Chapter 1: It is a commonly held view that the quality of unemployed workers varies countercyclically. During economic downturns, firms raise standards for retaining workers---better workers are fired, so it is natural to expect an accompanying rise in the unemployment pool's quality. However, I present a model in which the reverse is true. Firms learn about employee quality over time and fire their lowest quality workers, but workers enter unemployment also via quitting. In equilibrium, the quality of the unemployment pool reflects a balance between flows of selective firings and of (relatively higher quality) quits. Although firms fire better workers during economic downturns, there are more of these firings at such times, and quits are no longer sufficient to balance the corresponding negative selection---the unemployment pool thus \textit{declines} in quality. I use the model to explore the dynamic consequences of this. Firms limit hiring in response, and even after the economy rebounds otherwise, hiring will not resume until the unemployment pool's quality recovers. This offers a possible contributing factor to jobless recoveries. Using CPS micro-data and JOLTS, I then provide empirical support for several testable implications of the model, focusing on direct evidence for the mechanism driving the decline in unemployment pool quality. The model is consistent with other, previously-observed empirical patterns as well, and it provides a tractable framework for dynamic analysis of labor markets with private learning during employment.
Chapter 2: We consider a dynamic trading environment, where heterogeneous buyers and sellers are randomly paired in each period. Within each match, seller types become observable while buyer types remain private information, and sellers make take-it-or-leave-it offers. We first establish the existence of steady-state equilibrium where sellers offer prices that are continuous in their types. We then characterize properties of sorting under search frictions of varied strength, focusing on two extreme cases. With maximal search frictions---complete disregard for future payoffs---we demonstrate that log-supermodularity (log-submodularity) of the production function is a necessary and sufficient condition for positive (negative) assortative matching. Log-supermodularity (Log-submodularity) is stronger than the standard supermodularity (submodularity) sorting condition. The resistance to sorting comes from the fact that higher type sellers have stronger incentive to secure trade by lowering prices. At the other extreme, the incentive to secure trade grows inconsequential when search frictions vanish and hence the condition for positive (negative) sorting returns to supermodularity (submodularity).
Chapter 3: We study the dynamics of a market where agents trade assets that are heterogeneous in quality, but publicly indistinguishable. All agents begin with only public knowledge of the aggregate asset pool composition, but each owner learns privately about the quality of an asset in her possession. Ownership entails a constant choice between (i) the value of retaining the asset (and its corresponding payoffs) and (ii) that of selling it on the market for a uniform price that reflects the instantaneous average quality of assets being sold. In turn, the market composition reflects not only those owners who have opted for (ii), but also owners selling for reasons unrelated to asset quality.
Learning is gradual, so ownership can be understood as an optimal experimentation problem. Whereas an environment with public learning would entail symmetric timing of sales, private learning precludes this due to externalities sellers exert on other market participants. Instead, owners must spread sales over a broad time interval and, in turn, must experiment inefficiently.
Qualitatively, price dynamics resemble those found in speculation-fueled ``panics'' of the sort often invoked to explain market breakdowns. After an initial period without movement, prices enter a steady decline. Eventually, the stock---and corresponding flow---of owners looking to sell due to poor asset performance grows thin. Prices stop falling and finally rise as the presence of adverse selection fades from the market.
