A century of shocks: The evolution of the German city size distribution 1925–1999☆
Introduction
City size distributions and the underlying city size dynamics have received considerable attention in the urban economic literature in recent years. Empirical studies have in particular produced evidence with respect to three features of city size distributions. First, city size distributions are found to be remarkably stable over time. Second, the hierarchy of the individual cities making up these distributions is also often rather stable, which suggests proportionate city growth, see for example Eaton and Eckstein (1997) and Black and Henderson (2003). The third stylized fact is that city size distributions are very well approximated by a power law in the upper tail of the distribution. A special case of which is better known as Zipf's Law and has been found to hold for various countries at various points in time, see e.g. Soo (2005) and Nitsch (2005).
These empirical regularities have stimulated the development of city growth models that can explain these features of city size distributions in a coherent economic framework. Modern theories (e.g. Eeckhout, 2004, Rossi-Hansberg and Wright, 2007, Córdoba, 2008) try to explain the evolution of city size distributions in a way that is consistent with the empirical results. Either a stable city size distribution adhering to Zipf's Law in the upper tail follows directly from the model (Gabaix, 1999, Eeckhout, 2004), or it is one of the possible outcomes of the model (Rossi-Hansberg and Wright, 2007). These models have benefited substantially from the work of Gabaix (1999) who, building on earlier work by Simon (1955), showed that a stable city size distribution adhering to Zipf's Law in the upper tail naturally results if the individual city size growth process adheres to what is essentially Gibrat's Law of proportional effect, i.e. a city's expected growth rate and the variance of that growth rate are independent of its initial size (also referred to as proportionate city growth). The whole city size distribution would in that case be lognormal (see Eeckhout, 2004).1
Recent empirical papers on the evolution of the city size distribution focus exclusively on the US experience, e.g. Black and Henderson (2003), Overman and Ioannides (2001), Ioannides and Overman, 2003, Ioannides and Overman, 2004, Dobkins and Ioannides, 2000, Dobkins and Ioannides, 2001, or Eeckhout (2004). Besides some simple Zipf studies that do not look at distributional dynamics nor at evidence for Gibrat's Law of proportional effect, the only two papers we know of that offer a thorough look at the distributional dynamics of city size distributions for other countries than the USA are Eaton and Eckstein (1997) and Anderson and Ge (2005). The former provides evidence for France and Japan confirming the notion of a stable city size distribution, while the latter shows that in case of China the city size distribution has been affected in a predictable way by government policies.
The contributions of the present paper are the following. First, we examine the evolution of the city size distribution for West-Germany (from now on referred to as Germany). The interest in the German city size distribution can be dated back to as early as 1913 when the geographer Auerbach (1913), as one of the first, noted that the city size distribution could be approximated by a power law. For our empirical analysis we have constructed a unique data set of annual city population data for 62 of the largest cities in Germany over the period 1925–1999. This data set allows us to describe the evolution of the German city size distribution quite accurately. Second, the use of German data provides a specific empirical view on the evolution of the city size distribution, namely it offers a (unique) look at the effect of large shocks to the urban system. In the time period under consideration German cities were subject to a number of large ‘quasi-natural experiments’ namely the heavy destruction of cities during WWII and the split and subsequent reunification of Germany. Our data set allows us to look at the impact of these ‘quasi-natural experiments’ in a much more dynamic fashion than previous research on the same topic (Davis and Weinstein, 2002, Bosker et al., 2007, Redding and Sturm, 2005, Redding et al., 2007). Third, our annual data set allows us to perform unit root tests for each individual city in order to find evidence on Gibrat's Law of proportional effect.2 The present paper is among the first to provide (panel) unit root tests for cities that, given our extensive data set, arguably suffer less from low power problems that beset unit root tests based on a limited number of observations, while at the same time adequately controlling for the short-run dynamics in city size.
The results of our analysis of the German urban system can also help to distinguish between some of the proposed urban economic theories that try to explain the shape and evolution of city size distributions. Following Davis and Weinstein (2002), these theories can be grouped into three broad categories, i.e. increasing returns to scale, random growth and locational fundamentals.3 The models in all three categories predict a stable city size distribution in equilibrium; the reaction to shocks is however quite different. Models exhibiting increasing returns to scale can give rise to a stable distribution which is sensitive to shocks and which does not necessarily adhere to Zipf's Law (see also Chapter 12 of Fujita et al., 1999, Gabaix and Ioannides, 2004, Brakman et al., 1999). As a result a large shock has the potential to (radically) change the city size distribution. Models falling under the random growth category, e.g. Gabaix (1999) or Córdoba (2008), predict that shocks have a permanent effect on city sizes, but given that these shocks are distributed randomly over cities and mean- and variance independent of city size, they will in the limit result in a city size distribution that adheres to Zipf's Law in the upper tail. The effect of a large shock thus has no effect on the limiting city size distribution; it can however have a permanent impact on the relative position of cities within the distribution. Finally, the locational fundamentals approach suggests that the observed city size distribution is the result of fixed underlying locational fundamentals (first nature geography). A large shock will now result in both the city size distribution as a whole and the relative position of cities within this distribution returning to their pre-shock state.4 Given the three categories' different reaction to large shocks, the ‘quasi-natural experiments’ that the German urban system was subjected to, provide a way to try and distinguish between competing views of city size evolution.
Our first main finding is that the German city size distribution is permanently affected by the World War II shock, more so than by any other shocks. Cities that have been hit relatively hard due to the substantial bombings and the subsequent allied invasion do not recover the loss in relative size. After the war, the city size distribution does not revert to its pre-WWII level, but shifts to one characterized by a more even distribution of population over the cities in the sample. Compared to the impact of WWII, the separation from and later reunion with East-Germany has had a much less severe impact on relative city sizes. Our second finding is that, once corrected for the heavy destruction during WWII, (panel) unit root tests that are used to test for the validity of proportionate city growth reject Gibrat's Law for about 75% of all cities. Also we find strong evidence that the locational fundamentals approach does not seem to explain the evolution of Germany's urban system, which is in contrast to the findings of Davis and Weinstein, 2002, Davis and Weinstein, 2004 for Japan. Overall the evidence does seem to comply best with urban theories exhibiting increasing returns to scale.
Section snippets
Data
In constructing our data set, we first had to choose which cities to include in our sample. We choose to include those West-German cities in our data set that either had a population of over 50,000 inhabitants before the beginning of WWII or cities that were over the sample period classified as Großstädte, cities with a population of at least 100,000 people. Cities are defined on a city-proper or administrative basis in Germany. Adjustments to the administrative boundaries (and hence size) of
Evolution of the city size distribution
We start our analysis by giving a description of the evolution of the West-German urban system. Table 1 below shows that during our sample period total population increased by about 70% from about 39 million people in 1925 to 67 million in 1999.
During the same period, the share of Germany's population living in one of our sample cities declined by about 32% (or 13 ppt) suggesting a process of suburbanization over the sample period. The average city size in our sample increased by 16% from 258
Zipf's Law and Gibrat's Law of proportional effect
As already mentioned in the Introduction, the notion of a power law distribution describing the upper tail of city size distribution goes at least as far back as 1913 when the German geographer Auerbach (1913) noted this to be the case for Germany. The empirical literature has mainly focused on a special case of such a power law, namely that of city sizes in the upper tail of the distribution being distributed Pareto with coefficient a = 1.12
Unit root testing and parametric evidence on Gibrat's Law
The non-parametric kernel estimates of the previous section remain largely based on pooled panel data evidence. In order to fully exploit the time series dimension of our data set, we now turn to a, more dynamic way of testing for Gibrat's Law. Given the many observations over time in our data set, we follow the suggestion made by Gabaix and Ioannides (2004) who state: "Hence one can imagine that the next generation of city size evolution empirics could draw from the sophisticated econometric
Unit root testing and WWII's impact on relative German city sizes
In previous work, Brakman et al. (2004) and Bosker et al. (2007), we already looked at the immediate impact of WWII on German relative city size. Drawing on the methodology developed by Davis and Weinstein, 2002, Davis and Weinstein, 2004, these papers argue that the destruction during WWII was largely exogenous to the level of economic activity in cities and use the level of destruction during WWII as instruments for population growth during WWII when estimating the following equation:
Conclusions
Most of the empirical literature on city size distributions has focused on the USA. Other countries might experience a different evolution of their city size distribution, as this paper shows to be the case for West-Germany. Using a unique annual data set for 62 West-German cities that covers most of the 20th century, we look at the evolution of both the city size distribution as a whole and each individual city separately. The West-German case is of particular interest as its urban system has
References (46)
- et al.
The size distribution of Chinese cities
Regional Science and Urban Economics
(2005) On the distribution of city sizes
Journal of Urban Economics
(2008)- et al.
Cities and growth: theory and evidence from France and Japan
Regional Science and Urban Economics
(1997) - et al.
Testing for unit roots in heterogeneous panels
Journal of Econometrics
(2003) - et al.
Zipf's Law for cities: an empirical examination
Regional Science and Urban Economics
(2003) - et al.
Unit root tests in panel data: asymptotic and finite-sample properties
Journal of Econometrics
(2002) Zipf zipped
Journal of Urban Economics
(2005)- et al.
Cross-sectional evolution of the U.S. city size distribution
Journal of Urban Economics
(2001) Further evidence on breaking trend functions in macroeconomic variables
Journal of Econometrics
(1997)Empirical cross-section dynamics and economic growth
European Economic Review
(1993)
Persistence and stability in city growth
Journal of Urban Economics
Zipf's Law for cities: a cross-country investigation
Regional Science and Urban Economics
Das Gesetz der Bevölkerungskonzentration
Petermanns Geographische Mitteilungen
Urban evolution in the USA
Journal of Economic Geography
Looking for multiple equilibria when geography matters: German city growth and the WWII shock
Journal of Urban Economics
An Introduction to Geographical Economics
The return of Zipf: towards a further understanding of the rank-size rule
Journal of Regional Science
The strategic bombing of German cities during World War II and its impact on city growth
Journal of Economic Geography
Pitfalls and opportunities: what macroeconomists should know about unit roots
NBER working paper, no.100
Limited time series with a unit root
Econometric Theory
Gibrat's Law and the growth of Canadian cities
Urban Studies
Bones, bombs and breakpoints: the geography of economic activity
American Economic Review
Cited by (111)
Pandemics and cities: Evidence from the Black Death and the long-run
2024, Journal of Urban EconomicsHistory and urban economics
2022, Regional Science and Urban EconomicsCitation Excerpt :Two other papers falling into this literature look at the impact of shocks associated with plague outbreaks on cities. Bosker et al. (2008) looks at the impact of plagues outbreaks on the size of Italian cities. Jedwab et al. (2020) looks at the short and the long-run impact of a plague outbreak across European cities.
City origins
2022, Regional Science and Urban EconomicsWhat future for history dependence in spatial economics?
2022, Regional Science and Urban EconomicsDid Zipf's Law hold for Chinese cities and why? Evidence from multi-source data
2021, Land Use PolicyCitation Excerpt :The research of size distribution of cities has always been a hot topic of urban research (Beckmann and Mcpherson, 2006; Bergs, 2018; Bosker et al., 2008; Jing et al., 2018).
- ☆
We would like to thank the editor, three anonymous referees, Stephen Redding, Daniel Sturm, and Joppe de Ree, and seminar participants at the London School of Economics, the 2006 NARSC meeting in Las Vegas, the 2006 EEA meeting in Vienna, Utrecht University, and Radboud University Nijmegen for very useful comments and suggestions and we also like to thank Peter Koudijs for excellent research assistance.