The Econometrics of Structural Models

Paper Session

Sunday, Jan. 8, 2017 1:00 PM – 3:00 PM

Hyatt Regency Chicago, Water Tower
Hosted By: Econometric Society
  • Chair: Andres Aradillas-Lopez, Pennsylvania State University

Inference in Ordered Response Games With Complete Information

Andres Aradillas-Lopez
,
Pennsylvania State University
Adam M. Rosen
,
University College London

Abstract

We 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.

Dynamic Decisions Under Subjective Beliefs: A Structural Analysis

Yingyao Hu
,
Johns Hopkins University
Yonghong An
,
Texas A&M University

Abstract

Rational expectations of agents on state transitions are crucial but restrictive in Dynamic Discrete Choice (DDC) models.
This paper analyzes DDC models where agents' beliefs about state transition allowed to be different from the objective state transition. We show that the single agent's subjective beliefs in DDC models can be identified and estimated from multiple periods of observed conditional choice probabilities. Besides the widely-used assumptions, our results require that the agent's subjective beliefs corresponding to each choice to be different and that the conditional choice probabilities contain enough variations across time in the finite horizon case, or vary enough with respect to other state variables in which subjective beliefs equals objective ones in the infinite horizon case. Furthermore, our identification of subjective beliefs is nonparametric and global as they are expressed as a closed-form function of the observed conditional choice probabilities. Given the identified subjective beliefs, the model primitives may be estimated using the existing conditional choice probability approach.

Robust Identification in Mechanisms

Brendan Kline
,
University of Texas

Abstract

This paper develops identification results for the distribution of valuations in a class of mechanisms, including models of auctions, contests, and bargaining and trading. These mechanisms involve rules determining an allocation of an object and monetary transfers on the basis of the actions of the players. The identification strategy does not require that the econometrician have ex ante knowledge of the rules of the mechanism or the equilibrium solution of the mechanism. Therefore, the identification results apply to an incomplete model in the sense that the econometrician does not know ex ante the distribution of the observable data that would be generated for any given specification of the unknown distribution of valuations. Instead, the identification results are based on the shared structure of the mechanism framework. Consequently, the identification results are necessarily robust to the details of the specification of the model and flexibly accommodate unique features of the mechanism in particular empirical applications. Moreover, the identification results can flexibly deliver either point identification or partial identification, as appropriate based on the identifying content of data from the mechanism. Further, the paper explores the role of equilibrium assumptions, and shows that the identification of some features of the distribution of valuations are robust to partial failures of the equilibrium assumption.

Learning From Noncompliance in Social Experiments: Choice and Identification.

Rodrigo R. A. Pinto
,
University of California-Los Angeles

Abstract

The literature on the design of social experiments largely benefits from standard theory of randomized controlled trials (RCTs).<br />
In it, noncompliance is usually interpreted as a departure of a perfect randomization and a source of selection bias (Duflo et al., 2008). I develop a general framework for the design of social interventions that relies on revealed preference relations to identify causal parameters. The method differs from typical RCT design as noncompliance is not a drawback, but a key ingredient of identification analysis. I examine choice models with heterogeneous agents, multiple treatments and categorical instrumental variables. Identification relies on choice restrictions that arise from the incentives generated by the experimental design and axioms of choice. The framework broadly applies to the policy evaluation of social experiments with noncompliance.

A Structural Analysis of Procurement Auctions With Incomplete Contracts

Xun Tang
,
Rice University
Yonghong An
,
Texas A&M University

Abstract

We study a structural model of procurement auctions with incomplete contracts where a buyer chooses an initial project specification endogenously. The contract between the buyer and the winner of the auction is incomplete in that the two parties may agree to adopt a new feasible specification later, and negotiate an additional transfer via Nash Bargaining where both parties' disagreement values depend on the auction price. In a Perfect Bayesian Equilibrium, contractors competing in the auction take account of such incompleteness while quoting prices.<br />
We show that the model primitives are non-parametrically identified and propose a feasible estimation procedure. Using data from highway procurement auctions in California, we estimate contractor costs and infer how a contractor's bargaining power and mark-up. We find ignoring the existence of contract incompleteness in the structural analysis of bidding data leads to substantial over-estimation of the mark-ups in prices. Our estimates show contractual incompleteness lead to sizable holdups on the buyer (10.4% of engineering estimate on average). The holdup as a percentage of the engineering estimates is higher for contracts involving major jobs, and for contracts involving more active bidders. We also find that a counterfactual mechanism of auctioning cost-plus contracts would lead to lower buyer surplus for about 80% of the projects in the data, with an average difference of $305,000.
JEL Classifications
  • C0 - General