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Sorting along Business Cycles

Paweł Gola, Haozhou Tang

Abstract

We develop an analytically tractable model featuring heterogeneous workers and firms, where labor markets clear through a one-to-many sorting mechanism. Firms determine both the number and composition of their employees, shaping (1) the income distribution among workers and (2) the productivity distribution across firms. We study business cycles driven by market efficiency shocks that disproportionately benefit more productive firms. The model's implications are consistent with empirical regularities on the cyclical behavior of wage and productivity distributions.

Sorting along Business Cycles

Abstract

We develop an analytically tractable model featuring heterogeneous workers and firms, where labor markets clear through a one-to-many sorting mechanism. Firms determine both the number and composition of their employees, shaping (1) the income distribution among workers and (2) the productivity distribution across firms. We study business cycles driven by market efficiency shocks that disproportionately benefit more productive firms. The model's implications are consistent with empirical regularities on the cyclical behavior of wage and productivity distributions.
Paper Structure (33 sections, 6 theorems, 124 equations, 4 figures, 2 tables)

This paper contains 33 sections, 6 theorems, 124 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Literature review
  3. Model
  4. Household
  5. Production
  6. Final good producer
  7. Intermediate good producers
  8. Distortions and market efficiency shcoks
  9. Equilibrium Analysis
  10. One-to-many Sorting
  11. Firms' problem
  12. First-order conditions and wage schedule
  13. Equilibrium Job Distribution
  14. Aggregate Variables
  15. Prices and aggregate output
  16. ...and 18 more sections

Key Result

Lemma 3.1

Suppose that in period $t$ jobs $h$ are exponentially distributed with parameter $\lambda_t$, that is $h \sim \text{Exp}\left(\lambda_t\right)$. Then the equilibrium output $Q$, rented capital $k$, marginal cost $\chi$ and labor hired $l$ at firm of type $(\theta, \epsilon_1, \epsilon_2)$ are as fol where The time-dependent but type-independent constants $\bar{Q}_t, \bar{k}_t, \bar{\chi}_t,\bar{l

Figures (4)

  • Figure 1: Wage inequality over business cycles
  • Figure 2: Equilibrium determination of $\lambda_t$.
  • Figure 3: Equilibrium determination of $\lambda_t$ following an decrease of $z_t$
  • Figure 4: Impulse responses to a market-efficiency shock

Theorems & Definitions (8)

  • Lemma 3.1
  • Lemma 3.2
  • proof
  • Lemma 4.1
  • Proposition 1
  • Proposition 2
  • Proposition 3
  • proof