Bias in Returns to Tenure When Firm Wages and Employment Comove: A Quantitative Assessment and Solution

It is well known that, unless worker-firm match quality is controlled for, returns to firm tenure (RTT) estimated directly via reduced form wage (Mincer) equations will be biased. In this paper we argue that even if match quality is properly controlled for there is a further pervasive source of bias, namely the co-movement of firm employment and firm wages. In a simple mechanical model where human capital is absent and separation is exogenous we show that positively covarying shocks (either aggregate or firm level) to firm's employment and wages cause downward bias in OLS regression estimates of RTT. We show that the long established procedures for dealing with "traditional" RTT bias do not circumvent the additional problem we have identified. We argue that if a reduced form estimation of RTT is undertaken, firm-year fixed effects must be added in order to eliminate this bias. Estimates from two large panel datasets from Portugal and Germany show that the bias is empirically important. Adding firm-year fixed effects to the regression increases estimates of RTT in the two respective countries by between 3.5% and 4.5% of wages at 20 years of tenure — over 80% (50%) of the estimated RTT level itself. The results extend to tenure correlates used in macroeconomics such as the minimum unemployment rate since joining the firm. Adding firm-year fixed effects changes estimates of these estimates also.