Invariance of unemployment and vacancy dynamics with respect to diminishing returns to labor at the firm level

This paper shows analytically that introducing diminishing returns to labor at the firm level into the Diamond-Mortensen-Pissarides model, followed by recalibration, does not change aggregate 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 makes precise in which sense the common practice of abstracting from diminishing returns is innocuous. It 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.