Identifying Labor Market Sorting with Firm Dynamics

Transcription

1 Identifying Labor Market Sorting with Firm Dynamics Andreas Gulyas University of Mannheim November 10, 2017 Vienna Labormarket Workshop Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, / 18

2 Motivation Broad interest in how agents match in markets (Becker, 1973) Positive vs. negative sorting Marriage markets Labor markets Sorting crucial for understanding unobserved wage inequality Worker heterogeneity Differences in firm pay Sorting amplifies or dampens unobserved wage inequality Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, / 18

3 Motivation II Inherently difficult to identify unobserved heterogeneity and sorting (Abowd, Kramarz, and Margolis (1999), Eeckhout and Kircher (2011)) Conflicting evidence on sign and strength of sorting Current approaches assume fixed firm types Firm dynamics important feature of the labor market Firm dynamics impact incentives for sorting This Paper: Identification of sorting with changing firm types Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, / 18

4 This Paper Structural search and matching model with changing firm types How firms adjust the quality of their workforce as they expand/contract is informative about sorting Estimate model with indirect inference German social security data Info on 5000 establishments and all their employees Decompose sources of wage variation Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, / 18

5 Search and Matching Discrete time and random search Workers and firms are heterogenous in productivity Agents meet each other at random with some probability Upon meeting, agents decide whether to match or keep searching for a better partner Both agents have opportunity cost of matching Workers search off and on-the-job Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, / 18

6 Production Function Workers differ in productivity x Firms differ in productivity y ( Production function f (x, y) = f 1 x 1/ρ + y 1/ρ) ρ Higher types produce more f x (x, y) > 0, f y (x, y) > 0 ρ > 1 Positive sorting (high types match with high types) ρ < 1 Negative sorting (inputs substitutes) Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, / 18

7 Firms Firms are subject to idiosyncratic productivity shocks Firms expand and contract employment After shocks: Some worker types better matched, some worse Which workers are better matched depends on complementarity parameter ρ Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, / 18

8 Firm Level Adjustments Measure worker quality with their average incomes (worker fixed effect) Study firm dynamics to identify complementarities in production: Positive Sorting: Expanding firms: upgrade worker types Negative Sorting: Expanding firms: downgrade worker types Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, / 18

9 Mean Worker Quality Firm Size Firm Type Firm Dynamics with Positive Sorting (ρ = 2) Worker Quality Size Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, /

10 Mean Worker Quality Firm Size Firm Type Firm Dynamics with Negative Sorting (ρ = 0.5) Worker Quality Size Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, / 18

11 Percentage change of Mean Worker Skill Estimation % Wquality jt = α + γ firm growth jt + ɛ jt % Wquality jt : Percentage change in average workforce quality in firm j during year t ;=2 (PAM) ;=1 (No Sorting) ;=0.5 (NAM) Yearly Firm Growth Rate Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, / 18

12 Reorganization of Worker Quality % Wquality jt = α + 19 i=2 γ i D i growthbin jt + βx jt + ɛ jt X jt : Year, 3-digit industry and year industry Change of Average Worker Quality 95% Conf. Interval Percentage Change < Firm Growth Rates >0.5 Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, / 18 here

13 Reorganization of Worker Quality % Wquality jt = α + γ firm growth jt + βx jt + ɛ jt ˆγ consistently negative negative assortative matching firm growth SE Controls: Industry x x x x x x Year x x x x x x Industry x Yr. x x x x x x Size x Age x Sample Baseline Baseline Size>190 Age>15 3 Yr. Chg. 5 Yr. Chg. N Adj. R Reorganization by Industry: here Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, / 18

14 Estimation Results Table: Target Moments Target Moment Data Model Hire rate Unemployment rate Job-to-job transition rate Job filling rate Mean worker type distribution Stdev. of worker type distribution Stdev. of empl. weighted growth rates Emp. weighted autocorr. of firm size Size distribution P Regression Slope Coeff Notes: Size distribution P75 refers to the share of employment in the 75 percent smallest firms. Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, / 18

15 Parameters Table: Estimated Parameters Parameters Symbol Value Complementarity ρ Worker dist. location µ x Worker dist. scale σ x Meeting rate workers λ w Job-to-job meeting rate λ e Job destruction rate d Job creation cost, scale c Job creation cost, convexity c Firm shocks, frequency φ Firm shocks, range ȳ Notes: Confidence Interval on ρ: [0.616,0.677] Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, / 18

16 Estimation Result Weak negative sorting: Corr(x,y) = Hiring high type workers is expensive If firms can substitute technology for worker productivity Negative sorting to be expected ρ = Worker and firm types are substitutes Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, / 18

17 Sources of Wage Variation Wages are determined by 4 factors: i ii iii iv Worker type x Firm productivity y (At the time of bargaining) Bargaining Position b (At the time of bargaining) Sorting Compute counterfactual economies without these source Estimate contribution of each source taking general equilibrium effects into account Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, / 18

18 Variance Decomposition Table: Sources of Wage Dispersion Only firm heterogeneity Stdev Contribution 19.6 Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, / 18

19 Variance Decomposition Table: Sources of Wage Dispersion Only firm +bargaining heterogeneity positions Stdev Contribution Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, / 18

20 Variance Decomposition Table: Sources of Wage Dispersion Only firm +bargaining + Worker heterogeneity positions heterogeneity Stdev Contribution Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, / 18

21 Variance Decomposition Table: Sources of Wage Dispersion Only firm +bargaining + Worker +Sorting heterogeneity positions heterogeneity ρ = Stdev Contribution Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, / 18

22 Conclusion Develop approach to identify sorting with changing firm types Use structural estimation to study wage inequality in Germany Estimate negative sorting in Germany Worker heterogeneity plays the largest role in wage variation Sorting significantly dampens wage dispersion Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, / 18

23 Bibliography John M Abowd, Francis Kramarz, and David N Margolis. High wage workers and high wage firms. Econometrica, 67(2): , Gary S Becker. A theory of marriage: Part i. The Journal of Political Economy, pages , Jan Eeckhout and Philipp Kircher. Identifying sorting in theory. The Review of Economic Studies, page rdq034, Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, / 18

24 Worker Flows - Hires Quality of Hires Relative to Firm Average 95% Conf. Interval < Percentage Difference Yearly Firm Growth Rates >0.5 Back to Reorganization Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, / 18

25 Worker Flows - Separators Quality of Separators Relative to Firm Average 95% Conf. Interval < Percentage Difference Yearly Firm Growth Rates >0.5 Back to Reorganization Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, / 18

26 Worker Quality Adjustments by Industry Table: Worker Quality Adjustments by Industry Industry Point Estimate Standard Error Agriculture, hunting, forestry Mining, quarrying Manufacturing Construction, Utilities Wholesale & retail, hotels Transport, communications, finance Real Estate, renting, business activities Education Community, social, personal service Back to Reorganization Andreas Gulyas (Mannheim) Identifying Sorting Nov 10, / 18