Minu, Startu and all that:- Pitfalls in estimating the sensitivity of a workers wage to aggregate unemployment

In this paper we show that panel estimates of tenure speci…c sensitivity to the business cycle of wages is subject to serious pitfalls. Three canonical variates used in the literature the minimum unemployment rate during a worker’s time at the …rm(minu), the unemployment rate at the start of her tenure(Su) and the current unemployment rate interacted with a new hire dummy( u) can all be signi…cant and "correctly" signed even when each worker in the …rm receives the same wage, regardless of tenure (equal treatment). In matched data the problem can be resolved by the inclusion in the panel of …rm-year interaction dummies. In unmatched data where this is not possible, we propose a solution for minu and Su based on Solon, Barsky and Parker’s(1994) two step method. Our proposed solution method is however suboptimal because it removes a lot of potentially informative variation in average wages. Unfortunately u cannot be identi…ed in unmatched data because a di¤erential wage response to unemployment of new hires and incumbents will appear under both equal treatment and unequal treatment.