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

Directed Search with Multiple Job Applications

We develop an equilibrium directed search model of the labor market where workers can simultaneously apply for multiple jobs. The main result is that all equilibria exhibit wage dispersion despite the fact that workers and firms are homogeneous. Wage dispersion is driven by the simultaneity of application choice. Risk-neutral workers apply for both ‘safe’ and ‘risky’ jobs. The former yield a high probability of a job offer, but for low pay, and act as a fallback option; the latter provide with higher potential payoff, but are harder to get. Furthermore, the density of posted wages is decreasing, consistent with stylized facts. Unlike most directed search models, the equilibria are not constrained efficient.

Directed Search for Equilibrium Wage-Tenure Contracts

I analyze the equilibrium in a labor market where firms offer wage-tenure contracts to direct the search of employed and unemployed workers. Each applicant observes all offers and there is no coordination among individuals. Workers' applications (as well as firms' recruiting decisions) are optimal. This optimality requires the equilibrium to be formulated differently from the that in the literature of undirected search. I provide such a formulation and show that the equilibrium exists. In the equilibrium, individuals explicitly tradeoff between an offer and the matching rate at that offer. This tradeoff yields a unique offer which is optimal for each worker to apply, and applicants are separated endogenously according to their current values. Despite such uniqueness and separation, there is a non-degenerate and continuous wage distribution of employed workers in the stationary equilibrium. The density of this distribution is increasing at low wages and decreasing at high wages. In all equilibrium contracts, wages increase with tenure, which results in quit rates to decrease with tenure. Moreover, the model makes novel predictions about individuals' job-to-job transition and comparative statics.Directed search; on the job; wage tenure contracts

Money in search equilibrium, in competitive equilibrium, and in competitive search equilibrium

We compare three market structures for monetary economies: bargaining (search equilibrium); price taking (competitive equilibrium); and price posting (competitive search equilibrium). We also extend work on the microfoundations of money by allowing a general matching technology and entry. We study how equilibrium and the effects of policy depend on market structure.Money ; Equilibrium (Economics)

Monetary Exchange with Multilateral Matching

This paper analyzes monetary exchange in a search model allowing for multilateral matches to be formed, according to a standard urn-ball process. We consider three physical environments: indivisible goods and money, divisible goods and indivisible money, and divisible goods and money. We compare the results with Kiyotaki and Wright (1993), Trejos and Wright (1995), and Lagos and Wright (2005) respectively. We …nd that the multilateral matching setting generates very simple and intuitive equilibrium allocations that are similar to those in the other papers, but which have important di¤erences. In particular, sur- plus maximization can be achieved in this setting, in equilibrium, with a positive money supply. Moreover, with ‡exible prices and directed search, the …rst best allocation can be attained through price posting or through auctions with lotteries, but not through auctions without lotteries. Finally, analysis of the case of divisible goods and money can be performed without the assumption of large families (as in Shi (1997)) or the day and night structure of Lagos and Wright (2005)Matching, Money, Directed Search

Efficiency of Simultaneous Search

We analyze a labor search model in which workers choose their search intensity by deciding how often and where to apply for jobs. They observe firms’ wage postings prior to their decision. Due to coordination frictions a firm may not receive any applications; otherwise it is able to hire unless all its applicants have better offers. We show that in equilibrium the entry of firms, the search intensity and the number of filled vacancies are constrained efficient. Wage dispersion creates an (endogenous) safety net against unemployment that is essential for efficiency. As application costs vanish the equilibrium becomes unconstrained efficient.simultaneous search, directed search, efficient wage dispersion, modified Hosios condition, search with stable matchings

Pricing and Signaling with Frictions

In this paper, we introduce private information into a market with search frictions and evaluate the relative efficiency of two pricing mechanisms, price posting and bargaining. Each seller chooses investment that determines the quality of the good. This quality is the seller's private information before matching and it will be observed in a match. Sellers enter a search market competitively and can choose either to post prices or to bargain. In this environment, a pricing mechanism affects efficiency through the choice of quality and the number of trades. Bargaining induces the efficient choice of quality but an inefficient number of trades because the division of the match surplus is generically inefficient. By directing buyers' search, posted prices internalize search externalities and induce the constrained efficient outcome in the case of public information. However, when the quality is private information, this role of posted prices in directing search can conflict with their role in signaling quality. Focusing on this conflict, we find that bargaining could yield higher efficiency than price posting. We characterize the parameter regions in which each of the two mechanisms dominates in efficiency.Directed search; Signaling; Bargaining; Efficiency

Money in Search Equilibrium, in Competitive Equilibrium, and in Competitive Search Equilibrium

We compare three pricing mechanisms for monetary economies: bargaining (search equilibrium); price taking (competitive equilibrium); and price posting (competitive search equilibrium). We do this in a framework that, in addition to considering different mechanisms, extends existing work on the microfoundations of money by allowing a general matching technology and endogenous entry. We study how the nature of equilibrium and effects of policy depend on the mechanism. Under bargaining, trades and entry are both inefficient, and inflation implies a first-order welfare loss. Under price taking, the Friedman rule solves the first inefficiency but not the second, and inflation can actually improve welfare. Under posting, the Friedman rule implies first best, and inflation reduces welfare but the effect is second order.Money, Search

Monetary Exchange with Multilateral Matching

This paper analyzes monetary exchange in a search model allowing for multilateral matches to be formed, according to a standard urn-ballprocess. We consider three physical environments: indivisible goods and money, divisible goods and indivisible money, and divisible goods and money. We compare the results with Kiyotaki and Wright (1993), Trejos and Wright (1995), and Lagos and Wright (2005) respectively. We find that the multilateral matching setting generates very simple and intuitive equilibrium allocations that are similar to those in the other papers, but which have important differences. In particular, surplus maximization can be achieved in this setting, in equilibrium, with a positive money supply. Moreover, with flexible prices and directed search, the first best allocation can be attained through price posting or through auctions with lotteries, but not through auctions without lotteries. Finally, analysis of the case of divisible goods and money can be performed without the assumption of large families (as in Shi (1997)) or the day and night structure of Lagos and Wright (2005).monetary exchange; directed search; ex post bidding; multilateral matching