Federico Echenique

A Theory of Stability in Many-to-many Matching Markets

We develop a theory of stability in many-to-many matching markets. We give conditions under which the setwise-stable set, a core-like concept, is nonempty and can be approached through an algorithm. The usual core may be empty. The setwise-stable set coincides with the pairwise-stable set and with the predictions of a non-cooperative bargaining model. The setwise-stable set possesses the conflict/coincidence of interest properties from many-to-one, and one-to-one models. The theory parallels the standard theory of stability for many-to-one, and one-to-one, models. We provide results for a number of core-like solutions, besides the setwise-stable set.

Comparative Statics by Adaptive Dynamics and The Correspondence Principle

Federico Echenique JEL#: C61, C62, C72, C73 Keywords: Monotone comparative statics, supermodularity, strategic complements, learning, correspondence principle This paper formalizes the relation between comparative statics and the out-of-equilibrium explanation for how a system evolves after a change in parameters. The paper has two main results. First, an increase in an exogenous parameter sets o_ learning dynamics that involve larger values of the endogenous variables. Second, equilibrium selections that are not mono- tone increasing in the exogenous variables must be predicting unstable equilibria. Moreover, under some conditions monotone comparative statics and stability are equivalent. January 2000 (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version (This abstract was borrowed from another version of this item.)

Core many-to-one matchings by fixed-point methods

We characterize the core many-to-one matchings as fixed points of a map. Our characterization gives an algorithm for finding core allocations; the algorithm is efficient and simple to implement. Our characterization does not require substitutable preferences, so it is separate from the structure needed for the non-emptiness of the core. When preferences are substitutable, our characterization gives a simple proof of the lattice structure of core matchings, and it gives a method for computing the join and meet of two core matchings.

The Money Pump as a Measure of Revealed Preference Violations

We introduce a measure of the severity of violations of the revealed preference axioms, the money pump index (MPI). The MPI is the amount of money one can extract from a consumer who violates the axioms. It is also a statistical test for the hypothesis that a consumer is rational when behavior is observed with error. We present an application using a panel data set of food expenditures. The data exhibit many violations of the axioms. Mostly, the MPI for these violations is small. The MPI indicates that the hypothesis of consumer rationality cannot be rejected.

Mixed Equilibria are Unstable in Games of Strategic Complements

In games with strict strategic complementarities, properly mixed Nash equilibria - equilibria that are not in pure strategies - are unstable for broad class of learning dynamics.

Is School Segregation Good or Bad

It has been well documented that segregation across schools — denying access to resources, inferior educational production functions, and so on — exacerbates racial differences in achievement. Using an individual measure of social connections within schools, we have shown that this form of segregation — Asian kids sitting together in the cafeteria — has a substantively unimportant relationship with academic achievement or social behavior in school or later in life. There are important caveats to our analysis: (a) our estimates of the relationship between within - school segregation and outcomes are not causal; and (b) friendships may not be the only relevant cross-race social interaction that occurs within a school.

On the Measurement of Segregation

This paper develops a measure of segregation based on two premises: (1) a measure of segregation should disaggregate to the level of individuals, and (2) an individual is more segregated the more segregated are the agents with whom she interacts. Developing three desirable axioms that any segregation measure should satisfy, we prove that one and only one segregation index satisfies our three axioms, and the two aims mentioned above; which we coin the Spectral Segregation Index. We apply the index to two well-studied social phenomena: residential and school segregation. We calculate the extent of residential segregation across major US cities using data from the 2000 US Census. The correlation between the Spectral index and the commonly-used dissimilarity index is .42. Using detailed data on friendship networks, available in the National Longitudinal Study of Adolescent Health, we calculate the prevalence of within-school racial segregation. The results suggests that the percent of minority students within a school, commonly used as a substitute for a measure of in-school segregation, is a poor proxy for social interactions.

Supermodularity and preferences

We uncover the complete ordinal implications of supermodularity on finite lattices under the assumption of weak monotonicity. In this environment, we show that supermodularity is ordinally equivalent to the notion of quasisupermodularity introduced by Milgrom and Shannon. We conclude that supermodularity is a weak property, in the sense that many preferences have a supermodular representation.

Testing Models With Multiple Equilibria by Quantile Methods

This paper proposes a method for testing complementarities between explanatory and dependent variables in a large class of economic models. The proposed test is based on the monotone comparative statics (MCS) property of equilibria. Our main result is that MCS produces testable implications on the (small and large) quantiles of the dependent variable, despite the presence of multiple equilibria. The key features of our approach are that (i) we work with a nonparametric structural model of a continuous dependent variable in which the unobservable is allowed to be correlated with the explanatory variable in a reasonably general way; (ii) we do not require the structural function to be known or estimable; (iii) we remain fairly agnostic on how an equilibrium is selected. We illustrate the usefulness of our result for policy evaluation within Berry, Levinsohn, and Pakess (1999) model. Copyright 2009 The Econometric Society.

Clearinghouses for two‐sided matching: An experimental study

We experimentally study the Gale and Shapley, 1962 mechanism, which is utilized in a wide set of applications, most prominently the National Resident Matching Program (NRMP). Several insights come out of our analysis. First, only 48% of our observed outcomes are stable, and among those a large majority culminate at the receiver-optimal stable matching. Second, receivers rarely truncate their true preferences: it is the proposers who do not make offers in order of their preference, frequently skipping potential partners. Third, market characteristics affect behavior: both the cardinal representation and core size influence whether laboratory outcomes are stable. We conclude by using our controlled results and a behavioral model to shed light on a number of stylized facts we derive from new NRMP survey and outcome data, and to explain the small cores previously documented for the NRMP.