Durable-goods oligopoly with secondary markets: the case of automobiles.

We study the effects of durability and secondary markets on equilibrium firm behavior in the car market. We construct a dynamic oligopoly model of a differentiated product market to incorporate the equilibrium production dynamics that arise from the durability of the goods and their active trade in secondary markets. We derive an econometric model and estimate its parameters using data from the automobile industry over a 20-year period. Our estimates are used to provide a measure of the competitive importance of the secondary market.

1. Introduction

* In many durable-goods industries, used products are traded in decentralized secondary markets that are not directly controlled by the producers of new goods: the automobile industry is perhaps the most prominent example. In this article, we seek to understand the effects of durability and secondary markets on equilibrium production behavior in this industry. In the context of a dynamic equilibrium model, we model explicitly how product durability and trade in secondary markets affects equilibrium producer behavior in the automobile market.

The durability of cars and the existence of a secondary market have important competitive implications for new-car producers. The secondary market introduces, in the form of used cars, a large number of (imperfect) substitutes to the new cars produced each period, which limits the market power of each producer. In turn, rational firms recognize that their current production will reach the secondary market in the future and, by lowering prices in those markets, will erode future profits. A monopolist fully internalizes this effect by curtailing current production. In an oligopoly, however, each producer internalizes only the effect this has on its own future profits but not the detrimental effect it has on its rivals' future profits. (1) Indeed, each oligopolistic producer derives an indirect benefit from increases in current production if this causes its rivals to lower their future production levels; in equilibrium, therefore, a firm may choose to overproduce today if these indirect benefits outweigh the costs of more vigorous competition tomorrow.

Moreover, the presence of a secondary market also introduces an additional component--the resale value--to consumers' valuations of new cars. This dependence of new-car valuations on expected future prices introduces an intertemporal linkage between a firm's current profits and its own future behavior as well as the future behavior of its competitors. Given these linkages, the firm wishes to commit to low levels of production in the future to increase the expected resale value. Such behavior, however, would not be time consistent because, once the future arrives, the firm no longer cares about its past profits and is tempted to increase its production. Rational consumers will anticipate the firm's future actions and expect low resale prices, thus curbing current demand.

The intertemporal linkages between each firm's current profits and its own current, past and future production, as well as the current, past and future production of its rivals, makes for a rich dynamic game. In this article, we examine the equilibrium dynamics of this game within the context of the automobile industry. First, we construct a dynamic oligopoly model of a differentiated-product market that incorporates durability of the goods and their active trade in secondary markets. Second, we use data from the automobile market to estimate a tractable linear-quadratic version of the model. While the empirical model is quite stylized and incorporates restrictive assumptions, it represents (as far as we are aware) a first attempt at structural estimation of a dynamic durable goods model for this industry.

[] Background and existing literature. As the discussion above emphasized, durability and secondary markets introduce dynamics into both producers' output decisions and consumers' purchase decisions in the automobile market, which creates challenges for both theoretical and empirical work. In this article, we overcome these challenges by constructing a dynamic equilibrium model of the car market in which tractability is provided by its linear-quadratic structure. (2) Our model captures four key characteristics of the car industry: (i) oligopolistic time-consistent multiproduct automobile producers; (ii) an active, decentralized secondary market; (iii) differentiated products and (iv) depreciation schedules that differ across the competing car models.

However, we make some restrictive assumptions in deriving the linear-quadratic model: (a) consumers face no transactions costs in buying or selling cars, which makes the secondary market active by increasing the substitutability between new and used cars; (b) the automobile market is vertically differentiated, which places strong restrictions on the substitutability between cars in consumers' choice sets; and (c) there is perfect information, so we abstract away from adverse selection issues. (3) While the resulting model is quite stylized, our empirical results demonstrate the feasibility of estimating a dynamic durable-goods model for this industry and, we hope, encourage future progress.

Since the seminal work of Coase (1972), a large theoretical literature has analyzed how durability erodes market power for a monopoly producer. (4) Coase conjectured that a monopolist producing an infinitely durable good may lose all of its market power due to its inability to commit to high prices (or low production) in the future. Stokey (1981), Gul, Sonnenschein, and Wilson (1986) and Ausubel and Deneckere (1989) showed how Coase's conjecture can arise as an equilibrium limiting result in models where the time lag between the monopolist's price offers shrinks to zero. (5) In the presence of Coasian commitment problems, Liang (1999) shows that a secondary market can reduce the monopolist's temptation to increase future output because it reduces competition with the secondary market by selling more slowly to consumers, thus nearing the commitment solution.

The implications of durability and secondary markets on the dynamics of car demand have not been ignored in the literature. Berkovec (1985), Rust (1985a) and Stolyarov (2002) focus on dynamic consumer demand in a durable goods-market with primary, secondary and scrappage market segments. Adda and Cooper (2000) employ the optimal decision rules from a dynamic discrete-choice model to explore the effects of scrappage subsidies on car demand, where cars are held until scrapped and, hence, are not actively traded in the secondary market. Finally, Eberly (1994) and Attanasio (2000) consider (s, S) models of automobile demand in which idiosyncratic shocks lead consumers to change their stock of cars. In all these articles, the focus is on the timing of consumer purchases, so that automobile prices are assumed to evolve exogenously, and firms' automobile production decisions are not explicitly modeled. In our article, we model firms' equilibrium production decisions in a dynamic oligopoly model but abstract away from consumer transactions costs in order to ensure the tractability of the model.

Our emphasis on the equilibrium dynamics due to durability and secondary markets also distinguishes our work from existing market-level empirical studies of demand and supply in the automobile market. Bresnahan (1981), Berry, Levinsohn, and Pakes (1995) and Goldberg (1995) and Petrin (2002) have employed static models to quantify the degree of market power and the welfare effects of new product introductions in the car industry. These articles have focused on accommodating multiple dimensions of consumer heterogeneity in modeling the demand for automobiles. While some of these authors have allowed consumers to substitute between new and used cars in their models, they have not accommodated the intertemporal link between primary and secondary markets (i.e., that new cars today become used cars in the future), which is a crucial feature of our model. However, in order to maintain tractability in the dynamic oligopoly model, we restrict ourselves to a single-dimensional model of consumer heterogeneity.

Several articles have considered the empirical implications of durability and monopoly power. Suslow (1986) estimated a structural model of Alcoa's aluminum monopoly, taking into account the competition from the recycled aluminium sector. Iizuka (2007) and Chevalier and Goolsbee (2005) studied producer and consumer behavior in the academic-textbook market. For the automobile industry, Ramey (1989) estimated a durable-goods monopoly model to explain aggregate trends in car prices, and Porter and Sattler (1999) tested empirical predictions on the volume of trade in secondary car markets using a durable-goods monopoly model with transactions costs. There have been fewer articles on durable-goods oligopoly. Carlton and Gertner (1989) analyzed the effects of mergers among oligopolistic durable-goods producers, and Esteban (2002) characterizes the equilibrium production dynamics in a durable-goods oligopoly with homogeneous products.

The article proceeds as follows. In Section 2, we introduce the model and derive the Markov perfect equilibrium of the dynamic game. Subsequently, we derive a linear-quadratic specification of this model that is convenient for the empirical illustration. In Section 3, we describe the data and discuss the empirical implementation of the model. We also present our estimation results and conduct some counterfactual experiments. We conclude in Section 4.

2. A model of a durable-goods oligopoly with secondary markets