2019-2020 { Econ 0039 { Advanced Macro Lecture 2: The ... · IClosed economy IThree markets : goods money Bonds IPrices are xed IOutput is determined by demand IEconomic agents consume,

2019-2020 – Econ 0039 – Advanced Macro

Lecture 2: The Liquidity Trap

Franck [email protected]

University College London

Version 1.027/01/2020

1 / 70

mailto:[email protected]

Disclaimer

These are the slides I am using in class. They are not self-contained, do not alwaysconstitute original material and do contain some “cut and paste” pieces from varioussources that might not always explicitly referring to (although I am trying to cite mysources as much as possible). Therefore, they are not intended to be used outside ofthe course nor to be distributed. Thank you for signalling me typos or mistakes [email protected].

2 / 70

mailto:[email protected]

0. Introduction

I What is the Liquidity Trap? A situation in which :

× the nominal interest rate i is zero,× the economy is in a recession,× monetary policy is ineffective because it cannot reduce i any further

I Why can’t i be negative: it is possible on bonds (i is a contractual arrangement)

I But then people will hold money, not bonds, because the nominal interest rate onmoney is zero

I Is it technically possible to make the nominal interest rate on money negative?

× melting money× A tax on checking accounts if there is only electronic money

I Otherwise, the demand for bonds would be zero if i is negative on bonds but zeroon money.

3 / 70

0. Introduction

I We first briefly review the liquidity trap in IS-LMI Then we look at facts to show that it is not a theoretical curiosity:

× the US in the 1930’s (Great Depression),× Japan in the 1990’s (Lost Decade),× the US and the UK after 2008 (Great Recession).

I Then we construct a micro-founded model that gives a rigorous treatment of theliquidity trap.

I We will see in particular that expectations are crucial to understand what is goingon.

4 / 70

1. IS-LMAssumptions

I Static model

I Closed economyI Three markets :

× goods× money× Bonds

I Prices are fixed

I Output is determined by demand

I Economic agents consume, invest and make portfolio decisions and decide to holdmoney and bonds.

5 / 70

1. IS-LMIS

I Consumption function C = C (Y − T ), 1 > C ′ > 0I Investment function I = I (i), I ′ < 0I i = r + πe , where πe is expected inflation (πe = 0 because prices are assumed to

be fixed)I G is givenI G + BG = T + M/P.I G , T , M and BG given, and satisfy the Gvt budget constraintI Equilibrium for income and expenditures: Income Y creates demand that is equal

to income:C + I + G = Y (IS)

I IS is downward sloping in the plane (Y , i)

C (Y − T ) + I (i) + G = Y (IS)

I Fully differentiating wrt Y and i , keeping fixed G and T : di = 1−C ′

I ′ dY6 / 70

1. IS-LM

Figure 1: The IS curve

7 / 70

1. IS-LMLM

I Money supply is given M/P

I Real money demand is L = L(Y , i) with L′Y > 0 and L′i < 0I L(Y , i) is derived from an arbitrage between money and bonds:

× when income is high, money is needed for transaction, so that economic agents usemore money (and less bonds) as a mean of savings,

× when i is high, the opportunity cost of holding money is high, so that agents holdless money (and more bonds)

× Equilibrium (on the money market):

L(Y , i) = M/P (LM)

× LM is upward sloping in the plane (Y , i)× Fully differentiating wrt Y and i , keeping fixed M/P :

di = −L′YL′i

dY

8 / 70

1. IS-LM

Figure 2: The LM curve

9 / 70

IS-LMEquilibrium

I Equilibrium is (Y ?, i?) such that

× Income generates a demand for goods equal to income× Money market clears× By Walras law, the bond market also clears

I The equilibrium is at the intersection of IS and LM

10 / 70

1. IS-LM

Figure 3: Equilibrium in IS-LM

11 / 70

IS-LMNegative demand shock and the role of expansionary policy

I Suppose that aggregate demand goes down

I For example investment goes down following a stock market crash such that thenew investment function is I (i) < I (i) ∀ i .

I This is likely to create a recessionI Expansionary monetary policy can restore a high Y equilibrium:

× Expansionary monetary policy (associate with debt reduction dM = dBG ) reduces i× a drop in i increases I× the increase in I has a multiplier effect

12 / 70

1. IS-LM

Figure 4: A negative shock to aggregate demand

13 / 70

1. IS-LM

Figure 5: Expansionary monetary policy

14 / 70

IS-LMThe liquidity trap

I Assume there is a level of i that is so low (say i ≈ 0) such that

× the demand for bonds is vey low (because the return is almost zero)× an increase in money supply cannot decrease any more i because all the money

distributed is kept in cash and -is not used to buy bonds

I In the IS-LM language, L′i → −∞ when i is at the Zero Lower Bound.

I Monetary policy cannot reduce i , and is therefore ineffective.

I If the government cannot run a deficit (because public debt is already high), thenthere is no possibility to eliminate the recessionary effect of a negative demandshock.

15 / 70

1. IS-LM

Figure 6: The liquidity trap

16 / 70

1. IS-LM


17 / 70

1. IS-LM


18 / 70

2. Facts

I We look at facts to show that the liquidity trap is not a theoretical curiosity:

× the US in the 1930’s (Great Depression),× Japan in the 1990’s (Lost Decade),× the US and the UK after 2008 (Great Recession).

19 / 70

2. Facts

I In all cases, we observe a similar pattern:

× Asset prices (stock market) crashes× nominal interest rate is almost zero× there is a recession in output× unemployment is high× there is a initial period of deflation (not prolonged for the 2008 recession)

20 / 70

2. FactsThe US Great Depression

Figure 9: Short-term interest rates

Figure 1

Short-Term Interest Rates

0

1

2

3

4

5

6

1922 1924 1926 1928 1930 1932 1934 1936 1938

Percent

Notes: Weekly data. The solid line denotes the yield on new issues of 3-month Treasurybills or equivalents. The dotted lines (from 1934 to 1937) reflect yields on new issues of6- and 9-month Treasury bills. Solid (dashed) vertical lines denote NBER peak (trough)dates.

28

The solid line denotes the yield on new issues of 3-month Treasury bills or equivalents. Thedotted lines (from 1934 to 1937) reflect yields on new issues of 6- and 9-month Treasury bills.

21 / 70


Figure 10: Equity prices (Dow Jones Index)

Figure 3

Prices in the 1920s and 1930s

Consumer and Producer Prices

60

70

80

90

100

110

120

1922 1924 1926 1928 1930 1932 1934 1936 1938

1929=100

CPI PPI

Equity Prices (Dow Jones Index)

0

50

100

150

200

250

300

350

400

1922 1924 1926 1928 1930 1932 1934 1936 1938

Notes: Solid (dashed) vertical lines denote NBER peak (trough) dates.

30

22 / 70


Figure 11: Industrial production

Figure 2

Economic Activity in the 1920s and 1930s

Industrial Production

50

60

70

80

90

100

110

120

1922 1924 1926 1928 1930 1932 1934 1936 1938

1929=100

Unemployment Rate

0

5

10

15

20

25

30

1922 1924 1926 1928 1930 1932 1934 1936 1938

Percent

Notes: The dotted line in the top panel shows a log-linear trend fitted over the 1922-1929period. In the bottom panel, two alternative available estimates of the unemployment ratefor this period are shown, the annual series by Lebergott (solid line) and a monthly seriesby the National Industrial Conference Board (dotted line). Solid (dashed) vertical linesdenote NBER peak (trough) dates.

29

23 / 70


Figure 12: Unemployment rate

Figure 2

Economic Activity in the 1920s and 1930s


50

60

70

80

90

100

110

120

1922 1924 1926 1928 1930 1932 1934 1936 1938

1929=100

Unemployment Rate

0

5

10

15

20

25

30

1922 1924 1926 1928 1930 1932 1934 1936 1938

Percent

Notes: The dotted line in the top panel shows a log-linear trend fitted over the 1922-1929period. In the bottom panel, two alternative available estimates of the unemployment ratefor this period are shown, the annual series by Lebergott (solid line) and a monthly seriesby the National Industrial Conference Board (dotted line). Solid (dashed) vertical linesdenote NBER peak (trough) dates.

29

24 / 70


Figure 13: Consumer and Producer Prices

Figure 3

Prices in the 1920s and 1930s

Consumer and Producer Prices

60

70

80

90

100

110

120

1922 1924 1926 1928 1930 1932 1934 1936 1938

1929=100

CPI PPI

Equity Prices (Dow Jones Index)

0

50

100

150

200

250

300

350

400

1922 1924 1926 1928 1930 1932 1934 1936 1938

Notes: Solid (dashed) vertical lines denote NBER peak (trough) dates.

30

25 / 70

2. FactsThe Japan’s lost decade of the 1990s

Figure 14: Overnight Interest rateFigure 5

Overnight Interest Rate: Japan

0

2

4

6

8

10

12

14

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Percent

32

26 / 70


Figure 15: Equity prices (Nikkei Index)

Figure 7

Inflation and Equity Prices in Japan since 1980

Inflation

-2

0

2

4

6

8

1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001

Percent

CPI Inflation (4 quarter growth)GDP-deflator Inflation (4 quarter growth)

Equity Prices (Nikkei)

10000

15000

20000

25000

30000

35000

40000

45000

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

3427 / 70


Figure 16: Industrial production

Figure 6

Economic Activity in Japan since 1980


70

80

90

100

110

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Unemployment Rate

2

3

4

5

6

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Percent

33

28 / 70


Figure 17: Unemployment rate

Figure 6

Economic Activity in Japan since 1980


70

80

90

100

110

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Unemployment Rate

2

3

4

5

6

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Percent

33

29 / 70


Figure 18: Inflation (CPI and GDP deflator)

Figure 7

Inflation and Equity Prices in Japan since 1980

Inflation

-2

0

2

4

6

8

1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001

Percent

CPI Inflation (4 quarter growth)GDP-deflator Inflation (4 quarter growth)

Equity Prices (Nikkei)

10000

15000

20000

25000

30000

35000

40000

45000

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

34

30 / 70

2. FactsThe Great Recession Figure 19: Short term interest rates

Monetary Policy at the Zero Lower Bound

2 BROOKINGS Hutchins Center on Fiscal and Monetary Policy

History Matters: Reassessing the Risk of the Zero Lower Bound

The events of the past six years have called into question some of the assumptions that went into previous research that found that episodes of hitting the ZLB would likely be relatively infrequent and short-lived. Chung et al. (2012) show that a wide range of modern macroeconomic forecasting models constructed based on postwar U.S. data predict that the probability of recent events, including multiple years stuck at the ZLB, is extremely remote—essentially nonexistent. The overwhelming falsification of this prediction can be interpreted in one of two ways. Either recent events represent an extraordinary run of horribly bad luck—a 100-year flood, if you will—or the models are badly misspecified, in particular with regard to their implications for negative tail risk.

Given the limited real-world empirical evidence on the frequency and severity of ZLB episodes, researchers have had to rely on artificial data generated by stochastic simulations of macroeconomic models to infer these probabilities and effects. Although the results depend on the details of the model specification and other assumptions, two key factors affect the simulated probability of hitting the ZLB and the resulting effects of the ZLB on the macroeconomy: (1) the size and (2) the duration of the shocks hitting the economy. If the shocks are assumed to be typically small, then the monetary policy response will be correspondingly small and the ZLB will rarely come into play. Similarly, if the shocks are assumed to be transitory, episodes of the ZLB will also tend to be short and will have relatively modest effects on the economy.

The standard approach in the research literature has been to estimate the shock processes based on historical data. They key issue is this: What data should one use? Lack of availability of consistent time series of data covering a very long time period and a concern that structural change has made data from long ago no longer relevant caused most researchers to focus on evidence on macroeconomic disturbances from the past twenty-five to fifty years. The advantage of this approach is that it provides consistent, reasonably accurate data for analysis. The downside to relying on data from recent decades is that a relatively small sample can provide a misleading view of the frequency of tail events. This is particularly

FIGURE 1. The ZLB: Not Just an Academic Concern

Sources: Board of Governors of the Federal Reserve System (2013); Organisation for Economic Co-operation and Development (OECD; 2013).

0

3

6

9

12

15

90 92 94 96 98 00 02 04 06 08 10 12

Federal Reserve

Bank of England

European Central Bank

Short-term Interest Rates Percent

Bank of Japan

Year

31 / 70

2. FactsThe US Great Recession Figure 20: Federal Fund Rate

32 / 70

2. FactsThe US Great Recession Figure 21: Equity prices

33 / 70

2. FactsThe US Great Recession Figure 22: Real GDP

34 / 70

2. FactsThe US Great Recession Figure 23: Unemployment rate

35 / 70

2. FactsThe US Great Recession Figure 24: Consumer Price Index)

36 / 70

2. FactsThe UK Great Recession Figure 25: 90-day Interbank Rate

37 / 70

2. FactsThe UK Great Recession Figure 26: Equity prices (Total Share Price Index)

38 / 70

2. FactsThe UK Great Recession Figure 27: Real GDP

39 / 70

2. FactsThe UK Great Recession Figure 28: Unemployment rate

40 / 70

2. FactsThe UK Great Recession Figure 29: Consumer Price Index

41 / 70

3. A Microfounded ModelThe model

I A model proposed by Paul Krugman (1998)

I It gives a general equilibrium with micro-foundations and dynamics to IS-LM

I Deterministic economy

I Closed economy

I One representative household

U =∞∑t=0

βtu(ct)

with 1 > β > 0 and u′(ct) > 0.

I Endowment economy: yt given

I The good is perishable

I Two assets : Money Mt and Bonds Bt

42 / 70

3. A Microfounded ModelThe model

I Cash in Advance constraintPtct ≤ Mt + Xt

I Xt : money creation in period tI Timing:

txt

43 / 70

3. A Microfounded ModelSolving for the household optimal behavior

I The Hh maximizes utility under a sequence of period t budget constraint and cashin advance constraint:

Bt+1 + Mt+1 + Ptct ≤ (1 + it)Bt + Mt + Ptyt + Xt (λt)

Ptct ≤ Mt + Xt (µt)

I X is newly created money distributed to Hh

I λ and µ are positive or nul Lagrange multipliers

44 / 70


I The Lagrangian is

L =∞∑t=0

βtu(ct)

+∞∑t=0

λt ((1 + it)Bt + Mt + Ptyt + Xt − Bt+1 −Mt+1 − Ptct)

+∞∑t=0

µt (Mt + Xt − Ptct)

45 / 70


I and FOC are ∀ t ≥ 0

w.r.t. ct : βtu′(ct) = (µt + λt)Pt

w.r.t. Bt+1 : λt = (1 + it+1)λt+1

w.r.t. Mt+1 : λt = λt+1 + µt+1

slackness : µt(Mt + Xt − Ptct) = 0positivity : µt ≥ 0

slackness : λt

((1 + it)Bt + Mt + Ptyt

+Xt − Bt+1 −Mt+1 − PtCt

)= 0

positivity : λt ≥ 0

46 / 70


Proposition 1

The budget constraint always binds and λt > 0 ∀t

Proof : Assume λt = 0. Then the third FOC implies λt+1 + µt+1 = 0. As multipliersare positive or nul, this implies λt+1 = µt+1 = 0. Therefore, the first FOC in t + 1implies βt+1u′(ct+1) = 0. This is not possible because u′(c) > 0. Therefore λt = 0 isnot possible, so that λt > 0 for all t.

47 / 70


I From the FOCs: Take λt = λt+1 + µt+1 ⇐⇒ λt−1 = λt + µt , and replace inβtu′(ct) = (µt + λt)Pt to obtain λt−1 = βtu′(ct)/Pt

I Now take λt = (1 + it+1)λt+1 and rewrite it as λt−1 = (1 + it)λt . Replace λt−1by βtu′(ct)/Pt and λt by βt+1u′(ct+1)/Pt+1 to obtain

βtu′(ct)/Pt = (1 + it)βt+1u′(ct+1)/Pt+1.

Rearrange terms to obtain

1 + it =

(u′(ct)

βu′(ct+1)

)︸︷︷︸

1+rt

(Pt+1

Pt

)

48 / 70


Proposition 2

If it = 0, then µt = 0. If it > 0, then µt > 0

Proof : Take the FOC λt−1 = (1 + it)λt . If it = 0, then λt−1 = λt . If it > 0, thenλt−1 > λt .Take the FOC λt−1 = λt + µt . If λt−1 = λt , then µt = 0. If λt−1 > λt , then µt > 0.

I Then from the slackness condition µt(Mt + Xt − Ptct) = 0, we obtain:

I If it > 0, then the CIA constraint binds:

Ptct = Mt + Xt

I If it = 0, then µt = 0 : the CIA constraint may not be binding : Hh is indifferentbetween money and bonds.

49 / 70

3. A Microfounded ModelEquilibrium with flexible prices

I All agents are identical (representative household) The equilibrium on the bondmarket is

Bt = 0

I Money market equilibrium:Mt+1 = Mt + Xt

I Good market equilibriumct = yt

I Remark : the equilibrium quantities can be determined without using the FOC

I The FOC are determining equilibrium prices, i.e. the prices P and i such thatmarkets clear.

50 / 70

3. A Microfounded ModelEquilibrium with flexible prices

I In what follows, we restrict to a specific case:

× Period 0: y0 = y?, M0 = M?, X0 6= 0 if money creation.× Period 1: y1 = y?, M1 = M? ⇔ X1 = −X0 if money creation.× for t ≥ 1, yt = y?, Mt = M?, Xt = 0.

I When money is created in period ), it is only for one period it is destroyed inperiod 1.

I We can the solve the model in the following way

× Solve for period 1 and onwards× Solve for period 0

51 / 70

3. A Microfounded ModelEquilibrium with flexible prices - Period 1 and onwards

I ct = yt = y? implies

1 + r? =1

β> 1

such that r? > 0I Let us guess an equilibrium in which the CIA constraint binds:

P? =M?

y?

I In such a case,

1 + it =(1 + rt)Pt+1

Pt

I implies

1 + i? =(1 + r?)P?

P?= 1 + r?

I Therefore i? = r? > 0I Because i? > 0, the CIA binds, so that our guess was correct.

52 / 70

3. A Microfounded ModelEquilibrium with flexible prices - Period 0

I Assume for analytical tractability that u(c) = log c

I The equilibrium in period t ≥ 1 is therefore c? = y?, i? = r? = 1/β − 1,P? = M?/y?

I The equilibrium (i0,P0) in period 0 is given by the equations:

c0 = y?

i0 =y?

βy0

P?

P0− 1

P0 =M? + X0

y0if i0 > 0

P0 = P if i0 = 0

I where we have to define P

I P?

P0− 1 represents inflation between period 0 and period 1.

53 / 70


Figure 30: Equilibrium in period 0 - Flexible prices

is Po=M°y*

i. - -¥• DP

Po To io=tppP÷ . 1

i¥exzgE*⇒ Xo-- o )

54 / 70


I How does the model works?

I Suppose an increase in money supply today X0 > 0

I Prices today P0 increase

I As P? is given, inflation between and tomorrow is reduced.

I Because consumption is independent of monetary policy, c = y and the realinterest rate stays constant

I Therefore, the decrease in inflation decreases i

I Note that money is neutral

I Important : the above analysis is true as long as P0 < P, such that i > 0 and theCIA binds.

55 / 70


Figure 31: Equilibrium in period 0 - Flexible prices

D= Md .

isy*

Mot

i. - -¥(D

- - - - . --

- - .

• DP

Po To io=tppp÷ -1- D

nqmommanigqaq.mg

÷ xoxo

Bahia

56 / 70

3. A Microfounded ModelEquilibrium with flexible prices - Period 0 - The liquidity trap

I Consider the money creation X such that P0 = P and i0 = 0Figure 32: Equilibrium in period 0 - Flexible prices - M = M

D= td F=Iis

y*y*

i. - -¥• DP

Po To io=tppp÷ . 1

: *oEaaqfiqE

-

57 / 70


I Consider the money creation X such that P0 = P and i0 = 0

I What does happen if money creatioon is X > X?

I If P0 increases above P, then i0 < 0 which is not possible.

I Therefore, we must have i0 = 0, and then P0 = P

I As i0 = 0, the CIA does not bind

I All the increase in money supply is kept in money (not put in bonds), without anyimpact on the nominal interest rate i0.

58 / 70


Figure 33: Equilibrium in period 0 – Flexible prices – M0 = M? + X

is pansy Ftny Ff > F

- D

io - -€• DP

Po To io=fpp÷ -1

:MEEEEmqizEE.EE#GEGggp

59 / 70


I Remark : In the liquidity trap with flexible prices, money cannot reduce inflationbelow P?

P(which is actually deflation)

I But money is always neutral ... so that we do not care much about the liquiditytrap.

I Things will be different if we assume, as in IS-LM, that prices are fixed in period 0.

60 / 70

3. A Microfounded ModelEquilibrium with fix prices - Period 0

I Assume first that i0 > 0, so that the economy is not in the liquidity trap andX0 = 0.

I As the CIA constraints binds, we have P0c0 = M0 ,with c ≤ y

I Monetary policy now determines c0 as P0 is fixed

I Assume that M0 is “small”.

61 / 70


Figure 34: Equilibrium in period 0 - Fix prices

is Co=M÷

i. - -¥. •

DCco y*

io=tpd÷÷f÷-1

I •

B

Po larger

62 / 70


I The economy is in a configuration similar to IS-LM

I As c0 < y?, the equilibrium is inefficient (an amount y? − c0 of goods is wasted)

I Assume money creation X0 > 0 : to clear the money market, i0 needs to go down.As inflation is fixed, there real interest rate must decrease, which is achieved byan increase in c0.

63 / 70


Figure 35: Equilibrium in period 0 - Fix prices - Monetary policy is effective

Co --M= Co =tIis

po%

- .

i. - -¥. •

DCco

⇐y*io=tpbf÷÷¥÷-1

ia¥.

BBB

•

B

64 / 70

3. A Microfounded ModelEquilibrium with fix prices - Period 0 - The liquidity trap

I Now assume that P0 is large, such that B < y?.

I Do “large” money creation X0.

I The economy enters a liquidity trap

I The CIA is not binding anymore: the money increases will not decrease i0I The economy is stuck at c0 < y? and monetary policy is ineffective.

I For a money creation X0 > X0, no increase in co

65 / 70

3. A Microfounded ModelEquilibrium with fix prices - Period 0 - The liquidity trap


Co = MI

Co=Mois pPo °

io - --

- . - . - - \. •

p

DCCo co Y*iota

:÷÷÷t

- *zgtfo

-

ra

B

66 / 70

3. A Microfounded ModelEquilibrium with fix prices - Period 0 - The liquidity trap - Monetary policy is ineffective


co =M°_ Co=MI nonis p -

Po °

Po

io - -€. •

p

DCCo co Y*iota

:÷÷÷t

i.BE÷zE-

-MB

67 / 70

4. Effective policy in the liquidity trapManipulating expectations: “committing to be irresponsible”

I If the Central Bank can raise the inflation expectations of the agents (P?/P0) bybeing credible to creat money tomorrow:

I X1 > 0 s.t. Mt = M? + X1 ∀t ≥ 1,

I Then there will be an increase in the nominal interest rate today i0,

I and it is therefore possible to create money today˜X and close the gap between c

and y .

68 / 70

4. Effective policy in the liquidity trapManipulating expectations: “committing to be irresponsible”

Figure 38: Equilibrium in period 0 - Fix prices - increasing M and committing to increase M?

is Co=M÷

-

Nos MOP

/

io - --

. . - . - - • T *.e. - - -. -

-- - - - -

--

- -

• io=tsts÷P¥t•

(co

"

io=;d:÷p÷t'Y*÷s

[email protected]

69 / 70

5. References

I Blanchard, O., A. Amighini and F. Giavazzi, 2010, “Macroeconomics, A Europeanperspective”, Chapter 5, “Goods and Financial Markets: The IS-LM Model”

I J. Hicks, 1937, ”Mr. Keynes and the ”Classics”; A Suggested Interpretation”,Econometrica, Vol. 5, No. 2.

I P. Krugman, 1998, “It’s Baaack: Japan’s Slump and the Return of the LiquidityTrap”, Brookings Papers on Economic Activity, Vol. 29

I A. Orphanides, 2004, “Monetary policy in deflation: the liquidity trap in historyand practice”, The North American Journal of Economics and Finance, Volume15, Issue 1.

70 / 70

Documents

2019-2020 { Econ 0039 { Advanced Macro Lecture 2: The ... · IClosed economy IThree markets : goods money Bonds IPrices are xed IOutput is determined by demand IEconomic agents consume,