Asymmetric Labor Market Fluctuations in an Estimated Model of Equilibrium Unemployment

Transcription

1 Asymmetric Labor Market Fluctuations in an Estimated Model of Equilibrium Unemployment Nicolas Petrosky-Nadeau FRB San Francisco Benjamin Tengelsen CMU - Tepper Tsinghua - St.-Louis Fed Conference May 2016 The views expressed in this paper are those of the authors and do not necessarily reflect the position of the Federal Reserve Bank of San Francisco or the Federal Reserve System.

2 Introduction Cycles can be asymmetric: contractions are often deep, peaks moderate Neo-classical model - central to many policy discussions: symmetric cycles DSGE model estimation - often solved by linear approximation of equilibrium conditions 0.11 Unemployment rate, percent Petrosky-Nadeau,Tengelsen DMP Estimated 1 / 37

3 Introduction This paper: Estimate an model with search frictions labor market incorporating higher order moments Simulated Method of Moments estimation of model solved by projection Model fits skewness and kurtosis of unemployment rate times series Particle filter recovers history of shocks to productivity, matching efficiency, job separation Realizations of the states are normally distributed: time series asymmetry of the data generated by the model Focus counterfactuals on the Great Recession: Matching efficiency plays a part in peak unemployment, not the ensuing slow recovery Petrosky-Nadeau,Tengelsen DMP Estimated 2 / 37

4 Take away: Estimation Method of solving the model matters: bias in parameter estimates Projection Loglinearization Unemployment rate Period Petrosky-Nadeau,Tengelsen DMP Estimated 3 / 37

5 Take away: State Dependence Flip side of deepness: response to shock depend on current state of the economy Negative shock at peak Negative shock at peak Percentage Points Months Petrosky-Nadeau,Tengelsen DMP Estimated 4 / 37

6 Take away: State Dependence Flip side of deepness: response to shock depend on current state of the economy Negative shock at trough Positive shock at trough Negative shock at peak Negative shock at peak Percentage Points Months Petrosky-Nadeau,Tengelsen DMP Estimated 5 / 37

7 Take away: State Dependence Flip side of deepness: Stimulating when the labor market is tight is difficult - Bai, 20 May Negative shock at trough Positive shock at trough Negative shock at peak Negative shock at peak Percentage Points Months Petrosky-Nadeau,Tengelsen DMP Estimated 6 / 37

8 Take away: Particle Filter Observed time series asymmetry in unemployment model generated Recovered series of exogenous states normally distributed around means Productivity shocks drive bulk of business cycle Matching efficiency plays a role in outlier peaks and troughs Little evidence of efficiency explaining the slow recovery Constant matching efficiency All shocks Unemployment Rate Petrosky-Nadeau,Tengelsen DMP Estimated 7 / 37

9 Literature Business Cycle Asymmetries: Steep, deep, or delayed? Focus here on deepness: asymmetry in levels Capacity constraints: limit booms (Hanson and Prescott, 2005) Financial constraints: amplify downturns (Kocherlakota, 2000) Congestion in matching markets: constrain booms and amplify downturns (Petrosky-Nadeau and Zhang, 2013) Estimation of Non-linear DSGE models Ruge-Murcia (2012): skewness in the time series is generated by skewness of the shocks Models with search frictions: Cooper, Haltiwanger, Willis (2007) Petrosky-Nadeau,Tengelsen DMP Estimated 8 / 37

10 Model Petrosky-Nadeau,Tengelsen DMP Estimated 9 / 37

11 Model Overview Standard discrete time model of equilibrium unemployment Representative household with a unit measure of workers, employed (N t ) or unemployed (U t ) Representative firm with a continuum of jobs Random matching between unemployed and vacant jobs V t Stochastic productivity, matching efficiency, separation rate Petrosky-Nadeau,Tengelsen DMP Estimated 10 / 37

12 Matching Number of matches: M(U t, V t ) = χ Lt U η L t V 1 η L t Stochastic matching efficiency: χ Lt Exogenous separation Fixed component, δ C Stochastic component, δ St Law of motion for employment and unemployment U t+1 = U t + (δ C + (1 δ C )δ St )N t M(U t, V t ) M(U t, V t )/ V t > 0 and increasing in U t Generates business cycle asymmetry and state dependence Petrosky-Nadeau,Tengelsen DMP Estimated 11 / 37

13 Firm s Problem S(N t, γ t ) = max V t X } t N t W {{ t N t κ t V } t + βe t [S(N t+1, γ t+1 )] Period t profit subject to N t+1 = (1 δ C )(1 δ St )N t + q(θ t )V t V t 0 Labor market tightness: θ t = V t /U t Probability of filling vacancy: q t = M(U t, V t )/V t = q(θ t ), q (θ) < 0 and q (θ) > 0 X t : stochastic productivity κ t = κ 0 + κ 1 q t : vacancy cost γ t = [X t, δ St, χ Lt ]: vector of stochastic state variables Petrosky-Nadeau,Tengelsen DMP Estimated 12 / 37

14 Job Creation and Wage Conditions Firms post jobs until cost of marginal hire equals conditional payoff of a filled vacancy: [ ( )] κ 0 q(θ t ) + κ κ0 1 = βe t X t+1 W t+1 + (1 δ C )(1 δ St+1 ) q(θ t+1 ) + κ 1 Nash Bargained wage: W t = α L (X t + κ t θ t ) + (1 α L )z α L : worker bargaining weight z: flow utility from non-employment (reservation wage) Petrosky-Nadeau,Tengelsen DMP Estimated 13 / 37

15 Stochastic variables log X t ρ x 0 0 log δ St = ρ XδS ρ δs 0 log X t 1 σ x 0 0 log δ S,t σ δs 0 log χ Lt 0 0 ρ χl log χ L,t σ χl ε Xt ε δst ε χlt All ε are iid, standard normal Petrosky-Nadeau,Tengelsen DMP Estimated 14 / 37

16 Estimation Petrosky-Nadeau,Tengelsen DMP Estimated 15 / 37

17 Estimation - Simulated Method of Moments Vector of 14 parameters ω Vector of 14 moments of interest in the data µ and model µ s (ω) Model solved by projection (Petrosky-Nadeau and Zhang, 2013) Moments averaged over S = 1000 simulations Minimize the distance g(ω) = ( ) µ S 1 S s=1 µ s(ω) : ˆω = arg min ω g(ω) W 1 g(ω) Newey-West standard errors, optimal weighting matrix W Petrosky-Nadeau,Tengelsen DMP Estimated 16 / 37

18 Estimation - Data U.S., monthly, April 1976 to Dec. 2015: Unemployments rate: civilian population over 16 (BLS) Job vacancy rate: constructed from Conference Board Help-Wanted index, Barnichon, and JOLTS (Petrosky-Nadeau and Zhang, 2013) Job separation rate: CPS employment to unemployment transition rate, provided by Rob Valleta Wage: Compensation pour hour (BEA) Job filling rate: CPS unemployment to employment transition rate v-u raito; lines up with JOLTS Labor productivity: real output per worker (BEA) Petrosky-Nadeau,Tengelsen DMP Estimated 17 / 37

19 Estimation Results - data and model moments Transform to quarterly data (averages), HP filter proportional deviations from mean Labor market moments Data Model Unemployment: mean mean(u) Unemployment: volatility σ U Unemployment: skewness skew(u t ) Unemployment: kurtosis kurt(u t ) Vacancy rate volatility σ V (V, U) correlation: corr(v t, U t ) Wage volatility σ W Vacancy filling rate: mean mean(q t ) Petrosky-Nadeau,Tengelsen DMP Estimated 18 / 37

20 Estimation Results - data and model moments Transform to quarterly data (averages), HP filter proportional deviations from mean Labor market moments Data Model Unemployment: mean mean(u) Unemployment: volatility σ U Unemployment: skewness skew(u t ) Unemployment: kurtosis kurt(u t ) Vacancy rate volatility σ V (V, U) correlation: corr(v t, U t ) Wage volatility σ W Vacancy filling rate: mean mean(q t ) Petrosky-Nadeau,Tengelsen DMP Estimated 19 / 37

21 Estimation Results - data and model moments Transform to quarterly data (averages), HP filter proportional deviations from mean Stochastic process moments Data Model Separation: mean mean(δ St ) Separation: volatility σ δs Separation: autocorrelation corr(δ St, δ St 1 ) (V, δ S ) correlation corr(v t, δ St ) Productivity: volatility σ X Productivity: autocorrelation corr(x t, X t 1 ) Petrosky-Nadeau,Tengelsen DMP Estimated 20 / 37

22 Estimation Results - parameter estimates Estimate S.E. Matching function: elasticity η L Matching function: mean efficiency χ L Worker bargaining weight α L Vacancy cost κ V Fixed hiring cost κ V Unemployment value: z Job-separation rate: mean δ S log X t log X t log δ St = log δ S,t log χ Lt log χ L,t ε Xt ε δst ε χlt Petrosky-Nadeau,Tengelsen DMP Estimated 21 / 37

23 Estimation Results - parameter estimates Estimate S.E. Matching function: elasticity η L Matching function: mean efficiency χ L Worker bargaining weight α L Vacancy cost κ V Fixed hiring cost κ V Unemployment value: z Job-separation rate: mean δ S log X t log X t log δ St = log δ S,t log χ Lt log χ L,t ε Xt ε δst ε χlt Petrosky-Nadeau,Tengelsen DMP Estimated 22 / 37

24 Estimation Results - parameter estimates Estimate S.E. Matching function: elasticity η L Matching function: mean efficiency χ L Worker bargaining weight α L Vacancy cost κ V Fixed hiring cost κ V Unemployment value: z Job-separation rate: mean δ S log X t log X t log δ St = log δ S,t log χ Lt log χ L,t ε Xt ε δst ε χlt Petrosky-Nadeau,Tengelsen DMP Estimated 23 / 37

25 Estimation Results - parameter estimates Estimate S.E. Matching function: elasticity η L Matching function: mean efficiency χ L Worker bargaining weight α L Vacancy cost κ V Fixed hiring cost κ V Unemployment value: z Job-separation rate: mean δ S log X t log X t log δ St = log δ S,t log χ Lt log χ L,t ε Xt ε δst ε χlt Petrosky-Nadeau,Tengelsen DMP Estimated 24 / 37

26 Model Dynamics and Particle Filter Petrosky-Nadeau,Tengelsen DMP Estimated 25 / 37

27 Impulse Response Functions - market tightness Negative shock at peak Positive shock at peak Percentage Points Months Standard deviation shock to X at peak Petrosky-Nadeau,Tengelsen DMP Estimated 26 / 37

28 Impulse Response Functions - market tightness Negative shock at trough Positive shock at trough Negative shock at peak Positive shock at peak Percentage Points Months Standard deviation shock to X at trough Petrosky-Nadeau,Tengelsen DMP Estimated 27 / 37

29 Impulse Response Functions - unemployment Negative shock at peak Negative shock at peak Percentage Points Months Standard deviation shock to X at peak Petrosky-Nadeau,Tengelsen DMP Estimated 28 / 37

30 Impulse Response Functions - unemployment Negative shock at trough Positive shock at trough Negative shock at peak Negative shock at peak Percentage Points Months Standard deviation shock to X at trough Petrosky-Nadeau,Tengelsen DMP Estimated 29 / 37

31 Impulse Response Functions - unemployment Negative shock at trough Positive shock at trough Negative shock at peak Negative shock at peak Percentage Points Months Stimulating when the labor market is tight is difficult, Bai, May 2016 Petrosky-Nadeau,Tengelsen DMP Estimated 30 / 37

32 Particle Filter Particle filter determines the most likely sequence of innovations v t = {νt x, νχ L t, ν δ s t } in order for the model to generate the observed U t, V t and δ st The sequence of innovations yields a series of γ t = [X t, δ St, χ Lt ] over 1976 to 2015 Perform counterfactuals: Remove matching efficiency shocks Focus on the Great Recession Petrosky-Nadeau,Tengelsen DMP Estimated 31 / 37

33 Particle Filter - Results Technology series { } T ˆX t : normally distributed around mean t=1 Matching efficiency { ˆχ Lt } T t=1 : small, symmetric fluctuations Productivity 1 Matching Efficiency Quarters Quarters Petrosky-Nadeau,Tengelsen DMP Estimated 32 / 37

34 Counterfactuals Set ˆχ Lt = χ Lt t, impulse model with { ˆX t } T t=1 and { ˆδ St } T t= Constant matching efficiency All shocks Vacancy Rate Petrosky-Nadeau,Tengelsen DMP Estimated 33 / 37

35 Counterfactuals Set ˆχ Lt = χ Lt t, impulse model with { ˆX t } T t=1 and { ˆδ St } T t= Constant matching efficiency All shocks Unemployment Rate Petrosky-Nadeau,Tengelsen DMP Estimated 34 / 37

36 Great Recession Fix matching efficiency to its Dec. 2007, pre-great Recession, level All shocks Dec matching efficency Petrosky-Nadeau,Tengelsen DMP Estimated 35 / 37

37 Great Recession Fix matching efficiency to its Dec. 2007, pre-great Recession, level 0.1 Job Vacancy Rate All shocks Dec matching efficiency Unemployment Rate Petrosky-Nadeau,Tengelsen DMP Estimated 36 / 37

38 Conclusion - discussion A work in progress with promise: Well understood framework fits the non-linear dynamics of the data State dependence with important implications for policy analysis and counterfactuals Important elements still to incorporate: Endogenous job separation Endogenous labor productivity and include moments in estimation (cross-correlation) Most important: extend to frictional financial market Market well described by search friction Similar (more pronounced) time series asymmetries - returns, spreads,... Petrosky-Nadeau,Tengelsen DMP Estimated 37 / 37