Is assortative matching efficient?

Summary. This paper develops some general conditions under which complementarities between individual agents imply that assortative matching is efficient. Our analysis has four main findings. First, when agents are organized into equal-sized groups, just as in Becker (1973), the presence of within-group complementarities is sufficient for stratification to be efficient. Second, if group sizes vary, assortative matching may not be efficient even though complementarities are present, unless particular functional form assumptions are imposed. Third, the connection between assortative matching, complementarities and efficiency reemerges if one considers sequences of replications of the economy in which individual coalitions are uniformly bounded in size. Fourth, the presence of feedbacks from the composition of group memberships has important effects on efficient allocations and breaks any simple link between assortative matching and efficiency. Together, these results suggest that the characterization of the cross-section evolution of an efficiently sorted economy is likely to be highly complex. Received: September 25, 2001; revised version: February 26, 2002 RID="*" ID="*" We thank William Brock for many helpful conversations and Scott Page for detailed comments on an earlier draft of this paper. The National Science Foundation, John D. and Catherine T. MacArthur Foundation and Center for Urban Land Economic Research have generously provided financial support. Correspondence to: S. N. Durlauf     

Unravelling of Dynamic Sorting

We consider a two-sided, finite-horizon search and matching model with heterogeneous types and complementarity between types. The quality of the pool of potential partners deteriorates as agents who have found mutually agreeable matches exit the market. When search is costless and all agents participate in each matching round, the market performs a sorting function in that high types of agents have multiple chances to match with their peers. However, this sorting function is lost if agents incur an arbitrarily small cost in order to participate in each round. With a sufficiently rich type space, the market unravels as almost all agents rush to participate in the first round and match and exit with anyone they meet.     

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.     

Labor market characteristics and cultural choice

We develop a model of cultural selection based on the labor market characteristics of different cultural types. Following Borjas (1994, 1995) we assume that cultural heterogeneity increases labor productivity due to skill complementarities, however following Jackson and Xing (2014) we also assume that cultural heterogeneity hampers communication. We model this as a game in which individuals from two cultural types first engage in random matching, then once matched play a coordination game. Other‐type matches are thus potentially more productive, but also less likely to coordinate. We show that these two labor market characteristics serve as important primitives in determining if a cultural minority persists. Essentially, when the productivity advantages from a cross‐cultural match sufficiently outweigh the disadvantages of coordination problems then the cultural minority will persist. If not it will be assimilated. Further, we obtain results concerning the efficient size of the cultural minority, the effects of tax and welfare programs on the size and welfare of the cultural minority, and the relationship between the intensity of social interaction and size and welfare of the cultural minority.     

Strategic complementarities and search market equilibrium

In this paper, we apply supermodular game theory to the equilibrium search literature with sequential search. We identify necessary and sufficient conditions for the pricing game to exhibit strategic complementarities and prove existence of equilibrium. We then show that price dispersion is inherently incompatible with strategic complementarities in the sense that the Diamond Paradox obtains when firms are identical and is robust within the class of search cost densities that are small near zero and support strategic complementarities. We also show that a major criticism of the literature, that agents act as if they know the distribution of prices, can be justified in the sense of convergent best response dynamics.     

Screening Ethics when Honest Agents Keep their Word

Using a principal-agent setting, we introduce honesty that requires pre-commitment. The principal offers a menu of mechanisms to screen ethics. Agents may misrepresent ethics. Dishonest agents may misrepresent the match with the assigned task (good or bad), while honest agents reveal the match honestly if they have pre-committed. Ethics-screening, that allows for match-screening with dishonest agents while leaving a lower rent to honest agents, is optimal if both honesty and a good match are likely. Otherwise the optimal mechanism is the standard second-best or the first-best (where dishonest agents misrepresent the match), if dishonesty is likely or unlikely respectively.An earlier version of this paper was entitled “Honest Agents and Equilibrium Lies.” We are grateful to seminar participants at MIT, Université de Caen, University of St Andrews, University of Virginia, and ESEM 99, and two anonymous referees for useful comments.     

Should a team be homogeneous?

Should an organization hire people with similar backgrounds or with different backgrounds? We formulate this question within the framework of team theory. The team is formed by n agents. The type of each agent is endogenous and determines his information structure and his cost for the team. We show that the sign of complementarity between jobs determines workforce homogeneity. With positive complementarities, the team should be composed of agents of the same type, while, with negative complementarities, workforce heterogeneity is optimal. These results do not rely on the restrictions on the way uncertainty is modeled or on the feasible set of agent types: they can be explained in terms of correlation between errors committed by different agents.     

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.     

SOCIAL ASSETS*

We present a model incorporating both social and economic components and analyze their interaction. The notion of a social asset, an attribute that has value only because of the social institutions governing society, is introduced. In the basic model, agents match on the basis of income and unproductive attributes. An attribute has value in some equilibrium social institutions (matching patterns), but not in others. We then show that productive attributes (such as education) can have their value increased above their inherent productive value by some social institutions, leading to the notion of the social value of an asset.     

Independent random matching

Random matching models with a continuum population are widely used in economics to study environments where agents interact in small coalitions. This paper provides foundations to such models. In particular, the paper establishes an existence result for random matchings that are universal in the sense that certain desirable properties are satisfied for any assignment of types to agents. The result applies to infinitely many types of agents, thus covering random matching models which are currently used in the literature without a foundation. Furthermore, the paper provides conditions guaranteeing uniqueness of random matching.     

Strategic complementarity in multi-stage games

We provide sufficient conditions in finite-horizon multi-stage games for the value function of each player, associated to extremal Markov perfect equilibria, to display strategic complementarities and for the contemporaneous equilibrium to be increasing in the state variables. The author is grateful to Federico Echenique, Rabah Amir and one anonymous referee for useful comments, project SEJ2005-08263 at UPF and Project Consolider-Ingenio CSD2006-00016 of the Spanish Ministry of Education and Science, and the Barcelona Economics Program of CREA, for financial support.     

Innovation,complementarity, and exporting. Evidence from German manufacturing firms

This paper assesses whether there might be complementarities between different types of innovation activities (product, process and organizational) and how these effects may be linked to the likelihood that a firm will export. Complementarity is addressed through the properties of supermodular functions, and firm heterogeneity by export destination is explored. A new econometric strategy to test for pairwise complementarity in a function with three independent variables and a binary dependent variable is proposed. Exogenous and endogenous innovation variables are considered by using bootstrapping for hypothesis testing, propensity score matching and treatment effects models. The empirical analysis shows that complementarity relationships between innovation strategies are more likely to exist when firms export to multiple foreign markets.     

Assigning Refugees to Landlords in Sweden: Efficient,Stable, and Maximum Matchings*

In this paper, we investigate the problem of finding housing for refugees once they have been granted asylum. In particular, we demonstrate that market design can play an important role in a partial solution to the problem. More specifically, we investigate a specific matching system, and we propose an easy-to-implement mechanism that finds an efficient, stable, and maximum matching. Such a matching guarantees that housing is efficiently provided to a maximum number of refugees, and that no refugee prefers another specific landlord to their current match when, at the same time, that specific landlord prefers that refugee to their own current match.     

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.     

The Manipulability of Matching Rules via Segmentation

Our matching problems feature agents with endowments facing certain division rules. At any matching, the endowments of agents are reallocated between the matched pairs according to some given division rule, and this opens doors to an iterated matching problem and rematching, and to manipulation of some matching rules via segmentation. In this form of manipulation a coalition breaks off from the rest, matches within itself and rejoins the complementary coalition for a rematching at the new endowment profile. Under certain division rules this may benefit the coalition who breaks off without hurting the complementary coalition. Furthermore, both may benefit by first matching internally and then rejoining for a new match.     

Complementarities between firm-sponsored training and information technology use

In this article, we investigate the presence of possible complementarities between investments in information technology (IT) and firm-sponsored training using economy-wide longitudinal representative workplace-level data. Since information on the firm’s capital stock is often missing in such representative data, we match our workplace records to tax data to construct measures of the firm’s capital stock. We find some evidence of positive complementarities between investments in human capital and IT, suggesting that on-the-job training can also have a positive impact on productivity when complemented with investments in CAD or other technologies.     

On the efficiency of ex ante and ex post pricing institutions

Summary This paper compares the performance of three pricing institutions in a decentralized matching model in which random matching occurs. In the first, sellers make public ex ante commitments to trade at pre-specified prices before matching occurs. In the second, the buyer and seller engage in an alternating offer bargaining game once a match has occurred. In the final pricing institution, one party is chosen at random to make a take it or leave it price offer. The steady state equilibrium with ex ante pricing pareto dominates the steady state equilibrium with ex post take it or leave it offers, which in turn pareto dominates the steady state equilibrium with alternating offers. As the discount factor goes to one, the equilibrium with ex ante pricing generates participation rates that tend toward the pareto efficient level. The ex post pricing institutions generate participation rates that are bounded away from efficient levels. The surplus loss associated with switching from ex ante pricing to take it or leave it offers is small when the discount factor is close to one. Contrary to many models of decentralized trade, ex post pricing institutions encourage too much search by buyers.The financial support of the Social Sciences and Humanities Research Council of Canada is gratefully acknowledged. The research for this paper was completed while the author was visiting the University of California at San Diego. The author thanks Douglas Gale for comments.     

The good,the bad and the ugly: agent behavior and efficiency in open and closed organizations

Current literature has largely ignored the fact that some organizations are highly selective when admitting new agents while others are more open. In addition, some organizations audit or sort agent behavior within the organization more aggressively than others. One might expect a priori that closed, highly selective, organizations would always be more efficient because they screen out the worst types, which could lead to better agent behavior. We show that this is not the case. Specifically, when agent behavior in equilibrium is uniform across organizations (i.e., when the number of agents behaving the same way is identical), closed organizations are inefficient. However, when agent behavior varies across organizations, closed organizations may or may not be inefficient, depending on net payoffs to the organization and the agents. Our analysis implies that organizations should choose the open type when screening or sorting costs are high, when there is a high frequency of good agent types in the population, when agent misbehavior does not reduce output significantly, and when penalties for misbehavior are large. The paper has benefitted from useful comments by David Flath, Charles Knoeber, Claudio Mezzetti, two anonymous referees and participants of the Spring 2005 Midwest Economic Theory meetings at Vanderbilt University, the 2005 meetings of the Society for the Advancement of Economic Theory in Vigo, Spain, the 2005 conference on Research in Economic Theory and Econometrics in Syros, Greece, and workshops at North Carolina State University, Texas A&M University and McGill University.     

Optimal search,learning and implementation

We characterize the incentive compatible, constrained efficient policy (“second-best”) in a dynamic matching environment, where impatient, privately informed agents arrive over time, and where the designer gradually learns about the distribution of agents? values. We also derive conditions on the learning process ensuring that the complete-information, dynamically efficient allocation of resources (“first-best”) is incentive compatible. Our analysis reveals and exploits close, formal relations between the problem of ensuring implementable allocation rules in our dynamic allocation problems with incomplete information and learning, and between the classical problem, posed by Rothschild (1974) [20], of finding optimal stopping policies for search that are characterized by a reservation price property.     

Complementarities and spillovers in mergers: an empirical investigation using patent data

We investigate the merger behavior of firms in the plant biotechnology sector using firm-level patent data for public and private firms in the 1980s and 1990s. Conditional logit estimation is used to estimate the probability that the firms will match in mergers and spinoffs. We calculate several patent portfolio-based measures of complementarity and spillovers between firms, and find that both are important to defining a good match of acquirer and target. However, complementarities provide the more robust explanation. The mergers and spinoffs observed in plant biotechnology may have been designed to overcome the anti-commons problem of mutually blocking technology, an extreme form of complementarity. Our results highlight the need to integrate patent and competition policy.