Labor Market Shortages and the Phillips Curve: Identification under Heterogeneous Exposure to Common Shocks

Cross-sectional designs with time fixed effects are widely used in empirical macroeconomics, including when estimating the Phillips curve. We show that heterogeneous exposure to common shocks can bias slope estimates, conflate responses to idiosyncratic and synchronized slack, and overstate precision. We propose a two-step extension of interactive fixed effects that separates these responses under testable conditions. Using firms’ reported labor shortages across euro area sectors and countries, we find that a one standard deviation increase in local own tightness raises its inflation by about 0.25 percentage points – three times the time fixed effect estimate. A one standard deviation increase in synchronized tightness raises it by about 1.3 points, revealing a substantially stronger inflation response when shortages are pervasive.