scholarly journals The Econometrics and Some Properties of Separable Matching Models

2017 ◽  
Vol 107 (5) ◽  
pp. 251-255 ◽  
Author(s):  
Alfred Galichon ◽  
Bernard Salanié
Keyword(s):  
Comparative Statics ◽  
Transferable Utility ◽  
Separable Models ◽  
One To One ◽  
Matching Models

We present a class of one-to-one matching models with perfectly transferable utility. We discuss identification and inference in these separable models, and we show how their comparative statics are readily analyzed.

Matching under Transferable Utility: Applications

2017 ◽  
Author(s):  
Pierre-André Chiappori
Keyword(s):  
Higher Education ◽  
Birth Control ◽  
Marriage Market ◽  
Comparative Statics ◽  
Female Empowerment ◽  
Control Technology ◽  
Transferable Utility ◽  
Male And Female ◽  
Roe V Wade ◽  
Matching Models

This chapter considers two examples of applications of matching models under transferable utility (TU). The first example deals with the legalization of abortion by virtue of Roe v. Wade and the feminist claim that it empowered all women. The second example deals with the discrepancy between male and female demand for higher education over the last decades. After providing an overview of Roe v. Wade and how it resulted in female empowerment, the chapter describes the model that takes into account preferences and budget constraints, stable matching on the marriage market, and changes in birth control technology. It then examines gender differences in the demand for higher education using the CIW (Chiappori, Iyigun, and Weiss) model, with a focus on equilibrium, preferences for singlehood, comparative statics, empirical implementation, and the Low model showing that higher education results in a deterministic drop in fertility.

Matching with Transfers: Basic Notions

2017 ◽  
Author(s):  
Pierre-André Chiappori
Keyword(s):  
Metric Spaces ◽  
Transferable Utility ◽  
Equilibrium Concept ◽  
Matching Problem ◽  
Basic Equilibrium ◽  
One To One ◽  
Definition Of ◽  
Matching Models

This chapter describes the basic notions of matching with transfers. It first introduces the notations that will be used throughout the book, including two compact, separable metric spaces: the space of female characteristics and the space of male characteristics. In particular, it outlines a framework that is common to all (bipartite, one-to-one) matching models. It then considers how a matching problem is defined in the nontransferable utility, transferable utility, and imperfectly transferable utility cases. It also explains how the solution is defined in all three cases, noting that there are differences in the definition of an equilibrium. In all cases, the basic equilibrium concept is stability.

scholarly journals Pairwise Stable Matching in Large Economies

Econometrica ◽  
2021 ◽  
Vol 89 (6) ◽  
pp. 2929-2974 ◽  
Author(s):  
Michael Greinecker ◽  
Christopher Kah
Keyword(s):  
General Class ◽  
Stable Matching ◽  
High Dimensional ◽  
Transferable Utility ◽  
Stable Matchings ◽  
Matching Problems ◽  
Joint Distributions ◽  
Special Cases ◽  
Matching Models ◽  
Stability Notions

We formulate a stability notion for two‐sided pairwise matching problems with individually insignificant agents in distributional form. Matchings are formulated as joint distributions over the characteristics of the populations to be matched. Spaces of characteristics can be high‐dimensional and need not be compact. Stable matchings exist with and without transfers, and stable matchings correspond precisely to limits of stable matchings for finite‐agent models. We can embed existing continuum matching models and stability notions with transferable utility as special cases of our model and stability notion. In contrast to finite‐agent matching models, stable matchings exist under a general class of externalities.

Matching under Imperfectly Transferable Utility

2017 ◽  
Author(s):  
Pierre-André Chiappori
Keyword(s):  
Theoretical Framework ◽  
The Other ◽  
Assortative Matching ◽  
Transferable Utility ◽  
Matching Models

This chapter considers matching models under imperfectly transferable utility (ITU). Some of the techniques used in the transferable utility (TU) case can be extended to an ITU framework; for example, the Spence-Mirrlees condition, which is sufficient for positive assortative matching (PAM), can be generalized to the ITU case. Furthermore, individual utilities may be recovered (up to a constant, as in the TU case), using techniques which are essentially similar to their TU counterpart. After providing an overview of the basic notions and theoretical framework of matching under ITU, the chapter discusses the recovery of individual utilities, PAM, and econometrics of ITU. It also presents two examples of applications of ITU techniques, one dealing with matching on wages and the other with endogenous Pareto weights.

Matching under Transferable Utility: Theory

2017 ◽  
Author(s):  
Pierre-André Chiappori
Keyword(s):  
Pareto Frontier ◽  
Intrahousehold Allocation ◽  
Formal Definition ◽  
Hedonic Models ◽  
Transferable Utility ◽  
Property A ◽  
Hedonic Equilibrium ◽  
Definition Of ◽  
Matching Models ◽  
The Relationship

This chapter considers the theory of matching under transferable utility (TU). It first introduces a formal definition of the TU property: a group satisfies TU if there exists monotone transformations of individual utilities such that the Pareto frontier is a hyperplane. It then examines the cornerstone of the theory of nontransferable utility (NTU) matching, namely, the Gale-Shapley algorithm, before turning to a discussion of a crucial property of matching models under TU: their intrinsic relationship with optimal transportation. It also describes the notions of supermodularity and assortativeness, along with individual utilities and intrahousehold allocation. Finally, it looks at hedonic models, taking into account hedonic equilibrium and stable matching, and presents two examples that illustrate the relationship between matching and hedonic models: a competitive IO model and randomized matching.

Conclusion

2017 ◽  
Author(s):  
Pierre-André Chiappori
Keyword(s):  
Higher Education ◽  
Risk Sharing ◽  
Social Issues ◽  
Family Economics ◽  
Transferable Utility ◽  
Production Risk ◽  
Male And Female ◽  
Roe V Wade ◽  
Matching Models ◽  
The Relationship

This concluding chapter discusses the progress that has been made with matching models on both the theoretical and the empirical front. Regarding theory, the power and the limits of the transferable utility (TU) model are now better understood. The TU framework can (admittedly under specific assumptions on preferences) encompass most aspects of family economics, including fertility, domestic production, risk sharing, and the consumption of public commodities. On the empirical side, the econometrics of matching models have seen several major advances, with the Choo-Siow model as a prime example. The chapter also considers what matching models teach us about reality, such as the asymmetry between male and female demand for higher education, and the relationship between assortative matching and inequality. Furthermore, a host of social issues can only be analyzed from a general equilibrium perspective; this is evident in the case of Roe v. Wade.

Matching under Transferable Utility: Some Extensions

2017 ◽  
Author(s):  
Pierre-André Chiappori
Keyword(s):  
Human Capital ◽  
Risk Sharing ◽  
Marriage Market ◽  
Stable Matching ◽  
Coase Theorem ◽  
Transferable Utility ◽  
Matching Problem ◽  
Basic Model ◽  
Matching Models ◽  
Roommate Matching

This chapter considers some extensions of matching models under transferable utility (TU). It begins with a discussion of preinvestment, in which agents deliberately invest in education, and the stock of human capital that characterizes them when entering the marriage market is therefore (at least partly) endogenous. It is safe to assume that agents, when deciding their investment, take into account, among other things, its impact on the marriage market. An alternative argument is that agents are likely to invest too much. The chapter proceeds by analyzing the relevance of TU to risk sharing, multidimensional matching, and the roommate matching problem, taking into account the existence of a stable matching and the cloned bipartite problem. Finally, it describes the basic model of divorce and remarriage, focusing on compensations in the Becker-Coase theorem as well as violations of the theorem.

Introduction: Matching Models in Economics

2017 ◽  
Author(s):  
Pierre-André Chiappori
Keyword(s):  
Higher Education ◽  
United States ◽  
Family Formation ◽  
The United States ◽  
Household Behavior ◽  
Transferable Utility ◽  
Bargaining Models ◽  
Unitary Model ◽  
Matching Models ◽  
Gender Specific

This chapter considers two related puzzles that are directly related to family formation (and dissolution) and to intrafamily allocation: the first deals with the increase in inequality in the United States in recent decades, and the second has to do with some remarkable trends in gender-specific demand for higher education. In addition, it also describes the main features of matching models, including a frictionless environment and notion of transfers, with particular emphasis on nontransferable utility, transferable utility, and imperfectly transferable utility. Finally, it discusses existing models of household behavior, such as the unitary model, the collective model, and noncooperative models, as well as bargaining models of the household. An overview of the book's content is also presented.

scholarly journals The Balance Condition in Search‐and‐Matching Models

Econometrica ◽  
2020 ◽  
Vol 88 (2) ◽  
pp. 595-618
Author(s):  
Stephan Lauermann ◽  
Georg Nöldeke ◽  
Thomas Tröger
Keyword(s):  
Steady State ◽  
Random Search ◽  
Comparative Statics ◽  
Regularity Conditions ◽  
Search And Matching ◽  
Balance Condition ◽  
General Search ◽  
Search And Matching Models ◽  
Matching Models ◽  
Smith Model

Most of the literature that studies frictional search‐and‐matching models with heterogeneous agents and random search investigates steady state equilibria. Steady state equilibrium requires, in particular, that the flows of agents into and out of the population of unmatched agents balance. We investigate the structure of this balance condition, taking agents' matching behavior as given. Building on the “fundamental matching lemma” for quadratic search technologies in Shimer and Smith (2000), we establish existence, uniqueness, and comparative statics properties of the solution to the balance condition for any search technology satisfying minimal regularity conditions. Implications for the existence and structure of steady state equilibria in the Shimer–Smith model and extensions thereof are noted. These reinforce the point that much of the structure of search‐and‐matching models with quadratic search technologies carries over to more general search technologies.

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