Bryan Graham, UC Berkeley

"Efficient estimation of a model of oligopoly entry"

Abstract

In an oligopoly setting firms’ entry decisions drive market output, prices, profitability and consumer welfare. Understanding the drivers of these decisions helps to predict the effects of mergers, regulatory practices, and other policies. Entry is a strategic decision: a firm’s payoff from entering a market varies with which of its (potential) competitors also choose to enter. Payo↵ interdependence makes entry decisions a game. The econometric analysis of entry games was pioneered by, among others, Bresnahan and Reiss (1991) and Berry (1992). Indeed, the analysis of firm entry is simultaneously a core (substantive) topic in empirical industrial organization and a prototypical example used to motivate methodological research on the econometrics of games (e.g., Tamer, 2003; Berry and Tamer, 2007; Jia, 2008; Ciliberto and Tamer, 2009; Bontemps and Sampaio, 2020).

Econometric models of games are typically incomplete: for a given configuration of payoff parameters, and observed and unobserved payoff-relevant exogenous variables, multiple Nash Equilibria (NE) may exist. Unless we augment the model to include a mechanism for selecting a particular NE, it may not predict a unique game outcome.

Incompleteness is often associated with a failure of point identification (of payoff function parameters). Consequently, an important theme of research on the econometrics of games involves developing methods for characterizing and estimating identified sets. Methods of inference appropriate to settings with partial identification are also of primary interest (see Paula (2013) and Molinari (2020) for overviews).

In some games, however, payoff parameters are point-identified in spite of incompleteness. The entry model studied by Berry (1992), henceforth called the semiparametric entry game (SEG), provides a leading example. In this model, while the precise identity of who enters or not is underdetermined, the aggregate number of entrants is not. Berry (1992) uses this observation to demonstrate point identification of firms’ payoff function parameters – the K ⇥ 1 vector ✓ – and proposes concrete simulated-based estimation strategies.

In this paper we build on prior work in three ways. First, we characterize the set of all possible estimating equations (i.e., “moments”) for ✓ in the SEG. Second, we derive the semiparametric efficiency bound (SEB) for ✓. Finally, we propose a feasible estimator, based upon a novel importance sampling algorithm, that attains the SEB. Computational challenges loom large in entry game analysis (Bontemps and Kumar, 2020). Our algorithm, in addition to leading to a semiparametrically efficient estimator, is computationally attractive relative to extant alternatives (including, for example, the simulated method of moments procedure developed by Berry (1992)).

Contact person: Jesper Riis-Vestergaard Sørensen