Diminishing Returns and Labor Market Adjustments

Abstract

We amend the canonical matching model by assuming diminishing returns to labor. We put the model to the twin test of generating a high volatility of labor market variables in response to productivity shocks (the “Shimer puzzle”) and a moderate response to changes in unemployment benefits and find that it passes that test. It does not feature wage rigidity, nor is it based on a small surplus calibration. Diminishing returns introduce a distinction betweenmarginalandaveragesurplus. With a standard (large average surplus) calibration, we can have a small marginal surplus, and thus a strong response of hiring to productivity shocks, while obtaining a measured response of unemployment to changes in benefits.

Invariance of Unemployment and Vacancy Dynamics with Respect to Diminishing Returns to Labor at the Firm Level

“…Invariance reconciles the finding of amplification in Dao and Delacroix (2018) with the lack thereof in Faccini and Ortigueira (2010). The extensions for the calibration strategy of Shimer (2005) in Section 4.2 and for monopolistic competition in Section 6.3 imply that invariance under this strategy applies to Dao and Delacroix' model.…”

“…Appendix C examines this strategy in more detail, and shows that it implies that b/w * is strictly increasing in ν. As I discuss in Section 7, the lower fundamental surplus fraction explains why Dao and Delacroix (2018) find stronger amplification when they compare a model with diminishing returns to the model with constant returns in Shimer ( 2005), as their calibration approach results in similar values of b/p * and c/(q * p * ) across the two models. In the familiar thought experiment, calibrating the model with constant returns using this alternative strategy results in a fundamental surplus fraction that is too high.…”

“…Invariance in conjunction with exogeneity of labor productivity implies that this tension carries over exactly to the model with diminishing returns induced by monopolistic competition. In the next section I use this result as an analytical benchmark for the quantitative findings of Dao and Delacroix (2018), who revisit the tension identified by Costain and Reiter in a setting with diminishing returns due to monopolistic competition.…”

“…Both compare aggregate dynamics induced by aggregate productivity shocks to those in the model with constant returns of Shimer (2005). While Faccini and Ortigueira (2010) obtain very similar dynamics, Dao and Delacroix (2018) find that their model generates substantially higher volatility. I use the invariance result to reconcile these findings by comparing calibration strategies to the benchmark calibration strategy.…”

“…In Section 7 I use invariance as an analytical benchmark to discuss quantitative findings of studies that examine aggregate dynamics in models that combine a Diamond-Mortensen-Pissarides labor market with diminishing returns at the firm level. First, I discuss Faccini and Ortigueira (2010) and Dao and Delacroix (2018), who study models with homogeneous firms. Both compare aggregate dynamics induced by aggregate productivity shocks to those in the model with constant returns of Shimer (2005).…”