The Transmission of Monetary Policy Operations through Redistributions and Durable Purchases

Transcription

1 The Transmission of Monetary Policy Operations through Redistributions and Durable Purchases Vincent Sterk and Silvana Tenreyro UCL, LSE June 2014 Sterk and Tenreyro (UCL, LSE) OMO June / 52

2 The Monetary Transmission Mechanism Workhorse models of monetary policy: are centred on nominal rigidities (New Keynesian model) Sterk and Tenreyro (UCL, LSE) OMO June / 52

3 The Monetary Transmission Mechanism Workhorse models of monetary policy: are centred on nominal rigidities (New Keynesian model) abstract from redistributional effects (representative agent) Sterk and Tenreyro (UCL, LSE) OMO June / 52

4 The Monetary Transmission Mechanism Workhorse models of monetary policy: are centred on nominal rigidities (New Keynesian model) abstract from redistributional effects (representative agent) are typically not explicit about implementation of monetary policy (interest rate rules) Sterk and Tenreyro (UCL, LSE) OMO June / 52

5 This paper Study alternative channel of monetary transmission. Simple DSGE model no sticky prices or wages Sterk and Tenreyro (UCL, LSE) OMO June / 52

6 This paper Study alternative channel of monetary transmission. Simple DSGE model no sticky prices or wages integrate later Sterk and Tenreyro (UCL, LSE) OMO June / 52

7 This paper Study alternative channel of monetary transmission. Simple DSGE model no sticky prices or wages integrate later heterogeneous households Sterk and Tenreyro (UCL, LSE) OMO June / 52

8 This paper Study alternative channel of monetary transmission. Simple DSGE model no sticky prices or wages integrate later heterogeneous households parsimonious life-cycle structure; nests representative agent Sterk and Tenreyro (UCL, LSE) OMO June / 52

9 This paper Study alternative channel of monetary transmission. Simple DSGE model no sticky prices or wages integrate later heterogeneous households parsimonious life-cycle structure; nests representative agent monetary policy implemented through open market operations (OMO) Sterk and Tenreyro (UCL, LSE) OMO June / 52

10 This paper Study alternative channel of monetary transmission. Simple DSGE model no sticky prices or wages integrate later heterogeneous households parsimonious life-cycle structure; nests representative agent monetary policy implemented through open market operations (OMO) a given path for the nominal interest rate can have different effects Sterk and Tenreyro (UCL, LSE) OMO June / 52

11 This paper Study alternative channel of monetary transmission. Simple DSGE model no sticky prices or wages heterogeneous households monetary policy implemented through open market operations (OMO) Compare model dynamics to evidence from structural VAR non-durable and durable goods Sterk and Tenreyro (UCL, LSE) OMO June / 52

12 This paper Study alternative channel of monetary transmission. Simple DSGE model no sticky prices or wages heterogeneous households monetary policy implemented through open market operations (OMO) Compare model dynamics to evidence from structural VAR non-durable and durable goods key role for durables Sterk and Tenreyro (UCL, LSE) OMO June / 52

13 Monetary policy implementation Open Market Operation (OMO): central bank sells/buys short-term bonds Modern practice: main tool used for monetary policy Sterk and Tenreyro (UCL, LSE) OMO June / 52

14 Monetary policy implementation Open Market Operation (OMO): central bank sells/buys short-term bonds Modern practice: main tool used for monetary policy more sophisticated OMOs since financial crisis (longer-term securities, agency-debt, etc.) Sterk and Tenreyro (UCL, LSE) OMO June / 52

15 Monetary policy implementation Open Market Operation (OMO): central bank sells/buys short-term bonds Modern practice: main tool used for monetary policy more sophisticated OMOs since financial crisis (longer-term securities, agency-debt, etc.) Theoretical literature: irrelevance results found in: Sterk and Tenreyro (UCL, LSE) OMO June / 52

16 Monetary policy implementation Open Market Operation (OMO): central bank sells/buys short-term bonds Modern practice: main tool used for monetary policy more sophisticated OMOs since financial crisis (longer-term securities, agency-debt, etc.) Theoretical literature: irrelevance results found in: Wallace (1981), Sargent & Smith (1982), Sterk and Tenreyro (UCL, LSE) OMO June / 52

17 Monetary policy implementation Open Market Operation (OMO): central bank sells/buys short-term bonds Modern practice: main tool used for monetary policy more sophisticated OMOs since financial crisis (longer-term securities, agency-debt, etc.) Theoretical literature: irrelevance results found in: Wallace (1981), Sargent & Smith (1982), Eggertsson & Woodford (2003), Woodford (2011)... Sterk and Tenreyro (UCL, LSE) OMO June / 52

18 Monetary policy implementation Open Market Operation (OMO): central bank sells/buys short-term bonds Modern practice: main tool used for monetary policy more sophisticated OMOs since financial crisis (longer-term securities, agency-debt, etc.) Theoretical literature: irrelevance results found in: Wallace (1981), Sargent & Smith (1982), Eggertsson & Woodford (2003), Woodford (2011)......but all of the above rule out redistributional effects Sterk and Tenreyro (UCL, LSE) OMO June / 52

19 Monetary policy implementation Helicopter drop: increase in the money supply used to finance increase in government transfers Modern practice: rarely used Sterk and Tenreyro (UCL, LSE) OMO June / 52

20 Monetary policy implementation Helicopter drop: increase in the money supply used to finance increase in government transfers Modern practice: rarely used Theoretical literature: often used in models with cash-in-advance constraints or money-in-the-utility. Sterk and Tenreyro (UCL, LSE) OMO June / 52

21 Monetary policy implementation Helicopter drop: increase in the money supply used to finance increase in government transfers Modern practice: rarely used Theoretical literature: often used in models with cash-in-advance constraints or money-in-the-utility. (near-) zero effects on real activity found in flex-price models of Sidrauski (1967), Fischer (1979), Walsh (2003)... Sterk and Tenreyro (UCL, LSE) OMO June / 52

22 Monetary policy implementation Helicopter drop: increase in the money supply used to finance increase in government transfers Modern practice: rarely used Theoretical literature: often used in models with cash-in-advance constraints or money-in-the-utility. (near-) zero effects on real activity found in flex-price models of Sidrauski (1967), Fischer (1979), Walsh (2003)......motivated introduction of goods/labor market frictions (nominal rigidities)... Sterk and Tenreyro (UCL, LSE) OMO June / 52

23 Monetary policy implementation Helicopter drop: increase in the money supply used to finance increase in government transfers Modern practice: rarely used Theoretical literature: often used in models with cash-in-advance constraints or money-in-the-utility. (near-) zero effects on real activity found in flex-price models of Sidrauski (1967), Fischer (1979), Walsh (2003)......motivated introduction of goods/labor market frictions (nominal rigidities)......but again, the above references abstract from redistributional effects Sterk and Tenreyro (UCL, LSE) OMO June / 52

24 Monetary policy implementation Helicopter drop: increase in the money supply used to finance increase in government transfers Modern practice: rarely used Theoretical literature: often used in models with cash-in-advance constraints or money-in-the-utility. (near-) zero effects on real activity found in flex-price models of Sidrauski (1967), Fischer (1979), Walsh (2003)......motivated introduction of goods/labor market frictions (nominal rigidities)......but again, the above references abstract from redistributional effects Two interventions (OMO vs Heli) can generate a similar path for interest rates and yet have different effects Sterk and Tenreyro (UCL, LSE) OMO June / 52

25 The transmission channel in our model - preview Expansionary OMO triggers: an increase in prices, surprise destruction of nominal private wealth Sterk and Tenreyro (UCL, LSE) OMO June / 52

26 The transmission channel in our model - preview Expansionary OMO triggers: an increase in prices, surprise destruction of nominal private wealth a negative wealth effect for households, particularly old Sterk and Tenreyro (UCL, LSE) OMO June / 52

27 The transmission channel in our model - preview Expansionary OMO triggers: an increase in prices, surprise destruction of nominal private wealth a negative wealth effect for households, particularly old impaired life-cycle consumption smoothing Sterk and Tenreyro (UCL, LSE) OMO June / 52

28 The transmission channel in our model - preview Expansionary OMO triggers: an increase in prices, surprise destruction of nominal private wealth a negative wealth effect for households, particularly old impaired life-cycle consumption smoothing increased incentive to work/save for retirement lower real interest rate Sterk and Tenreyro (UCL, LSE) OMO June / 52

29 The transmission channel in our model - preview Expansionary OMO triggers: an increase in prices, surprise destruction of nominal private wealth a negative wealth effect for households, particularly old impaired life-cycle consumption smoothing increased incentive to work/save for retirement lower real interest rate a substitution towards durables Sterk and Tenreyro (UCL, LSE) OMO June / 52

30 The transmission channel in our model - preview Expansionary OMO triggers: an increase in prices, surprise destruction of nominal private wealth a negative wealth effect for households, particularly old impaired life-cycle consumption smoothing increased incentive to work/save for retirement lower real interest rate a substitution towards durables durable boom; increase in employment and output Sterk and Tenreyro (UCL, LSE) OMO June / 52

31 The transmission channel in our model - preview Expansionary OMO triggers: an increase in prices, surprise destruction of nominal private wealth a negative wealth effect for households, particularly old impaired life-cycle consumption smoothing increased incentive to work/save for retirement lower real interest rate a substitution towards durables durable boom; increase in employment and output positive revaluation of government wealth and persistent increase in central bank revenues Sterk and Tenreyro (UCL, LSE) OMO June / 52

32 The transmission channel in our model - preview Expansionary OMO triggers: an increase in prices, surprise destruction of nominal private wealth a negative wealth effect for households, particularly old impaired life-cycle consumption smoothing increased incentive to work/save for retirement lower real interest rate a substitution towards durables durable boom; increase in employment and output positive revaluation of government wealth and persistent increase in central bank revenues rebated to tax-payers via the Treasury (2-3% of G) Sterk and Tenreyro (UCL, LSE) OMO June / 52

33 The transmission channel in our model - preview Expansionary OMO triggers: an increase in prices, surprise destruction of nominal private wealth a negative wealth effect for households, particularly old impaired life-cycle consumption smoothing increased incentive to work/save for retirement lower real interest rate a substitution towards durables durable boom; increase in employment and output positive revaluation of government wealth and persistent increase in central bank revenues rebated to tax-payers via the Treasury (2-3% of G) monetary policy affects fiscal policy Sterk and Tenreyro (UCL, LSE) OMO June / 52

34 The transmission channel in our model - preview Expansionary OMO triggers: an increase in prices, surprise destruction of nominal private wealth a negative wealth effect for households, particularly old impaired life-cycle consumption smoothing increased incentive to work/save for retirement lower real interest rate a substitution towards durables durable boom; increase in employment and output positive revaluation of government wealth and persistent increase in central bank revenues rebated to tax-payers via the Treasury (2-3% of G) monetary policy affects fiscal policy Ricardian Equivalence breakdown MP is nonneutral Sterk and Tenreyro (UCL, LSE) OMO June / 52

35 Redistribution Estimated cumulative change in net income (bill.) Sterk and Tenreyro (UCL, LSE) OMO June / 52

36 Monetary Implementation Sterk and Tenreyro (UCL, LSE) OMO June / 52

37 Monetary Implementation Redistribution Sterk and Tenreyro (UCL, LSE) OMO June / 52

38 Monetary Implementation Redistribution Durables & Nominal rigidities Sterk and Tenreyro (UCL, LSE) OMO June / 52

39 Key role of durables The effect of a monetary expansion: 1966:Q1-2002:Q4 Sterk and Tenreyro (UCL, LSE) OMO June / 52

40 Nominal rigidities Sticky price models with durables have counterfactual properties Barsky et al. (AER 2007) Sterk and Tenreyro (UCL, LSE) OMO June / 52

41 Nominal rigidities Sticky price models with durables have counterfactual properties Barsky et al. (AER 2007) durable prices arguably relatively flexible Sterk and Tenreyro (UCL, LSE) OMO June / 52

42 Nominal rigidities Sticky price models with durables have counterfactual properties Barsky et al. (AER 2007) durable prices arguably relatively flexible relative price of durables increases after monetary expansion Sterk and Tenreyro (UCL, LSE) OMO June / 52

43 Nominal rigidities Sticky price models with durables have counterfactual properties Barsky et al. (AER 2007) durable prices arguably relatively flexible relative price of durables increases after monetary expansion leads to a decline in durable purchases Sterk and Tenreyro (UCL, LSE) OMO June / 52

44 Nominal rigidities Sticky price models with durables have counterfactual properties Barsky et al. (AER 2007) durable prices arguably relatively flexible relative price of durables increases after monetary expansion leads to a decline in durable purchases Flexibility of durable goods prices determines the effectiveness of monetary policy in sticky-price models. Sterk and Tenreyro (UCL, LSE) OMO June / 52

45 Nominal rigidities Sticky price models with durables have counterfactual properties Barsky et al. (AER 2007) durable prices arguably relatively flexible relative price of durables increases after monetary expansion leads to a decline in durable purchases Flexibility of durable goods prices determines the effectiveness of monetary policy in sticky-price models. Sticky wages can help Sterk and Tenreyro (UCL, LSE) OMO June / 52

46 Nominal rigidities Sticky price models with durables have counterfactual properties Barsky et al. (AER 2007) durable prices arguably relatively flexible relative price of durables increases after monetary expansion leads to a decline in durable purchases Flexibility of durable goods prices determines the effectiveness of monetary policy in sticky-price models. Sticky wages can help wage rigidity micro/macro evidence; non random examples: Olivei-Tenreyro (AER 2007, JME 2010) Sterk and Tenreyro (UCL, LSE) OMO June / 52

47 Nominal rigidities Sticky price models with durables have counterfactual properties Barsky et al. (AER 2007) durable prices arguably relatively flexible relative price of durables increases after monetary expansion leads to a decline in durable purchases Flexibility of durable goods prices determines the effectiveness of monetary policy in sticky-price models. Sticky wages can help wage rigidity micro/macro evidence; non random examples: Olivei-Tenreyro (AER 2007, JME 2010) Equally, other channels worth exploring! Sterk and Tenreyro (UCL, LSE) OMO June / 52

48 Nominal rigidities Sticky price models with durables have counterfactual properties Barsky et al. (AER 2007) durable prices arguably relatively flexible relative price of durables increases after monetary expansion leads to a decline in durable purchases Flexibility of durable goods prices determines the effectiveness of monetary policy in sticky-price models. Sticky wages can help wage rigidity micro/macro evidence; non random examples: Olivei-Tenreyro (AER 2007, JME 2010) Equally, other channels worth exploring! important implications: i) fiscal repercussions of monetary policy; ii) implementation. Sterk and Tenreyro (UCL, LSE) OMO June / 52

49 Nominal rigidities Sticky price models with durables have counterfactual properties Barsky et al. (AER 2007) durable prices arguably relatively flexible relative price of durables increases after monetary expansion leads to a decline in durable purchases Flexibility of durable goods prices determines the effectiveness of monetary policy in sticky-price models. Sticky wages can help wage rigidity micro/macro evidence; non random examples: Olivei-Tenreyro (AER 2007, JME 2010) Equally, other channels worth exploring! important implications: i) fiscal repercussions of monetary policy; ii) implementation. mechanism can complement the NK framework easy to embed in a bigger NK model Sterk and Tenreyro (UCL, LSE) OMO June / 52

50 Other literature Weiss (1983), Rotemberg (1984), Alvarez and Lippi (2012): segmentation in asset markets causes redistributional effects from monetary policy. Sterk and Tenreyro (UCL, LSE) OMO June / 52

51 Other literature Weiss (1983), Rotemberg (1984), Alvarez and Lippi (2012): segmentation in asset markets causes redistributional effects from monetary policy. Welfare effects of monetary policy in the presence of redistribution. Gottlieb (2012), Lippi, Sagni and Thrachter (2014). Sterk and Tenreyro (UCL, LSE) OMO June / 52

52 Other literature Weiss (1983), Rotemberg (1984), Alvarez and Lippi (2012): segmentation in asset markets causes redistributional effects from monetary policy. Welfare effects of monetary policy in the presence of redistribution. Gottlieb (2012), Lippi, Sagni and Thrachter (2014). Doepke and Schneider (2006): revaluation effects from MP expansions cause a contraction. (Households are net debtors in their model, hence gain from expansion and work less.) Sterk and Tenreyro (UCL, LSE) OMO June / 52

53 Model Sterk and Tenreyro (UCL, LSE) OMO June / 52

54 Setup Closed economy, overlapping generations. Sterk and Tenreyro (UCL, LSE) OMO June / 52

55 Setup Closed economy, overlapping generations. 2 life cycle stages (young, old), stochastic ageing (prob. ρ o ) and death (prob. ρ x ), Gertler (1999). Sterk and Tenreyro (UCL, LSE) OMO June / 52

56 Setup Closed economy, overlapping generations. 2 life cycle stages (young, old), stochastic ageing (prob. ρ o ) and death (prob. ρ x ), Gertler (1999). Following retirement, immediate death shock may occur. Sterk and Tenreyro (UCL, LSE) OMO June / 52

57 Setup Closed economy, overlapping generations. 2 life cycle stages (young, old), stochastic ageing (prob. ρ o ) and death (prob. ρ x ), Gertler (1999). Following retirement, immediate death shock may occur. Population size normalized to one. Stationary population: ρ o ν = ρ x (1 ν + ρ o ν) where ν is the fraction of young agents in the population (#newborn=#aging=#dying). Sterk and Tenreyro (UCL, LSE) OMO June / 52

58 Setup Young agents supply labor (h t ), old agents are not productive Sterk and Tenreyro (UCL, LSE) OMO June / 52

59 Setup Young agents supply labor (h t ), old agents are not productive Agents derive utility from non-durables (c t ), durables (d t ) and money (m t ) Sterk and Tenreyro (UCL, LSE) OMO June / 52

60 Setup Young agents supply labor (h t ), old agents are not productive Agents derive utility from non-durables (c t ), durables (d t ) and money (m t ) Agents can also save in bonds (b t ) Sterk and Tenreyro (UCL, LSE) OMO June / 52

61 Setup Firms are perfectly competitive, producing durables and non-durables with the same technology. They rent labor on an competitive labor market. Sterk and Tenreyro (UCL, LSE) OMO June / 52

62 Setup Firms are perfectly competitive, producing durables and non-durables with the same technology. They rent labor on an competitive labor market. Government consists of a central bank and a Treasury. Sterk and Tenreyro (UCL, LSE) OMO June / 52

63 Setup Firms are perfectly competitive, producing durables and non-durables with the same technology. They rent labor on an competitive labor market. Government consists of a central bank and a Treasury. The treasury makes a transfer τ s t to each household of type s. We denote an agent s life-cycle status by superscript s {n, y, o}, with n denoting a newborn young agent, y a pre-existing young agent, and o an old agents. Sterk and Tenreyro (UCL, LSE) OMO June / 52

64 Setup Firms are perfectly competitive, producing durables and non-durables with the same technology. They rent labor on an competitive labor market. Government consists of a central bank and a Treasury. The treasury makes a transfer τ s t to each household of type s. We denote an agent s life-cycle status by superscript s {n, y, o}, with n denoting a newborn young agent, y a pre-existing young agent, and o an old agents. Wealth of deceased agents equally distributed among the young. Agents derive no utility from leaving bequests. Sterk and Tenreyro (UCL, LSE) OMO June / 52

65 Old agents Optimization problem old agent (s = o) in real terms: V o (a, Γ) = max U(c, d, m) + β (1 ρ c,d,m,b x ) EV o (a, Γ ) s.t. c + d + m + b = a + τ o a (1 δ) d + m (1 + r) b π 1 + π, c, d, m 0, where V o (a, Γ) is the value function, a denotes individual wealth, Γ is the aggregate state and π is the net rate of inflation. Also, β is the agents subjective discount factor, δ is the depreciation rate of durables and E is the conditional expectations operator. Sterk and Tenreyro (UCL, LSE) OMO June / 52

66 Young agents Optimization problem young agents (s = n, y) V s h1+κ (a, Γ) = max U(c, d, m) ζ c,d,m,b,h 1 + κ + β (1 ρ o ) EV y (a, Γ ) +βρ o (1 ρ x ) EV o (a, Γ ) s.t. c + d + m + b = a + wh + τ bq + τ s, a (1 δ) d + m (1 + r) b π 1 + π, c, d, m 0, where w is the wage rate and τ bq is a bequest transfer. In the utility function ζ > 0 is a scaling s parameter and κ > 0 determines the Frisch elasticity of labor supply. Sterk and Tenreyro (UCL, LSE) OMO June / 52

67 Firms Firms operate on a linear production function: y t = h t. Profit maximization implies that w t = 1, that is, the real wage equals unity. Sterk and Tenreyro (UCL, LSE) OMO June / 52

68 Central Bank The central bank controls the nominal money supply, M t, by conducting open market operations. In particular, the central bank can sell or buy government bonds. We denote the stock of bonds held by the central bank as B cb t. Sterk and Tenreyro (UCL, LSE) OMO June / 52

69 Central Bank The central bank controls the nominal money supply, M t, by conducting open market operations. In particular, the central bank can sell or buy government bonds. We denote the stock of bonds held by the central bank as B cb t. The use of these open market operations implies that: B cb t B cb t 1 = M t M t 1. Sterk and Tenreyro (UCL, LSE) OMO June / 52

70 Central Bank The central bank controls the nominal money supply, M t, by conducting open market operations. In particular, the central bank can sell or buy government bonds. We denote the stock of bonds held by the central bank as B cb t. The use of these open market operations implies that: B cb t B cb t 1 = M t M t 1. The central bank transfers its accounting profit -seigniorage- to the treasury. The remittance, labeled τ cb t, is given by: τ cb t = r t 1b cb t π t. Sterk and Tenreyro (UCL, LSE) OMO June / 52

71 Central Bank The central bank controls the nominal money supply, M t, by conducting open market operations. In particular, the central bank can sell or buy government bonds. We denote the stock of bonds held by the central bank as B cb t. The use of these open market operations implies that: B cb t B cb t 1 = M t M t 1. The central bank transfers its accounting profit -seigniorage- to the treasury. The remittance, labeled τ cb t, is given by: τ cb t = r t 1b cb t π t. To analyze monetary policy shocks, we assume that M t is driven by an exogenous process subject to stochastic shocks. Sterk and Tenreyro (UCL, LSE) OMO June / 52

72 Treasury We abstract from government consumption. Sterk and Tenreyro (UCL, LSE) OMO June / 52

73 Treasury We abstract from government consumption. The treasury runs a balanced budget, but starts off with an initial level of bonds B g t 1 (which will be negative). The treasury s budget constraint in real terms is: r t 1 b g t 1 + τ cb t = νρ 1 + π o τ n t + ν (1 ρ o ) τ y t + (1 ν) τ o t t where the total amount of transfers is adjusted to balance the government s budget Sterk and Tenreyro (UCL, LSE) OMO June / 52

74 Treasury We abstract from government consumption. The treasury runs a balanced budget, but starts off with an initial level of bonds B g t 1 (which will be negative). The treasury s budget constraint in real terms is: r t 1 b g t 1 + τ cb t = νρ 1 + π o τ n t + ν (1 ρ o ) τ y t + (1 ν) τ o t t where the total amount of transfers is adjusted to balance the government s budget Net beneficiary is the government. Key how it redistributes gain. Sterk and Tenreyro (UCL, LSE) OMO June / 52

75 Treasury Retired agents are assumed not to be subject to transfers/taxes, i.e. we set τ o t = 0. Sterk and Tenreyro (UCL, LSE) OMO June / 52

76 Treasury Retired agents are assumed not to be subject to transfers/taxes, i.e. we set τ o t = 0. To render the model tractable, we assume that transfers to newborns equal the after tax wealth of pre-existing young agents. This is achieved by setting: a y t + τ y t = τ n t where a y t is the average wealth among pre-existing young agents. Sterk and Tenreyro (UCL, LSE) OMO June / 52

77 Treasury Retired agents are assumed not to be subject to transfers/taxes, i.e. we set τ o t = 0. To render the model tractable, we assume that transfers to newborns equal the after tax wealth of pre-existing young agents. This is achieved by setting: a y t + τ y t = τ n t where a y t is the average wealth among pre-existing young agents. What arises is a representative young agent. We preserve heterogeneity between old and young agents, as well as heterogeneity among old agents. Sterk and Tenreyro (UCL, LSE) OMO June / 52

78 Market clearing Market clearing constraints durables and non-durables: c t = νct y + (1 ν) ct o d t = νdt y + (1 ν) dt o, Resource constraint, clearing conditions for money and bond market: Magnitude bequest transfer: c t + d t = νh y t + (1 δ) d t 1, m t = νmt y + (1 ν) mt o, 0 = bt g + bt cb + νbt y + (1 ν) bt o τ bq t = ρ x i :s=o a i,t di + ρ o ρ x νa y t ν Sterk and Tenreyro (UCL, LSE) OMO June / 52

79 Equilibrium Definition. A recursive competitive equilibrium is defined by policy rules for non-durable consumption, c s (a, Γ), durable consumption, d s (a, Γ), money holdings, m s (a, Γ), bond holdings, b s (a, Γ), labor supply, h s (a, Γ), with s = n, y, o, cb, g, as well as laws of motion for inflation, the nominal interest rate and the real wage, such that households optimize their expected life-time utility subject to their constraints and the law of motion for the aggregate state, the treasury and central banks follow their specified policies, the markets for bonds, money, goods and labor clear in every period. The aggregate state Γ includes the value of the monetary policy shock, the distribution of wealth among agents, as well as the initial holdings of assets by households, the treasury and the central bank. Sterk and Tenreyro (UCL, LSE) OMO June / 52

80 Remainder of presentation 1 Representative agent version; contrast to full model 2 Quantitative implementation 3 Labor market frictions Sterk and Tenreyro (UCL, LSE) OMO June / 52

81 Representative agent version Sterk and Tenreyro (UCL, LSE) OMO June / 52

82 Representative agent version If we set ρ x = 1 old agents are effectively removed from the model. Sterk and Tenreyro (UCL, LSE) OMO June / 52

83 Representative agent version If we set ρ x = 1 old agents are effectively removed from the model. Given the transfers to newborns, the model becomes observationally equivalent to one with an infinitely-lived representative agent with subjective discount factor β = β (1 ρ o ). Sterk and Tenreyro (UCL, LSE) OMO June / 52

84 Monetary neutrality Following arguments similar to Sidrauski (1967) one can show that, provided that money and goods enter the utility function separably, monetary policy does not affect real outcomes. To show this, consider the representative agent s first-order conditions for durables, labor supply, and the aggregate resource constraint: U c,t = U d,t + β (1 δ) E t U c,t+1 U c,t = ζh κ t c t + d t = h t + (1 δ) d t 1 where U c,t and U d,t are, respectively, the agents marginal utilities with respect to non-durables and durables. Under preference separability, this is a closed dynamic system of 3 equations and 3 endogenous variables. No nominal variables enter this system. Sterk and Tenreyro (UCL, LSE) OMO June / 52

85 Impact on price level Consider the government s present-value budget constraint: E t s=t D k where D s s 1 ( ) rs m s τ g s = m t 1 (1 + r t 1 ) ( b g t 1 + bcb t r s 1 + π t k=t 1+π k+1 1+r k is the agent s valuation of one unit of nominal wealth received in period s > t, D t 1, and τ g νρ o τ n t + ν (1 ρ o ) τ y t is the total transfer to the households. ) Sterk and Tenreyro (UCL, LSE) OMO June / 52

86 Impact on price level Consider the government s present-value budget constraint: E t s=t D k where D s s 1 ( ) rs m s τ g s = m t 1 (1 + r t 1 ) ( b g t 1 + bcb t r s 1 + π t k=t 1+π k+1 1+r k is the agent s valuation of one unit of nominal wealth received in period s > t, D t 1, and τ g νρ o τ n t + ν (1 ρ o ) τ y t is the total transfer to the households. r s One can verify that 1+r s m s and D s are constant in the representative agent model. Given that m t 1, b g t 1 and bcb t 1 are predetermined, the impact of a monetary policy shock on the price level (π t ) is fully determined by its effect on the present value of government transfers, E t D k τ g s. s=t ) Sterk and Tenreyro (UCL, LSE) OMO June / 52

87 Wealth effects? From the government s budget constraint it also follows that monetary policy shocks do not create any wealth effect in the presentative agent model. Again, use that E t D k τ g s = m ( t 1 (1 + r t 1 ) b g t 1 + ) bcb t 1 (1) s=t 1 + π t and note that m t 1 (1+r t 1 )(b g t 1 +bcb t 1) 1+π t represents the net nominal claim of the representative household on the government. The surprise revaluation of nominal wealth of the representative households exactly offsets the change in the present value of government transfers. Hence monetary policy shocks do not create wealth effects in the representative agent model. With heterogeneous agents, the revaluation of nominal wealth and the change in transfers do not affect agents equally (Weil (1991)). Sterk and Tenreyro (UCL, LSE) OMO June / 52

88 Quantitative implementation Sterk and Tenreyro (UCL, LSE) OMO June / 52

89 Computation Models with wealth heterogeneity and aggregate fluctuations typically diffi cult to solve, because wealth distribution is part of the economic state (Krusell and Smith (1998)). Sterk and Tenreyro (UCL, LSE) OMO June / 52

90 Computation Models with wealth heterogeneity and aggregate fluctuations typically diffi cult to solve, because wealth distribution is part of the economic state (Krusell and Smith (1998)). Despite the presence of heterogeneity, our model can be solved using standard methods (first-order perturbation), under the following preferences: U(c i,t, d i,t, m i,t ) = x i,t 1 σ 1 1 σ, x i,t [c ɛ 1 ɛ i,t + ηd ɛ 1 ɛ i,t ] + µm ɛ 1 ɛ 1 ɛ ɛ i,t, σ, ɛ, η, µ > 0. Sterk and Tenreyro (UCL, LSE) OMO June / 52

91 Computation Idea: 1 Write decision rule of as x i,t = γ x,i,t a i,t with x = c, d, m, b Sterk and Tenreyro (UCL, LSE) OMO June / 52

92 Computation Idea: 1 Write decision rule of as x i,t = γ x,i,t a i,t with x = c, d, m, b 2 Derive equations that pin down γ x,i,t as functions of only aggregate variables, which implies that γ x,i,t = γ x,t is the same for all old agents. Sterk and Tenreyro (UCL, LSE) OMO June / 52

93 Computation Idea: 1 Write decision rule of as x i,t = γ x,i,t a i,t with x = c, d, m, b 2 Derive equations that pin down γ x,i,t as functions of only aggregate variables, which implies that γ x,i,t = γ x,t is the same for all old agents. 3 Compute aggregate variables of the old as: x o t = γ x,t a o t Sterk and Tenreyro (UCL, LSE) OMO June / 52

94 Computation Idea: 1 Write decision rule of as x i,t = γ x,i,t a i,t with x = c, d, m, b 2 Derive equations that pin down γ x,i,t as functions of only aggregate variables, which implies that γ x,i,t = γ x,t is the same for all old agents. 3 Compute aggregate variables of the old as: xt o = γ x,t at o ( where at o = (1 ρ x ) (1 δ) dt 1 o + mo t 1 +(1+r ) t 1)bt 1 o 1+π t + ρ o (1 ρ x ) ν 1 ν [ ] (1 δ) d y t 1 + my t 1 +(1+r t 1)b y t 1 1+π t. Sterk and Tenreyro (UCL, LSE) OMO June / 52

95 Shock process Money growth rule: M t M t 1 = 1 + z t where z t is an exogenous shock process following: z t = ξ (m t 1 m 0 ) + ε t, ξ [0, 1], where ε t is an i.i.d. shock innovation. (Implicit inflation target is zero.) Sterk and Tenreyro (UCL, LSE) OMO June / 52

96 Parameter values (quarterly model) value motivation β target 4% s.s. annual interest rate η 0.31 target 20% s.s. spending on durables (NIPA) µ target 1.8 s.s. M2 velocity ( y m ) (FRB/NIPA) σ 1 convention macro literature ɛ 1 convention macro literature κ 1 convention macro literature ζ normalize aggregate quarterly output to one ρ o average duration working life 40 years ρ x average duration retirement 20 years δ 0.04 Baxter (1996) b g government debt 60% of annual output b0 cb 0 no initial central bank debt ξ 0.15 half life response nominal interest rate 2.5 years j 4 one year delay Sterk and Tenreyro (UCL, LSE) OMO June / 52

97 % point devation from s.s. % point devation from s.s. % devation from s.s. % devation from s.s. % devation % devation from s.s. Monetary expansion 2 price level 0.04 output non durable purchases 0.6 durable purchases nominal interest rate (annualized) 0 real interest rate (annualized) Sterk and Tenreyro (UCL, LSE) OMO June / 52

98 Young versus old Redistributional effect consistent with Doepke and Schneider (2006) and Coibon et al. (2012) real money balances real government transfer to households non durable consumption (young) non durable consumption (old) durable consumption (young) durable consumption (old) Sterk and Tenreyro (UCL, LSE) OMO June / 52

99 The transmission channel with heterogeneous agents Following a monetary expansion negative wealth effect due to downward revaluation in nominal wealth redistribution towards government (future generations) old lose more than young larger drop in expected life-time income upon retirement (impaired life-cycle smoothing) stronger savings motive lower real interest rate more durable purchases Price response Sterk and Tenreyro (UCL, LSE) OMO June / 52

100 The transmission channel with heterogeneous agents Following a monetary expansion negative wealth effect due to downward revaluation in nominal wealth redistribution towards government (future generations) old lose more than young larger drop in expected life-time income upon retirement (impaired life-cycle smoothing) stronger savings motive lower real interest rate more durable purchases Price response need prices to respond before bonds reach maturity Sterk and Tenreyro (UCL, LSE) OMO June / 52

101 The transmission channel with heterogeneous agents Following a monetary expansion negative wealth effect due to downward revaluation in nominal wealth redistribution towards government (future generations) old lose more than young larger drop in expected life-time income upon retirement (impaired life-cycle smoothing) stronger savings motive lower real interest rate more durable purchases Price response need prices to respond before bonds reach maturity latest empirical results: prices respond on impact (Gertler and Karadi, 2014) Sterk and Tenreyro (UCL, LSE) OMO June / 52

102 The transmission channel with heterogeneous agents The effects of savings behavior can be seen from young agents first-order conditions for durables and bonds: U yo c,t+1 Uc,t y = U y d,t + β (1 ρ o ) (1 δ)e tu y c,t+1 + βρ o (1 ρ x ) E t 1 + π t+1 Uc,t y (1 + r t ) U y c,t+1 (1 + r t ) U yo c,t+1 = β (1 ρ o ) E t + βρ 1 + π o (1 ρ x ) E t t π t+1 where superscript yo denotes a newly retired agent. Redistributional effect increases U yo c,t+1 stronger savings motive more durable purchases, lower real interest rate Sterk and Tenreyro (UCL, LSE) OMO June / 52

103 The transmission channel with heterogeneous agents The effect on output can be seen from the young agents labor supply condition: U y c,t = ζh κ t Sterk and Tenreyro (UCL, LSE) OMO June / 52

104 The transmission channel with heterogeneous agents The effect on output can be seen from the young agents labor supply condition: U y c,t = ζh κ t Intuition: Sterk and Tenreyro (UCL, LSE) OMO June / 52

105 The transmission channel with heterogeneous agents The effect on output can be seen from the young agents labor supply condition: U y c,t = ζh κ t Intuition: decline in nominal wealth compensated for by increased durable purchases, at the expense of current non-durable consumption Sterk and Tenreyro (UCL, LSE) OMO June / 52

106 The transmission channel with heterogeneous agents The effect on output can be seen from the young agents labor supply condition: U y c,t = ζh κ t Intuition: decline in nominal wealth compensated for by increased durable purchases, at the expense of current non-durable consumption leisure is a normal good here, so young agents increase labor supply Sterk and Tenreyro (UCL, LSE) OMO June / 52

107 % point devation from s.s. % point devation from s.s. % devation from s.s. % devation from s.s. % devation % devation from s.s. Monetary expansion OMO vs helicopter drop 2 price level 0.04 output non durable purchases 0.6 durable purchases nominal interest rate (annualized) 0.03 real interest rate (annualized) OMO helicopter drop Sterk and Tenreyro (UCL, LSE) OMO June / 52

108 % point devation from s.s. % point devation from s.s. % devation from s.s. % devation from s.s. % devation % devation from s.s. Monetary expansion role of risk aversion 2 price level 0.04 output non durable purchases 0.6 durable purchases nominal interest rate (annualized) real interest rate (annualized) benchmark σ=1) ( lower risk aversion σ=0.6) ( Sterk and Tenreyro (UCL, LSE) OMO June / 52

109 New Keynesian literature Sticky price models with durables have counterfactual properties Barsky et al. (2007) durable prices arguably relatively flexible in that case, relative price of durable increases after monetary expansion this leads to a decline in durable purchases Sticky-wage models argued to be more successful, but large adjustment costs needed to avoid very short-lived spike in durables (Carlstrom and Fuerst (2006)) Sterk and Tenreyro (UCL, LSE) OMO June / 52

110 Labor market frictions Sterk and Tenreyro (UCL, LSE) OMO June / 52

111 Response of output In our benchmark model, the increase in output following an expansionary OMO is driven by a labor supply effect. It turns out that with search and matching frictions in the labor market, output also increases but due to a labor demand effect. Sterk and Tenreyro (UCL, LSE) OMO June / 52

112 Unemployment Young agents can be unemployed or matched with a firm. A worker-firm pair produces one unit of output. Separation occurs 1) with retirement; or 2) with probability ρ s. Overall separation probability ρ s = ρ o + (1 ρ o )ρ s Newborns enter the economy as unemployed Sterk and Tenreyro (UCL, LSE) OMO June / 52

113 The number of job searchers in the economy is s t = ρ o ν + (1 ρ o ) ρ s n t 1. Income insurance among workers. No heterogeneity among young agents. Matching occurs at the beginning of the period, after aggregate and individual shocks have realized, but before production takes place. The evolution of the employment rate among young agents, denoted n t, is given by: n t = (1 ρ s ) n t 1 + g t, where g t denotes the number of new hires in period t. Sterk and Tenreyro (UCL, LSE) OMO June / 52

114 The asset value of a firm matched with a worker is given by: V t = 1 w t + (1 ρ s ) Λ t,t+1 V t+1, where Λ t,t+1 is the stochastic discount factor of the owner of the firm. For simplicity we assume that only young agents are able to run firms. Unmatched firms search after paying a cost χ. Free entry of firms, which implies that χ = λ t v t, where λ t g t v t is the probability of finding a worker, v t is the total number of vacancies. Number of new matches follows from an aggregate matching function: g t = s t α v 1 α t. Sterk and Tenreyro (UCL, LSE) OMO June / 52

115 Wage setting + parameter values We assume the real wage is fixed, i.e. w t = w. (we check w is in the bargaining set) We use w to target a steady-state unemployment rate of 5%. Matching function elasticity, α is set to 0.5. Separation rate ρ s chosen to imply ρ s = 0.1, overall separation rate of ten percent per quarter. Vacancy cost, χ, calibrated to imply steady-state cost of hiring a worker of 5% of quarterly output. Sterk and Tenreyro (UCL, LSE) OMO June / 52

116 % point devation from s.s. % point devation from s.s. % devation from s.s. % devation from s.s. % devation % devation from s.s. Monetary expansion 2.5 price level 5 x 10 3 output non durable purchases 0.6 durable purchases nominal interest rate (annualized) 0 real interes t rate OMO helicopter drop Sterk and Tenreyro (UCL, LSE) OMO June / 52

117 Summary of Extensions Labour market frictions: search and matching frictions employment response due to firms demand, rather than increased labour supply Search and matching frictions plus Big OLG structure (deterministic aging, 40 years) Risk aversion Banks Sterk and Tenreyro (UCL, LSE) OMO June / 52

118 Take home messages Monetary non-neutrality even without nominal rigidities. Anything that breaks RE; allowing for retirement Transmission through wealth/redistributional effects Can help NK model in getting the right response of durables when their prices are more flexible Operating procedure (OMO, helicopter drops) important Similar interest rate changes can have different aggregate effects Monetary policy is fiscal policy Sterk and Tenreyro (UCL, LSE) OMO June / 52