Gibrat’s Law Explained

The infamous Gibrat Law was proposed by Robert Gibrat in 1931. The law states that the proportional rate of growth of a firm is independent of its absolute size. The law is also known by the names- Gibrat’s Rule of Proportionate Growth or The Law of Proportionate Effect.

Gibrat’s law is also applied to city’s size and growth rate, where proportionate growth process may give rise to a distribution of log-normal city sizes as predicted by Gibrat’s law. When considering the entire size distribution, and not merely the largest cities, the city size distribution is log-normal. The log-normality of the distribution reconciles with Gibrat’s law for cities: The law of proportionate effect will therefore imply that the logarithms of the variable will be distributed following the log-normal distribution.

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Origin Of The Law

Robert Gibrat suggested this law of proportionate effect after observing that the size of distribution of French manufacturing establishments closely resembled the log normal distribution. The law predicts that firm growth is a purely random effect and therefore should be independent of the size of the firm. He eventually succeeded in convincing the readers that this was a statistical regularity sufficiently shaped to provide a basis for a grave mathematical modeling.  

Is The Law Globally Valid?

The results of studies testing the validity of Gibrat’s law vary significantly. Some studies reject the law; others confirm it or present mixed results. It was found that in most of the manufacturing sector, Gibrat’s Law fails to hold but for the service sector the law is valid. Additionally, only a few empirical studies have investigated the law in developing countries; most of the studies have been conducted in developed countries. Most of the empirical studies that have been applied in the developed countries rejected the Gibrat’s Law.

It has also been argued that it is problematic to define cities through their fairly arbitrary legal boundaries. It is found that the growth of agglomerations is not consistent with the law: the mean and standard deviation of the growth rates of cities follows a power-law with the city size which has little to do with the Gibrat’s law.

Many researchers have focused on the relationship between firm growth rate and firm size. Some studies accepted the validity of the law and concluded that firm growth was independent of firm size. These studies were focused mostly on large and mature companies, including Buckley, Dunning, and Pearce, Hart and Prais, and Simon and Bonini.

It is clear that the results of studies testing the validity of Gibrat’s law differ. For this reason, some authors have investigated selected determinants that could influence the validity. Daunfeldt and Elert used a large sample of Swedish firms and showed that the validity of the law was industry specific. They showed that the likelihood that the law would be confirmed was greater in mature industries with high market concentration and a large share of group ownership.

Other factors affecting the validity of Gibrat’s law could be profitability performance and financial constraints.

Empirical Testing

Empirical regression model has been able to explain how the growth of the firm is influenced by firm’s age, liquidity ratio and net working capital. The simplicity of Gibrat’s Law has led to waves of studies. Unfortunately they are difficult to compare because the samples used and the methodologies applied differ widely. In the context of our recent studies we tried to set up a new survey of empirical studies. The comparison of empirical studies testing the Law is not always possible in a straightforward manner, since they differ in both the samples used and the methodologies applied.

Mansfield showed that Gilbert’s Law can be empirically tested in three different ways:

  • It can be assumed that it holds for all firms in a given industry, including those which have exited the industry during the period examined. This is carried out by setting the proportionate growth rate of disappearing firms equal to minus 1.
  • The next assumption is that the law only holds for firms that survive over the entire time period. If smaller firms are more likely to exit than their larger counterparts, this empirical test can be affected by a simple selection bias.
  • The third method states that the law only applies to firms large enough to overcome the Minimum Effect Scale (MES) of a given industry.

However, the first method cannot be studied in the case of persistence of growth. It is solely because it is not possible to analyze the persistence of growth for firms that leave the industry during the observation period.

Some critiques believe that Gibrat’s law holds for all the companies owing to the point that the interference phase in the development equation employs a first-order auto regressive process. This reflects that the growth process of the company will take a certain probabilistic approach, that it is possible that a company noticing above average growth in one period, will grow considerably in the following period.