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Bones, Bombs, and Break Points:The Geography of Economic Activity

By DONALD R. DAVIS AND DAVID E. WEINSTEIN*

We consider the distribution of economic activity within a country in light of threeleading theories—increasing returns, random growth, and locational fundamentals.To do so, we examine the distribution of regional population in Japan from theStone Age to the modern era. We also consider the Allied bombing of Japanese citiesin WWII as a shock to relative city sizes. Our results support a hybrid theory inwhich locational fundamentals establish the spatial pattern of relative regionaldensities, but increasing returns help to determine the degree of spatial differenti-ation. Long-run city size is robust even to large temporary shocks. (JEL D5, J1, N9, R1)

In the last decade, the field of economic ge-ography has enjoyed a renaissance.1 The centralquestion in this literature is how to explain thedistribution of economic activity across space—across countries of the world, across regionswithin a country, and across cities. Three prin-cipal theoretical approaches have emerged,which may be termed increasing returns, ran-dom growth, and locational fundamentals. Wedevelop stylized facts and empirical tests thathelp to evaluate the theories.

The increasing returns theories posit that ad-vantages of size may arise from knowledgespillovers, labor-market pooling, or the advan-tages of proximity for both suppliers and de-manders in a world of costly trade. In thisapproach, a distribution of city sizes may arisefrom technological characteristics of individualindustries (J. V. Henderson, 1974) or from thetacit competition among locations for mobilefactors of production (Krugman, 1991a). Impor-tant themes within this work include the possi-bilities of multiple equilibria, path dependence,and spatial catastrophes. An outstanding expo-sition of much of the new work is in MasahisaFujita et al. (1999).

The random growth theory (H. Simon, 1955)holds that a distribution of cities of quite differ-ent sizes emerges from very simple stochasticprocesses. One large advantage of this approachis that it is able to explain a key empiricalregularity known as Zipf’s Law regarding thedistribution of city sizes that, to date, the in-creasing returns theories cannot explain. A re-cent and very interesting development of thisapproach is Xavier Gabaix (1999).

What we term the locational fundamentalstheory may be thought of as a variant of therandom growth theory. Instead of city growthitself being random, it is fundamental economiccharacteristics of locations that are random. Afully specified locational fundamentals modelwould incorporate differences in Ricardiantechnological coefficients and Heckscher-Ohlinendowments, with the caveat that the primitive

* Department of Economics, Columbia University, 420West 118th Street, New York, NY 10027, and NationalBureau of Economic Research (e-mail: [email protected]; and [email protected]). The authors want to es-pecially thank Mary Berry, Wayne Farris, and Hiroshi Kitowho helped us enormously in obtaining and understandingthe historical demographic data. While their help was in-strumental, any remaining errors are the responsibility of theauthors. Kazuko Shirono gave us tremendous help with thearchival and data construction aspects of the paper. JoshuaGreenfield also helped input the bombing data. Weinsteinwants to also thank the Japan Society for the Promotion ofScience for funding part of this research, and SeiichiKatayama for providing him with research space and accessto the Kobe University library. This research was supportedby National Science Foundation Grant No. SBR-9810180.

1 Paul Krugman has argued that the study of the spatiallocation of economic activity should assume a stature in theprofession equal to one of the flagship fields such as inter-national trade (Krugman, 1995). A new Journal of Eco-nomic Geography has been founded. While demurring fromsome of Krugman’s strongest claims, J. Peter Neary, writinga review article in the Journal of Economic Literature,declares “New economic geography has come of age”(Neary, 2001, p. 536).

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endowments of interest would elaborate on theconcept of “land” to include a detailed descrip-tion of location-specific characteristics. A paperin this spirit is Jordan Rappaport and Jeffrey D.Sachs (2001). Following Krugman (1996), if weposit that these characteristics are distributedaccording to the same process as in Gabaix(1999), then the locational fundamentals theoryalso can account for Zipf’s Law. However, incontrast to the random growth theory, the loca-tional fundamentals story predicts that the sizeof specific locations should be robust even tolarge temporary shocks.2

In this paper, we will examine these threetheories empirically. A few key questionsemerge. How important are scale economies inexplaining the degree of spatial concentration ofeconomic activity?3 The premise that we workfrom is that the forces of increasing returnsmust be vastly stronger in a modern, knowl-edge-based economy than in more primitive,agricultural or pre-agricultural, economies. Toinvestigate this, we employ a unique data set onJapanese regional population over the past8,000 years. The answer that we provide hastwo parts. First, for the 8,000 years in our dataset, there has always been a great deal of vari-ation in measures of regional population den-sity. This alone suggests that important factors

other than increasing returns help to explain thevariation in the density of economic activity.Second, there has been a notable rise in concen-tration in the last century as Japan industrializedand became ever more integrated into the worldeconomy. This suggests that the increasing re-turns theories may help to account for the rise indispersion.

The same data set can be employed to addressa second key question. Over tens, hundreds, orthousands of years, how much persistenceshould we expect in the identity of the mostdensely settled regions? The increasing returnstheories do not answer with a single voice.Insofar as the size distribution is tied to techno-logical characteristics of particular industries,then as we move from hunter-gatherer societies,to agriculture-based societies, through feudal-ism, into and out of autarky, and finally to amodern industrial economy, one might guessthat there would be radical shifts over time inwhich are the densely populated regions. On theother hand, an important strand within the in-creasing returns theories has stressed the role ofpath dependence (Krugman, 1991b; Paul A.David, 2000). An early start in one locationprovides that site with advantages at each suc-ceeding stage of locational competition. Therandom growth theory is likewise consistentwith correlation across long stretches of time inthe spatial density of particular locations so longas the variance of growth rates is not too large.A clear prediction emerges from the locationalfundamentals theory, which would hold thatmany of the crucial characteristics for locationshave changed little over time even if the eco-nomic meaning may have evolved. For exam-ple, there are advantages of being near a river,on the coast, on a plain instead of a mountain ordesert, etc. Our empirical results strongly con-firm that there is a great deal of persistenceacross time in which are the densely settledregions. For the increasing returns theory, thiswould stress the importance of path depen-dence. For the random growth theory, this re-quires that the variance of growth have not beentoo high. However, we believe that this persis-tence arises most naturally from the locationalfundamentals story and suggests this may be animportant component of a complete answer.

Finally, the theories have quite distinct sto-ries to tell about how the distribution of city

2 Physical geography has played a quite limited role inmuch of the theoretical literature of the new economicgeography. There are exceptions, such as the very nicepaper of Fujita and Tomova Mori (1996) on the role ofports. More typical, though, is a tendency to focus almostexclusively on factors with no real geographical counter-part, as in the survey by Fujita and Jacques Francois Thisse(1996, p. 339): “The main reasons for the formation ofeconomic clusters involving firms and/or households areanalyzed: (i) externalities under perfect competition; (ii)increasing returns under monopolistic competition; and (iii)spatial competition under strategic interaction.”

3 Fujita et al. (1999) argue that, at varied levels ofgeographical aggregation, the locational fundamentals the-ory is of quite limited importance, and instead the key tounderstanding dispersion is increasing returns: “[T]he dra-matic spatial unevenness of the real economy—the dispar-ities between densely populated manufacturing belts andthinly populated farm belts, between congested cities anddesolate rural areas; the spectacular concentration of partic-ular industries in Silicon Valleys and Hollywoods—issurely the result not of inherent differences among locationsbut of some set of cumulative processes, necessarily involv-ing some form of increasing returns, whereby geographicconcentration can be self-reinforcing.” (Fujita et al., 1999,p. 2).

1270 THE AMERICAN ECONOMIC REVIEW DECEMBER 2002

sizes will be affected by a powerful, but tem-porary, shock. The increasing returns literature,as noted earlier, has given a prominent role topath dependence as well as to the possibilityof catastrophes in which even small shocksmay give rise to large and irreversible struc-tural changes in relative city sizes.4 By look-ing at a large shock, one can gauge howimportant these theoretical possibilities ofcatastrophic spatial change are in practice.The pure random growth theory predicts thatgrowth follows a random walk—all shockshave permanent effects. By contrast, the lo-cational fundamentals story holds that so longas the shock is purely temporary, even strongshocks should shortly be reversed, as the ad-vantages of the particular locations reassertthemselves in relatively rapid growth rates onthe path to recovery.

The particular experiment that we consider isthe Allied bombing of Japanese cities duringWorld War II. This is one of the most powerfulshocks to relative city sizes that the world hasever experienced. We find that, in the wake ofthe destruction, there was an extremely power-ful recovery. Most cities returned to their rela-tive position in the distribution of city sizeswithin about 15 years. This strikes moststrongly at the random growth theory, whichpredicts no reversion to the prior path. For theincreasing returns theory, this suggests thathowever appealing the theoretical possibility ofspatial catastrophes, in practice the distributionof city sizes seems to be highly robust to tem-porary shocks even of great magnitude. Finally,the reversion to the prior growth path wouldseem to be a strong confirmation of a locationalfundamentals theory.

In sum, our experiments are very problematicfor the pure random growth theory. While thistheory provides a foundation for understandingZipf’s Law, it fails utterly to predict the greatrobustness of particular locations to strong tem-

porary shocks. For the increasing returns theory,the message is more nuanced. There has longbeen a great deal of spatial dispersion of eco-nomic activity, so increasing returns is not nec-essary to explain this. Nonetheless, in the lastcentury there has been a substantial rise in thedegree of spatial dispersion, and this might wellbe accounted for by increasing returns. Theemphasis within the increasing returns literatureon the possibility of spatial catastrophes in thedistribution of city sizes seems to be of greaterinterest theoretically than empirically. Finally,the locational fundamentals theory fares quitewell in our empirical investigations. It has anadvantage over the increasing returns theoryin that it provides a simple account of Zipf’sLaw. It can provide a consistent story aboutwhy there has been a great deal of spatialdispersion over long stretches of time. It canexplain why there has been a great deal ofpersistence in which regions are most denselysettled. And it can explain why specific loca-tions are highly robust even to temporaryshocks of great magnitude. The one weaknessis that it does not provide a reason why thedegree of concentration in Japan should haveincreased in the last century.

These considerations lead us to believethat the most promising direction for re-search is to consider a hybrid theory in whichlocational fundamentals play a key role inestablishing the basic pattern of relative re-gional densities and in which increasing re-turns plays a strong role in determining thedegree of concentration.

I. Bones: Archaeology, History,and Economic Geography

A. The Data

In this section, we examine 8,000 yearsof data on Japanese regions in order to ad-dress key questions concerning variation andpersistence of regional population densities.Historically, how large has the variation inregional population density been and are thereimportant changes over time? How persistentis the identity of the regions that have beenmost densely settled? We then discuss theresults in light of the three theories notedabove.

4 For example, Krugman (1998, p. 7) writes: “The newwork is highly suggestive, particularly in indicating howhistorical accident can shape economic geography, and howgradual changes in underlying parameters can produce dis-continuous change in spatial structure.” A theoretical exam-ple can be found in Fujita et al. (1999), Figure 5.3. There ashock to relative region sizes that is sufficiently large canpermanently alter the relative size of regions.

1271VOL. 92 NO. 5 DAVIS AND WEINSTEIN: GEOGRAPHY OF ECONOMIC ACTIVITY

The data that we bring to bear is of two maintypes.5 As we move back in time two millenniaand more, one has access neither to regionalaccounts nor to population censuses. However,Shuzo Koyama (1978) provides detailed data onthe number of archaeological sites, including28,013 from the Jomon period (�6,000 to�300) and another 10,530 sites from the Yayoiperiod (�300 to 300). These have been dividedaccording to the 45 modern prefectures we use.6

We take a count of these archaeological sites forthe respective periods as a proxy for the level ofeconomic activity in the prefectures.

The second type of data is population. Inorder to provide a basis for taxation, Japanbegan censuses of population quite early. Thiswas done at a regional level because of thesubstantial autonomy of local lords. HiroshiKito (1996) provides the best estimates of re-gional population for 68 provinces (kuni) for theperiod beginning in 725 and ending in 1872. In1920 regional censuses began using a systembased on 47 prefectures (ken), and this systemcontinues through our most recent data for theyear 1998.7 Often we will find it convenient towork with data that allows a comparison acrossall of these periods of time. A quite close matchbetween the data sets can be achieved when weaggregate up to 39 regions. Kito (1996) alsoprovides estimates of total population of Japanfor the Jomon and Yayoi periods.

We need to discuss the unit of analysis. Agreat deal of work on economic geography con-siders cities rather than regions as the unit ofanalysis. We do have data on cities, and we willdiscuss it, but this data extends back only to1925. All of our earlier data concerns regions,which thus must be the unit of analysis. Thereare, nonetheless, good reasons why one mightprefer the regional data. The first is that sincethe definition of a city always involves a thresh-old, even purely uniform growth of populationin all locations may appear nonuniform becausepopulations may cross the threshold in somelocations but not others. A second reason is that,

especially over long stretches of time, the ap-propriate definition of cities changes. For exam-ple, areas that are considered core parts ofmodern Tokyo would not have been thought ofas part of historical Tokyo (Edo). It is not at allclear how one should or could deal with suchissues. Third, for some of our early periods,virtually all of the population lived outside ofanything that in modern terms would be thoughtof as a city. Taken together, these factors sug-gest that the turn to regional data may be anecessity, but it is one with many virtues.

By focusing on regional data, one transfor-mation becomes absolutely essential. Differ-ences in region sizes are large and thedemarcation between regions does not alwayscorrespond to an obvious economic rationale.This suggests that we work not with the rawregional population, but instead with the popu-lation deflated by the regional area. This mea-sure of regional population density will be theunit of analysis for this portion of our study.8

One of the key reasons for turning to thehistorical data is that economies of the remotepast look quite different from the modern econ-omy. By examining such data, we are able toabstract from forces that we think are importanttoday, but much less so in earlier times. Henceit is also important to have in mind the principalfeatures of the earlier economies (as outlined inTable 1).

Our earliest data on archaeological sites ofthe Jomon period (�6,000 to �300) takes usback to the Stone Age. The economy is basedon hunting and gathering. There are no metaltools or agriculture, although there is evidenceof pottery. The Yayoi period (�300 to 300) is arevolutionary time, with the introduction ofprimitive forms of agriculture, metallurgy, andsome coins. As yet, there is neither writing norcloth. Our next stop in history is the year 725. Afeudal regime has risen and we have the firstpopulation census. Writing is well developedand farming is widespread. The capital is Nara.By 800, the capital has moved to Kyoto andgreater protection of peasant property rights hasencouraged more widespread cultivation. Thenext century would see more extensive usage of5 Details on data construction are in the Appendix.

6 There are 47 prefectures in Japan, but we were forcedto drop Okinawa and Hokkaido because these prefectureswere not included in early censuses.

7 The move to prefectures occurred earlier, but the 1920census is the first to use these categories.

8 Rappaport and Sachs (2001) also focus on regionalpopulation densities in the United States for similar reasons.


TABLE 1—PRINCIPAL FEATURES OF HISTORICAL ECONOMIES

Year

Populationin

thousands

Share offive

largestregions

Relative var oflog population

densityZipf

coefficient

Rawcorrelationwith 1998

Rankcorrelationwith 1998 History

�6000 to�300

125 0.39 2.46 �0.809(0.217)

0.53 0.31 Hunter-gatherer society, not ethnicallyJapanese, no metal tools oragriculture.

�300 to300

595 0.23 0.93 �1.028(0.134)

0.67 0.50 First appearance of primitiveagriculture and ethnically Japanesepeople. Some metallurgical skills,some coins, no writing or cloth.

725 4,511 0.20 0.72 �1.207(0.133)

0.60 0.71 Creation of feudal regime, populationcensuses begin, writing welldeveloped, farming is widespread.Capital is Nara.

800 5,506 0.18 0.75 �1.184(0.152)

0.57 0.68 Capital moves to Kyoto. Propertyrights for peasant farmers continueto improve, leading to greatercultivation.

900 7,442 0.29 0.68 �1.230(0.166)

0.48 0.65 Use of metallic farm tools doublesover average for previous 300years. Improved irrigation and dry-crop technology.

1150 6,836 0.20 0.66 �1.169(0.141)

0.53 0.73 Multiple civil wars especially in (rice-rich) northern Japan. Generalpolitical instability and rebellions.

1600 12,266 0.30 0.64 �1.192(0.068)

0.76 0.83 Reunification achieved after bloodywar, extensive contact with West.Japan is a major regional tradingand military power.

1721 31,290 0.21 0.43 �1.582(0.113)

0.85 0.84 Closure of Japan to trade with minorexceptions around Nagasaki.Capital moves to Tokyo. Politicalstability achieved.

1798 30,531 0.21 0.37 �1.697(0.120)

0.83 0.81 Population is approximately 80percent farmers, 6 percent nobility.Population stability attributed toinfanticide, birth control, andfamines.

1872 33,748 0.18 0.30 �1.877(0.140)

0.76 0.78 Collapse of shogun’s government,civil war, jump to free trade, endof feudal regime, start subsidizedimport of foreign technology.

1920 53,032 0.25 0.43 �1.476(0.043)

0.94 0.93 Industrialization and militarization infull swing, but still 50 percent oflabor force is farmers. Japan is amajor exporter of silk and textiles.

1998 119,486 0.41 1.00 �0.963(0.025)

1.00 1.00 Japan is a fully industrialized country.Tokyo, with a population of 12million, is one of the largest citiesin the world.

Notes: Population for years prior to 725 is based on Koyama (1978). All time periods have 39 regions with Hokkaido andOkinawa dropped from all years. The relative variance of the log population is the variance of the log of population densityin year t divided by the variance of the log of population density in 1998. The Zipf coefficient is from a regression of log rankon log population density using 1920 log density as instruments for the years prior to 725 and 1998 data for later years.Standard errors are in parentheses. The correlation columns indicate the raw and rank correlations between regional densityin a given year and regional density in 1998.


metal farm tools, raising productivity. By 1150,Japan was racked by instability and civil war,particularly in the North.

By 1600, the reunification of Japan was com-plete and there is extensive trade and contactwith the West. Japan is a major regional power.By the 1630’s, however, Japan began more thantwo centuries of self-imposed isolation. By1721, the capital moved to Tokyo and popula-tion movement became more restricted. Even aslate as 1798, fully 80 percent of the populationwere farmers, about 6 percent nobility, withthe remainder merchants and artisans. By the1870’s, Japan witnessed a civil war, the endof the Shogun’s government, a jump from au-tarky to free trade, and the subsidized importof Western technology. This can be thoughtof as the very start of Japan’s industrial revolu-tion. By the 1920’s, industrialization and theaccompanying militarization are in full swing.Japan is a major exporter of silk and textiles.Nonetheless, approximately 50 percent of theworkforce is still composed of farmers. By1998, of course, Japan is a highly industrializedsociety, with farmers now comprising only 5percent of the population. Tokyo is one of theworld’s great cities with a population of 12million.

We conclude our data description by exam-ining the evolution of the total population ofJapan. The main features are developed in Table1. Kito (2000) estimates that the population inJomon-period Japan would have been approxi-mately 125,000; by 1998, it would fall just shyof 120 million. In short, our data encompasses aperiod in which Japanese population rises by afactor of nearly one thousand. If we restrictattention to the period for which we have cen-suses (i.e., from 725 to 1998), the populationrises from 4.5 million to nearly 120 million.That is, our census data encompasses a period inwhich total Japanese population rises by a factorgreater than 25. From the Jomon period throughabout 1721, the broad trend is substantial pop-ulation growth. In large measure, this reflectsthe development of agriculture and its imple-ments, extension of regions of cultivation, andestablishment of institutions that encouraged in-vestments in the land. For the next century anda half, through the 1870’s, there is very littlepopulation growth. In the next 120 years,through 1998, Japanese population would dou-

ble twice over, rising from 30 to 120 million. Insum, our data covers Japan from the Stone Ageto the modern era.

B. Variation in Regional Density

We begin by examining several measures ofvariation in regional population density (seeTable 1). A very coarse but simple measure isthe share of population accounted for by the fivemost populous regions. This concentration wasquite high, at 39 percent, in the Jomon period.This appears to reflect the fact that withoutagriculture, metal tools, or clothing, major sec-tions of Japan were virtually uninhabitable.From here through the dawn of the twentiethcentury, the share of the five largest regionstypically hovered around 20 percent, occasion-ally rising toward 30 percent. Remarkably, bythe end of the twentieth century, the share of thefive most populous regions would rise above 40percent.

A second measure of regional variation iswhat may be termed the relative variance of logpopulation density, which measures variance inproportional terms. To get this, first take logs ofthe regional population densities. For each pe-riod, this allows us to compute a variance of thelog population densities. If we now normalizethis by the same measure of variation for 1998,we get a measure that is above unity if thevariation is greater in the historical period thanin modern Japan and below unity in the reversecase.9

A first observation is that regional populationvariation is substantially higher in the modernperiod than at all prior dates except the Jomonand Yayoi periods. Again, one reason there is somuch variation in the Jomon and Yayoi periodsis simply that the economies were so primitivethat major sections of Japan were almost unin-habitable. A second observation is that all of thecensuses from 700 to 1600 show a great deal

9 An advantage of using this measure over simply usingthe variance in population density is that the former isinvariant to average density while the latter tends to risewith it. The reason for this is that as population, and henceaverage density, rises, the same proportional density differ-ences produce higher absolute variations in density. Sincewe wanted to sweep this effect out of the data, we calculatevariance based on log population density.


of variation in regional population density—typically two-thirds to three-fourths of the mod-ern variation. Indeed an F-test reveals that wecannot reject the hypothesis that variance inregional population density in any year prior to1721 was the same as the modern variance (atthe 5-percent level). Interestingly, the data from1721 through 1872 shows that the closure ofJapan seems to have been accompanied by asubstantial reduction in regional populationvariation. A plausible reason is that eight out ofthe 12 densest regions in 1600 comprised portcities whose share of population declined mark-edly over this time period.10 Closure to tradeprobably dramatically reduced the value of lo-cating in a port relative to remaining in farm-ing.11 Finally, the reopening of Japan and thedevelopment of the modern economy gave riseto a substantial increase in regional variation inpopulation density.

We can also examine a third measure ofvariation in regional density, the Zipf coeffi-cient. We have already noted, in reference to therandom growth theory, that there is an empiricalregularity known as Zipf’s Law for Cities. Tounderstand this, rank the cities by populationand now take logs of both the rank of the cityand of its population. Zipf’s Law for Citiesholds that a regression of the log rank againstlog population will have a slope of minus unity.Gabaix (1999) reports a slope of �1.004 for theUnited States and Kenneth T. Rosen andMitchel Resnick (1980) report slopes for a va-riety of OECD countries, many of which arereasonably close to minus unity.

In this context, the magnitude of the Zipfcoefficient provides information about variationin regional density. If there were only trivialvariation in regional population density, thenthe Zipf slope would be close to minus infinity.If virtually all of the population were clusteredin a single region, the Zipf coefficient wouldbe close to zero. Hence when the magnitudeof the Zipf coefficient is small, the variation is

large. Here we will report Zipf coefficientscomputed not on city populations but on re-gional population densities. As we will see,this transformation does little to disturb thebasic relation.

One should not directly run Zipf-style regres-sions on historical data since the population datais surely measured with error. In order to obtainunbiased estimates, we need an instrument cor-related with historical population data but notcorrelated with the measurement error in thatsurvey. An obvious instrument that fits the needis modern population density, since it isstrongly correlated with historical density butnot with historical census errors. We thereforeused density in 1998 as an instrument for earliercensus data. We had a different problem withthe Jomon and Yayoi data. Urban density in1998 is not a good instrument, since archaeo-logical discoveries might be correlated withmodern construction. However, since most Jap-anese archaeological discoveries of Jomon andYayoi sites occurred since 1960 [see Koyama(1978)], we used 1920 density data as an instru-ment for these regressions.

Table 1 reports the Zipf coefficient for eachof our time periods. The broad story that it tellsconfirms the results from the prior nonparamet-ric statistics. Dispersion was relatively high inthe Jomon and Yayoi periods—indeed veryclose to fitting Zipf’s Law. Regional variation indensity declined modestly for the period 725 to1600, before declining sharply in the period inwhich Japan was closed to the West. SinceJapan reopened and began its industrialization,regional variation has increased substantially,reaching a Zipf coefficient of �0.96 in 1998.12

The coefficients are quite precisely estimated.With the exception of the Jomon period, whichhas a standard error of 0.22, our standard errorson the Zipf coefficient range from 0.03 in 1998to 0.17 in the year 900. We cannot statistically

10 These were Chiba, Fukuoka, Kobe, Nagoya, Osaka,Tokyo, Yokkaichi, and Yokohama.

11 Other policies may also have affected city sizes suchas the construction of castle towns, tax evasion in ruralareas, and declining finances for samurai [See James Whit-ney Hall (1968) and Susan B. Hanley and Kozo Yamamura(1977)].

12 On first blush, this might appear to conflict with theresults of Jonathan Eaton and Zvi Eckstein (1997) thatshowed the stability of the Zipf coefficients for Japanesecities over the period 1925–1985 (a result that we canconfirm). Here the difference between their use of city dataand our use of regional data is crucial, since this suggeststhat even if there is little change in the distribution of citysizes, there may be important spatial correlation amongcities that are growing, which could explain the increasedvariation in regional densities.


distinguish the modern coefficient from that in1600 or any prior date.

Our examination of 8,000 years of Japaneseregional data reveals three important facts. First,regional population densities have always var-ied greatly in Japan. This is true in the StoneAge, at the dawn of the agricultural revolution,during the long period of feudalism, and it re-mains true in modern industrial Japan. Indeed,with the exception of Stone Age Japan, ourspread of Zipf coefficients is well within therange of coefficients that one would find in asample of OECD countries [cf., Rosen andResnick (1980)].13 Second, the closure of Japanto trade for more than two centuries was accom-panied by a substantial reduction in the varia-tion of regional population density. Large port-based regions appear to have lost ground relativeto regions directed more exclusively to nationalactivity. Third, the industrial revolution in Japan,coming hand in hand with its reopening to inter-national trade, does seem to have promoted a veryhigh degree of regional concentration and varia-tion in regional population density.

C. Persistence in Regional Population Densities

We now turn to consider persistence in theidentity of the regions that are densely settled.Table 1 reports both raw and rank correlationsbetween the regional population densities in thevarious periods with those for 1998. Considerfirst the Jomon data, dating from Japan’s StoneAge (�6,000 to �300). The raw and rank cor-relations of the density of archaeological sitesfrom this period and 1998 regional populationdensity are 0.53 and 0.31, respectively. Thehigher raw correlation especially captures thefact that the most densely settled regions arecommon in the two periods. The lower rank cor-relation captures the fact that large sections ofJapan were relatively untouched by the Jomonpeople and so the rankings among these are weak.

Consider next the Yayoi period (�300 to300). Agriculture and metallurgy are just beingintroduced. Writing has not yet appeared. In thenext two millennia, total population will rise by

a factor of 200. If we know the distribution ofthe regional density of archaeological sites fromthe Yayoi period, how much information wouldwe expect this to provide about the distributionof modern regional population densities? Theraw and rank correlations are 0.67 and 0.50respectively. Given that two millennia of Japa-nese history separate these dates, with the ac-companying economic transformations, weconsider this persistence to be quite remarkable.

In moving to the year 725, we now are able towork with the first census data and ask the samequestions. A feudal regime is in place. The vastmajority of the population is agricultural. None-theless, the raw and rank correlations of re-gional population densities in 725 and 1998 are0.60 and 0.71 respectively. Again, these show aremarkable persistence.

We will not discuss every date. Perhaps notsurprisingly, there is a general trend that rawand rank correlations with modern regional den-sities rise pretty steadily. We will cite just onelast date. If we look four centuries back to theyear 1600, a time in which Japan had a popu-lation just over 10 percent of its modern popu-lation, the raw and rank correlations with themodern regional densities are 0.76 and 0.83respectively.

In sum, it is absolutely striking how muchpersistence there is in the distribution of re-gional population density throughout Japanesehistory. The high correlations trace back virtu-ally to the Stone Age. The correlations betweenmodern regional densities and those of Japanfour centuries ago are remarkably strong. Per-sistence is a very strong feature of the data.14

13 Rosen and Resnick (1980) estimate the Zipf relation-ship for a broad set of countries using a comparable numberof observations. Within the OECD countries in their sample,Zipf coefficients range from �0.88 to �1.96.

14 This strong persistence raises an interesting ques-tion: Is the case of Japan special? One notable topograph-ical feature of Japan is that it is highly mountainous. Isthe simple contrast between uninviting mountains andinviting valleys the source of the persistence? Would onefind such persistence in a land with less stark contrasts?We believe that additional research is warranted. None-theless, we believe there is suggestive evidence in Rap-paport and Sachs (2001) that the pure role of geographyin determining the spatial distribution of activity is largeeven in a country with less apparently stark contrasts,such as the United States. They consider U.S. countiesproximate to an ocean, Great Lake, or navigable river;jointly these counties account for 15 percent of the U.S.land mass, but 54 percent of the population and 60percent of civilian income.


II. Bombs and Break Points

Imagine a calamity destroys a large share ofa city’s productive capacity and drastically re-duces its population. Will this temporary shockhave permanent effects? Or is there a strongtendency for locations to be robust even to largetemporary shocks so that this city will shortlyrevert to its former place in the constellation ofcities? An ideal experiment would have severalkey features. The shocks would be large, highlyvariable, clearly identifiable, and purely tempo-rary. In this section, we will consider the Alliedbombing of Japanese cities during World War IIas precisely such an experiment.

A. Data

Our data covers 303 Japanese cities with pop-ulation in excess of 30,000 in 1925. Populationis recorded at five-year intervals between 1925and 1965, with the exception that the regular1945 census is delayed until 1947 due to dis-ruption from the war. These data allow us tocompute population growth rates for the prewarperiod, 1925–1940; the period of the war itselfand its immediate aftermath, 1940–1947; andtwo measures of the recovery period, 1947–1960 and 1947–1965.15

One measure of the intensity of the shockswill be the dead and missing city residents dueto war actions. The missing are included be-cause the magnitude of the shocks frequentlymade recovery of bodies impossible, as for ex-ample with those vaporized by the Hiroshimanuclear blast. In order to have a measure of theintensity of the shocks, the dead and missingwill typically enter deflated by the number ofcity residents in 1940. A second measure of theintensity of the shocks will be the number ofbuildings destroyed per resident. We also attimes report the percentage of the built-up areadestroyed for the 66 Japanese cities covered bythe United States Strategic Bombing Survey(USSBS) (1947).

If we are to understand the impact of privateactions that may lead cities to recover, it isimportant to control for government actions.The Japan Statistical Yearbook (1950) provides

data on expenditures from U.S. and Japanesegovernment sources designated for the recon-struction of war damage in each prefecture. Weallocate these among the cities within the pre-fecture in proportion to the shares of buildingsdestroyed in that city. These are divided bythe population in the city in 1947 to createour variable, “government reconstruction ex-penses,” which is thousands of yen per capitaspent by the government to reconstruct a city.These geographically directed expenditures arequite small. For example, most food aid, incomeassistance, and industrial subsidy programs didnot discriminate on the basis of location, andtherefore do not count as regional subsidies.Interestingly, rural prefectures, which typicallysustained less war damage, received significantlymore aid relative to the number of buildings de-stroyed than more urban areas. This was probablydue to Japan’s long-term policy of subsidizingrural districts at the expense of urban ones.

B. Magnitude of the Shocks

The Allied strategic bombing of Japan inWorld War II devastated the targeted 66 cities.The bombing destroyed almost half of all struc-tures in these cities—a total of 2.2 millionbuildings. Two-thirds of productive capacityvanished. Three hundred thousand Japanesewere killed. Forty percent of the population wasrendered homeless. Some cities lost as much ashalf of their population owing to deaths, miss-ing, and refugees.16

The nuclear bombings of Hiroshima and Na-gasaki are, of course, well known. The firstatomic weapon was dropped on Hiroshima onAugust 6, 1945, and was the equivalent of 12kilotons of TNT. The temperature at the blastsite is believed to have surpassed one milliondegrees Celsius. Over two-thirds of the built-uparea of the city was destroyed. The blast mayhave killed as many as 80,000 people—morethan 20 percent of Hiroshima’s population. Thesecond atomic weapon was dropped on Nagasakion August 9 and had a power nearly twice that ofHiroshima, at 22 kilotons. The hilly topography ofNagasaki and the fact that the bomb missed itstarget by a wide margin kept the destruction of the

15 More detail is provided in the Appendix. 16 These numbers are from USSBS (1947).


built-up area under 40 percent. Still, more than25,000 were killed or went missing, approxi-mately 8.5 percent of city residents.

While the nuclear attacks on Hiroshima andNagasaki are widely known among the public inthe West, the devastation of other Japanese cit-ies is much less well known. An example of themagnitude of the destruction is a single fire-bombing raid on Tokyo the night of March 9,1945. United States B-29 Superfortress bomb-ers, based in the Marianas Islands, flew morethan 300-strong over Tokyo that night. Under anew strategy devised by General Curtis LeMay,the bombers flew with minimal defenses and atlow altitudes. This allowed them to maximizethe payload of napalm incendiaries and to re-lease these at precise intervals. The city hadreceived no rain in a week and the wind thatnight blew at 25 miles per hour. Tokyo—a cityof straw, paper, and wood—lay in wait. The B-29Superfortresses flew over Tokyo for just threehours on March 9, dropping 1.7 kilotons of na-palm incendiaries. This unleashed a firestorm.Rivers boiled. Asphalt streets liquefied and burstinto flame. The results were devastating. Sixteensquare miles of Tokyo were reduced to ash. Atleast 80,000 people were killed in that raid alone(Kenneth P. Werrell, 1996, p. 162–63).

The magnitude of destruction in the March 9raid on Tokyo was large not only by Japanesestandards; when it happened, it was the deadliestsingle-day air attack in the history of the world.The number of people killed was of the sameorder of magnitude as the nuclear bombing ofHiroshima. Japan suffered more civilian casualtiesin that one raid than Britain suffered in all ofWorld War II. And this was just the beginning. Bythe end of the war, the United States had destroyedmore square miles of Tokyo than the combineddestruction in the 15 most heavily bombed Ger-man cities (Werrell, 1996, p. 32).

A major reason why Tokyo stands out inJapanese data is due to the fact that with a 1940population of 7.3 million it was by far thelargest target in Japan. Given that Tokyo was 16times the size of Hiroshima and more than 20times the size of Nagasaki, even nuclear bombscould not kill as many people in these smallercities. This suggests the value of consideringdestruction in proportional rather than absoluteterms. Seen this way, the destruction in thecourse of the war of 56 square miles of Tokyo

only amounted to 50.8 percent of its built-uparea (USSBS, 1947, p. 42). This is actually justunder the median percentage of urban destruc-tion of 50.9 percent for the 66 targeted cities. Inshort, in terms of the destruction of built-up areafor the targeted cities, the devastation of Tokyowe described made it just a typical city.17

C. Variance of the Shocks

While the magnitude of the shocks to citysizes was large, there was also a great deal ofvariability in these shocks. In fact, approxi-mately 80 percent of the 300 cities in our sam-ple, collectively representing 37 percent of theurban population, were virtually untouched bythe bombings. This includes large cities. Kyoto,the fifth largest city at the beginning of the war,was not bombed at all.18 Given the city’s his-torical significance, it was believed that its de-struction might strengthen the Japanese will toresist. The large cities of Niigata and Kitakyu-shu escaped substantial damage because theywere preserved as potential nuclear bomb tar-gets. Cities in the North of Japan, such as Sap-poro, escaped heavy bombing because theywere largely out of range of U.S. bomber forces.

Even among those cities that did suffer fire-bombing, there is a high degree of variability inthe destruction. One reason is learning by doing.The creation of a firestorm from napalm incen-diaries depended on having a sufficient numberof planes, dropping the incendiaries in precisepatterns and at relatively close intervals. Whilesome tests of the incendiaries had been con-ducted on mock Japanese cities at the DugwayProving Grounds in Utah, it was only as a resultof the experience of actual bombing raids thatU.S. forces achieved the optimal pattern. More-over, cities such as Nagoya, which were fire-

17 The Allies dropped 17 pounds of incendiaries percapita on the median firebombed city, but only four poundsper capita on Tokyo. Tokyo nonetheless still stands out forthe number who died. It seems likely that in smaller citiesthere was greater opportunity to escape the firestorms.

18 Our definition of “virtually untouched” is casualties ofunder 100. Eric Hammel (1998) reports no air attacks onKyoto. Takahide Nakamura and Masayasu Miyazaki (1995)do report 82 casualties in Kyoto (1940 population 1.1 mil-lion) due to the war. Presumably these were due to targetingerrors, strafing, and/or Kyoto residents who were killed inother cities.


bombed early, had as a result of those raids theequivalent of firebreaks within the city. In thesubsequent raids, it became nearly impossible tocreate highly destructive firestorms.

In addition, there were a large number ofother factors at work that created variance in thedestruction of cities. These include the steadygrowth in the number of B-29s available forservice; the evolving defense capabilities of theJapanese cities (which was important notablyfor Osaka); the topography of specific cities;and sheer fortune, as in the fact that Nagasakiwas bombed only when the primary target,Kokura (now Kitakyushu), could not be visuallyidentified due to cloud cover.

D. Temporary Nature of the Shocks

Rarely does one find shocks that can so clearlybe identified as temporary. For much of WorldWar II, Japanese cities were simply out of range ofU.S. bombers. In the first year of the war, theUnited States managed only the single “Doolittleraid” on Japan from a U.S. carrier, and this hadlittle more than psychological impact. Later, theUnited States tried to use China as a base forattacks on Japanese cities. But the long flightsrequired and the difficult supply lines insured thatthese had only minimal effect. It was only with thecapture of the Marianas Islands as a B-29 base, theseizure of Iwo Jima (which lay directly betweenthe Marianas and Japan) as a base for fighterescorts, a rise in the number of planes available,and the introduction of new tactics by GeneralLeMay that the U.S. attacks reached an apogee.The most powerful attacks were compressed inthe last five months of the war.

While the devastation of many of these citieswas powerful, once the flames were out, thegeographical characteristics of particular loca-tions are affected little or not at all. The onepossible exception, of course, is the lingeringradiation in Hiroshima and Nagasaki. This willmake these particularly interesting cases to seewhether they were special cases in the period ofrecovery from the war.

E. Impact of the Shocks:Temporary or Permanent?

We now inquire whether temporary shockshave permanent effects on relative city sizes.

Let Sit be city i’s share of total population attime t, and let sit be the natural logarithm of thisshare. Suppose further that each city has aninitial size �i and is buffeted by city-specificshocks �it. In this case we can write the size ofany city at any point in time as,

(1) sit � � i � � it .

We can model the persistence in these shocks topopulation shares as:

(2) � it � 1 � �� it � � it � 1 .

The parameter � � [0, 1], and the innovation,�it, is an independently and identically distrib-uted error term.

We examine the evolution of this system byfirst-differencing equation (1). This yields

(3) sit � 1 � sit � � it � 1 � � it .

If we substitute equation (2) into equation (3),we then obtain

(4) sit � 1 � sit � �� 1�� it

� �� it � 1 � ��1 � �� it � 1 �.

The key parameter is �, which tells us howmuch of a temporary shock is dissipated in oneperiod. If � � 1, then all shocks are permanentand city size follows a random walk.19 In thiscase,

19 Equation (5) is identical to the key equation in Gabaix(1999)—what he terms “the basic idea.” We also considerone amendment to this basic idea in the empirical section.However, it is worth noting that we do not consider allpossible random walk processes. One could imagine a worldin which shocks come in two parts—one of which is meanreverting and the other a random walk. Over a short horizon,we might see very strong mean reversion, even though overa sufficiently long horizon the structure of city sizes isdetermined by the random walk component. If one is willingto believe that the random walk component is quite small,then this will be a very difficult hypothesis to reject. Theproblem with this explanation of Zipf’s Law is that if thispaper’s restrictions on the size of the permanent componentof the shock is appropriate, then it would take very longhorizons (possibly in the thousands of years) for the Zipfdistribution to emerge. In any case, over the shorter hori-zons of interest, this paper shows that mean reversion toshocks is a superior economic model.


(5) sit � 1 � sit � � it � 1 .

If � � [0, 1), then city share is stationary andany shock will dissipate over time. In otherwords, these two hypotheses can be distin-guished by identifying the parameter �.

One approach to investigating the magnitudeof � is to search for a unit root. It is well knownthat unit root tests usually have little power toseparate � 1 from � � 1. This is due to thefact that in traditional unit root tests the inno-vations are not observable and so identify � withvery large standard errors. A major advantageof our data set is that we can easily identify theinnovations due to bombing. In particular, sinceby hypothesis the innovation, �it, is uncorre-lated with the error term (in square brackets),then if we can identify the innovation, we canobtain an unbiased estimate of �.

An obvious method of looking at the innova-tion is to use the growth rate from 1940 to 1947.However, this measure of the innovation maycontain not only information about the bombingbut also past growth rates. This is a measure-ment error problem that could bias our estimatesin either direction depending on �. In order tosolve this, we instrument the growth rate from1940–1947 with buildings destroyed per capitaand deaths per capita.20

We can obtain a feel for the data by consid-ering the impact of bombing on city growthrates. As we argued earlier, if city growth ratesfollow a random walk, then all shocks to citiesshould be permanent. In this case, one shouldexpect to see no relationship between historicalshocks and future growth rates. Moreover, ifone believes that there is positive serial corre-lation in the data, then one should expect to seea positive correlation between past and futuregrowth rates. By contrast, if one believes thatlocation-specific factors are crucial in under-standing the distribution of population, then oneshould expect to see a negative relationshipbetween a historical shock and the subsequentgrowth rate. In Figure 1 we present a plot of

population growth between 1947 and 1960 withthat between 1940 and 1947. The sizes of thecircles represent the population of the city in1925. The figure reveals a very clear negativerelationship between the two growth rates. Thisindicates that cities that suffered the largestpopulation declines due to bombing tended tohave the fastest postwar growth rates, whilecities whose populations boomed converselyhad much lower growth rates thereafter.

In Table 2, we present a regression showingthe power of our instruments. Deaths per capitaand destruction per capita explain about 41 per-cent of the variance in population growth ofcities between 1940 and 1947. Interestingly,although both have the expected signs, destruc-tion seems to have had a more pronouncedeffect on the populations of cities. Presumably,this is because, with a few notable exceptions,the number of people killed was only a fewpercent of the city’s population.

We now turn to test whether the temporaryshocks give rise to permanent effects. In orderto estimate equation (4), we regress the growthrate of cities between 1947 and 1960 on thegrowth rate between 1940 and 1947 usingdeaths and destruction per capita as instrumentsfor the wartime growth rates. The coefficient ongrowth between 1940 and 1947 corresponds to(� � 1). In addition, we include governmentsubsidies to cities to control for policies de-signed to rebuild cities.

If one believes that cities follow a random

20 The actual estimating equation is si60 � si47 � (� �1)��47 � [�i60 � �(� � 1)�i34]. Our measure of theinnovation is the growth rate between 1940 and 1947 orsi47 � si40 � ��47 � [��i34 � �i40]. This is clearlycorrelated with the error term in the estimating equation,hence we instrument.

FIGURE 1. EFFECTS OF BOMBING ON CITIES WITH

MORE THAN 30,000 INHABITANTS

Note: The figure presents data for cities with positive casu-alty rates only.


walk or that catastrophes can permanently alterthe size of cities, then one should expect thecoefficient on the 1940–1947 growth rate, (� �1), should be zero. If one believes that thetemporary shocks have only temporary effects,then the coefficient on 1940–1947 growthshould be negative. A coefficient of �1 indi-cates that all of the shock was dissipated by1960.

The results are presented in Table 3. Thecoefficient on 1940–1947 growth is �1.048,indicating that at this interval � is approximatelyzero. This means that the typical city com-pletely recovered its former relative size within15 years following the end of World War II.Given the magnitude of the destruction, this isquite surprising. Apparently, U.S. bombing ofJapanese cities had no impact on the typicalcity’s size in 1960. This strongly rejects thehypothesis that growth in city-size share is arandom walk.

As expected, reconstruction subsidies seemto have had a positive and statistically signifi-cant impact on rebuilding cities. However, theeconomic impact is quite modest. Our estimatessuggest that a one standard deviation increase inreconstruction expenses would increase the sizeof a city in 1960 by 2.2 percent. Reconstructionexpenses probably had a small effect becauseboth the sums spent and the variance in thesums were small. In the cities that suffered theheaviest destruction—Tokyo, Hiroshima, Na-gasaki, and Osaka—our estimates indicate thatgovernment reconstruction expenses accountedfor less than one percentage point of their cu-mulative growth between 1947 and 1960. Given

that cumulative growth in these cities over thatperiod was between 55 and 96 percent, weconclude that reconstruction expenses had rela-tively small impacts. As we noted earlier, amajor reason for this was that reconstructionpolicies, like most Japanese regional policies,disproportionately sent money to rural areas. Asa result, the four biggest per capita recipients ofassistance were small northern cities that werenever targeted by U.S. bombers.

One potential problem with these results isthat it is possible that the United States inad-vertently targeted cities based on underlyinggrowth rates. While this was not an explicitstrategy, we cannot rule it out. If the UnitedStates bombed rapidly growing cities moreheavily, then we may be biasing our resultsdownwards. We therefore repeated our exerciseadding the growth rate between 1925 and 1940to our list of independent variables. This im-proves the fit, but does not qualitatively changethe results, although the coefficient on 1940–1947 growth falls to �0.76. This implies thatbombed cities had recovered over three-fourthsof their lost growth by 1960. One reasonablequestion to ask, then, is whether these citiesever returned to their prewar trajectories or not.If one believes in the location-specific model,then one should expect that the coefficient on

TABLE 2—INSTRUMENTAL VARIABLES EQUATION

(DEPENDENT VARIABLE � RATE OF GROWTH IN CITY

POPULATION BETWEEN 1940 AND 1947)

Independent variable Coefficient

Constant 0.213(0.006)

Deaths per capita �0.665(0.506)

Buildings destroyed per capita �2.335(0.184)

R2: 0.409Number of observations: 303

Note: Standard errors are in parentheses.

TABLE 3—TWO-STAGE LEAST-SQUARES ESTIMATES OF

IMPACT OF BOMBING ON CITIES

(INSTRUMENTS: DEATHS PER CAPITA AND BUILDINGS

DESTROYED PER CAPITA)

Independent variable

Dependentvariable �growth rate

of populationbetween1947 and

1960

Dependentvariable �growth rate

of populationbetween1947 and

1965

(i) (ii) (iii)

Growth rate of populationbetween 1940 and 1947

�1.048(0.097)

�0.759(0.094)

�1.027(0.163)

Government reconstructionexpenses

1.024(0.387)

0.628(0.298)

0.392(0.514)

Growth rate of populationbetween 1925 and 1940

0.444(0.054)

0.617(0.092)

R2: 0.279 0.566 0.386Number of observations: 303 303 303

Note: Standard errors are in parentheses.


wartime growth should asymptotically ap-proach unity as the end period increases. In thelast column of Table 3 we repeat the regression,only now extending the endpoint to 1965 in-stead of 1960. The estimated coefficient nowreaches �1.027. That is, after controlling forprewar growth trends, by 1965 cities have en-tirely reversed the damage due to the war.Again, the impact of reconstruction subsidiesalso lessens as we move into the future. To-gether, these results suggest that the effect ofthe temporary shocks vanishes completely inless than 20 years.

One possible objection to our interpretation isthat in most cases, the population changes cor-responded much more to refugees than deaths.Of the 144 cities with positive casualties, theaverage number of deaths per capita was only 1percent. Most of the population movement thatwe observe in our data is due to the fact that thevast destruction of buildings forced people tolive elsewhere. However, forcing them to moveout of their cities for a number of years may nothave sufficed to overcome the social networksand other draws of their home cities. Hence itmay seem uncertain whether they are movingback to take advantage of particular character-istics of these locations or simply moving backto the only real home they have known.

However, there are two cases in which thisargument cannot be made: Hiroshima and Na-

gasaki. In those cities, the number of deaths wassuch that if these cities recovered their popula-tions, it could not be because residents whotemporarily moved out of the city returned insubsequent years. We have already noted thatour data underestimates casualties in these cit-ies. Even so, our data suggest that the nuclearbombs immediately killed 8.5 percent of Na-gasaki’s population and 20.8 percent of Hiro-shima’s population. Moreover given that manyJapanese were worried about radiation poison-ing and actively discriminated against atomicbomb victims, it is unlikely that residents felt anunusually strong attachment to these cities orthat other Japanese felt a strong desire to movethere. Another reason why these cities are in-teresting to consider is that they were not par-ticularly large or famous cities in Japan. Their1940 populations made them the 8th and 12thlargest cities in Japan. Both cities were close toother cities of comparable size so that it wouldhave been relatively easy for other cities toabsorb the populations of these devastatedcities.

In Figure 2 we plot the population of thesetwo cities. What is striking in the graph is thateven in these two cities there is a clear indica-tion that they returned to their prewar growthtrends. This process seems to have taken a littlelonger in Hiroshima than in other cities, but thisis not surprising given the level of destruction.

FIGURE 2. POPULATION GROWTH


Taken together, these tests establish that eventhe spectacular destruction inflicted on Japanesecities by the U.S. strategic bombing of Japanesecities in WWII had virtually no long-run impacton the relative size of Japanese cities. Withinthe space of just 20 years, they recovered fromthe devastation to return to their former place inthe constellation of cities.

III. Three Theories in Light of the Evidence

The preceding two sections establish a seriesof stylized facts about the economic geographyof Japan. It is now time to collect those factsand consider them in light of the major theories.The facts are: (1) A high degree of variation inJapanese regional density has existed at allpoints in time. (2) Zipf’s Law holds approxi-mately for the distribution of regional densitiesthroughout Japanese history. (3) The variationin regional densities begins to rise in the veryperiod that Japan reopens to the world economyand begins its industrialization. (4) There istremendous persistence in the identity of themost densely settled regions. (5) Even verystrong temporary shocks have virtually no per-manent impact on the relative size of cities.

The three theories that we have identified areincreasing returns (IR), random growth (RG),and locational fundamentals (LF). Properly, theIR approach is less a theory than a family oftheories with common structural elements.Hence we do not think it is appropriate to con-sider our exercises a test of the IR theories.Rather, we will use the facts to consider whichof various themes that have featured promi-nently within the IR literature. We summarizeour findings in Table 4 where a “�” indicatesthat the stylized fact is predicted by the theory,a “�” indicates that the theory does not predictit, and a question mark indicates that the theoryeither makes no prediction or is ambiguous.

As a point of analysis, the increasing returnstheories frequently ask how spatial differentia-tion may emerge even in a framework in whichall locations are identical in terms of economicprimitives (Fujita et al., 1999). From an analyticstandpoint, this is precisely the right startingpoint because it emphasizes theoretical featuresof the IR approach that are unique and surpris-ing. However, it is an empirical question howmuch of the actual variation in regional densi-

ties owes to IR forces and how much to otherfactors. An extremely important advantage ofthe long time series with which we work is thatit is both able to examine the distribution ofregional densities for a period in which theforces of increasing returns must have beenvastly weaker than they are today and also tosee if there is a rise in regional variation in theperiod in which the theory predicts there shouldbe.

The fact that there has been a high degree ofvariation in regional population densities at allpoints in Japanese history, even those in whichincreasing returns is likely of at most modestimportance, strongly suggest that there areforces quite apart from increasing returns thathave long been important contributors to thisregional variation. However, the fact that thevariation in regional population density roseprecisely in the period in which Japan industri-alized is something that we may well have ex-pected based on the IR approach. This seemsreasonably strong evidence that IR theories dohave something important to contribute to acomplete theory of economic geography.

We have noted that the Zipf relation holdsreasonably well for the distribution of regionaldensities, just as it does for the distribution ofcity sizes. Fujita et al. (1999) have been veryforthright that the IR theories provide no obvi-ous account for the Zipf relation.

The IR theories do not provide a definitiveanswer to the degree of persistence one shouldexpect in regional densities. One strand ofthe theory, due to Henderson (1974), ties citysizes to technological characteristics of specific

TABLE 4—MATCH BETWEEN THEORIES AND PREDICTIONS

Stylized factIncreasing

returnsRandomgrowth

Locationalfundamentals

Large variation inregional densitiesat all times � � �

Zipf’s Law � � �Rise in variation

with IndustrialRevolution � � �

Persistence inregional densities ? ? �

Mean reversion aftertemporary shocks ? � �


industries. Since we are looking over periodswith very radical shifts in industrial structure,one might on this basis suppose that there wouldbe similarly radical shifts in regional densities(which we don’t observe). However, there is analternative tradition within the IR approach,typified by David (2000) and very evident inFujita et al. (1999), which stresses the role ofpath dependence. Small initial advantages cu-mulate, so that even as the industrial structurechanges radically, the head start provides anadvantage in the next stage of locational com-petition. It seems to us that if one is to interpretthe strong locational persistence from the per-spective of the IR framework that one does needto rely strongly on path dependence.

Finally, again the IR framework does notprovide a unique answer to whether temporaryshocks will have permanent effects. Nonethe-less, the investigation of the bombing of Japa-nese cities does prove useful. One of the moststriking features of the IR literature is the exis-tence of bifurcations in parameter space—whatFujita et al. term break points and sustainpoints—which separate radically different spa-tial equilibria.21 The literature emphasizes aswell that because of the existence of multiplestable equilibria, there may be irreversibility ofthese changes even when the forces that broughtabout the initial change are reversed. An impor-tant practical question, then, is whether suchspatial catastrophes are theoretical curiosa or acentral tendency in the data. Our results providean unambiguous answer: Even nuclear bombshave little effect on relative city sizes over thecourse of a couple of decades. The theoreticalpossibility of spatial catastrophes due to tempo-rary shocks is not a central tendency borne outin the data.

The random growth (RG) theory can be dis-cussed briefly. The most important advantage ofthe RG theory over the IR theory is simply thatit provides a foundation for understanding theZipf distribution, which is also evident in thedistribution of regional densities. The existenceof substantial variation in regional densities

across all of Japanese history is consistent withthe RG theory provided the stochastic processstarts sufficiently far back in time. The persis-tence of the identity of the densely settled re-gions can be made consistent with the RGtheory only if one is willing to believe that thevariance of growth rates is quite small. The RGtheory provides no explanation why the indus-trial revolution in Japan should have been ac-companied by a rise in the variation in regionaldensities. However, the most devastating strikeagainst the RG theory comes from the exami-nation of the bombing data. The RG theoryholds that growth will be a random walk. This isstrongly rejected by the data on the recovery ofJapanese cities in the wake of the WWII bomb-ing. Hence we consider this a decisive rejectionof the pure RG theory.

The locational fundamentals (LF) theoryholds that there are permanent features of spe-cific locations that make these locations an ex-cellent site for economic activity. Access to thesea, rivers, and a large plain has been useful atall points in time. Location on a mountaintop, inthe desert, or in harsh climactic conditions hasalways been a disadvantage. This provides avery natural account of the high degree of vari-ation in regional densities at all points in time. Ifthese fundamentals are distributed as suggestedby Krugman (1996) and Gabaix (1999), thenthey also provide an account for Zipf’s Law.Persistence is highly compatible with this ac-count. Moreover, since the bombing of citieswould not be expected to affect these funda-mentals, the LF theory provides a very naturalaccount for the postwar mean reversion of cit-ies. The one area in which there seems to be animportant shortfall is that the LF theory does notprovide an obvious explanation for the rise inthe variation of regional densities coincidentwith the industrial revolution in Japan.

IV. Policy

While we do not directly examine any policyinterventions, our results are pertinent to policydiscussions. One of the most important reasonsfor the renewed interest in economic geographyis precisely the possibility that in a world ofcumulative causation, path dependence, andcritical break points, even temporary policy in-terventions may alter the long-run spatial struc-

21 Formally, a break point is a parameter value thatmarks a threshold between values for which a symmetricequilibrium is stable or not. A sustain point, similarly,is the threshold governing the stability of a concentratedequilibrium.


ture of economic activity. These in turn mayhave important welfare consequences, particu-larly for immobile factors in the regions favoredor not. Our results suggest a great deal morestability in the spatial structure of economiesthan one might have guessed. There is tremen-dous persistence in which regions are mostdensely settled, even as the economy passesthrough multiple economic revolutions—therise of agriculture, the rise and decline of feu-dalism, the move to autarky and the reversal tofree trade, and finally the rise of the industrialrevolution. Destruction of half or more of acity’s structures and killing as much as 20 per-cent of its population does little to disturb thelong-run relative size of a city. In the face ofthese facts, how much chance is there that tem-porary subsidies of economically relevant mag-nitudes will significantly alter the long-runspatial structure of an economy?22

Sachs (2001) and various co-authors haveraised a policy-relevant question bearing on is-sues of economic development.23 To what ex-tent is geography destiny? Is living in thetropics instead of a temperate zone a long-runimpediment to economic development? Is thelack of a coast or navigable rivers an insupera-ble obstacle to growth? We believe that theevidence we provide complements the results ofSachs and others which stress that there aredeep, very likely geographical, characteristicsof particular locations that have a very stronginfluence on their opportunities for growth rel-ative to other locations in a common technolog-ical regime.

V. Conclusions

We began with the defining question of eco-nomic geography: What gives rise to the ob-served variation in economic activity acrossregions? It is impossible, of course, to provide

final answers to such an important question onthe basis of one study of the experience of onecountry. Nonetheless, we believe that thepresent study does allow important progress inunderstanding this question.

We examined data on regional populationdensity in Japan from the Stone Age to themodern era. We also considered the implica-tions for relative city sizes of the Allied bomb-ing of Japanese cities during World War II.These data exercises allowed us to develop anumber of key stylized facts. Variation in re-gional population density has been high at allpoints in time, obeys Zipf’s Law, and rose in theperiod coincident with the industrial revolution.There is a great deal of persistence in the iden-tity of the most densely settled regions. Andtemporary shocks, even of frightening magni-tude, appear to have little long-run impact onthe spatial structure of the economy.

We then used these facts to consider threeprominent theories designed to explain the dis-tribution of city sizes. The simple randomgrowth theory of Simon (1955) and Gabaix(1999) is decisively rejected by the bombingexperiment, since that theory counterfactuallypredicts that city sizes will follow a randomwalk. The strongest point in favor of the in-creasing returns theory is its clear suggestionthat industrialization should have raised thevariation of regional densities—a predictionconfirmed by the data. By contrast, the strongemphasis within the increasing returns literatureon the possibility of spatial catastrophes due tomultiple equilibria finds no support in our ex-periments. The locational fundamentals theoryemerges as an important part of a full account.It can explain why there is a great deal ofvariation in regional densities long before in-creasing returns is a plausible account; it ex-plains why the densities obey Zipf’s Law—something the increasing returns theory cannotdo; it predicts a great deal of persistence in thedistribution of regional densities; and it predictsthat even quite large temporary shocks will havelittle long-run impact. The one dimension inwhich the increasing returns theory clearlydominates the locational fundamentals theory isthe account that it provides of the rise in thevariation of regional densities in the period ofindustrialization. Taken together, these consid-erations lead us to favor a hybrid theory in

22 It is important to note that for these issues, the degreeof geographical aggregation may matter. For example, itmay well be that Tokyo was destined to be a great city, butit may have been harder to say which subregions of Tokyowould take on the specific character that they have. Simi-larly, this need not rule out that such subsidies could im-portantly affect the industrial mix as opposed to aggregateactivity.

23 Cf., Rappaport and Sachs (2001), John Luke Gallup etal. (1999), etc.


which locational fundamentals play a leadingrole in accounting for the spatial pattern ofrelative regional densities, but increasing re-turns may help to determine the degree of spa-tial differentiation.

APPENDIX: DETAILS ON THE CONSTRUCTION OF

REGIONAL POPULATION DATA

Japan has one of the most complete sets ofhistorical regional census data of any country inthe world. A major reason why data was col-lected on a regional level is that while Japanwas unified in theory, in practice local lordsoften had substantial autonomy and Japanesegovernment records reflected this. Until themid-1870’s Japan was divided into 68 prov-inces or kuni. However one of the kuni, Ezo,now Hokkaido, reported data very erraticallydue to the low Japanese population and wasdropped from our sample. These data were col-lected as a part of the Japanese tax systemenvisaged in the Taika reform of 646. However,a series of assassinations, coups, and civil warsdelayed full-scale implementation until 702. Atthat time, cultivators over the age of six wereallocated land from the government and in re-turn had to pay lump-sum in-kind taxes. (Hall,1979, p. 54). This forced the government’s Pop-ular Affairs Ministry to keep detailed popula-tion and tax records, many of which exist today.

The raw census data is hard to use, becausecensuses were done infrequently and often in-cluded different standards for covering samurai,non-landholders, women, children, etc. For ex-ample, Kii did not report people under the ageof eight while other provinces reported signifi-cantly younger children. Over the last 75 years,due in large measure to enormous efforts on thepart of Japanese historical demographers, nota-bly Goichi Sawada (1927), Naotaro Sekiyama(1958), and Kito (1996), these data have beencarefully organized and rendered systematic. Thistypically involves incorporating procedures toestimate the missing youth population based onage distributions in neighboring regions.

Our data on regional population between 725and 1872 is based on Kito (1996). The Kito dataset represents the culmination of these efforts byproviding best estimates of the provincial pop-ulation for 725, 800, 900, and 1150. For theseyears, data is either based on actual census data

where available or on the number of “villages”(go) per province. In the Japanese system usedat the time, each “village” or go was comprisedof three hamlets containing 50 households perhamlet. Hence, if one can estimate the numberof family members per household, based onexisting household data in some regions, onecan obtain reasonable estimates of the regionalpopulation based on the number of “villages.”

How well this method works can be assessedby how well these estimates conform to subse-quent discoveries of census data. For example,W. Wayne Farris (1984, p. 175) reports thatafter Sawada (1927) did his original analysis,archaeologists uncovered actual census data forHitachi province in the year 800, a missingdatum in Sawada. Sawada’s estimate of 217,000residents was quite close to the census numberof 190,000.

Data for 1600 is based on a major cadastralsurvey conducted under the order of ShogunHideyoshi Toyotomi. The frequency of censusdata increases from 1721 when Japan began touse these censuses as part of their anti-Christiancampaign. Unfortunately, there were no re-gional censuses taken between 1872 and 1920.Although some authors report figures for theintervening years, these are largely interpola-tions between the two end points.

Another complication arises from the factthat historical regional data is based on 68 prov-inces whose boundaries do not correspond pre-cisely to the 47 prefectures used in moderncensus reporting. For example, the province ofMusashi was broken up into two prefectures,Tokyo and Saitama. Others are harder to mapinto modern prefectures—e.g., the province Kiicontains all of Wakayama prefecture and part ofMie. Feudal lords in Japan ruled over severalhundred domains, which, in general did nothave boundaries that correspond to provincialboundaries. The borders of these domainschanged significantly over the course of the nextmillennium in response to wars and patronage,but the borders of the provinces did not. Wesolved this problem by using a historical mapprovided by Hanley and Yamamura (1977) andcomparing it with modern maps. This generatesa concordance, which we present in Table A1.We then checked our matching by comparingthe aggregate area of the provinces (from the1882 Japanese Imperial Statistical Yearbook)


with the areas of corresponding prefectures(from the 2000 Japan Statistical Yearbook).This suggests that we matched the data quiteclosely.

We measured regional density as the numberof people per square kilometer. One problemthat can arise is that regional definitions usingprovincial data may be slightly different fromthose using prefectural data. In order to elimi-nate this problem, we implemented the follow-ing procedure. Whenever we formed a regionusing provincial population data we deflated it

with provincial area data. Likewise, wheneverwe formed a region using prefectural populationdata, we deflated using prefectural area data.

While there is a very large literature in Japanon the accuracy of historical numbers, mostresearchers believe that the population numbers,at least from 1721 onwards, are accurate towithin 15 percent. The reason that we have agood sense about the accuracy is that in a fewcases provincial boundaries and feudal domainboundaries coincided. Sometimes the feudallord in these areas would conduct an indepen-dent population census of his domain, and thenwe can compare the results of the two surveys.So, for example, in the province of Bizen, cen-tral government data puts the 1798 populationat 321,221 while the lord of Okayama believedthe total to be 320,795. However, both of thesenumbers underreport the population of the cas-tle town, which Hanley and Yamamura (1977)suggest would take the total to 342,013. Thepoint, of course, is that while the data from 1721onwards is far from perfect, the level of mea-surement error is not so high as to render thedata meaningless.

Prior to 725, it is also possible to obtainestimates of the Japanese population based onarcheological evidence. Japan has been popu-lated for at least 10,000 years and there are28,013 archaeological sites from the Jomon pe-riod (�8000 to �300) and another 10,530 sitesfrom the Yayoi period (�300 to 300). Koyama(1978) has categorized these sites by prefectureand they can be used to provide a rough idea ofthe regional distribution of population byprefecture.

Details on Urban Data

There are two principal sources of informa-tion on death and destruction caused byWorld War II in Japan: the U.S. StrategicBombing Survey (USSBS) (1947) and Naka-mura and Miyazaki (1995). This latter sourceis basically a reprint of “The Report on Dam-age and Casualties of World War II” com-piled by the Central Economic StabilizationBoard (CESB) in 1949. The U.S. source isparticularly good for matching death and de-struction to particular U.S. air operations,while the Japanese source is a 600-page cen-sus of all death and destruction that occurred

TABLE A1—CONCORDANCE BETWEEN PROVINCES AND

PREFECTURES

Province (Kuni) Prefecture (Ken)

Iwaki, Iwashiro, Rikuzen,Rikuchu, and Mutsu

Aomori, Iwate, Miyagi,and Fukushima

Uzen-Ugo Akita and YamagataAwa1, Kazusa, and Shimo-osa ChibaAwa2 TokushimaBingo and Aki HiroshimaBungo OitaChikuzen, Buzen, and Chikugo FukuokaEchigo and Sado NiigataEtchu ToyamaHarima, Tajima, and Awaji HyogoHigo KumamotoHitachi IbarakiHizen, Tsushima, and Iki Nagasaki and SagaHyuga MiyazakiIga, Ise, and Shima MieInaba and Hoki TottoriIyo EhimeIzumo, Iwami, and Oki ShimaneKaga and Noto IshikawaKai YamanashiKawachi, Izumi, and Settsu OsakaKii WakayamaKozuke GunmaMimasaka, Bizen, Bitchu OkayamaMino and Hida GifuMusashi Tokyo and SaitamaOmi ShigaOsumi and Satsuma KagoshimaOwari and Mikawa AichiSagami KanagawaSanuki KagawaShimotsuke TochigiShinano NaganoSuo and Nagato YamaguchiTosa KochiTotomi, Suruga, and Izu ShizuokaWakasa and Echizen FukuiYamashiro, Tamba, and Tango KyotoYamato Nara


within Japan proper. As such, the Japanesesource provides a more complete record ofhow the war affected civilians.

Since our primary interest was obtaininginformation on the magnitude of shocks tocities regardless of the particular air operationthat gave rise to it, we felt the Japanese sourcewas more appropriate. Japanese numbers forcasualties and destruction tend to be largerthan the numbers reported above for a numberof reasons. First, the USSBS only covers de-struction due to planned strategic bombing. Ittherefore does not include urban deaths due toother bombing activities, strafing, naval bom-bardments of coastal cities, and the mining ofharbors, nor does it cover destruction arisingfrom accidentally bombing the wrong targets.Second, U.S. fatality data appear to be onlyreported for confirmed deaths. In nuclearbombing and firebombing, it is quite commonfor thousands, if not tens of thousands ofpeople, to be vaporized. People who wentmissing on the day of a bombing raid and didnot turn up within several years are notcounted as casualties in U.S. sources but arelisted as missing in CESB and are added tofatality numbers.24 Third, U.S. data does nottreat mortally injured people as fatalities,whereas Japanese data does. This is particu-larly a problem in Hiroshima and Nagasakiwhere large numbers of people died of radi-ation poisoning within a few years of theattack. This helps explain why the CESB re-ports twice as many fatalities in Nagasakias USSBS. A more difficult issue concernsradiation-induced deaths in the period be-tween 1949 and 1965. However, since directdeaths were so large, even high estimates (inthe tens of thousands) of the number dyingfrom radiation do not affect our numbers ondeaths per capita very much.

Urban population data were taken fromthe Kanketsu Showa Kokusei Soran (ToyoKeizai Shinposha, 1991). A key feature ofthis source is that city areas are held con-stant across the time period. This datasource reports urban populations for several

hundred cities based on censuses every fiveyears.25 The only exception is 1945. The 1945census of cities was not performed until 1947due to the war. This is actually fortunate forus. Japanese ground transportation waslargely unaffected by the war. This means thatby 1947, anyone who had fled due to the fearof air strikes could have returned providedthat housing and employment existed there.

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