5 money market equilibrium: deriving the lm curve we...

5. MONEY MARKET EQUILIBRIUM: DERIVING THE LM CURVE

5 Money Market Equilibrium: Deriving the LM Curve

• In this section, we derive a set of combinations of Y and i that ensures equilibrium in the moneymarket, which can be represented graphically as the LM curve.

— The open-economy LM curve is no different from the closed-economy LM curve.

5.1 Deriving the LM Curve

• Let’s first recap the money market:

— In the short run, the price level is assumed tobe sticky at a level P , and the money market isin equilibrium when the demand for real moneybalances L (i)Y equals the real money supplyM/P :

M

P= L (i)Y

Note that the nominal interest rate adjusts tobring the money market into equilibrium.

• We now derive the LM curve by asking a question:What happens in the money market when aneconomy’s output changes?

— Initially, the level of output is Y1 and the moneymarket is in equilibrium at point 1

′, wherereal money demand is on MD1 at M/P =L (i1)Y1.

— Then, an increase in output from Y1 to Y2 leads

to a rise in the interest rate from i1 to i2.

∗ Thus, the LM curve is downward-sloping, indicating that there is a negativerelationship between i and Y for which themoney market is in equilibrium.

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5.2 Factors That Shift the LM Curve

• We consider the factors that shift the LM curve.

— An important reason for a shift in the LM curveis a change in the real money supply M/P .

∗ The LM curve tells us the interest rate i thatequilibrates the money market at any givenlevel of output Y . Given Y , we know thatthe equilibrium interest rate i depends on realmoney supplyM/P , and so the position of theLM curve depends on M/P .

— As in the figure, an increase in the nominalmoney supply M with sticky prices raises realmoney supply fromM1/P toM2/P and shifts thereal money supply curve to the right from MS1

to MS2, thereby lowering the equilibrium interestrate from i1 to i2. This decrease in the interestrate when the level of output is unchanged at Ymeans a downward shift of the LM curve fromLM1 to LM2.

∗ Thus, the position of the LM curve is a func-tion of real money supply:

LM = LM(M/P

)· In this short-run model of the economy,prices are sticky and treated as given, soany change in the real money supply in theshort run is caused by changes in the nomi-nal money supplyM , which for now we takeas given (or exogenous).

• In addition to changes in the money supply, exogenous changes in real money demand will also cause theLM curve to shift.

— For example, for a given money supply, a decrease in the demand for real money balances at a given leveloutput Y will tend to lower the interest rate, all else equal, which would be depicted as a shift down inthe LM curve.

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5.3 Summing Up the LM Curve

• When prices are sticky, the LM curve summarize the relationship between output Y and the interest rate inecessary to keep the money market in short-run equilibrium.

1. The LM curve is upward-sloping.

— In the money market, if output rises, real money demand rises and to maintain equilibrium, real moneydemand must contract. This contraction in real money demand is accomplished by a rise in the interestrate.

— Thus, when output Y rises, the interest rate i also increases.

2. As for shifts in the LM curve, the following factors shift the LM curve shifts:

M ↑ (rise in nominal money supply)

Any shift left in the money demand function

⇒ IS curve shifts down/right︸︷︷︸Decrease in equilibrium interest rate i

at a given level of output Y

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6. THE SHORT-RUN IS-LM-FX MODEL OF AN OPEN ECONOMY

6 The Short-Run IS-LM-FX Model of an Open Economy

• We are now in a position to fully characterize an open economy that is in equilibrium in goods, money, andforex market, as shown in the IS-LM-FX figure that combines the goods market (the IS curve), the moneymarket (the LM curve), and the forex (FX) market diagrams.

1. In panel (a), the IS and LM curves are both drawn.

— The goods and forex markets are in equilibrium when the economy is on the IS curve. The moneymarket is in equilibrium when the economy is on the LM curve. Thus, all three markets are inequilibrium if and only if the economy is at point 1, the unique point of intersection of IS and LM .

2. In panel (b), the forex (FX) market is shown.

— The domestic return DR in the forex market equals the money market interest rate i. Equilibrium isat point 1

′ where the foreign return FR equals the domestic return DR equal to i.

• In the remainder of this chapter, we will use this IS-LM-FX model to analyze the short-run responseof an open economy to various types shocks. In particular, we look at how government policies affectthe economy in the short run and the extent to which they can be employed to enhance macroeconomicperformance and stability.

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6.1 Macroeconomic Policies in the Short Run

• We focus on the two main policy actions:

1. Changes in monetary policy, implemented through changes in the money supply M .

2. Changes in fiscal policy, involving changes in government spending G or taxes T .

That is, we use the IS-LM-FX model to look at how a nation’s key macro variables (output, exchange rates,trade balance) are affected in the short run by changes in these government macroeconomic policies.

• More importantly, we will examine only "temporary" changes in these policies.

— Long-run expectations about the future state of the economy are unaffected by the policy changes (inparticular, the expected future exchange rate Ee is held fixed.)

— This is because we are primarily interested in how governments use monetary and fiscal policies to handletemporary shocks and business cycles in the short run, and our model is applicable only in the short run.

• The key lesson of this section is that policies matter and can have significant macroeconomic effects in theshort run.

— Moreover, their impacts depend in a big way on the type of exchange rate regime in place. So, we willexamine temporary policy changes under (1) floating exchange rates and (2) fixed exchange ratesseparately.

• The key assumptions of this section are as follows:

— (1) The economy begins in a state of long-run equilibrium; (2) We then consider policy changes inthe home economy, assuming that conditions in the foreign economy (i.e., the rest of the world) areunchanged; (3) The home economy is subject to the usual short-run assumption of a sticky price level athome and abroad; (4) Furthermore, we assume that the forex market operates freely and unrestricted bycapital controls and that the exchange rate is determined by market forces.

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6.1.1 Monetary Policy under Floating Exchange Rates

• In this policy experiment, we consider a temporarymonetary expansion in the home country when theexchange rate is allowed to float.

• The results are shown in the figure below.

— M/P ↑ ⇒ LM shifts right (MS shifts right⇒i ↓ for any given Y ), causing i ↓ and thus, DRshifts down, causing E ↑ ⇒ Y ↑

— That is, monetary expansion tends to lower thehome interest rate, all else equal. A lower in-terest rate stimulates demand in two ways:

1. i ↓ ⇒ I ↑ directly in the goods market⇒ D ↑

2. i ↓ ⇒ E ↑ in the forex market ⇒ TB ↑(via expenditure switching) ⇒ D ↑

∗ Theoretically, what happens to TB can-not be predicted with certainty: (1) Y ↑⇒ IM ↑ ⇒ TB ↓; (2) E ↑ ⇒EP

∗/P ↑ ⇒ TB ↑. In practice, econo-

mists tend to assume that the latter out-weights the former.

— A temporary monetary expansion under float-ing exchange rates is effective in combatingeconomic downturns by boosting output — itraises output at home, lowers the interest rate,causes a depreciation of the exchange rate, andis usually predicted to increase the trade bal-ance.

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6.1.2 Monetary Policy under Fixed Exchange Rates

• Now let’s look at what happens when a tempo-rary monetary expansion occurs in a home coun-try that pegs its exchange rate with respect tothe foreign country at E.

— The key to understanding this experiment isto recall the UIP: the home interest rate mustequal the foreign interest rate under a fixedexchange rate.

• The figure shows the results:

— A temporary monetary expansion that in-creases the money supply from M1 to M2

would shift the LM curve down in panel (a). Inpanel (b), the lower interest rate would implythat the exchange rate must depreciate, risingfrom E to E2. This depreciation is inconsis-tent with the pegged exchange rate. So thepolicy makers cannot move LM in this way.They must leave the money supply equal toM1 and the economy cannot deviate from itsinitial equilibrium.

∗ Under a fixed exchange rate, au-tonomous monetary policy is not an op-tion.

· Remember that under a fixed exchangerate, the home interest rate must exactlyequal the foreign interest rate, i = i∗,according to the UIP condition, so any

shift in the LM curve would violate thisrestriction and break the fixed exchangerate.

— Monetary policy under fixed exchange rates isimpossible to undertake. Fixing the exchangerate means giving up monetary policy auton-omy. In an earlier chapter, we learned aboutthe trilemma: countries cannot simultaneouslyallow capital mobility, maintain fixed exchangerates, and pursue an autonomous monetarypolicy, which work in the IS-LM-FX framework.

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6.1.3 Fiscal Policy under Floating Exchange Rates

• We consider a temporary increase in governmentspending from G1 to G2 in the home country thatadopts a floating exchange rate regime.

• The results are shown the figure.

— G ↑ ⇒ IS shifts right, causing i ↑ and DRshifts up, causing E ↑.

1. Direct effect: G ↑ ⇒ D ↑

2. Indirect effect: (1) i ↑ ⇒ I ↓ ⇒ D ↓; (2)i ↑ ⇒ E ↓ ⇒ TB ↓ ⇒ D ↓

∗ As the interest rate rises (decreasing in-vestment) and the exchange rate appre-ciates (decreasing the trade balance), de-mand falls. This limits the rise in demandto less than the increase in governmentspending. Note that this impact of fiscalexpansion on investment is often referredto as crowding out.

∗ Thus, in an open economy, fiscal expan-sion not only crowds out investment (byraising the interest rate) but also crowdsout net exports (by causing the exchangerate to appreciate). Over time, it limitsthe rise in output to less than the increasein government spending.

— An expansion of fiscal policy under floating ex-change rates might be temporary effective. Itraises output at home, raises the interest rate,causes an appreciation of the exchange rate,and decreases the trade balance. It indirectlyleads to a crowding out of investment and netexports, and thus limits the rise in output toless than an increase in government spending.

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6.1.4 Fiscal Policy under Fixed Exchange Rates

• We consider a temporary increase in governmentspending when the home country pegs its exchangerate with respect to the foreign country at E.

— The key to understanding this experiment isthat any fiscal policy action will be pairedwith a change in the money supply thatshifts the LM curve: under a fixed exchangerate regime, the real money supply must beadjusted to ensure the nominal exchange rateremains fixed.

• The results are shown in the figure below.

— A temporary fiscal expansion would shift theIS curve to the right in panel (a), leading to anincrease in the interest rate, which would thencause the domestic return to rise. In panel (b),the higher interest rate would imply that theexchange rate must appreciate, falling from Eto E2.

∗ To maintain the peg, however, the mone-tary authority must now intervene, shiftingthe LM curve down, from LM1 to LM2.The fiscal expansion thus prompts amonetary expansion.

— In the end, the interest rate and exchange rateare left unchanged, and output expands dra-matically from Y1 to Y2.

∗ Thus, when a country is operating undera fixed exchange, fiscal policy is superef-fective because any fiscal expansion by thegovernment forces an immediate monetaryexpansion by the central bank to keep theexchange rate steady — the double and si-multaneous expansion of demand by thefiscal and monetary authorities imposes ahuge stimulus on the economy.

— A temporary expansion of fiscal policy underfixed exchange rates raises output at home bya considerable amount.

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6.2 Summary of the Impacts of Monetary and Fiscal Policies

• We have examined the operation of fiscal and mone-tary policies under both floating and fixed exchangerates and have seen how the impacts of these poli-cies differ dramatically depending on the exchangerate regime.

• The outcomes can be summarized as follows (theeffects would be reversed for contractionary poli-cies):

— Note that the row of zeros for monetary ex-pansion under fixed exchange rates reflects thefact that this infeasible policy cannot be un-dertaken.

1. In a floating exchange rate regime, autonomousmonetary and fiscal polices are feasible.

(a) The power of monetary policy to expand de-mand comes from two forces in the shortrun: (1) lower interest rates boost investmentand (2) a depreciated exchange rate (causedby lower interest rates) boosts the trade bal-ance, all else equal. In the end, though, thetrade balance will experience downward pres-sure from an import rise due to the increase inhome output/income.

• The net effect on output and investment ispositive, and the net effect on the trade bal-ance is unclear —but in practice, it is likelyto be positive too.

(b) Expansionary fiscal policy is also effective, eventhough the impact of extra spending is offsetby crowding out in two areas: (1) investment iscrowed out by higher interest rates and (2) thetrade balance is crowed out by an appreciatedexchange rate.

• Thus, on net, investment falls and the tradebalance also falls, the latter effect is un-ambiguously amplified by additional importdemand due to increased home output.

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2. In a fixed exchange rate regime, only fiscal policy isfeasible.

(a) Monetary policy loses its power for two rea-sons: (1) interest parity implies that the do-mestic interest rate cannot move indepen-dently of the foreign interest rate, so invest-ment demand cannot be manipulated; (2) thepeg means that there can be no movement inthe exchange rate, so the trade balance cannotbe manipulated by expenditure switching.

(b) Fiscal expansion requires a monetary expan-sion to keep interest rates steady and maintainthe peg. Fiscal policy becomes ultra-power ina fixed exchange rate setting — the reason forthis is that if interest rates and exchange ratesare held steady by the central bank, invest-ment and the trade balance are never crowedout by fiscal policy. Monetary policy followsfiscal policy and amplifies it.

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7. STABILIZATION POLICY

7 Stabilization Policy

• We have seen that macroeconomic policies can affect economic activity in the short run

— These effects open up the possibility that the authorities can use changes in policies to try to keep theeconomy at or near its full-employment level of output —this is the essence of stabilization policy.

∗ If the economy is hit by a temporary adverse shock, policy makers could use expansionary monetaryand fiscal policies to prevent a deep recession.

· For example, suppose a temporary adverse shock such as a sudden decline in investment, consump-tion, or export demand shifts the IS curve to the left. Or suppose an adverse shock such as asudden increase in money demand suddenly moves the LM curve up. Either shock would causehome output to fall.

· In principle, the home policy makers could offset these shocks by using fiscal/monetary policy toshift either the IS curve or LM curve (or both) to cause an offsetting increase in output.

∗ Conversely, if the economy is pushed by a shock above its full employment level of output, contrac-tionary policies could tame the boom.

— When used judiciously, monetary and fiscal policies can thus be used to stabilize the economy and absorbshocks.

∗ In practice, however, stabilization policy is challenging.

· If the economy is stable and growing, an additional temporary monetary or fiscal stimulus may causean unsustainable boom that will, when the stimulus is withdrawn, turn into an undesirable bust —mistakes in both fiscal and monetary policy have been made in the past and will undoubtedly bemade in the future.

∗ In their efforts to do good, policy makers must be careful not to destabilize the economy through theill-timed, inappropriate, or excessive use of monetary and fiscal policies.

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7.1 Application: Australia, New Zealand, and the Asian Crisis of 1997

• Australia and New Zealand are open economies thatrely on export demand from East Asian economies.In 1997, the East Asian economic crisis led to arecession in these countries, reducing demand forexports of Australia and New Zealand.

— Australia and New Zealand represent the homecountry and East Asian economies do the for-eign country.

— A decrease in foreign output, Y ∗, leads to adecrease in the home country’s trade balance(through decreasing exports).

∗ This is illustrated as a leftward shift inthe IS on Figure 18-19. As a result, thiswould lead to an economic contraction inthe home country (i.e., Australia and NewZealand).

— What is the appropriate stabilization policy? Inthis case, either fiscal or monetary expansionis the answer.

∗ Both countries chose to use monetary pol-icy. The central banks in both countries ex-panded the real money supply, shifting theLM curve to the right and reducing interestrates.

— From the model, the net effect of the decreasein export demand and the monetary expansionis as follows:

1. No change in output.

2. Decrease in nominal interest rate — invest-ment increases.

3. Increase in the exchange rate — ambigu-ous effect on the trade balance becausedecrease in foreign income reduces exportswhereas depreciation increases exports.

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• The figure shows data for the Australia and NewZealand economies in this period.

— Australian and New Zealand exports were likelyto be badly hit after the 1997 Asian crisis asthe incomes of their key trading partners con-tracted.

1. Both countries were operating on a float-ing exchange rate. To bolster demand, thecentral banks in both countries pursued anexpansionary monetary policy, lowering in-terest rates, as shown in panel (a), and al-lowing the domestic currency to depreciateabout 30% in nominal terms, as shown inpanel (b).

2. This contributed to a real depreciation ofabout 20% to 30% in the short run, asshown in panel (c). As a result, the tradebalance of both countries moved stronglytoward surplus, illustrated in panel (d), andthus demand was higher than it would oth-erwise have been. In each country, a reces-sion was avoided.

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7.2 Problems in Policy Design and Implementation

• We have looked at open-economy macroeconomics in the short run and at the roles that monetary and fiscalpolicies can play in determining economic outcomes.

— Our simple models have clear consequences.

∗ If policy makers were really operating in such an uncomplicated environment, they would have theability to exert substantial control and could always keep output steady with no unemployed resourcesand no inflation pressures.

— However, in practice, their ability to implement such policies is limited by several factors.

1. Policy constraints

• Policy makers may not always have the freedom to implement desirable stabilization policies.

— For example, a fixed exchange rate rules out any use of monetary policy. In the case of fiscal policy,countries with weak tax systems or poor creditworthiness —problems that affl ict developing countries—may find themselves unable to tax or borrow to finance an expansion of spending even if they wishedto do so.

2. Incomplete information and the inside lag

• Our models assume that the policy makers have full knowledge of the state of the economy before theytake corrective action: they observe the economy’s IS and LM curves and what shocks have hit.

• In reality, macroeconomic data are compiled slowly and it may take weeks/months for policy makersto fully understand the state of the economy today. Even then, it will take time to formulate a policyresponse (the lag between the timing of the shock and the policy action is known as an inside lag).

— On the monetary side, there may be a delay between policy meetings.

— On the fiscal side, it may take time to pass a bill through the legislature and then enable a real change

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in spending or taxing activity by the public sector.

3. Policy response and the outside lag

• Even with perfect information on the economy, policy makers then have to formulate the right responsegiven by the model.

— In particular, they must not be distracted by other policies or agendas, nor subject to influence byinterest groups that might wish to see different policies enacted.

• It may also take time for an implemented policy to have real economic effects, through the spendingdecisions of the public and private sectors (the lag between policy actions and effects is called an outsidelag).

— The outside lag is a particular problem for monetary policy. While the central bank can control short-term nominal interest rates, what matters for investment spending is long-term real interest rates. Itusually takes more than a year for a change in monetary policy to seriously impact the real economy.

4. Long-horizon plans

• If households and businesses making decisions about consumption and investment plan over long horizons,they may be less responsive to temporary policy changes.

— For example, if a business borrows to finance capital expansion, it will likely borrow over a long periodof time. Slightly higher interest rates today may be unsuccessful in deterring this investment decisionbecause the business knows the higher interest rates are temporary.

5. Weak links from the nominal exchange rate to the real exchange rate

• Our models assume that changes in nominal exchange rates translate into changes in the real exchangerate, the rate that matters for export/import decisions. But, the reality can be somewhat different forsome goods and services.

— For example, the dollar depreciated 42% against the euro from 2002 to 2004, but the U.S. prices of

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German cars like BMWs barely changed. Why?

∗ There are a number of reasons for this weak pass-through phenomenon, including the dollarizationof trade and large distribution margins that create a wedge between port prices and retail prices.

— The forces of arbitrage may also be weak as a result of noncompetitive market structures.

∗ For example, BMW sells through exclusive dealers and government regulation requires that carsmeet different standards in Europe versus the U.S.. These obstacles allow a firm like BMW to priceto market: to charge a steady U.S. price even as the exchange rate moves temporarily. If a firm canbear the exchange rate risk, it might do this to avoid the volatile sales and alienated customers thatmight result from repeatedly changing its U.S. retail price list.

6. Weak links from the real exchange rate to the trade balance

• Our models assume that real exchange rate changes lead to changes in the trade balance.

• However, there may be several reasons why these linkages are weak in reality. One major reason istransaction costs.

— Suppose the exchange rate is $1 per euro and an American is consuming a domestic good that costs$100 as opposed to a European good costing €100 = $100. If the dollar appreciates to $0.95 pereuro, then the European good looks cheaper on paper, only $95. Should the American switch to theimport?

(a) Yes, if the good can be moved without cost —but there are few such goods.

(b) If shipping costs $10, it still makes sense to consume the domestic good until the exchange ratefalls below $0.90 per euro. Practically, this means that expenditure switching may be a nonlinearphenomenon: it will be weak at first and then much stronger as the real exchange rate change growslarger.

— This phenomenon, coupled with the J curve effects discussed earlier, may cause the response of thetrade balance in the short run to be small or even in the wrong direction.

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7. Pegged currency blocs

• Our model predictions are also affected by the fact that for some major countries in the real world, theirexchange rate arrangements are characterized — often not as a result of their own choice — by a mix offloating and fixed exchange rate system with different trading partners.

— From 2002 to 2004, the U.S. dollar depreciated markedly against the euro, pound, and several otherfloating currencies, but in the "Dollar Bloc" (Japan, China, India, and others), the monetary authoritieshave ensured that the variation in the value of their currencies against the dollar is small or zero.

∗ When a large bloc of other currencies pegs to the U.S. dollar, this limits the ability of the U.S. toengineer a real effective depreciation.

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7.3 Application: Macroeconomic Policies in the Liquidity Trap

• One of the most controversial experiments in macroeconomic policy making began in 2008—2010 as monetaryand fiscal authorities around the world tried to respond to the major recession that followed the global financialcrisis.

— The unusual aspect of this crisis was the very rapid realization that monetary policy "alone" could notfully offset the magnitude of the shock to demand.

• Here is the situation after a severe negative shock to demand.

— In the context of our IS-LM-FX model, as consumption and investment fell for exogenous reasons, theshock moved the IS curve very far leftward.

∗ One major source of the demand shock was that banks were very afraid of taking on risk and sharplyreduced their lending to firms and households —and even when they did lend, they were still chargingvery high interest rates.

— Thus, even with very expansionary monetary policy, that is, a large rightward shift of the LM curve, lowpolicy rates did not translate into cheap borrowing for the private sector.

∗ Once the U.S. Fed had brought its policy rate to zero in December 2008, there was little more it coulddo to simulate demand using conventional monetary policies.

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• This particular situation is depicted by the blue lines in the figure.

— After the demand shock and the Fed’s responseto it, the IS curve has moved so far in to IS1

and the LM curve has moved so far out to LM1,so that the IS and LM curves now intersect ata very low interest rate: so low that it is equal tozero.

∗ The situation is unusual because monetarypolicy is powerless in this situation: it can-not be used to lower interest rates becauseinterest rates can’t go any lower.

· In the diagram, moving the LM curve outto LM2 does not dislodge the economy fromthe horizontal portion of the LM curve: weare still stuck on the IS1 curve at a point 1and a 0% percent interest rate.

· This unfortunate state of affairs is knownas the zero lower bound (ZLB). It is alsoknown as a liquidity trap because liquidmoney and interest-bearing assets have thesame interest rate of zero, so there is no op-portunity cost to holding money, and thuschanges in the supply of central bank moneyhave no effect on the incentive to switch be-tween money and interest-bearing assets.

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• Can anything be done? YES.

— The bad news is that fiscal policy is the only tool now available to increase demand. The good news isthat fiscal policy has the potential to be super powerful in this situation, because as long as interestrates are stuck at zero and the monetary authorities keep them there, government spending willnot crowd out investment or net exports, in contrast to the typical situation we studied earlier.

∗ In 2009 because the Fed and the private sector anticipated more than a year or two of very highunemployment and falling inflation, everyone had expectations of zero interest rates for a long period.

∗ The U.S. used fiscal policy to try to counteract the recession, but it did not work as well as onemight have hoped.

• The U.S. government’s fiscal response took two forms.

1. First were the automatic stabilizer built into existing fiscal policies, changes in government spending andtaxes that automatically move in countercyclical directions.

— In our models, we have assumed that taxes and government spending are fixed. In reality, however,they are not fixed, but vary systematically with income.

∗ When income Y falls in a recession, receipts from income taxes, sales taxes, and so on, all tend tofall as well.

2. The second was the American Recovery and Reinvestment Act (ARRA), better known as the "stimulus"bill.

— This policy was signed into law on Feb. 17, 2009; Originally hoped for a $1.4 trillion package, mostlyfor extra government consumption and investment spending, and also for aid to states; Spread over 2to 3 years from 2009—2011.

— However, the final compromise deal with Congress was only half as big, $787 billion over three years,and was tilted toward temporary tax cuts; Most of the stimulus was scheduled to take effect in2010, not 2009, reflecting the policy lags.

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• Some key outcomes are shown in the figure.

1. In the U.S. economic slump of 2008—2010, actualGDP had fallen 6% below the estimate potential(full-employment) level of GDP by the first quar-ter of 2009, as seen in panel (a) — this was theworst U.S. recession since the 1930s.

— This output gap of 6% of GDP or over $1trillion at an annual rate left a huge hole tobe filled by fiscal policy. Even if the entirestimulus was spent, the fiscal package couldat best have filled only about 1.5% of GDP.Thus, Policy makers in the government andmany observers knew the package was toosmall, but politics stood in the way of a largerpackage.

2. One intention of ARRA was to support privatespending through tax cuts, but this tax part ofthe stimulus appeared to do very little:

— Significant reductions in federal taxes seen inpanel (b) were insuffi cient to prop up consump-tion expenditure, as seen in panel (a), becauseconsumers used whatever "extra" money theygot from tax cuts to pay down their debts orsave, being unsure about the economic recov-ery and worried about the risks of unemploy-ment.

3. Thus, government spending G was left to do agreat deal of the stimulation, but problems arosebecause of the contrary effects of state andlocal government policies: on the governmentspending side there was no stimulus at all in theaggregate.

— Increases in federal government expenditurewere fully offset by cuts in state and local gov-ernment expenditure, as seen in panel (b)

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• To sum up, the aggregate U.S. fiscal stimulus had four major weakness:

1. It was rolled out too slowly, due to policy lags.

2. The overall package was too small, given the magnitude of the decline in aggregate demand.

3. The government spending portion of the stimulus, for which positive expenditure effects were certain,ended up being close to zero, due to state and local cuts.

4. This left almost all the work to tax cuts (automatic and discretionary) that recipients, for good reasons,were more likely to save rather than spend.

• With monetary policy impotent and fiscal policy weak and ill designed, the economy remained mired in itsworst slump since the 1930s Great Depression.

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8. THE APPENDIX

8 The Appendix

8.1 The Marshall-Lerner Condition

• Our model assumes that a depreciation of a country’s currency (a rise in q) will cause the trade balance TBto move toward surplus (a rise in TB).

q ↑ ⇒ TB ↑

— Is this assumption justified?

• For simplicity, assume TB = 0 or EX = IM . Let’s consider a small percentage change in the real exchangerate, say, ∆q/q = +1% (a home real depreciation of 1%), indicating that this is approximately a foreign realappreciation of 1% since the foreign real exchange rate q∗ = 1/q, and thus, ∆q∗/q∗ = −1%:

∆q

q= +1%;

∆q∗

q∗= −1%

— As we have argued, when home exports look cheaper to foreigners (foreign exports look cheaper to homeentities), the real value of home (foreign) exports expressed in home (foreign) units of output, that is,real exports, will "unambiguously" rise — in other words, when the real exchange rate increases, realexports must rise.

∗ This effect is described by the elasticity of home (foreign) exports with respect to the home(foreign) real exchange rate denoted by η (η∗):

∆EX (q)

EX (q)= η × ∆q

q= η%;

∆EX∗ (q∗)

EX∗ (q∗)= η∗ × ∆q∗

q∗= η∗%

· Note that these elasticity can be rewritten as:

∆EX (q)

EX (q)

/∆q

q=d log (EX (q))

d log (q)= η;

∆EX∗ (q∗)

EX∗ (q∗)

/∆q∗

q∗=d log (EX∗ (q∗))

d log (q∗)= η∗ (8.1)

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8. THE APPENDIX

— We now consider the trade link between the two countries: Foreign exports must equal home imports,measured in any consistent units. In home real output units,

Home importsin units of home ouput = IM (q)︸︷︷︸

Home imports(real)

and

Foreign exportsin units of home ouput =

(1/P )︸︷︷︸Divided by home price level

to convert to home output units

× E︸︷︷︸Exchange rate

converts foreign todomestic currency

× P ∗︸︷︷︸Price of

foreign basket inforeign currency

× EX∗ (q∗)︸︷︷︸Foreign imports

(real)︸︷︷︸Value of foreign exports in foreign currency︸︷︷︸

Value of foreign exports in home currency

∗ Equating these two terms, we find that:

IM (q) =EP ∗

P× EX∗ (q∗) or IM (q) = q × EX∗ (q∗) (8.2)

· Intuitively, the quantity of home imports (measured in home output) IM must equal the quantityof foreign exports EX∗ (measured in foreign output units) multiplied by a factor q that convertsunits of foreign goods to units of home goods (since q is the price of foreign goods relative to homegoods, that is, home goods per unit of foreign goods).

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8. THE APPENDIX

∗ From equation (8.2), we have:

d log (IM (q))

d log (q)= 1 +

d log (EX∗ (q∗))

d log (q)

Since q = 1/q∗ and d log (EX∗ (q∗)) /d log (q∗) = η∗, this elasticity of home imports with respect tothe home real exchange rate (the left hand side) can be expressed as:

∆IM(q)IM(q)

/∆qq

= d log(IM(q))d log(q)

= 1− η∗ (8.3)

What is going on here? On the home import side, two effects come into play:

· Foreigners export a lower volume of their more expensive goods measured in foreign output units(a volume effect of −η∗%), but those goods will cost more for home importers in terms of homeoutput (a price effect of +1%) —the price effect follows because the real exchange rate (the relativeprice of foreign goods in terms of domestic goods) has increased (by 1%), and this makes every unitof imports cost more in home real terms.

— Finally, we examine the effect of the real depreciation on the trade balance, based on the elasticitiesof exports and imports with respect to the real exchange rate (i.e., equations (8.1) and (8.3)).

∗ Starting from balanced trade with EX = IM , a 1% home real depreciation will cause EX to changeby η% and IM to change by 1−η∗%. Thus, the trade balance (initially zero) will increase (to becomepositive) if and only if the former impact on EX exceeds the latter impact on IM (η > 1 − η∗) or,equivalently:

η + η∗ > 1 (8.4)

· It is known as theMarshall-Lerner condition: it says that the trade balance will increase only aftera real depreciation if the responsiveness of trade volumes to real exchange rate changes is suffi cientlylarge (or suffi ciently elastic) to ensure that the volume effect (η + η∗) exceed the price effects (1).

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5 money market equilibrium: deriving the lm curve we...

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