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.
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 0.09 0.07 0.05 0.03 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 Petrosky-Nadeau,Tengelsen DMP Estimated 1 / 37
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
Take away: Estimation Method of solving the model matters: bias in parameter estimates 0.18 0.16 Projection Loglinearization Unemployment rate 0.14 0.12 0.1 0.08 0.06 0.04 0 200 400 600 800 1000 1200 1400 1600 Period Petrosky-Nadeau,Tengelsen DMP Estimated 3 / 37
Take away: State Dependence Flip side of deepness: response to shock depend on current state of the economy 1 0.5 Negative shock at peak Negative shock at peak Percentage Points 0-0.5-1 0 10 20 30 40 50 60 Months Petrosky-Nadeau,Tengelsen DMP Estimated 4 / 37
Take away: State Dependence Flip side of deepness: response to shock depend on current state of the economy 1 0.5 Negative shock at trough Positive shock at trough Negative shock at peak Negative shock at peak Percentage Points 0-0.5-1 0 10 20 30 40 50 60 Months Petrosky-Nadeau,Tengelsen DMP Estimated 5 / 37
Take away: State Dependence Flip side of deepness: Stimulating when the labor market is tight is difficult - Bai, 20 May 2016 1 0.5 Negative shock at trough Positive shock at trough Negative shock at peak Negative shock at peak Percentage Points 0-0.5-1 0 10 20 30 40 50 60 Months Petrosky-Nadeau,Tengelsen DMP Estimated 6 / 37
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 0.08 0.075 Constant matching efficiency All shocks Unemployment Rate 0.07 0.065 0.06 0.055 0.05 1976 1981 1986 1991 1996 2002 2007 2012 Petrosky-Nadeau,Tengelsen DMP Estimated 7 / 37
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
Model Petrosky-Nadeau,Tengelsen DMP Estimated 9 / 37
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
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
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
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
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 1 + 0 σ δs 0 log χ Lt 0 0 ρ χl log χ L,t 1 0 0 σ χl ε Xt ε δst ε χlt All ε are iid, standard normal Petrosky-Nadeau,Tengelsen DMP Estimated 14 / 37
Estimation Petrosky-Nadeau,Tengelsen DMP Estimated 15 / 37
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
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
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) 0.064 0.060 Unemployment: volatility σ U 0.117 0.101 Unemployment: skewness skew(u t ) 0.547 0.521 Unemployment: kurtosis kurt(u t ) 3.353 3.793 Vacancy rate volatility σ V 0.118 0.129 (V, U) correlation: corr(v t, U t ) -0.882-0.689 Wage volatility σ W 0.010 0.010 Vacancy filling rate: mean mean(q t ) 0.430 0.441 Petrosky-Nadeau,Tengelsen DMP Estimated 18 / 37
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) 0.064 0.060 Unemployment: volatility σ U 0.117 0.101 Unemployment: skewness skew(u t ) 0.547 0.521 Unemployment: kurtosis kurt(u t ) 3.353 3.793 Vacancy rate volatility σ V 0.118 0.129 (V, U) correlation: corr(v t, U t ) -0.882-0.689 Wage volatility σ W 0.010 0.010 Vacancy filling rate: mean mean(q t ) 0.430 0.441 Petrosky-Nadeau,Tengelsen DMP Estimated 19 / 37
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 ) 0.044 0.044 Separation: volatility σ δs 0.042 0.036 Separation: autocorrelation corr(δ St, δ St 1 ) 0.970 0.772 (V, δ S ) correlation corr(v t, δ St ) -0.854-0.492 Productivity: volatility σ X 0.009 0.011 Productivity: autocorrelation corr(x t, X t 1 ) 0.735 0.757 Petrosky-Nadeau,Tengelsen DMP Estimated 20 / 37
Estimation Results - parameter estimates Estimate S.E. Matching function: elasticity η L 0.566 0.115 Matching function: mean efficiency χ L 0.491 0.267 Worker bargaining weight α L 0.197 0.111 Vacancy cost κ V0 0.056 0.040 Fixed hiring cost κ V1 0.477 0.393 Unemployment value: z 0.887 0.002 Job-separation rate: mean δ S 0.015 0.005 log X t.966 0 0 log X t 1.005 0 0 log δ St =.819.765 0 log δ S,t 1 + 0.003 0 log χ Lt 0 0.356 log χ L,t 1 0 0.010 ε Xt ε δst ε χlt Petrosky-Nadeau,Tengelsen DMP Estimated 21 / 37
Estimation Results - parameter estimates Estimate S.E. Matching function: elasticity η L 0.566 0.115 Matching function: mean efficiency χ L 0.491 0.267 Worker bargaining weight α L 0.197 0.111 Vacancy cost κ V0 0.056 0.040 Fixed hiring cost κ V1 0.477 0.393 Unemployment value: z 0.887 0.002 Job-separation rate: mean δ S 0.015 0.005 log X t.966 0 0 log X t 1.005 0 0 log δ St =.819.765 0 log δ S,t 1 + 0.003 0 log χ Lt 0 0.356 log χ L,t 1 0 0.010 ε Xt ε δst ε χlt Petrosky-Nadeau,Tengelsen DMP Estimated 22 / 37
Estimation Results - parameter estimates Estimate S.E. Matching function: elasticity η L 0.566 0.115 Matching function: mean efficiency χ L 0.491 0.267 Worker bargaining weight α L 0.197 0.111 Vacancy cost κ V0 0.056 0.040 Fixed hiring cost κ V1 0.477 0.393 Unemployment value: z 0.887 0.002 Job-separation rate: mean δ S 0.015 0.005 log X t.966 0 0 log X t 1.005 0 0 log δ St =.819.765 0 log δ S,t 1 + 0.003 0 log χ Lt 0 0.356 log χ L,t 1 0 0.010 ε Xt ε δst ε χlt Petrosky-Nadeau,Tengelsen DMP Estimated 23 / 37
Estimation Results - parameter estimates Estimate S.E. Matching function: elasticity η L 0.566 0.115 Matching function: mean efficiency χ L 0.491 0.267 Worker bargaining weight α L 0.197 0.111 Vacancy cost κ V0 0.056 0.040 Fixed hiring cost κ V1 0.477 0.393 Unemployment value: z 0.887 0.002 Job-separation rate: mean δ S 0.015 0.005 log X t.966 0 0 log X t 1.005 0 0 log δ St =.819.765 0 log δ S,t 1 + 0.003 0 log χ Lt 0 0.356 log χ L,t 1 0 0.010 ε Xt ε δst ε χlt Petrosky-Nadeau,Tengelsen DMP Estimated 24 / 37
Model Dynamics and Particle Filter Petrosky-Nadeau,Tengelsen DMP Estimated 25 / 37
Impulse Response Functions - market tightness 15 10 Negative shock at peak Positive shock at peak Percentage Points 5 0-5 -10-15 0 10 20 30 40 50 60 Months Standard deviation shock to X at peak Petrosky-Nadeau,Tengelsen DMP Estimated 26 / 37
Impulse Response Functions - market tightness 15 10 Negative shock at trough Positive shock at trough Negative shock at peak Positive shock at peak Percentage Points 5 0-5 -10-15 0 10 20 30 40 50 60 Months Standard deviation shock to X at trough Petrosky-Nadeau,Tengelsen DMP Estimated 27 / 37
Impulse Response Functions - unemployment 1 0.5 Negative shock at peak Negative shock at peak Percentage Points 0-0.5-1 0 10 20 30 40 50 60 Months Standard deviation shock to X at peak Petrosky-Nadeau,Tengelsen DMP Estimated 28 / 37
Impulse Response Functions - unemployment 1 0.5 Negative shock at trough Positive shock at trough Negative shock at peak Negative shock at peak Percentage Points 0-0.5-1 0 10 20 30 40 50 60 Months Standard deviation shock to X at trough Petrosky-Nadeau,Tengelsen DMP Estimated 29 / 37
Impulse Response Functions - unemployment 1 0.5 Negative shock at trough Positive shock at trough Negative shock at peak Negative shock at peak Percentage Points 0-0.5-1 0 10 20 30 40 50 60 Months Stimulating when the labor market is tight is difficult, Bai, May 2016 Petrosky-Nadeau,Tengelsen DMP Estimated 30 / 37
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
Particle Filter - Results Technology series { } T ˆX t : normally distributed around mean t=1 Matching efficiency { ˆχ Lt } T t=1 : small, symmetric fluctuations 1.04 0.51 0.505 1.02 0.5 Productivity 1 Matching Efficiency 0.495 0.49 0.485 0.98 0.48 0.475 0.96 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 Quarters 0.47 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 Quarters Petrosky-Nadeau,Tengelsen DMP Estimated 32 / 37
Counterfactuals Set ˆχ Lt = χ Lt t, impulse model with { ˆX t } T t=1 and { ˆδ St } T t=1 0.11 0.105 Constant matching efficiency All shocks Vacancy Rate 0.1 0.095 0.09 0.085 0.08 0.075 0.07 0.065 1976 1981 1986 1991 1996 2002 2007 2012 Petrosky-Nadeau,Tengelsen DMP Estimated 33 / 37
Counterfactuals Set ˆχ Lt = χ Lt t, impulse model with { ˆX t } T t=1 and { ˆδ St } T t=1 0.08 0.075 Constant matching efficiency All shocks Unemployment Rate 0.07 0.065 0.06 0.055 0.05 1976 1981 1986 1991 1996 2002 2007 2012 Petrosky-Nadeau,Tengelsen DMP Estimated 34 / 37
Great Recession Fix matching efficiency to its Dec. 2007, pre-great Recession, level 0.075 0.07 0.065 0.06 0.055 All shocks Dec. 2007 matching efficency 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 Petrosky-Nadeau,Tengelsen DMP Estimated 35 / 37
Great Recession Fix matching efficiency to its Dec. 2007, pre-great Recession, level 0.1 Job Vacancy Rate 0.095 0.09 0.085 0.08 All shocks Dec. 2007 matching efficiency 0.075 0.07 0.055 0.06 0.065 0.07 0.075 Unemployment Rate Petrosky-Nadeau,Tengelsen DMP Estimated 36 / 37
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