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Defending Gibrat’s Law as a long-run regularity

Abstract

According to Gibrat’s Law of Proportionate Effect, the growth rate of a given firm is independent of its size at the beginning of the period examined. While earlier studies tended to confirm the Law, more recent research generally rejects it. This article reconciles these two streams of literature, taking into account the role of market selection and learning in reshaping a given population of firms through time. Consistently with previous studies, we find that Gibrat’s Law has to be rejected ex ante, since smaller firms tend to grow faster than their larger counterparts. However, a significant convergence toward Gibrat-like behavior can be detected ex post. This finding is an indication that market selection “cleans” the original population of firms, so that the resulting industrial “core” does not depart from a Gibrat-like pattern of growth. From a theoretical point of view, this result is consistent with those models based on passive and active learning, and can be seen as a defense of the validity of the Law in the long-run.

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Notes

  1. These methodological issues will be treated in detail in Sect. 3.

  2. Jovanovic’s model can be seen as a modern version of a theory of entrepreneurship which depicts new firm founders as risk-taking agents (see Knight 1921; Oxenfeldt 1943; cf. also Kihlstrom and Laffont 1979; Endres and Woods 2006).

  3. To our knowledge, this is the first attempt to test Gibrat’s Law through time in search of a possible convergence to the Law; the only exceptions being previous works by the authors of the present paper (Lotti et al. 2001, 2003). However, in those papers we dealt solely with newborn firms across (almost) the entire spectrum of Italian industrial sectors. On the peculiarities which characterize the entry and post-entry performance of new Italian manufacturing firms, see also Foti and Vivarelli (1994) and Vivarelli (2004).

  4. Focusing on a sole industry permits the wiping out of significant intersectoral differences in the patterns of firms’ entry, exit, and growth (see Dunne et al. 1988).

  5. All private Italian firms are obliged to pay national security contributions for their employees to INPS. Consequently, the registration of a new firm as “active” signals an entry into the market, while the cancellation of a firm denotes an exit from it (this happens when a firm finally stops paying national security contributions). For administrative reasons—delays in payment, for instance, or uncertainty about the actual status of the firm—cancellation may sometimes be preceded by a period during which the firm is “suspended”. The present paper considers these suspended firms as exiting from the market at the moment of their transition from the status of “active” to that of “suspended”, while firms which have halted operations only temporarily during the follow-up period, and which were “active” in January 1994, have been treated as survivors.

  6. Already around the mid-1990s the examined sector had become one of the most R&D-intensive in Italy, accounting for about one-fourth of total R&D expenditures in the country (CNEL 2001).

  7. We thank one of the referees for this useful interpretation. As also shown by previous studies (e.g., Bartelsman et al. 2005), industries characterized by rapid technological change and market experimentation are more likely to exhibit greater firm churning.

  8. This view is shared by industry insiders and experts; in addition, the overall Italian macroeconomic recession in the early ‘90s made the examined shakeout even more remarkable.

  9. Following a random walk (with drift) stochastic process.

  10. We use Φ to denote the cumulative density function of the Normal distribution and ø to denote its density function.

  11. Squared size has been inserted in the selection equation to check for possible non-linearities in the relationship between initial size and survival.

  12. Since a two-step Heckman’s (1979) estimator may be inefficient and biased for small samples.

  13. The sample selection approach treats exit as being heterogeneous as compared with a negative rate of change in size; instead, the growth approach considers exit as a growth of minus 100%. Whether exit should be considered either as a discontinuity or as something comparable with decline in size is a disputable issue. The cautious approach adopted here is that of developing both approaches and seeing whether empirical results are consistent. We thank one of the referees for suggesting the implementation of the second methodology.

  14. The test statistic is LR = 2 (log LU − log LR), where log LU and log LR are the log-likelihoods for the unrestricted and restricted versions of the model, that is distributed as a χ2 statistic with 1 degree of freedom under the null hypothesis that the restriction ρ = 0 is valid.

  15. There is an initial drop in the significance of the coefficient in the fourth year (from 99% to 90% level of confidence) and then full loss of significance in the last year.

  16. While it was only barely significant in 90/91, 91/92, and 92/93 in the previous table; however, by looking at the values of both coefficients and standard errors, the reader can easily see that although they cross the 90% threshold of statistical significance, outcomes from the two tables are fairly similar.

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Acknowledgments

Previous versions of this article have been presented at the International Workshop on “The Post-entry Performance of Firms: Technology, Growth, and Survival” (University of Bologna, 22 and 23 November 2002), at the 30th Annual E.A.R.I.E. Conference (Helsinki, 24–26 August 2003), and at the Workshop on “Entrepreneurship Research” (Max Planck Institute, Jena, 8 March 2004). We thank the participants for their helpful suggestions. Comments and suggestions by two anonymous referees were particularly useful for improving and extending this contribution. Financial support from MIUR (Year 2000; protocol (MM13038538_001; project leader: E. Santarelli) is gratefully acknowledged. The views expressed by F. Lotti do not necessarily reflect those of the Bank of Italy.

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Lotti, F., Santarelli, E. & Vivarelli, M. Defending Gibrat’s Law as a long-run regularity. Small Bus Econ 32, 31–44 (2009). https://doi.org/10.1007/s11187-007-9071-0

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Keywords

  • Gibrat’s Law
  • Firm size
  • Firm age
  • Firm survival
  • Firm growth

JEL Classification

  • L11
  • L26