Identify the best proxy for national occupation-level productivity shocks in the IV estimation

Determine which of the three instrumental-variable productivity-shock proxies—firm-level log productivity measured in the LIAB, industry-by-year fixed effects, and the leave-one-out sum of vacancies within the occupation-by-year cell—most effectively removes upward bias from national occupation-level productivity shocks in the leave-one-out IV estimate of the elasticity of log wages with respect to log labor market tightness, while preserving valid identification-relevant variation in log tightness.

Background

The paper instruments log labor market tightness using a leave-one-out average across regions for the same occupation and year. While this approach addresses reverse causality and local productivity shocks, it can still be biased by national occupation-level productivity shocks correlated across regions.

To gauge this potential upward bias, the authors introduce three IV-compatible proxies to control for such shocks: (i) firm-level log productivity (from the LIAB), (ii) industry-by-year fixed effects, and (iii) the leave-one-out sum of vacancies within the occupation-by-year cell. Each proxy yields different elasticities (e.g., 0.010, 0.006, 0.004), but the authors note it is unclear which proxy best balances removing productivity-related bias without discarding valid variation in tightness. Consequently, they proceed with robustness and heterogeneity analyses based on the upper-bound baseline IV specification.