Output Gaps and Robust Monetary Policy Rules

Transcription

1 Output Gaps and Robust Monetary Policy Rules Roberto M. Billi Sveriges Riksbank Conference on Monetary Policy Challenges from a Small Country Perspective, National Bank of Slovakia Bratislava, November 216

2 Should monetary policy focus on output gaps? Policy makers often use the output gap to guide monetary policy, even though nominal gross domestic product (GDP) and prices are measured in real time more accurately than the output gap. Employing a small New Keynesian model with a zero lower bound (ZLB) on nominal interest rates, this article compares the performance of monetary-policy rules that are robust to errors in measuring the output gap, nominal GDP level, or price level. The analysis shows that a robust policy rule that focuses on stabilizing the price level improves economic performance, especially when the analysis accounts for persistent measurement errors as faced in practice.

3 Should monetary policy focus on output gaps? Policy makers often use the output gap to guide monetary policy, even though nominal gross domestic product (GDP) and prices are measured in real time more accurately than the output gap. Employing a small New Keynesian model with a zero lower bound (ZLB) on nominal interest rates, this article compares the performance of monetary-policy rules that are robust to errors in measuring the output gap, nominal GDP level, or price level. The analysis shows that a robust policy rule that focuses on stabilizing the price level improves economic performance, especially when the analysis accounts for persistent measurement errors as faced in practice.

4 Should monetary policy focus on output gaps? Policy makers often use the output gap to guide monetary policy, even though nominal gross domestic product (GDP) and prices are measured in real time more accurately than the output gap. Employing a small New Keynesian model with a zero lower bound (ZLB) on nominal interest rates, this article compares the performance of monetary-policy rules that are robust to errors in measuring the output gap, nominal GDP level, or price level. The analysis shows that a robust policy rule that focuses on stabilizing the price level improves economic performance, especially when the analysis accounts for persistent measurement errors as faced in practice.

5 Contacts with ZLB and data uncertainty literature Absent data uncertainty: Svensson (1999), Eggertsson and Woodford (23), Svensson (23), Wolman (25), Adam and Billi (26, 27), Vestin (26), Nakov (28), Evans (212), and Giannoni (214). Absent the ZLB constraint: Orphanides et al. (2), Orphanides (21, 23), Rudebusch (22), Smets (22), Aoki (23, 26), Svensson and Woodford (23, 24), Boehm and House (214), Garín, Lester and Sims (216). ZLB and purely-temporary measurement errors only: Gust, Johannsen and Lopez-Salido (215). Proponents of nominal-gdp-level targets: Hatzius and Stehn (211, 213), Sumner (211, 214), Woodford (212, 213), Frankel (213), among others.

6 Outline The model and monetary policy rules Noisy equilibrium Policy evaluation: 1 noise absent 2 white noise 3 persistent noise Conclude

7 Small New Keynesian model as in Woodford (21) An Euler equation describes the household s expenditure decisions y t = E t y t+1 ϕ (i t r E t π t+1 v t ) (1) A Phillips curve describes the optimal price-setting behavior of firms π t = βe t π t+1 + κ (y t yt n ) + u t (2) Where y t yt n = x t is the output gap. The structural shocks (yt n, u t, v t ) follow AR(1) stochastic processes yt n = ρ y yt 1 n + σ εy ε yt u t = ρ u u t 1 + σ εu ε ut v t = ρ v v t 1 + σ εv ε vt

8 Policy evaluation based on social welfare function Usual approx. of the lifetime utility function of the household [ ] E β t π 2 t + λxt 2 t= (3) The Ramsey plan, the optimal commitment policy determined at time zero, used as a benchmark for the policy evaluation.

9 The simple policy rules I Inertial Taylor rule along the lines of Taylor and Williams (21) i u t = φ i i u t 1 + (1 φ i ) [(r + φ π πo t + φ x x o t )] (4) i t = max (, i u t ) Where π o t = π t + e π t and x o t = x t + e x t are observed. e π t and e x t are noise shocks that follow AR(1) stochastic processes.

10 The simple policy rules II Strict-price-level (SPL) rule i t = max ( ), r + φ p pt o (5) Nominal-GDP-level (NGDPL) rule i t = max (, r + φ n nt o ) (6) Where pt o = p t + et p and nt o = n t + et n are observed. p t = p t 1 + π t and n t = p t + y t. et p and et n are AR(1) noise shocks.

11 The noisy rational-expectations equilibrium (NREE) An equilibrium is given by: a response function y (s t ) = {y (s t ), p (s t ), π (s t ), i (s t )} and expectations function E t y (s t+1 ) = y (s t+1 ) f (ε t+1 ) d (ε t+1 ) where ε t+1 are future innovations of structural and noise shocks Policy rule Equilibrium conditions State vector Inertial Taylor rule (1), (2) and (4) s t = ( yt n, u t, v t, et π, ex t, ) iu t 1 Strict-price-level rule (1), (2) and (5) s t = ( yt n, u t, v t, et p, p ) t 1 Nominal-GDP-level rule (1), (2) and (6) s t = (yt n, u t, v t, et n, p t 1)

12 Policy evaluation in three distinct economic environments 1 Noise absent 2 White noise 3 Persistent noise

13 Baseline calibration as in Billi (MD, forthcoming), Tab. 1 Definition Parameter Numerical value Discount factor β.99 Interest elasticity of aggregate demand ϕ 6.25 Share of firms keeping prices fixed α.66 Price elasticity of demand θ 7.66 Elasticity of a firms marginal cost ω.47 Slope of aggregate supply curve κ.24 Weight on output gap λ.3 Taylor rule coeffi cients φ π,x,i 1.5;.25;.85 Std. deviation of technology shock σ y.8% Std. deviation of mark-up shock σ u.5% Std. deviation of demand shock σ v.8% AR(1) parameter of shocks ρ y,u,v.8 Notes: Because in the model a period is one quarter, shown are parameter values corresponding to inflation and interest rates measured at a quarterly rate. The values of the inertial Taylor rule coeffi cients are taken from English, Lopez-Salido and Tetlow (IMF Economic Review, 215).

14 Fig. 1: Evolution of the economy if no measurement errors pa.1 Real interest rate pp.1 Price level pp 2 Nominal GD P level Quarters after +yn shock 1 pa pa Quarters after u shock Quarters after v shock Taylor rule SPL rule NGDPL rule Quarters after +yn shock 1 pp Quarters after u shock 1 pp Quarters after v shock Quarters after +yn shock 6 pp Quarters after u shock 1 pp Quarters after v shock

15 Tab. 1: Economic performance if no measurement errors Rule coeff. ZLB episodes Welfare loss b φ i,p,n Freq. c Duration d Tot. Inertial Taylor rule Techn. shock only Mark-up shock only Demand shock only Strict-price-level rule Techn. shock only 1... Mark-up shock only Demand shock only Nominal-GDP-level rule Techn. shock only Mark-up shock only Demand shock only a. Baseline calibration but with optimal rule coeffi cients. b. Permanent consumption loss (basis points). c. Expected percent of time at the ZLB. d. Expected number of consecutive quarters at the ZLB.

16 Calibration of the measurement errors Noise shocks in the model are fit to historical revisions of U.S. data for the period 1991Q1-215Q4: Output gap (x) from Congressional Budget Offi ce Prices (π, p) measured by core personal consumption expenditures Nominal GDP (n) from Bureau of Economic Analysis Historical revisions x π p n Std. deviation Autocorrelation

17 Fig. 2: Evolution after white-noise shock pa 1 Nominal interest rate pa 1 Real interest rate 1 2 Taylor rule SPL rule NGDPL rule Quarters after negative measurment error Quarters after negative measurment error pa.4 Inflation rate pp 5 Output gap Quarters after negative measurment error Quarters after negative measurment error

18 Fig. 3: Evolution after persistent-noise shock pa 1 Nominal interest rate pa 1 Real interest rate 1 2 Taylor rule SPL rule NGDPL rule Quarters after negative measurment error Quarters after negative measurment error pa 2.5 Inflation rate pp 8 Output gap Quarters after negative measurment error Quarters after negative measurment error

19 Tab. 6: Effects of noise on economic performance Rule coeff. ZLB episodes Welfare loss b φ i,p,n Freq. c Duration d Tot. Without measurement errors Inertial Taylor rule Strict-price-level rule Nominal-GDP-level rule Purely-temporary measurement errors Inertial Taylor rule Strict-price-level rule Nominal-GDP-level rule Persistent measurement errors Inertial Taylor rule Strict-price-level rule Nominal-GDP-level rule a. Baseline calibration but with optimal rule coeffi cients. b. Permanent consumption loss (basis points). c. Expected percent of time at the ZLB. d. Expected number of consecutive quarters at the ZLB.

20 Monetary policy should focus on the price level Some argue that monetary-policy rules should ignore the output gap and seek to stabilize the level of nominal GDP because: monetary policy would be more robust to measurement errors; and would ensure greater stimulus during ZLB episodes. However, because prices are measured in real time more accurately than nominal GDP, why not stabilize the price level? Still, as the analysis is conducted in a stylized model, further study is needed to extend the results to a broader class of models.