Econ 3029 Advanced Macro. Lecture 2: The Liquidity Trap

Transcription

1 Econ 3029 Advanced Macro Lecture 2: The Liquidity Trap Franck Portier University College London Version /01/2018 Changes from version 1.0 are in red 1 / 73

2 Disclaimer These are the slides I am using in class. They are not self-contained, do not always constitute original material and do contain some cut and paste pieces from various sources that might not always explicitly referring to (although I am trying to cite my sources as much as possible). Therefore, they are not intended to be used outside of the course nor to be distributed. Thank you for signalling me typos or mistakes at F.Portier@UCL.ac.uk. 2 / 73

3 0. Introduction 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 inefficient because it cannot reduce i any further Why can t i be negative: it is possible on bonds (i is a contractual arrangement) But then people will hold money, not bonds, because the nominal interest rate on money is zero 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 Otherwise, the demand for bonds would be zero if i is negative on bonds but zero on money. 3 / 73

4 0. Introduction We first briefly review the liquidity trap in IS-LM 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). Then we construct a micro-founded model that gives a rigorous treatment of the liquidity trap. We will see in particular that expectations are crucial to understand what is going on. 4 / 73

5 1. IS-LM Assumptions Static model Closed economy Three markets : goods money Bonds Prices are fixed Output is determined by demand Economic agents consume, invest and make portfolio decisions and decide to hold money and bonds. 5 / 73

6 1. IS-LM IS Consumption function C = C(Y T ), 1 > C > 0 Investment function I = I (i), I < 0 i = r + π, where π is inflation (π = 0 because prices are assumed to be fixed) G is given G + B G = T + M/P. G, T, M and B G given, and satisfy the Gvt budget constraint Equilibrium for income and expenditures: Income Y creates demand that is equal to income: C + I + G = Y (IS) IS is downward sloping in the plane (Y, i) C(Y T ) + I (i) + G = Y Fully differentiating wrt Y and i, keeping fixed G and T : di = 1 C I dy (IS) 6 / 73

7 1. IS-LM Figure 1: The IS curve 7 / 73

8 1. IS-LM LM Money supply is given M/P Real money demand is L = L(Y, i) with L Y > 0 and L i < 0 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 use more money (and less bonds) as a mean of savings, when i is high, the opportunity cost of holding money is high, so that agents hold less 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 Y L dy i 8 / 73

9 1. IS-LM Figure 2: The LM curve 9 / 73

10 IS-LM Equilibrium 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 The equilibrium is at the intersection of IS and LM 10 / 73

11 1. IS-LM Figure 3: Equilibrium in IS-LM 11 / 73

12 IS-LM Negative demand shock and the role of expansionary policy Suppose that aggregate demand goes down For example investment goes down following a stock market crash such that the new investment function is Î (i) < I (i) i. This is likely to create a recession Expansionary monetary policy can restore a high Y equilibrium: Expansionary monetary policy (associate with debt reduction dm = db G ) reduces i a drop in i increases I the increase in I has a multiplier effect 12 / 73

13 1. IS-LM Figure 4: A negative shock to aggregate demand 13 / 73

14 1. IS-LM Figure 5: Expansionary monetary policy 14 / 73

15 IS-LM The liquidity trap 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 In the IS-LM language, L i + when i is at the Zero Lower Bound. Monetary policy cannot reduce i, and is therefore inefficient. If the government cannot run a deficit (because public debt is already high), then there is no possibility to eliminate the recessionary effect of a negative demand shock. 15 / 73

16 1. IS-LM Figure 6: The liquidity trap 16 / 73

17 1. IS-LM Figure 7: The liquidity trap 17 / 73

18 1. IS-LM Figure 8: The liquidity trap 18 / 73

19 2. Facts 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 / 73

20 2. Facts 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 / 73

21 2. Facts The US Great Depression Figure 1 Short-Term Interest Rates Figure 9: Short-term interest rates 6 Percent The solid line denotes the yield on new issues of 3-month Treasury bills or equivalents. The dotted lines (from 1934 to 1937) reflect yields on new issues of 6- and 9-month Treasury bills. Notes: Weekly data. The solid line denotes the yield on new issues of 3-month Treasury bills or equivalents. The dotted lines (from 1934 to 1937) reflect yields on new issues of 6- and 9-month Treasury bills. Solid (dashed) vertical lines denote NBER peak (trough) dates. 21 / 73

22 2. Facts The US Great Depression Figure 10: Equity prices (Dow Jones Index) Equity Prices (Dow Jones Index) Notes: Solid (dashed) vertical lines denote NBER peak (trough) dates. 22 / 73

23 2. Facts The US Great Depression Figure 2 Economic Activity in the 1920s and 1930s Figure 11: Industrial production Industrial Production 1929= Unemployment Rate 23 / 73

24 2. Facts The US Great Depression Percent FigureUnemployment 12: Unemployment Rate rate Notes: The dotted line in the top panel shows a log-linear trend fitted over the / 73

25 2. Facts The US Great Depression Figure 3 Prices in the 1920s and 1930s Figure 13: Consumer and Producer Prices Consumer and Producer Prices 1929= CPI PPI Equity Prices (Dow Jones Index) 25 / 73

26 2. Facts The Japan s lost decade of the 1990s Figure 5 Figure 14: Overnight Interest rate Overnight Interest Rate: Japan Percent / 73

27 2. Facts The Japan s lost decade of the 1990s Figure 15: Equity prices (Nikkei Index) Equity Prices (Nikkei) / 73

28 2. Facts The Japan s lost decade of the 1990s 110 Figure 6 Economic Activity in Japan since 1980 Figure 16: Industrial production Industrial Production Unemployment Rate 28 / 73

29 2. Facts The Japan s lost decade of the 1990s Percent 6 Figure 17: Unemployment rate Unemployment Rate / 73

30 2. Facts Figure 7 The Japan s lost decade of the 1990s Inflation and Equity Prices in Japan since 1980 Figure 18: Inflation (CPI and GDP deflator) Inflation Percent 8 CPI Inflation (4 quarter growth) GDP-deflator Inflation (4 quarter growth) / 73

31 2. Facts The Great Recession Monetary Policy at the Zero Lower Bound Figure 19: Short term interest rates FIGURE 1. The ZLB: Not Just an Academic Concern Short-term Interest Rates Percent 15 Federal Reserve Bank of England European Central Bank Bank of Japan Year / 73

32 2. Facts The US Great Recession Figure 20: Federal Fund Rate 32 / 73

33 2. Facts The US Great Recession Figure 21: Equity prices 33 / 73

34 2. Facts The US Great Recession Figure 22: Real GDP 34 / 73

35 2. Facts The US Great Recession Figure 23: Unemployment rate 35 / 73

36 2. Facts The US Great Recession Figure 24: Consumer Price Index) 36 / 73

37 2. Facts The UK Great Recession Figure 25: 90-day Interbank Rate 37 / 73

38 2. Facts The UK Great Recession Figure 26: Equity prices (Total Share Price Index) 38 / 73

39 2. Facts The UK Great Recession Figure 27: Real GDP 39 / 73

40 2. Facts The UK Great Recession Figure 28: Unemployment rate 40 / 73

41 2. Facts The UK Great Recession Figure 29: Consumer Price Index 41 / 73

42 3. A Microfounded Model The model A model proposed by Paul Krugman (1998) It gives a general equilibrium with micro-foundations and dynamics to IS-LM Deterministic economy One representative household with 1 > β > 0 and u (c t ) > 0. Endowment economy: y t given The good is perishable U = Two assets : Money M t and Bonds B t β t u(c t ) t=0 42 / 73

43 3. A Microfounded Model The model Cash in Advance constraint P t c t M t Timing: 43 / 73

44 3. A Microfounded Model Solving for the household optimal behavior The Hh maximizes utility under a sequence of period t budget constraint and cash in advance constraint: B t+1 + M t+1 + P t c t (1 + i t )B t + M t + P t y t + X t (λ t ) X is newly created money distributed to Hh λ and µ are positive or nul Lagrange multipliers P t c t M t (µ t ) 44 / 73

45 3. A Microfounded Model Solving for the household optimal behavior The Lagrangian is L = + + β t u(c t ) t=0 λ t ((1 + i t )B t + M t + P t y t + X t B t+1 M t+1 P t c t ) t=0 µ t (M t P t c t ) t=0 45 / 73

46 3. A Microfounded Model Solving for the household optimal behavior and FOC are t 0 w.r.t. c t : β t u (c t ) = (µ t + λ t )P t w.r.t. B t+1 : λ t = (1 + i t+1 )λ t+1 w.r.t. M t+1 : λ t = λ t+1 + µ t+1 slackness : µ t (M t P t c t ) = 0 positivity : µ t 0 slackness : λ t ((1 + i t )B t + M t + P t y t +X t B t+1 M t+1 P t C t ) = 0 positivity : λ t 0 46 / 73

47 3. A Microfounded Model Solving for the household optimal behavior Proposition 1 The budget constraint always binds and λ t > 0 t Proof : Assume λ t = 0. Then the third FOC implies λ t+1 + µ t+1 = 0. As multipliers are positive or nul, this implies λ t+1 = µ t+1 = 0. Therefore, the first FOC in t + 1 implies β t+1 u (c t+1 ) = 0. This is not possible because u (c) > 0. Therefore λ t = 0 is not possible, so that λ t > 0 for all t. 47 / 73

48 3. A Microfounded Model Solving for the household optimal behavior Which gives (see details in class) ( u ) (c t ) 1 + i t = βu (c t+1 }{{} 1+r t ( Pt+1 P t P t c t = M t if i t > 0 If i t = 0, then µ t = 0 : the CIA constraint may not be binding : Hh is indifferent between money and bonds. ) 48 / 73

49 3. A Microfounded Model Equilibrium with flexible prices All agents are identical (representative household) The equilibrium on the bond market is B t = 0 Money market equilibrium: Good market equilibrium M t+1 = M t + X t c t = y t Remark : the equilibrium quantities can be determined without using the FOC The FOC are determining equilibrium prices, i.e. the prices P and i such that markets clear. 49 / 73

50 3. A Microfounded Model Equilibrium with flexible prices In what follows, we restrict to a specific case: for t 1, y t = y, M t = M. Period 0: y, M 0. We can the solve the model in the following way Solve for period 1 and onwards Solve for period 0 50 / 73

51 3. A Microfounded Model Equilibrium with flexible prices - Period 1 and onwards c t = y t = y implies 1 + r = 1 β > 1 such that r > 0 Let us guess an equilibrium in which the CIA constraint binds: In such a case, implies P = M y 1 + i t = (1 + r t)p t+1 P t 1 + i = (1 + r )P P = 1 + r Therefore i = r > 0 Because i > 0, the CIA binds, so that our guess was correct. 51 / 73

52 3. A Microfounded Model Equilibrium with flexible prices - Period 0 The equilibrium in period t 1 is therefore c = y, i = r = 1/β, P = M /y The equilibrium (i 0, P 0 ) in period 0 is given by the equations: where we have to define P c 0 = y i 0 = y βy 0 P P 0 1 P 0 = M 0 y 0 if i > 0 P 0 = P if i = 0 P P 0 1 represents inflation between period 0 and period / 73

53 - 3. A Microfounded Model Equilibrium with flexible prices - Period 0 Figure 30: Equilibrium in period 0 - Flexible prices is Po=M y* i. - DP Po To io=tppp / 73

54 3. A Microfounded Model Equilibrium with flexible prices - Period 0 How does the model works? Suppose an increase in money supply today M Prices today P increase As P is given, inflation is reduced. Because consumption is independent of monetary policy, c = y and the real interest rate stays constant Therefore, the decrease in inflation decreases i Note that money is neutral Important : the above analysis is true as long as P > P, such that i > 0 and the CIA binds. 54 / 73

55 A Microfounded Model Equilibrium with flexible prices - Period 0 Figure 31: Equilibrium in period 0 - Flexible prices is D= Md. y* Mot i. - ( D - DP Po - D To io=tppp / 73

56 - 3. A Microfounded Model Equilibrium with flexible prices - Period 0 - The liquidity trap Consider the money supply M such that P = P and i = 0 Figure 32: Equilibrium in period 0 - Flexible prices - M = M is D= td F=I y* y* i. - DP Po To io=tppp / 73

57 3. A Microfounded Model Equilibrium with flexible prices - Period 0 - The liquidity trap Consider the money supply M such that P = P and i = 0 What does happen if M increases above M to the level M If P increases above P, then i < 0 which is not possible. Therefore, we must have i = 0, and then P = P As i = 0, the CIA does not bind All the increase in money supply is kept in money (not put in bonds), without any impact on the nominal interest rate i. 57 / 73

58 - 3. A Microfounded Model Equilibrium with flexible prices - Period 0 - The liquidity trap Figure 33: Equilibrium in period 0 - Flexible prices - M = M is pansy Ftny Ff > F - D io - DP Po To io=fpp / 73

59 3. A Microfounded Model Equilibrium with flexible prices - Period 0 - The liquidity trap Remark : In the liquidity trap with flexible prices, money cannot reduce inflation below P (which is actually deflation) P But money is always neutral... so that we do not care much about the liquidity trap. Things will be different if we assume, as in IS-LM, that prices are fixed in period / 73

60 3. A Microfounded Model Equilibrium with fix prices - Period 0 Assume first that i > 0, so that the economy is not in the liquidity trap. As the CIA constraints binds, we have Pc = M,with c y Monetary policy now determines c as P is fixed 60 / 73

61 3. A Microfounded Model Equilibrium with fix prices - Period 0 Figure 34: Equilibrium in period 0 - Fix prices is Co=M io=tpd f - i. -. DC co y* / 73

62 3. A Microfounded Model Equilibrium with fix prices - Period 0 The economy is in a configuration similar to IS-LM As c < y, the equilibrium is inefficient (an amount y c of goods is wasted) Assume an increase in M, for given M : to clear the money market, i needs to go down. As inflation is fixed, there real interest rate must decrease, which is achieved by an increase in c. 62 / 73

63 3. A Microfounded Model Equilibrium with fix prices - Period 0 Figure 35: Equilibrium in period 0 - Fix prices - Monetary policy is efficient is Co --M= po Co =ti % -. io=tpbf y* - i. -. DC co / 73

64 3. A Microfounded Model Equilibrium with fix prices - Period 0 - The liquidity trap Now assume that M = M such that i = 0 The economy enters a liquidity trap The CIA is not binding anymore: the money increases will not decrease i The economy is stuck at c < y and monetary policy is inefficient. For a money supply M, no increase in c 64 / 73

65 A Microfounded Model Equilibrium with fix prices - Period 0 - The liquidity trap Figure 36: Equilibrium in period 0 - Fix prices s Co = MI p Po Co=Moi - io \. DCp Co co Y* iota: t 65 / 73

66 -. 3. A Microfounded Model Equilibrium with fix prices - Period 0 - The liquidity trap - Monetary policy is inefficient Figure 37: Equilibrium in period 0 - Fix prices is co =M _ Co=MI non p - Po Po io - DCp Co co Y* iota: t 66 / 73

67 4. Effective policy in the liquidity trap Manipulating expectations: committing to be irresponsible If the Central Bank can raise the inflation expectations of the agents (P /P) by being credible to increase M tomorrow, Then in increases the nominal interest rate today, and it is therefore possible to increase M and close the gap between c and y. 67 / 73

68 / " Effective policy in the liquidity trap Manipulating 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=;d: p t 'Y* -. - e. co io=tsts P t T * ( 68 / 73

69 4. Effective policy in the liquidity trap Fiscal policy Assume now that the government taxes agents using lump sum tax and spends on goods, g in period 0 and g = 0 after. Assume that g is a pure waste of goods Also a Cash-In-Advance constraint for the government Consider first the flex price case Total demand in now y = c + g, and consumption is therefore c = y g The equilibrium equations become: i = y P β(y 1 g) P 0 P = M y if i > 0 P = P if i = 0 When g > 0, the nominal interest curve is shifted up. 69 / 73

70 4. Effective policy in the liquidity trap Fiscal policy Figure 39: Equilibrium in period 0 - Euler Equation - comparison between g = 0 and g > 0 is µ D F n tpy gf ' P F is'pf p i ' 70 / 73

71 4. Effective policy in the liquidity trap Fiscal policy Assume that the economy is in the liquidity trap with fix prices Fiscal policy will push up the nominal interest rate by decreasing c This will make the CIA constraint binding and c will increase. 71 / 73

72 4. Effective policy in the liquidity trap Fiscal policy Figure 40: Equilibrium in period 0 - Fix prices - Fiscal policy in the liquidity trap R.IO Po=I is co e " "=y&g i e g %=g[fg ' DC. Co G ' co,. g* 72 / 73

73 5. References J. Hicks, 1937, Mr. Keynes and the Classics ; A Suggested Interpretation, Econometrica, Vol. 5, No. 2. P. Krugman, 1998, It s Baaack: Japan s Slump and the Return of the Liquidity Trap, Brookings Papers on Economic Activity, Vol. 29 A. Orphanides, 2004, Monetary policy in deflation: the liquidity trap in history and practice, The North American Journal of Economics and Finance, Volume 15, Issue / 73