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When is Gibrat’s law a law?

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Abstract

The purpose of this article is to investigate if the industry context matters for whether Gibrat’s law is rejected or not using a dataset that consists of all limited firms in five-digit NACE-industries in Sweden during 1998–2004. The results reject Gibrat’s law on an aggregate level, since small firms grow faster than large firms. However, Gibrat’s law is confirmed about as often as it is rejected when industry-specific regressions are estimated. It is also found that the industry context—e.g., minimum efficient scale, market concentration rate, and number of young firms in the industry—matters for whether Gibrat’s law is rejected or not.

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Notes

  1. In this case an abbreviation for “Medium Efficient Size”, but the meaning is the same.

  2. This period is chosen because of data availability.

  3. Gibrat’s law is tested by using the lagged firm size as an independent variable; see Eq. 1. The dependent variables in Eq. 2 are thus identified in terms of the relationship between the size of the firm in period t and t − 1. To alleviate a possible endogeneity problem, since the previous year’s values are predetermined, all independent variables (except industry-age) are therefore included as two period lags in Eq. 2.

  4. To analyze if the results are sensitive to the definition of MES, four other ways of measuring MES were used as well. See Table 4 in the Appendix.

  5. In Manfield’s (1962) renditions, the regressions testing the law used growth rate, not the log-size of the firm, as the dependent variable. In Model I, a growth rate of −100% was attributed to firms that exited. Using Eq. 1 a similar operation is not possible, as this would entail assigning the size 0 to firms that exited. As the log of 0 is impossible, we instead delete firms that exit.

  6. To investigate whether we have a problem with multicollinearity, we employ a correlation analysis that shows small positive or negative correlations between the independent variables. The highest correlation (0.38) was found between GROUP jt−2 and AGE jt .

  7. We have also estimated annual industry-specific regressions for the period 1998–2004. The results—available from the authors upon request—are qualitatively similar, although Gibrat’s law holds for more industries.

  8. As a robustness check, we also perform regressions testing whether Gibrat’s law holds or not at the four-digit industry level. The results are presented in Figs. 3 and 4 in the Appendix. They are very similar to the results from the five-digit level, the only substantial difference being that, when size is measured as number of employees in Model 1, Gibrat’s Law holds less often than at the five-digit level, but still more often than when size is measured by revenue.

  9. Table 5 in the Appendix shows results from the same regression undertaken at the four-digit industry level. In general, they are very similar to the results at the five-digit level. The main exception is the city variable, whose coefficients are never significant at the four-digit level.

  10. The explanatory power increase when time-specific fixed effects are included in the model, indicating that the probability that Gibrat’s law holds is influenced by time-specific heterogeneity. The results are available from the authors upon request.

  11. We also try to omit INDSIZE jt−2 from the estimations. The Pseudo R 2 statistics decreased from about 0.17 to 0.07, but the results were qualitatively similar. The main difference was that MES jt−2 was never significantly determined, whereas UNCERT jt−2 was negative and significant in two regressions. The results are available from the authors upon request.

  12. This result also holds when in a separate set of regressions R&D spending was not weighted for revenue. These results are available from the authors upon request.

  13. Four other ways to measure MES were tested. Although the significance of some of the other coefficients was affected, the signs of the estimated coefficients remained the same. The results are available from the authors upon request.

  14. We also used industry average cash-flow as a measure of industry liquidity. The estimated coefficient had the same sign, but was only significant when only continuing firms were studied and revenues were used as our growth measure.

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Acknowledgments

We would like to thank Daniel Halvarsson, two anonymous referees, and participants at the 2010 Ratio Colloquium for Young Social Scientists for valuable comments.

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Authors and Affiliations

  1. HUI Research AB, 103 29, Stockholm, Sweden

    Sven-Olov Daunfeldt

  2. Department of Economics, Dalarna University, 781 88, Borlänge, Sweden

    Sven-Olov Daunfeldt & Niklas Elert

  3. The Ratio Institute (RATIO), P.O. Box 3203, 103 64, Stockholm, Sweden

    Niklas Elert

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  1. Sven-Olov Daunfeldt
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Correspondence to Sven-Olov Daunfeldt.

Appendix

Appendix

See Tables 4 and 5.

Table 4 Means, standard deviations (SD) and definitions of other MES variables
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Table 5 Estimation results on four-digit level, marginal effects (z-values in parentheses)
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See Figs. 3 and 4.

Fig. 3
figure 3

Model I: results from industry-specific regressions testing Gibrat’s law for all firms in four-digit industries, 1998–2004, with firm size measured by employment and revenue

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Fig. 4
figure 4

Model II: results from industry-specific regressions testing Gibrat’s law for continuing firms in four-digit industries, 1998–2004, with firm size measured by employment and revenue

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Daunfeldt, SO., Elert, N. When is Gibrat’s law a law?. Small Bus Econ 41, 133–147 (2013). https://doi.org/10.1007/s11187-011-9404-x

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