Endogenous markups, intensity of competition, and persistence of business cycles.

1. Introduction

It is well known that standard real business-cycle (RBC) models in connection with perfect competition and constant returns to scale, while capable of capturing a number of stylized features of U.S. business cycles, have problems matching the observed persistence in output growth for the U.S. economy. In other words, they appear to lack a strong endogenous propagation mechanism, where exogenous technological shocks are the prime source of fluctuations. This weak propagation has been documented in many empirical studies (see, among others, Rouwenhorst 1991; Watson 1993; Cogley and Nason 1995; Rotemberg and Woodford 1996). A number of possible ways have been proposed in the literature to resolve this weak propagation problem. For example, one considers the likely presence of labor hoarding (Burnside and Eichenbaum 1996), another introduces complementary present-past leisure relations due to certain habit formation (Wen 1998), and some others attempt to break the negative relation between consumption and labor at periods other than impact (Perli 1998). (1)

In order to find added persistence in output in an RBC paradigm, one distinct approach emphasizes introducing new elements into standard RBC models, such as imperfect competition, diversity for preferences, and free entry and exit of firms over the business cycle (see, among others, Chatterjee and Cooper 1993; Devereux, Head, and Lapham 1993, 1996; Benassy 1996). Such an approach is largely based on microeconomic evidence, which suggests that firms tend to set prices above their marginal costs, that the average profits are low for many U.S. industries, (2) and that there is considerable magnification and propagation of exogenous disturbances. The key lies in a positive feedback in entry decisions, in a sense that more entries encourage more effort and accumulation, which in turn encourage more entries in the current and future periods.

However, there is a common assumption implicitly embedded in these studies: Entry and exit of firms do not affect the intensity of competition and thus the markups of incumbent firms. In a sense, this is a typical type of analysis with exogenous markups. There are good reasons to believe that this assumption is not only quite restrictive but also inconsistent with empirical findings. According to Audretsch and Acs (1994), microeconomic evidence indicates that net business formation (essentially entry less exit) is a strongly cyclical activity: It is strongest during a macroeconomic expansion, while it is quite low during economic downturns due to the increase in business failures. Thus, one can envisage that such a cyclical nature of entry and exit will have substantial implications for the ability of firms to set markups of price over marginal cost. In general, the larger (smaller) the number of competing firms in the same industry, the more (less) intense the competition, and thus the lower (higher) the markups; in other words, there exists a negative relation between markups and the number of firms. Since the number of firms is procyclical, one expects markups to be countercyclical. Empirical evidence of quite strong countercyclical markups in the U.S. data is provided by Bils (1987) and Rotemberg and Woodford (1991). (3) Hence, there is a need to incorporate this empirical regularity into a theoretical RBC framework. (4)

In this paper, along the same lines as Gali (1995) and Wu and Zhang (2000, 2001), the above assumption is relaxed in an otherwise standard RBC model in conjunction with imperfect competition and increasing returns to scale, and different ways of getting a stronger propagation mechanism from a theoretical perspective are explored. To this end, I focus on one feature in particular, namely, how the intensity of competition in a differentiated goods industry affects market structure and output persistence by distinguishing between different regimes of oligopolistic competition. (5) This is made possible by the fact that markups are endogenous in this framework. Following Sutton (1991), competition is defined to be most intense in the regime where profit margins are smallest, given an arbitrary level of concentration, as measured by the number of rivals in the market.

With endogenous markups, I consider two standard forms of competition that firms engage in: price and quantity competition. Under price competition, I assume that a sufficiently large number of firms play a one-stage game in which they choose their prices both simultaneously and noncooperatively by taking quantities of their rivals as given. Next, quantities are determined so as to equate supply and demand. The resulting equilibrium has Nash characteristics. This is known as Bertrand competition. Under quantity competition, firms take prices of their rivals as given and choose their own quantities; this is known as Cournot competition. It is well known in the literature on oligopolistic competition that these two strategies lead to distinct equilibrium characteristics, including prices, quantities, profit rates, etc. In this paper, the objective is to see whether different forms of competition result in different propagation mechanisms in an RBC framework.

Specifically, I attempt to address the following interesting issues. First, along the line suggested by Sutton (1991), I intend to determine which form of competition, Bertrand or Cournot, is more intense by comparing the respective equilibrium number of firms, perceived elasticity of demand, markup rates, and induced elasticity of the firms' markups with respect to endogenous entry. Second, I seek to understand under which form of competition the propagation mechanism is greater. (6) Third, since the key element in this analysis lies in endogenous modelling of markups, it will be useful and informative to compare this case of endogenous markups with the usual case of exogenous markups. Finally, in order to explore the role of imperfect competition in this kind of model, it is also interesting to compare output persistence in an imperfectly competitive economy with or without endogenous markups with a benchmark economy of perfect competition.

Two papers are closely related to this study, Devereux, Head, and Lapham (1996) and Cook (2001). (7) Both of these studies allow entry and exit of firms in the intermediate industries and examine aggregate fluctuations in a real business-cycle model with imperfect competition and increasing returns. The main difference between their models and this one lies in the fact that they investigate how aggregate variables respond to a technology shock once market power and increasing returns are introduced, that is by comparing the propagation mechanism under the new regime with that of a standard one; I move one step further by examining whether and how the form of competition (or market power), Bertrand or Cournot, makes a difference in propagating shocks. Of course, other minor modelling differences also exist. For example, Devereux, Head, and Lapham (1996) use constant markups (i.e., exogenous markups), while Cook (2001) and this study use endogenous markups. However, for tractability and simplicity, Cook restricts his analysis on duopoly and assumes that each company's markup is a function of its share of duopolized markets. In comparison, as stated already, I consider a general market with oligopolistic competition and model markups as in Gali (1995) and others.

The paper is organized as follows. Section 2 casts the model, while section 3 characterizes the steady state of the model. In section 4, I study the propagation mechanism for Bertrand and Cournot competition. These findings are also compared with a case of exogenous markups and a benchmark of perfect competition. In section 5, I extend the basic model to allow for general degrees of returns to specialization. All of the theoretical predictions are confronted with a quantitative investigation undertaken in section 6. Section 7 extends the basic model to include endogenous labor supply decisions and nonzero capital depreciation. Finally, section 8 presents conclusions. Proofs of all propositions are relegated to the Appendix.

2. The Economy

The presentation of this general equilibrium RBC model begins with the supply side.

Producers

In the model economy, there exists a number of intermediate-goods producers, indexed by j [member of] [0, [N.sub.t]], where [N.sub.t] is the number of intermediate goods. A homogeneous final good, which is taken as the numeraire, is produced by competitive firms according to the following technology (see Dixit and Stiglitz 1977):

[Y.sub.t = ([Nt.summation over (j=1)] [x.sup.([epsilon]-1)/[epsilon]].sub.jt]).sup. [epsilon]/([epsilon]-1)], (1)

where [Y.sub.t] is the final output, [x.sub.jt] is the amount of intermediate inputs used, and [epsilon] 1 is the (intrasector) elasticity of substitution among intermediate goods. A large [epsilon] value presents a high degree of substitution, or a low degree of product differentiation, as perceived by consumers.

It is well known that the constant elasticity of substitution (CES) form of Equation 1 with [epsilon] > 1 implies the existence of a preference for diversity effect, also termed the degree of (increasing) returns to specialization (e.g., Benassy 1996). Under symmetry, [x.sub.jt] = [x.sub.t], = [X.sub.t]/[N.sub.t], [Y.sub.t] = [N.sup.1/[epsilon]-1].sub.t] [X.sub.t], in which the preference for diversity effect is set equal to a particular value, 1/([epsilon] - 1). (8) By contrast, in many macroeconomic applications, this effect is generally switched off. (9)

The final good producer is a price taker and chooses its intermediate inputs to maximize the profit of