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Generalising Gibrat: using Chinese evidence founded on fieldwork

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Abstract

This paper reports on determinants of small firm growth and survival, using fieldwork evidence collected by face-to-face and telephone interviews. It extends the ‘basic’ size-age model to a ‘comprehensive’ growth model with two types of additional explanatory variables: firm specific and business environmental. Estimation is by log-linear regression on Chinese cross-section data, with corrections for sample selection bias and heteroskedasticity. Our results from the comprehensive model highlight the importance of location choice and customer orientation for the growth of Chinese private firms.

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Notes

  1. It should be noted that some of these studies—like Farinas and Moreno (2000), Audtretsch et al. (2004)—implied this negative relationship between growth and size was subject to certain conditions e.g. size, survival, age, sector.

  2. This is sensitive to how growth is defined. For example, in Heshmati (2001), Gibrat’s Law holds if the growth variable is defined by employment, yet fails if it is defined by sales.

  3. In terms of Eq. 3, it would imply that β becomes closer to unity, as size increases. In the limit, when β = 1, the Gibrat Law holds.

  4. These were students and faculty, in international business and finance, at the Guangdong University of Foreign Studies. They were trained by one of the co-authors, who also prototyped the instrumentation, and participated in the fieldwork, including bench-testing the instrumentation in pilot interviews.

  5. For instance, the employment growth rate is defined as [ln(employment2006) − ln(employment2004)]/1.5. The time interval between our two interviews was approximated as 1.5 years.

  6. We did not have sufficiently detailed data to compute full time equivalent workers, or to use hours worked as a measure of labour input or effort.

  7. In the sense of the industrial, commercial and business environment.

  8. Inspired by Kalecki (1945) and popularised by Klein (1962).

  9. This equation lends itself to a convenient phase-space representation, with S t as ordinate and S t−1 as abscissa, and 0 < β < 1 being a stable equilibrium condition. The closer β is to unity, the closer is the model to Gibrat’s Law, until for β = 1, Gibrat’s Law is satisfied, cf. Reid (2007, Chap. 16).

  10. This involves evaluating the ratio of the normal density function to the cumulative normal density function.

  11. Finally, using the Expectation–Prediction matrix for the probit of Table 2, the % Correct is as high as 96.92% and the Percent Gain from default (constant probability) specification reaches the level of 66.67%, which suggests that the specification of the selection model is statistically satisfactory. See Yi (2002) on diagnostic interpretation.

  12. In general, the IMR is computed as φ(Zγ )/Φ(Zγ) for y = 1, and the same expression minus unity for y = 0, where φ is the normal pdf and Φ is the normal pdf, from the probit y = Zγ + ν.

  13. The variance inflation factor (VIF) for the i’th regressor X i is 1/(1 − R 2 i ), where i = 1, 2,…, K. When X i is highly correlated with the remaining regressors, its variance inflation factor will be very large. When X j is orthogonal to the remaining regressors, its variance inflation factor will be 1.

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Acknowledgments

This study would not have been possible without grants from the Russell Trust (University of St Andrews, UK) and from the Young Teacher Research Fellowship (Guangdong University of Foreign Studies, China), for which we express thanks. Earlier versions of this material have been presented to the School of Economics & Finance, University of St Andrews, the Scottish Economic Society Annual Conference, Perth, and the European Economic Association Annual Conference, Glasgow University. We express thanks for the feedback provided by numerous conference and seminar participants on these occasions. Specifically, the work has benefited from the comments of Paul Hare, Klaus Beckmann, Felix FitzRoy, Julia Smith, Tobias Wentzel, Federico Tamagni, and Alessandra Guariglia, to all of whom we are especially grateful. The Editor and the referees are also thanked for detailed and constructive comment and guidance. However, the authors accept full responsibility for the paper, and for any errors of omission or commission it may yet contain.

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  1. CRIEFF, School of Economics & Finance, St. Salvator’s College, University of St. Andrews, St. Andrews, Fife, KY16 9AL, Scotland, UK

    Gavin C. Reid & Zhibin Xu

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  1. Gavin C. Reid
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Correspondence to Gavin C. Reid.

Appendix

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Table 5 Definition of variables used in main text
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Reid, G.C., Xu, Z. Generalising Gibrat: using Chinese evidence founded on fieldwork. Small Bus Econ 39, 1017–1028 (2012). https://doi.org/10.1007/s11187-011-9338-3

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