Technological opportunity and the growth process of firms

Technological opportunity and the growth process of firms

Arun K. Mukhopadhyay


The question of whether the growth process of firms is best explained by identifiable systematic influences, or by an essentially random process, is an important one in the literature on market structure. Within this context, the issue of whether firm size has a systematic influence on the growth rate of a firm has been the subject of extensive empirical studies. This paper attempts to re-examine the firm’s size-growth relationship using data on large firms in the USA over the 1994-2000 period. The overall empirical results emanating from this study point to a tendency for the smaller firms to grow faster, and this tendency is stronger for industries facing greater technological opportunity.


Is the growth process of firms best explained by identifiable systematic influences, or is it essentially a random process? Numerous studies have dealt with this empirical issue which was first addressed by Gibrat. Robert Gibrat demonstrated in his 1931 book that the skewed distributions of enterprise and plant sizes in the French manufacturing establishments can be explained very well by a random growth process. This assumption of random growth has been subsequently christened the “Gibrat’s law”; see Sutton (1997) and Caves (1998) for discussions on the theory and empirical studies.

Gibrat’s law implies that with a random growth process, the expected growth rate is independent of a firm’s size and other identifiable firm and industry characteristics. The issue of whether firm size has a systematic influence on the growth rate of a firm has been the subject of extensive investigation in empirical studies because this size-growth relation is most directly involved in explaining the size-distribution of firms. Following Simon (1955), several studies have used the Gibrat’s law to explain the size-distribution of the large firms in the United States. See, for instance, Iriji and Simon (1974) and Vining (1976). In an empirical study, AmirKhalkhali and Mukhopadhyay (1993)investigated the validity of Gibrat’s law, examining both the growth rates and the size-distributions of firms, for the large firms in the USA during the 1965-1987 period. The focus in that study was whether research and development (RD) activities and the resulting technological competition imply a qualification of Gibrat’s law, that is, whether the size-growth relationship and the consequent size-distribution of firms depend on whether or not the firms are operating in RD- intensive industries. The overall conclusion of the study was that smaller firms tend to have an advantage in the growth process and that this advantage is more pronounced in the industries offering greater technological opportunities. This paper extends the investigation of the size-growth relationship to the 1994-2000 period.


The basic stylized fact resulting from the various empirical studies on Gibrat’s law is that the law does not exactly hold: large firms have a tendency to grow slower while they have a greater propensity to survive, although there is support for Gibrat’s law in some studies. As examples, Evans (1987) reported a negative relation between size and growth rate for a large sample of U.S. firms, while Hall (1987), also studying U.S. firms, found that Gibrat’s law held for the larger firms, but size had a weak positive effect on growth for the smaller firms. This lack of robustness in empirical results on the size-growth relationship is also evident from the U.K. data: Kumar (1985) found a weak negative effect of size on growth, and the study by Singh and Whittington showed a mildly positive relationship. Studies involving the large international firms (Droucopoulos (1982, 1983), Buckley, Dunning, and Pearce (1984)) similarly reveal conflicting results on the size-growth relationship. In a more recent study, Hart and Oulton (1996) found from a large data base for the U.K. during 1989-93, that among the surviving companies during this period, only the very small companies (those with no more than 8 employees) grew faster; among the remaining companies there was little tendency for the proportionate growth of the firm to vary with its size.

While the studies on Gibrat’s law have essentially focussed on whether or not firm size has a systematic effect on firm growth, the central issue of our inquiry is to find out whether the size-growth relationship is influenced by the process of RD in the technologically competitive industries. The basis of suspecting such an influence is rooted in the well-known Schumpeterian hypothesis. This hypothesis suggests that bigger firms have an advantage in the RD process in that these firms enjoy an economy of scale in the RD effort and also have a superior ability to exploit the results of research (Schumpeter(1950); Kamien and Schwartz(1982)). It is reasonable to expect that this Schumpeterian research advantage would lead to a faster growth for the bigger firms, and that this phenomenon would be evident in the technologically progressive (RD-intensive) industries, whereas the non-RD-intensive industries will be largely unaffected by this size–advantage of research and development. Thus, the size–growth relationship would be different between these two groups of industries. The simulation models formulated by Nelson and Winter (1978, 1982a, 1982b) are examples of this expected outcome, where the larger firms have a higher expected growth rate that is attributable to their research advantage in technological competition. In the present paper, we test for this group-specific difference in the size-growth relationship arising out of the Schumpeterian hypothesis.


The sample used in this study is taken from the Fortune list of 1000 largest firms in the USA in the years 1994, 1997 and 2000. Cross-sectional statistics shown in Table 1 are derived for these 1000 firms for each of these years, while the study of the growth relations is based on the subset of 498 firms maintaining their identity over the 1994-2000 period.

The firms in the samples are divided into the groups of RD-intensive (RD) and non-RD-intensive (NRD) categories. Industries which are classified as RD intensive are: aerospace and defense, chemicals, medical equipment, pharmaceuticals, scientific and photographic equipment, computers, electronics and electrical equipment, network and communications equipment, industrial and office equipment, motor vehicles, and telecommunications. For the 498 identity-maintaining firms, this classification yields 148 firms in the RD intensive category (RD) and 350 in the non-RD-intensive category (NRD). The sample period is broken down into two sub-periods: 1994-1997 and 1997-2000.

Table 1 reports the annual growth rates of RD and NRD firms over two periods as well as the average growth rate over the period 1994-2000. NRD firms outperformed the RD firms in terms of growth during both periods. The former group of firms also enjoyed significantly higher growth rates in the second period.

Table 1a presents a summary measure of firm size inequality, as indicated by the coefficient of variation. In general, the inequality coefficients follow a decreasing trend for the RD firms and the total group over the period under study. This trend may reflect a tendency for the smaller RD firms to grow faster. The trend is different for the NRD firms. Despite some decline in inequality in the 1994-1997 period, the inequality coefficient increases for the NRD firms over the 1997-2000 period.


We start with the following log linear regression for testing the Law of Proportionate Effect for a set of firms surviving over a period of time:

(1) log[] = [[alpha].sub.1] + [[alpha].sub.2] log[] + []

where [Y.sub.i] represents the size of the ith firm (denoted by sales in this study), [[alpha].sub.1] and [[alpha].sub.2] are parameters, and [u.sub.i] is the random term. Note that subscripts t-l and t refer to the beginning-of-the-period and the end-of-the-period values of the variables, respectively.

In this model, the Law of Proportionate Effect holds if [[alpha].sub.2] = 1, i.e., firm growth is independent of size. If [[alpha].sub.2] 1 then the opposite would be true.

We estimate the model (1) using generalized least squares (GLS) and the results are presented in Table 2. (Note that the numbers in parenthesis are standard errors and * denote significance at the .05 level.) While the group-wise results do not seem significantly different, the period-wise results do. In other words, it can be seen that [[alpha].sub.2] is significantly less than one in both RD as well as NRD industries in the 1994-97 period, implying that smaller firms grew faster than larger firms during this period. However, the null hypothesis of no relationship between size and growth embodied in the law, i.e., [[alpha].sub.2] = 1, cannot be rejected during the 1997-2000 period.

We then use an alternative model of directly testing the size-growth relation. Define the growth rate of the ith firm as: [] = ([] – [])/[].

Using Taylor expansion and combining with equation (1) it approximately holds that

(2) [] = [[beta].sub.1] + [[beta].sub.2] log [] + []

Note that [[beta].sub.2] = [[alpha].sub.1] – 1 and the model expressed in equation (2) can now be used to conduct direct tests concerning the relationship between firm growth rate and its initial size.

Table 3 gives the GLS results of estimating model (2) relating firms’ growth rate directly to initial size. These results show that the relationship between growth and initial size for both the RD and NRD firms as well as the total group is negative in both sub-periods. However, it is only significant in the first sub-period 1994-97. These results are also not that different between the two groups of firms.

Following AmirKhalkhali & Mukhopadhyay (1993), we also estimate the following autoregressive model for the 1997-2000 period:

(3) [] = [[??].sub.1] + [[??].sub.2] log [] + [[??].sub.3] [] + [[??]]

where [] denotes the past growth rate. Note that the statistical significance of [[??].sub.3] indicates autocorrelated growth rates The least-squares estimates of equation 3 are reported in Table 4. The relationship between growth and initial size remains negative but insignificant. The persistency of growth rates appears to be the most visible phenomenon in all cases. The reported adjusted [R.sup.2] also point to not only the improvement in the explanatory of the model but also the relevance of the past growth rate variable in the model. In the 1997-2000 period, the positive effect of past growth rates appears higher for NRD firms but not significantly different between the two groups.


The overall empirical result emanating from this study points to the basic conclusion that there is a tendency for the smaller firms to grow faster, and that this tendency seems stronger for the RD-intensive group of firms. However, this pattern is quite weak in the 1997-2000 period, while it is statistically significant in the earlier period of 1994-1997. The results indicate that growth rates are significantly autocorrelated for all firms in the 1997-2000 period, suggesting that Gibrat’s Law does not hold for these firms. These results are somewhat similar to our earlier study of the largest U.S. firms maintaining their identity over the 1965-1987 period. Taken together, these two studies covering most of the last 35 years of growth-history of the large U.S. companies, point to the evidence that firm size has a systematic, but often weak, negative influence on firm growth, and that this effect is more pronounced in industries facing greater technological opportunity. The group-specific results of this study do not bear out the Schumpeterian hypothesis as expressed through the size-growth relationship for the RD group of firms. This is not to deny that larger firms may have certain advantages in the process of research and in the exploitation of its results. But clearly, smaller firms have advantages in some other ways, so that the overall statistical result comes out as a negation of the Schumpeterian hypothesis. It is well known that entry of smaller firms takes away market shares from the larger firms in the presence of technological opportunity in a growing market (Mukhopadhyay (1985)). Recently, Acs and Audretsch (1988) and Audretsch (1995) have explored how the innovative advantage differs between large and small firms in the research-oriented industries. Their analysis follows Nelson and Winter (1982b) and Gort and Klepper (1982) who contend that in some industries the underlying knowledge conditions favor the larger firms whereas the opposite is true in other industries. The former is the case of the routinized regime, while the latter case is termed the entrepreneurial regime. This is an interesting distinction calling for further empirical tests. In this study we are only able to distinguish between industries which are technologically progressive and those which are not, from the evidence of their RD-intensities. Thereby, the RD group in our study show only the aggregate effect of the two regimes with their opposite impacts on the relative advantages of larger firms.




Period All RD NRD

1994-1997 9.7% 8.6% 10.4%

1997-2000 11.8 8.3 14.7




Year All RD NRD

1994 1.94 2.23 1.44

1997 1.74 2.05 1.31

2000 1.66 1.83 1.47



Log [Y.sub.i(1997)] = [[empty set].sub.1] + [[empty set].sub.2] log

[Y.sub.i(1994) + []

Year Group [[empty set].sub.1] [[empty set].sub.2] [R.sup.2]

1997 All 1.001 * .914 * .87

(.131) (.016)

RD 1.261 * .884 * .85

(.090) (.030)

NRD .870 * .929 * .87

(.153) (.018)

log [Y.sub.i(2000)] = [[empty set].sub.1] + [[empty set].sub.2] log

[Y.sub.i(1997)] + []

Year Group [[empty set].sub.1] [[empty set].sub.2] [R.sup.2]

2000 All .340 * .989 * .88

(.136) (.024)

RD .488 * .970 * .88

(.251) (.029)

NRD .236 1.005 * .88

(.163) (.019)



[G.sub.i(1994-97)]=[[beta].sub.1] + [[beta].sub.2] log [Y.sub.i(1994) +


Period Group [[beta].sub.1] [[beta].sub.2] [R.sup.2]

1994-1997 All 1.575 * -.138 * .043

(.239) (.029)

RD 1.963 * -.179 * .074

(.417) (.050)

NRD 1.405 * -.120 * .027

(.295) (.036)

[G.sub.i(1997-2000)] = [[beta].sub.1] + [[beta].sub.2] log

[Y.sub.i(1997)] + []

Period Group [[beta].sub.1] [[beta].sub.2] [R.sup.2]

1997-2000 All .448 -.007 .000

(.228) (.027)

RD .658 -.047 .008

(.374) (.043)

NRD .257 -.017 .000

(.285) (.033)


Growth-Size Results

[G.sub.i(1997-2000)]=[[empty set].sub.1] + [[empty set].sub.2] log

[Y.sub.i(1997)] + [[empty set].sub.3] [G.sub.i(1994-1997)] +


Period Group [[empty set].sub.1] [[empty set].sub.2]

1997-2000 All .558 * -.038

(.211) (.025)

RD .749 * -.063

(.349) (.041)

NRD .431 -.022

(.265) (.032)

Period Group [[empty set].sub.3] Adjusted [R.sup.2]

1997-2000 All .331 * .137


RD .292 * .129


NRD .350 * .139



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Author Profile

Dr. Arun K. Mukhopadhyay (PhD 1979, Brown University. USA), Professor of Economics, Sobey School of Business, Saint Mary’s University, Halifax, Canada

Dr. Sal AmirKhalkhali (PhD 1984, Dalhousie University, Canada), Professor of Economics, Sobey School of Business, Saint Mary’s University, Halifax, Canada

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