sustained speculative bubbles in the real estateand equity markets with foreign capital.

� We have already alluded to the serious current account de�cits thisbehavior created in aggregate. But to appreciate the extent of theproblem, let�s not forget that capital in�ows were much greater thancurrent account de�cits (which are just the net in�ows). For instance,Korea�s current account de�cit in1996 was $ 23 billion, but gross in�owswere $ 41.3 billion - the rest was o¤set by out�ows, which tend, however,not to come back during a crisis.

� In addition, debt structure was unfavorable. Short-term obligations(debt service plus short-term debt) exceeded foreign reserves in Korea,Thailand, Indonesia, and the Philippines, implying substantial defaultrisk in the event of a shock. Asia�s high current account de�cits in the1990s were a matter of concern as they created short-term debt thatdid not �nance productive, forex-generating activities. In fact, theysupported speculation and marginal (often high-risk) projects that were

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unlikely to contribute to debt repayment. Which raises the question:why did lenders supply funds for such purposes?

� Until the 1990s, state banks dominated most Asian credit markets,and private �nancial institutions were strictly regulated (excepting thesophisticated banking sectors of Singapore, Hong Kong and Taiwan).By the 1990s, this arrangement had become an obvious constraint ongrowth, and governments began to implement ��nancial liberalization�policies, that is they made private credit more freely available.

� To give a speci�c example, Indonesia had �ve state-owned banks in1980, which handled 80% to 90% of all credit. Private start-ups thatemerged after reforms in 1988 and 1989 overtook the state banks inmarket share as early as 1994.

� Private credit and bank lending seems to have run ahead of devel-opment �especially in Malaysia and Thailand, where �nancial depthexceeded that of the US by 1997 and private sector liabilities continuedto expand at full steam up to the time of the crisis.

� Formerly restricted or non-existent �nancial institutions were suddenlythrown into the hot water that were Asia�s buoyant economies, andthe private sector clamored for funds to invest in risky enterprises likeproperty and stock market speculation. Banks ignored much of the riskfor two reasons: (1) Competitive pressure; for the newcomers, it was astruggle to survive, and they needed clients. (2) There was a real orperceived commitment of governments to bail out technically bankrupt�rms. As NYU�s Nouriel Roubini put it, �the market operated underthe impression that return on investment was insured.�

� To provide the coveted funds, banks themselves borrowed from abroad.Here, too, they accepted an unusual amount of risk: they would typi-cally not hedge against exchange rate �uctuations. Banks saw no needto hedge (pay premium forward rates), since the currencies were cred-ibly pegged by their governments.

� Moreover, banks and �rms were highly leveraged and susceptible tobankruptcy. Banks had typically a lot more foreign liabilities than as-sets; often more than 50% of the debt was short-term, foreign-currencydenominated, and unhedged. Thai banks, in particular, had more than

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eight times as many foreign liabilities as assets toward BIS (Bank ofInternational Settlements) a¢ liates. (The ratio exceeded ten towardall banks). Taiwan was the only Asian country whose banks were in-ternational net creditors.

� To get a sense of corporate exposure, consider some aggregate statisticsof the thirty biggest Korean chaebols on the eve of the crisis. They hada median debt-to-equity ratio of �ve at the end of 1996 (compared toa ratio of one which is typical for US companies), and a dismal medianreturn on sales of 0.1% (even though 1996 was still a decent year forKorea).

� Such hazardous debt structure at the �rm and bank level underscoredthe danger of the current account de�cits. Newly liberalized banks wereexposed to exchange rate and cash �ow risks, and many of their clientswere excessively leveraged and unpro�table. Asia�s premature �nancialsystem in the 1990s, characterized by distorted incentives, funded thebubble economies and steered them to the edge of crisis.

� Now it remains to be explained whether and why governments failed tointervene. The quasi-�xed exchange rate regime is at the heart of this;it was a blessing during years when Asia grew in the productive, export-oriented sectors, since it provided stability and security for investors.It was a curse in the early 1990s.

� Let me begin with an overview of the speci�c exchange rate systemsthen in use around Asia. We have essentially four or �ve types, withmoderate to no �exbility. Hong Kong had a currency board, that is thepeg to the US dollar was �xed by law, and monetary policy �automati-cally�defended it at all times. Malaysia, Thailand, and the Philippinespegged their exchange rates to a basket of currencies, but the US dollarhad so much weight that we might call it an �implicit peg�to the USdollar. In practice, the ringgit and the baht moved in a narrow rangearound a �xed value to the US dollar between 1990 and 1997, and thesame is true for the Philippine peso between 1995 and 1997.

� Indonesia and Taiwan targeted a �xed real exchange rate against the USdollar. Since Indonesia and Taiwan had higher in�ation than the US inthe 1990s, this means that their currencies depreciated nominally to the

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dollar (the rupiah by 26% and the new Taiwan dollar by 16% from 1990to 1997). China and Korea maintained fairly constant exchange ratesagainst the US dollar at most times, but made occasional adjustmentsas macroeconomic conditions require. China devalued by a full 50%in 1994, since it had experienced rapid in�ation, but afterwards therenminbi was stable. The won was allowed to depreciate against thedollar by 14% in the early 1990s, and another 10% at the end of 1996.

� Singapore�s policy came closest to a �oat. The Singapore dollar ap-preciated by 18% between 1990 and 1997. With the exception of Sin-gapore, Asian currencies were therefore explicitly or e¤ectively tied tothe US dollar; the Hong Kong dollar, ringgit, baht and peso, especially,would move closely with the US dollar in nominal terms.

� Such a quasi-�xed exchange rate regime has some attractive features fora developing economy: (1) It keeps in�ation near the world level. Sup-pose local prices rose faster than American prices. Arbitrageurs couldthen import US goods (without having to pay a currency premium),forcing local prices down. (2) It imposes �scal discipline. Supposethe local government tried to run a budget de�cit and �nance it byhaving the central bank print money. The increase in money supplydepreciates the currency, so the central bank must reduce the moneysupply through bond issues. Hence budget de�cits will be �nanced byborrowing from the private sector, not by seignorage.

� But the obvious downside of a �xed exchange rate is that central banksmust surrender their autonomy in managing the money supply andsubject monetary policy to the defense of the currency. This implies,for instance, that central banks had little power to �ght overheatingahead of the Asian crisis.

� There is another hidden caveat that is of some importance in practice.Controlling in�ation is a motivation in �xing the exchange rate. Butinformation barriers, tari¤s, and transportation costs usually preventcomplete price convergence. We have already seen that Malaysia, Thai-land, and the Philippines continued to have higher in�ation than theUS. A country that starts out with high in�ation and then pegs usu-ally experiences real appreciation (since the nominal exchange rate is�xed, but the price level remains somewhat higher). At the same time,

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excess in�ation keeps nominal interest at a premium, prompting capi-tal in�ows. The current account worsens, and more capital injectionsare required, accumulating more debt �until investors lose con�dencein the country�s ability to service the debt and maintain the peg, atwhich point the central bank must sell reserves to defend the currency.Clearly a crisis scenario.

� Unfortunately, the US dollar itself gained in real terms against Eu-ropean, Japanese and Asian currencies from the second half of 1995,appreciating the pegged currencies in its wake. Real appreciation, withrather than against the dollar, was a key development that shares re-sponsibility for the crisis. After nominal depreciation against the yenand mark in the �rst half of the decade, the dollar gained 56% onthe yen between spring and summer 1995. The peso and the ring-git, but also the Hong Kong and Singapore dollars, appreciated be-tween 15% and 25% in the 1990s, largely because of the US dollarmovements. Countries with e¤ectively �xed exchange rate regimes(Malaysia, Philipppines, Thailand, Hong Kong) tended to undergomuch greater real appreciation.

� Since the real exchange rate is re�ected in the price of exports, countrieswith more overvalued currencies generally experienced greater deterio-ration in their current accounts. China and Taiwan, whose currenciesdepreciated in real terms, had current account surpluses. Korea suf-fered large and increasing current account de�cits despite real depre-ciation of its currency. Circumstances were a bit unique here �recallthat the chaebols borrowed for survival, and Korea was hit especiallyhard by bad export markets.

� The crisis, with its watershed nominal and real devaluations, was there-fore a necessary correction to adjust the current account positions ofmany Asian economies. Nominal exchange rates (to the US dollar) laterdepreciated by 42% in Thailand, 37% in Indonesia, 26% in Malaysiaand 28% in the Philippines between end of 1996 and the beginning ofSeptember 1997.

� Once this correction was underway in some economies, others had tofollow suit because their currencies had now appreciated greatly, in realterms, against those of regional export competitors. The Korean won,

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for example, which depreciated by only 8% nominally against the USdollar between December 1996 and end of September 1997, appreci-ated in nominal (and real) terms by 34%, 29%, 20%, and 18% againstthe currencies of Thailand, Indonesia, the Philippines and Malaysia,respectively. The result was a drastic loss of competitiveness � andpressure on the won to fall further.

� The previously useful policy of pegging the currency had turned mali-cious in the 1990s, leaving central banks powerless to sti�e the bubbleand causing a disastrous real appreciation against many of the world�scurrencies as the dollar began to surge in 1995. This exacerbated prob-lems, since the weak, risk-exposed and debt-laden corporate sector wasdealt a competitive disadvantage in the face of already dwindling ex-port markets. Recall that banks had lent heavily to these �rms andhad accumulated foreign-currency denominated debt in order to do so.I think the scope of the di¢ culties is now apparent. Let�s see whathappened in the summer of 1997.

� On July 2, 1997, Thailand devalued the baht by 20% and asked for IMFassistance. What momentous event had set the avalanche in motion?Well, avalanches aren�t triggered by momentous events; one small dis-turbance in�icts another, and then turmoil builds until the whole fragilesystem crumbles and collapses. Same with an economic crisis. The mo-mentous events - those that undermined the system - happened longbefore.

� Thailand capitulated to a rumor: investors thought that the Japanesecentral bank was about to raise interest rates, and they sold some bahtassets to acquire yen assets. The Thai central bank had to step in andbuy baht, in order to defend the peg. That�s when Thailand�s centralbankers and foreign investors were alerted to the fact that, owing tohuge current account de�cits in the recent past, dollar reserves hadshrunk to a minimum and were too small to support the current pegmuch longer. Investors moved more foreign currency out of the country,in anticipation of a devaluation, which forced the central bank to giveup the peg �a self-ful�lling prophecy.

� At di¤erent points during the crisis, Thailand and Korea ran downtheir forex reserves to almost half the level of 1996. Malaysia su¤ered

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considerable depletion as well. Investors were wary now and looked forother devaluation candidates in the region, who were running out ofreserves. Capital started moving out of the Philippines, and on July11, the Philippine central bank had to devalue the peso and ask foran IMF package. In the next weeks, as the full picture of the region�sproblems came into view and investor sentiments turned gloomier, theslide of the baht, peso, ringgit and rupiah accelerated.

� On August 14, Indonesia gave up all pretense of supporting its currencyand let it fall freely, collecting $ 40 billion in IMF support over the nextmonths (despite bad blood and battles over policy). The rupiah�s de-scent continued for months because of political uncertainty (concludingwith president Suharto�s resignation amid riots in May 1998). In Jan-uary 1998, the country suspended service of its foreign debt.

� In September, Singapore and Taiwan gave way to pressure for depreci-ation (Taiwan switched to a �oat). By October, the baht, peso, ringgit,rupiah, Singapore dollar and New Taiwan dollar had on average depre-ciated by 40%. Late October saw the panic spread to the Hong Kongstock market, which lost a quarter of its value in four days, becauseinvestors anticipated devaluation. A few days later, Western stockmarkets fell through the �oor: the Dow Jones saw the largest one-dayloss ever (554 points) as �rm performance was expected to su¤er frominvestment losses in Asia and low-cost import competition.

� Another chapter opened when, on November 17, the won collapsed andKorea requested and got a $ 60 billion bail-out package from the IMF.Three months later, after foreign banks demanded immediate repay-ment of short-term loans, and conglomerates and �nancial institutionsdrowned in a wave of defaults, Korea negotiated a $ 24 billion debtroll-over with a creditor consortium. In the course of the crisis, onlyHong Kong and China avoided devaluation; the rupiah su¤ered themost dramatic decline, losing more than 80% of its value.

� At this point, I might clarify what I mean by a �crisis.�It is, in my de�-nition, a situation where the going policy cannot be maintained withoutoutside help, or the market has to be restrained. Thus I classify Thai-land, Philippines, Indonesia, and Korea, who sought IMF assistance,

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and Malaysia, who implemented capital controls, as economies in crisisin 1997.

� Having let the events pass before our minds, we�ll endeavor to explainthem brie�y. I think it presents itself as no coincidence that the collapseoriginated in Thailand: this was the country with the most severecurrent account de�cit, the thinnest reserves and most perilous foreigndebt structure among its commercial banks; in short, this economy wasmost vulnerable to a shock, even of a small magnitude.

� The baht crisis spread next to similarly indebted and structurally weakeconomies in the region: Philippines, Malaysia and Indonesia. Youmight have expected to see Korea on this list, and Korea had someof the worst problems. But one problem Korea did not have: a �xedexchange rate. In mid-1997, investors were concerned with devaluationand what their assets were worth. The won had already depreciated inlate 1996, and this adjustment probably spared Korea for a few months.

� In the fall of 1997, the currencies of Singapore, Taiwan, Hong Kongand Korea came under pressure for a di¤erent reason. These countrieswere linked to the crisis-struck economies by competition in exportmarkets. The massive devaluations among their competitors translatedinto equally massive real appreciation and loss of competitiveness.

� In the context of contagion and pressure for depreciation, Hong Konggot in trouble because its currency was so rigidly �xed, and investorsfeared that in trying to defend the peg, Hong Kong might deplete itsreserves and face a crisis as well. Hong Kong was, however, successfulin avoiding devaluation �at the price of a recession, as we shall see.In the case of Korea, real appreciation added to its many structuralproblems and pushed corporations and banks into default. The sharpcollapse of the won in November and December burdened the othercurrencies with new real appreciation that was not sustainable giventhe shaky �nancial conditions around the region.

� Depreciation cycles continued through November and December, eachsetting the stage for yet another round, until the injections of IMFmoney and agreements on debt roll-overs began to limit the damage andrestore some con�dence among investors. Meanwhile, depreciation had

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disastrous e¤ects on the region�s frail businesses: their external debtmultiplied in real terms and foreign creditors, �nding their exposure tothe region much too risky, insisted on collecting short-term debt thattheir clients expected to roll over. Firms and their banks collapsedin domino fashion. Japanese �nancial �rms had lent heavily in Asia,facing very low interest rates at home. Thus the Asian disease creptinto the Japanese economy as well, and lenders collapsed, worseningJapan�s macroeconomic woes.

� Baht, won and ringgit recovered somewhat in early 1998. The post-crisis adjustments suggest that investors had been overly cautious andthus exacerbated the situation. Their behavior can be accounted for:(1) Information asymmetry: when negative disclosures about asset po-sitions of countries and businesses take investors by surprise, they sus-pect more skeletons in the closet and pull out. Let�s call it �collectivelyprobing the limits� and �guring out how bad things really are. Butacross-the-board refusals to roll over loans forced viable borrowers intobankruptcy, and pegs that might have been sustainable broke downdue to investor skepticism. (2) The policy calculus: when and wherebusinesses failed, and government bail-outs seemed likely, investors ex-pected an increase in in�ation (due to seignorage to fund the bail-outs),which raised expected real exchange rates and perceived overvaluationfurther.

� This is the time to consider the role of the IMF in bringing the crisisto closure. I�m sure you are at least faintly aware that a lot of criticismwas lodged against the IMF at the time �so you might expect thatthere was a di¤erence of opinions about how to �ght the crisis.

� Maybe a more accurate way of stating it is that there weren�t any pain-less cures and that disagreements persist about which was least painful.The IMF had a particular philosophy: it didn�t just want to address thesymptoms; the IMF wanted to �x the system that had produced overlyrisky debt structures and overvalued currencies. IMF critics tended toadvocate more gradual solutions that would give struggling businessestime to recover.

� But, to begin at the beginning, why could Asian central banks not�ght the pressure on their currencies alone? I see two reasons: (1) In

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a way, they didn�t want to, because the cost of maintaining the pegwould have been recession. (2) Once investors stampeded out of Asiaand depreciation became self-reinforcing, a de facto guarantee of forexsupplies, as IMF intervention provided, was the only way to restorecon�dence and halt the crisis.

� To understand why the price of defending the peg was a recession, let�srevisit the idea of interest parity. Arbitrage in �nancial assets will en-sure that expected returns on assets, in terms of a given currency, areequal everywhere. If the exchange rate is nominally pegged, but in-vestors begin to expect a devaluation, the only way to restore expectedreturns on local �nancial assets to parity with US assets is to raise localinterest rates. The central bank can raise interest rates by contractingthe money supply (selling bonds), but a consequence is a reduction ininvestment spending and economic activity. Hong Kong alone followedthis route: the monetary authorities drastically tightened the moneysupply, saving the peg, but steering the economy into recession.

� Asian central banks were reluctant to raise interest rates because itwould have complicated the position of heavily indebted �rms further:they would have had to re�nance at greater expense, and the recessionwould have further deteriorated earnings. Initially, some central bankstook the opposite route: they sterilized forex market interventions (i.e.the sale of reserves, which has the e¤ect of reducing the money supply)by buying bonds to the keep interest rates low and the currency pegged.But this just prompts further demand for foreign currency, given thatreturns on local assets remain as low as before, so that the rationale forthe initial out�ow persists. As the central bank continues to sell andsterilize, it depletes foreign reserves without any improvement. Asiancentral banks soon gave that strategy up.

� Instead, Thailand and Malaysia implemented capital controls to delinkonshore and o¤shore money markets (so that the central banks couldinject money, lowering interest, but not the exchange rate), which waslargely ine¤ective, as capital controls usually are. If people really wantto move their money out of a country, they manage to do so somehow.

� The result of loose montary policies, which were corrected much toolate, was a further depreciation of the currencies and increased real

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value of the private external debt. The IMF was the last resort ascurrencies plummeted and forex reserves vanished, but the IMF doesnot regard its rescue packages as grants. They are loans, and the IMFexpects to be repaid. Therefore the IMF requires borrowers to takesuch steps as it believes to be conducive to a current account surplus.

� I have argued that Asia�s defunct �nancial systems were partially toblame for the crisis, and the IMF�s reform programs, which were ne-gotiated together with the loan amount with each country, addressed,besides �scal, monetary, and external imbalances, the �nancial and reg-ulatory architecture. Typical features of these reform programs were�scal discipline (low budget de�cits), contractionary money supply toraise interest rates and avoid capital out�ows and banking sector re-structuring (e.g. foreclosure of ailing banks and increased reserve re-quirements).

� Especially the IMF�s stipulations to raise interest rates and let banksfail (without government deposit insurance) were controversial, sincethey spelled bankruptcy for heavily indebted corporations and carriedsigni�cant social costs (rise in unemployment, bank runs in Indonesia).

� The main alternative proposition was to control capital out�ows (asa remedial measure) and capital in�ows (as a preventive measure, tolimit future current account de�cits). Supporters argue that, whilebarriers to capital �ows are permeable in the long run, they can promotehealthy debt practices in the short run (limiting foreign liabilities) andaid in rebuilding the �nancial sector. China installed successful capitalcontrols during the Asian crisis. Its central bank was able to lowerinterest rates and maintain macroeconomic prowess (the only majorAsian economy to avoid a recession in 1997/1998) without depreciatingits currency. Paul Krugman thinks, this is why China evaded the crisisdespite having had many of the usual structural problems.

� What is the best way to deal with a crisis, once it is underway, remainsa hotly debated topic. The eventual goals in Asia were clear: �xingthe �nancial system and the current accounts. The IMF�s approach� to strengthen returns to local assets by raising interest rates, andthereby �ush out mismanaged corporations and banks �was economi-cally and socially disruptive, but quickly improved structures and put

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the Asian economies back on a healthy growth track, as history hasshown. Capital controls appear to be a more �friendly� solution forthe short term, as long as they can be made e¤ective. However, theyhave the decided disadvantage of undermining investor con�dence inthe market in the future. No one likes the prospect of having his or herreturns temporarily �con�scated�as the government sees �t.

� In choosing an appropriate policy mix, much would appear to dependon the particular circumstances of the economy in question. But nonewill be costless; past negligence in creating a solid �nancial architectureand good economic fundamentals must be paid for when a crisis strikes.

� I hope we have given some sensical explanations for Asia�s crisis, andyet an inconspicuous (you might say random) incident, a mere rumor,got the train of events rolling. Yet there is no doubt that the bub-ble economy of the 1990s, given too much latitude by weak �nancialsystems that looked to the wrong incentives, drove Asia into the neigh-borhood of a crisis, piling up current account de�cits and excessivedebt. There also is no doubt that quasi-�xed exchange rates, that dis-couraged risk management through hedging and, appreciating with thedollar, had grown out of line with fundamentals, pushed Asia to thebrink of devaluation and a debt crisis.

� What I am getting at is that the eruption of the crisis on July 2, 1997,was not inevitable, and in that sense there is a random element. But:shocks will come, and the shock that was to push Asia over was boundto come, given the lack of resilience. In this sense, and I think it is themore important sense, the crisis was no accident.

� Economies that left the market some room to adjust fared consider-ably better than those which stuck to pegged currencies. Singaporeand Taiwan permitted currency depreciations; of course, their �nancialsystems were also healthier than most in the region, but so was HongKong�s, and Hong Kong su¤ered severely in maintaining its currencyboard.

� Indonesia and Korea, which also preserved some nominal �exibility, hadstructural problems and current account de�cits of such magnitude thatthey could not escape the crisis once it unfolded around them. Thai-land, Malaysia and the Philippines were the prototype crisis economies

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�overinvested in unproductive sectors and deeply indebted to foreigncreditors, they had pegged, overvalued currencies and a loose moneysupply for too long.

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