My dissertation contributes towards our understanding of the determinants of wage inequality and to the causes of the emergence of jobless recoveries. It consists of two chapters. The first, "Identifying Labor Market Sorting with Firm Dynamics" studies the determinants of wage inequality, which requires understanding how workers and firms match. I propose a novel strategy to identify the complementarities in production between unobserved worker and firm attributes, based on the idea that positive (negative) sorting implies that firms upgrade (downgrade) their workforce quality when they grow in size. I use German matched employer-employee data to estimate a search and matching model with worker-firm complementarities, job-to-job transitions, and firm dynamics. The relationship between changes in workforce quality and firm growth rates in the data informs the strength of complementarities in the model. Thus, this strategy bypasses the lack of identification inherent to environments with constant firm types. I find evidence of negative sorting and a significant dampening effect of worker-firm complementarities on wage inequality. Worker and firm heterogeneity, differential bargaining positions, and sorting contribute 71\%, 20\%, 32\% and -23\% to wage dispersion, respectively. Reallocating workers across firms to the first-best allocation without mismatch yields an output gain of less than one percent.\
My second chapter, "Does the Cyclicality of Employment Depend on Trends in the Participation Rate?" studies the fact that the past three recessions were characterized by sluggish recovery of the employment to population ratio. The reasons behind these ”jobless recoveries” are not well understood. Contrary to other post-WWII recessions, these ”jobless recoveries” occurred during times with downward trending labor force participation rate(LFPR). I extend the directed search setup of Menzio et al. (2012) with a labor force participation decision to study whether trends in LFPR cause jobless recessions. I then show that that recoveries during times of declining LFPR look very different to recoveries during positive LFPR trend. The basic intuition is as follows: During downward trending LFPR, many low productivity workers cling on to their jobs, but once separated, it does not pay off for them to pay the search cost to re-enter the market. If the recession happens during increasing trend LFPR, then the employment recovery is helped by persons entering the labor market. Thus, I highlight that contrary to the usual approach in the literature, it is important to explicitly account for the trend of the LFPR.
