Under these assumptions, the payoffs to the firms are those displayed in Table 1. The monopoly profit for firm i is labelled flu, duopoly profit is labelled 11),, and ...
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Research Paper No. 883
Entry in Monopoly Markets by
Timothy F. Bresnahan and
Peter C. Reiss May 1986
I Star~ord Business ~ 0
N
Entry in Monopoly Markets
Timothy F. Bresnahan Department of Economics, Stanford University Stanford, California 94305 and Peter C. Reiss Graduate School of Business, Stanford University Stanford, California 94305
ABSTRACT: Existing empirical, models of entry in concentrated markets make indirect inferences about the competitive effect of entry. We propose empirical models whose stiuctural equations are those of several different game-theoretic models of entry. These models are used to estimate the competitive effect that entry has on the margins of monopoly automobile dealerships in the U.S.
Draft: May, 1986. Comments welcome. Seminar participants at Chicago, the Federal Trade Commission, Stanford Business School and Yale provided helpful comments on earlier drafts of this paper. We also wish to thank Joy Mundy for her expert assistance in programming the likelihood functions. Margaret Miller was of great help in developing the data base.
1
1.
Introduction
Industrial organization economists have long debated whether firms in concentrated markets can persistently charge noncompetitive prices. Early empirical work on entry by Bain (1956) and others suggested that firms in concentrated markets can erect entry barriers and create market power. Later work by Stigler (1968), Demsetz (1974)
,
and others offered
both a different theory of entry and a different interpretation of the empirical evidence. Recent game-theoretic models of entry have supported both sides of this theoretical debate. We now have well-posed theoretical models in which incumbent firms can prevent entry while earning monopoly rents, as well as other theories which imply that potential entry disciplines incumbent behavior.’ Although studies have sought to test the implications of these different theoretical views, their tests are indirect. The most common test is a cross section regression that relates profits in manufacturing industries to proxy measures of so-called entry barriers. These studies presume that deviations in profit rates across industries ‘constitute evidence that entry barriers are present.2 Similar’ inferences are drawn by studies that relate entry rates to the same entry barriers. (See for example Bain (1956), Weiss (1974), Orr (1974), Chappell et al. (1974) Hannan (1983) and Geroski (1983).) Neither type of study is immune to reinterpretations that claim the results are consistent with perfect competition. For example, important work on perfectly competitive entry by Hause and du Rietz (1985) has shown that competitive entry rates can vary dramatically with different patterns of demand growth. A major reason why empirical studies have not made more direct use of theory is that the variables identified by the theory are often unobservable. These unobservables include incumbents’ and entrants’ costs and their beliefs about competitive interaction. Progress ~ For a recent survey of theoretical treatments of entry deterrence, see Roberts (1985). Baumol (1982) reviews work that shows that potential competition is as effective as actual competition. 2 See Demsetz for a reinterpretation of the evidence in these studies, and Schmalensee, (1987, forthcoming) for a summary of what has been learned from this work. 2
in modelling strategic entry therefore requires empirical models that can use observations on actual instances of entry to draw inferences about these unobservables. This paper constructs such techniques and uses them to estimate the competitive impact of entry into monopoly markets. First, we formulate empirical models of strategic interaction among potential entrants. These models include simultaneous-move and sequential-move games where the players are the potential entrants into a market. Although these games have important analytical differences, both can be handled within the same general econometric framework. This framework models each potential entrant’s profits as an unobserved (latent) variable that is known to the firms but not to the researcher. In this respect, our models are similar to single-agent discrete choice models.3 An important difference between our models and single-agent discrete choice models is we model how multiple agents interact. That is, we specify how each firm’s expected profits (and choices) depend on the other firms’ actions in equilibrium. As a result, our econometric models have the form of a simultaneous-equation system with discrete endogenous variables that determine the number of firms in a market.4 In the second part of the paper, we use these econometric specifications to estimate the competitive impact of.entry into monopoly automobile markets. Retail trade in new cars offers a unique opportunity to study strategic entry. Our sample consists of automobile dealers in a cross-section of small, isolated markets that have at most a few dealers. (The markets pass a demanding series of tests before we consider them isolated. See Appendix A for details.)
Following Pashigian (1961), we emphasize the importance of fixed and
sunk costs in the analysis of entry and show how geographic variations in demand can be used to measure the magnitude of these costs for the first firm in the market. Using the level of demand needed to support one firm as a benchmark, we use different theories of ~ These econometric models (see for example MacFadden (1974, 1982), Amemiya (1974, 1982), and Hausman and Wise (1978)) relate qualitative information about consumption decisions to threshold conditions involving unobservable utility functions. ~ See for example Heckman (1978) and Lee’s (1981) survey. 3
strategic entry to interpret the observed size of the market that is necessary to support two firms. That is, we use the size of the market to test whether strategic entry deterrence is present. We find that the density of demand explains most of the variation in the number of dealerships across small markets, and that price-cost margins do not fall by much when entry by the second firm occurs. Moreover, we find entry into monopoly dealer markets is extremely easy. Specifically, that two firms can be sustained in a market only slightly more than twice as large as that needed to sustain a monopoly.
2.
Models of Entry by the First and Second Firm into a Market
This section derives econometric models of entry by the first and second firm into a market. The first firm enters when demand is sufficient to cover costs. For the second (and later) firm, however, strategic interactions affect the profitability of entry, This includes not only entry “barriers” erected by the first firm, but also the competitiveness of postentry pricing behavior. We follow the recent theoretical literature by casting the entry problem as a game between potential entrants. For simplicity we treat the case of two players. Each firm i picks a binary action a2, action 0 being “do not -enter the market” and action 1 being “enter”. The possible entry outcomes for this market thus involve zero, one, or two firms in the market. In this section, we follow the convention of the theoretical literature and treat ‘the equilibrium profits of each firm as given. Later on, we reinterpret these fixed profits as profits that vary with the price or quantity decisions made by the two firms. Finally, we temporarily assume that the profits of nonproducers are Under these assumptions, the payoffs to the firms are those displayed in Table 1. The monopoly profit for firm i is labelled
flu,
duopoly profit is labelled 11),, and
i~ is
the
~ This is a simplifying assumption that can be readily relaxed. Below, we generalize “profits” to include variation in the value of the entrepreneur/entrant’s time in alternative occupations.” 4
change in each firm’s profits between monopoly and duopoly. Table 1 Player l’s Payoffs a2
=
0
a’=O
0
a’=l
fl~1
a2
Player 2’s Payoffs a2
1
=
0
rlk+~’~rrb
=
a2
0
=
1
0
rr2
0
fl2+&=112
If entrants are uncertain about costs or demand. then we reinterpret these variables as the players expected profitability assessments.6
2.1.
Simultaneous Move Games
-
The simplest model of entry is’ one in which potential entrants simultaneously and noncooperatively pick their actions.’ The (Nash) equilibrium conditions for this game can be expressed as a pair of inequalities:
-
a’
=
0
l1~+a2L~’0
~
(1) a2
=
0
11L+a’~20
~
Under the economic assumption that duopoly profits are less than or equal to monopoly profits, ~
~ 0, this model has substantial empirical content: it determines the equilibrium
number of firms as a function of the exogenous variables fl~,This can be seen by noting that the inequalities (1) divide the equilibrium outcomes into the five regions of the payoff Extensions to three or more firms and arbitrary payoffs can be handled with this framework. For subtleties that are introduced when the game has incomplete information see Bresnahan and Reiss (1986). 6
5
space given in Table 2.~ Table 2 Region Definition
Equilibria (a1, a2)
fl~0
(1,1)
l1~>0>flb, J1~>0>fl~,
(1,0)or(0,l)
flA.~.>0, rr~, 0 X)
Pr(1 firms I X)
=
1
—
Pr(0 firms I X)
—
(3)
Pr(2 firms X)
~ For example, in a recent model by Katz and Shapiro (1984) firms have increasing returns to scale technologies there are equilibria where either of the two firms could be a natural monopoly. 7
Equation (3) is the basis for the likelihood functions that are used in Section 4.
2.2.
Consistency Conditions In Simultaneous-Move Games
Many of the above problems with writing down a consistent econometric model of discrete outcomes have received considerable attention in the econometric literature. Indeed, it is easy to see that if the errors in (2) are normal, then the model of a discrete game is similar to one of Heckman’s (1978) dummy endogenous probit models.9 Although techniques to estimate these types of models are available, both Heckman (1978) and Schmidt (1981) have shown that a necessary and sufficient condition for this model to have a well-defined reduced form is that the model be recursive.10 Recursivity requires A’ x A2
=
0. In
our application, this is an overly restrictive statement about how potential competitors affect profits. If, for example, we impose recursivity by setting A’
=
0, then monopoly
and duopoly profits are identical for firm 1. In other words, firm l’s incremental profits from entry are the same, independent of whether the other firm is in the market. Such an assumption clearly rules out most interesting entry models. In (3), we escaped the need to impose recursivity by requiring only that the model be able to make probability statements about the number of firms in the market, not about the individual actions. As a result, we made the weaker structural assumption A~ 0, not A’
=
0 for some i. In our application, this is a more natural economic assumption about
the payoffs: duopoly profits for both firms are less than or equal to monopoly profits. (In Figure 1 this assumption is that the lines marked —flM and ~flD never switch position.) It is useful, however, to explore what happens when A’ can be positive. When this occurs, the five regions in Table 2 and Figure 1 do not exhaust all of the possible outcomes. Three of the new possibilities are disturbing:” ~ It is exactly Heckman’s Case 4 simultaneous probit if A’ is set equal to a constant. Amemiya (1974) makes a similar point for general equation systems with truncated endogenous variables. ~ The other events have one of the two monopolies as a unique equilibrium. 10
S
Table 3 Event
Value of Payoffs
ri~
