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We take advantage of a new data set on Belgian cities to test random growth, that is, Gibrat’s law. This unique data set provides annual population estimates for all Belgian municipalities (2680 cities) from 1880 to 1970. The use of panel data methodology and unit root tests can provide a precise test of Gibrat’s law (a unit root is equivalent to random growth). We run both time series and panel data unit root tests, thus obtaining strong support for random growth in the long term. Results hold when allowing for the presence of one and two structural breaks in the mean, with the timing of the breaks coinciding with some major historical events, such as the World Wars and the economic crisis of 1929–1933.

Populations are affected by shocks of different kinds, and wars, a priori, may be among the most prominent. This article studies the effect of the Spanish Civil War (1936–1939) shock on the distribution of population, especially on cities. One of the main contributions of this study is that it underlines the importance of distinguishing between winning and losing sides, an aspect which until now has been largely overlooked. While previous research on war shocks has also tended to be concerned with inter-state wars, this paper concentrates on a civil war. We take advantage of a new, long-term, annual data set. Our results show that, overall, the Spanish Civil War did not have a significant effect on city growth. However, we also find a significant and negative effect in the growth of cities that aligned themselves with the losing side. These results are robust to heterogeneity in the effect of the war shock, measured as war severity and duration. Although short lived, the temporary effect on growth results in a permanent effect on the size of cities on the losing side.

This paper discusses parametric, nonparametric, and semiparametric models of urban growth. To illustrate differences across approaches, we test Gibrat's law in the long run, using the three methods and three different datasets: Spanish capital cities and regions (1900–2011, annual data) and US MSAs (1900–2000, decennial data). Our results reveal that the estimation of the relationship between growth and initial size can significantly vary across methods. We suggest and encourage the use of semiparametric methods in future research of urban growth.

This paper examines the effect of the Spanish Civil War (1936–1939) shock on city shares of population applying the methodology proposed by Davis, D. R., and D. E. Weinstein. 2002. “Bones, Bombs, and Break Points: The Geography of Economic Activity.” The American Economic Review 92 (5): 1269–89. We make use of an unexploited long-term, historical dataset of populations disaggregated at the city level. Our instruments, a key methodological issue, are based on dead and wounded data collected by historians. We show that the effect of the Spanish Civil War on capital cities was temporary, and argue that the locational fundamentals theory is the principal explanation.

There was an unprecedented wave of foreclosures and evictions in Spain after the 2008 global financial crisis. The subsequent Great Recession had strong economic, social and environmental consequences. This paper explores the frequency of permanent shocks in foreclosure quarterly rates (defined as the number of judicial foreclosures per 1000 inhabitants) for 50 Spanish provinces (NUTS 3 regions) during the period from 2001 (Q1) to 2019 (Q4) using time series analysis. We examine whether the foreclosure rate is a stationary series, exhibits a unit root or is stationary around a process subject to structural breaks. A clear finding from this analysis is that not all shocks have transitory effects on the foreclosure rate. The percentage of unit root rejections is around 40%, thus, providing the evidence of both stationarity around occasional shocks that have permanent effects, and of a unit root, where all shocks have a permanent effect on the foreclosure rate. We also test for unit roots allowing for the presence of one and two structural breaks. Most of the structural breaks are positive, and the majority are grouped from 2008 onwards, coinciding with the financial crisis and the subsequent collapse of the Spanish housing bubble. We also find a later decrease in foreclosures in some regions that can be related to the effectiveness of the Code of Good Practice for banks and financial institutions approved in 2012. Nevertheless, the level of the foreclosure rate time series has not returned to the pre-2008 level in any case.

We examine the effects of the legal reform passed in 2012 in Spain to protect mortgage debtors. Under the new regime, it is difficult for low-income debtors who meet certain requirements to be evic...

Long-term population estimates are usually based on decennial (or roughly decennial), census-type data, especially those that go beyond the aggregate or national level. The lack of annual population datasets, however, restricts the range of analysis and therefore our knowledge of populations’ behaviour over time. This paper contributes to this scant literature by providing two new long-term, annually and spatially disaggregated population estimates for Spain, a key case study. We use a set of official sources and propose a straightforward method to estimate Spanish annual populations at two levels of spatial disaggregation, the provinces (NUTS III) and their capital cities (a selection of LAU II/NUTS V), between 1900 and 2011. For the cities, our estimates account for changes in boundaries. Our proposed method is especially suitable for countries with a lack of long-term, systematic, historical migration statistics, a common issue. To test the robustness of our estimates, some comparisons are made with previous more aggregated-level or decennial census-based estimates, and a preliminary analysis of the evolution of disaggregated Spanish population is presented.

This paper investigates the determinants of the diffusion and intensity of the COVID-19 at the country level, focusing on the role played by urban agglomeration, measured using three urban variables: percentage of the urban population, population density, and primacy. We estimate the influence of urban agglomeration on two outcome variables: cumulative number of cases and deaths per 100, 000 inhabitants up to 31 December 2020, using both parametric and semiparametric models. We also explore possible spatial effects. The non-linear effects of the urban variables on the intensity of the disease reveal non-monotonous relationships, suggesting that it is the size of the urban system that is linked to a stronger incidence.

The aim of this study is to examine the link between house prices and marriage in Spain. We consider data from 50 Spanish provinces (NUTS III regions) and from local civil registries in 282 cities with populations greater than 25, 000 inhabitants. The regional data cover the 1995–2018 period, whereas the local sample includes information from 2005 to 2018. The marriage rate is defined as the annual absolute number of marriages per thousand inhabitants in each region or city. We used data on Spain because the Spanish housing market experienced a strong rise in house prices until 2006, when the housing bubble ended and prices dramatically decreased. By using different econometric techniques (panel data models with fixed effects and dynamic panel data models), our results reveal that there is a significant negative relationship between house prices and the marriage rate at both the regional and local levels. Overall, this study highlights the important consequences of rising house prices on family formations. Therefore, public authorities should try to reduce fluctuations in house prices and to facilitate access to home ownership for young couples. © 2022 by the author. Licensee MDPI, Basel, Switzerland.

This paper studies the impact on reported coronavirus 2019 (COVID-19) cases and deaths in Spain resulting from large mass gatherings that occurred from March 6 to March 8, 2020. To study these outcomes, the geographic differences in the planned pre-pandemic major events that took place on these dates were exploited, which is a quasi-random source of variation for identification purposes. We collected daily and detailed information about the number of attendees at football (soccer) and basketball matches in addition to individuals participating in the Women''s Day marches across Spain, which we merged with daily data on reported COVID-19 cases and deaths at the provincial level. Our results reveal evidence of non-negligible COVID-19 cases related to the differences in the percentage of attendees at these major events from March 6 to March 8. In a typical province, approximately 31% of the average daily reported COVID-19 cases per 100, 000 inhabitants between mid-March and early April 2020 can be explained by the participation rate in those major events. A back-of-the-envelope calculation suggests that this implies almost five million euros (169, 000 euros/day) of additional economic cost in the health system of a typical province with one million inhabitants in the period under consideration. Several mechanisms behind the spread of COVID-19 are also examined.

This paper analyses the long‐term relationship between regional inequality and economic development. Our data set includes information on national and regional per capita GDP for four countries: France, Italy, Portugal and Spain, compiled on a decadal basis for the period 1860–2010. Using parametric and semiparametric regressions, our results confirm the rise and fall of regional inequalities over time although in recent decades they are on the rise again. Finally, we identify structural change as being a significant transmission mechanism of the inverted‐U relationship. The arrival of technological shocks, beginning during the onset of industrialization, and the transition from agrarian to industrial economies, would explain this result. Este articulo analiza la relacion a largo plazo entre la desigualdad regional y el desarrollo economico. El conjunto de datos utilizado incluye informacion sobre el PIB per capita nacional y regional de cuatro paises: Francia, Italia, Portugal y Espana, compilados por decenios para el periodo 1860‐2010. Mediante el uso de regresiones parametricas y semiparametricas, los resultados confirman el aumento y la disminucion de las desigualdades regionales a lo largo del tiempo, aunque en las ultimas decadas han vuelto a aumentar. Finalmente, se identifica el cambio estructural como un mecanismo significativo de transmision de la relacion de U invertida. La llegada de las perturbaciones tecnologicas, que comenzo a partir del inicio de la industrializacion, y la transicion de las economias agrarias a las industriales, explicarian este resultado. 本稿では地域の不公平と経済発展の長期的な関連性を分析する。今回使用するデータセットには、1860~2010年までの10年単位でまとめた、フランス、イタリア、ポルトガル、スペイン、以上の4カ国の、全国および地方の一人あたりGDPに関する情報を含んでいる。パラメトリック回帰分析およびセミパラメトリック回帰分析を行った結果から、地域の不公平は経時的に上昇、また下降しており、最近の10年単位では上昇していることが確認された。最終的には、構造的な変化が、著明な逆U字の関連性を示すトランスミッション・メカニズムとして確認された。この結果は、産業革命の始まりにおける技術的ショックの到来と農耕社会から産業経済への移行によって説明される。

In this paper, we consider the distribution of bilateral distances between all pairs of cities to estimate K-densities using the methodology by Duranton and Overman (2005), identifying different spatial patterns. By using data from different definitions of US cities in 2010 (places, urban areas, and core-based statistical areas), we analyse the spatial distribution of cities, finding significant patterns of dispersion depending on the city size and city definition. Our results lend support to a hierarchical system of US cities in which the central cities of each subsystem are far away from each other.

This paper analyses whether the size distribution of nearby cities is lognormally distributed by using a distance-based approach. We use data from three different definitions of US cities in 2010, considering all possible combinations of cities within a 300-mile radius. The results indicate that support for the lognormal distribution decreases with distance, although the lognormal distribution cannot be rejected in most of the cases for distances below 100 miles.

This paper analyses the probability distribution of worldwide forest areas. We find moderate support for a Pareto-type distribution (power law) using FAO data from 1990 to 2015. Power laws are common features of many complex systems in nature. A power law is a plausible model for the world probability distribution of forest areas in all examined years, although the log-normal distribution is a plausible alternative model that cannot be rejected. The random growth of forest areas could generate a power law or log-normal distribution. We study the change in forest coverage using parametric and non-parametric methods. We identified a slight convergence of forest areas over the time reviewed, however, random forest area growth cannot be rejected for most of the distribution of forest areas. Therefore, our results give support to theoretical models of stochastic forest growth.

This paper focuses on spatial city-size distribution in the United States. It proposes a new distance-based approach to analyze the influence of distance on the city-size distribution parameter by considering the Pareto distribution and using data from different definitions of US cities in 2010. Considering all possible combinations of cities within a 300-mile radius, the results indicate that the Pareto distribution cannot be rejected in most cases regardless of city size. Placebo regressions validate the results, thereby confirming the significant effect of geography on the Pareto exponent.

In this paper, we study the evolution of US divorce rates across states, from 1956 to 1998. Using a cluster algorithm, we identify different groups of states that converge on each other in the evolution of their divorce rates. We find strong empirical support for the club classification. For the whole 1956–1998 period, we find evidence of convergence in divorce rates for the majority of the states, but when we split the sample, a different pattern emerges. In the pre-unilateral divorce reform period (1956–1972), we find that most of the states had converging divorce rates within several convergence clubs, but the club classification of states significantly changed in the post-reform period (1973–1998). Finally, we analyze the explanatory factors of the club classification of states in both sub-periods, using geographical, socio-economic, and demographic variables.

We develop a theoretical model that provides an additional explanation for the forest transition based on a trade liberalization scenario. We introduce a renewable natural resource (wood), used as an input by manufacturing firms, in a framework with economic geography foundations: transport costs affect the spatial distribution of firms. In a general equilibrium, the results reproduce the forest transition at a global scale: a decrease in transport costs has an initial negative effect on the worldwide stock of the natural resource, but this effect is offset over time as a consequence of industrial reallocation and eventually disappears in the long run.

This paper analyses the evolution of the European urban system from a long-term perspective (from 1300 to 1800). Using the method recently proposed by Clauset, Shalizi, and Newman (2009), a Pareto-type city size distribution (power law) is rejected from 1300 to 1600. A power law is a plausible model for the city size distribution only in 1700 and 1800, although the log-normal distribution is another plausible alternative model that we cannot reject. Moreover, the random growth of cities is rejected using parametric and non-parametric methods. The results reveal a clear pattern of convergent growth in all the periods.

In this paper, we analyze the effects of productive specialization and productive diversity on employment growth at the local level during the Great Recession in Aragon, a NUTS II region in Spain. This region is characterized by (i) a high population density in the capital city (around half of the total population), giving rise to a very uneven population distribution and therefore a lot of small cities and municipalities, and (ii) a large proportion of small businesses (95% of the firms in this region have fewer than ten employees). We use annual data from 2000 to 2015 and panel data models, and grouped local business activities into three main categories: industry, construction and services. Our results show that, during this period, local specialization in any of these activities hurt local employment growth, whereas diversity had a non-significant effect on employment growth. Only in the case of services did we obtain a positive effect of diversity on local employment growth, which was restricted to the most populated cities (i.e., cities with more than 3000 inhabitants). Therefore, only diversity in services activities located in large cities contributed to employment growth during the Great Recession.

In this paper we discuss the relationship between economic growth and natural resources at a global level, taking into account geography. With this aim, our model integrates elements of the theories of endogenous growth, natural resources and new economic geography. We find that an increase in the world growth rate can lead to a higher depletion of the natural resources following an increase in the world demand due to expansion in population. However, the consideration of geography and growth mechanisms make the relationship between growth and natural resources more complex, and can even lead to the opposite conclusion when the forces behind growth are different from world demand. Indeed, either a reduction in transport costs or an increase in R&D productivity appears to be able to generate a faster growth compatible with a lower depletion of natural resources.

This paper analyses the statistical distribution of war sizes. Using a new methodology we find moderate support for a Pareto-type distribution (power law), considering data from different sources (COW and UCDP) and periods. A power law is a plausible model for the size distribution of a pool of all wars and a sample of wars in many years, although the log-normal distribution is a plausible alternative model that we cannot reject. The random growth of conflicts could generate both types of distribution. We study the growth rates of battle deaths and random growth cannot be rejected for most of the distribution, although the results also reveal a clear decreasing pattern; the growth of deaths declines faster if the number of initial deaths is greater.

In this paper, we employ parametric and nonparametric techniques to analyse the effect of market potential on the structure and growth of Spanish cities during the period 1860-1960. Even though a few attempts have been made to analyse whether market potential might influence urban structures, this period is especially interesting because it is characterised by advances in the economic integration of the national market together with an intense process of industrialisation. By using an elaborated measure of market potential at the city level, our results show a positive influence of this market potential on city growth, although this influence is heterogeneous over time. Only changes in the market potential from 1900 have a significant effect on population growth.

We study the US city size distribution over space. This paper makes two contributions to the empirical literature on city size distributions. First, this study uses data from different definitions of US cities in 2010 to study the distribution of cities in space, finding significant patterns of dispersion depending on city size. Second, the paper proposes a new distance-based approach to analyse the influence of distance on the city size distribution parameters, considering both the Pareto and lognormal distributions. By using all possible combinations of cities within a 300-mile radius, results indicate that the Pareto distribution cannot be rejected in most of the cases regardless of city size. Placebo regressions validate our results, thereby confirming the significant effect of geography on the Pareto exponent.

This paper analyses the growth of American cities, understood as the growth of the population or of the per capita income, from 1990 to 2000. This empirical analysis uses data from all the cities (incorporated places) with more than 25,000 inhabitants in the year 2000 (1,152 cities). The results show that while common convergence behaviour is observed in both population and per capita income growth, there are differences in the evolution of the distributions: the population distribution remains almost unchanged, while the per capita income distribution makes a great movement to the right. We use two different methodologies to test cross-sectional convergence across cities: linear growth models (allowing for spatial spillovers between locations) and spatial quantile regressions. We find evidence of significant spatial effects and nonlinear behaviour.

This article analyses the performance of the graphs traditionally used to study size distributions: histograms, Zipf plots (double logarithmic graphs of rank compared to size) and plotted cumulative density functions. A lognormal distribution is fitted to urban data from three countries (the United States, Spain and Italy) over all of the twentieth century. We explain the advantages and disadvantages associated with these graphic methods and derive some statistical properties.

This paper analyses the evolution of the European urban system from a long-term perspective (from 1300 to 1800) considering the historical data set of Bairoch et al. (1988). Using the method recently proposed by Clauset et al. (2009), a Pareto-type city size distribution (power law) is rejected from 1300 to 1600. A power law is a plausible model for the city size distribution only in 1700 and 1800, although the log-normal distribution is another plausible alternative model that we cannot reject. Moreover, random growth of cities is rejected using parametric and non-parametric methods. The results reveal a clear pattern of convergent growth in all periods.

This paper explores the frequency of permanent shocks in divorce rates for 16 European countries during the period 1930–2006. We examine whether the divorce rate is a stationary series, exhibits a unit root, or is stationary around a process subject to structural breaks. A clear finding from this analysis is that not all shocks have transitory effects on the divorce rate. Our results provide evidence of both stationarity around occasional shocks that have permanent effects, and of a unit root, where all shocks have a permanent effect on the divorce rate. All of the permanent shocks are positive, and most are grouped in the 1970s. These shocks can be related to major events that occurred throughout Europe at that time: the divorce law reforms, suggesting that those policies play an important role in the movement of European divorce rates.

This paper explores the response of the divorce rate to law reforms introducing unilateral divorce after controlling for law reforms concerning the aftermath of divorce, which are omitted from most previous studies. We introduce two main policy changes that have swept the US since the late 1970s: the approval of the joint custody regime and the Child Support Enforcement program. Because those reforms affect divorce decisions by counteracting the reallocation of property rights generated by the unilateral divorce procedure and by increasing the expected financial costs of divorce, it is arguable that their omissions might obscure the impact of unilateral divorce reforms on divorce rates. After allowing for changes in laws concerning the aftermath of divorce, we find that the positive impact of unilateral divorce reforms on divorce rates does not vanish over time, suggesting that the Coase theorem may not apply to changes in divorce laws. Supplemental analysis, developed to examine the frequency of permanent shocks in US divorce rates, indicates that the positive permanent changes in divorce rates can be associated with the implementation of unilateral divorce reforms and that the negative permanent changes can be related to the law reforms concerning living arrangements in the aftermath of divorce. This seems to confirm the important role of these policies in the evolution of divorce rates.

This paper analyses the evolution of city size distribution in the United States throughout the twentieth century. In particular, it tests the validity of two empirical regularities studied in urban economics: Zipf’s law, which postulates that the product between rank and size of a population is constant, and Gibrat’s law or the law of proportionate growth, according to which the growth rate of a variable is independent of its initial size. To achieve this, we use parametric and nonparametric methods. The main contribution of this work is the use of a new database with information on all the cities (understood as incorporated places), thus covering the entire distribution (without size restrictions). Our results enable us to confirm, from a long term perspective, that Gibrat’s law holds (weakly) and that Zipf’s law holds only if the sample is sufficiently restricted at the top, not for a larger sample, because city size distribution follows a lognormal when we consider all cities.

A reassessment of Gibrat’s Law in the context of country size is carried out in this paper. In addition, how similarly population is distributed in cities and countries is analyzed from a temporal perspective. Although evidence of Gibrat’s Law is found, it is weaker than that previously established in Rose (J Money Credit Bank 38(8):2225–2246, 2006). This is due to the methodology applied and is especially appreciable in very small countries. Nonetheless, we observe that the population growth process in countries is similar to that of cities. As a result, the similarities between how the population is distributed in these two geographical categories have increased over time.

In this paper, we examine the role of the business cycle in divorce. To do so, we use a panel of 30 European countries covering the period from 1991 to 2010. We find a negative effect of the unemployment rate on the divorce rate, pointing to a pro-cyclical evolution of the divorce rate, even after controlling for socio-economic variables and unobservable characteristics that can vary by country, and/or over time. Results indicate that a one-percentage-point increase in the unemployment rate involves almost 0.02 fewer divorces per thousand inhabitants. The impact is small but significant, representing around 1% of the average divorce rate in Europe during the period considered. Supplementary analysis, developed to explore a possible non-parametric pattern, confirms a clearly negative relationship between unemployment and divorce in European countries, with the inverse relationship being more pronounced when the unemployment rate is greater than 15%.

In this paper, we examine whether the business cycle plays a role in marriage and divorce. We use data on Spain, since the differences between recession and expansion periods across regions are quite pronounced in that country. We find that the unemployment rate is negatively associated with the marriage rate, pointing to a pro-cyclical evolution of marriage; however the response of the divorce rate to the business cycle is mixed. Results show the existence of different patterns, depending on geography: divorce rates in coastal regions are pro-cyclical, while in inland regions divorces react to unemployment in a counter-cyclical way. Other factors, such as changes in divorce law and duration of the marriage also have a significant effect on divorce rates.

This article analyses empirically the main existing theories on income and population city growth: increasing returns to scale, locational fundamentals and random growth. To do this we consider a large database of urban, climatological and macroeconomic data from 1,173 US cities observed in 1990 and 2000. The econometric model is robust to the presence of spatial effects. Our analysis shows the existence of increasing returns and two distinct equilibria in per-capita income and population growth. We also find important differences in the structure of productive activity, unemployment rates and geographical location between cities in low-income and high-income regimes.RésuméCet article analyse de façon empirique les principales théories actuelles sur l'expansion des revenus et de la population dans les villes: augmentation des revenus à l'échelle, principes fondamentaux de la situation, et expansion aléatoire. Pour ceci, nous examinons une importante base de données urbaines, climatologiques et macroéconomiques relevées dans 1 173 villes des États-Unis de 1990 jusqu'à l'an 2000. Le modèle économétrique est solide en présence d'effets spatiaux. Notre analyse indique la présence de revenus en augmentation, et de deux équilibres distincts entre les revenus par personne et l'expansion de la population. Nous relevons également la présence d'importantes différences au niveau de la structure de l'activité de production, des taux de chômage, et de la situation géographique entre des villes à faibles revenus et à revenu élevé.ResumenEste artículo analiza de manera empírica las principales teorías existentes sobre el aumento de la renta y la población en las ciudades: rendimientos crecientes a escala, fundamentos de ubicación y crecimiento aleatorio. Para hacer esto consideramos una gran base de datos urbanos, climatológicos y macroeconómicos de 1.173 ciudades estadounidenses observadas en 1990 y 2000. El modelo econométrico es sólido ante la presencia de efectos espaciales. Nuestro análisis demuestra la existencia de rendimientos crecientes y dos equilibrios distintos en los ingresos per cápita y el incremento de la población. También encontramos diferencias importantes en la estructura de la actividad productiva, las tasas de desempleo y la ubicación geográfica entre las ciudades de regímenes de renta baja y alta.

This paper uses un-truncated city population data from six countries (the United States, Spain, Italy, France, England and Japan) to illustrate how parametric growth regressions can lead to biased results when testing for Gibrat’s law in city size distributions. The OLS results show non-monotonic behaviours depending on the sample size. Moreover, it is possible to find a critical sample size from which we reject Gibrat’s law.

espanolEn este articulo se utilizan tecnicas parametricas y no parametricas para el analisis del impacto de los cambios registrados en el potencial de mercado de las regiones espanolas sobre su dinamica de crecimiento en el periodo 1860‐1930. El estudio del caso espanol permite analizar si la construccion de nuevas infraestructuras de transporte, asi como los cambios en la politica comercial, al afectar al potencial de mercado relativo de las regiones espanolas, acabaron por moldear sus trayectorias de crecimiento. Para la realizacion del analisis se utilizan nuevas estimaciones retrospectivas de PIB per capita de las NUTS III espanolas (provincias) y una estimacion a la Harris del potencial de mercado regional en la que se considera las distancias economicas entre regiones y su evolucion de acuerdo a los cambios registrados en la red de transportes, en los precios del mismo y en la politica arancelaria de los principales socios comerciales de Espana. Los resultados avalan la existencia de una robusta relacion positiva entre el potencial de mercado y el crecimiento regional, en particular durante los anos 1900‐1930 EnglishIn this paper we employ parametric and nonparametric techniques to analyse the effect of the changes registered on regional market potential on the growth of Spanish regions during the period 1860-1930. The study of the Spanish experience during these years conforms a case study that allows analyzing whether the construction of new transport infrastructure, as well as the changes in trade policy, that affected the relative market potential of the Spanish regions, ended up shaping regional growth trajectories. In order to carry out the analysis we make use of new evidence on regional inequality patterns in the long term based on recent estimations of per capita GDP for NUTS III Spanish regions (provinces) and an a la Harris measure of regional market potential that takes into account the economic distance between territories according to the changes registered in transport networks, the variations in the actual transport costs and the tariff policy followed over the period. Our results show a clear positive influence of market potential on regional economic growth, particularly along the years 1900-1930.

This paper studies the effect of the Spanish Reconquest, a military campaign that aimed to expel the Muslims from the Iberian Peninsula, on the population of its most important cities. The almost four centuries of Reconquest offer a "quasi-natural" experiment to study the persistence of population shocks at the city level. Analyzing city growth before and after the onset of the Reconquest, we find that it had a significant negative effect on the population of the main Iberian cities. However, when we control for time effects, we conclude that in most cities this effect was transitory. In order to quantify the duration of the shock driven by the Reconquest we then estimate its average effect on the urban share of these cities considering the time dimension of the entire panel of cities simultaneously and adding city-specific time trends. Our estimates suggest that these cities regained their pre-Reconquest shares on average in less than 100 years. These results are robust to controlling for a large set of country and city-specific socioeconomic indicators and spatial effects. Our findings suggest that the locational fundamentals that determined the relative size of Iberian cities before the Reconquest were more important determinants of the fate of these cities than the direct negative impact that the Reconquest had on their population.

We study US city size distribution using places data from the Census, without size restrictions, for the period 1900-2010, and the recently constructed US City Clustering Algorithm (CCA) data for 1991 and 2000. We compare the lognormal, two distributions named after Ioannides and Skouras (2013) and the double Pareto lognormal with two newly introduced distributions. The empirical results are overwhelming: one of the new distributions greatly outperforms any of the previously-used density functions for both types of data. We also develop a theory compatible with the new distributions based on the standard geometric Brownian motion for the population in the short term. We propose some extensions of the theory in order to deal with the long term empirical features.

This paper analyses the statistical distribution of war size. We find strong support for a Pareto-type distribution (power law) using data from different sources (COW and UCDP) and periods. A power law describes accurately the size distribution of all wars, but also the distribution of the sample of wars in any given period. The estimated Pareto exponent is always less than 1, indicating that the distribution is heavy-tailed; this means that the war average loss is controlled by the largest conflicts. Furthermore, the study of battle deaths’ growth rates reveals a clear decreasing pattern; the growth of deaths declines faster the greater the number of initial deaths.

This paper reconsiders the evolution of the growth of American cities since 1790 in light of new theories of urban growth. Our null hypothesis for long-term growth is random growth. We obtain evidence supporting random growth against the alternative of mean reversion (convergence) in city sizes using panel unit root tests. We also examine mobility within the distribution to try to extract growth patterns different from the general unit root trend detected. We find evidence of high mobility when we model growth as a first-order Markov process. Finally, using a cluster procedure we find strong evidence in favor of conditional convergence in city growth rates within convergence clubs, which we interpret as 'local' mean-reverting behaviors. We interpret the high mobility and the results of the clustering analysis as signs of a sequential city growth pattern.

We provide empirical evidence of the dynamics of city size distribution for the whole of the twentieth century in U.S. cities and metropolitan areas. We focus our analysis on the new cities that were created during the period of analysis. The main contribution of this paper, therefore, is the parametric and nonparametric analysis of the population growth experienced by these new-born cities. Our results enable us to confirm that, when cities appear, they grow very rapidly and, as the decades pass, their growth slows or even falls into decline. This is consistent with the theoretical framework regarding mean reversion (convergence) in the steady state and with the theories of sequential city growth. Keywords: cities, sequential city growth, city size distribution JEL classification: O18, R11, R12

The aim of this work is to test empirically the validity of Gibrat’s law on the growth of cities, using data on the complete distribution of cities (without size restrictions) from three countries (the US, Spain and Italy) for the entire 20th century. In order to achieve this, different techniques are used. First, panel data unit root tests tend to confirm the validity of Gibrat’s law in the upper-tail distribution. Secondly, when the entire distribution is considered using non-parametric methods, it is found that Gibrat’s law does not hold exactly in the long term (in general, size affects the variance of the growth process but not its mean). Moreover, the log-normal distribution works well as a description of city size distributions across the whole century when no truncation point is considered.

This paper analyses the determinants of growth of American cities, understood as growth of the population or of per capita income, from 1990 to 2000. This empirical analysis uses data from all cities with more than 25,000 inhabitants in the year 2000 (1154 cities). The results show that while a common convergence behaviour is observed in both population and per capita income growth, there are differences in the evolution of the distributions: population distribution remains almost unchanged, while per capita income distribution makes a great movement to the right. We propose two hypotheses related with the influence of service activities and geography on urban growth, and test them with different empirical methods: linear models and Multinomial Logit Models.

This article analyzes empirically the main existing theories on income and population city growth: increasing returns to scale, locational fundamentals and random growth. To do this we implement a threshold nonlinearity test that extends standard linear growth regression models to a dataset on urban, climatological and macroeconomic variables on 1,175 U.S. cities. Our analysis reveals the existence of increasing returns when per-capita income levels are beyond $19; 264. Despite this, income growth is mostly explained by social and locational fundamentals. Population growth also exhibits two distinct equilibria determined by a threshold value of 116,300 inhabitants beyond which city population grows at a higher rate. Income and population growth do not go hand in hand, implying an optimal level of population beyond which income growth stagnates or deteriorates.

The methodology proposed by Ioannides and Overman (2003 Regional Science and Urban Economics 33 127–137) is applied to estimate a local Zipf exponent using data for the entire 20th century of the complete distribution of cities (incorporated places) without any size restrictions in the US. First, kernel regressions are run using the Nadaraya–Watson estimator, excluding some atypical observations (5.66% of the sample). The results reject Zipf’s law from a long-term perspective, but the evidence supports Gibrat’s law. In the short term, decade by decade, the evidence in favour of Zipf’s law is stronger. Second, to consider the whole sample the LOcally WEighted Scatter plot Smoothing (LOWESS) algorithm is applied. From a long-term perspective the evidence supporting Zipf’s law increases, but the evidence supporting Gibrat’s law is weaker, as small cities exhibit higher variance than the other cities. Finally, the estimated values by decade are again closer to Zipf’s law. Keywords: Zipf’s law, Gibrat’s law, urban growth

The aim of this work is to test empirically the validity of Gibrat's Law in the growth of cities, using data for all the twentieth century of the complete distribution of cities (without any size restrictions) in three countries: the US, Spain and Italy. For this we use different techniques (parametric and non-parametric methods), obtaining mixed evidence. Our results confirm that Gibrat's law for means holds only as a long-run average. In the short term, considered decade by decade, we find that growth was divergent in all three countries. Despite this, the distribution of growth in the cities can be approached as a lognormal. In the long term, panel data unit root tests confirm the validity of Gibrat's Law in the upper tail distribution. Finally we find evidence in favour of a weak Gibrat's Law (size affects the variance of the growth process but not its mean) when using non-parametric methods which relate the growth rate to city size.

This paper presents a simple method for calculating deviations between actual city size and the size which would correspond to it with a Pareto exponent equal to one (Zipf’s law). The results show two differentiated behaviours: most cities (80.25 per cent) present a greater size than that which would fulfil Zipf’s law, while small cities (19.75 per cent) tend to be too small. The aim of the paper is to analyse the distribution element by element, using data about city characteristics from all American cities in 2000, and to explain the deviation between the size predicted by Zipf’s law and the actual size of each city. To do this, a multinomial logit model is used. The most important variables affecting the probability of a city presenting a negative or positive deviation are per capita income, human capital levels and the percentage of the population employed in some sectors.

This paper analyses the evolution of the size distribution of the stock of immigrants in the period 1960–2000. In particular, we are interested in testing the validity of two empirical regularities: Zipf’s law, which postulates that the product between the rank and size of a population is constant; and Gibrat’s law, according to which the growth rate of a variable is independent of its initial size. We use parametric and nonparametric methods and apply them to absolute (stock of immigrants) and relative (migration density, defined as the quotient between the stock of immigrants of a country and its total population) measurements. We find that both the stock of immigrants and migration density follow similar size distributions to those of cities and of countries. Contrary to what traditional migrations models predict, growth in the stock of immigrants is independent of the initial stock. Moreover, the growth of migration density shows a divergent behaviour, which could be explained by the lower birth rates of host countries and the reduction in the cost of emigration produced by the presence of a previous stock of immigrants in the country.