"Invariance of Unemployment and Vacancy Dynamics with Respect to Diminishing Returns to Labor at the Firm Level"
This paper show analytically that introducing diminishing returns to labor at the firm level into the Diamond-Mortensen-Pissarides model, followed by recalibration, does not change the dynamics of unemployment and vacancies. This invariance result holds for several standard calibration strategies developed for the model with constant returns, alternative bargaining solutions for the setting with diminishing returns, and different sources of diminishing returns.
Invariance implies that quantitative findings obtained using the Diamond-Mortensen-Pissarides model with constant returns are robust to adding realism by allowing for diminishing returns to return, and provides an analytical benchmark for quantitative findings obtained in models that do combine a Diamond-Mortensen-Pissarides labor market with diminishing returns at the firm level.
Here is a link to a preliminary draft: