Gibrat's law
Encyclopedia
Gibrat's law, sometimes called Gibrat's rule of proportionate growth is a rule defined by Robert Gibrat (1904-1980) stating that the size of a firm and its growth rate are independent. The law proportionate growth gives rise to a distribution that is log-normal. Gibrat's law is also applied to cities
size and growth rate, where proportionate growth process may give rise to a distribution of city sizes that is lognormal, as predicted by Gibrat's law. While the city size distribution is often associated with Zipf's law, this holds only in the upper tail, because empirically the tail of a lognormal distribution cannot be distinguished from Zipf's law. A study using administrative boundaries (places) to define cities finds that the entire distribution of cities, not just the largest ones, is lognormal .
However, it has been argued
that it is problematic to define cities through their fairly
arbitrary legal boundaries (the places method treats Cambridge and
Boston, USA as two separate units). A clustering method to construct cities from the bottom up by clustering
populated areas obtained from high-resolution data finds a power-law distribution of city size consistent with Zipf's law in almost the entire range of sizes .
Furthermore, the clustering method allows for a direct assessment of Gibrat's law. It is found that
the growth of agglomerations is not consistent with Gibrat's law: the mean and standard deviation of the growth rates of cities follows a power-law with the city size .
In general, processes characterized by Gibrat's law converge to a limiting distribution, which may be log-normal or power law
, depending on more specific assumptions about the stochastic
growth process.
In the study of the firms
(business), the scholars do not agree that the foundation and the outcome of Gibrat's law are empirically correct.
City
A city is a relatively large and permanent settlement. Although there is no agreement on how a city is distinguished from a town within general English language meanings, many cities have a particular administrative, legal, or historical status based on local law.For example, in the U.S...
size and growth rate, where proportionate growth process may give rise to a distribution of city sizes that is lognormal, as predicted by Gibrat's law. While the city size distribution is often associated with Zipf's law, this holds only in the upper tail, because empirically the tail of a lognormal distribution cannot be distinguished from Zipf's law. A study using administrative boundaries (places) to define cities finds that the entire distribution of cities, not just the largest ones, is lognormal .
However, it has been argued
that it is problematic to define cities through their fairly
arbitrary legal boundaries (the places method treats Cambridge and
Boston, USA as two separate units). A clustering method to construct cities from the bottom up by clustering
populated areas obtained from high-resolution data finds a power-law distribution of city size consistent with Zipf's law in almost the entire range of sizes .
Furthermore, the clustering method allows for a direct assessment of Gibrat's law. It is found that
the growth of agglomerations is not consistent with Gibrat's law: the mean and standard deviation of the growth rates of cities follows a power-law with the city size .
In general, processes characterized by Gibrat's law converge to a limiting distribution, which may be log-normal or power law
Power law
A power law is a special kind of mathematical relationship between two quantities. When the frequency of an event varies as a power of some attribute of that event , the frequency is said to follow a power law. For instance, the number of cities having a certain population size is found to vary...
, depending on more specific assumptions about the stochastic
Stochastic
Stochastic refers to systems whose behaviour is intrinsically non-deterministic. A stochastic process is one whose behavior is non-deterministic, in that a system's subsequent state is determined both by the process's predictable actions and by a random element. However, according to M. Kac and E...
growth process.
In the study of the firms
Business
A business is an organization engaged in the trade of goods, services, or both to consumers. Businesses are predominant in capitalist economies, where most of them are privately owned and administered to earn profit to increase the wealth of their owners. Businesses may also be not-for-profit...
(business), the scholars do not agree that the foundation and the outcome of Gibrat's law are empirically correct.