The Econometrics of Matching Models

In October 2012 the Nobel prize was attributed to Al Roth and Lloyd Shapley for their work on matching. Both the seminal Gale-Shapley (1962) paper and most of Roth’s work were concerned with allocation mechanisms when prices or other transfers cannot be used—what we will call non-transferable utility (NTU) in this survey. Gale and Shapley used college admissions, marriage, and roommate assignments as examples; and Roth’s fundamental work in market design has led to major improvements in the National Resident Matching Program (Roth and Peranson 1999) and to the creation of a mechanism for kidney exchange (Roth, Sönmez and Ünver 2004.) The resulting insights have been applied to a host of issues, including the allocation of students to schools, the marriage market with unbalanced gender distributions, the role of marital prospects in human capital investment decisions, the social impact of improved birth control technologies and many others. The econometrics of matching models have recently been reconsidered, from different and equally innovative perspectives. The goal of the present project will be to survey these methodological advances. We shall describe the main difficulties at stake, the various answers provided so far, and the issues that remain open

Modeling Competition and Market Equilibrium in Insurance: Empirical Issues

In the last decade or so, numerous papers have been devoted to empirical investigations based on contract theory. Many contributions use insurance data, and specifically files provided by firms. A typical paper would analyze the relationship between individual characteristics, the contracts chosen and the corresponding “outcome,” as measured by claims. The natural next step in this research agenda is to model empirically market equilibrium on insurance markets. Empirical models of competitive insurance markets are important in many respects. First, such models are an indispensable first step for the empirical analysis of existing markets. The discussion of optimal pricing strategies or the definition of new insurance contract would greatly benefit from such models. From a policy perspective, the design of any regulation requires estimating its likely impact on the market allocation. For instance, while a ban on specific pricing options (based, say, on gender or age) is often advocated on ethical grounds, a precise assessment of its impact on insurance markets is needed before any decision is made; and an empirical model is required to provide such an assessment. From a purely theoretical perspective, any description of insurance markets that aims at a modicum of realism needs to come to terms with a host of complex features (horizontal differentiation of products, unobserved heterogeneity of preferences, frictions of various types), the theoretical analysis of which may be forbiddingly complex. A simple model that can be solved or at least numerically simulated may, in that case, be particularly helpful. Finally, a tractable model of insurance equilibrium can be used to run experiments, which should help us understand individual behavior in such strategic settings as competition under asymmetric information. On the other hand, modeling insurance markets raises several theoretical and empirical issues, starting, of course, with the well-known pitfalls in modeling equilibrium in contracts. The goal of the present paper is to discuss these problems and summarize the knowledge acquired so far. We successively discuss modeling of the demand side, the supply side, and the equilibrium itself

Divorce and the Duality of Marital Payoff

Empirical studies on the determinants of divorce are scarce in economics. One reason is the duality of the value of marriage, which combines economic gains for which proxies can be found and non-pecuniary gains that are much harder to measure. The literature on marital stability has therefore focused on the impact of income differentials between partners, omitting shocks to the non-economic components of the value of the marriage. We fill in the gap by extending the model of marriage dissolution to account for a time-varying non-pecuniary quality of the match. To explore its importance, we exploit a unique data set from the Russia Longitudinal Monitoring Survey (RLMS) which provides both labor market outcomes of the couples and subjective well-being data. Our results suggest that the monetary and non-monetary components enter the joint surplus additively, with gender-specific marginal rates of substitution. The valuation of the monetary components also reveals gender asymmetry, which we link to differences in remarriage prospects

Learning From a Piece of Pie

We investigate the empirical content of the Nash solution to two-player bar-gaining games. The bargaining environment is described by a set of variables that may affect agents' preferences over the agreement sharing, the status quo outcome, or both. The outcomes (i.e., whether an agreement is reached, and if so the individual shares) and the environment (including the size of the pie) are known, but neither are the agents' utilities nor their threat points. We consider both a deterministic version of the model in which the econometrician observes the shares as deterministic functions of the variables under consideration, and a stochastic one in which because of latent disturbances only the joint distribution of incomes and outcomes is recorded. We show that in the most general framework any outcome can be rationalized as a Nash solution. However, even mild exclusion restrictions generate strong implications that can be used to test the Nash bargaining assumption. Stronger conditions further allow to recover the underlying structure of the bargaining, and in particular, the cardinal representation of individual preferences in the absence of uncertainty. An implication of this finding is that empirical works entailing Nash bargaining could (and should) use much more general and robust versions than they usually do

Early Starters versus Late Beginners

We consider a model of wage formation characterized by two features, learning and downward rigidity. We show that wages should exhibit a late‐beginning property: when one controls for the wage at date t, the wage at date t + 1 should be negatively correlated with the wage at date 6–1. We test this property on a sample of about 1,000 executives of a French state‐owned firm whose careers we observe for 15 years. This organization exhibits the features that charecterize internal labor markets; in particular, careers consist of sequences of discrete promotions, a fact that generates specific econometric problems. The results confirm the prediction

Fatter Attraction: Anthropometric and Socioeconomic Matching on the Marriage Market

We construct a matching model on the marriage market along more than one characteristic, where individuals have preferences over physical attractiveness and socioeconomic characteristics that can be summarized by a one-dimensional index combining these various attributes. We show that under a (testable) separability assumption, the indices are ordinally identified. We estimate the model using data from the PSID. Our separability tests do not reject. We find that among men, a 10% increase in BMI can be compensated by a higher wage of around 3%. Similarly, for women, an additional year of education may compensate up to three BMI units

Matching with a Handicap: The Case of Smoking in the Marriage Market

We develop a matching model on the marriage market, where individuals have preferences over the smoking status of potential mates, and over their socioeconomic quality. Spousal smoking is bad for non-smokers, but it is neutral for smokers, while individuals always prefer high socioeconomic quality. Furthermore, there is a gender difference in smoking prevalence, there being more smoking men than smoking women for all education levels, so that smoking women and non-smoking men are in short supply. The model generates clear cut conditions regarding matching patterns. Using CPS data and its Tobacco Use Supplements for the years 1996 to 2007, and proxing socioeconomic status by educational attainment, we .nd that these conditions are satis.ed. There are fewer "mixed" couples where the wife smokes than vice-versa, and matching is assortative on education within smoking types of couples. Among non-smoking wives those with smoking husbands have on average 0.14 fewer years of completed education than those with non-smoking husbands. Finally, and somewhat counterintuitively, we find that, as theory predicts, among smoking husbands those who marry smoking wives have on average 0.16 more years of completed education than those with non-smoking wives

From Aggregate Betting Data to Individual Risk Preferences

As a textbook model of contingent markets, horse races are an attractive environment to study the attitudes towards risk of bettors. We innovate on the literature by explicitly considering heterogeneous bettors and allowing for very general risk preferences, including non-expected utility. We build on a standard single-crossing condition on preferences to derive testable implications; and we show how parimutuel data allow us to uniquely identify the distribution of preferences among the population of bettors. We then estimate the model on data from US races. Within the expected utility class, the most usual specfications (CARA and CRRA) fit the data very badly. Our results show evidence for both heterogeneity and nonlinear probability weighting

On Human Capital and Team Stability

In many economic contexts, agents from a same population team up to better exploit their human capital. In such contexts (often called “roommate matching problems”), stable matchings may fail to exist even when utility is transferable. We show that when each individual has a close substitute, a stable matching can be implemented with minimal policy intervention. Our results shed light on the stability of partnerships on the labor market. Moreover, they imply that the tools crafted in empirical studies of the marriage problem can easily be adapted to many roommate problems