Gibrat's Law about Firm Size
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Gibrat's law
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.[1] The law of proportionate growth gives rise to a distribution that is log-normal.[2] 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 log-normal, 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 log-normal 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 log-normal.[3]
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, Massachusetts, 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.[4] Note that populated areas are still aggregated rather than individual based. A new method based on individual street nodes for the clustering process leads to the concept of natural cities. It has been found that natural cities exhibit a striking Zipf's law [5] 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.[6]
In general, processes characterized by Gibrat's law converge to a limiting distribution, which may be log-normal or power law, depending
Gibrat's law
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.[1] The law of proportionate growth gives rise to a distribution that is log-normal.[2] 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 log-normal, 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 log-normal 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 log-normal.[3]
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, Massachusetts, 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.[4] Note that populated areas are still aggregated rather than individual based. A new method based on individual street nodes for the clustering process leads to the concept of natural cities. It has been found that natural cities exhibit a striking Zipf's law [5] 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.[6]
In general, processes characterized by Gibrat's law converge to a limiting distribution, which may be log-normal or power law, depending