Block Recursive Equilibria for Stochastic Models of Search on the Job

In this paper, we develop a general stochastic model of directed search on the job. Analogous to models of random search on the job, the state of the economy in our model includes the infinite-dimensional distribution of workers across different employment states (unemployment, and employment at different wages). Unlike the models of random search on the job, our model admits an equilibrium in which agents' value and policy functions do not depend on the distribution of workers. We refer to this type of equilibrium as a Block Recursive Equilibrium (BRE). Therefore, while solving the equilibrium of a random search model in a stochastic environment is a difficult task both analytically and computationally, solving the Block Recursive Equilibrium of our model is as easy as solving a representative agent model. We prove existence of a BRE under various specifications of workers' preferences and contractual environments, including dynamic contracts and fixed-wage contracts.Directed Search; On the Job Search; Heterogeneity; Aggregate Fluctuations

Block Recursive Equilibria for Stochastic Models of Search on the Job

In this paper, we develop a general stochastic model of directed search on the job. Like in the analogous models of random search on the job, the state of the economy in our model includes the infinite-dimensional distribution of workers across different employment states (unemployment, and employment at different wages). Unlike the analogous models of random search on the job, our model admits an equilibrium in which the agents' value and policy functions do not depend on the distribution of workers. We refer to this type of equilibrium as a Block Recursive Equilibrium. Therefore, while solving the equilibrium of a random search model in a stochastic environment is a difficult task both analytically and computationally, solving the Block Recursive Equilibrium of our model is as easy as solving a representative agent model.

Efficient Search on the Job and the Business Cycle, Second Version

We build a directed search model of the labor market in which workers’ transitions between unemployment, employment, and across employers are endogenous. We prove the existence, uniqueness and efficiency of a recursive equilibrium with the property that the distribution of workers across employment states affects neither the agents’ values and strategies nor the market tightness. Because of this property, we are able to compute the equilibrium outside the non-stochastic steady-state. We use a calibrated version of the model to measure the effect of productivity shocks on the US labor market. We find that productivity shocks generate procyclical fluctuations in the rate at which unemployed workers become employed and countercyclical fluctuations in the rate at which employed workers become unemployed. Moreover, we find that productivity shocks generate large counter-cyclical fluctuations in the number of vacancies opened for unemployed workers and even larger procyclical fluctuations in the number of vacancies created for employed workers. Overall, productivity shocks alone can account for 80 percent of unemployment volatility, 30 percent of vacancy volatility and for the nearly perfect negative correlation between unemployment and vacancies.Directed search, On the Job Search, Business Cycles

Efficient Search on the Job and the Business Cycle

The paper develops a model of directed search on the job where transitions of workers between unemployment, employment and across employers are driven by heterogeneity in the quality of firm-worker matches. The equilibrium is such that the agents' value and policy functions are independent of the distribution of workers across employment states. Hence, the model can be solved outside of steady-state and used to measure the effect of cyclical productivity shocks on the labor market. Productivity shocks are found to generate large fluctuations in workers' transitions, unemployment and vacancies when matches are experience good, but not when matches are inspection goods.Directed search; On the Job Search; Business Cycles; Unemployment

Efficient Search on the Job and the Business Cycle

The paper develops a model of directed search on the job where transitions of workers between unemployment, employment and across employers are driven by heterogeneity in the quality of firm-worker matches. The equilibrium is such that the agents' value and policy functions are independent of the distribution of workers across employment states. Hence, the model can be solved outside of steady-state and used to measure the effect of cyclical productivity shocks on the labor market. Productivity shocks are found to generate large fluctuations in workers' transitions, unemployment and vacancies when matches are experience good, but not when matches are inspection goods.Directed search; On the Job Search; Business Cycles; Unemployment

Efficient Search on the Job and the Business Cycle

We build a directed search model of the labor market in which workers' transitions between unemployment, employment, and across employers are endogenous. We prove the existence, uniqueness and efficiency of a recursive equilibrium with the property that the distribution of workers across employment states does not affect the agents' values and strategies. Because of this property, we are able to compute the equilibrium outside the non-stochastic steady-state. We use a calibrated version of the model to measure the effect of productivity shocks on the US labor market. We find that productivity shocks generate procyclical fluctuations in the rate at which unemployed workers become employed and countercyclical fluctuations in the rate at which employed workers become unemployed. Moreover, we find that productivity shocks generate large countercyclical fluctuations in the number of vacancies opened for unemployed workers and even larger procyclical fluctuations in the number of vacancies created for employed workers. Overall, productivity shocks alone can account for 80 percent of unemployment volatility, 30 percent of vacancy volatility and for the nearly perfect negative correlation between unemployment and vacancies.Directed search; On the Job Search; Business Cycles

Efficient Search on the Job and the Business Cycle

We build a directed search model of the labor market in which workers’ transitions between unemployment, employment, and across employers are endogenous. We prove the existence, uniqueness and efficiency of a recursive equilibrium with the property that the distribution of workers across employment states does not affect the agents’ values and strategies. Because of this property, we are able to compute the equilibrium outside the non-stochastic steady-state. We use a calibrated version of the model to measure the effect of productivity shocks on the US labor market. We find that productivity shocks generate procyclical fluctuations in the rate at which unemployed workers become employed and countercyclical fluctuations in the rate at which employed workers become unemployed. Moreover, we find that productivity shocks generate large countercyclical fluctuations in the number of vacancies opened for unemployed workers and even larger procyclical fluctuations in the number of vacancies created for employed workers. Overall, productivity shocks alone can account for 80 percent of unemployment volatility, 30 percent of vacancy volatility and for the nearly perfect negative correlation between unemployment and vacancies.Directed Search, On the Job Search, Business Cycles

Directed Search on the Job, Heterogeneity, and Aggregate Fluctuations

We study a labor market where workers search for jobs both on the job and off the job. In the model, there are aggregate productivity shocks and match-specific shocks. We outline the proof of existence of an equilibrium which we call a block recursive equilibrium (BRE), in which individuals' decisions and market tightness are independent of the distribution of workers over wages or contracts. A critical assumption that is responsible for a BRE to exist is that search is directed by firms' posting of contracts. We explain why a BRE does exist under the assumption of directed search and why it does not under the assumption of random search. Finally, we generalize the proof of existence of a BRE to allow workers to be ex-ante heterogeneous with respect to some observable characteristics such as education and skill.Directed Search; On the Job Search; Heterogeneity; Aggregate Fluctuations

Efficient Search on the Job and the Business Cycle

We build a directed search model of the labor market in which workers' transitions between unemployment, employment, and across employers are endogenous. We prove the existence, uniqueness and efficiency of a recursive equilibrium with the property that the distribution of workers across employment states affects neither the agents' values and strategies nor the market tightness. Because of this property, we are able to compute the equilibrium outside the non-stochastic steady-state. We use a calibrated version of the model to measure the effect of productivity shocks on the US labor market. We find that productivity shocks generate procyclical fluctuations in the rate at which unemployed workers become employed and countercyclical fluctuations in the rate at which employed workers become unemployed. Moreover, we find that productivity shocks generate large countercyclical fluctuations in the number of vacancies opened for unemployed workers and even larger procyclical fluctuations in the number of vacancies created for employed workers. Overall, productivity shocks alone can account for 80 percent of unemployment volatility, 30 percent of vacancy volatility and for the nearly perfect negative correlation between unemployment and vacancies.

Efficient Firm Dynamics in a Frictional Labor Market

The introduction of firm size into labor search models raises the question how wages are set when average and marginal product differ. We develop and analyze an alternative to the existing bargaining framework: Firms compete for labor by publicly posting long–term contracts. In such a competitive search setting, firms achieve faster growth not only by posting more vacancies, but also by offering higher lifetime wages that attract more workers which allows to fill vacancies with higher probability, consistent with empirical regularities. The model also captures several other observations about firm size, job flows, and pay. In contrast to bargaining models, efficiency obtains on all margins of job creation and destruction, both with idiosyncratic and aggregate shocks. The planner solution allows a tractable characterization which is useful for computational applications.labor market search, multi-worker firms, job creation and job destruction