Inference in ordered response games with complete information

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractWe study econometric models of complete information games with ordered action spaces, such as the number of store fronts operated in a market by a firm, or the daily number of flights on a city-pair offered by an airline. The model generalizes single agent models such as ordered probit and logit to a simultaneous equations model of ordered response, allowing for multiple equilibria and set identification. We characterize identified sets for model parameters under mild shape restrictions on agents' payoff functions. We then propose a novel inference method for a parametric version of our model based on a test statistic that embeds conditional moment inequalities implied by equilibrium behavior. Using maximal inequalities for U-processes, we show that an asymptotically valid confidence set is attained by employing an easy to compute fixed critical value, namely the appropriate quantile of a chi-square random variable. We apply our method to study capacity decisions measured as the number of stores operated by Lowe's and Home Depot in geographic markets. We demonstrate how our confidence sets for model parameters can be used to perform inference on other quantities of economic interest, such as the probability that any given outcome is an equilibrium and the propensity with which any particular outcome is selected when it is one of multiple equilibria, and we perform a counterfactual analysis of store configurations under both collusive and monopolistic regimes.

An empirical model of non-equilibrium behavior in games

“…Therefore, it is not possible to infer the number of steps of unanchored strategic reasoning that an individual uses by inspecting whether the action taken by that individual is equal to that predicted by a particular number of steps of unanchored strategic reasoning. For example, the observation that an individual uses a particular action could be consistent with that individual using 1 Papers in that literature (among papers that study complete information), typically based on Nash equilibrium, include Tamer (2003), Aradillas-Lopez and Tamer (2008), Bajari, Hong, and Ryan (2010), Kline and Tamer (2012), Aradillas-Lopez and Rosen (2013), Dunker, Hoderlein, and Kaido (2013), Kline (2015Kline ( , 2016, and Fox and Lazzati (2017). See de Paula (2013) for a review.…”

Identification of discrete choice models for bundles and binary games

“…3 Gentzkow uses a parametric, multivariate probit model. To our knowledge, we are the first to give conditions for nonparametric identification in models of demand for bundles, at least without relying on bundle-specific prices and treating each bundle as a separate good in the usual multinomial choice framework where a consumer picks only one product.…”

Characterizations of identified sets delivered by structural econometric models

“…It is shown that these sets can be expressed as systems of moment inequalities and equalities to which recently developed inferential procedures are applicable. See for example and Aradillas-Lopez and Rosen (2013) for empirical applications using treatment e¤ect and simultaneous ordered response models.…”