Labour-Market Matching with Precautionary Savings and Aggregate Fluctuations

Abstract

We analyse a Bewley–Huggett–Aiyagari incomplete‐markets model with labour‐market frictions. Consumers are subject to idiosyncratic employment shocks against which they cannot insure directly. The labour market has a Diamond–Mortensen–Pissarides structure: firms enter by posting vacancies and match with workers bilaterally, with match probabilities given by an aggregate matching function. Wages are determined through Nash bargaining. We also consider aggregate productivity shocks and a complete set of contingent claims conditional on this risk. We use the model to evaluate a tax‐financed unemployment insurance scheme. Higher insurance is beneficial for consumption smoothing, but because it raises workers' outside option value, it discourages firm entry. We find that the latter effect is more potent for welfare outcomes; we tabulate the effects quantitatively for different kinds of consumers. We also demonstrate that productivity changes in the model—in steady state as well as stochastic ones—generate rather limited unemployment effects, unless workers are close to indifferent between working and not working; thus, recent findings are corroborated in our more general setting.

Job displacement risk and severance pay

“…If firms had positive bargaining power, the distribution of wages would depend on the workers' asset distribution, as shown in Krusell et al's (2010) version of Mortensen and Pissarides (1994) with CRRA preferences, period-by-period wage bargaining with symmetric weights and endogenous interest rate. Reassuringly, Krusell et al (2010) find that the dependence of wages on workers' asset position does not have quantitatively significant effects. We have actually verified that introducing a severance payment up to 6 months of wages in the steady-state version of Krusell et al (2010) has a negligible impact on the equilibrium allocation of labor and the interest rate.…”

“…Reassuringly, Krusell et al (2010) find that the dependence of wages on workers' asset position does not have quantitatively significant effects. We have actually verified that introducing a severance payment up to 6 months of wages in the steady-state version of Krusell et al (2010) has a negligible impact on the equilibrium allocation of labor and the interest rate. 40…”

“…This is the same bargaining solution used in Krusell et al (2010). Contrary to Alvarez and Veracierto (2001), but in line with the standard matching literature, it implies that wages are privately efficient, subject to the constraint that bargaining is over spot wages rather than contracts.…”

“…This would substantially complicate the problem as one could not solve recursively for equilibrium wages independently of the equilibrium wealth distribution. Krusell et al (2010) show that, when firms' bargaining power is positive, wealth affects only the wages of workers very close to the borrowing limit. Furthermore, the effect is small and hardly relevant for wage dispersion.…”

The welfare effects of involuntary part-time work

“…Consistent with the data sources that inform our characterization of involuntary part-time work (worker-level data covering individuals over short labor market spells), we focus on its short-run welfare implications and abstract from its broader macroeconomic consequences. We see our study as groundwork for a general-equilibrium analysis of involuntary part-time employment under incomplete insurance markets and frictions in the labor market (in the spirit, for instance, of Krusell et al [2010]'s study of the effects of unemployment insurance). A crucial element of that analysis, we think, is the development of a theory explaining why full-time employment relationships can be temporarily suspended in the face of negative shocks, and thereby lead to involuntary part-time work.…”