Two-Sided Search, Marriages, and Matchmakers

This article analyzes the provision of matching services in a model of two-sided search. Agents belong to two heterogeneous populations and are distributed on [0, 1]. Their utility is equal to the index of their mate. In a search equilibrium agents form subintervals and are only matched to agents inside their class. Marriage brokers match agents according to a centralized procedure. If the matchmaker charges a uniform participation fee, only agents of higher quality participate in the centralized procedure. If the matchmaker charges a commission on the matching surplus, only agents of lower quality go to the intermediary.     

Price discrimination and efficient matching

This paper considers the problem of a monopoly matchmaker that uses a schedule of entrance fees to sort different types of agents on the two sides of a matching market into exclusive meeting places, where agents randomly form pairwise matches. We make the standard assumption that the match value function exhibits complementarities, so that matching types at equal percentiles maximizes total match value and is efficient. We provide necessary conditions and sufficient conditions for the revenue-maximizing sorting to be efficient. These conditions require the match value function, modified to incorporate the incentive cost of eliciting private type information, to exhibit complementarities in types.JEL Clalssification Numbers C7, D4We thank Jonathan Levin, Tracy Lewis, and the seminar audience at University of California at Los Angeles, University of British Columbia, Duke University, and 2003 Econometric Society North American Summer Meeting for comments and suggestions. We are also grateful for helpful suggestions from the referees and the Editor     

Limited duration employment

This paper analyzes a matching model in which labor market participants use temporary employment as a waiting station between searches. Searchers entering the market see all available options. The best match, however, may not be particularly productive. Since all currently available traders are known, immediate search is not worthwhile. Over time, turnover replenishes the stock of potential traders and poor matches eventually find it profitable to search again. Searchers therefore take the best available match and simultaneously formulate if and when to look again. The best matches become indefinite; lower quality matches coexist as temporary employment. This duration increases with match quality and declines as matching improves.     

Truthtelling in Matching Markets

We analyze a search and matching model with non‐transferable utility and asymmetric information. Randomly paired agents go through an evaluation phase, at the end of which they discover each other's types and choose to match or not. Before deciding to enter this phase, agents can communicate through cheap talk. We provide conditions for this communication to be informative, and we examine how it affects agents' welfare. We show that communication is Pareto‐improving only when the matching is assortative in the absence of communication and left unchanged by information transmission.     

Sorting by search intensity

In this paper, I characterize matching in an on-the-job search model with endogenous search intensity, heterogeneous workers and firms, and match surplus is shared between workers and firms through bargaining. I provide proof of existence and uniqueness of steady state equilibrium. Given equally efficient matched and unmatched search, the worker skill conditional distribution of firm productivity over matches is stochastically increasing (decreasing) in worker skill if the production function is supermodular (submodular). I also show that this strong notion of sorting does not obtain everywhere for the firm productivity conditional match distribution.     

Measuring Search Frictions Using Japanese Microdata

This paper estimates individual‐level matching functions to measure search frictions in the Japanese labour market and presents the determinants of search duration. We employ administrative microdata that track the job search process of job seekers who left or lost their job in August 2005 and subsequently registered at their local public employment service. Our finding is that the matching function exhibits decreasing rather than constant returns‐to‐scale for job seekers and vacancies. We also find that after controlling for the benefits period, job seekers who lost their job involuntarily were more likely than those quitting voluntarily to exit from unemployment.     

Contractual distortions in a market with frictions

This paper analyses contract design in a decentralized market environment with frictions. While principals (e.g., firms) have all contractual power, their market power is constrained as agents (e.g., workers) can choose to wait and search for better offers. We find that results depend crucially on how market frictions affect agents’ utilities. With type-independent costs of search and waiting, equilibrium contracts are always first-best. If agents are impatient and discount future payoffs, however, distortions vanish only gradually. In the latter case, we also characterize equilibrium offers and show that the market exhibits two types of externalities, both of which are absent in the case of type-independent costs of search.     

A TEST BETWEEN STOCK‐FLOW MATCHING AND THE RANDOM MATCHING FUNCTION APPROACH*

This article tests between the standard “random matching function” approach and “stock‐flow” matching while controlling for temporal aggregation bias. Consistent with previous empirical work, the random matching function fits the matching data reasonably well. But match flows are more highly correlated with vacancy inflows than is consistent with the random matching approach. Instead the data support stock‐flow matching, where unemployed workers match directly with suitable new vacancies as such vacancies come on to the market.     

Screening in a Matching Market

Contract design under incomplete information is often analysed in a bilaterally monopolistic setting. If the informed party's reservation value does not depend on its private information (its type), it is a standard result that the uninformed side offers "low" types distorted contracts to reduce the information rent left to "high7rdquo; types.
We challenge this result by embedding contract design in a matching market environment. We consider a market where players meet pairwise and where, in each match, either side may be chosen to make a take-it-or-leave-it offer. As frictions become sufficiently low, we find that the set of equilibria is independent of whether there is complete or incomplete information. In particular, all contracts are free of distortions.     

Competing cybermediaries

We examine a price competition game between two intermediaries offering to match two sides of a market on the Internet. Competition is characterized by asymmetric network externalities. We account for some specificities of cybermediation, in particular access versus usage pricing and the possibility of using the services of several intermediaries. When only registration fees are used and agents register with at most one cybermediary, there exists an equilibrium where one firm corners the market with positive profits. Introducing either fees contingent on successful matching or the possibility of registration with two cybermediaries make these profits vanish. Other types of equilibria are discussed.     

Stock-flow matching and the performance of the labor market

We estimate outflow equations for vacancies and unemployed workers in Britain, departing from the stock-based analysis of matching in two ways. First, we deal with the temporal aggregation problem that arises when discrete time data are used to describe continuous time processes. Second, we allow for a stock-flow matching mechanism in which the stock of traders on one side of the market matches with the flow of traders on the other side. Our estimates are in line with the predictions of stock-flow matching in terms of higher exit rates of flows and of matching combinations between labor market stocks and flows. Furthermore, employer search effectiveness did not seem to decline between the 1960s and the 1990s. Nevertheless, some deterioration in worker search effectiveness is detected, however less severe than that implied by previous, stock-based work.     

Disclosure of information in matching markets with non-transferable utility

We present a model of two-sided matching where utility is non-transferable and information about individualsʼ skills is private, utilities are strictly increasing in the partnerʼs skill and satisfy increasing differences. Skills can be either revealed or kept hidden, but while agents on one side have verifiable skills, agents on the other side have skills that are unverifiable unless certified, and certification is costly. Agents who have revealed their skill enter a standard matching market, while others are matched randomly. We find that in equilibrium only agents with skills above a cutoff reveal, and then they match assortatively. We show that an equilibrium always exists, and we discuss multiplicity. Increasing differences play an important role to shape equilibria, and we remark that this is unusual in matching models with non-transferable utility. We close the paper with some comparative statics exercises where we show the existence of non-trivial externalities and welfare implications.     

Assortative matching of risk-averse agents with endogenous risk

A standard risk-sharing matching game predicts negative assortative matching over agents’ risk attitudes. In regards to risk sharing, less risk-averse agents prefer highly risk-averse partners, who pay a high risk premium. Negative sorting is, however, inconsistent with empirical and experimental literature. To resolve this conflict, we propose a model where agents can control the risks to their incomes. In regards to risk management, agents prefer similar partners because of their aligned objectives in risk management. When it is easy to control risks or all agents are sufficiently risk-averse, the risk-management effect dominates, leading to positive sorting.     

Spatial competition with intermediated matching

This paper studies a two-sided market where the one type of agents needs the service of a middleman or matchmaker in order to be matched with the other type. The matchmakers compete for agents of both types by means of commission fees. In addition to the fee, the agents also lose a certain transaction cost in case of a match, which may differ among agents. Furthermore, agents have a limited willingness to pay for the service provided by the matchmakers. In certain cases the matchmakers are willing to subsidize one side of the market. Then one of the types of agents is free-riding.     

Accounting for endogeneity in matching function estimation

We show that equilibrium matching models imply that standard estimates of the matching function elasticities are exposed to an endogeneity bias, which arises from the search behavior of agents on either side of the market. We offer an estimation method which, under certain structural assumptions about the process driving shocks to matching efficiency, is immune from that bias. Application of our method to the estimation of a basic version of the matching function using aggregate U.S. data from the Job Openings and Labor Turnover Survey (JOLTS) suggests that the bias can be quantitatively important.     

Strategic Bargaining and Competitive Bidding in a Dynamic Market Equilibrium

This paper extends the bargaining and matching literature, such as Rubinstein and Wolinsky (1985), by considering a new matching process. We assume that a central information agency exists, such as real estate agencies in the housing market and employment agencies (or newspapers) in the labour market, which puts traders into direct contact with each other. With heterogeneity of trader preferences, equilibrium trade is characterized by existing traders on each side of the market trying to match with the flow of new traders on the other side (since existing traders have already sampled and rejected each other). Two procedures of trade co-exist, namely a strategic bilateral bargaining process and a competitive bidding process, depending on the number of potential matches a new trader obtains. We characterize the unique symmetric Markov perfect equilibrium to this stochastic trading game.     

A note on the life-cycle search and matching model with segmented labor markets

Recently, there has been renewed interest in labor search and matching models that incorporate a life-cycle structure by assuming finite horizons. Existing studies provide detailed analyses on the age dynamics of job creation and destruction, assuming that workers of all ages search for jobs in the same market. This paper examines a related environment that has drawn less attention, where the labor market is exogenously segmented by age. The paper finds sufficient conditions for the model to yield unambiguous predictions on the age profiles of key variables, and compares them with the corresponding conditions in models with a single market. The paper further examines the age profiles of these key variables in the efficient allocation. In particular, with no persistence in idiosyncratic match productivity, the efficient allocation is found to exhibit monotonic age profiles for the job finding and separation rates.     

NEW MICROFOUNDATIONS FOR THE AGGREGATE MATCHING FUNCTION*

Empirical studies of the aggregate labor market matching function have favored a Cobb–Douglas functional form, for which there are no microfoundations in the existing literature. I present a new model for the matching process, based on a “telephone‐line” Poisson queuing process, which, unlike other microeconomic approaches, can be integrated directly into standard theoretical search models. This implies a CES matching function, approximately Cobb–Douglas when search costs are approximately linear. The model allows empirical estimates of matching function parameters to be interpreted in terms of the costs and benefits of search.     

Matching and bargaining models of markets: approximating small markets by large markets

Summary. We show that the equilibrium of a matching and bargaining model of a market in which there is a finite number of agents at each date need not be near the equilibrium of a market with a continuum of agents, although matching probabilities are the same in both markets. Holding the matching process fixed, as the finite market becomes large its equilibrium approaches the equilibrium of its continuum limit.Received: January 22, 1996; revised version: September 24, 1996This revised version was published online in February 2005 with corrections to the cover date.     

Credit mismatch and breakdown

This paper studies the phenomenon of mismatch in a decentralized credit market where borrowers and lenders must engage in costly search to establish credit relationships. Our dynamic general equilibrium framework integrates incentive based informational frictions with a matching process highlighted by (i) borrowers' endogenous market entry and exit decision (entry frictions) and (ii) time and resource costs necessary to locate credit opportunities (search frictions). A key feature of the incentive compatible loan contract negotiated between borrowers and lenders is the interaction of informational frictions (in the form of moral hazard) with entry and search frictions. We find that the removal of entry barriers can eliminate incentive-based equilibrium credit rationing. More generally, entry and incentive frictions are important in understanding the extent of credit rationing and credit mismatch, while search and incentive frictions are important for understanding credit market breakdown.