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Identification and Estimation of Dynamic Discrete Games

Authors:
Victor Aguirregabiria at University of Toronto
Victor Aguirregabiria
Pedro Mira at Centro de Estudios Monetarios y Financieros
Pedro Mira
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Abstract

This paper studies three econometric issues which appear in the estimation of dynamic discrete games: (1) the identification of strategic interactions among players; (2) the existence of multiple equilibria, that makes maximum likelihood estimation unfeasible even in relatively simple models; and (3) the exponential degree of complexity in the solution and estimation. First, we present conditions for nonparametric identification of players' payoff functions which apply regardless multiplicity of equilibria. Second, we propose a simple pseudo-maximum likelihood estimator (PMLE) and prove its consistency and asymptotic normality. We present also a version of this estimator that exploits randomization techniques to approximate value functions. This estimator can be computed in polynomial time, and it is asymptotically equivalent to the PMLE if sqrt(T) /R  0 as T goes to inifinity, where T is the sample size and R is the number of simulations.
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Efficient and Convergent Sequential Pseudo-Likelihood Estimation of Dynamic Discrete Games
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We propose a new sequential Efficient Pseudo-Likelihood (к-EPL) estimator for dynamic discrete choice games of incomplete information. к-EPL considers the joint behavior of multiple players simultaneously, as opposed to individual responses to other agents' equilibrium play. This, in addition to reframing the problem from conditional choice probability (CCP) space to value function space, yields a computationally tractable, stable, and efficient estimator. We show that each iteration in the к-EPL sequence is consistent and asymptotically efficient, so the first-order asymptotic properties do not vary across iterations. Furthermore, we show the sequence achieves higher-order equivalence to the finite-sample maximum likelihood estimator with iteration and that the sequence of estimators converges almost surely to the maximum likelihood estimator at a nearly-superlinear rate when the data are generated by any regular Markov perfect equilibrium, including equilibria that lead to inconsistency of other sequential estimators. When utility is linear in parameters, к-EPL iterations are computationally simple, only requiring that the researcher solve linear systems of equations to generate pseudo-regressors which are used in a static logit/probit regression. Monte Carlo simulations demonstrate the theoretical results and show к-EPL's good performance in finite samples in both small-and large-scale games, even when the game admits spurious equilibria in addition to one that generated the data. We apply the estimator analyze competition in the U.S. wholesale club industry.
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Dynamic Demand Estimation in Auction Markets
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We study demand estimation in a large auction market. In our model, a dynamically evolving population of buyers with unit demand and heterogeneous and privately known preferences for a finite set of differentiated products compete in a sequence of auctions that occur in discrete time. We define an empirically tractable equilibrium concept in which bidders behave as though they are competing with the stationary distribution of opposing bids, characterize bidding strategies, and prove existence of equilibrium. Having developed this demand system, we prove that it is non-parametrically identified from panel data. We extend the model to consider a random coefficients demand system akin to workhorse demand models in industrial organization, and show that this too is non-parametrically identified. We apply the model to estimate demand and show how large sellers can exercise market power by using persistent reserve price policies, which induce higher bids and, therefore, revenues. Our analysis highlights the importance of both dynamic bidding strategies and panel data sample selection issues when analyzing these markets.
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Multidimensional Barriers to Entry in the Insurance Industry
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In this paper, we introduce and employ a multi-agent model of entry to analyze barriers to entry in the U.S. property casualty insurance industry. Our estimations are conducted at the market-year level, enabling a detailed exploration of the relative importance of barriers across three dimensions: geography, product, and time. Our findings reveal that entry barriers are both prevalent and significant in the U.S. property casualty insurance industry, with de novo entrants encountering the most challenges from product barriers across all markets. We observe that expanding across product lines is more costly than expanding across states. Particularly, New York and California exhibit the strongest state barriers. Among various product lines, our research identifies that insurance expertise in mortgage guaranty and medical professional liability insurance presents the most substantial barriers to entry. This study contributes valuable insights into the dynamics of entry barriers in the U.S. property casualty insurance industry, highlighting the importance of considering geographic and product-specific knowledge, as well as temporal factors, in the context of market entry. Through analyses across these dimensions, we enhance the understanding of the challenges faced by new entrants and shed light on the specific market conditions shaping entry barriers.
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