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Published July 2009 | public
Journal Article

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 Pakes's (1999) model.

Additional Information

© 2009 Econometric Society. Manuscript received December, 2005; final revision received November, 2008. Many thanks to Rabah Amir, Kate Antonovics, Andrés Aradillas-López, Patrick Bajari, Peter Bossaerts, Colin Camerer, Chris Chambers, Xiaohong Chen, Valentino Dardanoni, Han Hong, Joel Horowitz, Matt Jackson, Michael Jansson, Chuck Manski, Andrea Mattozzi, Rosa Matzkin, Tom Palfrey, Jim Powell, Andrea Rotnitzky, Paul Ruud, Max Stinchcombe, Andrew Sweeting, Elie Tamer, Xavier Vives, Quang Vuong, Hal White, and Bill Zame, as well as participants at presentations given at Northwestern University, UC Berkeley, UC Davis, and the North American Econometric Society summer meeting, the EEE2005 conference, and the 2005 ESSET workshop. Echenique thanks the NSF for its support through award SES-0751980. Anonymous referees and a co-editor provided excellent suggestions and comments that greatly improved an earlier version of the paper. All remaining errors are ours.

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