The Dark Corners of the Labor Market Vincent Sterk Conference on Persistent Output Gaps: Causes and Policy Remedies EABCN / University of Cambridge / INET University College London September 2015 Sterk (University College London Dark Corners September 2015 1 / 31
Dark Corners The main lesson of the crisis is that we were much closer to those dark corners than we thought and the corners were even darker than we had thought too. Olivier Blanchard (2014, in Where Danger Lurks. Sterk (University College London Dark Corners September 2015 2 / 31
Single vs multiple steady states ݑ ௧ ଵ ݑ ௧ ଵ ܤ ܣ ܣ ݑ ௧ ݑ ௧ Sterk (University College London Dark Corners September 2015 3 / 31
Contribution Theoretical models. multiple s.s. rates of unemployment found in e.g.: Diamond (1982, Blanchard and Summers (1986,1987, Pissarides (1992, Saint-Paul (1992, Den Haan (2007, Kaplan and Menzio (2014, etc. This paper: look for evidence in U.S. labor market data: i Estimate reduced-form model of the labor market and infer steady state(s. ii Quantitative horse race between standard DMP model and extension with multiple steady states. Result: at least 3 steady states: A : u 5% (stable B : u 10% (unstable C : u > 10% (stable Sterk (University College London Dark Corners September 2015 4 / 31
Part I: reduced-form model u t = ρ x,t = ρ x (S t ρ f,t = ρ f (S t ( (1 ρ f,t u t 1 + ρ x,t 1 ρ f,t (1 u t 1 }{{}}{{} previously unemployed newly unemployed u t : ρ f,t : ρ x,t : S t : unemployment rate job finding rate job loss rate vector containing m aggregate state variables Sterk (University College London Dark Corners September 2015 5 / 31
Steady states: example Example : ρ x (S t = ρ x, ρ f (S t =γ 0 + γ 1 u t 1 = u = (1 γ 0 γ 1 u u + ρ x (1 γ 0 γ 1 u (1 u quadratic equation, two solutions for u. Only one state variable (S t = u t 1. Sterk (University College London Dark Corners September 2015 6 / 31
Estimating steady states Let x t R n be a vector of observed outcomes (including ρ x,t, ρ f,t and possibly other variables, but not u t. Sterk (University College London Dark Corners September 2015 7 / 31
Estimating steady states Let x t R n be a vector of observed outcomes (including ρ x,t, ρ f,t and possibly other variables, but not u t. Estimate direct k step ahead forecasting function: E t x t+k = E [ x t+k S t ] Sterk (University College London Dark Corners September 2015 7 / 31
Estimating steady states Let x t R n be a vector of observed outcomes (including ρ x,t, ρ f,t and possibly other variables, but not u t. Estimate direct k step ahead forecasting function: E t x t+k = E [ x t+k S t ] = E[ x t+k s 1,t }{{} observed ; s 2,t }{{} unobserved ] Sterk (University College London Dark Corners September 2015 7 / 31
Estimating steady states Let x t R n be a vector of observed outcomes (including ρ x,t, ρ f,t and possibly other variables, but not u t. Estimate direct k step ahead forecasting function: E t x t+k = E [ x t+k S t ] = E[ x t+k s 1,t }{{} observed ; s 2,t }{{} unobserved ] = E[ x t+k s 1,t ; x t ] where s 1,t R m n contains lags of variables in [x t ; u t ], and s 2,t R n. Sterk (University College London Dark Corners September 2015 7 / 31
Estimating steady states Let x t R n be a vector of observed outcomes (including ρ x,t, ρ f,t and possibly other variables, but not u t. Estimate direct k step ahead forecasting function: E t x t+k = E [ x t+k S t ] = E[ x t+k s 1,t }{{} observed ; s 2,t }{{} unobserved ] = E[ x t+k s 1,t ; x t ] where s 1,t R m n contains lags of variables in [x t ; u t ], and s 2,t R n. Assumption underlying third equality: equilibrium mapping from [s 1,t ; s 2,t ] to [s 1,t ; x t ] is invertible. Sterk (University College London Dark Corners September 2015 7 / 31
Estimating steady states Let x t R n be a vector of observed outcomes (including ρ x,t, ρ f,t and possibly other variables, but not u t. Estimate direct k step ahead forecasting function: E t x t+k = E [ x t+k S t ] = E[ x t+k s 1,t }{{} observed ; s 2,t }{{} unobserved ] = E[ x t+k s 1,t ; x t ] where s 1,t R m n contains lags of variables in [x t ; u t ], and s 2,t R n. Assumption underlying third equality: equilibrium mapping from [s 1,t ; s 2,t ] to [s 1,t ; x t ] is invertible. Satisfied by linearized DSGE models. May need more than m observables if outcomes are non-monotonic functions of the state variables. Sterk (University College London Dark Corners September 2015 7 / 31
Estimating steady states Let x t R n be a vector of observed outcomes (including ρ x,t, ρ f,t and possibly other variables, but not u t. Estimate direct k step ahead forecasting function: E t x t+k = E [ x t+k S t ] = E[ x t+k s 1,t }{{} observed ; s 2,t }{{} unobserved ] = E[ x t+k s 1,t ; x t ] where s 1,t R m n contains lags of variables in [x t ; u t ], and s 2,t R n. Assumption underlying third equality: equilibrium mapping from [s 1,t ; s 2,t ] to [s 1,t ; x t ] is invertible. Satisfied by linearized DSGE models. May need more than m observables if outcomes are non-monotonic functions of the state variables. Check that forecasts condition on enough variables (residual autocorrelation, more observables, more lags, etc.. Sterk (University College London Dark Corners September 2015 7 / 31
Estimating steady states Steady state (s satisfy: x = E[ x t+k s 1 ; x] u = ρ x (1 ρ f / (ρ x (1 ρ f + ρ f which is a system of n + 1 equations in n + 1 unknowns. Sterk (University College London Dark Corners September 2015 8 / 31
Data Monthly data from February 1990 until November 2014. CPS data on unemployment rate and flow rate from U to E (gross-flows. Construct job loss rate to be consistent with transition identity. IV estimator to account for noise in observations, using lagged values as instruments. Sterk (University College London Dark Corners September 2015 9 / 31
Data 0.4 A. Job finding rate ( f 0.35 0.3 0.25 0.2 0.15 0.1 1990 1995 2000 2005 2010 2015 0.035 B. Job loss rate ( x 0.03 0.025 0.02 0.015 0.01 1990 1995 2000 2005 2010 2015 0.12 C. Unemployment rate (u 0.1 0.08 0.06 0.04 0.02 u u * 0 1990 1995 2000 2005 2010 2015 ( where ut = ρ x,t 1 ρ f,t / (ρ x,t (1 ρ f,t + ρ f,t ; Hall (2005. Sterk (University College London Dark Corners September 2015 10 / 31
Model specifications Three specifications turn out to summarize the main results: (I E t ρ f,t+k = γ 0 + γ 1 ρ x,t + γ 2 ρ f,t + ε t+k (II E t ρ f,t+k = γ 0 + γ 1 ρ x,t + γ 2 ρ f,t + γ 3 u t + ε t+k, (III E t ρ f,t+k = γ 0 + γ 1 ρ x,t + γ 2 ρ f,t + γ 3 u t + γ 3 u 2 t + ε t+k plus AR(1 for ρ x,t. Sterk (University College London Dark Corners September 2015 11 / 31
Model selection Diagnostics statistics 1 Correlation t, t+k+1 1 R 2 statistic 0.5 0.8 0 0.6 0.4-0.5 0.2-1 10 20 30 forecast horizon in months (k 0 10 20 30 forecast horizon in months (k Model (I: f,t+k = 0 + 1 f,t + 2 x,t + t+k Model (II: f,t+k = 0 + 1 f,t + 2 x,t + 3 u t + t+k Model (III: f,t+k = 0 + 1 f,t + 2 x,t + 3 u t + 4 u t 2 + t+k RMSE statistic 10 20 30 forecast horizon in months (k Sterk (University College London Dark Corners September 2015 12 / 31
Implied steady states k=6 k=12 0.1 0.1 0.09 0.09 0.08 0.08 u * t+k 0.07 u * t+k 0.07 0.06 0.06 0.05 0.05 0.04 0.04 0.06 0.08 0.1 0.04 0.04 0.06 0.08 0.1 u * t u * t k=24 k=36 0.1 0.1 0.09 0.09 0.08 0.08 u * t+k 0.07 u * t+k 0.07 0.06 0.06 0.05 0.05 0.04 0.04 0.06 0.08 0.1 0.04 0.04 0.06 0.08 0.1 u * t Model (II Model (III : baseline u * t Steady state curve for ρx,t = ρ x. Shaded area s denote 90 percent (bootstrapped confidence bands. 1 1.5 2 2.5 3 Sterk (University College London Dark Corners September 2015 13 / 31
Robustness 1 Additional higher-order terms similar results to model (III; 2 AR(1 specification similar to model (I invalidated 3 Alternative data source (duration-based CPS data similar results; 4 Longer data sample (1960-2014 similar results; 5 Additional macro variables / unobserved states (Industrial Production, Consumer Price Inflation, Federal Funds Rate similar results; 6 Alternative estimator (OLS similar results; 7 Additional lags similar results; Sterk (University College London Dark Corners September 2015 14 / 31
Phase diagram 0.4 f =0 0.35 u =0 2000:9 0.3 job finding rate ( f 0.25 0.2 2009:7 0.15 2009:11 DARK CORNER 0.1 0.04 0.05 0.06 0.07 0.08 0.09 0.1 unemployment rate ( u Sterk (University College London Dark Corners September 2015 15 / 31
Part II: horse race between search and matching models Feed job loss rates observed in the data through: 1. standard Diamond-Mortensen-Pissarides model single steady state 2. extension with skill losses à la Pissarides (1992 multiple steady states.....but unique dynamic equilibrium Sterk (University College London Dark Corners September 2015 16 / 31
Model -Risk neutral agents -Random search -Exogenous but stochastic rate of job loss -Timing within period: 1. Rate of job loss is revealed and job losses take place. 2. Job losers and previously unemployed workers find a job with an endogenous probability ρ f,t. Vacancies (v t 0 are posted at a cost κ > 0 per unit and filled with an endogenous probability q t. 3. Production and consumption take place. Employed workers produce A units of goods and receive a wage. Unemployed workers receive b < A units of goods. Sterk (University College London Dark Corners September 2015 17 / 31
Model: skill losses Job losers who immediately find a new job retain their productivity. Job losers who become unemployed need to be re-trained upon re-employment, at a cost χ 0 to the employer. Basic DMP model is obtained by setting χ = 0. The fraction of job searchers with reduced skills, p t, is given by: p t = u t 1 u t 1 + ρ x,t (1 u t 1. Sterk (University College London Dark Corners September 2015 18 / 31
Vacancy posting (free-entry condition where κ q t + p t χ }{{} exp. hiring cost = E t β t ( s t,t+k A wt+j +ξ t k =0 }{{} exp. present value profits s t,t+k k (1 ρ x,t+j is the probability that the match survives until j=1 period t + k ξ t is the Lagrange multiplier on the constraint v t 0. Sterk (University College London Dark Corners September 2015 19 / 31
Labor market Matching function: m t = s α t v 1 α t, where s t u t 1 + ρ x,t (1 u t 1 is the number of searchers ρ f,t = m t s t and q t = m t v t = ρ α α 1 f,t. Assume firms have all bargaining power w t = w = b (rigid real wage. Could be relaxed. Sterk (University College London Dark Corners September 2015 20 / 31
Model summary u t = p t = (1 ρ f,t u t 1 + ρ x,t (1 ρ f,t (1 u t 1 (1 u t 1 u t 1 + ρ x,t (1 u t 1 ρ x,t = (1 λ x ρ x + λ x ρ x,t 1 + ε x,t (3 ( 1 α βe t 1 ρ x,t+1 (χp t+1 ξ t+1 + κρ α f,t+1 = χp 1 α t ξ t + κρ α f,t A + w (4 An equilibrium is characterized by laws of motion for u t, ρ f,t, ρ f,t, p t and ξ t that satisfy the above four equations, and the complementary slackness condition ρ f,t ξ t = 0. The state of the aggregate economy can be summarized as } S t = {ρ x,t, u t 1. (2 Sterk (University College London Dark Corners September 2015 21 / 31
Phase diagram: no skill losses 45 8 0123 04567 1 Sterk (University College London Dark Corners September 2015 22 / 31
Phase diagram: skill losses 04567 45 8 0123 1 9 Sterk (University College London Dark Corners September 2015 23 / 31
Parameter values Model period: 1 month Steady-state targets: target no skill losses skill losses u A 0.055 0.055 u B 0.095 Sterk (University College London Dark Corners September 2015 24 / 31
Parameter values parameter description no skill losses skill losses β discount factor 1.04 12 1 1.04 12 1 α matching function elast. 0.6 0.6 κ vacancy cost 0.989 0.989 A worker productivity 1 1 ρ x s.s. job loss rate 0.021 0.021 λ x persistence job loss rate shocks 0.896 0.896 σ x s.t. deviation job loss shocks 7.91e 4 7.91e 4 χ re-training cost 0 0.688 b flow from unemployment 0.997 0.985 Sterk (University College London Dark Corners September 2015 25 / 31
Propagation deterministic simulation 0.095 unemployment rate (u t 0.09 0.085 DMP model + skill losses 0.08 0.075 0.07 0.065 basic DMP model 0.06 0.055 0.05 10 20 30 40 50 60 70 80 90 100 110 120 month Sterk (University College London Dark Corners September 2015 26 / 31
Simulation 1990 1995 2000 2005 2010 2015 0.35 job finding rate ( f,t 0.3 0.03 0.25 0.2 job loss rate ( x,t 0.028 1990 1995 2000 2005 2010 2015 0.026 0.024 0.022 0.02 0.1 0.09 0.08 0.07 0.06 unemployment rate (u t 0.018 0.05 0.04 0.016 0.03 1990 1995 2000 1990 1995 2005 2000 2005 2010 2010 2015 2015 0.35 job finding rate ( f,t data DMP model with skill losses basic DMP model constant job finding rate 0.3 0.25 Sterk (University College London Dark Corners September 2015 27 / 31
0.022 0.02 Simulation 0.018 1990 1995 2000 2005 2010 2015 job finding rate ( f,t 0.35 0.3 0.016 1990 1995 0.252000 2005 2010 2015 0.35 0.2 job finding rate ( f,t 1990 1995 2000 2005 2010 2015 0.3 0.25 0.1 0.09 0.08 0.07 unemployment rate (u t 0.2 0.06 0.05 0.04 0.03 1990 1995 2000 2005 2010 2015 1990 1995 2000 2005 2010 2015 0.1 data unemployment DMP model with skill rate losses (u t basic DMP model constant job finding rate 0.09 0.08 0.07 0.06 Sterk (University College London Dark Corners September 2015 28 / 31
Simulation 0.2 1990 1995 2000 2005 2010 2015 0.35 job finding rate ( f,t 0.3 1990 1995 2000 2005 2010 2015 0.25 0.1 0.09 0.2 unemployment rate (u t 1990 1995 2000 2005 2010 2015 0.08 0.07 0.06 0.05 0.1 0.09 0.08 0.07 0.06 unemployment rate (u t 0.04 0.05 0.04 0.03 0.03 1990 1995 2000 2005 2010 2015 1990 1995 2000 2005 2010 2015 data DMP model with skill losses basic DMP model constant job finding rate data DMP model with skill losses basic DMP model constant job finding rate Sterk (University College London Dark Corners September 2015 29 / 31
Conclusion Multiple-steady state model provides superior description of data. Threshold at around 10% unemployment. Possibly large and non-linear policy implications. Sterk (University College London Dark Corners September 2015 30 / 31
Appendix: firm decision problem Large firms with constant returns-to-scale technologies decide on number of vacancies (v t, hires (h t and employment (n t. Decision problem: ( V (n t 1, S t = max A wt nt ((χ d t p t + κqt h t h t,n t,v t +βe t V (n t, S t+1, subject to n t = (1 ρ x,t n t 1 + h t, h t = q t v t, h t 0, where w t is the wage and d t is a possible wage deduction for newly hired workers with reduced skills. Sterk (University College London Dark Corners September 2015 31 / 31