Understanding the role of risk and labor market frictions are important topics in modern macroeconomics.This dissertation is concerned with three applications related to these topics: (i) the role of search frictions in the allocation of workers across firms and the role of productivity in wage determination, (ii) representing general stochastic processes in a parsimonious way to aid computation, and (iii) the interaction of search frictions and public policy for understanding the volatility of labor market variables. In the first chapter, I propose a multiworker firm model with on-the-job search and decreasing returns-to-scale production. A coalition bargaining solution between a firm and its incumbent workers yields tractability, results in privately efficient recruiting decisions, and delivers an explicit expression for the wage function. The paper shows how a stylized calibrated version of the model can replicate untargeted empirical facts on the cross-sectional dispersion in firm growth and on measured elasticities of separation rates, quitting rates and vacancy duration with respect to wages. It can also replicate observed net poaching rates by firm size and firm wage, therefore rationalizing the absence of firm size ladders and the presence of wage ladders. In terms of business cycles, the model can replicate the cyclical properties of job flows and worker flows. In the second chapter, coauthored with Eva F. Janssens, we propose a novel finite-state Markov chain approximation method for Markov processes with continuous support, providing both an optimal grid and transition probability matrix. The method can be used for multivariate processes, as well as non-stationary processes such as those with a life-cycle component. The method is based on minimizing the information loss between a Hidden Markov Model and the true data-generating process. We provide sufficient conditions under which this information loss can be made arbitrarily small if enough grid points are used. We compare our method to existing methods through the lens of an asset-pricing model, and a life-cycle consumption-savings model. We find our method leads to more parsimonious discretizations and more accurate solutions, and the discretization matters for the welfare costs of risk, the marginal propensities to consume, and the amount of wealth inequality a life-cycle model can generate. In the third chapter, I revisit the quantitative implications of unemployment benefits in a real business cycle model with labor market search. Combining data on flows in and out of benefit recipiency from the Department of Labor and the Survey of Income and Program Participation, I document that recipients of unemployment benefits take longer to regain employment than non- recipients. Using these estimates, I embed a take-up decision in an otherwise standard real business cycle labor search model. The model is able to replicate the counter-cyclical take-up of unemployment benefits and the volatility of labor market variables. The cyclicality of benefit claims combined with a high steady state value of leisure provides a significant amplification channel for movements in labor productivity. Both elements are necessary for propagation and are consistent with a procyclical value of leisure.