Technology and the Size Distribution of Firms: Evidence from Dutch Manufacturing

Transcription

1 Review of Industrial Organization (2005) 27: Springer 2005 DOI /s z Technology and the Size Distribution of Firms: Evidence from Dutch Manufacturing ORIETTA MARSILI Rotterdam School of Management, Erasmus University, Burg. Oudlaan 50, 3000 DR Rotterdam, The Netherlands, Abstract. Empirical studies have shown that the size distribution of firms can be described as a Pareto distribution. However, these studies have focused on large firms and aggregate statistics. Little attention has been placed on the role of technology in shaping firm size distributions. Using a comprehensive dataset of manufacturing firms and the Community Innovation Survey from the Netherlands, the paper investigates the relationship between firm size and technology. It shows that technological factors shape the distribution of firm size, suggesting that the Pareto law is not an invariant property and that technology can constrain the self-organising character of industrial economies. Key words: firm size, Gibrat s law, innovation, Pareto distribution. JEL Classifications: L11, L60, O33. I. Introduction The Pareto law is a well-known property of the size distribution of firms. It says that the frequency of firms in a population above a certain size is inversely proportional to the firm size. In logarithms, this relationship can be represented graphically as a straight line. A number of studies have tested empirically this hypothesis and formulated models able to generate Pareto-like distributions (Steindl, 1965; Ijiri and Simon, 1977). These studies have been extremely influential in industrial economics and elsewhere. For example, there has been a renewed interest in the Pareto distribution across many different disciplines. This interest focuses on the properties of the Pareto distribution, as a power law able to describe the organisation of different scientific and social systems (Krugman, 1996; Bak, 1997). If distributed according to a power law, the structure of the industrial system would depend only on the interaction between its components and not on external factors or the individual behaviour. In addition, a similar structural form would be observed at different levels of aggregation, such as countries and sectors. Finally, this

2 304 ORIETTA MARSILI structure is consistent with the firm size being the cumulative outcome of purely random factors, according to Gibrat s law of proportionate effect (Gibrat, 1931). Running alongside these studies of the Pareto, there has been an empirical tradition investigating cross-sector differences of industrial structures (Cohen and Levin, 1989). In particular, the approaches of the Schumpeterian tradition have stressed the importance of the innovative behaviour of firms in shaping performance and market structure (Nelson and Winter, 1982; Geroski, 1994). Innovation, it is argued, is one of the main factors behind the process of competition of firms in the market, and it varies across sectors in response to the nature of the technology specific to the sector. Differences in technologies help to explain the cross-sectors differences in market structures. Yet, as pointed out by Sutton (1998), rarely are these two traditions in industrial economics integrated. While the former addresses the general properties in the structure of a population of firms, the latter focuses on the constraints that both technology and demand conditions, specific to each industry, impose on such structure. Although the random factors underlying the Pareto law play an important role, Sutton argued that there are bounds to the structure that can be observed across sectors (Sutton, 1998). Combining the two literatures, it is expected that distributions resembling the Pareto law are more likely to be observed at the aggregate level, as outcome of aggregation and random effects, and less so at the sectoral level, as outcome of more stringent technological constraints. In response to this expectation, this paper examines, first, the goodness of fit of the Pareto law for Dutch manufacturing firms, observed at the aggregate level and at the sectoral level. Then, it introduces technological variables of sectors into the estimation and relates them to the departure from the Pareto law. The data draws on two databases collected by the Central Bureau of Statistics Netherlands (CBS). First, the Business Register dataset provides information on the number of employees, here used as a measure of size, of all the firms registered for tax purposes in the Netherlands. In particular, this dataset allows the estimation of the Pareto law to be extended to small firms, down to zero employees (self-employment) and thus to overcome the limitations of earlier studies based on samples of large firms. Second, the second Community Innovation Survey (CIS-2) provides information on the innovative activities of an extensive sample of firms in the Netherlands. The results show that for the Dutch case of a small and open economy, even at the aggregate level of the manufacturing sector, the size distribution displays a systematic departure from the Pareto law. This departure is more evident than, for example, was observed for US firms (Axtell, 2001). At the level of industrial sectors, the departure from the Pareto law is more

3 TECHNOLOGY AND THE SIZE DISTRIBUTION OF FIRMS 305 remarked and depends on the nature of technology. Specifically, if innovation is incremental, instead of radical, and persistent over time, the presence of firms in the central classes of the distribution is higher than under the Pareto law. This result gives empirical support to Ijiri and Simon s (1974) argument that autocorrelation in firm growth rate may lead to a greater share of medium-sized firms than the Pareto. This paper is organised as follows. Section II reviews the empirical and theoretical literature on the Pareto law. Section III introduces the data and the variables to estimate the size distribution and to measure technological conditions of sectors. Section IV discusses the results of the estimation of the Pareto law and the effects of technology. Section V is the conclusions. II. Background and Literature Review Power law behaviour of empirical distributions can be observed in many diverse fields, such as the distribution of words in a text (Simon, 1955) or of earthquake magnitudes as one of the many examples in physical sciences (see Bak (1997) for an overview). In social sciences, typical examples are the distributions of income (Pareto, 1987), firm size (Ijiri and Simon, 1977), cities population (Krugman, 1995), scientific publications (Katz, 1999) and the returns from innovation (Scherer, 1998; Scherer and Harhoff, 2000; Scherer et al., 2000). When applied to the size distribution of firms, this power law behaviour is generally referred to as Pareto law, and it is expressed in terms of the frequency of units with size greater than s, that is, in terms of the right-cumulative distribution function (CDF), F( ). Therefore, it holds that: F(s)= Fr{S s}=(s/s 0 ) α, s>0 (1) where s 0 is the minimum size and α is a positive parameter. The Pareto law is easy to be represented graphically, as its CDF is a straight line on a double-logarithmic scale. 1 The coefficient α, slope of this line, is a measure of market concentration. It is equal, in absolute value, to the relative frequency of small firms in the distribution (Simon and Bonini, 1958). The importance of the Pareto law for the size distribution of firms resides in its direct link with the Gibrat s law, and the properties of the dynamic processes of growth and turnover of firms. Testing the Pareto law can be seen as an alternative test to Gibrat s law. The Gibrat s law states that firm growth can be characterised by a random walk, expressed in logarithms. In other words, it assumes that firms growth rates are purely random variables ( white noise ) and mutually independent. The Gibrat s 1 Another method to describe a power law, especially used in physics, is through the Zipf s law or rank-size rule. This looks at the relationship between the ranks of firms and their corresponding size, relationship that is linear in logarithms.

4 306 ORIETTA MARSILI law per se generates a Lognormal distribution with infinite variance in the limit (Steindl, 1965). However, assuming Gibrat s law, or weaker versions of it, and constant rates of entry of new firms, should generate Pareto-like distributions in steady state (Ijiri and Simon, 1977). 2 Empirical studies testing the Gibrat s law have shown that growth rates, especially in large firms, have a significant random component (Sutton, 1997). Although the randomness of firm growth leads to size distributions that resemble the Pareto law, the latter appeared to represent the actual shape only in a first approximation. In particular, the empirical CDFs in logarithms tend to be non-linear. They display a concave shape, suggesting that the Pareto law underestimates the frequencies of the medium-sized classes. For example, Ijiri and Simon (1974) observed similarly concave pattern for the size of the 500 firms of the Fortune list, and Scherer (1998) for the returns to innovation. This early empirical evidence on the size distribution refers to large firms, indicating that the Pareto law may be a property of the upper tail of the distribution. More recent studies that extend the analysis of the shape of the size distribution to larger samples or to the entire population of firms display contrasting results. Stanley et al. (1995) observe that the Lognormal distribution well represents the Compustat population of publicly traded firms with the exception of the upper tail of the distribution. However, Cabral and Mata (2003) argue that the Lognormal distribution also fails to provide a good representation of the data at the lower tail of the distribution. In fact, in a study of the complete population of Portuguese manufacturing firms, Cabral and Mata observe that the Lognormal underestimates the skewness of the distribution. Finally, Axtell (2001) finds support for the Pareto law using Census data for the entire population of US firms. Divergent interpretations have been given to explain the departure from the Pareto distribution, and the concavity of the CDF curve on a log log scale. Ijiri and Simon (l974) argued that it results from the existence of auto-correlation in firm growth. In addition, merges and acquisitions can contribute to such a departure as, they suggested, external growth is more constrained by firm size (and less random) than internal growth (Ijiri and Simon, 1971). In both interpretations, the authors maintained the assumption of constant returns to scale entailed in Gibrat s law. In contrast, Vining (1976) argued that the concavity of the distribution originates in the existence of decreasing returns to scale. 2 Weaker versions of Gibrat s law refer to the average growth rates (instead of the individual values) being independent on size, or introduce autocorrelation (Ijiri and Simon, 1977). They generally produce a Yule distribution, within the same class of skewed distributions identified by Simon (1955).

5 TECHNOLOGY AND THE SIZE DISTRIBUTION OF FIRMS 307 Because of the departure from the Pareto law, it has been suggested that more than one Pareto law applies to different size classes. For each size class, the Pareto law has a different slope (Gopikrishnan et al., 1999), Reed (2001) showed that a double Pareto distribution that is, a Pareto distribution with different slope at the two tails can be generated as outcome of growth processes alagibrat. This distribution is because of the aggregation of different cohorts of firms, which are observed at different, randomly distributed, ages. Recently, attention has turned to the Pareto distribution as a general property able to represent the structure of different social and natural phenomena (Buchanan, 1997). As a power law, two properties have been related to the Pareto distribution (Krugman, 1996). First, a power law is indicative of a self-organising system. That is, the properties of the overall system emerge out of the interaction of the single parts and cannot be ascribed to the characteristics of its single components. If firm size were distributed according to Pareto, the distribution would not be affected by the purposeful action of firms or by external factors and constraints. Second, a power law is indicative of a self-similar system. It displays scaleindependent property, which can be observed at any level of aggregation. This property is satisfied by the Pareto distribution, when the coefficient α is lower than two. In this interval, the size distribution does not depend on the central moments, as the variance and the higher moments are asymptotically infinite. 3 A particular case, or Zipf s law, is represented by the parameter α being equal to one (Krugman, 1996). Whether or not, firm size distribution follows a power law is a matter for discussion. In fact, the size distribution may not be invariant over time. Macro-economic and institutional changes may influence the coefficient of the size distribution of firms in the long run (Henrekson and Johansson, 1999). Also the size distribution may not be scale independent. If the Pareto distribution holds for the industrial system a whole, it should be invariant across industrial sectors or countries. The empirical evidence suggests, however, that there are systematic departures from the Pareto law at the level of industrial sectors (Kwoka, 1982) and that a scale-dependent distribution, such as the Lognormal, may provide a better fit in some industries (Quandt, 1966; Silberman, 1967). Furthermore, industry cases have shown that neither the Pareto nor the Lognormal distribution may fit the empirical distributions; for example a double-humped curve was observed for the top pharmaceutical firms (Bottazzi et al., 2001). Alternatively, by using a non-parametric approach to the estimation of the size distribution, Machado and Mata (2000) have found that the effects of 3 A self-similar distribution may have finite mean, for 1 <α 2.

6 308 ORIETTA MARSILI industry characteristics on firm size vary at the different quartiles of the size distribution. The evidence at the sectoral level thus suggests that structural factors may constrain and shape the size distribution of firms. To identify these factors, it is necessary to turn to another literature, which focuses on the interpretation of cross-sectors differences in market structure. In particular, the approaches following the Schumpeterian tradition have stressed the importance for market structure of the innovative behaviour of firms and the nature of technology influencing such behaviour (Nelson and Winter, 1982; Dosi, 1988; Sutton, 1998). When the intensity of R&D expenditure was used to measure innovative activities, however, a weak relationship with market structure was found in the empirical literature (Cohen, 1995). Such a relationship appeared to be influenced by the characteristics of the underlying technologies. These were expressed by a wide set of variables: technological opportunity and appropriability conditions (Levin et al., 1985), the cumulativeness of innovation (Breschi et al., 2000), and the relative importance of product and process innovations (Gort and Klepper, 1982). These conditions distinguish between different technological regimes across industrial sectors (Dosi, 1982; Nelson and Winter, 1982; Marsili, 2001). In an entrepreneurial regime, innovation is mainly generated by the entrepreneurial activity and creativity of small and new firms, leading to low market concentration. In a routinised regime, innovation originates in the formal R&D activity of large and established firms, leading to high market concentration (Breschi et al., 2000). In particular, the empirical studies suggest that market concentration is positively associated with the contribution of scientific knowledge to technological opportunity, cumulativeness of innovation and process innovation. In contrast, it is negatively associated with the opportunities for innovation stemming from the vertical chain of production, in particular from suppliers, and product innovation. For the purpose of this paper, these effects would be reflected in changes of the slope of the Pareto distribution. No predictions on the higher moments of the distributions, and therefore on the departure from Pareto, can be made, however, from this literature. This paper addresses two questions: is the Dutch firm size distribution a Pareto and, if not why not? The data will be considered as a whole, and I will return to these questions, and propose answers in the conclusions. III. The Data The analysis uses two micro-economic databases collected from the Central Bureau of Statistics Netherlands (CBS): the Business Register database and the Second Community Innovation Survey (CIS-2) in the Netherlands.

7 TECHNOLOGY AND THE SIZE DISTRIBUTION OF FIRMS 309 The Business Register is used for estimating the size distribution, and the CIS is used for measuring the characteristics of technologies that may affect the size distribution. The Business Register database reports employment statistics and sector of activity at 6-digit of the Standard Industrial Classification of all the manufacturing firms registered in the Netherlands. The population includes also firms with zero employees, referred to as self-employment. Table I reports the descriptive statistics of the size distribution of the population of Dutch firms, including self-employment, over the period On average around 61,000 firms are observed each year. The mean firm size is 16.3 employees (18.1 for firms with size greater than 0). The positive value of the skewness coefficient confirms that the size distribution is skewed to the right, that is, the long tail of the distribution is in the positive direction (Greene, 2000, p. 64). The high value of the kurtosis coefficient indicates that the size distribution tends to be leptokurtic, that is, the distribution is more peaked and has fatter tails than the normal distribution. Looking in more detail into the dataset, Table II reports the frequency of firms in the population by size class from 1996 to The size distribution is highly skewed. It is characterised by a large prevalence of self-employed firms, on average about 45% of the entire population. The percentage of firms is much lower, to a value of just above 15%, for the class of firms with one employee. Gradually, it decreases with the increase of the size class, to the minimum of 0.4%, for the highest size class of firms with more than 500 employees. This pattern is fairly invariant over time. Although very small firms represent a large share of the manufacturing sector, traditionally they have not been included in the estimation of the Pareto law. The data used in earlier studies were generally left-censored databases. Recently, as more extensive micro-economic databases have become available, empirical studies have tested the Pareto law on the entire range of firm size. For the United States, for example, Axtell (2001) used data on Table I. Descriptive statistics of the size distribution of the population of manufacturing firms in the Netherlands Mean Std. deviation Skewness Kurtosis N

8 310 ORIETTA MARSILI Table II. Percentage distribution of firms by size class Size class and more Total self-employment and the firms with at least one employee. His study extended previous results based on the distribution of publicly traded firms from the Compustat database (Stanley et a1., 1995). In this study, I use the comprehensive Business Register database to estimate the Pareto law for all the firms with employment and self-employment from 1996 to To characterise the nature of technology, the CIS-2 dataset is used. This dataset provides information on the innovative activities of firms in the Netherlands in 1994 to The survey was done by Statistics Netherlands and it includes all of the private sector firms with at least 10 employees. In manufacturing, a total of 3299 responses were obtained with a response rate of 71 per cent. This sample is representative of a population of 10,260 firms of which 6069 are innovators. To calculate indicators of the nature of technologies across different sectors, I used a classification of sectors between 2- and 4-digit level. This aggregates sectors at 6-digit level according to Statistics Netherlands standard classification of industries as of As a result, 62 sectors were defined. IV. Empirical Results The first problem to be addressed is whether the size distribution follows the Pareto law for the aggregate manufacturing and for industrial sectors. The empirical exploration of the Pareto law in Dutch manufacturing is carried out in two stages. First, I examine its properties in the aggregate manufacturing, using non-parametric and parametric methods. Then, I examine differences in the shape of the distribution across sectors and introduce industry-fixed effects in the estimation of the Pareto law.

9 TECHNOLOGY AND THE SIZE DISTRIBUTION OF FIRMS 311 Figure 1. The size distribution of Dutch manufacturing firms: Note: Log log plot of the right cumulative distribution function of firms with at least one employee. 1. FIRM SIZE DISTRIBUTION IN AGGREGATE MANUFACTURING Preliminary insight into the shape of the distribution is given by plotting the empirical cumulative distribution functions in 1996 to 1998, in Figure 1. This shows that the empirical distributions largely overlap, and that they display a concave shape of the distribution throughout the considered time period. To assess whether the Pareto law is appropriate to represent the size distribution of firms in the Netherlands, Figure 2 presents the p p plots of the theoretical distribution and the empirical distribution in These graphs plot the theoretical cumulative distribution function against the empirical one. Because the Pareto law is considered to fit better the upper tail of the size distribution, the distributions are plotted for the whole population and separately for different size classes. For the firms that have size larger than 0, three size classes are compared: small firms with less than 10 employees (67 per cent of firms); large firms with 500 and more employees (0.7 per cent of firms); and the extreme upper tail of the distribution as composed of firms with 1000 and more employees (0.1 per cent). The graphs show that there is a departure of the empirical distribution from the Pareto law for the overall population. This departure from Pareto is especially evident for the class of small firms. In contrast, the Pareto law fits well the data at the

10 312 ORIETTA MARSILI Figure 2. Pareto p p plots of the size distribution of firms in upper tail of the distribution, although this tail represents only about 0.7 per cent of the population of firms. Does the Lognormal distribution fit better the overall size distribution of firms when small firms are included in the population, as in this case? To address this question, Figure 3 reports the p p plots comparing the empirical distribution functions to the Lognormal distribution in the total population and by size class. The plots suggest that again there is a systematic departure of the empirical distribution of the population of firms from the theoretical one. By size class, the Lognormal distribution fits well the data for the class of small firms (below 10 employees), which is a significant proportion of the population (67 per cent). Yet, the upper tail of the large firms in the population departs considerably from Lognormality. Alternative methods for fitting the Pareto law to the data and estimating the exponent of the Pareto law can be found in the literature. One method uses the log log linear regression of the cumulative distribution function.

11 TECHNOLOGY AND THE SIZE DISTRIBUTION OF FIRMS 313 Figure 3. Lognormal p p plots of the size distribution of firms in The other method is based on the Hill estimator (Weron, 2001). I begin by estimating the Pareto law using the linear regression of the empirical CDF on a log log scale, for the entire population of firms with employees. For this purpose, Equation (1) is transformed into logarithms and time-fixed effects are introduced to account for changes in the slope, α, of the Pareto law. The basic model specification is: log F(x)= t α t d t log(x), x > 0 (2) where x is firm size, F( ) is the right-cumulated distribution function up to size x and d t is a dummy for time t (t = 1996, 1997, 1998). The constant term in Equation (2) is set equal to 0, as by definition the right-cumulated distribution function is equal to one at the minimum size. The equation is estimated by using pooled ordinary least squares (OLS). This method of estimation is most commonly used, although, because of non-linearity, the standard assumptions for OLS regression do not hold. This method should

12 314 ORIETTA MARSILI be considered heuristic, recognising that too much weight should not be put on estimated standard errors and p-values, although the method is still useful for comparison with previous results (Scherer, 1998). Then, I extend the estimation of the Pareto law to include firms with zero employees. This requires the following transformation of the basic model (Axtell, 2001): 4 log F(x)= t α t d t log(x + 1), x 0. (3) The size classes for all the regressions were defined by using a binning system of 0.3 on logarithmic scale, with the highest open size class set at the midpoint of 9. 5 In the equations, each size class is identified by the corresponding midpoint. Following Scherer (1998) a quadratic term is added to the basic model to account for the concavity of the distribution. In addition, time-fixed effects of all coefficients are included, producing the following equation: log F(x)= t α 1t d t log(x) + t α 2t d t [log(x)] 2 (4) where α 1 is the coefficient of the Pareto law and α 2 measures the departure of the size distribution from the Pareto law. The distribution is concave if α 2 < 0, and convex if α 2 > 0. A similar transformation to Equation (3) was applied for the population of firms with self-employment. Table III reports the estimated coefficients of the linear and quadratic model for the population of firms with at least one employee and that including also self-employment. For both populations, the results of the linear model would lead one to conclude that the Pareto law provides a good representation of the size distribution, with an R-squared of about 0.93 in either case. This value of the goodness-of-fit is, however, lower than observed in other countries, in particular the US, for which an R-squared approximately, equal to one was observed (Axtell, 2001). The coefficient of the Pareto law is equal to 0.90 in 1996 for the firms with employees and slightly higher for those including self-employment, and it did not significantly vary between 1997 and The departure from the Pareto law is even more evident when the quadratic term is added. In Table III, for both populations of firms, the coefficient α 2 is statistically significant and negative in 1996, thus displaying 4 Let X be the size of a firm with employees (x 1) following a Pareto distribution F( ). The right-cumulated distribution function of the S size of any firm including self-employment (s 0), then defined by G(s) = Fr{S s}=fr{x 1 s}=fr{x s + 1}= F(s+ 1) = (s + 1) α. 5 Alternative binning systems of 0.15, 0.20 and 0.40 have been applied in the aggregate manufacturing. These have given rise to similar shapes of the size distribution.

13 TECHNOLOGY AND THE SIZE DISTRIBUTION OF FIRMS 315 Table III. Results from pooled OLS regressions of F(x) in aggregate manufacturing (absolute t-statistics in parentheses) Firms with employees All firms Variable Linear Quadratic Linear Quadratic Size ( 34.68) ( 18.59) ( 35.94) ( 21.24) Size (d 1997 d 1996 ) ( 0.60) (1.00) ( 0.57) (1.18) Size (d 1998 d 1996 ) ( 0.73) (1.33) ( 0.63) (1.73) Size ( 22.1) ( 23.3) Size 2 (d 1997 d 1996 ) ( 1.75) ( 1.93) Size 2 (d 1998 d 1996 ) ( 2.24) ( 2.58) DF Adjusted R Increase in adjusted R 2 Notes: The population of all firms includes self-employment. Firm size and the CDF of size, F(x), are in logarithms. significant at 1%; significant at 5%; significant at 10%. the existence of a concavity of the distribution. In addition, the concavity tended to increase in 1997 and This result is in contrast to the evidence available for the US economy. For US companies, Axtell (2001) observed a slightly concave distribution. It was associated, however, to the behaviour at the two extreme size classes only and therefore was interpreted as the statistical outcome of finite size cut-offs at the two extremes of very small and very large firms (Axtell, 2001). In contrast, the Dutch data, based on a more disaggregated definition of the size classes, suggest a more pronounced concavity. In order to compare more closely the estimates of the Pareto law based on the Dutch Business Register data in 1996 to 1998, with the estimates obtained by Axtell (2001) from the US Census data in 1997, I also apply Axtell s definition of size classes. As in Axtell, I calculate the size classes with bins of increasing size, in powers of three, and carry out OLS estimation of the log log regression of the empirical CDF. It is worth noting that the main difference in the data is that the Dutch data include only the manufacturing sector while the data in Axtell s work deal with

14 316 ORIETTA MARSILI the economy as a whole, including for example services firms. Table IV reports the results of the estimation for the Dutch data in the same form as reported in Axtell (2001). The estimated coefficient of the Pareto law, on this more aggregate definition of size classes, is fairly close to one (ranging between and 1.025), either including or excluding self-employment in the population. These values are just above Axtell s estimates of and 0.995, for firms with employees and all businesses respectively. However, the R-squared values in Table IV suggest that the goodness of fit of the Pareto law is lower for the Dutch data (ranging between and 0.957) than for the US data (equal to and in Axtell s estimation). A goodness of fit comparable to the value reported by Axtell can be obtained for the Dutch data when adding a squared term to the linear log log regression (ranging between and 0.998). These findings confirm that the size distribution of Dutch firms shows a greater departure from the Pareto law, in the form of a concavity of the CDF curve, than the size distribution of US firms. Hill Estimator Because the OLS estimates of the log log linear regression can be biased, and tend to overestimate the true slope of the Pareto distribution, alternative methods have been applied. In particular, Hill (1975) has proposed a maximum likelihood estimator for the tail index α of a class of Generalised Pareto distributions, with their upper tails that converge to the ordinary Pareto distribution of exponent α (Weron, 2001). If X (1),X (2),...,X (N) are the order statistics of firm size in the sample, that is, X (1) X (2) X (N), then the Hill estimate of α based on the k largest observations is: [ 1 α Hill (k) = k k 1 (log X (i) log X (k+1) )]. (5) i=1 Table IV. Power law exponents of Dutch firms according to Axtell s (2001) size classes Year Type Estimated coefficient Adjusted R Firms with employees (0.042) All businesses (0.042) Firms with employees (0.047) All businesses (0.047) Firms with employees (0.047) All businesses (0.047) 0.949

15 TECHNOLOGY AND THE SIZE DISTRIBUTION OF FIRMS 317 Table V. Results from pooled OLS regressions of F(x) in industrial sectors (absolute t-statistics in parentheses) Sector-fixed effects Variable Linear Quadratic Linear Quadratic Size [ 1.148, 0.280] + [ 1.060, 0.163] + ( 95.44) ( 22.03) (a) (b) Size (d 1997 d 1996 ) ( 0.64) ( 0.33) ( 2.01) ( 0.65) Size (d 1998 d 1996 ) ( 1.48) (0.05) ( 2.45) ( 0.89) Size [ 0.180, 0.043] + ( 6.8) (c) Size 2 (d 1997 d 1996 ) (0.12) ( 0.73) Size 2 (d 1998 d 1996 ) ( 0.55) ( 0.78) DF Adjusted R Increase in adjusted R Notes: Firm size and the CDF of size, F(x), are in logarithms. significant at 1%; significant at 5%; significant at 10%. (+) The range of the coefficients of the sector dummies is shown in order to conserve space. (a) Significant at 1% in all sectors. (b) Significant at 1% in 76% of sectors, at 5% in 8% of sectors, at 10% in 3% of sectors. (c) Significant at 1% in 94% of sectors and at 10% in 3% of sectors. In order to establish whether k converge to a value, which will then be used to estimate the coefficient α of the Pareto distribution, the values of α Hill (k) are plotted against k and the value of k is selected in correspondence of a region in which the plot levels off (Weron, 2001). Figure 4 reports the Hill estimates for the size distribution for the entire population of firms in The plot of the Hill estimates appears to be fairly stable in the range of k approximately, between 80 and 130, which corresponds to an upper tail of about 0.1 per cent of firms. For this tail, the estimates of α Hill (k) indicate a Pareto coefficient ranging between 1.5 and 1.7. These results suggest that the Pareto law fits well the size distribution at the very extreme upper tail, with finite mean (α>1) and infinite variance (α<2). 2. FIRM SIZE DISTRIBUTION BY SECTOR In order to assess whether the Pareto law is invariant across industrial sectors, I present the p p plots for four industrial sectors, at two-digit level of

16 318 ORIETTA MARSILI Figure 4. Hill estimates of α for the size distribution of firms in industrial classification in Figure 5. These sectors can be considered typical of both high technology sectors and more traditional industrial sectors. The visual inspection of these plots indicates that a variety of patterns can be observed across sectors. Indeed, depending on the industrial sector, the Pareto law seems to underestimate the presence of small firms, of medium sized firms and of large firms. To estimate the departure from Pareto at the sector level, I first estimate a baseline model by applying Equations (2) and (4) to the sectoral data of the size distribution, with equal coefficients across sectors. Then, I add to this component common across sectors, sector-fixed effects, and I compare them to the baseline model with equal coefficients. The following equation, in the more general version, is thus defined: log F(x)= tj α 1tj d t ds j log(x) + tj α 2tj d t ds j [log(x)] 2 (6) where x is the firm size, F( ) is the right-hand side CDF, ds j is a dummy variable for sector j, d t is a dummy variable for time t, α 1tj and α 2tj are parameters respectively, for the coefficient of the Pareto law at time t and sector j, and the deviation from Pareto law. 6 Time-fixed effects are allowed for the cross-sectors means only (that is, α 1tj = α 1t and α 2tj = α 2t,fort>1). Table V presents the estimates of the pooled OLS regressions for the linear and quadratic specification of the baseline model and the model with sector-fixed effects. The population is that of firms with employment. 6 The linear model for the Pareto law is given by setting α 1tj = α tj and α 2tj = 0 in Equation (6).

17 TECHNOLOGY AND THE SIZE DISTRIBUTION OF FIRMS 319 Figure 5. Pareto p p plots for selected industrial sectors. As shown in Table V, assuming identical coefficients across sectors leads to a poor fit. With respect to this baseline model, the model with sectorfixed effects produces a remarked improvement, with a goodness-of-fit comparable to that found in the aggregate manufacturing. Specifically, the increase in the adjusted R-squared is equal to 0.22 in the linear model and to 0.28 in the quadratic model. Both differences are statistically significant at 0.1 per cent. In particular, adding the quadratic term improves the R-squared especially when sector-fixed effects are considered. For this model, the coefficients of the time-dummies are not statistically significant (column [4]). This suggests that cross-sectors differences in the slope and shape of the distribution are significant and, on average, persistent over the considered time period.

18 320 ORIETTA MARSILI Looking more in detail into the sector-specific coefficients of the quadratic term, the sign of the coefficient differs across sectors. Most often, the coefficients are statistically significant and of negative sign (56 sectors out of the 62). Within this group, machinery industries have the lowest coefficients and most evident concavity. However, in four industries (telecommunication equipment, computers, motor vehicles and glass products), the coefficient is statistically significant and of positive sign. Finally, in two industries (photographic equipment and publishing), the coefficient is not statistically significant. 3. THE ROLE OF TECHNOLOGY This section investigates whether the departure from the Pareto law can be explained on the ground of differences in the nature of technology. With this aim, the sector-specific fixed effects of Equation (6) are distinguished into a component common to all sectors and a component depending on the industry technological variables. Therefore, in Equation (6) it is set α ktj = α kt + δ k S j,(k = 1, 2) where S j is the vector of technological variables of sector j, assumed invariant over the considered period, and δ k a vector of parameters. This produces the following equation: log F(x)= t α 1t d t log(x) + t α 2t d t [log(x)] 2 +δ 1 S j log(x) + δ 2 S j [log(x)] 2. (7) Technological Variables Four categories of variables are included in the vector S j of technological variables: (i) the level of technological opportunity, (ii) the cumulativeness of innovation, (iii) the sources of technological opportunity and (iv) the relative importance of product and process innovation. The variables are constructed at the level of industrial sector, using CIS-2 data. Direct measures of innovative activity are derived through a combination of input and output indicators. These are (a) the intensity of R&D expenditure as the ratio of the total R&D expenditure in the period on the total sales in 1996, (b) the percentage of turnover on the total sales in 1996 attributed to innovative products, distinguished in the three categories of products new for the firm, products new for the market and improved products and (c) the percentage of innovators in 1994 to 1996 that carry out R&D activities on a permanent basis, as opposed to occasional or not at all. These five variables are then summarised by applying a principal component analysis. This approach allowed me to extract

19 TECHNOLOGY AND THE SIZE DISTRIBUTION OF FIRMS 321 two main factors. 7 The first factor is positively correlated with all the measures of innovation intensity and can be interpreted as the general level of technological opportunity, or potential for innovation (Technological opportunity). The second factor is positively correlated with the turnover due to improved products and the share of innovators with permanent R&D activities; it can be interpreted as an indicator of the incremental and cumulative nature of innovation (Cumulativeness). In general, measures of the sources of technological opportunity are derived from innovation surveys by looking at the sources of information that are relevant for industrial innovation (Cohen et al., 1987). In particular, the CIS-2 listed l2 sources, which are rated by the firm on a fourpoint Likert scale, ranging from 0 not-used to 3 very important. The importance of each source for innovation, at the level of industrial sector, is thus measured as the percentage of innovators that rated the source as important or very important. The information generated from this step was summarised, via a principal component analysis, into four main factors. The first factor is positively correlated with the contribution of public research from Universities and other research institutes, and the contribution of codified sources of publicly available knowledge (patent disclosure and computer based information). This factor is interpreted as a measure of the relevance of scientific knowledge for innovation (Science). The second factor is positively correlated with the contribution of information from suppliers and from publicly available sources of professional knowledge, such as conferences and journals 8 and fairs and exhibitions. It is regarded as indicative of supplier-dominated industries (Suppliers), following Pavitt (1984) interpretation. The third factor reflects the contribution of customers, in combination with the use of in-house sources (Users). The last, fourth factor contrasts the contribution of competing firms within the industry to the contribution of innovation centres, which act as bridging institutions between the industry and the public system. I label it as the industry factor (Industry). The relative importance of product versus process innovations is measured by the ratio between the number of firms with at least one product innovation and with at least one process innovation (PDT/PCS). Because responses to the innovation survey may differ between small and large firms, I controlled for the relative size of innovative firms in a sector. This was measured as the ratio between the average sales of innovative firms and the average sales of the population in the sector at 1996 (Innovator size). This variable reflects the existence of scale economies in 7 The results of the principal component analysis are not reported here for reason of space and they are available upon request. 8 This category includes both academic and professional journals.

20 322 ORIETTA MARSILI the innovation process. Finally, to account for the relationship between market concentration and the mobility of firm market shares (Caves, 1998) an index of persistence of firms size (Persistence) is built on the basis of the Business Register dataset. This index measures the percentage of all the continuing firms that remain within the same size class between 1997 and Note that the aim of estimating the model is not to fully identifying the determinants of the size distribution of firms. I do not wish to exclude the possibility that other variables could be important, for example, market demand. Table VI presents the results of the OLS estimates of Equation (7) for the linear and quadratic specification. The variables Innovator size and Persistence are added as control variables. Table VI shows that the technological variables have a significant effect on the slope of the Pareto law. I begin by examining the results for the linear estimation of the model. These results show that adding the technology variables increases significantly the R-squared with respect to the baseline model of identical sectoral coefficients. Specifically, the level of technological opportunity, the cumulativeness of innovation and the contribution of knowledge from the science system, industry and users have a positive effect on the Pareto coefficient (which decreases in absolute value), leading to higher market concentration. In contrast, the contribution of knowledge from suppliers and the prevalence of product innovation on process innovation have a negative effect on the Pareto coefficients, leading to lower market concentration. This findings mirror the results of Breschi et al. (2000). Adding a quadratic term to the model leads to a further statistically significant increase of the R-squared. Although this increase is modest, it modifies the overall pattern of relationships with the technological variables. In particular, the level of technological opportunity does not have a statistically significant effect on the slope and concavity (or convexity) of the distribution. This confirms the weak results found for this variable in other studies (Levin et al., 1985). Interestingly, the cumulativeness of innovation has a significant negative effect on the quadratic term. Cumulativeness of learning thus increases the concavity of the distribution with respect to the Pareto law. This result is consistent with Ijiri and Simon (1974) argument that autocorrelation in firm growth would result in a concave distribution of firm size. One possible interpretation could be that the cumulativeness of innovation is a source of the autocorrelation in the firm growth processes. With regard to the sources of knowledge, the contribution of science has a significant (positive) effect on the shape of the distribution. Science-based sectors show decreasing concavity of the distribution, that is, a

21 TECHNOLOGY AND THE SIZE DISTRIBUTION OF FIRMS 323 Table VI. Results from pooled OLS regressions of F(x) on technology variables (absolute t-statistics in parentheses) Variable Linear Quadratic Size ( 31.01) ( 21.86) ( 31.76) ( 28.64) Technological opportunity (4.27) (4.45) (1.31) (1.16) Cumulativeness (12.19) (12.07) (12.24) (12.03) Science (17.69) (17.65) (2.02) (2.05) Suppliers ( 17.36) ( 17.39) ( 6.46) ( 6.72) Users (6.91) (7.04) ( 0.18) ( 0.46) Industry (14.97) (14.77) (5.47) (5.62) PDT/PCS ( 16.53) ( 16.58) ( 0.96) Innovator size (1.34) Persistence Size 2 Technological opportunity 2 ( 0.5) ( 0.13) Cumulativeness ( 9.42) ( 9.24) Science (4.81) (4.65) Suppliers (1.76) (2.19) Users (2.91) (3.44) Industry (0.23) (0.04) PDT/PCS ( 13.58) ( 21.45) Innovator size ( 1.11) Persistence (4.37)

22 324 ORIETTA MARSILI Table VI. Continued Variable Linear Quadratic DF Adjusted R Increase in a adjusted R 2 Notes: Firm size and the CDF of size, F(x), are in logarithms. significant at 1%; significant at 5%; significant at 10%. The variable was excluded from the estimation because of collinearity. a Difference calculated with respect to the baseline linear model of colum [1] in Table V. relatively lower presence of medium-sized firms. In contrast, the contribution of knowledge from suppliers has a significant negative effect on the slope of the distribution and a positive (although slightly significant) effect on the curve shape. In other words, supplier-dominated sectors (Pavitt, 1984) are characterised by low market concentration and a slightly less concave distribution. Sources within the industry tend to increase the level of market concentration. The contribution of users leads to a less concave distribution, but it has no statistically significant effect on the slope of the distribution. Finally, the nature of innovation has a statistically significant (negative) effect on the coefficient of the quadratic term. Industries where product innovations are dominant over process innovations display a more pronounced concavity of the distribution. The control variable for the existence of scale advantages in innovation does not have a statistically significant effect in either the linear or quadratic versions of the model. In contrast, a significant effect is observed for the measure of persistence within the distribution. In particular, the degree of persistence within the distribution has a significant and positive effect on the quadratic term of the model. Therefore, increasing mobility of firms across size classes leads to increasing concavity of the distribution. Thus, distributions with more mobility are characterised by higher presence of firms in the central size classes than under the Pareto law, and less skewness towards small firms. V. Conclusions This paper has had two tasks, the first preparatory for the second. First, it has provided an empirical investigation of the properties of the size distribution. Using data on the Dutch manufacturing firms, these properties have been explored at the level of the aggregate manufacturing and across industrial sectors. Second, the paper has attempted to establish whether

23 TECHNOLOGY AND THE SIZE DISTRIBUTION OF FIRMS 325 systematic departures from the Pareto law emerged at the different levels of analysis and whether such departures could be related to the nature of technology. In order to explore the two questions, the employment data from the Business Register of the population of manufacturing firms in the Netherlands in 1996 to 1998 have been linked with the data from the CIS for the Dutch manufacturing sector in 1994 to Overall, I found that the Pareto law fits the size distribution of firms only as a first approximation. At the aggregate level, the size distribution displays a certain concavity. This result is consistent with previous studies (Ijiri and Simon, 1974; Scherer, 1998). The results based on a finer tabulation of size classes suggest that the concavity of the distribution is not a pure statistical outcome of the extreme classes definition (Axtell, 2001). The Dutch manufacturing system appears to depart more systematically from the structure of a self-organising system, than was observed for example in the US economy. This result suggests that the Dutch system might be more sensitive to external factors than to its own internal processes, compared to a large economy as the US. In the Netherlands, the size distribution is characterised by lower skewness towards small firms and higher presence of medium sized firms, than expected under a power law. Here power law behaviour is observed only at the extreme upper tail of the distribution, corresponding to less than one per cent of the population. The analysis at the sectoral-level showed that the departures from the Pareto law were more pronounced than at the aggregate level. A variety of distributional forms appears to emerge across industrial sectors. In other words, sectoral characteristics shape the distribution of firm size. These sectoral characteristics are often linked to features of technology present in these sectors (Nelson and Winter, 1982; Dosi et al., 1995). Three characteristics appear here to be associated with concave distributions: the cumulative nature of innovation, the dominance of product on process innovation, and the mobility of firms in their relative position. A possible interpretation would be that the Schumpeterian process of dynamic competition that originates in the continuous introduction of new products varieties enables small firms to growth, to reach the middle range of the size distribution. In contrast, more radical innovations, generated by scientific developments, are necessary to reach the upper tail of the size distribution and maintain such a position over time. This result provides a different perspective, based on the nature of technology, on the interpretation of the departures from Pareto earlier suggested by Ijiri and Simon (1974). Their suggestions were based on the autocorrelation of firm growth rates. I want to suggest this autocorrelation might originate in the persistence of innovation due to the cumulative learning processes of firms (Mazzucato and Geroski, 2002).