LECTURE 4:
MONEY AND SAVINGS IN THE NEW KEYNESIAN MODEL
Reading:
• Sanjay K. Chugh, Modern Macroeconomics, Chapter 14
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1. INTRODUCTION AND BACKGROUND
INTRODUCTION AND BACKGROUND
In this lecture we will:
• Introduce the concept of money
• Discuss notions of return on assets: nominal and real
• Study simple motivations for holding multiple assets at once
• Introduce a simple New Keynesian model of the macroeconomy
• Study (simple) monetary policy and its effect on assets and the macroeconomy
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2. AN INTRODUCTION TO THE NEW KEYNESIAN MODEL
INTRODUCTION AND BACKGROUND
• The ideas of John Maynard Keynes dominated macroeconomics in the early 20th century
• Keynesian macroeconomics (e.g. the IS-LM-AS model) studied government policies that
might stabilize output in response to shocks
• The RBC model, with its lack of government stabilization policy, dominated
macroeconomics from the 1970s
• But continuing to believe in the importance of government policy, macroeconomists then
developed what is now called the New Keynesian Model
• Like the RBC model, the New Keynesian Model:
• Has micro foundations of economic behaviour
• Has agents with rational expectations about the future
• Can be calibrated to match various business cycle statistics about the macroeconomy
• Unlike the RBC model, the New Keynesian Model:
• Features price and/or wages that are sticky (i.e. do not update in response to economic shocks) • Describes a macroeconomy that does not respond efficiently to shocks
• May lead to output and employment being far from their socially optimal levels
• Allows a role for macroeconomic stabilization via monetary policy and/or fiscal policy
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INTRODUCTION AND BACKGROUND
• For our purposes in this class:
• The New Keynesian model describes the importance of money as an asset for households
• This role for money helps explain the relationship between money supply (controlled by the
central bank) and the business cycle
• The New Keynesian model is careful to distinguish between nominal and real values of assets
• And this helps to explain how asset holdings and consumption respond to the real inflation
adjusted return on assets (i.e. real returns)
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3. INFLATION, AND NOMINAL AND REAL INTEREST RATES
INFLATION
• Define the general price level in an economy: Pt ≡ price index • I.e. the dollar cost of a representative basket of consumer goods
• Inflation: πt ≡ percent change in the price index :
πt = Pt −Pt−1
Pt−1
= Pt −1 Pt−1
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DATA ILLUSTRATION: INTERNATIONAL INFLATION RATES
20
15
10
5
0
1960 1970
1980 1990 2000
2010 2020
International Inflation Rates
US
UK
Japan Australia New Zealand
Source: Federal Reserve Economic Database
6
Inflation rate (Annual, %)
DEFINITIONS OF NOMINAL VARIABLES
• Nominal interest rate: rnt ≡ rate of return on an asset, in period t dollars
• Asset price: St ≡ dollar price of a discount bond that pays one dollar next period
• Discount bond: a bond that is issued or traded at less than its face—value
• Face-value: amount the bond issuer pays to the bondholder once maturity is reached • Maturity: length of time a bond is held e.g. one month, one quarter, a year
• If rnt is the rate of return on the discount bond, then we we compute this as: r nt = 1 − S t = 1 − 1
1 + r nt • Note: In this case, rnt is also the yield of the bond
St St ⇒ St= 1
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REAL VS. NOMINAL INTEREST RATES AND THE FISHER EQUATION
• Purchasing power of one dollar ≡ 1 Pt
• Purchasing power represents the number of consumption goods one dollar can buy
• The “ex-post” real interest rate rt ≡ realized return on the bond in units of consumption:
rt=1/Pt+1−St/Pt=1Pt −1 St/Pt St Pt+1
⇒ 1 + r t = 1 + r nt 1 + πt+1
1+rnt =(1+rt)(1+πt+1)
= 1+rt +πt+1 +rtπt+1
• Rearranging:
• Since rtπt+1 ≈ 0 for small values of rt and πt+1:
r t ≈ r nt − π t + 1
• Which is known as the Fisher Equation
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EXPECTED VS. EX-POST REAL INTEREST RATE
• Again, the Fisher Equation:
• The expected real rate is Et (rt):
r t ≈ r nt − π t + 1
Et(rt) ≈ Et(rnt ) − Et(πt+1) = rnt − Et(πt+1)
• Et(xt+1) ≡ “expected value” of a variable xt+1 given information at time t
• Et(rnt ) = rnt , since rnt is known at time t as we know the price of the bond St when purchasing • Therefore, the nominal rate is:
rnt ≈ Et(rt) + Et(πt+1)
• The Fisher Hypothesis:
• Assuming that the real interest rate Et(rt) is constant
• Then the nominal rate rnt moves one-for-one with expected inflation Et(πt+1)
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DATA ILLUSTRATION:
NOMINAL INTEREST RATES AND INFLATION
30
20
10
USA
30
20
10
UK
Nominal Rate Inflation
Nominal Rate Inflation
00
1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020
30
20
10
Australia
30
20
10
New Zealand
Nominal Rate Inflation
Nominal Rate Inflation
00
1960 1970 1980 1990 2000 2010 2020 1960 1970 1980 1990 2000 2010 2020
Source: Federal Reserve Economic Database
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THE RATE OF RETURN ON MONEY
• We can also think of money as a type of asset. • But what is the rate of return on money?
• Since the nominal rate of return rnm,t = 0, the real return is: rm,t = rnm,t − Et(πt+1)
⇒ rm,t = −Et(πt+1) • The return on money falls as expected inflation rises
• So why do people hold money when its return is much lower than other assets?
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THE RATE OF RETURN ON MONEY
• We can also think of money as a type of asset. • But what is the rate of return on money?
• Since the nominal rate of return rnm,t = 0, the real return is: rm,t = rnm,t − Et(πt+1)
⇒ rm,t = −Et(πt+1) • The return on money falls as expected inflation rises
• So why do people hold money when its return is much lower than other assets?
• Convenience: money has a role as a medium of exchange (i.e. avoid the shoe leather costs of
returning to the bank)
• Risk: fear of bank failures/financial market collapse (e.g. “money under the mattress”)
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RETURNS ON MONEY VS. BONDS
• Recall:
• Real rate of return on money:
• (Expected) real rate of return on bonds:
• Assuming the Fisher Hypothesis (i.e. that nominal rates move with inflation)
• Then fluctuations in inflation change return on money relative to the return on bonds
• Therefore, when monetary policy influences inflation, it also affects the incentive to hold different kinds of assets
rm,t = −Et(πt+1) Et(rt) ≈ rnt − Et(πt+1)
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QUANTITY THEORY OF MONEY
• Consider again the Fisher Hypothesis:
rnt ≈ Et(rt) + Et(πt+1)
• If nominal interest rates move with inflation, what drives inflation?
• Much empirical evidence suggests a link between money growth and inflation
• Evidence across time within a given country (mainly low-frequency e.g. long-run averages) • Evidence across countries
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DATA ILLUSTRATION: INFLATION AND MONEY
Inflation and Money Growth
Inflation M1
MZ (Broad Money)
30
25
20
15
10
5
0
5
1960 1970
1980 1990 2000 2010
Source: Federal Reserve Economic Database
14
Growth rate (Annual, \%)
DATA ILLUSTRATION: INFLATION AND MONEY
Inflation and Money Growth
Inflation M1
MZ (Broad Money)
140
120
100
80
60
40
20
0
1960 1970
1980 1990 2000
2010 2020
Source: Federal Reserve Economic Database
15
Growth rate (Annual, \%)
QUANTITY THEORY OF MONEY
• Irving Fisher developed the Quantity Theory of Money (QTM):
• A theory of the price level that explains what determines the value of a unity of money
• Begin with an accounting identity:
expenditures ≡ receipts
• Let M ≡ stock of money; V ≡velocity of money (i.e. number of times a unit of money
changes hands per period); Y ≡real output
• Then:
M × V = expenditures P × Y = receipts
⇒ MV = PY
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QUANTITY THEORY OF MONEY
• Start with the Quantity theory identity:
• Rearranging:
MtVt = PtYt
⇒ ∆lnMt + ∆lnVt = ∆lnPt + ∆lnYt
∆lnPt = ∆lnMt + ∆lnVt − ∆lnYt
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QUANTITY THEORY OF MONEY
• From the quantity identity relationships:
∆lnPt = ∆lnMt + ∆lnVt − ∆lnYt
• The Quantity Theory then states:
• Assumption (1) ∆ ln Yt is independent of ∆ ln Pt , ∆ ln Mt , ∆ ln Vt (i.e. neo-classical assumption of
monetary neutrality)
• Assumption(2)∆lnVt =0
⇒∆lnPt =∆lnMt −∆lnYt
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QUANTITY THEORY OF MONEY EXAMINING THE ASSUMPTIONS
1. Why assume Y is independent of M, P, V?
• Neo-Classical theory argues only real factors matter for Y (e.g. technology)
2. Why assume stable velocity of money?
• Fisher assumed money demand was proportional to nominal income:
M = κPY ⇒ M 1 = PY
κ
⇒V= 1, soVisconstant κ
• This might be true if financial institutions and technologies change slowly over time
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QUANTITY THEORY OF MONEY EXAMINING THE ASSUMPTIONS
1. Y independent of M, P, V? No!
• Much evidence shows that Y is clearly not independent of M
• Periods when central banks have sharply contracted the money supply have been followed by large real output declines
• E.g.: Great Depression of the 1930s; large disinflations of the 1980s/1990s
• Why? Temporary nominal price rigidities mean M affects Y in short run
• If P is sticky in the short run, then variation in M will affect Y
Y=V×
M P
Real Money Supply
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QUANTITY THEORY OF MONEY EXAMINING THE ASSUMPTIONS
30 25 20 15 10
5 0
1960 1970
1980 1990 2000 2010
GDP and Money Growth
∆ GDP
∆M2
∆ MZ (Broad Money)
Source: Federal Reserve Economic Database
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Growth rate (Annual, %)
QUANTITY THEORY OF MONEY EXAMINING THE ASSUMPTIONS
25
20
15
10
5
0
1960 1970 1980
Source: Federal Reserve Economic Database
1990 2000 2010
GDP and Money Growth (Australia)
∆ GDP ∆M3
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Growth rate (Annual, %)
QUANTITY THEORY OF MONEY EXAMINING THE ASSUMPTIONS
2. Stable velocity of money? No!
• Velocity is not constant and appears to be strongly pro-cyclical • Problem:
• Changes in financial technology provide easier to access money/substitutes (e.g. on-call savings accounts, EFTPOS, Pay-Wave), which changes velocity
• The opportunity cost of holding money – i.e. the nominal interest rate on other assets rnt – also matters
• Empirically, money demand does not have a simple proportional relationship to output
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FROM THE QUANTITY THEORY TO THE NEW KESYNESIAN MODEL
• The modern New Keynesian model provides a more comprehensive description of macroeconomy
• The model describes the relationship between money, prices, and macroeconomic activity
• And the model builds from the same optimizing household behaviour of the RBC model
• We turn to this next
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4. A SIMPLE NEW KEYNESIAN MODEL
INTRODUCTION TO A SIMPLE NEW KEYNESIAN MODEL
• Household chooses consumption, nominal bonds, and money
• Simplified demand for money due to utility of holding real money balances
• Represents the “convenience yield” of money holdings
• But is something of a short-cut to characterize various desires for holding money
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HOUSEHOLD CHOICE PROBLEM
• Household choice problem is:
max logC1+ωlog M1 +βlogC2
C1 ,C2 ,M1 ,B2 P1
s.t. P1C1+M1+B2=P1Y1
P2C2 = P2Y2 +M1 +B2(1+rn) • Where M1/P1 are real money balances
• The inter-temporal real budget constraint is:
C1+M1 + C2 P2 =Y1+ Y2 P2 +M1/P1
P1 1+rn P1 1+rn P1 1+rn
• The Lagrangian Problem is:
Y2 P2 M1/P1 M1 C2 P2 L=logC1+ωlog P1 +βlogC2 +λ Y1 + 1+rn P1 + 1+rn −C1 − P1 − 1+rn P1
M1
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FIRST ORDER CONDITIONS
• The first order conditions for the problem are: C1: 1−λ=0
C1
C2: β1−λ 1 P2=0
C2 1+rn P1
M1: ω1 1 +λ 1 1−λ1=0
P1 M1/P1 1+rn P1 P1
• Combining the first two yields the consumption Euler equation:
1 =β(1+rn)P1 1 C1 P2 C2
• Combining the first and third yields the consumption-money optimality condition: C1 rn
• which states that the marginal rate of substitution between consumption and money balances is governed by the nominal interst rate on bonds
ωM1/P1 = 1+rn
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MONEY DEMAND
• We can represent the consumption-money optimality condition as a money demand equation in (M1/P1, rn)-space
rn
MD
M P
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THE MONEY MARKET IN EQUILIBRIUM: DEMAND AND SUPPLY FOR MONEY
• Suppose the central bank supplies money inelastically with respect to the interest rate
rn
MS
M1 M P1 P
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MD
SIMPLE MONETARY POLICY
• The New Keynesian model suggestions that money affects the real economy • Simple example:
• Assume that nominal price rigidities mean that prices are constant: P1 = P2 = P • Now consider an unexpected increase in money supply ↑ MS1
• What happens to consumption (C1, C2)?
• Note: These assumptions only hold in the short run!
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SIMPLE MONETARY POLICY: INCREASE IN MONEY SUPPLY
• With sticky prices (i.e. P constant), an increase in the money supply decreases the nominal interest rate
rn
MS MS′
rn
rn′
MD
M1 M′M
P1 1P 31 P1
SIMPLE MONETARY POLICY: INCREASE IN MONEY SUPPLY
• To solve for changes in consumption take the inter-temporal budget constraint, money demand, and Euler equations (assuming that P1 = P2):
C1+M1 + C2 =Y1+ Y2 +M1/P1 (1)
P1 1 + rn 1 + rn C1 rn
1 + rn
ωM1/P1 = 1+rn
1 =β(1+rn)1
(2)
(3)
C1 C2
• Substituting the money demand and Euler equations into the budget constraint, we get the
consumption functions:
1 Y2 β(1+rn) Y2 C1 = 1 + ω + β Y1 + 1 + rn , C2 = 1 + ω + β Y1 + 1 + rn
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SIMPLE MONETARY POLICY: INCREASE IN MONEY SUPPLY
• Remember the increase in money supply leads to a decrease in rn • Thus, consumption in period 1 rises:
↑ C1 = 1 Y1 + 1 + ω + β
• And consumption in period 2 falls:
Y2 , 1 + rn
↓
↓
n n
↓ C2 = β(1 + r ) Y1 + Y2 = β(1 + r ) Y1 +
1 + ω + β 1 + rn 1 + ω + β
β Y2 1 + ω + β
• So sticky prices mean that monetary policy is non-neutral in the short run • That is, monetary policy can have real effects on the macroeconomy!
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SIMPLE MONETARY POLICY: DEMAND FOR MONEY VS. DEMAND FOR BONDS
• Changes in monetary policy also affect demand for assets
• Derive the bond demand equation using the period 1 budget constraint and the money demand equation:
B2 =Y1−C1−M1
P1 P1 1
= Y1 − C1 − ωC1 1 + rn
• Which shows that real bond demand is increasing in the nominal interest rate rn
• So households adjust their asset portfolio according to the return on bonds
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SIMPLE MONETARY POLICY: DEMAND FOR MONEY VS. DEMAND FOR BONDS
• Changes in monetary policy affect real asset portfolio allocation decisions
• Household composition of assets varies with the relative return on the assets available
• So a decrease in money supply raises the nominal interest rate, which increases bond holdings
• Since the nominal return on money is zero, an increase in the nominal return on bonds leads to a shift away from money and towards bonds
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SIMPLE MONETARY POLICY: DEMAND FOR MONEY VS. DEMAND FOR BONDS
rn
BD
MD
M,B PP
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5. LIMITATIONS OF NEW KEYNESIAN MODELS
5.A) LIMITATIONS OF THE NEW KEYNESIAN MODEL FOR UNDERSTANDING THE MACROECONOMY
• The source of price rigidities is often not well-microfounded • Typically introduce ad-hoc “price stickiness” to models
• New Keynesian models often do not account for macroeconomic data much better than RBC models
• Despite their basis in monetary economics, New Keynesian models often do a poor job of explaining fluctuations in inflation
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5.B) LIMITATIONS OF THE NEW KEYNESIAN MODEL FOR UNDERSTANDING ASSET MARKETS
• As was the case for the RBC model, most New Keynesian models are not solved with economic risk in mind
• So, again, these models are not ideal for studying some of the main motives for asset holdings
• Both RBC and New Keynesian models contain a single, representative household
• This household has no one else to trade with, so the notion of a financial market is limited
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