Chapter 5 – Money

Master EPP 2011

Macroeconomics 2, Yann Algan

Introduction…

Up to now, centralized economy and complete markets: no room for money

Which assumptions should be relaxed ?

• Complete markets: if no Arrow-Debreu and contingent markets, real balances could be used as a buffer stock against idiosyncratic income shocks (incomplete market and heterogeneity)

• Timing of markets: spot markets which open in turn (goods, labor, bonds)But an auctioneer could make intertemporal transfers

• Required assumptions:- Decentralized markets without auctioneer - Money as a solution for the double coincidence of want

(barter would be costly)

…Introduction

• Consensus on large and positive correlation between money and output- Friedman and Schwartz (1963): Monetary History- Evidence at business cycle frequency (Cooley (1995))

Correlation between current money and leads and lag outputUS postwar data

• But how to identify monetary shocks ? Ex. what if the monetary policy rule reacts to technological shocks?

• What is the causality at work ?

Questions

• How does a monetary economy look like ?

• What determine the demand for money, price and interest rates levels ?

• What are the long-run effects of money on output ? What about the dynamics ?

• How can we explain hyperinflation episodes ?

1. A cash in advance model

• Easiest way to give a role for money: assume a decentralized economy in which the bond market opens after good market

1.1 Consumption/Saving choice

subject to

•Resources constraint

•Cash-in-advance constraint

(1)

(2)

(3)

Price of goods

Money holdings, Bond holdings and Capital holdings at the beginning of the period

Nominal wages and Nominal profit

Nominal interest rate, Real (in terms of goods) interest rate

• Budget resources constraint (2)

Money transfers

Money newly created X is transferred to households

- Simple way of modelizing the impact of monetary policy on the economyFiction of helicopter drop

-Could be modelized by assuming that there are public spending financedby fiscal tax and inflation tax

• Law of motion of aggregate supply of money

Newly created money transferred to households

• Cash in advance constraint (3)

- What about another constraint: total cash in hands

• If the budget constraint was the only one: no role for money since it is a dominated asset compared to bonds and capital which pay interest and rent

Need an additional constraint

• Role for money: people must enter the period with enough money cash to buy goods

Interpretation: Liquidity services of moneyHousehold is both a consumer and a worker, but needs to finance consumption during the week before he gets paid at the end of week

• Different representation depending of the timing assumption

- Or trade in both the bond and money market before the good marketLucas (1982)

- Distinction between cash goods and credit goods: Lucas and Stokey (1987)

• Lagrangien

Budget constraint

CIA constraint

(4)

(5)

(6)

(7)

• FOC

Interpretations

• Nominal and real interest rates

By combining (6) and (7)

)

Fisher equation

• Intertemporal trade-off: new Euler equation

By using (4) and (5), and replacing in (6)

• Modified Euler equation

- Due to CIA, people must carry on money one period in advance, thus the effective price of consumption is (1+i) [rather than 1]

-If nominal interest rates were to be constant, we are back tothe Euler equation

• Optimal money demand

From (5) and (6)

If nominal interest rate i is positive, thus is positive

Pure quantity theory: money demand only for transactions purpose(Think about traditional LM equation without interest rate elasticity)

Firms

• Competitive market and static program (firms rent capital to households)

• If constant returns to scale, profits are nil

• Competitive labor market and inelastic labor supply = 1

1.2 General equilibrium

• Notice that it would have been possible to write down directly the budget constraint as

Market equilibrium

• Net supply of bonds

• Law of motion of Money

Equilibrium

Key equations of the model

1.3 Steady state

• At the steady state, constant growth of money supply

-All aggregates (in real terms!) are constant

In particular

And inflation rate is equal to the growth rate of nominal money(!! This results will no longer hold during the dynamics in general)

• Superneutrality result

- Real interest rate pinned down by discounting factor: traditional golden rule

- Consumption only given by real factor

Neutrality result

CIA constraint

Pure quantitative theory of money: money is neutral, any increase in Myields an increase in P

- Inflation is equal to money growth -Real interest rate is pinned down only by preference and technological factors

An increase in money growth translates to a an identical increase to nominal interest rate without any effect on real interest rate : Fisher result

• But implication of the model is even stronger

Superneutrality: growth rate (an not only the level) of money has no impact on real economy

Look at the Fisher equation at the steady state

• Welfare cost of inflation

-Suitable framework to assess the welfare cost of inflation sincebehavioral relations consistent with utility maximization

-Unfortunately, in CIA model, there is no optimal rate of inflation that maximizes steady-state welfare of the representative agent

where steady state consumption is independent from moneyThus any inflation rate is as good as any other

-This result is no longer robust if introduction of labor-leisure choice… or money in the utility function

1.4 Dynamic of the model

• Dynamics of the model is harder to characterizeEffect comes from the consumption side : anticipated changes in effectiveprice in goods, depends on nominal interest rate, which depends on Inflation… which depends on money growth

• First important result: - Unexpected permanent increase in money and in money growth have

no real effects !! (different from sticky prices or Lucas’s imperfect information)

-Only expected future monetary shocks can have real effects by Modifying intertemporal consumption/saving or labor/leisure trade-off

(From Walsh, Chapter 3)

• Channel through the labor-leisure trade-off

Extension by Cooley-Hansen (1989) RBC + CIAExactly the same program as before but with endogenous labor supply

- Anticipated inflation causes people to substitute away from activities that require cash, such as consumption, for activities that do not require cash, such as leisure

-A monetary positive shock would lower labor and output (and welfare)

- Over-adjustment of inflation following the monetary shock (due toflexible price assumption)

Impulse response completely at odds with observed fluctuations!!(See program CIA.m in Ulhig toolkit and Walsh (chapter 3))

• Channel through consumption/saving trade-off

-1 0 1 2 3 4 5 6 7 8-0.04

-0.035

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005Im pulse responses to a shock in m oney growth

Y ears after shock

Per

cent

dev

iatio

n fro

m s

tead

y st

ate

output

em ploym ent

2. Money in the utility function

• Money directly praised in the utility function (Sidrauski model)Direct role for money: short cut for taking into account its service:

more efficient in shopping, increase leisure time

• Room for welfare analysis : what are the welfare costs of inflation ?Lucas (2000)• Role of assumptions about the utility functions

• Budget constraint in nominal terms, But utility depends on real balances

FOC

Without uncertainty and by denoting the Lagrangian multiplier

• Intratemporal condition

Trade-off between consumption and real money holdings

TMS between consumption and real cash has to be equal to the opportunity cost to carry on money to next period, which is given bythe nominal interest rate i

• Intertemporal conditionsModified Euler equation

Example : Log Utility function

• FOC

• Interpretation as an IS-LM curve

IS curve: the higher the interest rate, the lower the level of current consumption

LM curve: demand for money increases with consumptions (transaction motives)and decreases with opportunity cost of holding money (speculation motives)

(Note that MIU endogenously leads to a CIA constraint !! )

2.1 Steady state : Superneutrality result

Steady state

Same real allocation as the model with CIA or the model without money

Superneutrality: money growth has no real effect on output, consumption

Level of real balances M/P inversely proportional to money growth rate: one for one decrease

2.2 Dynamic effects

• In general, some real effect of monetary shock on real activity

(!! Except for some particular case such as log-utility)

• But real effect on output and inflation are fairly small See figure and Walsh (Chapter2)

• And impulse response at odds with observed evidence- Overshooting of inflation- Decrease in employment and output following a rise in money growth

-1 0 1 2 3 4 5 6 7 8-0.2

0

0.2

0.4

0.6

0.8

1

1.2Impulse responses to a shock in money growth

Years after shock

Per

cent

dev

iatio

n fro

m s

tead

y st

ate

capital

money balances

output employment

nominal rate

real rate

inflation

• MIU model with endogeneous labor and capital accumulation(See program MIU.m in Ulhig toolkit and Walsh (chapter 2))

3. Welfare costs of inflation and Optimal quantity of money

Bailey (1956), Friedman (1969), Lucas (2000)

• Private opportunity cost of holding money depends on nominal interest rate• Social marginal cost of producing money is essentially zero

Wedge between private marginal cost and social marginal cost raises an inefficiency which would be eliminated if nominal interest rate is driven down to zero

• Optimal inflation rate should thus drive down the nominal interest rate (opportunity cost to carry on money) to zero

• What is the welfare cost of deviating from this optimum quantity of money ?

- Bailey’s tradition (1956): welfare cost calculated as the area under the money demand curve (money demand as a function of nominal interest rate). It provides a measure of the consumer surplus lost due to a positivenominal interest rate.

-Lucas result:Welfare costs of inflation in the US estimated between [0.85%-3%]of real GNP per percentage rise in the nominal interest rate above zeroLoss equivalent to 88-310 billion 2002 dollars per year

-Lucas’s conclusion: welfare costs of inflation much higher thanwelfare cost of fluctuations!!

Conclusion

• First pass to provide micro-foundations for money demand: CIA or MIU

• Effect of interest rates - Nominal interest rate affect money demand- Real interest rate affect intertemporal saving decisions and the slope of C

• Dynamics:- Only anticipated monetary shocks do matter

- Quantitative impact of monetary shock are really poor (much of the effect transit through price adjustment and the real effect dies out quickly)

- Qualitative answers at odds with observed fluctuationsIn the data: inflation inertia (instead of overshooting) and increase in outputand labor, following an expansionary monetary shock

• Welfare costs of inflation

- Welfare costs of reducing inflation could be even more important !!Go back to the sacrifice ratio: Ball (1993) estimated approximatively2.4 percent of output per one percent of inflation reduction

- Money is superneutral in this framework: Overestimation of the welfare costs of inflation by ignoring long-run positive real effect of inflation on capital

Potential extensions: Fiscal distortions (Phelps, 1973), Incomplete markets…