An empirical model of firm entry with endogenous product-type choices.

I describe a model of entry with endogenous product-type choices. These choices are formalized as the outcomes of a game of incomplete information in which rivals' differentiated products have nonuniform competitive effects on profits. I estimate the model for location choices in the video retail industry using a nested fixed-point algorithm solution. The results imply significant returns to product differentiation. Simulations illustrate the tradeoff between demand and intensified competition and the extent to which markets with more scope for differentiation support greater entry.

1. Introduction

[] Firms frequently compete in the characteristics of products that they offer to consumers. Economic theory going back to Hotelling (1929) and Lancaster (1966, 1979) has framed such product differentiation as competition between products located at different positions in an abstract characteristics space, with consumers having idiosyncratic preferences over these positions. A firm's location in characteristics space is a strategic variable, depending endogenously on the choices of its competitors.

Previous studies of entry have modelled the tradeoff between available demand and the intensity of competition faced by a new entrant, but the strategic importance of product positioning within a market has received less attention. Product differentiation allows a firm to better serve consumers' differing preferences and to acquire a degree of local market power. One determinant of the degree of market power is the scope for differentiation afforded by the product. For example, is local market power greater for automobile manufacturers with vast differentiation opportunities, or for makers of products such as yogurt that are characterized by fewer attributes? Or does the larger diversity of consumer preferences associated with more complex products erode such profit opportunities due to insufficient demand for highly differentiated varieties?

I present an empirically tractable equilibrium model to analyze the determinants of firms' product positions. I focus on location decisions for a sample of video retailers. The empirical results support the intuition that firms use spatial differentiation to shield themselves from competition. Distant competitors affect payoffs significantly less than do nearby competitors. This competitive interaction helps to explain the location choices found in the data. The payoffs to product differentiation motivate an analysis of the size of the characteristics space, measured by market area in my retail application, and its effect on market structure. I illustrate the effect of the geographic dispersion of demand on the entry process. As market area grows, firms can obtain more local market power, as there is more scope for spatial differentiation. However, payoffs from differentiation are lower as the population is more dispersed and demand falls. In the case of the video retail industry, which has highly localized demand, I find that the net effect of these two forces is that as population and market area grow, the number of firms increases only slightly. The extent of local market power generated by product differentiation depends on the interplay between differentiation possibilities and the strength of consumer preferences for particular product varieties.

My model addresses several difficulties in the empirical implementation of models of product differentiation and market structure. First, previous empirical work using discrete games to model product positioning decisions yields equilibrium strategies that are tractable only for a limited number of locations. Bresnahan and Reiss (1990, 1991) and Berry (1992) model firms' entry decisions as the equilibrium outcome of a discrete game played between potential entrants. Mazzeo (2002) extends this framework to predict firms' joint entry and quality-level choice. (1) An analytically appealing feature of his model is that firms have complete information about their rivals. A location distribution constitutes an equilibrium if no firm can increase profits by unilaterally changing its location. To confirm that a given configuration is an equilibrium entails comparing that configuration to every alternative configuration for every firm. Hence, computing an equilibrium configuration is difficult with large numbers of locations and firms. Mazzeo's (2002) application to the motel industry shows that, even with three quality levels, estimation is burdensome due to the large number of profit constraints that must hold.

In contrast to the complete-information framework, my model allows idiosyncratic sources of profitability, which are not observed by rivals. Examples include differences in cost or in intangible assets such as managerial talent, customer service, and inventory maintenance. Such factors affect profits, and they may not be observed by rivals who must separate the role of unobservables in a firm's success from other factors. I assume firms possess private information about their own profitability. Payoffs in a simultaneous-entry game thus depend on the firm's expectation of its rivals' location choices, as well as its idiosyncratic component. As Rust (1994) notes, the resulting Bayesian Nash equilibrium conjectures, which represent the probability of a particular strategy, can be derived more easily than in the complete-information framework, which solves for an exact equilibrium strategy. The incomplete-information model simplifies the computation of equilibrium strategies for a large-dimensional set of product types. Recent work on the estimation of discrete dynamic games (e.g., Aguirregabiria and Mira, 2006; Pakes, Ostrovsky, and Berry, 2005; and Pesendorfer and Schmidt-Dengler, 2003) also exploits information asymmetries to reduce the burden of computing dynamic entry and exit strategies.

My framework can accommodate a number of horizontal or vertical product differentiation choices, including discrete product attributes, combinations of attributes, or continuous attributes that can be discretized into distinct categories. (2) The model has been extended to a number of economic contexts. Watson (2005) uses a similar model to study firms' product variety choices in the context of eyeglass retailing. Augereau, Greenstein, and Rysman (forthcoming) analyze the importance of competition in a technology-adoption game between internet service providers and suggest differentiation between providers as an explanation for the absence of a single technological standard.

A second difficulty in empirical research on product-type choices stems from the need for detailed data on prices and quantities to estimate demand for various product space positions. Price and, in particular, quantity data are frequently not available. I do not have detailed outlet pricing and rental data, so I exploit firms' location choices to make inferences about profitability. In doing so, I make the same type of assumption found in work by Sutton (1991,1998), Bresnahan and Reiss (1990, 1991), and Berry (1992) that market structure reveals information about firms' underlying profits and the intensity of competition.

A last difficulty in estimating discrete strategic games is the possibility of multiple equilibria. Much of the literature (Berry, 1992; Bresnahan and Reiss, 1991; and Berry and Waldfogel, 1999) circumvents multiple equilibria in individual players' actions by examining unique market and equilibrium outcomes. (3) For example, entry models can predict a unique equilibrium number of entrants, but not the identity of the entrants. Asymmetric information in a discrete game does not necessarily guarantee a unique equilibrium. I show, however, that for a simplified version of my model, a unique equilibrium exists under reasonable restrictions on the model parameters. I present simulation evidence for the more general model.

The remainder of the article proceeds as follows. In Section 2, I present the model of entry and location choice and discusses econometric estimation. Section 3 describes the dataset. Section 4 presents the estimation results and counterfactual analyses of the effect of spatial differentiation on entry. In Section 5, I conclude.

2. Model

[] Setup and payoffs. I examine a firm's choice of product position among a set of discrete locations in characteristics space. To ensure that equilibrium strategies can be computed for many locations, my model is static. Accordingly, each firm makes its entry and location choice based on a comparison of expected post-entry, single-period profits across locations.

Two opposing forces drive profits. On the one hand, firms are attracted to locations with favorable demand characteristics. Firm behavior also depends endogenously on the choices of other firms because increased competition at a given location adversely affects profits. Profits vary between firms in the same location due to differences in costs and other firm-specific factors. I assume that such differences are observed only by the firm itself. Entry and location choices are thus determined by the demand characteristics in each market location, firms' expectations of their competitors' location choices, and each firm's idiosyncratic profitability.