Resolving the Missing Deflation Puzzle. June 7, 2018

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1 Resolving the Missing Deflation Puzzle Jesper Lindé Sveriges Riksbank Mathias Trabandt Freie Universität Berlin June 7, 218

2 Motivation Key observations during the Great Recession: Extraordinary contraction in GDP but only small drop in inflation. Source: Christiano, Eichenbaum and Trabandt (215, AEJ: Macro)

3 Motivation Small drop in inflation referred to as the missing deflation puzzle : Hall (211), Ball and Mazumder (211), Coibion and Gorodnichenko (215), King and Watson (212), Fratto and Uhlig (218). John C. Williams (21, p. 8): The surprise [about inflation] is that it s fallen so little, given the depth and duration of the recent downturn. Based on the experience of past severe recessions, I would have expected inflation to fall by twice as much as it has.

4 Motivation Recent work emphasizes role of financial frictions to address the missing deflation puzzle: Del Negro, Giannoni and Schorfheide (215), Christiano, Eichenbaum and Trabandt (215), Gilchrist, Schoenle, Sim and Zakrajsek (217). We propose an alternative resolution of the puzzle: Importance of nonlinearities in price and wage-setting when the economy is exposed to large shocks.

5 What We Do Study inflation and output dynamics in linearized and nonlinear formulations of the NK model. Key modification: Add real rigidity to reconcile macroevidence of low Phillips curve slope and microevidence of frequent price re-setting. Real rigidity: Kimball (1995) state-dependent demand elasticity. Study implications for: Propagation of shocks Nonlinear Phillips curves Unconditional distribution of inflation (skewness)

6 Framework Benchmark model: Erceg-Henderson-Levin (2) model. Monopolistic competition and Calvo sticky prices and wages. Fixed aggregate capital stock. ZLB constraint on nominal interest rate. Estimated model: Christiano-Eichenbaum-Evans (25)/Smets and Wouters (27) model with endogenous capital.

7 Outline Benchmark model Parameterization Results Analysis in estimated model Conclusions

8 Model: Households Household j preferences: ( ) E Â b t V ln C t j,t w N1+c j,t t= 1 + c V t discount factor shock. Household budget constraint: P t C j,t + B j,t = W j,t N j,t + R K t K j + (1 + i t 1 ) B j,t 1 + G j,t + A j,t

9 Model: Households Standard Euler equation # 1 = be t d t i t C t 1 + p t+1 C t+1 $ d t+1 V t+1 V t where d t follows an AR(1) process. Calvo sticky wages (same conceptual setup as for sticky prices, discussed next).

10 Model: Final Good Firms Competitive firms aggregate intermediate goods Y t (f ) into final good Y t using technology R 1 G Y (Y t (f ) /Y t ) df = 1. Following Dotsey-King (25) and Levin-Lopez-Salido-Yun (27): # $ Yt (f ) G Y = w p Y t 1 + y p & ' ( # $ ) 1 Y t (f ) w w p 1 + y p y Y p +1 t 1 + y p y p < : Kimball (1995), y p = : Dixit-Stiglitz. Kimball aggregator: demand elasticity for intermediate goods increasing function of relative price. Dampens firms price response to changes in marginal costs.

11 Levin, Lopez-Salido and Yun (27) 1.2 Demand Curves 1.15 Dixit-Stiglitz ( =) Relative Price P i /P, log-scale Kimball ( =-12) Kimball ( =-3) Relative Demand y i /y, log-scale

12 Model: Intermediate Good Firms Continuum of monopolistically competitive firms f Hire workers and rent capital; production technology Y t (f )=K (f ) a N t (f ) 1 a Calvo sticky prices: optimal price setting with probability 1 x p, otherwise simple updating P t = (1 + p) P t 1. Fixed aggregate capital stock K R K (f ) df.

13 Model: Aggregate Resources Aggregate resource constraint: C t = Y t 1 p t (w t ) 1 a K a N t 1 a where p t and w t are Yun s (1996) aggregate price and wage dispersion terms.

14 Model: Monetary Policy Taylor rule: # & ) 1 + gp & ) gx $ pt Yt 1 + i t = max 1, (1 + i) 1 + p Yt pot where Y pot t denotes flex price-wage output. Taylor rule in linearized model: i t i = max { i, g p (p t p) + g x x t }

15 Solving the Model Solve linearized and nonlinear model using Fair-Taylor (1983, ECMA): Two-point boundary value problem. Solution of nonlinear model imposes certainty equivalence (just as linearized model solution does by definition). Use Dynare for computations: perfect foresight solution / deterministic simulation. Solution algorithm traces out implications of not linearizing equilibrium equations. Robustness: global solution with shock uncertainty, see Lindé and Trabandt (218).

16 Parameterization Price setting: x p =.67 (3 quarter price contracts), f p = 1.1 (1%markup). y p = 12.2 (Kimball)andb =.9975 (discounting) so that k p (1 x p)(1 bx p ) 1 x p 1 f p y =.12 in ˆp t = be t ˆp t+1 + k p cmc t p (Gertler-Gali 1999, Sbordone, 22, ACEL 211). Wage setting: x w =.75, f w = 1.1 andy w = 6 (approx. estimate in estimated model).

17 Parameterization Labor share =.7 (a =.3), linear labor disutil. (c = ) Steady state inflation 2 percent, nominal interest rate 3 percent. Taylor rule: g p = 1.5, g x =.125. d t follows AR(1) with r =.95

18 Results: E ects of a Discount Factor Shock Follow ZLB literature: assume negative demand shock hits the economy. Discount factor shock d t rises by 1 percent before gradually receding.

19 Figure 2: Impulse Responses to a 1% Discount Factor Shock Panel A: ZLB Not Imposed Panel B: ZLB Imposed Nonlinear Model Linearized Model 3 Nominal Interest Rate 3 Nominal Interest Rate Annualized Percent Inflation 2 Inflation Annualized Percent Output Gap Output Gap -2-2 Percent Quarters Quarters

20 Results: Stochastic Simulations Next, do stochastic simulations of linearized and nonlinear model using discount factor shocks. Subject both models to long sequence of discount factor shocks: d t d =.95 (d t 1 d) + s# t with # t N(, 1) Set s such that prob(zlb) =.1 in both models.

21 Figure 3: Stochastic Simulation of Nonlinear and Linearized Model Panel A: Nonlinear Model Inflation Panel B: Linearized Model Inflation Annualized Percent Output Gap 1 Output Gap Percent Nominal Interest Rate Nominal Interest Rate Annualized Percent

22 Results: Phillips Curves

23 Analysis in Estimated Model Assess robustness in CEE/SW workhorse model with endogenous capital. Key model features: Nominal price stickiness Nominal wage stickiness Habit persistence and investment adjustment costs Variable capital utilization

24 Analysis in Estimated Model Estimate linearized model on standard macro data (SW 27) Output, consumption, investment, hours worked per capita, inflation, wage inflation and federal funds rate. Pre-crisis sample: 1965Q1-27Q4. Same seven shocks as in SW (27). Estimate 27 parameters Calibrate price and wage stickiness parameters (x p =.667 and x w =.75) and markups (f p =f w =1.1). Estimate Kimball parameters y p (post. mean -12.5) and y w (post. mean -8.3).

25 Analysis in Estimated Model: Great Recession Next, we aim to examine the model s ability to shed light on the missing deflation puzzle. Subject nonlinear and linearized model to risk premium shock: Risk premium shock as in Smets-Wouters (27). Bondholding FOC: l t = be t l t+1 e RP,t R t P t+1. e RP,t elevated for 16 quarters before gradually receding. Increase e RP,t such that both models deliver a fall in output as in the data. Compare resulting paths of model and data for inflation.

26 Analysis in Estimated Model: Great Recession Data (Min-Max Range) Data (Mean) Nonlinear Model Linearized Model GDP (%) 1 Inflation (p.p., y-o-y) Federal Funds Rate (ann. p.p.) Consumption (%) Investment (%) Employment (p.p.) Wage Inflation (y-o-y, p.p., Earnings) Notes: Data and model variables expressed in deviation from no-great Recession baseline. Data from Christiano, Eichenbaum and Trabandt (215)

27 Analysis in Estimated Model: Great Recession Next, study the implications of the nonlinear and linearized model for the Phillips curve. Simulate the model for each of the seven exogenous processes using the estimated model parameters.

28 Analysis in Estimated Model: Phillips Curves

29 Analysis in Estimated Model: Inflation Densities Data (1965Q1-27Q4) Linearized Medium-Sized Model Nonlinear Medium-Sized Model.35 Core PCE Inflation.35 Wage Inflation (Hourly Earnings) Density Annualized Percent Annualized Percent

30 Conclusions Our analysis focuses on nonlinearities in price and wage- setting using Kimball (1995) aggregation. Our nonlinear NK model with Kimball aggregation resolves the missing deflation puzzle while the linearized version fails to do so. Our nonlinear model generates nonlinear Phillips curves and reproduces the skewness of price and wage inflation observed in post-war U.S. data. All told, our results caution against the common practice of using linearized models when the economy is exposed to large shocks.

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