Origins and proportionate effect
In Les inégalités économiques (1931), the French engineer Robert Gibrat sought to explain why economic variables such as firm size and income have distributions with long right tails. He proposed the law of proportionate effect: if each unit grows through a series of random shocks proportional to its current size, the logarithm of size will be normally distributed. In other words, a large firm and a small firm have the same probability of growing or shrinking by 10 percent. Kalecki (1945) pointed out that the variance of such a distribution keeps increasing and proposed a modified model.
Research on firm size distributions
Hart and Prais (1956) analyzed the relationship between Gibrat's law and industrial concentration using British company data, and Simon and Bonini (1958) and Ijiri and Simon (1977) showed that stochastic models with entry of new firms generate highly skewed size distributions close to Zipf's law. Mansfield (1962) found in US industry data that small firms, if they survive, tend to grow faster. Evans (1987) and Hall (1987) likewise reported that firm growth declines with size and age, providing evidence that the strict form of Gibrat's law does not hold among small firms. Jovanovic (1982) explained this with a selection model in which firms learn about their own efficiency and either survive or exit.
Assessment and city growth
In Gibrat's Legacy, Sutton (1997) concluded that the law served as a starting point for industrial organization but that actual firm growth depends heavily on industry structure and competition. Stanley et al. (1996) discovered that the volatility of growth rates declines as a power of firm size. Lotti, Santarelli and Vivarelli (2003) reported that young, small firms do not follow the law at first but converge toward it once established in the market. In urban economics, Eeckhout (2004) found that Gibrat's law broadly holds across all US cities, and Gabaix derived the power law in city sizes from it.
FAQ
- What is Gibrat's law in simple terms?
- It assumes that whether a firm is large or small, the percentage by which it grows next year is drawn from the same odds, regardless of its size.
- Does Gibrat's law actually hold?
- It fits reasonably well among large firms, but many studies find that small, young firms that survive tend to grow faster, so the strict form of the law often fails.
Sources reviewed: 2026-10-26
References
- Gibrat, R. (1931). Les inégalités économiques. Paris: Librairie du Recueil Sirey.
- Kalecki, M. (1945). On the Gibrat distribution. Econometrica, 13(2), 161–170.
- Simon, H. A., & Bonini, C. P. (1958). The size distribution of business firms. American Economic Review, 48(4), 607–617.
- Hart, P. E., & Prais, S. J. (1956). The analysis of business concentration: A statistical approach. Journal of the Royal Statistical Society, Series A, 119(2), 150–191.
- Mansfield, E. (1962). Entry, Gibrat's law, innovation, and the growth of firms. American Economic Review, 52(5), 1023–1051.
- Ijiri, Y., & Simon, H. A. (1977). Skew Distributions and the Sizes of Business Firms. Amsterdam: North-Holland.
- Jovanovic, B. (1982). Selection and the evolution of industry. Econometrica, 50(3), 649–670.
- Evans, D. S. (1987). The relationship between firm growth, size, and age. Journal of Industrial Economics, 35(4), 567–581.
- Hall, B. H. (1987). The relationship between firm size and firm growth in the US manufacturing sector. Journal of Industrial Economics, 35(4), 583–606.
- Sutton, J. (1997). Gibrat's legacy. Journal of Economic Literature, 35(1), 40–59.
- Stanley, M. H. R., et al. (1996). Scaling behaviour in the growth of companies. Nature, 379(6568), 804–806.
- Lotti, F., Santarelli, E., & Vivarelli, M. (2003). Does Gibrat's law hold among young, small firms? Journal of Evolutionary Economics, 13(3), 213–235.
- Eeckhout, J. (2004). Gibrat's law for (all) cities. American Economic Review, 94(5), 1429–1451.