Macroeconomics II Lecture 6 Chapter 10. A Monetary ...
Macroeconomics II Lecture 6 Krzysztof Makarski Fall 2010 Chapter 10. A Monetary Intertemporal Model
Intro Next we augment our model with the nominal side: we introduce money. What is Money?
What is money? • Functions of Money
Medium of Exchange Store of Value Unit of Account • Measuring the Money Supply
The Monetary Base ∗ Currency Outside the Fed ∗ Depository Institution Deposits at the Fed M1, Table 11.1 ∗ Currency Held by the Public ∗ Traveler's Checks ∗ Demand Deposits ∗ Other Checkable Deposits M2 = M1 + ∗ Savings Deposits ∗ Small-Denomination Time Deposits ∗ Retail Money Market Mutual Funds M3 = M2 + ∗ Large-Denomination Time Deposits ∗ Institutional Money Market Mutual Funds ∗ Repurchase Agreements ∗ Eurodollars
A Monetary Intertemporal Model
Need for Money • The Need for Money - Money facilitates Transactions. We assume that consumption goods must be
purchased with money.
1
Real and Nominal Interest Rates, Fisher Relation • Bond is an asset that sells for one unit of money in the current period and pays 1 + r units in the future period. Therefore R− is nominal interest rate. • Let i denote in ation rate than the real interest rate is determined by the Fisher relation 1+r =
1+R 1+i
after cross multiplying gives r = R − i − ir ' R − i
(11.2) (11.3)
• For relation between real and nominal interest rate see Figure 11.1
Banks • Two types deposits: transactions deposits (checking account) and savings deposits (savings account).
deposits can be withdrawn from the checking account anytime, no interest. deposits can be withdrawn from the savings account only at the beginning of the next period, pay interest R • Three types of assets: money, credit card balances and bonds. • Balance sheet, see Table 11.2. • Extending credit balances is costly, for supply curve see Figure 11.2
Transactions • Firms and consumers face collectively the following transactions constraint (sometimes called cash-in-
advanced constraint)
Pt (Ct + It + Tt ) + Btd = Mt−1 + (1 + Rt−1 )Bt−1 + Pt Xtd
(11.4)
where Xtd - credit card transactions (in real terms). • Firms and households budget constraint Pt (Ct + It + Tt ) + Btd + Mtd + Pt qt Xtd = Mt−1 + (1 + Rt−1 )Bt−1 + Pt Yt
(11.5)
Demand for money • Deducting (11.4) from (11.5) we get Mtd + Pt qt Xtd = Pt Yt − Pt Xtd Mtd + Pt (1 + qt )Xtd = Pt Yt
(11.6)
(assuming that the velocity of money is one) • Since money or credit cards can be used to purchase goods the gain from holding the credit card they can increase their saving deposits (gain Rt ) but have to pay for each dollar on the credit card qt , thus
2
Table 11.1 Monetary Aggregates, June 2009 (in $billions)
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Figure 11.1 Real and Nominal Interest Rates
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Table 11.2 A Typical Bank’s Balance Sheet
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Figure 11.2 The Supply Curve for Credit Card Balances
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if Rt > qt they will not use money for purchases but credit card only and from (11.6) Xtd = spend everything on their credit cards, if Rt < qt than Xt = 0, h
Yt −0 1+qt
i
Yt . and if Rt = qt then they are indierent Xtd ∈ 0, 1+q t
See Figure 11.3. • An increase in the interest rate increases real credit card balances X ∗ (R) is increasing in R, see Figure 11.4. Thus from (11.6) Mtd = Pt [Yt − (1 + qt ) Xt∗ (Rt )] (11.7) • For convenience we rewrite (11.7) as
Since R ' r + i
Mtd = Pt L(Yt , Rt )
(11.8)
Mtd = Pt L(Yt , rt + it )
(11.9)
Since in the next chapters we deal with experiments that do not deal with the eects of changes in long run in ation, that is all of the experiments we consider in these chapters leave i unaected (remember for some questions it may matter). When i is constant it is harmless to set it to zero for convenience, see Figure 11.5 Mtd = Pt L(Yt , rt ) (11.10) When output goes up money demand goes up (more transactions need to be carried out), see Figure 11.6
Government Government receives apart from taxes income from money Pt Gt + (1 + Rt−1 )Bt−1 = Pt Tt + Bt + Mt − Mt−1
(11.11)
Competitive Equilibrium - The Complete Monetary Intertemporal Model • We add one market to the previous ones. In our model real variables are determined by real side and
nominal by nominal side of the economy.
• Graphical Apparatus The money market is in equilibrium, when money demand equal money supply M d = M s , (see Figure 11.7) which after substituting from (11.10) M = P L(Y, r)
The rest of the analysis is the same as in the previous chapter, see Figure 11.8
5
(11.12)
Figure 11.3 Equilibrium in the Market for Credit Card Balances
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Figure 11.4 The Effect of an Increase in the Nominal Interest Rate on the Market for Credit Card Balances
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Figure 11.5 The Nominal Money Demand Curve in the Monetary Intertemporal Model
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Figure 11.6 The Effect of an Increase in Current Real Income on the Nominal Money Demand Curve
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Figure 11.7 The Current Money Market in the Monetary Intertemporal Model
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Figure 11.8 The Complete Monetary Intertemporal Model
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A Level Increase in the Money Supply ...
A Level Increase in the Money Supply. • Sources of Changes in the Money Supply
Helicopter Drops: Taxes/Transfers: Increase in money supply decreases taxes. Open-Market Operations: An open market purchase is an exchange of money for interest bearing bonds (which increases money supply) Seigniorage: Printing money in order to nance government spending.
For our purposes we assume that the money supply increase occurs through helicopter drops. • Classical Dichotomy What happens when the money supply level increases as in Figure 11.9? Since
the level of the money supply does not matter for labor supply, labor demand the demand and supply of goods, the equilibrium determination of N, Y, r, and w in Figure 11.10 is unaected by the current money supply M . That is, there is a classical dichotomy: the model solves for all the real variables (N, Y, r, and w) in the labor market and the goods market and the price level is then determined, given real output, in the money market. Real activity is completely separated from nominal variables.
• Neutrality of Money In this model money is neutral. Money neutrality is said to hold if a change in
the level of the money supply results only in a proportionate increase in prices, with no eect on any real variables.
A Temporary Decrease in TFP
A Change in Current Total Factor Productivity • Real Eects A decrease in z decreases the current marginal product of labor, which shifts N d curve to
the left, and the output supply curve shifts to the left. In equilibrium the real interest rate rises, the current aggregate output falls. Because of the increase in the real interest rate, the current consumption and current investment decrease. Also, the higher real interest rate results in intertemporal substitution of leisure, and N s curve shifts to the right. In equilibrium the shift in the labor supply curve is su ciently small that the employment falls from N1 to N2 and the real wage falls from w1 to w2 . See Figure 11.11
• Price-Level Eects The equilibrium decrease in current real income Y money demand and the increase
in the real interest rate also reduces money demand. Therefore the money demand curve shifts to the left. The money supply is xed at M and so in equilibrium the price level goes up.
TCD: Change in Relative Price of Energy and the Price Level • We observe in the data positive correlation between the relative price of energy and the price level, see
Figure 11.12 and Figure 11.13
• This is consistent with the view that shocks to the price of energy are essentially negative productivity
shocks.
9
Figure 11.9 A Level Increase in the Money Supply in the Current Period
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Figure 11.10 The Effects of a Level Increase in M— The Neutrality of Money
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Figure 11.11 Short-Run Analysis of a Temporary Decrease in Total Factor Productivity
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Figure 11.12 Percentage Deviations from Trend in the Price Level and in the Relative Price of Energy
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Shifts in the Demand for Money • These shifts are important for how monetary policy should be conducted. • Shifts in the demand for money that occur within a day, week or month (the very short run) are a
critical for the central bank.
• Figure 11.14 and Figure 11.15
Monetary Policy: Targets and Policy Rules
How to conduct monetary policy? • Suppose that the Fed nds 2% in ation rate is optimal, behavior of the Fed indicates it. For our analysis suppose that the optimal in ation rate π ∗ = 0 . • Shocks that the central bank is concerned with (in our model): shifts in money demand - see Figure
11.16, output demand - see Figure 11.17, output supply - see Figure 11.18.
• If these shocks were observed directly the responses would be obvious. • Key problem for the central bank: it cannot observe the shocks directly, and does not have timely
information on all economic variables.
• Practice: In ation Targeting - in ation target (usually 2% plus a band and independence)
In ation Targeting (see also lecture notes #9)? • Most central banks in developed countries and as well as many in developing countries use so called
in ation targeting regime while conducting monetary policy.
• What is in ation targeting:
in ation target (usually 2% plus a band) working independence (not only declared) • Why?
transparency brings credibility anchors expectations solves (partially) the problems from the previous slide. • Why 2%?
in ation distorts the functioning of the informational role of the price system (recall 1st and 2nd welfare theorem) thus, in a frictionless world optimal in ation satis es the Friedman rule which calls for the nominal interest rates to be equal to zero (and implies de ation), but than there is no room for monetary expansion during recessions
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Figure 11.13 Scatter Plot of the Price Level Versus the Relative Price of Energy for 1947–2009
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Figure 11.14 A Decrease in the Supply of Credit Card Balances
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Figure 11.15 A Shift in the Demand for Money
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Figure 11.16 A Shift in the Demand for Money
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Figure 11.17 A Shift in the Output Demand Curve
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Figure 11.18 A Shift in the Output Supply Curve
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in a frictionless world (RBC world) this poses no problem in a world with nominal frictions (new Keynesian world) it implies deeper recessions not much experience with negative in ation and zero interest rate to see the results
deviation from the zero interest rate to 2% creates small costs of in ation (since it is a small deviation) and but oers room to smooth at least partially the business cycle uctuations (lower volatility) MiA: Should monetary policy respond to asset prices? • Higher in ation as it distorts the functioning of the informational role of the price system (recall 1st
and 2nd welfare theorem), so the central bank has well speci ed and justi ed goal.
• But, should it worry about asset prices? • It may aect the economy through either:
irrational exuberance ' nancial accelerator' eects (which amplify the eects of shocks to the economy through nancial market frictions • Bernanke and Gerlter (1999) nd that it should not react directly, and only if they aect in ation
expectations (indirectly)
• They nd that the optimal policy is exible in ation targeting (allows for short run deviations of
in ation from its target).
PoFC: Increase in the Monetary Base and the Fed's Balance Sheet • read it yourself
Summary • What is money? • Monetary intertemporal model. • Increase in money level in the frictionless model. • TFP shock in the frictionless model. • In ation targeting. • Assets prices and monetary policy.
Reading • Williamson, Chapter 10 without the monetary rule and the interest rate rule.
16
Intro Next we augment our model with the nominal side: we introduce money. What is Money?
What is money? • Functions of Money
Medium of Exchange Store of Value Unit of Account • Measuring the Money Supply
The Monetary Base ∗ Currency Outside the Fed ∗ Depository Institution Deposits at the Fed M1, Table 11.1 ∗ Currency Held by the Public ∗ Traveler's Checks ∗ Demand Deposits ∗ Other Checkable Deposits M2 = M1 + ∗ Savings Deposits ∗ Small-Denomination Time Deposits ∗ Retail Money Market Mutual Funds M3 = M2 + ∗ Large-Denomination Time Deposits ∗ Institutional Money Market Mutual Funds ∗ Repurchase Agreements ∗ Eurodollars
A Monetary Intertemporal Model
Need for Money • The Need for Money - Money facilitates Transactions. We assume that consumption goods must be
purchased with money.
1
Real and Nominal Interest Rates, Fisher Relation • Bond is an asset that sells for one unit of money in the current period and pays 1 + r units in the future period. Therefore R− is nominal interest rate. • Let i denote in ation rate than the real interest rate is determined by the Fisher relation 1+r =
1+R 1+i
after cross multiplying gives r = R − i − ir ' R − i
(11.2) (11.3)
• For relation between real and nominal interest rate see Figure 11.1
Banks • Two types deposits: transactions deposits (checking account) and savings deposits (savings account).
deposits can be withdrawn from the checking account anytime, no interest. deposits can be withdrawn from the savings account only at the beginning of the next period, pay interest R • Three types of assets: money, credit card balances and bonds. • Balance sheet, see Table 11.2. • Extending credit balances is costly, for supply curve see Figure 11.2
Transactions • Firms and consumers face collectively the following transactions constraint (sometimes called cash-in-
advanced constraint)
Pt (Ct + It + Tt ) + Btd = Mt−1 + (1 + Rt−1 )Bt−1 + Pt Xtd
(11.4)
where Xtd - credit card transactions (in real terms). • Firms and households budget constraint Pt (Ct + It + Tt ) + Btd + Mtd + Pt qt Xtd = Mt−1 + (1 + Rt−1 )Bt−1 + Pt Yt
(11.5)
Demand for money • Deducting (11.4) from (11.5) we get Mtd + Pt qt Xtd = Pt Yt − Pt Xtd Mtd + Pt (1 + qt )Xtd = Pt Yt
(11.6)
(assuming that the velocity of money is one) • Since money or credit cards can be used to purchase goods the gain from holding the credit card they can increase their saving deposits (gain Rt ) but have to pay for each dollar on the credit card qt , thus
2
Table 11.1 Monetary Aggregates, June 2009 (in $billions)
11-5
© 2011 Pearson Addison-Wesley. All rights reserved.
return
Figure 11.1 Real and Nominal Interest Rates
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Table 11.2 A Typical Bank’s Balance Sheet
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Figure 11.2 The Supply Curve for Credit Card Balances
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if Rt > qt they will not use money for purchases but credit card only and from (11.6) Xtd = spend everything on their credit cards, if Rt < qt than Xt = 0, h
Yt −0 1+qt
i
Yt . and if Rt = qt then they are indierent Xtd ∈ 0, 1+q t
See Figure 11.3. • An increase in the interest rate increases real credit card balances X ∗ (R) is increasing in R, see Figure 11.4. Thus from (11.6) Mtd = Pt [Yt − (1 + qt ) Xt∗ (Rt )] (11.7) • For convenience we rewrite (11.7) as
Since R ' r + i
Mtd = Pt L(Yt , Rt )
(11.8)
Mtd = Pt L(Yt , rt + it )
(11.9)
Since in the next chapters we deal with experiments that do not deal with the eects of changes in long run in ation, that is all of the experiments we consider in these chapters leave i unaected (remember for some questions it may matter). When i is constant it is harmless to set it to zero for convenience, see Figure 11.5 Mtd = Pt L(Yt , rt ) (11.10) When output goes up money demand goes up (more transactions need to be carried out), see Figure 11.6
Government Government receives apart from taxes income from money Pt Gt + (1 + Rt−1 )Bt−1 = Pt Tt + Bt + Mt − Mt−1
(11.11)
Competitive Equilibrium - The Complete Monetary Intertemporal Model • We add one market to the previous ones. In our model real variables are determined by real side and
nominal by nominal side of the economy.
• Graphical Apparatus The money market is in equilibrium, when money demand equal money supply M d = M s , (see Figure 11.7) which after substituting from (11.10) M = P L(Y, r)
The rest of the analysis is the same as in the previous chapter, see Figure 11.8
5
(11.12)
Figure 11.3 Equilibrium in the Market for Credit Card Balances
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Figure 11.4 The Effect of an Increase in the Nominal Interest Rate on the Market for Credit Card Balances
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Figure 11.5 The Nominal Money Demand Curve in the Monetary Intertemporal Model
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Figure 11.6 The Effect of an Increase in Current Real Income on the Nominal Money Demand Curve
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Figure 11.7 The Current Money Market in the Monetary Intertemporal Model
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Figure 11.8 The Complete Monetary Intertemporal Model
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A Level Increase in the Money Supply ...
A Level Increase in the Money Supply. • Sources of Changes in the Money Supply
Helicopter Drops: Taxes/Transfers: Increase in money supply decreases taxes. Open-Market Operations: An open market purchase is an exchange of money for interest bearing bonds (which increases money supply) Seigniorage: Printing money in order to nance government spending.
For our purposes we assume that the money supply increase occurs through helicopter drops. • Classical Dichotomy What happens when the money supply level increases as in Figure 11.9? Since
the level of the money supply does not matter for labor supply, labor demand the demand and supply of goods, the equilibrium determination of N, Y, r, and w in Figure 11.10 is unaected by the current money supply M . That is, there is a classical dichotomy: the model solves for all the real variables (N, Y, r, and w) in the labor market and the goods market and the price level is then determined, given real output, in the money market. Real activity is completely separated from nominal variables.
• Neutrality of Money In this model money is neutral. Money neutrality is said to hold if a change in
the level of the money supply results only in a proportionate increase in prices, with no eect on any real variables.
A Temporary Decrease in TFP
A Change in Current Total Factor Productivity • Real Eects A decrease in z decreases the current marginal product of labor, which shifts N d curve to
the left, and the output supply curve shifts to the left. In equilibrium the real interest rate rises, the current aggregate output falls. Because of the increase in the real interest rate, the current consumption and current investment decrease. Also, the higher real interest rate results in intertemporal substitution of leisure, and N s curve shifts to the right. In equilibrium the shift in the labor supply curve is su ciently small that the employment falls from N1 to N2 and the real wage falls from w1 to w2 . See Figure 11.11
• Price-Level Eects The equilibrium decrease in current real income Y money demand and the increase
in the real interest rate also reduces money demand. Therefore the money demand curve shifts to the left. The money supply is xed at M and so in equilibrium the price level goes up.
TCD: Change in Relative Price of Energy and the Price Level • We observe in the data positive correlation between the relative price of energy and the price level, see
Figure 11.12 and Figure 11.13
• This is consistent with the view that shocks to the price of energy are essentially negative productivity
shocks.
9
Figure 11.9 A Level Increase in the Money Supply in the Current Period
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Figure 11.10 The Effects of a Level Increase in M— The Neutrality of Money
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Figure 11.11 Short-Run Analysis of a Temporary Decrease in Total Factor Productivity
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Figure 11.12 Percentage Deviations from Trend in the Price Level and in the Relative Price of Energy
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Shifts in the Demand for Money • These shifts are important for how monetary policy should be conducted. • Shifts in the demand for money that occur within a day, week or month (the very short run) are a
critical for the central bank.
• Figure 11.14 and Figure 11.15
Monetary Policy: Targets and Policy Rules
How to conduct monetary policy? • Suppose that the Fed nds 2% in ation rate is optimal, behavior of the Fed indicates it. For our analysis suppose that the optimal in ation rate π ∗ = 0 . • Shocks that the central bank is concerned with (in our model): shifts in money demand - see Figure
11.16, output demand - see Figure 11.17, output supply - see Figure 11.18.
• If these shocks were observed directly the responses would be obvious. • Key problem for the central bank: it cannot observe the shocks directly, and does not have timely
information on all economic variables.
• Practice: In ation Targeting - in ation target (usually 2% plus a band and independence)
In ation Targeting (see also lecture notes #9)? • Most central banks in developed countries and as well as many in developing countries use so called
in ation targeting regime while conducting monetary policy.
• What is in ation targeting:
in ation target (usually 2% plus a band) working independence (not only declared) • Why?
transparency brings credibility anchors expectations solves (partially) the problems from the previous slide. • Why 2%?
in ation distorts the functioning of the informational role of the price system (recall 1st and 2nd welfare theorem) thus, in a frictionless world optimal in ation satis es the Friedman rule which calls for the nominal interest rates to be equal to zero (and implies de ation), but than there is no room for monetary expansion during recessions
12
Figure 11.13 Scatter Plot of the Price Level Versus the Relative Price of Energy for 1947–2009
11-33
© 2011 Pearson Addison-Wesley. All rights reserved.
return
Figure 11.14 A Decrease in the Supply of Credit Card Balances
11-35
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, return 13
Figure 11.15 A Shift in the Demand for Money
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, return
Figure 11.16 A Shift in the Demand for Money
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Figure 11.17 A Shift in the Output Demand Curve
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Figure 11.18 A Shift in the Output Supply Curve
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in a frictionless world (RBC world) this poses no problem in a world with nominal frictions (new Keynesian world) it implies deeper recessions not much experience with negative in ation and zero interest rate to see the results
deviation from the zero interest rate to 2% creates small costs of in ation (since it is a small deviation) and but oers room to smooth at least partially the business cycle uctuations (lower volatility) MiA: Should monetary policy respond to asset prices? • Higher in ation as it distorts the functioning of the informational role of the price system (recall 1st
and 2nd welfare theorem), so the central bank has well speci ed and justi ed goal.
• But, should it worry about asset prices? • It may aect the economy through either:
irrational exuberance ' nancial accelerator' eects (which amplify the eects of shocks to the economy through nancial market frictions • Bernanke and Gerlter (1999) nd that it should not react directly, and only if they aect in ation
expectations (indirectly)
• They nd that the optimal policy is exible in ation targeting (allows for short run deviations of
in ation from its target).
PoFC: Increase in the Monetary Base and the Fed's Balance Sheet • read it yourself
Summary • What is money? • Monetary intertemporal model. • Increase in money level in the frictionless model. • TFP shock in the frictionless model. • In ation targeting. • Assets prices and monetary policy.
Reading • Williamson, Chapter 10 without the monetary rule and the interest rate rule.
16
