A Search Theory of Rigid Prices

In this paper, I build a model marketplace populated by a finite number of sellers – each producing its own variety of the good – and a continuum of buyers–each searching for a variety he likes. Using the model, I study the response of a seller’s price to privately observed fluctuations in its idiosyncratic production cost. I find that the qualitative properties of this response critically depend on the persistence of the production cost. In particular, if the cost is i.i.d., the seller’s price does not respond at all. If the cost is somewhat persistent, the seller’s price responds slowly and incompletely. If the cost is very persistent, the seller’s price adjusts instantaneously and efficiently to all fluctuations in productivity. I argue that these findings can explain why the monthly frequency of a price change is so much lower for processed than for raw goods.Search Frictions, Asymmetric Information, Rigid Prices, Sticky Prices

A Theory of Partially Directed Search

This paper studies a search model of the labor market where firms have private information about the quality of their vacancies, they can costlessly communicate with unemployed workers before the beginning of the application process, but the content of the communication does not constitute a contractual obligation. At the end of the application process, wages are determined as the outcome of an alternating offer bargaining game. The model is used to show that vague non-contractual announcements about compensation - such as those one is likely to find in help-wanted ads - can be correlated with actual wages and can partially direct the search strategy of workers.Random search, directed search, non-cooperative bargaining, Coase conjecture, cheap-talk games

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

Worker Replacement

We consider a frictional labor market in which firms want to insure their senior employees against income fluctuations and, at the same time, want to recruit new employees to fill their vacant positions. Firms can commit to a wage schedule, i.e. a schedule that specifies the wage paid by the firm to its employees as function of their tenure and other observables. However, firms cannot commit to the employment relationship with any of their workers, i.e. firms can dismiss workers at will. We find that, because of the firm’s limited commitment, the optimal schedule prescribes not only a rigid wage for senior employees, but also a downward rigid wage for new hires. Moreover, we find that, while the rigidity of the wage of senior workers does not affect the allocation of labor, the rigidity of the wage of new hires magnifies the response of unemployment and vacancies to negative shocks to the aggregate productivity of labor.Competitive Search, Risk Sharing, Unemployment, 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

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

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 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