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Artikel Original Teori Ukuran Perusahaan

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Artikel Original Teori Ukuran Perusahaan

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Artikel Original Teori Ukuran Perusahaan

  1. 1. What Determines Firm Size? Krishna B. Kumar Marshall School of Business, University of Southern California Raghuram G. Rajan International Monetary Fund & NBER Luigi Zingales∗ Graduate School of Business, University of Chicago, NBER, & CEPR Abstract In this paper we study how industry-specific and institutional factors affect the size of corporations. We find that countries that have better institutional development, as measured by the efficiency of their judicial system, have larger firms. Once we correct for institutional development, there is little evidence that richer countries or countries with better developed capital markets have larger firms. Interaction effects are perhaps of greatest use in discriminating between theories. We find the efficiency of the judicial system has the strongest relationship with firm size in industries with low physical cap- ital intensity, a finding consistent with a broad class of theories emphasizing “Critical Resources” as central to determining the boundaries of firms. ∗ We thank Eugene Fama, Doug Gollin, Ananth Madhavan, John Matsusaka, Andrei Shleifer, and work- shop participants at Chicago, Copenhagen, Norwegian School of Management-BI, and USC for comments. Kumar acknowledges support from the US Department of Education and USC’s CIBEAR. Rajan and Zingales acknowledge financial support from the Sloan Foundation (officer grant) and the Stigler Center.
  2. 2. An interesting aspect of economic growth is that much of it takes place through the growth in the size of existing organizations.1 What are the potential determinants of the size of economic organizations? What are the constraints to size and, hence, potential constraints to growth? Even if one were totally uninterested in economic growth, one would still encounter firm size in many other sub-fields of economics. For instance, firm size has often been used as an exogenous variable in explaining financing decisions (see Barclay and Smith (1995 a and b)), managerial compensation (Jensen and Murphy (1990)), and even required rate of returns (Banz (1981), Fama and French (1992)). While this approach has produced great insights, there are reasons to open the black box enveloping firm size: as we have come to better understand financial decisions taking the size of firms as fixed, the intellectual payoffs to developing a better understanding of the determinants of the boundaries of firms have increased. After all, they may not be orthogonal to financial decisions (see Zingales (2000)). Moreover, the boundaries of corporations are themselves changing rapidly (see, for example, Pryor (2000) or Rajan and Zingales, 2000) increasing the urgency for such studies. While our focus is on firm size, we face a problem that studies on organizational form have faced, that is of taking the theory of the boundaries of firms to the data.2 One approach researchers have taken to tackling this problem is to focus on a particular industry and study it intensely (see, for example, Berger et al. (2001), Brinckley et al. (2001), Mullainathan and Scharfstein (2000) or Eldenberg, et al. (2001)). While this focus allows cleaner tests of the theories, it makes it harder to identify generalizable patterns. What is a persistent organizational form in an industry in a country may be a result of simply historical accident. The alternative is to take a broader brush approach to identifying common robust pat- terns across industries and countries. While such an aggregate analysis can, at best, tell us what theories may be worth investigating further, when combined with the more detailed micro-analysis, it can give us greater confidence in our understanding. Obviously, both approaches are necessary. It is the latter approach that we take in this paper. More precisely, we examine the size of firms as a measure of where organizational boundaries are set. We do this across a variety of countries and industries. We use the lens of broad classes of models we label “technological,” “organizational,” or “institutional,” to sharpen our focus and develop some understanding on what might account for the immense observed variation in firm size. Specifically, we ask the following questions: Is it sufficient to think of the firm as a black box, as technological 1 For instance, in the sample of 43 countries they study, Rajan and Zingales (1998a) find that two-thirds of the growth in industries over the 1980s comes from the growth in the size of existing establishments, and only the remaining one-third from the creation of new ones. 2 See, for example, the work on joint ventures and alliances by Desai and Hines(1999), Lerner and Merges (1998), and Robinson (2001). 2
  3. 3. theories typically do, or do we need to be concerned with features such as asset specificity and the allocation of control that are at the center of organizational theories? Which regressors will aid in discriminating between these theories? What broad patterns hold in the data, and where should we concentrate our future search for determinants? Since some of the proposed determinants of firm size are common across theories, our econometric exercise cannot distinguish among specific theories unless they have opposite predictions for the same variable. Our approach is best suited to assess the broad success of classes of theories than those of competing models within a single class. We attempt to establish the nature of relationships between likely determinants suggested by theory and firm size using data on the size distribution of firms across industries in 15 European countries. This data set is particularly well suited for our purposes because these are all fairly well-developed countries, so the minimum conditions for the existence of firms such as a basic respect for property rights, the widespread rule of law, and the educational levels to manage complex hierarchies exist. This enables us to focus on more subtle institutional factors which exhibit considerable variation even in this sample of well- developed countries.3 We also have a large number of industries, and the variation across industries in their use of different factors can provide an understanding of the effects of production technology on firm size. Most importantly, we are able to study the interactions between institutional and technological effects suggested by theories that provide specifics on the mechanism by which size is affected. By examining these interactions we get the clearest insights into the possible determinants of firm size. We first examine patterns in firm size across industries and countries. At the industry level, we find physical capital intensive industries, high wage industries, and industries that do a lot of R&D have larger firms.4 We also find that, on average, firms facing larger markets are larger. At the country level, the most salient findings are that countries with efficient judicial systems have larger firms, though, contrary to conventional wisdom, there is little evidence that richer or higher human capital countries have larger firms. Similarly, while countries that are more financially developed have larger firms, this seems to reflect the greater institutional development of those countries (such as greater judicial efficiency) rather than the effects of finance per se.5 The cross-industry results are broadly consistent 3 The wide variation seen in the regressors of our sample is discussed in greater detail in Section 2.3. 4 Some of these cross-industry correlations are not surprising given the past literature on intra-industry patterns (see Audretsch and Mahmood (1995), Caves and Pugel (1980), Klepper (1996), Sutton (1991), for example). There are also a number of cross-industry studies on the determinants of industry concentration (see Schmalensee (1989) for a survey). While we do not believe there is a one-to-one correspondence between concentration and firm size, some of the cross-industry correlations (for example, that between R&D and size) may be viewed as reinforcing the findings of that literature. 5 This finding is not surprising. The effects of financial development on average firm size are, as we will 3
  4. 4. with all three classes of theories, but at the country level organizational and institutional theories fare better, with the efficiency of the judicial system emerging as a correlate worthy of further study. These broad correlations, however, can take us only so far in identifying theories with the most promising structural determinants of firm size. For this reason, we study the effects of interactions between an industry’s characteristics and a country’s environment on size, after correcting for industry and country effects. The analysis of these interactions, which are best able to discriminate between theories, is perhaps the most novel aspect of this paper. Organizational theories, which model the micro mechanisms in greater detail, are more amenable to such tests. A central finding is that the relative size of firms in capital intensive industries diminishes as the judicial system becomes more efficient. This is in large measure because the average size of firms in industries that are not physical asset intensive is larger in countries with better judicial systems. One way to interpret this finding is that firms in consulting and advertising, which are based on intangible assets such as reputations, client relationships, or intellectual property, tend to be much bigger in countries with a better legal system because a sophisticated legal system is necessary to protect these assets. By contrast, only a crude legal system is necessary to enforce the property rights associated with physical capital, so basic physical capital intensive industries like steel or chemicals will have relatively larger firms in countries with an underdeveloped legal system. In further support of this argument, we find that R&D intensive industries have larger firms in countries that have better patent protection, suggesting that the judicial system may be particularly important in protecting intangible resources, enabling larger firms to emerge in industries that depend on such resources. We address issues of endogeneity by using instruments for variables such as the market size, predetermined values for institutional variables such as judicial efficiency, and averages over several countries for industry variables such as investment per worker. We also use interactions of technological and institutional variables, which are likely to be more exogenous than level variables with respect to firm size. Our evidence suggests that theories emphasizing the fundamental importance of own- ership of physical assets in determining the boundaries of the firm, and those that suggest mechanisms other than ownership can expand firm boundaries when the judicial system im- proves – organizational theories we refer to as “Critical Resource” theories – are promising frameworks with which to explore the determinants of firm size. It also appears that fur- ther attention can be more fruitfully focused not on technological variables or institutional variables by themselves, but on interactions between these variables. A caveat is in order. There is a large literature on how the forces affecting competition between firms (see Sutton (1991) for an excellent review) determine the concentration of argue, ambiguous. 4
  5. 5. the market and, indirectly, firm size. While there may be some overlap between our cross- industry findings and the vast literature on the cross-industry determinants of concentration, not all the patterns we establish for firm size can simply be inferred from the literature on concentration. More important, following the spirit of Sutton (1991) our most persuasive results are on interactions, which are hard to explain using theories of market structure. Nevertheless, we acknowledge that the focus on firm size necessitated by the macro level data we have, which ignores the forces of competition, is likely to offer as partial an answer as one resulting from an analysis of competition, which ignores other internal or institutional constraints on firm size. The rest of the paper proceeds as follows. In section 1, we provide a candidate list of determinants of firm size suggested by the theories, and in section 2 we present the data and discuss the broad patterns. We report partial correlations of size with industry specific characteristics (section 3), country specific variables (section 4), and interactions between the two (section 5) correcting for industry and country characteristics. We discuss the results in section 6 and conclude with suggestions for future research. 1 Existing Theories There exists an immense literature that, directly or indirectly, deals with firm size. To simplify our analysis we classify theories broadly as technological, organizational, and insti- tutional, based on whether they focus on the production function, the process of control, or influences of the economic environment. Clearly, the classification will be somewhat ar- bitrary because some theories combine elements of different approaches. Moreover, space constraints do not permit us the luxury of being exhaustive, and the theories discussed be- low should only be viewed as representative with those more amenable to proxies we have access to receiving special attention. 1.1 Technological Theories Technological theories go back to Adam Smith (1776), who suggests that the extent of specialization is limited by the size of the market. If a worker needs to acquire task-specific human capital, there is a “set-up” cost incurred every time the worker is assigned to a new task. Workers perform specialized tasks and a firm needs to hire more workers when its production process becomes more specialized. Therefore, not only the extent of specialization but also the size of firms is limited by the size of the market being served. However, Smith’s prediction has not remained unchallenged. Becker and Murphy (1992) point to the existence of multiple firms serving most markets to argue that coordination costs play a major role in limiting the size of firms before the size of the market becomes binding. Hence, the effect of market size is ultimately an empirical question. 5
  6. 6. An important formulation of the neoclassical theory of firm size is Lucas (1978). He identifies a firm with a manager (and the capital and labor under the manager’s control) and assumes that the “talent for managing” is unevenly distributed among agents. If the elasticity of substitution between capital and labor is less than one, an increase in per capita capital raises wages relative to managerial rents, inducing marginal managers to become employees, and increasing the ratio of employees to managers. Therefore, greater capital intensity, proxied by investment per worker or R&D intensity, should be associated with larger firms. Human capital is suggested as a positive correlate of firm size in the theories in Rosen (1982) and Kremer (1993). Rosen (1982) considers a hierarchical organizational structure, where improved labor productivity at any given level filters through lower levels. The tradeoff between managerial scale economies and the loss of control associated with larger organiza- tions results in determinate firm sizes. In equilibrium, persons with the highest skills are placed in the highest positions of the largest and deepest firms. The multiplicative pro- ductivity interactions mentioned above make the equilibrium distribution of firm size more skewed than the underlying distribution of talent. Kremer (1993) models human capital as the probability that a worker will successfully complete a task. Each task is performed by one worker, so the output of the firm (a sequence of tasks) depends on the product of the skill levels of all workers. Firms using technologies that need several tasks will employ highly skilled workers because mistakes are more costly to such firms. Kremer then assumes that the number of tasks and number of workers are likely to be positively correlated, and finds his model consistent with the stylized fact that richer (higher human capital) countries specialize in complicated products and have larger firms. An ancillary implication of the model is that firm size should be positively correlated with the wage per worker, since higher wage implies a higher quality worker.6 While we refine some of these hypotheses in our empirical discussion, a broad summary of the empirical implications of this class of theories can be stated as follows: • There should be a positive connection between market size and firm size according to Smith (1776), but not according to Becker and Murphy (1992). • Firms in richer countries should be larger. Investment per worker and R&D intensity should be positively associated with firm size. 6 The lack of a hierarchical structure in Kremer’s model makes the relationship between average human capital of the workforce and average firm size more explicit, unlike the models of Lucas and Rosen where the human capital of managers, who typically constitute a small fraction of the workforce, is what matters. A recent contribution in this genre is Garicano (2000). In his model the size of a managerial hierarchy is determined by a trade-off between communication and knowledge acquisition costs. The theory is promising but the data requirements for shedding light on whether it matters are beyond the scope of an analysis like ours (see, however, Rajan and Wulf (2002) for an initial attempt). 6
  7. 7. • Firm size should increase with human capital and wage per worker. 1.2 Organizational Theories Organizational theories fall into three broad categories. One set of theories – often referred to as “Contracting Cost” theories (see, for example, Alchian and Demsetz (1972) and Jensen and Meckling (1976)) – suggest little difference in the contracts at work ‘inside a firm’ and in the market. Instead, the firm is simply a particular configuration of contracts characterized by a central common party to all the contracts, who also has the residual claim to the cash flows. While these theories are extremely useful in explaining contractual arrangements inside the firm, they do not provide sharp predictions on the boundaries of the firm. A second set of theories, mostly associated with Williamson (1975, 1985)) and Klein, Crawford and Alchian 1978, can be loosely labeled “Transaction Cost” theories. These theories offer more guidance as to whether a transaction should take place between two arm’s length entities or within a firm, where a firm can be loosely defined as an entity with a common governance structure. The advantage of doing a transaction within a firm is that the firm brings incentives to bear that cannot be reproduced in an arm’s length market. Unfortunately, factors that typically determine the extent of integration in these theories, such as asset specificity and informational asymmetry, are hard to proxy for even with detailed data, let alone in a relatively macro-level study such as ours. The third set of theories, which can collectively be described as “Critical Resource” theories of the firm (see Grossman and Hart (1986) for the seminal work in this area and Hart (1995) for an excellent survey of the early literature), however, offer greater grist for empirical mills. The starting point of these theories is that transactions can either be fully governed by contracts enforced by courts or by other mechanisms that confer power in non- contractual ways to one or the other party to the transaction. The non-contractual source of power is usually a critical resource that is valuable to the production process. A variety of (non-contractual) mechanisms attach the critical resource to one of the parties in a way that maximizes the creation of surplus. For example, the Property Rights approach (see Grossman and Hart (1986), Hart and Moore (1990)) emphasizes physical assets as the primary critical resource, and ownership as the mechanism that attaches this resource to the right agent. According to this view, ownership differs from ordinary contracts because it confers on the owner the residual rights of control over the asset (the right to decide in situations not covered by contract). The power associated with the common ownership of physical assets is what makes the firm different from ordinary market contracting. More recent developments of this theory (see Rajan and Zingales (1998b) and (2001), Holmstrom (1999), and Holmstrom and Roberts (1998) for example) emphasize that the crit- ical resource can be different from an alienable physical asset, and mechanisms other than 7
  8. 8. ownership, which work by fostering complementarities between agents, and between agents and the critical resource, can be sources of power within the firm. For instance, Rajan and Zingales (2001) analyze a model where an entrepreneur’s property rights to the critical re- source are allowed to vary. This model has the implication that as long as the government respects property rights broadly, physical assets are hard to make away with and thus phys- ical capital intensive firms will typically be larger. But as legal institutions improve, other forms of protection become available to the entrepreneur – patent rights protect intellectual property, while non-compete clauses restrain employees from departing. Thus firms that rely on intangible forms of critical resources, such as brand names, intellectual property, or inno- vative processes, should become larger as the legal environment improves. This implication forms the cornerstone of our analysis of interactions involving judicial efficiency and capital intensity.7 In summary, this class of theories gives rise to the following empirical implications: • Higher levels of capital – a critical resource – should be associated with greater firm size. • By offering better protection for critical resources, a better legal environment should lead to larger firms. • Firms that rely on intangible critical resources should become disproportionately larger as the legal environment improves. 1.3 Institutional theories There are many channels through which institutions can affect firm size beyond what is predicted by the technological and organizational theories. We group these channels into two main categories: regulatory and financial. On the regulatory side, many costly regulations apply only to larger firms (for example the obligation to provide health insurance in the United States or Union Laws in Italy). This tilts the playing field towards small firms. Other regulations, such as strong product liability laws, favor the creation of separate legal entities that can avail themselves of the protection afforded by limited liability. This should lead to smaller firms. For instance, each taxi cab in New York is a separate firm. This effect has been found to be important in explaining the time variation of size of firms in the United States (Ringleb and Wiggins (1990)). In the 7 Of course, courts are not the only enforcement mechanism. In repeated relationships contracts can be self-enforcing. Unfortunately, we do not have a good proxy for the repeated nature of a relationship. It is reasonable to assume, though, that the frequency of interaction varies by industry and as such should be captured by our industry dummies. 8
  9. 9. same way, a strict enforcement of anti-trust laws can have an effect in reducing the average size of firms. If the availability of external funds is important for firms to grow, firm size should be positively correlated with financial development and, more generally, with factors promot- ing the development of financial markets. Rajan and Zingales (1998a), however, find that financial development affects growth in both the average size of existing establishments and in the number of new establishments in industries dependent on external finance (though disproportionately the former). With the development of financial markets, more firms will be born, reducing the average size of firms; however, existing firms will be able to grow faster, increasing the average size of firms. Whether the average size of firms in industries that rely on external finance is larger is, therefore, ultimately an empirical question, which we will try to resolve. La Porta, Lopez-De-Silanes, Shleifer, and Vishny (1997a) find that a country with a Common Law judicial system, and having strict enforcement of the law, has a more developed financial system. This would suggest that there is also an indirect channel through which sound laws and judicial efficiency affect firm size - through their effect on financial market development. The empirical implications of the institutional theories can be summarized as follows: • Stricter liability and anti-trust laws give rise to smaller firms. • Financial development exerts an ambiguous effect on firm size. • A higher quality of the legal environment should result in larger firms. We have attempted in the preceding paragraphs to describe some important technical, legal, and institutional influences on firm size. Several of these effects are country specific. Given the large number of possible effects and the limited number of countries we have data for, we will not attempt to capture them all, but will typically control for them by inserting country fixed effects. 1.4 Existing Empirical Literature 1.4.1 Market Structure Much of the evidence we have comes indirectly from the vast literature on market struc- ture. Most of the early cross-industry work appealed to the structure-conduct-performance paradigm of Bain (1956). However, this literature came under criticism, especially after the extensive work on game theory in the 1980s, when it became clear that the theoretical pre- dictions were much more nuanced than allowed for in the empirical work. As a result, much 9
  10. 10. work since has been within-industry because it is easier to map the underlying characteristics of specific industries to particular theoretical models.8 However, more recently Sutton (1991) has argued that “too rigid adherence to such a view runs the risk of abandoning a central part of the traditional agenda of the subject, which concerns the investigation of regularities of behavior that hold across the general run of industries”. Instead, he argues for investigating robust predictions that are likely to hold across a class of models. In particular, he argues when up front sunk costs are exogenous, and the degree of price competition is fixed, a robust prediction is that the size of the market and the concentration of the market should be negatively related. Intuitively, the larger the market, the greater the ability to amortize fixed costs, and the greater the amount of entry. The results on concentration (e.g., see the early work by Pashigian (1968)and Stigler (1968)) do not, however, map one to one onto results on firm size. Bresnahan and Reiss (1991) argue that price competition does not change much with entry. If so, the number of firms should expand linearly with the market, and there should be no predicted relationship between market size and firm size. By contrast, other theories of firm size predict a positive relationship between the size of the market and the size of firms, and the evidence, we will see, is consistent with this prediction. Because our focus is on technological, managerial, and institutional determinants of firm size and not on competition within a market for a specific product, we can afford to examine industries defined fairly broadly so long as the underlying technological characteristics of firms within each broad industry group are strongly correlated. To this extent, we also reduce the importance of a particular product’s market structure for our findings. And by emphasizing interaction effects that are unlikely to come from theories of competition, we hope to establish the independent validity of our focus. Of course, ultimately, theory should address both the determinants of firm size arising from external competition, and those arising from factors like the capabilities of the firms themselves (see Penrose (1959)). Pending such a theory, a focus on either the competitive forces determining market structure or on the technological, managerial or institutional forces determining firm size, can only be partial, however careful the empirical work. 1.4.2 Institutional differences and firm size There have been few cross-country studies focusing on the effects of institutional differences on firm size. Davis and Henrekson (1997) find that the institutional structure in Sweden forces a tilt (relative to the US) towards industries that are dominated by large firms. Their interest, however, is in the relative distribution of employment across sectors, not in the determinants of firm size per se. La Porta, Lopez-De-Silanes, Shleifer, and Vishny (1997b) 8 Though see Caves and Pugel (1980), Audretsch and Mahmood (1995), and Mata (1996) 10
  11. 11. find a positive correlation between an indicator of the level of trust prevailing in a country and the share of GDP represented by large organizations (defined as the 20 largest publicly traded corporations by sales). Their focus, however, is on the relative importance of large organizations, while our focus is on the determinants of the absolute size of organizations. 2 The Data In 1988, Directorate-General XXIII of the European Commission and Eurostat launched a project to improve the collection and compilation of statistics on small and medium en- terprises. This project led to the publication of Enterprises in Europe by the European Commission in 1994. This data set contains statistics on enterprises, employment, and pro- duction for all economic sectors (except agriculture) in the European Union (EU) and the European Free Trade Agreement (EFTA) countries. One of the explicit purposes of this effort was to assemble “comparable and reliable statistics which make it possible to identify the relative importance of different categories of enterprises.” (Enterprises in Europe, Third Report, v.I, p. xxii). In spite of the effort to homogenize the statistical criteria Eurostat warns that several methodological differences in the classification and coverage of units remain. Thus, the cross-country analysis should be interpreted with more caution, while the cross-sector analysis or interactions, which control for country fixed-effects, are less sensitive to this problem. With all its limitations this is the first source we know of that provides comparable data on firm size across countries. Enterprises in Europe provides us with the size distribution of firms (number of employ- ees) in each NACE two-digit industry (we use “industry” interchangeably with “sector”).9 We exclude from the analysis Iceland, Luxembourg, and Liechtenstein because of their ex- tremely small size. We also drop Ireland, because data are not consistently reported. This leaves us with 15 countries. For all these countries, data are available for either 1991 or 1992. Further details on the data are presented in the data appendix. We have data on how many firms and employees belong to each firm size bin (e.g., there are 30,065 employees and 109 firms in the bin containing 200-499 employees in “Electricity” in Germany).10 2.1 The Theoretical Unit of Interest and the Empirical Unit Technological theories focus on the allocation of productive inputs across various activities and the effect this has on the size of the production process, rather than on the ways in which 9 NACE is the general industrial classification of economic activities within the EU. Two-digit NACE industry roughly corresponds to two-digit SIC sectors. 10 We use the terms “bin” and “size class” interchangeably. 11
  12. 12. hierarchical control is exerted. The length of the production process is thus the theoretical size of the firm. These theories would not, for example, make much of a distinction between Toyota and its supplier network, and General Motors (a much more vertically integrated firm) and its supplier network, since both feed into broadly similar production processes. Organizational theories, on the other hand, focus on how hierarchical control is exerted. The Property Rights view asserts that control exerted through an arm’s length contract (General Motors over its suppliers) is not the same thing as control exerted through ownership (General Motors over its divisions). According to this view, the economic definition of a firm corresponds to the legal view – a firm is a set of commonly owned assets. However, more recent developments (see Rajan and Zingales (1998b, 2001), for example) go further and suggest that if the economic distinction between transactions that are firm-like and market- like turns on whether hierarchical, non-contractual control is exerted, common ownership is neither necessary nor sufficient to define the economic limits of a firm. Toyota may exert much more control over its suppliers who are tied to it by a long history of specific investment than General Motors, which puts supply contracts up for widespread competitive bidding. Toyota and its suppliers, although distinct legal entities, could thus be thought of as a firm in the economic sense, while General Motors and its suppliers are distinct economic and legal entities. Thus, in general, the firm described by the theories does not correspond to the legal entity. However, data are available only for the legal entity. The unit of analysis is the enterprise, defined as “the smallest combination of legal units that is an organizational unit producing goods or services, which benefits from a certain degree of autonomy in decision-making, especially for the allocation of its current resources. An enterprise carries out one or more activity at one or more location” (Enterprises in Europe, Third Report, v.II, p. 5). The reference to “organizational unit producing goods or service”, however, suggests that the definition takes into consideration also the length of a production process. The emphasis on the “smallest combination of legal units” is also important. Conversations with Eurostat managers indicates that subsidiaries of conglomerates are treated as firms in their own right, as are subsidiaries of multinationals.11 Some subjectivity, however, is introduced because Eurostat looks also for autonomy in decision making in drawing the boundary of the enterprise. To this extent, the enterprise corresponds to the economic entity discussed above – the economic realm over which centralized control is exercised. In sum, the definition used for the enterprise is a combination of the “legal”, and what we call the “economic”, firm. To make some headway, we have to assume that it is also a good proxy for the length of the production process. All we need is the plausible assumption that factors permitting a longer chain of production should also increase the average size of 11 Foreign subsidiaries of a multinational with headquarters in a particular country do not, therefore, add to the enterprise’s size in the country of the parent. 12
  13. 13. the autonomous legal entity called the firm. 2.2 What Do We Mean by Average Size? Should we measure the size of a firm in terms of its output, its value added, or the number of its employees? Value added is clearly preferable to output, because the complexity of the organization is related to the value of its contribution rather than to the value of the output sold. Enterprises in Europe reports that value added per employee is fairly stable across different size-classes, which implies a measure of firm size based on the number of employees is likely to be very similar to one based on value added. Yet, coordination costs, which are present both in the technological and the organizational theories of the firms, are in terms of number of employees, not their productivity. This argues for a measure based on number of employees, which is what we use in the rest of the paper. Such a measure has a long intellectual tradition (e.g., Pashighian (1968)).12 What is the most appropriate measure of average firm size for our data? The simple average, obtained by dividing the total employment in the country-sector combination by the total number of firms in that combination, is inappropriate for two reasons. First, it ignores the richness of the data on the distribution of firm size. Second, it could give us a number that has little bearing on the size of the firm that is “typical” of the sector or has the greatest share in the sector’s production. For instance, in the automobile sector in Spain, 78% of the employees work for 29 firms which employ 38,302 employees. There are, however, 1,302 self-employed people, who account for an equal number of firms. Taken together with the intermediate categories, the simplest measure would suggest that the average firm has only 57 employees. The theories we surveyed in Section 1 have little to say about the degenerate firm of size one; therefore, using the simple average to test the empirical implications of these theories would be misguided. We instead calculate the size of the typical firm in the following way. We locate the bin in which the median employee of a country-sector combination works. We divide the total employment in that bin by the number of firms in that bin to get the average firm size. For the remainder of this paper when we refer to firm size without qualification, we mean the “typical” firm’s size calculated in this fashion (or the log of this size in the regressions).13 In 12 The number of employees is available for many more country-sector combinations than is value added, which further motivates our choice. 13 In addition to focusing on firms that carry out the bulk of the economic activity in a sector, this measure is also more likely to capture firms at or near their optimal scale. The theories we have described suggest the determinants of the optimal scale of firms. Likewise, the measure mitigates the problem of not knowing firm entry and exit details in our cross-sectional data. When there is entry and exit, firms grow substantially when young, and there is inter-industry variation in these rates of growth (see Caves (1998) and Pakes and Ericson (1998)). Despite this problem, since we have countries at relatively similar stages of development, industries 13
  14. 14. the above example of automobile manufacturing in Spain, this measure gives an average firm size of 3,820 employees.14 The correlation in our sample between the average firm size and the “typical” firm size is 0.39; more relevant for the regressions is the correlation between the log of these measures, which is 0.86.15 2.3 Summary Statistics In Table 1, we present statistics on firm size by country. The firm size is calculated either as a simple average or as the “typical” firm’s size described above for each country-sector combination; the mean across sectors for a given country is presented. The correlation coefficient between the two measures of size is 0.25 and the Spearman’s rank correlation is 0.4. Greece, Portugal, and Austria have the smallest typical firm size. The UK and Italy have firms with the highest typical size, in fact, substantially higher than the remaining should be at similar stages of the product life cycle across countries (see Klepper (1996) for a formalization of the effects of the PLC). Hence, the cross-country and interaction effects should indeed reflect the effects of institutional differences on average size. More important, Sutton (1997, p52) argues that most entry and exit has relatively little effect on the largest firms in the industry (which are likely to have achieved the optimal scale). 14 Our measure is similar in spirit to the coworker mean suggested by Davis and Henrekson (1997) to emphasize the number of employees at the average worker’s place of employment. It is the size-weighted mean of employer size; by squaring the number of employees in each firm, this measure clearly emphasizes the larger firms. If we were to adapt this measure to our data, which are available only at the level of firm size bins, we would compute a weighted average size as follows. The average firm size in each size bin is first calculated by dividing the number of employees by the number of firms. The average size for the entire sector is then calculated as the weighted sum of these bin averages, using as weights the proportion of the total sectoral employment in that bin. This produces a “employee-weighted” average of firm size. Employee Weighted Average Number of Employees = n bin=1 NEmp bin NEmp Sector NEmp bin NF irms bin where NEmp bin is the total number of employees in a bin, NEmp Sector is the total number of employees in the sector, and NF irms bin is the total number of firms in a bin. In contrast to the firm-weighted simple average, the employee-weighted average emphasizes the larger firms; note the squaring of bin employment in the numerator. Our results are virtually unchanged, qualitatively, if we were to use this employee-weighted measure than the size of the “typical” firm we have adopted. 15 When we do use the simple average, which we have argued is a noisy measure of firm size, the significance of the cross-industry coefficients are preserved but most coefficients in the other regressions lose significance. However, the results are not overturned in the sense that a positive and significant coefficient with the “typical” firm size does not become negative and significant with the simple average. 14
  15. 15. countries. Since Italy is reputed to have many small firms, it might come as a surprise that it has the second highest average size. This is mainly due to the composition of industries in Italy, the utility sectors in particular. When we control for industry fixed effects (reported in the second to last column), Italy’s firms are smaller; only Greece and Portugal have smaller firms.16 Spearman’s rank correlation between the typical size and the relative size controlled for industry effects is 0.36, suggesting differences in size are not simply driven by a different industry composition.17 We present in Table 2 the summary statistics for the explanatory variables used in the subsequent analysis as well as their cross-correlations. Two variables that we will focus attention on are an index of the efficiency of the judicial system, henceforth termed “judicial efficiency”, and an index of patent rights termed “patent protection”. Judicial efficiency is an assessment of the “efficiency and integrity of the legal environment as it affects business, particularly foreign firms”. It is produced by the country risk rating agency Business International Corp. We use the measure to capture the degree to which the rights of contractual parties are protected by the courts. Because it emphasizes foreign firms, we believe it also reflects the ease of access to the judicial system by all parties, not just insiders. We have the average between 1980 and 1983 on a scale from zero to 10 with lower scores reflecting lower efficiency levels. Patent protection is from Ginarte and Park (1997). They compute an index for 110 countries using a coding scheme applied to national patent laws. The five aspects of patent laws examined were (1) the extent of coverage, (2) membership in international patent agree- ments, (3) provisions for loss of protection, (4) enforcement mechanisms, and (5) duration of protection. Each of these categories was scored on a scale of 0 to 1, and the sum was the value of the index of patent protection, with higher values indicating greater protection. We use value of the index computed in 1985. The definitions of all these variables are contained in the Data Appendix.18 16 When we look at the total number of firms in the country, Italy has by far the most firms. One must be careful, though, because the number of sectors reported differ by country. This might explain the relatively low number of firms in Austria and Denmark. The anomalous observation is Greece, which reports a sizeable number of sectors, but appears to have very few firms. The reason is that only enterprises with more than 10 employees are reported in Greece. While this biases the average size upwards, our typical firm size minimizes the effect. Nevertheless, we verify that our results are robust to the exclusion of Greece. 17 These are the residuals across countries from the regression: log (Employee weighted average sizec,s) = cons + βs · ds + εc,s where, ds is a vector of sector dummies. 18 The use of institutional variables from an earlier time period than the one for which firm size data is available might work in our favor. Using these “pre-determined” variables might partially address issues 15
  16. 16. Two facts are worth pointing out. First, despite the homogeneity of the sample (all the countries are European and would be classified as developed), there is enough variation in most of the explanatory variables. For example, per capita income varies between $6,783 (Greece) and $16,245 (Switzerland) and the measure for human capital varies between 3.8 years (Portugal) and 10.4 (Norway). Likewise, judicial efficiency, an important variable in our analysis, ranges from 5.5 to 10. The second fact is that some of these measures are highly correlated. For example, judicial efficiency has a correlation of 0.9 with human capital. However, using interactions to test the specific mechanics of the theories will shed some light on their individual effects on firm size. 3 Cross-Industry Correlations As mentioned earlier, the empirical results involving interactions between industry-level and country-level variables are the most important and novel aspect of our study. However, we briefly present our analysis of the correlation between firm size and each of these sets of variables first, to see what they reveal about each type of theory and to identify the broad correlations that hold in data. 3.1 Proxies As a proxy for the size of the actual market we use the log of total employment in the industry in that country.19 There are two problems with this measure. First, theories (e.g., Smith (1776)) obviously refer to the potential market. Second, and following from the first, there may be spurious correlation between average firm size and our measure of the market size. For example, in the case of monopolies, there will be a one-to-one correspondence between average firm size and our proxy for the size of the market. To correct for this, we instrument our measure of market size with the logarithm of GDP, the country population, and the ratio of exports to GDP (1960-85 average). These country level variables should be uncorrelated with industry level constraints, but should be correlated with the size of the potential market, hence they should be good instruments.20 of endogeneity such as larger firms lobbying for more efficient judicial systems and a high level of patent protection. 19 Whenever we require the logarithm of a variable, we always add one before taking logs. 20 Note that we are using log total GDP and population individually as instruments instead of per capita GDP. Indeed, we use log per capita GDP as a regressor while studying cross-country correlations, which will require us to drop either total GDP or population as an instrument there. 16
  17. 17. While we do not have a direct measure of capital stock in an industry to enable us to calculate physical capital intensity, we have the gross investment in an industry. Dividing this by the number of workers in that industry, we have investment per worker. In order to obtain a more exogenous measure, we take the mean of this variable across all the countries for which we have this data.21 To measure an industry’s dependence on intangible capital, we use the R&D done in that industry as a share of the country’s total R&D. Unlike physical capital, we do not compute per worker intensity of R&D because R&D is a nonrival input that impacts the whole firm.22 The R&D data is from OECD’s ANBERD database, with appropriate conversion done from ISIC to NACE. Again, the mean across all countries is used. Finally, Rajan and Zingales (1998a) compute an industry’s dependence on external funds as the fraction of capital expenditure in that industry in the United States funded from external sources. We use the Rajan and Zingales measure of external dependence and weight it by the investment per worker in an industry to get the amount per worker that has to be raised from external sources. The maintained assumption in using these proxies is that there are technological char- acteristics of certain industries that carry over countries.23 In other words, if Drugs and Pharmaceuticals is more research intensive in the United States than Leather goods, it will continue to be so in Italy. While this assumption allows us to use independent variables that are likely to be more exogenous, and also overcome the paucity of data, a failure of this assumption means, of course, that some of our independent variables are noise and should have little explanatory power. 3.2 Results We report in Table 3, the estimates from a regression of log typical firm size on industry characteristics, when the size of the market (measured as total sectoral employment) is instrumented. The partial correlation of market size with firm size is positive, though not statistically significant.24 21 This includes the United States. Dropping the United States in the calculation does not change the results qualitatively. Neither does using the median across countries. All industry variables are winsorized at the 5% and 95% levels to reduce the effects of outliers. 22 The intensity with respect to sales, rather than to employees, is an alternate measure, but given the paucity of sales data we chose the sectoral R&D share. 23 This is also the assumption made in Rajan and Zingales (1998a). Since we are primarily interested in the sign of coefficients, what we really require is that the relative relationship between industries carry over rather than the precise levels. 24 Henceforth, “significant” will denote significance at the 10% level or better. 17
  18. 18. We also include investment per worker, R&D intensity, wages per worker, and amount financed externally per worker. The first three explanatory variables are positively and sig- nificantly correlated with size, while the amount financed externally is negatively correlated, but is not statistically significant. While we expected investment, wages, and R&D expen- diture to be positively correlated, as discussed in Section 1.3, we had no strong prior on the sign of the correlation between the amount financed externally and size. The magnitudes of the effects are also considerable. According to the estimates in Table 3, an increase in investment per worker, R&D intensity, and wage per worker from the 25th percentile to the 75th percentile of the variable are associated with an increase in log firm size of 18%, 14%, and 43% of its inter-quartile range respectively. The explanatory power of the regression is also considerable (R2 = 0.45). These significant correlations are robust to the inclusion of country fixed effects (which necessitates dropping country level instruments), and including the explanatory variables one at a time. These robustness results have been omitted from the paper in the interest of brevity, and to focus attention on the section on interactions. These and other omitted results can be obtained from the authors on request. Which theories are these correlations consistent with? Recall our discussion of the em- pirical implications of existing theories in Section 1. If industries are located in specific areas and there is a high cost to labor mobility, or if agents have industry specific human capital, then the Lucas (1978) model could be applied industry by industry in a country.25 The positive partial correlation between investment per worker and size is consistent with Lucas. It is also consistent with Critical Resource theories of the firm where a firm of larger size is easier to control when the critical resource is physical capital. Lucas does not distinguish between investment in physical capital and investment in R&D. Thus we should expect a positive correlation between size and R&D expenditure. Similarly, from the perspective of Critical Resource theories, if the critical resource is intel- lectual property and it is protected to some extent by patent laws, we should expect such a correlation. The positive correlation between wages per worker and size is consistent with the thrust of Lucas’ (1978) notion that the incentive to become an entrepreneur is relatively small when wages are high. It is also consistent with Rosen’s view that large firms have better managers who are paid more, or Kremer’s (1993) view that if wages are a proxy for the quality of a worker, higher wages should be associated with larger firms. In this regression, we are mainly constrained by the availability of data on investment per worker and wage per worker; the number of observations is thus smaller than the one in the regressions in Table 4. 25 The immobility of labor is particularly relevant in the European context. For instance, Decressin and Fatas (1995) show that economic shocks in Europe are mostly absorbed by changes in the participation rate while, in the US, it is immediately reflected in migration. 18
  19. 19. Finally, the insignificant correlation between the amount financed externally and size suggests the adverse effects on average size of financial constraints on the growth of existing firms may offset the positive size effect caused by reduced entry of new firms in financially dependent industries. Before we conclude this section, we should point out that we are not the first to find some of these patterns. For example, Caves and Pugel (1980) find that size is correlated with capital intensity within industry, while the relationship between firm size and total firm R&D investment within an industry is well known (see Cohen and Klepper (1996) for references). However, our finding is across industries and countries and, therefore, we establish the greater generality of these patterns. In summary, the cross-industry correlations are consistent with multiple theories and do not provide enough room to discriminate between technological and organizational theories. Nevertheless, the correlations are not irrelevant in that they provide a minimum set of patterns that theories should fit. 4 Cross-country correlations Let us now examine the partial correlations of country level variables with firm size. 4.1 Results The first variable we include in the regression is the log of per capita income. This can be interpreted as a proxy for per capita capital (as in Lucas (1978)) or, more generally, as a measure of a country’s wealth. As a measure of human capital, which is suggested by the technological theories, we use the average years of schooling in the population over age 25. This comes from the Barro-Lee database and is measured in the year 1985. In Table 4, column I, we present partial correlations of size with the cross-country ex- planatory variables. We include industry fixed effects and the size of the market, which is instrumented by the log of GDP and the ratio of exports to GDP.26 The coefficient on the market size is now positive and highly significant; an increase in the market size from the 25th percentile to the 75th percentile is associated with an increase in log firm size by 26% of its inter-quartile range. Other than market size, the only variable with a positive and highly significant coefficient is the efficiency of the judicial system. An increase in judicial efficiency from the 25th percentile to the 75th percentile is associated with an increase in log firm size by 45% of its inter-quartile range. The coefficient on log per capita income is 26 Since we use log per capita GDP as an explanatory variable, of the three instruments used earlier, log GDP, log population, and ratio of export over GDP, we can use only two otherwise they would be perfectly collinear with log per capita GDP. 19
  20. 20. significant but negative. However, when included alone (column II), the coefficient on per capita income is positive, while when human capital is included (column III), the coefficient on human capital is positive and significant, while the coefficient on per capita income turns negative. We also inserted a number of other variables in our specification, one at a time, in place of judicial efficiency in the specification in column I. We include Ginarte and Park (1997)’s index of the protection given to patent rights in different countries, the quality of accounting standards which Rajan and Zingales (1998a) argue is a good proxy for the extent of financial sector development in a country, as also proxies for regulatory constraints and a measure of product liability. It turns out that none of these is significant alone or when judicial efficiency is included. The coefficient estimate for judicial efficiency, however, always remains positive and highly statistically significant, and that for log per capita income is negative. The “stylized fact” that richer countries have larger firms seems true only when we examine the obvious difference between the size of firms in really poor countries where there is little industry to speak of, and those in the rich developed countries, and when we do not correct for differences in institutions.27 Within the set of industrialized countries, however, there seems to be little evidence of a significant positive partial correlation between per capita GDP and size, or human capital and size.28 With reference to the theories discussed in Section 1, the large positive correlation of firm size with judicial efficiency is consistent with multiple classes of theories. An efficient legal system eases management’s ability to use critical resources other than physical assets as sources of power. This leads to the establishment of firms of larger size (see Rajan and Zingales (2001)). It also protects outside investors better and allows larger firms to be financed (see La Porta et al. (1997a,1998)). Finally, it reduces coordination costs and allows larger organizations (Becker and Murphy (1992)). This cross-country analysis should be interpreted with caution because it is most sen- sitive to differences in the definition of enterprise across countries. Moreover, some of the explanatory variables are strongly correlated. For example, judicial efficiency has a correla- tion of 0.90 with our measure of human capital, 0.65 with accounting standards, and 0.52 with patent protection. This is a traditional problem with cross-country regressions – all measures of institutional and human capital development are typically highly correlated. 27 See Gollin (1998) for an example of a study that focuses on economic development and firm formation. 28 One could argue that our dependent variable is a proxy for labor intensity, and high per capita income countries could be substituting cheap capital for labor. This would yield a negative correlation between size and per capita income. To check that this is not driving our result, we would need data on sales. Unfortunately, data on sales present in Enterprises in Europe are sporadic. Nevertheless, we experimented with the limited sample available. Even with sales weighted average sales as dependent variable, the coefficient estimate for per capita income is never significantly positive. 20
  21. 21. This is one of the reasons we stress our results on interactions in the next section, where we control for both country and industry effects. Nevertheless, two results seem to emerge from the cross-country analysis. First, the correlation between per-capita income and firm size is not as clear as previously thought and may, in fact, be a proxy for institutional development. Second, judicial efficiency seems to have the most clear cut correlation with firm size and deserves more detailed study. 5 Interactions Cross-country regressions could be biased by differences in the definition of the enterprise as well as effectively have fewer degrees of freedom. Hence, it is hard to estimate anything with accuracy, and know whether something is really a proxy for what it purports to be. One way to reduce both these problems is to test predictions that rely on an interaction between country and industry characteristics, after controlling for both country and industry effects. By doing so, we not only use more of the information in the data, but also test a more detailed implication of the theory, which helps distinguish theories that have the same prediction for direct or level effects. Organizational theories, which model the micro mechanisms in greater detail, are more amenable to such tests. 5.1 Predictions and Proxies As we have seen, greater judicial efficiency is correlated with bigger firms. In all the countries in our sample, basic property rights over physical assets are protected, and guarantee owners a certain degree of power. However, the increased protection afforded to intellectual property, management techniques, firm-client relationships, etc., by a more efficient judicial system should allow more resources (even inalienable ones) to come into their own as sources of power. Therefore, according to Critical Resource theory, we should expect judicial efficiency to particularly enhance management’s control rights for firms with relatively few physical assets resulting in larger firms in such industries. This will imply the interaction between judicial efficiency and investment per worker (a proxy for physical asset intensity) should be negatively correlated with size.29 Indeed, when we divide our sample into “knowledge” intensive and non-intensive indus- tries and rerun the cross-country regression in Table 4, column I, both the coefficient on and significance of judicial efficiency are higher for the knowledge-intensive sample. This provides 29 Note that this is not a direct implication of theories like Lucas (1978), which emphasize the rents created for workers by physical capital but not its control properties, or Becker and Murphy (1992), which, refers to the coordination benefits of a better judicial system without emphasizing specific channels through which it works. 21
  22. 22. some confirmation of the above reasoning as well as a greater incentive to understand the mechanism by which judicial efficiency increases firm size.30 5.2 Results One of the advantages of looking at interaction effects is that we can include both country and industry indicators to absorb all the direct effects. Thus we do not need to worry about which country or industry variables to include. The problem, however, is that we cannot instrument the size of the market because the instruments are collinear with the country indicators. This is why we will try specifications both with and without country indicators. In Table 5, we report estimates for the coefficient of the interaction variable (included along with market size, country indicators, and industry indicators). Capital intensive in- dustries have relatively smaller firms in countries with better judicial systems. In column I, an increase in judicial efficiency from its 25th percentile to its 75th percentile is associated with a decrease in the difference in log average size between firms in industries at the 75th percentile of capital intensity and firms in industries at the 25th percentile of capital intensity of approximately 19% of the inter quartile range of log size. Put differently, in countries with a better legal system, the evidence indicates that the difference in size between automobile manufacturers and consulting firms is smaller. The negative correlation between the judicial efficiency-capital intensity interaction and firm size is therefore consistent with Critical Resource theories of the firm. The importance of the interaction effect is in giving us greater assurance that the main effects (such as the effect of capital intensity or judicial efficiency on firm size) are correlated, at least in part, for the particular theoretical reasons we attribute to them. Perhaps a greater reason to focus on interaction effects is their value in distinguishing otherwise hard-to-disentangle level effects.31 Recall that both physical investment per worker and R&D intensity were positively corre- lated with firm size. Critical Resource theory, however, predicts different interaction effects. 30 The knowledge-intensive industries are: Chemicals, Manufacturing of office machinery, Electrical engi- neering, Instrument engineering, Communication, Banking & finance and auxiliary businesses, Insurance, Education, R&D, and Health. 31 Could judicial efficiency be a proxy for low levels of tax evasion, given that a better judicial system is generally associated with better tax enforcement? This would be consistent with the finding that countries with a better judicial system (less easy to evade taxes) have bigger firms, since the rationale for staying small to evade taxes is absent in such economies. However, if tax evasion were the real determinant of size, capital intensive firms, which are more easily detectable, have a particularly strong incentive to stay small and evade taxes when enforcement is ineffective. These are the firms most likely to find the rationale for staying small disappear with improved judicial efficiency, and the interaction effect of capital intensity and judicial efficiency should be positive in size regressions. But this is contrary to the results presented in Table 5; thus tax evasion is unlikely to be the real reason behind the regression results on judicial efficiency. 22
  23. 23. The theory would suggest that R&D intensive firms, which rely more on intangible assets, should benefit much more from protections offered by the law. So R&D intensive firms should be larger in countries with better patent protection. In column II, we include the interaction between R&D and patent protection. The interaction effect is positive, suggesting that firms in R&D intensive industries are larger in countries with better patent protection, but it is significant at only the 20th percent level. The problem with including country indicators is that we cannot instrument for the size of the market, and we know there may be significant biases in including it directly. So in column III, we drop country indicators but include instruments, and also the level of judicial efficiency and the level of patent protection. The interaction between judicial efficiency and capital intensity is again negative and statistically significant, while the direct effect of judicial efficiency is positive and significant. The interaction between patent protection and R&D intensity is again positive, but now statistically significant. Interestingly, the direct correlation between firm size and patent protection is now negative. This correlation was obscured in earlier specifications. A high level of patent protection can be the result of the presence of large R&D-intensive firms, which lobbied for it, rather than the cause. To mitigate the effects of this possible reverse causation, in column IV we instrument patent protection (both as a level and in the interaction with R&D intensity) with the rule of law index, which captures how strongly laws in general are enforced in a country. The results are essentially unchanged. The effect of patent protection is quantitatively bigger and still statistically significant, both as a level and interacted with R&D intensity. While the interaction effects seem consistent with Critical Resource theory the direct effect of patent protection seems puzzling. Why, as the estimates indicate, is greater patent protection associated with a lower size of firm outside R&D intensive industries while it is associated with a higher size of firm in R&D intensive industries? One explanation consistent with Critical Resource theory is the following: In countries where R&D is poorly protected, it may be that firms relying on R&D alone cannot command critical resources sufficient to achieve scale. This is why firms from industries based on other, more appropriable, resources, have the scale and thus a comparative advantage, in undertaking R&D. When patents become better protected, firms in R&D intensive industries can themselves reach the necessary scale. Thus R&D activity migrates away from firms outside R&D intensive industries to firms in those industries, reducing the size of the former, and increasing the size of the latter. While this is admittedly an ex post-facto rationalization, there is some evidence consistent with it. If, in fact, there is migration of activity across firms in different industries, we should see the share of employment in R&D intensive industries increase in countries with better patent protection. This is indeed the case. When we run a regression of an industry’s share of total employment in a country against country indicators, industry indicators, and the 23
  24. 24. interaction between the industry’s R&D intensity and patent protection in that country, we find a positive and significant coefficient on the interaction. Thus R&D intensive sectors are a greater fraction of total employment in countries with better protection of R&D. 5.3 Why Does a Better Judicial System Reduce the Impact of Capital Intensity on Size? Thus far, the results do not tell whether the negative interaction effect between improved judicial efficiency and capital intensity comes from firms with relatively few physical assets becoming larger or from capital intensive firms becoming smaller. Being able to distinguish between these effects would provide more insight into why we observe this correlation. We have argued that improved judicial efficiency will enable management to gain control from legal devices other than ownership rights over physical assets. This suggests that the effect should largely come from the increase in size of firms in industries that are not physical capital intensive (this will also provide additional support for the causal link we want to draw for the R&D intensity-patent protection interaction). There is, however, another possibility. If the residual rights arising from ownership of physical assets are what distinguish firms from markets, as judicial efficiency improves, contractibility improves, and the rights associated with physical assets become less important. Also, physical assets become easier to finance for departing employees, therefore becoming less unique and well protected, and again residual control rights associated with them diminish. This implies that capital intensive firms should become smaller with improvements in judicial efficiency, which could also explain the result. To test this, we replace the interaction variable with judicial efficiency multiplied by indicators if an industry is in the highest or lowest tertile of physical capital intensity in Table 5B. As column I shows, the coefficient on the interaction between judicial efficiency and the highest tertile indicator is negative but not significant. Most of the action comes from the lowest tertile indicator which is positive and significant. This suggests that the effects of improvements in judicial efficiency come primarily from the growth in the size of firms that are not physical capital intensive. In column II, we re-estimate the same regression instrumenting for patent protection with the rule of law index. The results are essentially unchanged. Therefore, the interaction effect seems consistent with the direct influence of capital intensity and judicial efficiency on firm size as postulated by the Critical Resource theory, suggesting that these theories might be worthy of further investigation. 24
  25. 25. 6 Discussion 6.1 Relevance of Technological Theories The cross-industry results are consistent with the technological theories. The cross-country evidence, however, is mixed. For example, log per capita income has, if anything, a negative correlation with firm size after correcting for institutional variables that should be irrelevant in technological theories. Similarly, the level of human capital has an insignificant correlation with firm size after we correct for the efficiency of the judicial system. This result is to be expected, as technological theories often abstract from institutional features that vary across countries and affect firm formation. They instead focus on the organization of a typical sector within a given economy, and are thus most likely to be consistent with time-series evidence, as in Lucas (1978), or cross-industry evidence, as in the early part of our study. One way to get at more detailed implications of technological theories may be to examine the influences on the dispersion of firm size within industry. For example, Kremer’s (1993) results on assortative matching based on human capital, and higher human capital firms undertaking more complex processes (larger firms) can be combined to get the implication that greater inequality in human capital would be correlated with greater dispersion in firm size. Rosen’s (1982) model has a similar implication - with more skilled managers running large firms and less skilled managers running small firms. As a measure of inequality in human capital we compute the coefficient of variation in educational attainments.32 In Table 6, we regress the employee-weighted coefficient of variation of firm size against this measure of inequality.33 We find, as predicted, the coefficient on inequality to be positive and highly statistically significant. One could, however, argue that institutional development reduces the importance of factors like talent and incumbency for the exercise of managerial control, and levels the playing field. For example, greater judicial efficiency could help even small entrants secure their property, thus ensuring they reach optimal scale for production. Therefore, we would 32 Barro and Lee (1993) have data on the percentage of population over 25 in 4 categories of educational at- tainment – none, primary, secondary, higher – for each country. They also have years of education attainment of each type – PYR25, SYR25, and HYR25. We assign the following years of education to the four-category frequency distribution mentioned above: 0, PYR25, PYR25+SYR25, and PYR25+SYR25+HYR25. The coefficient of variation is then computed the usual way and used as a measure of human capital inequality. All human capital data is for the year 1985. 33 Since we need to account for the whole distribution, the typical firm size of the earlier regressions cannot be used. Therefore, we resort to the employee-weighted coefficient of variation calculated using the employee- weighted average firm size outlined in footnote 14 and an analogous measure of employee-weighted standard deviation. 25
  26. 26. expect measures of institutional development to be negatively correlated with dispersion. This is, in fact, the case. When we include judicial efficiency in column II, it is strongly negatively correlated with the weighted coefficient of variation of firm size, and inequality in human capital, while still positive, is no longer statistically significant. Finally, the inclusion of per capita income in column III does not change our conclusions. As done for organizational theories, we could conduct more convincing tests of techno- logical theories if we could exploit the way differences in institutional environments across countries affect the use of particular technologies or the organizational structures. One could tease out of the technological theories tests for such interactions, even if it is hard to do so. For instance, in Kremer (1993) when the value added in a particular technology is high, human capital will be more important. For such technologies, firm size will be larger when the human capital available in the country is better. This suggests a positive correlation between firm size and the interaction of human capital in the country with value added per worker. This correlation is actually negative, but insignificant, when we include this interac- tion in the model in Table 5A, column III. Of course, our measures are noisy, so more work is warranted before definite conclusions are drawn. Even if one can devise more careful tests that discriminate between technological and organizational explanations of the size of firms, it is likely that they will be biased in favor of the latter. The firm’s definition in our dataset is closer to the legal one, which is the one organizational theories focus on. Clearly, they should have more explanatory power. By contrast, technological theories focus more on the technological limits to production. The unit of observation to test such theories should be the length of a production process from raw material input to final output. This may extend across several firms. Unfortunately, we do not have data on the length of processes, hence the bias. 6.2 Vertical vs. horizontal integration Firms could become larger because they become more vertically integrated or because they expand horizontally. A few theories are very specific about which of these forces leads to greater size. For example, Adam Smith’s view that size is related to the extent of the market clearly refers to a firm expanding by doing more of the same when the market grows, i.e., horizontal expansion. By contrast, the Property Rights view of Grossman and Hart was first set in the context of vertical integration. In general, however, with this and most theories of firm size, similar predictions can be obtained regardless of whether expansion comes from increased vertical, or horizontal, integration. For this reason, we have purposefully avoided the question thus far of whether differences in size arise from differences in the level of vertical, or horizontal, integration. Nevertheless, it is of some interest to examine how size and the extent of vertical inte- gration are related. A traditional measure of vertical integration is the value added to sales 26
  27. 27. ratio (Adelman, 1955). More vertically integrated firms have higher value added per unit of sales and, thus, will have a higher ratio. Unfortunately, Enterprises in Europe report the data on value added and sales only for a subset of sector-country observations (249 overall). Furthermore, these do not coincide perfectly with the sector-country observations for which we have data on size distribution (only 146 sector-country observations have both data). Thus, our analysis is, by necessity, exploratory. Table 7A reports the average value-added-to-sales ratio across countries (column I). With the exception of Denmark and Greece, all countries have a similar level of vertical integration, where the value added generated by an enterprise corresponds to roughly 35% of sales.34 The pattern is unchanged if we correct for the different industry composition in the various countries, as shown in column II. A possible explanation of this remarkable homogeneity across the European countries is the long-standing presence of a valued added tax system among members of the European Union. Unlike sales taxes, a valued added tax is neutral with respect to the integration decision. Thus, our sample of European countries appears particularly suitable to explore other determinants of size, because it is unaffected by biases stemming from taxes on sales. Table 7B reports the average value-added-to-sales ratio across industries (column I). Here we do observe a lot of cross sectional variation. In fact, in an analysis of variance, sector dummies account for 58% of the overall variability, while country dummies only 10%. As seems quite plausible, the least vertically integrated sectors are Agents, Wholesale Distri- bution, Coke Oven, Retail Distribution, and Oil Refining. At the other extreme, the most vertically integrated sectors are Railways, Services, and Research & Development. How much of the differences in size across industries and countries are driven by differ- ences in the degree of vertical integration? To examine this, we determine the correlation between our measure of the “typical” firm’s size and the degree of vertical integration. Sur- prisingly, the correlation is approximately zero (0.006). This continues to be true if we control for country fixed effects and industry fixed effects. This is consistent with Jovanovic (1993), who documents empirical evidence on the joint trend toward greater size and diver- sification (i.e., horizontal integration) of firms in the United States and other countries. If firms achieve greater size largely through horizontal integration we may indeed find that size and the degree of vertical integration are uncorrelated. We then substitute the measure of firm size with the value-added-to-sales ratio and re- estimate all the above specifications in Tables 3 and 4 (estimates not reported). While the coefficient signs are generally the same as in the tables, none of the coefficients is statistically 34 The different levels of integration in Denmark and Greece are probably attributable to differences in the definitions of enterprise. As reported by Eurostat (Enterprises in Europe 3 vol. I, p. xxvi) Greece uses a narrower definition of enterprise, which is more similar to the notion of establishment, while Denmark uses a broader definition, based on the legal entity. 27
  28. 28. significant. The only exception is the log of per capita income, which enters positively and significantly when the dependent variable is vertical integration, and negatively and insignifi- cantly when the dependent variable is size. While the limited sample at our disposition (146 observations) and the likely noisiness of the measure prevent any strong conclusions, the results seem to indicate that the differences in size we capture are not driven by differences in the extent of vertical integration. 7 Conclusion We believe we have uncovered a number of regularities that can provide some answers to the questions that started this paper as well as offer guidance for future empirical and theoretical work on the determinants of firm size. The broad patterns are that firms in capital-intensive industries are larger, as are firms in countries with efficient judicial systems. The cross- industry results are consistent with both technological and organizational theories, while the cross-country results are understandably less supportive of the technological theories. The most novel aspect of this study is the use of interactions between institutional and technological variables to test detailed mechanics of the theories; organizational theories are particularly amenable to such tests. A central finding is that firms in capital intensive industries are relatively smaller when located in countries with efficient judicial systems, which lends support to organizational theories. Moreover, R&D intensive industries have larger firms when patents are better protected, though firms outside R&D intensive industries are smaller. We have addressed the issue of causality to some extent by investigating the detailed implications of theories. Our work suggests that more detailed investigation of theories such as the Critical Re- source theory is warranted. Such an analysis, we hope, will eventually enable us to shed more light on the following question: Which mergers make sense from an organizational per- spective? Which projects should be left to a separate entity, as opposed to being undertaken as a joint venture, a cooperative alliance, or an in-house venture? Much remains to be done. 28
  29. 29. Table 1 Firm Size by Country The source of the data is Enterprises in Europe which provides us with the distribution of firm size in each NACE two-digit industry in a number of European countries in 1991-92. The average number of employees is calculated for each country-sector combination; the average of this measures across sectors is presented for each country as the average size. We then locate the bin in which the median employee of a country-sector combination works. We divide the total employment in that bin by the number of firms in that bin to get the “typical” firm size; the average of this measures across sectors is presented for each country as the “typical” size. Relative size correcting for industry effects is the average residual for that sector obtained after regressing the logarithm of typical firm size on industry indicators. It can be interpreted as the relative deviation of the size of firms in that country after purging industry effects. A: Different Measures of Size Relative size Number Number of correcting of sectors Average firms in the “Typical” for industry with firm size country firm size effect data AUSTRIA 77.5 8,124 286.7 0.46 8 BELGIUM 322.8 177,973 1,366.8 0.46 53 DENMARK 21.9 53,400 302.7 -0.05 8 FINLAND 166.3 199,942 1,234.9 0.18 47 FRANCE 39.8 1,555,064 1,222.0 0.32 29 GERMANY 69.2 2,159,489 949.2 0.62 33 GREECE 47.0 8,342 226.1 -0.82 22 ITALY 100.7 3,242,062 2,346.4 -0.51 54 NETHER 32.0 154,364 379.0 -0.09 17 NORWAY 96.4 83,018 305.4 -0.23 33 PORTUGAL 21.1 280,185 233.7 -0.74 17 SPAIN 70.5 2,373,379 1,136.5 -0.45 49 SWEDEN 28.4 132,662 508.6 0.39 16 SWITZ 63.0 268,653 1,378.0 -0.13 50 UK 37.8 1,165,907 2,674.0 0.95 25 29
  30. 30. Table 2 Summary Statistics A detailed description of all the variables as well as their sources is contained in the data appendix. A: Summary statistics Country variables Mean Median Std. Deviation Minimum Maximum N Per capita income 12,642 13,281 2,698 6,783 16,245 15 Human capital 7.949 8.572 1.905 3.827 10.382 15 Inequality in human capital 0.295 0.265 0.135 0.127 0.625 15 Judicial efficiency 8.767 9.500 1.616 5.500 10.000 15 Patent protection 3.489 3.710 0.621 1.980 4.240 15 Accounting standards 64.600 64.000 11.488 36.000 83.000 15 Sectoral variables Investment per worker 0.009 0.006 0.007 0.002 0.025 36 R&D intensity 0.031 0.016 0.044 0.0002 0.164 33 Sector wage 0.028 0.028 0.010 0.013 0.046 36 External dependence 0.004 0.002 0.004 -0.001 0.015 34 Variables that change by country and sector Log of size of firms 4.804 4.575 2.238 0.629 11.118 463 Size of the market 10.535 10.786 2.186 1.099 14.940 463 Judicial efficiency x 0.067 0.049 0.052 0.010 0.254 348 investment per worker Patent protection x 0.114 0.048 0.164 0.0004 0.695 316 R&D intensity B: Correlation across country variables Country variables log typical Log per capita Human Inequality in Judicial Patent firm’s size income Capital human capital Efficiency Protection Log per capita income 0.464 Human capital 0.520 0.699 Inequality in human capital -0.637 -0.572 -0.744 Judicial efficiency 0.661 0.760 0.901 -0.711 Patent protection 0.432 0.790 0.422 -0.438 0.520 Accounting standards 0.551 0.606 0.696 -0.609 0.651 0.397 C: Correlation across sectoral variables Sectoral variables log typical Capital R&D Sector firm’s size intensity intensity wage Investment per worker 0.349 R&D intensity 0.088 0.124 Sector wage 0.593 0.651 0.371 External dependence 0.023 0.532 0.431 0.465 30
  31. 31. D: Correlation across variables that change both by country and sector Variables that change log typical Market Jud. eff. x Pat. prot. by country and sector firm’s size size cap. int. R&D int. Size of the market 0.021 Judicial efficiency x 0.326 -0.361 investment per worker Patent protection x 0.216 -0.023 0.162 R&D intensity 31
  32. 32. Table 3 Cross-Industry Determinants of Firm Size The dependent variable is the logarithm of the typical firm’s size in each NACE two-digit industry in each country. The size of the market is measured as the logarithm of total employment in a NACE two-digit industry in a country. Investment per worker is from OECD’s ISIS Database. The average across European countries and the US is used. Wage per worker is from the same database, and the average across European countries and the US is used. For an industry’s R&D intensity, we use the R&D done in that industry as a share of the country’s total R&D. The R&D data is from OECD’s ANBERD database, with appropriate conversion done from ISIC to NACE. Again, the average across European countries and the US is used. Amount financed externally is the product of capital expenditures that U.S. companies in the same NACE two-digit sector finance externally (see Rajan and Zingales, 1998a) and investment per worker calculated above. Estimates have been obtained by instrumental variable estimation, where the instruments for the size of the market are the logarithm of population, GDP, and the ratio of export to GDP. Heteroskedasticity- robust standard errors are reported in parenthesis. The standard errors are also adjusted for the possible dependence of observations in the same industry across different countries. Size of the market 0.13 ( 0.08 ) Investment per worker 64.32 ( 28.87 ) R&D intensity 15.33 ( 3.95 ) Sector wage 122.86 ( 36.94 ) External dependence -121.48 ( 86.31 ) R-squared 0.45 N 266 32
  33. 33. Table 4 Cross-Country Determinants of Firm Size The dependent variable is the logarithm of the typical firm’s size in each NACE two-digit industry in each country. The size of the market is measured as the logarithm of total employment in a NACE two- digit industry. Per capita income is the log of per capita income in 1990. The data are from the Penn World Table, Mark 5.6. Human capital is measured as the average number of school years (Barro-Lee, 1993). Judicial efficiency is an assessment of the “efficiency and integrity of the legal environment as it affects business”. It is an average of the index between 1980 and 1983. The table reports the instrumental variable estimates, where the instruments for the size of the market are the logarithm of population and the ratio of export to GDP. Heterosckedasticity-robust standard errors are reported in parenthesis. The standard errors are also adjusted for the possible dependence of the errors of observations in the same countries across different industries. Industry fixed effects are included in all columns. I II III Size of the market 0.31 0.05 0.27 ( 0.05 ) ( 0.12 ) ( 0.12 ) Per capita income -1.04 1.18 -0.40 ( 0.43 ) ( 0.40 ) ( 0.70 ) Human capital -0.06 0.27 ( 0.12 ) ( 0.11 ) Judicial efficiency 0.47 ( 0.12 ) R-squared 0.78 0.72 0.76 N 463 463 463 33
  34. 34. Table 5 Interaction Effects The dependent variable is the logarithm of the typical firm’s size in each NACE two-digit industry in each country. The size of the market is measured as the logarithm of total employment in that NACE two-digit industry in a country. Per capita income is the log of per capita income in 1990 as reported by the Penn World Table, Mark 5.6. Judicial efficiency is an assessment of the “efficiency and integrity of the legal environment as it affects business.” Investment per worker is from OECD’s ISIS Database. The average across European countries and the US is used. Patent protection is an index that measures the strength of patent laws, with higher values indicating greater protection. The source is Ginarte and Park (1997). We use value of the index computed in 1985. For an industry’s R&D intensity, we use the R&D done in that industry as a share of the country’s total R&D. The R&D data is from OECD’s ANBERD database, with appropriate conversion done from ISIC to NACE. Again, the average across European countries and the US is used. Columns I and II of Panel A are estimated by OLS and contain industry fixed effects and country fixed effects. Column III of Panel A is estimated using the logarithm of population and the ratio of export to GDP as instrumental variables for the size of the market, and does not include country fixed effects. Column IV additionally instruments patent protection with the rule of law index. In panel B, low investment per worker is a dummy equal to one for sectors in the lowest tertile of investment per worker. High investment per worker is a dummy equal to one for sectors in the highest tertile of investment per worker. Industry fixed effects and instrumental variables, as in column III of Panel A, are used. Heteroskedasticity-robust standard errors are reported in parenthesis. Panel A I II III IV Size of the market 0.68 0.60 0.32 0.43 ( 0.08 ) ( 0.10 ) ( 0.09 ) ( 0.15 ) Judicial efficiency X -22.71 -28.72 -26.72 -29.88 investment per worker ( 7.04 ) ( 9.51 ) ( 10.25 ) ( 10.63 ) Patent protection X 4.15 4.57 10.5 R&D intensity ( 2.87 ) ( 2.60 ) ( 4.25 ) Judicial efficiency 0.55 0.62 ( 0.11 ) ( 0.12 ) Patent protection -0.54 -1.04 ( 0.24 ) ( 0.44 ) R-squared 0.78 0.80 0.76 0.76 N 348 266 266 266 34
  35. 35. Panel B I II Size of the market 0.33 0.42 ( 0.09 ) ( 0.14 ) Patent protection X 4.42 9.98 R&D intensity ( 2.65 ) ( 3.99 ) Judicial efficiency 0.32 0.35 ( 0.09 ) ( 0.09 ) Patent protection -0.50 -0.93 ( 0.23 ) ( 0.40 ) Judicial efficiency X -0.05 -0.05 high investment per worker ( 0.11 ) ( 0.11 ) Judicial efficiency X 0.16 0.21 low investment per worker ( 0.06 ) ( 0.08 ) R-squared 0.76 0.76 N 266 266 35
  36. 36. Table 6 The Determinants of Dispersion in Firm Size The dependent variable is the employee-weighted coefficient of variation of the number of employees per firm in each NACE two-digit industry in each country. Inequality in human capital is measured as the product of the percentage of the population with the highest educational achievement and percentage of the population with the lowest educational achievement. The numbers are from Barro-Lee, 1993. Judicial efficiency is an assessment of the “efficiency and integrity of the legal environment as it affects business.” Per capita income is the log of per capita income in 1990 as reported by the Penn World Table, Mark 5.6. All estimates are obtained by OLS and contain industry fixed effects. Heteroskedasticity-robust standard errors are reported in parentheses. The standard errors are also adjusted for the possible dependence of the errors of observations in the same countries across different industries. I II III Inequality in human capital 1.22 0.25 0.09 ( 0.51 ) ( 0.56 ) ( 0.45 ) Judicial efficiency -0.12 -0.19 ( 0.03 ) ( 0.05 ) GDP per capita 0.60 ( 0.24 ) R-squared 0.68 0.71 0.72 N 463 463 463 36
  37. 37. Table 7 Vertical Integration The source of the data is Enterprises in Europe which, for a subset of countries, provides us with the value added in each NACE two-digit industry. The measure of vertical integration used is the ratio of the value added to sales. The first column in Panel A is the average of this ratio across industries in the same country. The second column is the average residual for that country obtained after regressing the logarithm of the value added to sales ratio on industry indicators. It can be interpreted as the percentage deviation of the ratio in that country after purging industry effects. The first column in Panel B is the average of the value added to sales ratio across countries. The second column is the average residual for that sector obtained after regressing the logarithm of the value added to sales ratio on country indicators. It can be interpreted as the percentage deviation of the ratio in that sector after purging country effects. A: At the country level Value added/ Turnover Average correcting Value added/ for sector Turnover effects N AUSTRIA BELGIUM DENMARK 0.495 0.343 36 FINLAND FRANCE 0.397 -0.024 54 GERMANY 0.337 -0.032 30 GREECE 0.263 -0.240 16 ITALY 0.340 -0.023 23 NETHER 0.376 -0.028 36 NORWAY PORTUGAL 0.353 -0.063 37 SPAIN SWEDEN 0.322 -0.139 17 SWITZ UK 37
  38. 38. B: At the industry level Average correcting Value added/ for country Turnover effects N Extraction solid fuels 0.507 0.328 2 Coke ovens 0.164 -0.836 2 Extraction petroleum 0.510 0.372 1 Oil refining 0.208 -0.886 4 Nuclear fuels 0.453 0.305 2 Electricity 0.509 0.327 4 Water supply 0.567 0.515 4 Extraction-metal 0.378 0.084 4 Production-metal 0.295 -0.289 3 Extraction-other 0.425 0.150 4 Manufacture-non metal 0.387 0.145 7 Chemical industry 0.300 -0.139 7 Man-made fibers 0.271 -0.205 2 Manufacture- metal 0.358 0.024 7 Mechanical engineering 0.378 0.119 7 Office machinery 0.385 0.098 7 Electrical engineering 0.347 0.030 7 Motor vehicles 0.238 -0.344 8 Other means transportation 0.317 -0.058 7 Instrument engineering 0.435 0.245 7 Food and tobacco 0.243 -0.343 8 Textile 0.316 -0.067 7 Leather goods 0.316 -0.053 7 Footwear and clothing 0.335 -0.001 7 Timber and furniture 0.335 0.012 8 Paper products and publishing 0.378 0.129 8 Rubber and plastic 0.319 0.025 7 Other manufacturing 0.352 0.106 5 Building and civil engin. 0.354 0.014 6 Wholesale distrib. 0.145 -0.902 6 Scrap and waste 0.223 -0.573 3 Agents 0.134 -1.045 3 Retail distribution 0.188 -0.641 6 Hotels and catering 0.436 0.184 5 Repair of consumer goods 0.334 -0.178 5 Railways 0.954 0.999 1 Other land transport 0.495 0.342 6 Inland water transport 0.522 0.263 3 Sea transport 0.298 -0.241 5 Air transport 0.433 0.041 2 Supporting services 0.737 0.704 4 Travel agents 0.318 -0.220 7 Communication 0.619 0.600 4 Banking and finance 0.534 0.402 3 Insurance 0.258 -0.269 3 Auxiliary services 0.456 0.169 4 Renting, leasing 0.450 0.108 3 Letting of real estate 0.588 0.516 1 Public administration 0.708 0.692 5 Sanitary services 0.578 0.498 1 Education 0.467 0.285 1 Research and development 0.643 0.458 2 Medical and others 0.430 0.092 3 Recreational services 0.622 0.518 4 Personal services 0 38
  39. 39. A Appendix A.1 Formulas for Statistical Measures Let ei denote the employment in bin i, and nidenote the number of firms in bin i for any given country-sector combination. Omit country-sector subscripts for convenience. Let E denote the total employment for the country-sector and N the total number of firms. The simple average is given by: av = i ni N ei ni = E N . The employee-weighted average is given by: ewav = i ei E ei ni . The simple variance is given by: var = i ni N ei ni − av 2 sd = √ var. The analagous quantity for the employee-weighted variance is: ewvar = i ei E ei ni − ewav 2 ewsd = √ ewvar. The simple coefficient of variation is given by: cv = sd av . The analagous one for the employee-weighted measure is: ewcv = ewsd ewav . The “employee-weighted mode” is defined by: ewmode = arg max ei E ei ni . The average size of the modal bin is reported. The employee-weighted median will be the first i for which 1 ewav i ei E ei ni becomes ≥ 0.5. Pearson’s measure for employee-weighted skewness is (ewmean−ewmode) ewsd . A.2 Data Appendix In this appendix, we discuss the data sources and the construction of our regression variables. In the interest of brevity, we present only the main points on the construction of a unified database from disparate sources. More comprehensive notes are available from the authors. Employee-weighted average firm size: 39

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