advertisement

Optimal monetary policy with incomplete markets Optimal monetary policy when asset markets are incomplete R. Anton Braun1 1 University 2 Kyoto Tomoyuki Nakajima2 of Tokyo, and CREI University, and RIETI December 19, 2008 Optimal monetary policy with incomplete markets Outline 1 Introduction 2 Model Individuals Aggregation Firms Aggregate shocks Government 3 Results Permanent productivity shock Temporary productivity shock 4 Conclusion Optimal monetary policy with incomplete markets Introduction Outline 1 Introduction 2 Model Individuals Aggregation Firms Aggregate shocks Government 3 Results Permanent productivity shock Temporary productivity shock 4 Conclusion Optimal monetary policy with incomplete markets Introduction Inflation-output tradeoff in the representative-agent framework In the standard sticky price model, the optimal monetary policy is approximately given by complete inflation stabilization. Schmitt-Grohé and Uribe (2007), etc. Concerning the output-inflation tradeoff, the monetary authority should place exclusive weight on the inflation stabilization. The welfare cost of business cycles is nil in the representative-agent framework used in the standard New Keynesian model. Optimal monetary policy with incomplete markets Introduction Uninsured idiosyncratic shocks Idiosyncratic income shocks are very persistent and their variance fluctuate countercyclically. Storesletten, Telmer and Yaron (2004), Meghir and Pistaferri (2004), etc. The existence of such idiosyncratic shocks may generate a large welfare-cost of business cycles. Krebs (2003), De Santis (2007), etc. How does it affect optimal monetary policy? In particular, how does it change the weight the monetary authority should place on the inflation stabilization? Optimal monetary policy with incomplete markets Introduction This paper Individuals face uninsured idiosyncratic income shocks with countercyclical variance. The model is otherwise standard new Keynesian model with: monopolistic competition; Calvo price setting; capital accumulation. Consider optimal monetary policy (Ramsey policy). Optimal monetary policy with incomplete markets Introduction Main findings Countercyclical idiosyncratic risk can generate a very large welfare-cost of business cycles. But it does not affect the inflation-output tradeoff much. The optimal monetary policy is essentially characterized as complete price-level stabilization. Thus, the monetary authority should place almost exclusive weight on the stabilization of inflation. Optimal monetary policy with incomplete markets Model Outline 1 Introduction 2 Model Individuals Aggregation Firms Aggregate shocks Government 3 Results Permanent productivity shock Temporary productivity shock 4 Conclusion Optimal monetary policy with incomplete markets Model Composite good Yt = aggregate output of a composite good: 1 Z Yt = 0 1− 1 Yj,t ζ ! dj 1 1− 1 ζ which can be consumed or invested: Yt = Ct + It Pt = price index: Z Pt = 0 1 ! 1−ζ Pj,t dj 1 1−ζ Optimal monetary policy with incomplete markets Model Individuals Preferences of individuals A continuum of ex-ante identical individuals. Preferences: ui,0 = E0i ∞ X t=0 βt i1−γ 1 h θ ci,t (1 − li,t )1−θ 1−γ Let 1/γc = elasticity of intertemporal substitution of consumption for a fixed level of leisure: γc ≡ 1 − θ(1 − γ) Optimal monetary policy with incomplete markets Model Individuals Idiosyncratic shocks Two assumptions for tractability In general, with uninsured idiosyncratic shocks, the wealth distribution, an infinite-dimensional object, must be included in the state variable. We circumvent this problem by assuming that idiosyncratic shocks follow random walk processes; idiosyncratic shocks affect both labor and capital income. Optimal monetary policy with incomplete markets Model Individuals Idiosyncratic shocks Random walk with countercyclical variance ηi,t = the idiosyncratic shock for individual i: ln ηi,t = ln ηi,t−1 + ση,t η,i,t − 2 ση,t 2 where η,i,t is i.i.d., and N(0, 1). ση,t = variance of innovations to idiosyncratic shocks, which is assumed to fluctuate countercyclically. Optimal monetary policy with incomplete markets Model Individuals Idiosyncratic shocks Flow budget constraint Assume that ηi,t affects i’s income in two ways. ηi,t equals the productivity of individual i’s labor. ηi,t also affects the return to savings of individual i. The flow budget constraint of i is given by ci,t + ki,t + si,t ηi,t = Rk ,t ki,t−1 + Rs,t si,t−1 + ηi,t wt li,t ηi,t−1 where ki,t = physical capital and si,t = value of shares. Optimal monetary policy with incomplete markets Model Individuals Idiosyncratic shocks Remarks The assumption that ηi,t also operates as a shock to the return to individual savings is artificial, but ... Without this assumption, the wealth distribution would have to be included as a state variable. With this assumption, the effect of the presence of idiosyncratic shocks would be overemphasized. Our finding is that the tradeoff faced by the monetary authority is little affected by the presence of idiosyncratic shocks. Hence, dropping this assumption would strengthen our result. Optimal monetary policy with incomplete markets Model Aggregation Associated representative-agent problem Consider a representative-agent’s utility maximization problem: max U0 = E0 ∞ X t=0 βt h i1−γ 1 νt Ctθ (1 − Lt )1−θ 1−γ subject to Ct + Kt + St = Rk ,t Kt−1 + Rs,t St−1 + wt Lt Here, νt is a preference shock defined by " # t X 1 2 νt ≡ exp γc (γc − 1) ση,s 2 s=0 = 1−γc Et [ηi,t ] Optimal monetary policy with incomplete markets Model Aggregation Aggregation result Proposition Suppose that {Ct∗ , L∗t , Kt∗ , St∗ }∞ t=0 is a solution to the representative agent’s problem. For each i ∈ [0, 1], let ∗ ci,t = ηi,t Ct∗ ∗ = L∗t li,t ∗ ki,t = ηi,t Kt∗ ∗ si,t = ηi,t St∗ ∗ , l ∗ , k ∗ , s ∗ }∞ is a solution to the problem of Then {ci,t i,t i,t i,t t=0 individual i. Optimal monetary policy with incomplete markets Model Aggregation Remark 1 The utility of the representative agent is indeed the cross-sectional average of individual utility: U0 = E0 [ui,0 ] Optimal monetary policy with incomplete markets Model Aggregation Remark 2 How idiosyncratic shocks affect the aggregate economy can be understood by looking at the “effective discount factor”: β̃t,t+1 ≡ β νt+1 νt = β exp 1 2 γc (γc − 1)ση,t+1 2 Thus ( 2 ↑ ση,t+1 =⇒ ↑ β̃t,t+1 if γc > 1 ↓ β̃t,t+1 if γc < 1 Optimal monetary policy with incomplete markets Model Aggregation Remark 3 The SDF used by individual i is λi,t+1 λt+1 ηi,t+1 −γc β =β λi,t λt ηi,t λt+1 γc 2 =β exp −γc ση,t+1 η,i,t+1 + ση,t+1 λt 2 It follows that individuals agree on the present value of the profit stream of each firm. In particular, they agree with the representative agent, whose SDF is given by β λt+1 νt+1 λt ν t . Optimal monetary policy with incomplete markets Model Firms Firms Standard model with monopolistic competition and Calvo price setting. Production technology of firm j: α 1−α Yj,t = zt1−α Kj,t Lj,t − Φt where zt is aggregate productivity shock, and Φt is a fixed cost of production. Demand for variety j: Yj,t = Pj,t Pt −ζ Yt 1 − ξ = probability of arriving an opportunity to change the price of each variety. Optimal monetary policy with incomplete markets Model Aggregate shocks Aggregate shocks Productivity shock is either permanent or temporary. 1 The case of permanent productivity shock: ln zt = ln zt−1 + µ + σz z,t − 2 ση,t = σ̄η2 + bσz z,t σz2 2 Optimal monetary policy with incomplete markets Model Aggregate shocks Aggregate shocks Productivity shock is either permanent or temporary. 1 The case of permanent productivity shock: ln zt = ln zt−1 + µ + σz z,t − σz2 2 2 ση,t = σ̄η2 + bσz z,t 2 The case of temporary productivity shock: ln zt = ρz ln zt−1 + σz z,t − 2 ση,t = σ̄η2 + b ln zt σz2 2(1 + ρz ) Optimal monetary policy with incomplete markets Model Government Government Fiscal policy: no taxes, no debt, etc. Monetary policy: Set the state-contingent path of the inflation rate {πt }. Two monetary policy regimes: 1 Ramsey regime: Set {πt } so as to maximize the ex ante utility of individuals. 2 Inflation-targeting regime: Set πt = 1 at all times. Optimal monetary policy with incomplete markets Results Outline 1 Introduction 2 Model Individuals Aggregation Firms Aggregate shocks Government 3 Results Permanent productivity shock Temporary productivity shock 4 Conclusion Optimal monetary policy with incomplete markets Results Experiments Most parameters are calibrated following Boldrin, Christiano and Fisher (2001) and Schmitt-Grohé and Uribe (2007). We compare the following cases: γc = 0.7, 2; b = 0, −0.8; productivity shock is either permanent or temporary; the monetary policy regime is either Ramsey or inflation-targeting. Optimal monetary policy with incomplete markets Results Welfare measures ∆bc = welfare cost of business cycles: ∞ X β t ν̄t t=0 i1−γ 1 h ((1 − ∆bc )C̄)θ (1 − L̄)1−θ 1−γ = E−1 ∞ X β t νt t=0 i1−γ 1 h rbc θ 1−θ (Ct ) (1 − Lrbc ) t 1−γ ∆inf = welfare cost of the inflation-targeting regime: E−1 ∞ X β t νt t=0 = E−1 i1−γ 1 h 1−θ ((1 − ∆inf )Ctram )θ (1 − Lram ) t 1−γ ∞ X t=0 β t νt i1−γ 1 h inf θ 1−θ (Ct ) (1 − Linf ) t 1−γ Optimal monetary policy with incomplete markets Results Permanent productivity shock Permanent productivity shock Welfare costs of business cycles and the inflation-targeting regime γc 0.7 0.7 2 2 b 0 -0.8 0 -0.8 ∆bc (%) -0.8191 -1.2983 2.0938 7.3301 ∆inf (%) 0.0000 0.0000 0.0002 0.0006 Optimal monetary policy with incomplete markets Results Permanent productivity shock Permanent productivity shock Impulse responses when γc = 0.7 and b = 0. output growth 1.8 0.45 1.6 consumption growth 4 0.35 1.2 0.3 1 3 0.25 0.8 2 0.2 0.6 0.15 0.4 0.2 0.1 0 0.05 -0.2 investment growth 5 0.4 1.4 1 0 0 5 10 15 20 labor 1 0 5 0.9 0 x 10 5 10 15 20 15 20 -1 0 5 10 15 20 inflation -3 4 0.8 3 0.7 0.6 2 0.5 1 0.4 0 0.3 0.2 0 5 10 15 20 -1 0 5 10 Solid lines: Ramsey policy; dashed lines: inflation targeting. Optimal monetary policy with incomplete markets Results Permanent productivity shock Permanent productivity shock Impulse responses when γc = 0.7 and b = −0.8. output growth 1.8 0.45 1.6 consumption growth 4 0.35 1.2 0.3 1 3 0.25 0.8 2 0.2 0.6 0.15 0.4 0.2 0.1 0 0.05 -0.2 investment growth 5 0.4 1.4 1 0 0 5 10 15 20 labor 1 0 5 0.9 0 x 10 5 10 15 20 15 20 -1 0 5 10 15 20 inflation -3 4 0.8 3 0.7 0.6 2 0.5 1 0.4 0 0.3 0.2 0 5 10 15 20 -1 0 5 10 Solid lines: Ramsey policy; dashed lines: inflation targeting. Optimal monetary policy with incomplete markets Results Permanent productivity shock Permanent productivity shock Impulse responses when γc = 2 and b = 0. output growth 1.4 1 1.2 1 consumption growth 1.4 0.8 1.2 0.7 1 0.6 0.8 investment growth 1.6 0.9 0.8 0.5 0.6 0.6 0.4 0.4 0.3 0.4 0.2 0.2 0.2 0 0 0.1 0 5 10 15 20 labor 0.21 0 18 0.2 16 0.19 14 0 x 10 5 10 15 20 15 20 -0.2 0 5 10 15 20 inflation -4 12 0.18 10 0.17 8 0.16 6 0.15 4 0.14 2 0.13 0.12 0 0 5 10 15 20 -2 0 5 10 Solid lines: Ramsey policy; dashed lines: inflation targeting. Optimal monetary policy with incomplete markets Results Permanent productivity shock Permanent productivity shock Impulse responses when γc = 2 and b = −0.8. output growth 1.4 1 1.2 1 consumption growth 1.4 0.8 1.2 0.7 1 0.6 0.8 investment growth 1.6 0.9 0.8 0.5 0.6 0.6 0.4 0.4 0.3 0.4 0.2 0.2 0.2 0 0 0.1 0 5 10 15 20 labor 0.21 0 18 0.2 16 0.19 14 0 x 10 5 10 15 20 15 20 -0.2 0 5 10 15 20 inflation -4 12 0.18 10 0.17 8 0.16 6 0.15 4 0.14 2 0.13 0.12 0 0 5 10 15 20 -2 0 5 10 Solid lines: Ramsey policy; dashed lines: inflation targeting. Optimal monetary policy with incomplete markets Results Temporary productivity shock Temporary productivity shock Welfare costs of business cycles and the inflation-targeting regime γc 0.7 0.7 2 2 b 0 -0.8 0 -0.8 ∆bc (%) -0.0171 -0.6191 -0.0073 12.2258 ∆inf (%) 0.0000 0.0001 0.0000 0.0024 Optimal monetary policy with incomplete markets Results Temporary productivity shock Temporary productivity shock Impulse responses when γc = 0.7 and b = 0. output 1.5 consumption 0.35 5 0.25 1 investment 6 0.3 4 0.2 3 0.15 2 0.1 0.5 1 0.05 0 0 0 0 5 10 15 20 labor 0.8 -0.05 0.5 0 x 10 5 10 15 20 15 20 -1 0 5 10 15 20 inflation -3 0.7 0 0.6 0.5 -0.5 0.4 0.3 -1 0.2 -1.5 0.1 0 -2 -0.1 -0.2 0 5 10 15 20 -2.5 0 5 10 Solid lines: Ramsey policy; dashed lines: inflation targeting. Optimal monetary policy with incomplete markets Results Temporary productivity shock Temporary productivity shock Impulse responses when γc = 0.7 and b = −0.8. output 2.5 consumption 0.6 investment 12 0.4 10 0.2 8 0 6 -0.2 4 -0.4 2 2 1.5 1 0.5 -0.6 0 0 5 10 15 20 labor 2 -0.8 0.5 0 0 x 10 5 10 15 20 15 20 -2 0 5 10 15 20 inflation -3 0 1.5 -0.5 1 -1 -1.5 0.5 -2 0 -2.5 -0.5 0 5 10 15 20 -3 0 5 10 Solid lines: Ramsey policy; dashed lines: inflation targeting. Optimal monetary policy with incomplete markets Results Temporary productivity shock Temporary productivity shock Impulse responses when γc = 2 and b = 0. output 1.1 consumption 0.34 1 investment 3.5 0.32 0.9 3 0.3 2.5 0.8 0.28 0.7 0.26 2 0.24 1.5 0.6 0.5 0.22 0.4 1 0.3 0.2 0.2 0.18 0.1 0 5 10 15 20 labor 0.4 0.16 1 0.5 0 x 10 5 10 15 20 15 20 0 0 5 10 15 20 inflation -3 0.35 0 0.3 0.25 -1 0.2 -2 0.15 0.1 -3 0.05 -4 0 -0.05 0 5 10 15 20 -5 0 5 10 Solid lines: Ramsey policy; dashed lines: inflation targeting. Optimal monetary policy with incomplete markets Results Temporary productivity shock Temporary productivity shock Impulse responses when γc = 2 and b = −0.8. output -0.04 consumption 1.6 investment 0 1.4 -0.06 -1 1.2 -0.08 1 -0.1 -2 0.8 -0.12 -3 0.6 -0.14 0.4 -0.16 -0.2 -4 0.2 -5 -0.18 0 0 5 10 15 20 labor 0.2 -0.2 5 0 0 x 10 5 10 15 20 15 20 -6 0 5 10 15 20 inflation -3 4 -0.2 3 -0.4 2 -0.6 1 -0.8 0 -1 -1.2 0 5 10 15 20 -1 0 5 10 Solid lines: Ramsey policy; dashed lines: inflation targeting. Optimal monetary policy with incomplete markets Conclusion Outline 1 Introduction 2 Model Individuals Aggregation Firms Aggregate shocks Government 3 Results Permanent productivity shock Temporary productivity shock 4 Conclusion Optimal monetary policy with incomplete markets Conclusion Conclusion We have developed a New Keynesian model with uninsurable idiosyncratic income shocks. The welfare cost of business cycles can be very large when the variance of idiosyncratic shocks fluctuates countercyclically. Nevertheless, the optimal monetary policy is roughly the same as the zero-inflation policy. The presence of countercyclical idiosyncratic shocks does not affect the inflation-output tradeoff.