Abstract

AbstractIn the search‐and‐matching model, equilibrium indeterminacy obtains when wages respond strongly to a labor market tightening, and hiring is very elastic. We introduce two types of effort into such a model. Variable labor effort gives rise to short‐run increasing returns to hours in production. This amplifies profit expectations and firms' hiring incentives expanding the indeterminacy region. Variable search effort makes workers search more intensively in a tighter labor market. The procyclical nature of the resource cost of searching stabilizes firms' inclination to hire, shrinking the indeterminacy region. Indeterminacy disappears completely when vacancy posting costs are replaced with hiring costs.

Highlights

  • We introduce two types of effort, worker effort and search effort by job-seekers, into a simple search-and-matching model

  • As shown in the literature, indeterminacy can arise in the canonical labor search model when the price of a worker, i.e. the wage, increases strongly in response to firms’ vacancy posting and the ensuing tightening of the labor market

  • In addition to clarifying the mechanism leading to indeterminacy in the standard search model, we show how different calibration strategies alter the regions of indeterminacy in the two-dimensional parameter space spanned by the match elasticity and the bargaining share

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Summary

Introduction1

We investigate how two types of effort, namely labor effort by the employed and search effort by the unemployed, affect existence and uniqueness of the equilibrium dynamics in an otherwise standard labor search-and-matching model ala Diamond-Mortensen-Pissarides, DMP (Pissarides, 2000). Equation (a) represents the definition of the unemployment rate; equation (b) the definition of the labor market tightness; equation (c) the definition of the job finding rate; equation (d) the definition of the probability of a vacancy being filled; equation (e) the law of motion for employment; equation (f) the matching function; equation (g) the optimality condition for hours; equation (h) the production function; equation (i) the aggregate resource constraint; equation (j) the vacancy posting condition; equation (k) the optimality condition for the bargaining wage; equation (l) the equilibrium search intensity; equation (m) the definition of labor disutility given the optimal effort choice; and equation (n) the definition of the search cost function. Unemployment, ut Tightness, θt Job finding rate, pt Vacancy filling rate, vt Employment, nt Matches, mt Hours, ht Production, yt GDP, Yt Vacancies, qt Wages, wt Search intensity, st Labor disutility, g(ht) Search cost, G(st).

Determinacy in the standard labor search model
Analytical results under risk neutrality
Search externalities and indeterminacy
Numerical results under risk aversion
Labor market policies
Determinacy in the labor search model with effort
An alternative model with hiring costs
Model setup
Determinacy analysis
Conclusion
Preliminaries
Utility and worker’s match surplus
Wage bargaining
Recursive steady state
Linearization of equilibrium conditions
1.10 Model solution
1.11 Special case: risk neutrality
1.12 Labor market liquidity
Model with Hours and Labor Effort
Utility and worker’s match surplus max
Effort
Model with Search Effort
Functional form for search costs
Model solution
3.10 Special case: risk neutrality
Findings
Special case: risk neutrality

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