Abstract We survey the phenomenon of the growth of ? rms drawing on literature from economics, management, and sociology. We begin with a review of empirical ‘stylised facts’ before discussing theoretical contributions. Firm growth is characterized by a predominant stochastic element, making it di? cult to predict. Indeed, previous empirical research into the determinants of ? rm growth has had a limited success. We also observe that theoretical propositions concerning the growth of ? rms are often amiss. We conclude that progress in this area requires solid empirical work, perhaps making use of novel statistical techniques.

JEL codes: L25, L11 Keywords: Firm Growth, Size Distribution, Growth Rates Distribution, Gibrat’s Law, Theory of the Firm, Diversi? cation, ‘Stages of Growth’ models. ? I thank Giulio Bottazzi, Giovanni Dosi, Ha? da El-Younsi, Jacques Mairesse, Bernard Paulr? , Rekha Rao, e Angelo Secchi and Ulrich Witt for helpful comments. Nevertheless, I am solely responsible for any errors or confusion that may remain. This version: May 2007 † Corresponding Author : Alex Coad, Max Planck Institute of Economics, Evolutionary Economics Group, Kahlaische Strasse 10, D-07745 Jena, Germany. Phone: +49 3641 686822. Fax : +49 3641 686868.

E-mail : [email protected] mpg. de 1 #0703 Contents 1 Introduction 3 2 Empirical evidence on ? rm growth 2. 1 Size and growth rates distributions . . . . 2. 1. 1 Size distributions . . . . . . . . . . 2. 1. 2 Growth rates distributions . . . . . 2. 2 Gibrat’s Law . . . . . . . . . . . . . . . . 2. 2. 1 Gibrat’s model . . . . . . . . . . . 2. 2. 2 Firm size and average growth . . . 2. 2. 3 Firm size and growth rate variance 2. 2. 4 Autocorrelation of growth rates . . 2. 3 Other determinants of ? rm growth . . . . 2. 3. 1 Age . . . . . . . . . . . . . . . . . 2. 3. 2 Innovation . . . . . . . . . . . . . . 2. 3.

3 Financial performance . . . . . . . 2. 3. 4 Relative productivity . . . . . . . . 2. 3. 5 Other ? rm-speci? c factors . . . . . 2. 3. 6 Industry-speci? c factors . . . . . . 2. 3. 7 Macroeconomic factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 4 4 5 9 9 11 14 15 18 18 19 23 25 26 28 29 3 Theoretical contributions 3. 1 Neoclassical foundations – growth towards an ‘optimal size’ .

. . . 3. 2 Penrose’s ‘Theory of the Growth of the Firm’ . . . . . . . . . . . 3. 3 Marris and ‘managerialism’ . . . . . . . . . . . . . . . . . . . . . 3. 4 Evolutionary Economics and the principle of ‘growth of the ? tter’ 3. 5 Population ecology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 31 32 34 35 38 . . . . . . . 39 39 40 43 44 45 46 49 5 Growth of small and large ? rms 5. 1 Di? erences in growth patterns for small and large ? rms . . . . . . . . . . . . . 5. 2 Modelling the ‘stages of growth’ . . . . . . . . . . . . .

. . . . . . . . . . . . . 51 51 53 6 Conclusion 56 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Growth strategies 4. 1 Attitudes to growth . . . . . . . . . . . . . . . . . . . 4. 1. 1 The desirability of growth . . . . . . . . . . . 4. 1. 2 Is growth intentional or does it ‘just happen’ ? 4. 2 Growth strategies – replication or diversi? cation . . . 4. 2. 1 Growth by replication . . . . . . . . . . . . . 4. 2. 2 Growth by diversi? cation . . . . . . . . .

. . . 4. 3 Internal growth vs growth by acquisition . . . . . . . 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . #0703 1 Introduction The aim of this survey is to provide an overview of research into the growth of ? rms, while also highlighting areas in need of further research.

It is a multidisciplinary survey, drawing on contributions made in economics, management and also sociology. There are many di? erent measures of ? rm size, some of the more usual indicators being employment, total sales, value-added, total assets, or total pro? ts; and some of the less conventional ones such as ‘acres of land’ or ‘head of cattle’ (Weiss, 1998). In this survey we consider growth in terms of a range of indicators, although we devote little attention to the growth of pro? ts (this latter being more of a ? nancial than an economic variable). There are also di? erent ways of measuring growth rates.

Some authors (such as Delmar et al. , 2003) make the distinction between relative growth (i. e. the growth rate in percentage terms) and absolute growth (usually measured in the absolute increase in numbers of employees). In this vein, we can mention the ‘Birch index’ which is a weighted average of both relative and absolute growth rates (this latter being taken into account to emphasize that large ? rms, due to their large size, have the potential to create many jobs). This survey focuses on relative growth rates only. Furthermore, in our discussion of the processes of expansion we emphasize positive growth and not so much negative growth.

1 In true Simonian style,2 we begin with some empirical insights in Section 2, considering ? rst the distributions of size and growth rates, and moving on to look for determinants of growth rates. We then present some theories of ? rm growth and evaluate their performance in explaining the stylised facts that emerge from empirical work (Section 3). In Section 4 we consider the demand and supply sides of growth by discussing the attitudes of ? rms towards growth opportunities as well as investigating the processes by which ? rms actually grow (growth by ‘more of the same’, growth by diversi? cation, growth by acquisition).

In Section 5 we examine the di? erences between the growth of small and large ? rms in greater depth. We also review the ‘stages of growth’ models. Section 6 concludes. 2 Empirical evidence on ? rm growth To begin with, we take a non-parametric look at the distributions of ? rm size and growth rates, before moving on to results from regressions that investigate the determinants of growth rates. 1 2 For an introduction to organizational decline, see Whetten (1987). See in particular Simon (1968). 3 #0703 2. 1 Size and growth rates distributions A suitable starting point for studies into industrial structure and dynamics is the ?rm size distribution.

In fact, it was by contemplating the empirical size distribution that Robert Gibrat (1931) proposed the well-known ‘Law of Proportionate E? ect’ (also known as ‘Gibrat’s law’). We also discuss the results of research into the growth rates distribution. The regularity that ? rm growth rates are approximately exponentially distributed was discovered only recently, but o? ers unique insights into the growth patterns of ? rms. 2. 1. 1 Size distributions The observation that the ? rm-size distribution is positively skewed proved to be a useful point of entry for research into the structure of industries.

(See Figures 1 and 2 for some examples of aggregate ? rm size distributions. ) Robert Gibrat (1931) considered the size of French ? rms in terms of employees and concluded that the lognormal distribution was a valid heuristic. Hart and Prais (1956) presented further evidence on the size distribution, using data on quoted UK ? rms, and also concluded in favour of a lognormal model. The lognormal distribution, however, can be viewed as just one of several candidate skew distributions. Although Simon and Bonini (1958) maintained that the “lognormal generally ?

ts quite well” (1958: p611), they preferred to consider the lognormal distribution as a special case in the wider family of ‘Yule’ distributions. The advantage of the Yule family of distributions was that the phenomenon of arrival of new ? rms could be incorporated into the model. Steindl (1965) applied Austrian data to his analysis of the ? rm size distribution, and preferred the Pareto distribution to the lognormal on account of its superior performance in describing the upper tail of the distribution. Similarly, Ijiri and Simon (1964, 1971, 1974) apply the Pareto distribution to analyse the size distribution oflarge US ? rms.

E? orts have been made to discriminate between the various candidate skew distributions. One problem with the Pareto distribution is that the empirical density has many more middlesized ? rms and fewer very large ? rms than would be theoretically predicted (Vining, 1976). Other research on the lognormal distribution has shown that the upper tail of the empirical size distribution of ? rms is too thin relative to the lognormal (Stanley et al. , 1995). Quandt (1966) compares the performance of the lognormal and three versions of the Pareto distribution, using data disaggregated according to industry.

He reports the superiority of the lognormal over the three types of Pareto distribution, although each of the distributions produces a best-? t for at least one sample. Furthermore, it may be that some industries (e. g. the footwear industry) are not ? tted well by any distribution. More generally, Quandt’s results on disaggregated data lead us to suspect that the regu4 #0703 larities of the ? rm-size distribution observed at the aggregate level do not hold with sectoral disaggregation. Silberman (1967) also ? nds signi? cant departures from lognormality in his analysis of 90 four-digit SIC sectors.

It has been suggested that, while the ? rm size distribution has a smooth regular shape at the aggregate level, this may merely be due to a statistical aggregation e? ect rather than a phenomenon bearing any deeper economic meaning (Dosi et al, 1995; Dosi, 2007). Empirical results lend support to these conjectures by showing that the regular unimodal ? rm size distributions observed at the aggregate level can be decomposed into much ‘messier’ distributions at the industry level, some of which are visibly multimodal (Bottazzi and Secchi, 2003; Bottazzi et al. , 2005).

For example, Bottazzi and Secchi (2005) present evidence of signi? cant bimodality in the ? rm size distribution of the worldwide pharmaceutical industry, and relate this to a cleavage between the industry leaders and fringe competitors. Other work on the ? rm-size distribution has focused on the evolution of the shape of the distribution over time. It would appear that the initial size distribution for new ? rms is particularly right-skewed, although the log-size distribution tends to become more symmetric as time goes by. This is consistent with observations that small young ? rms grow faster than their larger counterparts.

As a result, it has been suggested that the log-normal can be seen as a kind of ‘limit distribution’ to which a given cohort of ? rms will eventually converge. Lotti and Santarelli (2001) present support for this hypothesis by tracking cohorts of new ? rms in several sectors of Italian manufacturing. Cabral and Mata (2003) ? nd similar results in their analysis of cohorts of new Portuguese ? rms.

However, Cabral and Mata interpret their results by referring to ? nancial constraints that restrict the scale of operations for new ? rms, but become less binding over time, thus allowing these small ?rms to grow relatively rapidly and reach their preferred size. They also argue that selection does not have a strong e? ect on the evolution of market structure.

Although the skewed nature of the ? rm size distribution is a robust ? nding, there may be some other features of this distribution that are speci? c to countries. Table 1, taken from Bartelsman et al. (2005), highlights some di? erences in the structure of industries across countries. Among other things, one observes that large ? rms account for a considerable share of French industry, whereas in Italy ? rms tend to be much smaller on average.

(These international di? erences cannot simply be attributed to di? erences in sectoral specialization across countries. ) 2. 1. 2 Growth rates distributions It has long been known that the distribution of ? rm growth rates is fat-tailed. In an early contribution, Ashton (1926) considers the growth patterns of British textile ? rms and observes 5 US 86. 7 69. 9 87. 9 16. 6 5. 8 Western Germany 87. 9 77. 9 90. 2 23. 6 11. 3 78. 6 73. 6 78. 8 13. 9 17. 0 France Italy 93. 1 87. 5 96. 5 34. 4 30. 3 74. 9 8. 3 UK Canada Denmark 90. 0 74. 0 90. 8 30. 2 16. 1 92. 6 84. 8 94. 5 25. 8 13. 0 Finland Netherlands 95. 8 86.

7 96. 8 31. 2 16. 9 86. 3 70. 5 92. 8 27. 7 15. 7 Portugal Source: Bartelsman et al. (2005: Tables 2 and 3). Notes: the columns labelled ‘share of employment’ refer to the employment share 6 26. 4 17. 0 33. 5 10. 5 12. 7 13. 3 13. 0 6. 5 16. 8 Total economy 80. 3 39. 1 32. 1 15. 3 40. 7 40. 5 30. 4 27. 8 18. 3 31. 0 Manufacturing 21. 4 11. 5 35. 7 6. 8 12. 0 12. 7 9. 9 5. 3 11. 4 Business services Ave. No. Employees per ? rm of ? rms with fewer than 20 employees. 20. 6 33. 8 12. 1 46. 3 33. 4 33. 0 41. 9 39. 8 Business services Total economy Manufacturing Share of employment (%) Business services Total economy.

Manufacturing Absolute number (%) Table 1: The importance of small ? rms (i. e. ?rms with fewer than 20 employees) across broad sectors and countries, 1989-94 #0703 #0703 1 Pr 1998 2000 2002 0. 1 0. 01 0. 001 1e-04 -4 -2 0 s 2 4 6 Figure 1: Kernel estimates of the density of ?rm size (total sales) in 1998, 2000 and 2002, for French manufacturing ? rms with more than 20 employees. Source: Bottazzi et al. , 2005. Figure 2: Probability density function of the sizes of US manufacturing ? rms in 1997. Source: Axtell, 2001. that “In their growth they obey no one law. A few apparently undergo a steady expansion.. .

With others, increase in size takes place by a sudden leap” (Ashton 1926: 572-573). Little (1962) investigates the distribution of growth rates, and also ? nds that the distribution is fat-tailed. Similarly, Geroski and Gugler (2004) compare the distribution of growth rates to the normal case and comment on the fat-tailed nature of the empirical density. Recent empirical research, from an ‘econophysics’ background, has discovered that the distribution of ? rm growth rates closely follows the parametric form of the Laplace density. Using the Compustat database of US manufacturing ? rms, Stanley et al.

(1996) observe a ‘tent-shaped’ distribution on log-log plots that corresponds to the symmetric exponential, or Laplace distribution (see also Amaral et al. (1997) and Lee et al. (1998)). The quality of the ? t of the empirical distribution to the Laplace density is quite remarkable. The Laplace distribution is also found to be a rather useful representation when considering growth rates of ? rms in the worldwide pharmaceutical industry (Bottazzi et al. , 2001). Giulio Bottazzi and coauthors extend these ? ndings by considering the Laplace density in the wider context of the family of Subbotin distributions (beginning with Bottazzi et al., 2002).

They ? nd that, for the Compustat database, the Laplace is indeed a suitable distribution for modelling ? rm growth rates, at both aggregate and disaggregated levels of analysis (Bottazzi and Secchi 2003a). The exponential nature of the distribution of growth rates also holds for other databases, such as Italian manufacturing (Bottazzi et al. (2007)). In addition, the exponential distribution appears to hold across a variety of ? rm growth indicators, such as Sales growth, employment growth or Value Added growth (Bottazzi et al. , 2007). The growth rates of French manufacturing ?

rms have also been studied, and roughly speaking a similar shape was observed, although it must be said that the empirical density was noticeably fatter-tailed than the Laplace (see Bottazzi et al. , 2005). 3 3 The observed subbotin b parameter (the ‘shape’ parameter) is signi? cantly lower than the Laplace value of 1. This highlights the importance of following Bottazzi et al. (2002) and considering the Laplace as a special 7 #0703 1998 2000 2002 1998 2000 2002 1 prob. prob. 1 0. 1 0. 01 0. 1 0. 01 0. 001 0. 001 -3 -2 -1 0 1 2 -2 -1. 5 -1 conditional growth rate -0. 5 0 0. 5 1 1. 5 2 conditional growth rate.

Figure 3: Distribution of sales growth rates of French manufacturing ? rms. Source: Bottazzi et al. , 2005. Figure 4: Distribution of employment growth rates of French manufacturing ? rms. Source: Coad, 2006b. Research into Danish manufacturing ? rms presents further evidence that the growth rate distribution is heavy-tailed, although it is suggested that the distribution for individual sectors may not be symmetric but right-skewed (Reichstein and Jensen (2005)).

Generally speaking, however, it would appear that the shape of the growth rate distribution is more robust to disaggregation than the shape of the ?rm size distribution. In other words, whilst the smooth shape of the aggregate ? rm size distribution may be little more than a statistical aggregation e? ect, the ‘tent-shapes’ observed for the aggregate growth rate distribution are usually still visible even at disaggregated levels (Bottazzi and Secchi, 2003a; Bottazzi et al. , 2005). This means that extreme growth events can be expected to occur relatively frequently, and make a disproportionately large contribution to the evolution of industries.

Figures 3 and 4 show plots of the distribution of sales and employment growth rates for French manufacturing ?rms with over 20 employees. Although research suggests that both the size distribution and the growth rate distribution are relatively stable over time, it should be noted that there is great persistence in ? rm size but much less persistence in growth rates on average (more on growth rate persistence is presented in Section 2. 2. 4). As a result, it is of interest to investigate how the moments of the growth rates distribution change over the business cycle. Indeed, several studies have focused on these issues and some preliminary results can be mentioned here.

It has been suggested that the variance of growth rates changes over time for the employment growth of large US ? rms (Hall, 1987) and that this variance is procyclical in the case of growth of assets (Geroski et al. , 2003). This is consistent with the hypothesis that ? rms have a lot of discretion in their growth rates of assets during booms but face stricter discipline during recessions. Higson et al. (2002, 2004) consider the evolution of the ? rst four moments of distributions of the growth of sales, for large US and UK ?rms over periods of 30 years or more.

They observe that higher moments of the distribution of sales growth rates have signi? cant cyclical patterns. In case in the Subbotin family of distributions. 8 #0703 particular, evidence from both US and UK ? rms suggests that the variance and skewness are countercyclical, whereas the kurtosis is pro-cyclical. Higson et al. (2002: 1551) explain the counter-cyclical movements in skewness in these words: “The central mass of the growth rate distribution responds more strongly to the aggregate shock than the tails.

So a negative shock moves the central mass closer to the left of the distribution leaving the right tail behind and generates positive skewness. A positive shock shifts the central mass to the right, closer to the group of rapidly growing ? rms and away from the group of declining ? rms. So negative skewness results. ” The procyclical nature of kurtosis (despite their puzzling ? nding of countercyclical variance) emphasizes that economic downturns change the shape of the growth rate distribution by reducing a key parameter of the ‘spread’ or ‘variation’ between ? rms. 2. 2 Gibrat’s Law.

Gibrat’s law continues to receive a huge amount of attention in the empirical industrial organization literature, more than 75 years after Gibrat’s (1931) seminal publication. We begin by presenting the ‘Law’, and then review some of the related empirical literature. We do not attempt to provide an exhaustive survey of the literature on Gibrat’s law, because the number of relevant studies is indeed very large. (For other reviews of empirical tests of Gibrat’s Law, the reader is referred to the survey by Lotti et al (2003); for a survey of how Gibrat’s law holds for the services sector see Audretsch et al.

(2004). ) Instead, we try to provide an overview of the essential results. We investigate how expected growth rates and growth rate variance are in? uenced by ? rm size, and also investigate the possible existence of patterns of serial correlation in ? rm growth. 2. 2. 1 Gibrat’s model Robert Gibrat’s (1931) theory of a ‘law of proportionate e? ect’ was hatched when he observed that the distribution of French manufacturing establishments followed a skew distribution that resembled the lognormal.

Gibrat considered the emergence of the ?rm-size distribution as an outcome or explanandum and wanted to see which underlying growth process could be responsible for generating it. In its simplest form, Gibrat’s law maintains that the expected growth rate of a given ? rm is independent of its size at the beginning of the period examined. Alternatively, as Mans? eld (1962: 1030) puts it, “the probability of a given proportionate change in size during a speci? ed 9 #0703 period is the same for all ? rms in a given industry – regardless of their size at the beginning of the period.

” More formally, we can explain the growth of ? rms in the following framework. Let xt be the size of a ? rm at time t, and let ? t be random variable representing an idiosyncratic, multiplicative growth shock over the period t ? 1 to t. We have xt ? xt? 1 = ? t xt? 1 (1) xt = (1 + ? t )xt? 1 = x0 (1 + ? 1 )(1 + ? 2 ) . . . (1 + ? t ) (2) which can be developed to obtain It is then possible to take logarithms in order to approximate log(1 + ? t ) by ? t to obtain4 t log(xt ) ? log(x0 ) + ? 1 + ? 2 + . . . + ? t = log(x0 ) + ?s (3) s=1

In the limit, as t becomes large, the log(x0 ) term will become insigni? cant, and we obtain t log(xt ) ? ?s (4) s=1 In this way, a ? rm’s size at time t can be explained purely in terms of its idiosyncratic history of multiplicative shocks. If we further assume that all ? rms in an industry are independent realizations of i. i. d. normally distributed growth shocks, then this stochastic process leads to the emergence of a lognormal ? rm size distribution. There are of course several serious limitations to such a simple vision of industrial dynamics.

We have already seen that the distribution of growth rates is not normally distributed, but instead resembles the Laplace or ‘symmetric exponential’. Furthermore, contrary to results implied by Gibrat’s model, it is not reasonable to suppose that the variance of ? rm size tends to in? nity (Kalecki, 1945). In addition, we do not observe the secular and unlimited increase in industrial concentration that would be predicted by Gibrat’s law (Caves, 1998).

Whilst a ‘weak’ version of Gibrat’s law merely supposes that expected growth rate is independent of ?rm size, stronger versions of Gibrat’s law imply a range of other issues.

For example, Chesher (1979) rejects Gibrat’s law due to the existence of an autocorrelation structure in the growth shocks. Bottazzi and Secchi (2006a) reject Gibrat’s law on the basis of a negative relationship between growth rate variance and ? rm size. Reichstein and Jensen (2005) reject Gibrat’s law 4 This logarithmic approximation is only justi? ed if ? t is ‘small’ enough (i. e. close to zero), which can be reasonably assumed by taking a short time period (Sutton, 1997). 10 #0703after observing that the annual growth rate distribution is not normally distributed. 2.

2. 2 Firm size and average growth Although Gibrat’s (1931) seminal book did not provoke much of an immediate reaction, in recent decades it has spawned a ? ood of empirical work. Nowadays, Gibrat’s ‘Law of Proportionate E? ect’ constitutes a benchmark model for a broad range of investigations into industrial dynamics. Another possible reason for the popularity of research into Gibrat’s law, one could suggest quite cynically, is that it is a relatively easy paper to write.

First of all, it has been argued that there is a minimalistic theoretical background behind the process (because growth is assumed to be purely random). Then, all that needs to be done is to take the IO economist’s ‘favourite’ variable (i. e. ?rm size, a variable which is easily observable and readily available) and regress the di? erence on the lagged level. In addition, few control variables are required beyond industry dummies and year dummies, because growth rates are characteristically random.

Empirical investigations of Gibrat’s law rely on estimation of equations of the type: log(xt ) = ?+ ? log(xt? 1 ) + (5) where a ? rm’s ‘size’ is represented by xt , ? is a constant term (industry-wide growth trend) and is a residual error. Research into Gibrat’s law focuses on the coe? cient ?. If ? rm growth is independent of size, then ? takes the value of unity. If ? is smaller than one, then smaller ? rms grow faster than their larger counterparts, and we can speak of ‘regression to the mean’. Conversely, if ? is larger than one, then larger ? rms grow relatively rapidly and there is a tendency to concentration and monopoly.

A signi?cant early contribution was made by Edwin Mans? eld’s (1962) study of the US steel, petroleum, and rubber tire industries. In particular interest here is what Mans? eld identi? ed as three di? erent renditions of Gibrat’s law. According to the ? rst, Gibrat-type regressions consist of both surviving and exiting ? rms and attribute a growth rate of -100% to exiting ? rms. However, one caveat of this approach is that smaller ? rms have a higher exit hazard which may obfuscate the relationship between size and growth.

The second version, on the other hand, considers only those ?rms that survive. Research along these lines has typically shown that smaller ? rms have higher expected growth rates than larger ? rms. The third version considers only those large surviving ? rms that are already larger than the industry Minimum E? cient Scale of production (with exiting ? rms often being excluded from the analysis). Generally speaking, empirical analysis corresponding to this third approach suggests that growth rates are more or less independent from ? rm size, which lends support to Gibrat’s law. 11 #0703 The early studies focused on large ?

rms only, presumably partly due to reasons of data availability. A series of papers analyzing UK manufacturing ? rms found a value of ? greater than unity, which would indicate a tendency for larger ? rms to have higher percentage growth rates (Hart (1962), Samuels (1965), Prais (1974), Singh and Whittington (1975)). However, the majority of subsequent studies using more recent datasets have found values of ? slightly lower than unity, which implies that, on average, small ? rms seem to grow faster than larger ? rms. This result is frequently labelled ‘reversion to the mean size’ or ‘mean-reversion’.

5 Among a large and growing body of research that reports a negative relationship between size and growth, we can mention here the work by Kumar (1985) and Dunne and Hughes (1994) for quoted UK manufacturing ? rms, Hall (1987), Amirkhalkhali and Mukhopadhyay (1993) and Bottazzi and Secchi (2003) for quoted US manufacturing ? rms (see also Evans (1987a, 1987b) for US manufacturing ? rms of a somewhat smaller size), Gabe and Kraybill (2002) for establishments in Ohio, and Goddard et al. (2002) for quoted Japanese manufacturing ? rms. Studies focusing on small businesses have also found a negative relationship between ?

rm size and expected growth – see for example Yasuda (2005) for Japanese manufacturing ? rms, Calvo (2006) for Spanish manufacturing, McPherson (1996) for Southern African micro businesses, and Wagner (1992) and Almus and Nerlinger (2000) for German manufacturing. Dunne et al. (1989) analyse plant-level data (as opposed to ? rm-level data) and also observe that growth rates decline along size classes. Research into Gibrat’s law using data for speci? c sectors also ? nds that small ? rms grow relatively faster (see e. g. Barron et al. (1994) for New York credit unions, Weiss (1998) for Austrian farms, Liu et al.

(1999) for Taiwanese electronics plants, and Bottazzi and Secchi (2005) for an analysis of the worldwide pharmaceutical sector). Indeed, there is a lot of evidence that a slight negative dependence of growth rate on size is present at various levels of industrial aggregation. Although most empirical investigations into Gibrat’s law consider only the manufacturing sector, some have focused on the services sector. The results, however, are often qualitatively similar – there appears to be a negative relationship between size and expected growth rate for services too (see Variyam and Kraybill (1992), Johnson et al.

(1999)) Nevertheless, it should be mentioned that in some cases a weak version of Gibrat’s law cannot be convincingly rejected, since there appears to be no signi? cant relationship between expected growth rate and size (see the analyses provided by Bottazzi et al. (2005) for French manufacturing ? rms, Droucopoulos (1983) for the world’s largest ? rms, Hardwick and Adams (2002) for UK Life Insurance companies, and Audretsch et al. (2004) for small-scale Dutch services). Notwithstanding these latter studies, however, we acknowledge that in most cases a negative relationship between ?

rm size and growth is observed. Indeed, 5 We should be aware, however, that ‘mean-reversion’ does not imply that ? rms are converging to anything resembling a common steady-state size, even within narrowly-de? ned industries (see in particular the empirical work by Geroski et al. (2003) and Ce? s et al. (2006)). 12 #0703 it is quite common for theoretically-minded authors to consider this to be a ‘stylised fact’ for the purposes of constructing and validating economic models (see for example Cooley and Quadrini (2001), Gomes (2001) and Clementi and Hopenhayn (2006)).

Furthermore, John Sutton refers to this negative dependence of growth on size as a ‘statistical regularity’ in his revered survey of Gibrat’s law (Sutton, 1997: 46). A number of researchers maintain that Gibrat’s law does hold for ? rms above a certain size threshold. This corresponds to acceptance of Gibrat’s law according to Mans? eld’s third rendition, although ‘mean reversion’ leads us to reject Gibrat’s Law as described in Mans? eld’s second rendition. Mowery (1983), for example, analyzes two samples of ? rms, one of which contains small ? rms while the other contains large ?

rms. Gibrat’s law is seen to hold in the latter sample, whereas mean reversion is observed in the former. Hart and Oulton (1996) consider a large sample of UK ? rms and ? nd that, whilst mean reversion is observed in the pooled data, a decomposition of the sample according to size classes reveals essentially no relation between size and growth for the larger ? rms. Lotti et al. (2003) follow a cohort of new Italian startups and ? nd that, although smaller ? rms initially grow faster, it becomes more di? cult to reject the independence of size and growth as time passes.

Similarly, results reported by Becchetti and Trovato (2002) for Italian manufacturing ? rms, Geroski and Gugler (2004) for large European ? rms and Ce? s et al. (2006) for the worldwide pharmaceutical industry also ? nd that the growth of large ? rms is independent of their size, although including smaller ? rms in the analysis introduces a dependence of growth on size. It is of interest to remark that Caves (1998) concludes his survey of industrial dynamics with the ‘substantive conclusion’ that Gibrat’s law holds for ? rms above a certain size threshold, whilst for smaller ? rms growth rates decrease with size.

Concern about econometric issues has often been raised. Sample selection bias, or ‘sample attrition’, is one of the main problems, because smaller ? rms have a higher probability of exit. Failure to account for the fact that exit hazards decrease with size may lead to underestimation of the regression coe? cient (i. e. ?). Hall (1987) was among the ? rst to tackle the problem of sample selection, using a Tobit model.

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