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...they operate are destroyed. This simple framework can transparently explain wide range of well-known regularities about industry dynamics, most notably the subtle relationships between size, age, growth, and survival. Data on the laser industry, where submarkets are prominent, further illustrate the ability of the model to explain distinctive patterns in the evolution of industries and firms.
1. Introduction
* A remarkable feature of most industries is that at any given moment there is great variation in the size of producers. The bulk of the firms are concentrated at smaller sizes, but there are also a number of larger firms whose size distribution closely resembles the upper tail of the Log-Normal and its cousins, the Pareto and Yule distributions. These patterns have been shown to be consistent with a simple model in which for firms above a minimum efficient size, production is subject to constant returns to scale and firm growth rates are stochastic realizations from a distribution whose mean and variance is independent of firm size. Apart from the constant-returns-to-scale specification, these models do not have much economic content. Consequently, they cannot tell us much about the fundamental drivers of firm growth or about the moments of the firm-size distribution, which are the key determinants of an industry's market structure.
In some ways it has been fortunate that the empirical reality of firm growth has turned out to be more complicated than the early stochastic growth models assumed. Increased availability in recent years of confidential establishment data, along with the development of a few comparable panel datasets, has enabled a more complete understanding of the empirics of firm growth. It has become apparent that among surviving producers, both the mean and variance of firm growth decline with firm size and also with firm age, even after controlling for the other factor. The probability of exit also similarly declines with both firm size and age, but if exiting firms are assigned a--100% growth rate and included in the analysis, then mean growth is no longer related to firm age. (1) The size distribution of firms within a single age cohort also evolves with age; its mean and variance rise and the skewness falls as the cohort ages (Cabral and Mata, 2003). These patterns have been challenging to explain, suggesting that they should be revealing about the fundamental determinants of firm growth and market structure. The age effects have posed the greatest challenges--the size effects can be explained by models in which firms experience persistent productivity shocks and production is subject to decreasing returns to scale (see Hopenhayn, 1992). But the effects of age on growth and exit suggest there are other factors correlated with age that remain unaccounted for in our analyses.
Remarkably, few theories identify what these missing factors might be. A pioneering exception is Jovanovic's (1982) model of selection, which famously predicts a negative effect of firm age on the variance of growth and, in many datasets, a positive effect of age on survival. (2) His omitted variable is the precision of a firm's beliefs about its quality, which rises with age. More recently, Cooley and Quadrini (2001) have generated size-conditional age effects on growth from a model that combines financial market frictions with persistent shocks to firm productivity. Young firms are assumed to enter the industry as high-productivity firms, and in the presence of financial frictions, high-productivity firms experience more rapid and more volatile growth. The omitted variable in this case is variations in the debt-equity ratio that are correlated with age. (3) While both theories are impressive in their explanatory power, it is also important to recognize their limitations. Jovanovic's model does not predict the effect of age on mean growth, and Cooley and Quadrini's model does not predict the effect of age on the probability of exit. Furthermore, neither model addresses why the age effect on mean growth only holds for surviving producers. Both models also require some rather precise assumptions--priors and signals in Jovanovic's model must be normally distributed (Pakes and Ericson, 1998), and entrants must be more productive than all incumbents in Cooley and Quadrini's model.
The main purpose of this article is to propose another channel through which age affects firm performance that transparently accounts for all the age-size regularities as well as additional related regularities. We start from the self-evident fact that the way we are accustomed to define industries in empirical work (almost invariably by SIC code) suppresses a large amount of heterogeneity in firm activity. Firms defined as belonging to the same industry could, if only we had the appropriate data, be differentiated along numerous dimensions, such as the technology they use, the services they provide, the customer segments they target, or the geographic areas in which they operate. We call these different activities submarkets. It is equally self-evident that in many industries, these submarkets have their own dynamics. New opportunities arise, and only firms that succeed in exploiting them benefit from their arrival. Existing submarkets vanish as technologies become obsolete, as geographic areas decline, or as regulations change, and all firms dependent on these submarkets suffer as a consequence. Indeed, firms that are specialized in a single submarket can be expected to vanish when the submarket dies.
We can't imagine that our distinction between the static, homogeneous, industry-as-SIC-code world of empirical analysis, and the dynamic, heterogeneous collection of submarkets that most industries consist of is either contentious or surprising to most readers. Perhaps more surprising is that, in a world of submarkets, age will be found to affect growth and survival anytime the econometrician fails to control for the number of submarkets in which each firm is active. We show this in a model in which industries consist of finitely lived, differentiated submarkets, which we cast as the sole driving force behind entry, exit, and firm growth. A firm's growth is negatively related, and its survival positively related, to the number of submarkets in which it is active. At the same time, the number of submarkets in which a firm is active is increasing in age. We show that this simple framework transparently generates precisely the effects of age on mean growth, the variance of growth, and the evolution of the size distribution that have been observed in the data. We show that it also explains a number of other regularities, including properties of the firm-size distribution, mean reversion in firm size over long, but not short, time horizons, and variations in the sizes and diversity of entrants, exiting firms, and surviving firms.
Submarkets have already been the subject of some recent theorizing about industry evolution. Sutton (1998) used the idea of growth opportunities appearing randomly in the form of new submarkets in an industry to develop his theory of the firm-size distribution. (4) Without using the nomenclature of submarkets, Klette and Kortum (2004) develop a model driven by optimizing behavior that is similar in spirit to Sutton's. Their model is also consistent with the regularities about the firm size distribution, and also the relationship between firm size, growth, and exit. (5)
Our model is similar to Sutton's in that we assume all opportunities for growth correspond to the creation of new submarkets. But similar to Klette and Kortum, we also build in a mechanism for firm contraction and exit. We do so by assuming that all submarkets have randomly determined but finite life. We also assume that each submarket consists of multiple firms with varying market share. As will become evident below, these two features are the means by which our model generates the precise effects of age on growth and survival observed in the data.
We hope that our ability to explain all the age-size regularities using a ubiquitous feature of industrial activity will inspire confidence in the importance of submarket phenomena in the process of firm growth. We can also readily point to industries analyzed by others where submarkets have been the key to differential rates of firm growth. For example, in hard disk drives Christensen (1993) implicates new submarkets opened by smaller disk drives as the cause of the leading incumbents repeatedly being displaced by new entrants and other incumbents. (6) In pharmaceuticals, Bottazzi et al. (2001) develop a stylized model of submarket branching to explain variations in firm growth rates. We go beyond these examples to analyze the importance of submarkets in yet another modern industry, the laser industry. We derive a series of distinctive hypotheses from our model that we test using data on the types of lasers produced by entrants into the industry over its first 30 years. Our analysis suggests that submarket creation and destruction played a key role in the entry, exit, and growth of laser producers.
Much as the early stochastic growth models were criticized for their lack of economic content, it will be tempting to criticize our model similarly. Unlike the early stochastic growth models, though, our model identifies the source of firm growth and provides structure on how it is expected to operate. It is true that our model is consistent with a lot of different underlying economic mechanisms, but we see this as a virtue because it shows off the power of submarket phenomena to explain the accumulating regularities. It also demonstrates that the regularities may not be as revealing as we might have hoped about the mechanisms underlying firm growth. With three explanations on the table for the regularities, evidence will be needed about the quantitative importance of each to judge their relevance. The industry examples noted above and our analysis of the laser industry represent our initial foray into this domain. At the same time, the fact that we can explain all the regularities with such a simple model suggests that it might be useful to look elsewhere to come up with further insights into the determinants of firm growth. One place where we suggest looking is industry irregularities--patterns that hold only in some industries, particularly patterns regarding market structure, which was the impetus for much of this literature. Our model predicts that the number of firms in a new industry should monotonically rise over time, which is what occurred in the laser industry. But it has also been shown that certain industries, such as autos, tires, and television receivers, experienced extremely sharp shakeouts in the number of producers as they aged despite robust growth in total production (Klepper and Simons, 1997). Our model provides a way to think about what might have been different in these industries regarding submarkets that could account for their shakeouts. This discussion also helps delineate the kinds of industries to which our model is most applicable.
The article is organized as follows. In Section 2 we develop the model and derive its implications for the effects of age and size on firm growth and survival. In Section 3 we report additional predictions of the model and compare them with the evidence. In Section 4 we relate the model to evidence from the laser industry. Section 5 offers some observations on the implications of our analysis.
2. Submarkets and the effects of age and size
* An industry is composed of various submarkets. The industry begins at time t = when its first submarket is created. Subsequently, submarkets are created according to a homogeneous Poisson point process with mean intensity [lambda], so that to a first-order approximation there is a probability [lambda]dt of a new submarket being created in the interval dt. Each submarket has a random life, z, drawn from the distribution H(z). It is assumed only that H(z) is differentiable almost everywhere with finite mean submarket life, [mu] = [[integral].sup.[infinity].sub.0] zdH(z). (7) There are C potential entrants to each submarket. Each has a probability of [theta] of entering a new submarket, where [theta] is the same for all firms and submarkets. Upon entering, the firm's size in the submarket is drawn from the distribution F(x), F(0) = 0, where F is continuous and strictly increasing. This size remains constant for the duration of the submarket and then goes to zero as soon as the submarket is destroyed. Total firm size at any point in time is therefore the random sum of n draws from the distribution F, where n is the number of currently existing submarkets that the firm entered.
In modelling industry evolution and firm dynamics as an exogenous stochastic process, we do not intend to discount the role of rational firm choice. To the contrary, we assume that the stochastic process is driven by a well-defined maximization problem for each firm. But whatever the details of the maximization problem, it will yield an equilibrium entry rate, [theta], and a distribution of firm sizes among entrants, F(x). (8) None of our results depends on the particular value of [theta] or the form of F(x), and we do not analyze the effects of policy. Hence, the generality afforded by the reduced form serves us well.
Firms may enter and exit a state of zero submarket activity, and in this setting, all firms live forever. To address questions of entry and exit, we therefore adopt the following convenient stylization. Consider two sampling times, t and t + T. At time t, we define the age, s(t), of the firm as the length of time that has elapsed since it last entered a state of zero submarket activity. At time t + T, we identify a firm as an exit if it is active in no submarkets and it was in one or more submarkets at time t. An entrant is defined symmetrically as a firm active in one or more submarkets at time t + T that was active in no submarkets at time t. This treatment enables us to exploit properties of generalized equilibrium Poisson point processes to address questions that have usually proved intractable.
* Preliminary results. The number of active submarkets in the industry changes over time, which causes the number of active submarkets in which firms participate to change over time. Our first task is to establish distributions for the number of active submarkets and for firm participation in submarkets. While we can characterize transitory distributions for any time t, much of our analysis is concerned with market structure in the...
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