Gibrat's Law Research Articles

Spatial and Temporal Dimensions of Urban Expansion in China.

The scale of urbanization in China during the past three decades is unprecedented in human history, and the processes are poorly understood. Here we present an effort to map the urban land expansion processes of 32 major cities in China from 1978 to 2010 using Landsat satellite data to understand the temporal and spatial characteristics. Results showed that the urban extent of the 32 cities expanded exponentially with very high annual rates varying from 3.2% to 12.8%. Temporal fluctuation in urban expansion rates in these 32 cities was obvious, with unexpected and alarming expansion rates from 2005 to 2010 that drastically exceeded their expectation, which was calculated from the long-term trend between 1978 and 2005, by 45%. Overall, we found that the growth rates of cities during the entire study period were inversely related to city size, contradicting the theory or Gibrat's law, which states that the growth rate is independent of city size. More detailed analysis indicated that city growth in China has transitioned from contradicting to conforming to Gibrat's law since 1995. Our study suggests that the urban expansion theory (i.e., Gibrat's law) does not fit Chinese expansion consistently over time, and the exact causes are unknown. Exploring the causes in future research will improve our understanding of the theory and, more importantly, understand the feasibility of the theoretical relationship between city size and expansion rate in guiding contemporary urban expansion planning.

A Comparative Analysis of Gibrat's and Zipf's Law on Urban Population

The regional economics and geography literature on urban population size has in recent years shown interesting conceptual and methodological contributions on the validity of Gibrat’s Law and Zipf’s Law. Despite distinct modeling features, they express similar fundamental characteristics in an equilibrium situation. Zipf’s law is formalized in a static form, while its associated dynamic process is articulated by Gibrat’s Law. Thus, it is likely that both Zipf’s Law and Gibrat’s Law share a common root. Unfortunately, empirical investigations on the direct relationship between Gibrat’s Law and Zipf’s Law are rather rare and not conclusive.The present paper aims to answer the question whether (a generalisation of) Gibrat’s Law allows us to infer Zipf’s Law, and vice versa? In our conceptual and applied framework, particular attention will be paid to the role of the mean and the variance of city population as key indicators for assessing the (non-) validity of the generalised Gibrat’s Law.Our empirical experiments are based on a comparative analysis between the dynamics of the urban population of four countries with entirely mutually contrasting spatial-economic and geographic characteristics: Botswana, Germany, Hungary and Luxembourg. We arrive at the following results: if (i) the mean is independent of city size (first necessary condition of Gibrat’s law) and (ii) the coefficient of the rank-size rule/Zipf’s Law is different from one, then the variance is dependent on city size.

On the Economic Geography of International Migration

AbstractWe exploit the bilateral and skill dimensions from recent data sets of international migration to test for the existence of Zipf's and Gibrat's laws in the context of aggregate and high‐skilled international immigration and emigration using graphical, parametric and non‐parametric analysis. The top tails of the distributions of aggregate and high‐skilled immigrants and emigrants adhere to a Pareto distribution with an exponent of unity, that is Zipf's law holds. We find some evidence in favour of Gibrat's law holding for immigration stocks, such that the growth in stocks is independent of their initial values and stronger evidence that immigration densities are diverging over time. Conversely, emigrant stocks are converging in the sense that countries with smaller emigrant stocks are growing faster than their larger sovereign counterparts. Lastly, high‐skilled immigration and emigration stocks expressed in levels or as densities all exhibit signs of convergence. We conclude by discussing some competing mechanisms that could be driving the observed patterns including differing fertility rates, reductions in emigration restrictions, migrant sorting and selective immigration policies, immigrant networks and persisting wage differentials.

Gibrat's Law and the Impact of Ownership: A Case Study of Croatia's Hotel Industry

This paper tests the hypothesis that in conditions of economic transition Gibrat's Law of proportionate growth holds, regardless of the type of firm ownership. The hypothesis is tested on a population of Croatian hotel companies, divided into three ownership type groups, operating continuously from 1998 to 2008. The developed dynamic multiple linear regression model of Croatian hotel firms evaluated by the two step Arellano–Bond estimator is used as a basis for analysis. Estimation of model parameters suggests that the dynamics of firms in transition conditions are not just a reflection of random effects, but are also affected by size and ownership factors. The results show that smaller companies grow more rapidly than larger ones and that growth varies depending on firm ownership, with slower growth in state-owned firms.

The Validity of Gibrat's Law: Evidence from the Service Sector in Jordan

Abstract Gibrat's Law or law of proportionate effect (1931) suggested that the growth of the firm is independent of the firm size. This law has been widely studied over the last 40 years until the present time. A lot of studies on Gibrat's Law have been applied in developed countries; however, there is a lack of research on Gibrat's Law in the developing countries. The purpose of this study is to test Gibrat's Law for the service sector in Jordan by using the transition matrix over the period of 2009-2011. Furthermore, the data will be provided by the Department of Statistic, Jordan, using sales as a measurement of firm size.The study rejects Gibrat's Law for the service sector. This means that small firms grow faster than large firm. Consequently, small firms are an important consideration for the policy makers, firm's shareholders and international organizations to create employment in Jordan to solve the problems of unemployment.

On the Economic Geography of International Migration

We exploit the bilateral and skill dimensions from recent data sets of international migration to test for the existence of Zipf's and Gibrat's Laws in the context of aggregate and high-skilled international immigration and emigration using graphical, parametric and non-parametric analysis. The top tails of the distributions of aggregate and high-skilled immigrants and emigrants adhere to a Pareto distribution with an exponent of unity i.e. Zipf's Law holds. We find some evidence in favour of Gibrat's Law holding for immigration stocks, i.e. that the growth in stocks is independent of their initial values and stronger evidence that immigration densities are diverging over time. Conversely, emigrant stocks are converging in the sense that countries with smaller emigrant stocks are growing faster than their larger sovereign counterparts. Lastly, high skilled immigration and emigration stocks expressed in levels or as densities all exhibit signs of convergence. We conclude by discussing some competing mechanisms that could be driving the observed patterns including: differing fertility rates, reductions in emigration restrictions, migrant sorting and selective immigration policies, immigrant networks and persisting wage differentials.

The Role of Science Parks: A Puzzle of Growth, Innovation and R&D Investments

This paper investigates the impact of Science Parks on growth and innovativeness of affiliated firms. Both the role and the effectiveness of these policy instruments in sustaining tenants’ performances are still open issues. We rely on unique Italian data and compare the performance of firms located within a park with a control sample of off-park firms. Firstly, we focus on the estimation of the treatment effect of being located within the park. Our results show a significant difference between on and off park firms with respect to their innovativeness and propensity to invest in RD to the contrary, firms’ growth appears unaffected by location effects. Secondly, we analyse what features of Science Parks drive the impact on the diverse measures of performance. Our main finding is that both patenting activity and R&D investments are actively sustained by the presence and quantity of research centres located within the park. Growth remains a largely unexplained phenomenon and Gibrat law is found to hold robustly within the class of on-park firms.

The Matthew effect in economics reconsidered

Abstract We apply the test of Ijiri and Simon (1974) to a large data set of authors in economics. This test has been used by Tol, 2009 , Tol, 2013a to identify a (within-author) Matthew effect for authors based on citations. We show that the test is quite sensitive to its underlying assumptions and identifies too often a potential Matthew effect. We propose an alternative test based on the pure form of Gibrat's law. It states that stochastic proportionate citation growth, i.e. independent of its size, leads to a lognormal distribution. By using a one-sided Kolmogorov–Smirnov test we test for deviations from the lognormal distribution which we interpret as an indication of the Matthew effect. Using our large data set we also explore potential empirical characteristics of economists with a Matthew effect.

Profitability and Firm Size–Growth Relationship in Construction Companies in Malaysia From 2003 to 2010

In this study, we intended to examine empirically how a firm's profitability performance would impact its growth process and the inference for Gibrat's Law. The basic study looks at small, medium and large firms' tendency to grow when their internally generated profits are high. The sample is 124 construction companies listed from years 2003 to 2010 at BURSA Malaysia. Data used is secondary data collected from BURSA Malaysia and annual reports. The result indicated that "growth" contributed significantly to profitability in both small and medium-sized construction companies, but was not significant in large companies. Thus, hypothesis two was supported. This study supports Gibrat's Law, showing that size and growth rate are independent.

How do online social networks grow?

Online social networks such as Facebook, Twitter and Gowalla allow people to communicate and interact across borders. In past years online social networks have become increasingly important for studying the behavior of individuals, group formation, and the emergence of online societies. Here we focus on the characterization of the average growth of online social networks and try to understand which are possible processes behind seemingly long-range temporal correlated collective behavior. In agreement with recent findings, but in contrast to Gibrat's law of proportionate growth, we find scaling in the average growth rate and its standard deviation. In contrast, Renren and Twitter deviate, however, in certain important aspects significantly from those found in many social and economic systems. Whereas independent methods suggest no significance for temporally long-range correlated behavior for Renren and Twitter, a scaling analysis of the standard deviation does suggest long-range temporal correlated growth in Gowalla. However, we demonstrate that seemingly long-range temporal correlations in the growth of online social networks, such as in Gowalla, can be explained by a decomposition into temporally and spatially independent growth processes with a large variety of entry rates. Our analysis thus suggests that temporally or spatially correlated behavior does not play a major role in the growth of online social networks.

Origin of Gibrat law in Internet: asymmetric distribution of the correlation.

Although Gibrat's law and its generalized versions have been widely used, the organizing principle behind its phenomenological theory has been poorly studied for network-structured systems. More important, its fluctuation behavior, which contradicts the prediction of the preferential attachment (PA), indicates a nontrivial mechanism that goes beyond our present knowledge based on the traditional mean-field approach. Here, we take advantage of the rich data of the Internet and aim to identify the origin of Gibrat's law by studying the empirical fluctuation behavior. We show how the correlation between the fluctuations of the node degree increment affects the dynamics of the network. Specifically, if the distribution of the correlation is symmetric, the network evolves as the classical PA, while if such symmetry breaks, the fluctuation becomes macroscopically positively correlated and contributes to the emergence of Gibrat's law. These results indicate a local collective increase in the actual network evolution, which provides a new paradigm and understanding of the related microcosmic dynamics.

LEY DE ZIPF Y DE GIBRAT PARA COLOMBIA Y SUS REGIONES: 1835-2005

RESUMENEn este documento se analiza la jerarquía urbana de Colombia y sus regiones utilizando información censal de entre 1835 y 2005. Se estudian tres aspectos: 1) la distribución del tamaño poblacional a través de las regularidades empíricas de Zipf y de Gibrat; 2) el cambio en el modelo de crecimiento poblacional, y 3) la validación empírica sobre la coincidencia de la dinámica poblacional para un país y sus regiones. Haciendo uso de la relación rango-tamaño y de técnicas no paramétricas, se encuentra coincidencia nacional y regional desde 1964 del cumplimiento de la ley de Zipf y parcialmente de la ley de Gibrat, lo cual evidencia un cambio en el modelo de crecimiento poblacional desde mediados del siglo XX en los ámbitos nacional y regional.

The Validity of Gibrat's Law in Developed and Developing Countries (2008–2013): Comparison based Assessment

The Gibrat's Law of Proportionate Effect, indicated that the growth rate of a given firm is independent of its size at the beginning of the examined period. While earlier studies tended to confirm the Law, more recent research generally rejects it. This paper aims to highlight important empirical studies that performed analysis of Gibrat's Law in which about 50 papers were taken into account for this study. The main objective of this paper is to investigate the validity of Gibrat's Law in developing countries based in developed countries. In this paper the literature on Gibrat's Law was reviewed based on three types of empirical results: the first type accepts Gibrat's Law, the second type rejects Gibrat's Law, and the third classification reconciles both acceptance and rejection of Gibrat's Law. It was found that in most of the manufacturing sector, Gibrat's Law fails to hold but for the service sector Gibrat's law was valid. Additionally, only a few empirical studies have investigated Gibrat's law in developing countries; most of the studies have been conducted in developed countries. Furthermore, most of the empirical studies that have been applied in the developed countries rejected the Gibrat's Law. Finally, based on the features of SMEs that it's a labour intensive, and has the ability to absorb a lot of labour due to the low cost of creating job opportunities for both developed and developing countries. From this overview, it can be deduced that it is possible to implement the law for developing countries, which in turn could probably have the same result that the Gibrat's Law is not valid as smaller firms tend to grow faster than larger firms.

Zipf’s Law and the Gibrat’s Law: What Do the Facts Have to Say about the Brazilian Cities?

Despite attempts to relate the economic theory with the statistical data, the theory is usually sufficiently clear, supplying simple and well-defined forecasts, whilst the real world tends to produce complicated and disorganized results. However, with reference to models on the distribution of city sizes the inverse occurs. That is; the data, surprisingly offers a sufficiently clear picture with high degrees of difficulty of being reproduced theoretically. This work aims at verifying whether two of the most well known and intriguing phenomena, Zipf's Law and Gibrat's Law, occur in Brazil, and also to make a theoretical analysis of such phenomena. The study uses the Brazilian demographic census data of 1970, 1980, 1991 and 2000 and the 1996 population counting. The results confirm that these empirical regularities indeed occur in the distribution of the Brazilian cities.

경기지역 IT산업의 대·중소기업간 성장성 분석

2008년 글로벌금융위기 이후 더욱 심화된 기업간 양극화 문제의 해소와 관련하여 현재 대중소기업간 동반성장의 필요성이 그 어느 때보다 크게 대두되고 있다. 이에 본고는 KISVALUE를 통해 517개(대기업 80개, 중소기업 437개) 경기지역 소재 IT기업의 15년(1996~2010년)간의 기업패널 자료를 구축하고 pooled OLS 기법을 이용하여 Gibrat 법칙 및 Jovanovich 가설의 성립여부에 대한 엄밀한 분석을 시도하였다. 실증분석 결과, 기업의 규모를 대리하는 추정계수 값이 1보다 작게 나타나 기업의 규모와 성장률간에는 상관관계가 없다는 Gibrat법칙은 성립하지 않는 것으로 나타났다. 반면, 기업의 업력을 대리하는 추정계수 값이 유의하게 음(-)의 값을 나타내고 있어 기업의 업력과 성장률간에는 역의 상관관계가 있다는 Jovanovic 가설은 성립하는 것으로 나타났다. 이상의 분석결과는 대체로 기업의 업력이 짧은 중소기업은 업력이 긴 대기업보다 성장률이 높을 수 있음을 의미하고, 또한 수출 및 기술혁신 지향적인 기업일수록 기업의 성장률이 높은 것으로 나타났다. The necessity for co-prosperity between large and small businesses has emerged as a top policy priority as economic polarization has been exacerbated since the 2008 global financial crisis. Against this background this paper makes a detailed analysis of differences between SMEs (Small and Medium sized businesses) and large enterprises located in Gyeong-do, in respect of growth. The data set used in the analysis is the 15 year(1996-2010) panel data of IT companies (large enterprises: 80 data and SMEs: 437 data) collected from the KISVALUE database. The estimation results of Pooled OLS indicate that the coefficients representing corporate size are less than 1, which implies that the Gibrat's law, no correlation between the size of a firm and its growth rate, is not supported by the data. In the meantime, the estimated coefficients representing corporate age are negative, which implies that Jovanovic hypothesis, inverse correlation between the age and the growth rate of a firm, is consistent with the data. In short, SMEs, which are generally younger than big enterprises can achieve higher growth rate than the latter ones which are usually believed to be older. In addition, the more export- and innovation-oriented the firm, the higher its growth rates.

Evolutionary Model of the City Size Distribution

An evolutionary model of the city size distribution is presented that explains the size of a city from the reproduction process and the migration of humans between cities. The model suggests that the city size distribution is a lognormal distribution with a power law tail in agreement with empirical results and computer simulations. The main idea of the model is that the competition between cities in the migration process is the origin of Gibrat's law. While growth rate fluctuations generate the lognormal branch of the size distribution, the power law tail for large cities is caused by a small mean growth rate.

Non-Gaussian behavior of the internet topological fluctuations

The traditional Gibrat's hypotheses were once used to model the topological fluctuations of Internet. Although it seems to reproduce the scaling relation of Internet's degree distribution, the detailed micro-dynamics have never been empirically validated. Here, we analyze the distribution of degree growth rates of the Internet for various time scales. We find that in contrast to the traditional Gibrat's assumptions, none of the degree growth rates are normally distributed, but behaves as an exponential decrease on its body and a power-law decay on its tail. Moreover, the observed growth rate distribution turns out independent of the initial degree when the time interval enlarges to a year. Our observations do not consist with the traditional Gibrat law model and suggest a more complex fluctuation mechanism underlying the evolution of Internet.

Spatially Distributed Social Complex Networks

We propose a bare-bones stochastic model that takes into account both the geographical distribution of people within a country and their complex network of connections. The model, which is designed to give rise to a scale-free network of social connections and to visually resemble the geographical spread seen in satellite pictures of the Earth at night, gives rise to a power-law distribution for the ranking of cities by population size (but for the largest cities) and reflects the notion that highly connected individuals tend to live in highly populated areas. It also yields some interesting insights regarding Gibrat's law for the rates of city growth (by population size), in partial support of the findings in a recent analysis of real data [Rozenfeld et al., Proc. Natl. Acad. Sci. U.S.A. 105, 18702 (2008)]. The model produces a nontrivial relation between city population and city population density and a superlinear relationship between social connectivity and city population, both of which seem quite in line with real data.

Firm size and growth in Sweden's life insurance market between 1855 and 1947: A test of Gibrat's law

Using data for the period from 1855 to 1947 and the two sub-periods, 1855–1902 and 1903–47, the article examines whether the organic growth rates of 38 Swedish life insurance firms are independent of size, as predicted by Gibrat's (1931) Law of Proportionate Effects. Using panel unit root tests and panel Generalised Method of Moments (GMM) regression, the article finds a significant difference between the growth rates of small and large Swedish life insurance firms (with smaller firms tending to grow faster than larger firms), a result that clearly contradicts Gibrat's Law as a long-run tendency in the Swedish life insurance sector. significant influences were also found on firm growth from profitability, organisational form, reinsurance, the real rate of interest and the Swedish regulatory environment.

Limited Urban Growth: London's Street Network Dynamics since the 18th Century

We investigate the growth dynamics of Greater London defined by the administrative boundary of the Greater London Authority, based on the evolution of its street network during the last two centuries. This is done by employing a unique dataset, consisting of the planar graph representation of nine time slices of Greater London's road network spanning 224 years, from 1786 to 2010. Within this time-frame, we address the concept of the metropolitan area or city in physical terms, in that urban evolution reveals observable transitions in the distribution of relevant geometrical properties. Given that London has a hard boundary enforced by its long standing green belt, we show that its street network dynamics can be described as a fractal space-filling phenomena up to a capacitated limit, whence its growth can be predicted with a striking level of accuracy. This observation is confirmed by the analytical calculation of key topological properties of the planar graph, such as the topological growth of the network and its average connectivity. This study thus represents an example of a strong violation of Gibrat's law. In particular, we are able to show analytically how London evolves from a more loop-like structure, typical of planned cities, toward a more tree-like structure, typical of self-organized cities. These observations are relevant to the discourse on sustainable urban planning with respect to the control of urban sprawl in many large cities which have developed under the conditions of spatial constraints imposed by green belts and hard urban boundaries.