Industry dynamics and the distribution of firm sizes: a nonparametric approach.

• Author: Lotti, Francesca

1. Introduction

   Ever since the seminal works of Herbert Simon and his coauthors (Simon and Bonini 1958; Ijiri and Simon 1974, 1977) the distribution of firm sizes (FSD) has received considerable empirical attention. Previous studies have typically found that the FSD is reasonably well described by a lognormal distribution at both the industry and the economy-wide level, implying that the distribution is right skewed. This piece of evidence is consistent with the so-called Law of Proportionate Effect, also known as Gibrat's (1931) Law. As Simon and Bonini (1958, p. 609) point out, if one "incorporates the law of proportionate effect in the transition matrix of a stochastic process, ... then the resulting steady-state distribution of the process will be a highly skewed distribution."

   Recent evidence, however, based on more complete data sets, suggests that Gibrat's Law is not confirmed for either new entrants or established firms tracked for a five-year or longer time period (cf. the surveys by Mata 1994; Geroski 1995; Audretsch et al. 2002; Lotti, Santarelli, and Vivarelli 2003) since smaller firms grow more than proportionally with respect to larger ones. This decreasing relationship between size and growth suggests that the distribution of firm sizes is not stationary over time and may differ from the lognormal distribution.

   We use quarterly data from Italy for 12 cohorts of new manufacturing firms to examine the evolution of the FSD over time in the case of young firms. Moreover, we try to reconcile our empirical evidence with the predictions of three complementary views of industry dynamics, drawing on theoretical work of Jovanovic (1982), Audretsch (1995), and Ericson and Pakes (1995). Section 2 contains a review of the empirical evidence about Gibrat's Law and the FSD as well as an overview of some recent explanations of industry dynamics. Section 3 describes the data and the methodology used, whereas Section 4 summarizes the main empirical findings. Finally, Section 5 contains some concluding remarks.

2. Theory or Stylized Facts?

   Gibrat's Law, applied to the analysis of market structure, is the first attempt to explain in stochastic terms the systematically skewed pattern of the size distribution of firms within an industry (Sutton 1997). The Law of Proportionate Effect can be empirically tested in at least three different ways. First, one can assume that it holds for all firms in a given industry, including those that have exited the industry during the period examined (setting the proportional growth rate of disappearing firms equal to -1). Second, one can postulate that it holds only for firms that survive over the entire time period. If survival is not independent of firm's initial size--that is, if smaller firms are more likely to exit than their larger counterparts--this empirical test can be affected by a sample selection bias, and estimates must take account of this possibility. Third, one can state that Gibrat's Law applies only to firms large enough to have overcome the minimum efficient scale (MES) of a given industry (e.g., Simon and Bonini 1958 found that the law was confirmed for the 500 largest U.S. industrial corporations).

   In effect, the law cannot be rejected if (i) firm growth follows a random process and is independent from initial size and (ii) the resulting distributions of firms' size are approximately lognormal. Of course, when identifying a FSD skewed to the right, one cannot a priori exclude that the skewness is the result of turbulence, namely, the presence of new entrants in the right tail of the distribution. Although from a theoretical viewpoint labeled "unrealistic" since Kalecki's (1945) study on the size distribution of factories in U.S. manufacturing, this result was initially consistent with some empirical studies dealing with incumbent, large firms (Hart and Prais 1956; Simon and Bonini 1958; Hymer and Pashigian 1962). In recent years, most studies have instead identified an overall negative relationship between initial size and postentry rate of growth. (1) Nevertheless, Lotti, Santarelli, and Vivarelli (2001a, b) have shown that, in the case of newborn firms, the growth rates are negatively correlated with their initial size only during their infancy: Gibrat's Law fails to hold in the year(s) immediately following start-up, when smaller firms have to rush in order to reach a size large enough to enhance their likelihood of survival; but in the subsequent years, the patterns of growth of entrants do not differ significantly from the landscape of the industry as a whole.

   In the present paper, we argue that explanation of this phenomenon of self-selection should more carefully consider the firms' learning and evolution processes theorized by Jovanovic (1982), Audretsch (1995), and Ericson and Pakes (1995). According to these authors, entrants are uncertain about their relative level of efficiency, and only once they are in the market do they learn about their possibilities of survival and growth. The main advantage of these theories is that they allow for (i) heterogeneity among firms, (ii) idiosyncratic sources of uncertainty and discrete possible events, and (iii) entry and exit. In particular, these complementary views of firm and industry dynamics provide a role for uncertainty in entrant decisions and selection mechanisms, which imply changes in the size distribution of an entering cohort over time.

   Jovanovic (1982) proposes a Bayesian model of noisy selection, according to which efficient firms grow and survive, whereas inefficient firms decline and fall. In particular, Jovanovic's model of passive learning deals with a small industry in which the product is homogeneous, the time path of the demand for the product is deterministic and known, and the factors are supplied at a constant price. In this competitive environment, firms are initially endowed with uncertain, time-invariant characteristics (i.e., efficiency parameters), and for each firm the mean of its costs is a proxy of its "true cost." Thus, in every period each firm has to decide its strategy: whether to exit, continue with the same size, grow in size, or reduce its productive capacity. Because of a particular kind of selection process in this model, the most efficient firms survive and grow, while the others are bound to shrink or to exit from the market. Under the hypotheses of small industry size and product homogeneity, there is no room for pursuing niche strategies characterized by different paths of convergence to the lognormal distribution. In particular, as a new firm with a suboptimal scale discovers that its true costs are low, it adjusts its size as rapidly as it can through accelerated growth. Within this perspective, one expects to observe a "strictly monotone" convergence, with the size distribution of survivors increasing stochastically from period to period.

   Like the passive learning model, Ericson and Pakes's (1995) model of active learning assumes that all the decisions taken by firms are meant to maximize the expected discounted value of the future net cash flow, conditional on the current information set. In this model, a firm knows both its own characteristics and those of its competitors, along with the future distribution of industry structure, conditional on the current structure. Jovanovic's assumptions concerning small industry size and product homogeneity are instead relaxed in Ericson and Pakes's model, in which new entries may either adjust their size to the MES level of output of the "core" of the industry or choose/find a niche within which the likelihood of survival is relatively high even though the firm does not grow fast. The model of active learning can be usefully employed in explanation of "entry mistakes" (as defined by Cabral 1997), namely, the fact that in every period and every industry more firms enter than the market can sustain: Within an active learning perspective, such mistakes occur because of lags in observation of rivals' entry decision or just because entry investments take time (Cabral 1997). In an industry with similar dynamics, therefore, convergence to the lognormal distribution of firm sizes is a process that might take more time and will eventually occur non-monotonically.

   In a subsequent work, Pakes and Ericson (1998) examined two cohorts of firms from Wisconsin belonging to the retail and the manufacturing industries and found that the structure of the former industry was compatible with Jovanovic's passive learning model, while that of the latter was compatible with their model of active exploration (learning). After eight years the retail cohort seems to have reached the size distribution of the industry as a whole, while the manufacturing cohort, even though it achieved higher growth rates, was still far from the size distribution of the entire industry after the same number of years. Such marked differences in the speed of convergence are not surprising since the manufacturing aggregate is much less homogeneous than the retailing one, which to some extent displays the features of Sutton's (1997, 1998) "strategic dependence" hypothesis of homogeneous submarkets. Moreover, Pakes and Ericson (1998) claim that the major nonparametric difference between the two models relates to the distinction between heterogeneity and the phenomenon of state dependence (Heckman 1981). Accordingly, the passive learning model implies that the stochastic process generating the size of a firm is characterized by a form of heterogeneity, while the active learning model implies that such stochastic process is generated by a general form of state dependence, even if with ergodic characteristics.

   Audretsch (1995; cf. Audretsch and Fritsch 2002) expanded the passive learning approach put forward in Jovanovic's (1982) theoretical work into an evolutionary perspective, which emphasizes the interindustry differences in the likelihood of survival of newborn...