DPRIETI Discussion Paper Series 11-E-060

Urban Density, Human Capital, and Productivity:
An empirical analysis using wage data
MORIKAWA Masayuki
RIETI

The Research Institute of Economy, Trade and Industry

http://www.rieti.go.jp/en/

RIETI Discussion Paper Series 11-E-060

July 2011

Urban Density, Human Capital, and Productivity:
An empirical analysis using wage data*
MORIKAWA Masayuki (RIETI)

Abstract
Numerous studies have indicated that densely populated cities enhance the productivity ofworkers through knowledge spillover and superior matching with employers in the labormarket. This paper quantitatively analyzes the relationship among urban density, humancapital, and wages by using micro data from the Basic Survey on Wage Structure for the years
from 1990 to 2009. According to the estimation of standard wage functions augmented withpopulation density, the agglomeration premium is larger for workers with higher observableskills such as education, tenure, and potential experience, which suggests rapid learning andsuperior matching in densely populated cities. Under structural changes such as a declining
population and the trend toward a knowledge-based service economy, forming densely
populated areas by facilitating the migration of workers has desirable effects throughout Japanon both individual wages and firm productivity.
Keywords: agglomeration, population density, human capital, and wage function.
JEL Classification: J24; J31; R32

RIETI Discussion Papers Series aims at widely disseminating research results in the form of professional
papers, thereby stimulating lively discussion. The views expressed in the papers are solely those of theauthor(s), and do not represent those of the Research Institute of Economy, Trade and Industry.

* The author is grateful to Reiko Aoki, Hiroyuki Chuma, Masahiro Hori, Daiji Kawaguchi, Hyeog Ug
Kwon, Sadao Nagaoka, Kazuhiko Odaki, Yosuke Okada, and the participants of the workshop at
Hitotsubashi University and seminar at RIETI for their valuable comments and suggestions. I would liketo thank the Ministry of Health, Labour and Welfare for providing the micro data of the Basic Survey on
Wage Structure employed in this study.

1. Introduction
This paper empirically analyzes the relationship among urban density, human capital, andwages by using individual micro data on wages in Japan.
Faced with an aging population and a decreasing labor force, Japan must now focus its
economic policy on enhancing productivity to achieve sustainable economic growth. It is awell-known fact that accumulation of human capital is an important contributor toward
productivity growth. 1 Investments in human capital include not only formal education
through schooling but also skill accumulation through employer-provided training programs
and on-the-job learning. Recent empirical studies, surveyed in the next section, have pointed
out that the contribution of human capital toward worker productivity is related to theeconomies of agglomeration. Human capital spillover, learning through experience, superiormatching in the labor market, and the sorting of workforce based on ability are pointed out as
the theoretical mechanisms behind the facts.
The population in Japan is projected to decrease rapidly. If the contribution of human capital
toward productivity is stronger in large, densely populated cities, spatial redistribution of
population through internal migration may have an impact on Japan’s economic growth. Undera trend toward a knowledge-based economy, investment in and utilization of human capitalis becoming increasingly important. Fujita (2007), for example, argues that the optimal city
size will become larger in parallel with the heterogeneity of knowledge that is more importantin the knowledge production process.
Against this background, this paper empirically analyzes the interconnection between humancapital and population density in determining wages using data from the Basic Survey on Wage
Structure. Specifically, we estimate wage elasticity to density for different observable skill
groups to deepen our understanding on the heterogeneous effects of agglomeration. Notably,by comparing a “standard worker,” who has not changed employers after graduation, with a“non-standard worker,” who has changed jobs, we attempt to disentangle the channels causing
the agglomeration wage premium, such as learning through experience in dense cities andsuperior matching between employer and employee.
As explained in the next section, the endogenous quality of labor is one of the possible
sources of bias in the estimation for agglomeration economies. That is, workers with superior
unobservable human capital may sort into denser and more productive regions. Recent
1

There have been numerous studies on the relationship between human capital and economic growth orproductivity. Topel (1999), Blundell et al. (1999), Krueger and Lindahl (2001), and Hanushek andWoessmann (2008) present good surveys on education and economic growth.

-1-empirical studies have made efforts to remove this bias by using individual-level panel dataset.
Unfortunately, a large panel dataset that tracks individual workers is unavailable in Japan. As aresult, a limitation to this paper is that the analysis is of a cross-sectional nature. However,according to empirical studies tackling workforce sorting issues, the magnitude of theendogeneity bias cannot be ignored as there still remain economically significant
agglomeration economies, even after correcting this bias.
The major results of the analysis in this paper can be summarized as follows.
(1) Simple elasticity of nominal wages with respect to municipal population density is about
0.08. Even after controlling for individual worker characteristics, firm size, and regional
price disparities, significant agglomeration (urban) wage premium is observed, althoughelasticity drops to about 0.03.
(2) The urban wage premium is larger for university graduates. This suggests
agglomeration economies and skills are complementary.
(3) The urban wage premium increases with worker tenure, until around 20 years of tenure.
The result suggests that human capital accumulation through learning by experience
within a firm is relatively large in densely populated cities.
(4) The urban wage premium increases with the potential experience of workers, until
around 30 years of experience. This relationship is stronger for the non-standard worker
who changed jobs than the standard worker who worked at a single firm for a long time.
This result suggests that, in addition to learning effects, quality of matching between
workers and firms through labor turnover is better in densely populated cities.
The remainder of this paper is structured as follows. Section 2 briefly reviews the literatureon the relationship among agglomeration, productivity, and wages. Attention is paid to studies
on the relationship between human capital and city size. Section 3 describes the data employed
and the method of analysis. Section 4 reports the estimation results of the wage function.
Section 5 presents conclusions with policy implications.

2. Literature Review
2.1 Urban Wage Premium
It is a stylized fact confirmed by numerous empirical studies that measured productivity ishigher in spatial areas where economic activities are agglomerated (see Rosenthal and
Strange, 2004; Combes, Mayer, and Thisse, 2008; Strange, 2009; Glaeser and Gottlieb, 2009;
Puga, 2010). The measures of agglomeration used in these studies include population,-2-

population density, worker density, and the number of establishments. The mechanisms
behind this stylized fact have been considered to be economies of scale and positive
externalities in production. The externalities arise from labor market pooling, input sharing,and knowledge spillovers. Rosenthal and Strange (2004), who conducted a representative
survey in the area, conclude that productivity increases by 3%–8% when regional population
density doubles. A meta-analysis by Melo et al. (2009) depicts that the mean and median of theestimated elasticity of productivity with respect to density are 0.031 and 0.034, respectively. 2
Most of the previous studies estimate 1) production functions to derive the agglomeration
effect on productivity or 2) wage functions to find the agglomeration premium on factor
prices. The analysis in this paper belongs to the latter category. Representative studies
adopting this approach include Glaeser and Mare (2001), Wheaton and Lewis (2002), andYankow (2006) for the U.S., Combes, Duranton, and Gobillon (2008) for France, and Mionand Paolo (2009) for Italy.
When estimating wage function to analyze agglomeration wage premium the potentiallymajor sources of bias are 1) endogeneity of population and 2) endogeneity of the quality ofworkforce i.e., worker sorting. Recent empirical studies referred to these efforts to overcome
the endogeneity issues. Notably, several studies estimates wage functions and controlled forworker-fixed effects by using individual-level panel data. Glaeser and Mare (2001) utilized
individual-level panel data for the U.S. and found that controlling for observable worker
characteristics and individual fixed-effects considerably reduced the urban wage premium, butthat a substantial urban wage premium still existed, which was not the result of omitted ability
biases. Yankow (2006) conducted a fixed-effects estimation for U.S. panel data (NLSY79) andfound that two-thirds of the urban wage premium could be explained by cities attracting
workers of higher unmeasured skills and ability, and that the remaining urban wage premium
consisted of both a wage level effect and a wage growth effect. Combes, Duranton, andGobillon (2008) estimated a wage determination model across local labor markets using a large
panel of French workers and control for worker characteristics, worker fixed effects, industry
fixed effects, and the characteristics of the local labor market. According to their analysis,skilled workers tended to sort into larger and denser local labor markets, and differences in theskill composition of the labor force accounted for 40%–50% of aggregate spatial wage
disparities. Combes, Duranton, Gobillon, and Roux (2010) analyzed the agglomeration wage
premium by employing an instrumental variable approach to deal with the endogenous quantityof labor bias and a worker fixed-effect approach to deal with the endogenous quality of laborbias. Their results show that the raw elasticity of mean wages to density is slightly below 5%,
2

Most of the studies focus on manufacturing, but Morikawa (2011) found that the productivity effect ofagglomeration is substantially larger for service industries than for manufacturing.

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but the figure dropped to 2.7% after controlling for both endogenous quality and quantity
biases. Mion and Paolo (2009) estimated a wage function using a matched employer-employee
panel data for Italy and found that skills were sorted across space and accounted for nearly
75% of the spatial wage variation. Krashinsky (2011) conducted a unique study that examined
the selection effects on measured agglomeration wage premium by using datasets of identicaltwins and siblings in the U.S. to control family fixed effects. He found large and significant
effects of unobserved ability for agglomeration wage premium.
On the other hand, Fu and Ross (2010), who use residential location as a proxy for worker’s
unobserved productivity, found that the agglomeration estimates are robust to comparisons
within residential locations, suggesting that the productivity differences across locations are
due to agglomeration rather than productivity differences across individuals. Baum-Snow andPavan (2011) decomposed the U.S. urban wage premium into various components such aslatent ability, search frictions, firm-worker match quality, human capital accumulation, andendogenous migration, and conducted counterfactual simulations. Their simulations depict thatsorting on the basis of unobserved ability contributes little to these observed urban wage
premium.
To summarize, although the biases from endogenous quantity and endogenous quality oflabor cannot be ignored, there remains a quantitatively significant agglomeration wage
premium. Strange (2009), who conducted a survey on recent research on agglomeration
economies, states “we have strong evidence of endogenous quality of labor, but also strong
evidence for a relationship between urbanization and a wage correcting for this.” Combes,
Duranton, and Gobillon (2011), who reviewed empirical studies on the elasticity of wages withrespect to urban scale focusing on various estimation biases and econometric solutions,concluded that standard estimates for the density elasticity of wages now typically range from0.02 to 0.05. They then argue that while better estimates are needed, it is also important to
explore what lies behind the “average” values and that knowing more about how different
types of workers and firms benefit from agglomeration is of first order importance. The present
paper follows this line of research.

2.2 Human Capital and Agglomeration Economies
There are many possible mechanisms behind the high productivity of workers in densely
populated cities. In addition to the establishment-level factors, such as scale economies andtechnological differences, labor market factors including rapid human capital accumulationand superior matching of employers and employees are also important.

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The relationship between human capital and wages has been a major research topic inlabor economics and has had an extensive history. Certain recent studies on the urban wage
premium focus on the different agglomeration effects of observable skills of workers, such as
education and tenure. Glaeser and Mare (2001), Wheeler (2001, 2006), Gould (2007), Di
Addario and Patacchini (2008), Chung et al. (2009), Bacolod et al. (2009), and Christoffersen
and Sarkissian (2009) are examples of this line of research.
Glaeser and Mare (2001), as previously referred to, indicate that a significant fraction of theurban wage premium is accumulated with workers’ experience in the urban labor market.
Wheeler (2001) depicts evidence for the U.S. that wages of highly educated workers rises
significantly compared with less educated workers as local population increases. Wheeler(2006), by analyzing U.S. panel data (NLSY79), found that wage growth is positively
associated with local market size, and that this association is the product of rapid wage growthfrom job changes rather than from wage increases experienced while on a particular job. Basedon the results, he concludes that cities enhance worker productivity through a job search andmatching process. Gould (2007) analyzes the relationship between wages and city size for bothblue-collar and white-collar workers by estimating a structural model for the U.S. The results
indicate that the selection of individuals into occupations and locations can almost explain theurban wage premium for blue-collar workers, but explains only a third of the regional wage
gap for white-collar workers. Moreover, he concludes that cities make white-collar workers
more productive. Chung, Clark, and Kim (2009), using cross-sectional data for the U.S.,
indicate that virtually all skill wage premium growth over the 1980s in the U.S. was confined
to metropolitans. They offered the possible explanation that skilled workers may decrease thecost of acquiring knowledge and facilitating communication for urban employers more
effectively than non-urban ones. Bacolod et al. (2009), making use of the Dictionary of
Occupational Titles (DOT) and data from the U.S. census and the NLSY, estimate the impactof agglomeration on the hedonic prices of worker skills. According to their analysis, the urban
wage premium is greater for workers with high cognitive and people skills, but not for workers
with high motor skills. Specifically, an increase of one standard deviation from the mean incognitive skills increases wage elasticity with respect to the MSA population by one-fifth.
Christoffersen and Sarkissian (2009) analyzed the relationship between city size and theperformance of U.S. equity mutual funds and found that funds in financial centers performbetter than other funds. Interestingly, this difference is driven only by more experienced
managers, and there is strong evidence of a positive relationship between performance andmanager experience among funds in financial centers such as New York. They argue that the-5-result is evidence of knowledge spillover and learning in cities.3
To summarize, most empirical studies in the U.S. and other advanced countries found thatthe effects of worker skills such as education and experience on wages are greater in populated
cities. These studies suggest that density enhances worker productivity through rapid
accumulation of human capital and superior matching between employers and employees.
Based on these previous studies, this paper empirically analyzes the relationship between
wage premium for various observable skills—education, tenure, and potential experience—andpopulation density in Japan. Special attention is paid to different agglomeration wage effects
between standard workers i.e., lifelong employees and non-standard workers who experienced
job changes.

3. Data and Methodology
This paper uses individual-level micro data from the Basic Survey on Wage Structure(Ministry of Health, Labour and Welfare). To link the data with published population census
data; we used data for the years 1990, 1995, 2000, 2005, and 2009, which is the latest
available data.
The survey is the most frequently utilized source of official statistics on estimating wage
functions. The objective of the survey is to clarify the wage structure of employees in majorindustries by type of employment, work, occupation, sex, age, education, length of tenure,occupational career, and other factors. Since 1948 the survey has been carried out once a year.
Approximately 80,000 establishments were sampled according to a fixed ratio by region,industry, and size of establishment. In addition, a number of workers from among those
employed in the sampled establishments were chosen according to a fixed ratio by industry
and size of establishment. The items surveyed include; actual numbers of scheduled hours
worked, actual number of overtime worked, contractual cash earnings, scheduled cash earnings,
annual special cash earnings (bonus), industry, size of enterprise, sex, age, tenure (length ofservice), and education. The number of workers surveyed is about 1.2 million, of which 1.0
million are full-time regular workers. Since data on education are unavailable for part-timeworkers, analysis in this paper is conducted only on full-time regular workers.

3

In contrast to these studies, Di Addario and Patacchini (2008), by using data for Italy, found that urban
scale does not affect returns to experience and that it reduces returns to education and tenure with thecurrent firm.

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The standard worker is a special notion of the survey, and is defined as “a worker whojoined a firm just after graduation and served the firm continuously.” More specifically,
standard workers are identified as workers whose age minus tenure equals 15 years forjunior high school graduates, 18 years for senior high school graduates, 20 years for juniorcollege or technical college graduates, and 22 or 23 years for university graduates. This
paper estimates wage functions separately for standard and non-standard workers whennecessary. The number of standard workers in the sample is about 300,000 or roughly 30%of the number of full-time regular workers (see Table 1).
Survey items utilized in this paper include prefecture and city code, industry classification,
worker characteristics (sex, type of employment, type of work, education, age, and tenure),working hours, and wages. Among these, type of employment is classified into 1) regular
worker and 2) non-regular worker, and type of work is classified into 1) full-time work and 2)
part-time work.4
During the last decade, the Standard Industry Classification has been revised
fundamentally. In the 2005 survey, several new single-digit industries, such as “informationand communications,” “medical, health care and welfare,” “education and learning support,”and “compound services” were established, and “restaurants” were separated from thecategory of “wholesale, retail, and restaurants.” Furthermore, in the 2009 survey “goods
rental,” formerly a part of “professional and technical services,” was reclassified into “realestate, goods rental, and leasing.” Thus, we construct a single-digit industry classification
harmonized from 1990 to 2009. Concretely, we classified 11 industries: mining,
construction, manufacturing, electricity and gas, transportation and communication,
wholesale, retail, restaurants, finance and insurance, real estate, and services.
In this study, monthly wage is calculated as the sum of monthly contractual cash earnings(including overtime allowance) and annual special cash earnings (bonus) divided by twelve.
Hourly wage rate (hundred yen per hour) is the monthly wage divided by the actual number ofhours worked. In estimating wage functions, the natural log of hourly wage rate is used.
Potential experience of workers is calculated by subtracting normal graduation age (15 forjunior high school graduates, 18 for senior high school graduates, 20 for junior collage ortechnical collage graduates, and 22 for university graduates) from current age.
City-level data on population, area, and price level are merged with the above mentioned
individual-level data to construct the final dataset. Population and area data at the city level
are taken from the website of the Statistical Bureau of the Ministry of Internal Affairs and4

In 2005, the classification of the type of employment was altered and, as a result, employees are nowclassified into “regular staff for an indefinite period,” “regular staff for a definite period,” “non-regularstaff for an indefinite period,” “non-regular staff for a definite period,” and “temporary employees.”-7-Communications. 5 The Index of Regional Prices for all households from the National
Survey of Prices is used to construct regional price data, which is implemented to calculate
real wages.6 These statistics cover all cities with a population of more than 1000; however,
unfortunately, cities with population below 100,000 were sampled, and sampling rates werefrom 12.5% to 50% depending on city size. As a result, the sample size becomes relatively
small for the estimations using real wages as a dependent variable. Since the National Surveyof Prices has been conducted every five years (1997, 2002, and 2007) and the years do notcoincide with the years of the population census. We used price data for 2007 whencalculating real wages for 2005 and 2009, and price data for 2002 when calculating real
wages for 2000.7 It should be noted that the effect of the two years’ difference in the pricedata is minimal, as the price level in Japan was stable during the period of analysis.
The method of analysis in this paper is quite simple, including OLS estimates of standard
wage functions, where the dependent variable is the log hourly wage rate (lnwage) andpopulation density at the city level (lnpopdens) was a main explanatory variable.8 Ordinary
individual characteristics—sex (female dummy: female), potential experience (potexp) and its
square (potexpsq), tenure (tenure) and its square (tenuresq), education dummies—andsingle-digit industry dummies are also used. Education is used as a dummy variable forjunior collage or technical collage graduates (edudum_c) and for university graduates(edudum_u). In short, the equation to be estimated can be expressed as follows:
lnwage = ß0 + ß1 female dummy + ß2 potexp + ß3 potexp2 + ß4 tenure + ß5 tenure2+ ß6 education dummies + ß7 lnpopdens + ßi ∑industry dummies +ε
When pooled data was used in the estimation, year dummies for 1990, 1995, 2000, and2005 were added. In the baseline estimation, we do not include firm size as an explanatory
variable, but for certain specifications firm size dummies are added to check the robustness

5

Data on city population from 1990 to 2005 were taken from the population census. Population data forthe year 2009 came from the Basic Resident Registers (Statistics Bureau, Ministry of Internal
Affairs and Communications).
6
Specifically, the city-level price index is calculated as the price index of prefectures (national average= 100) multiplied by the price index of cities (prefecture average = 100).
7
Since detailed regional price data was not available before 1997, the analysis for real wages isrestricted to the years 2000, 2005, and 2009.
8
Instead of simple population density, we use worker density (the number of workers divided by thearea) as the explanatory variable for the year 2005, where data on the number of workers bymunicipalities were available. The results are qualitatively and quantitatively quite similar to the results
using simple population density.

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of the results.9
When estimating the wage function for standard workers who joined a firm just after
graduating from school and served the firm continuously, tenure and its square are excluded
from the explanatory variable because potential experience and tenure are the same bydefinition.
In addition to the baseline equation written above, population density interacted witheducation, potential experience, or tenure is added to analyze the different effects of humancapital on wages by urban density.
Summary statistics of the major variables for the sample of full-time regular workers areindicated in Table 2.

4. Results
4.1 Baseline Estimation
Table 3 depicts the estimation results for all full-time regular workers. Columns (1) and (2)are for the year 2009 and columns (3) and (4) are the results of pooling five years, from 1990
to 2009. Results for the years 1990, 1995, 2000, and 2005 are not reported here to avoid
redundancy, but the results are essentially similar to that of the year 2009.
The raw wage elasticity with respect to population density without controlling for individual
characteristics is between 0.08 and 0.09 (not reported in the table), but the figure drops toabout 0.06 after controlling for sex, education, experience, and tenure (see Table 3, columns(1), (3)). This indicates that around a third of the observed regional wage disparity is explainedby the different individual characteristics. The elasticity drops further to 0.04–0.05, when firm
size dummies are added (columns (2), (4)). Although the effect of the inclusion of firm size on
agglomeration wage premium is small, the results indicate that large firms tend to locate theirestablishments in populated regions, suggesting spatial sorting of firms.
Since price levels are generally higher in densely populated cities, the elasticity of real
wages with respect to density is expected to be lower than that of nominal wages. Table 4reports the results using log real wages as a dependent variable. The estimated elasticity is
about 0.03–0.04, which indicates that about 2 percentage points of the measured nominal wage
elasticity is accounted for by the fact that price levels are higher in denser cities. When using
real wages, some of the small cities are excluded from the sample because of a lack of price9

In the Survey, firm size is classified into eight categories based on the number of employees (5–9,
10–29, 30–99, 100–299, 300–499, 500–999, 1000–4999, 5000 or more).

-9-data, and data for 1990 and 1995 were unavailable. Thus, in principle, we use nominal wages
in the following analysis, but it should be remembered that the agglomeration wage premiumin real terms adjusted by price level is lower by about 2 percentage points.
As explained in Section 2, when estimating the agglomeration wage premium, the bias
caused by the endogenous selection (sorting) of workers is an important econometric issue.
Although we unfortunately do not have panel data to control the possible sorting bias. To deal
with this issue we restrict the sample to standard workers, who served a firm continuously
after graduation. The estimation results are presented in Table 5. Even when the sample isrestricted to standard workers, the sorting effect at the time of hiring cannot be eliminated, but
the effects of selection through job changes are reduced.10 The estimated wage elasticity topopulation density is close to 0.05 (Table 5 column (1)).
Even among standard workers, those in large firms with multiple establishments at various
locations may be transferred among different locations during their career with the firm. In
considering this possibility, we further limit the sample to 1) small- and medium-sized firms
with total regular employees less than 300 (column (2)), and 2) single establishments in whicha firm has only one establishment (column (3)). The estimated wage elasticity is quantitatively
similar in magnitude to that obtained for all establishments.

4.2 Agglomeration Wage Premium by Education
In this and the following subsections, we analyze the relationship between observable
human capital and agglomeration wage effects. Specifically, we estimate wage functions
including interaction terms of population density with education, potential experience, or
tenure to investigate the different effects of human capital on wages by the degree of
population density.
Table 6 reports the results for education. For junior college or technical college graduates,
wage elasticity with density was not significantly different from that of high school graduates,
but university graduates’ wage elasticity was often large and significantly different from that ofhigh school graduates. This suggests that workers with higher human capital benefit more fromagglomeration, which is basically consistent with the results obtained in the U.S. (Wheeler,
2001; Chung, Clark, and Kim, 2009). The size of the coefficients for the interaction term forthe year 2009 was about 0.01 (see Table 6, column (1), (2)), indicating that the wage premiumof university graduates is about 1% larger when the local population density doubles. The size
10

As described in the text, potential experience and tenure is the same for standard workers bydefinition. We exclude tenure and its square from the explanatory variables in this estimation.

- 10 -

is only 0.003 for pooled regression results (see column (3) of the table), which is far smaller inmagnitude compared with the coefficients for the university graduates dummy variable (around0.3).11 The coefficient for the interaction term is insignificant in the regression, including
firm-size dummies.12 In recent years, workers with higher education benefitted more fromurban agglomeration, but the magnitude of this relationship is quantitatively limited.

4.3 Agglomeration Wage Premium by Tenure
Next, we estimate wage functions where interaction terms for population density with tenure
and its square are used as explanatory variables. Similar to the previous analysis, all of theobservable worker characteristics are controlled. The coefficients for density interacted withtenure and its square are both highly significant, and the former is positive and the latter isnegative (see Table 7).In this case, wage elasticity with density increases with tenure until 21
years of service and then decreases gradually. For example, the elasticity is about 0.05 at three
years of tenure, but the figure grew closer to 0.07 at 20 years of tenure.
This result suggests that the rate of accumulation of human capital and productivity growthof workers are faster at establishments located in densely populated areas, suggesting astronger on-the-job learning effect.

4.4 Agglomeration Wage Premium by Potential Experience
The results of wage functions with the interaction terms of population density with potential
experience and its square are reported in Table 8. Similar to the results of the previous
subsection, the coefficients for the interaction terms are both statistically significant, and thesigns are positive and negative. The peak of wage elasticity with density is about 30 to 31
years of potential experience, ten years later than the peak for tenure.13 Figure 1 illustrates theexperience-wage curve for hypothetical cities with different population densities. The upper
11

It should be noted, however, the standard deviation of the log population density is about 1.5 (see thesummary statistics). One standard deviation for a denser city’s wage premium for university graduates is
10% higher in the estimation for the year 2009.
12
In considering the possibility that the form of the wage function may be different by educationalgroups, we conducted separate estimations by educational categories. The results are essentially similar
to the results using the interaction terms described in the text. The wage elasticity with respect topopulation density is about 0.01 larger for university graduates.
13
When interaction terms of both tenure and potential experience with population density(tenure*lnpopdens, potexp*lnpopdens) are used simultaneously in the equation, the size of thecoefficient for the interaction term with potential experience was relatively large.

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line represents the curve for a city with one standard deviation higher population density fromthe sample mean, and the lower curve represents a city with one standard deviation lower
density.14 The intercept depicts the effect of different population densities for workers hired
just after their graduation, which can be interpreted as a sorting effect by unobservable skills at
the time of hiring. The shape of the curve is steeper in a denser city and the magnitude isquantitatively larger. The result here is consistent with Glaeser and Mare (2001), whichindicates that the coefficient for the interaction term for experience and city size is positive in
the U.S.
The sample for the above analysis includes all full-time regular workers. We then divide thesample into standard workers and non-standard workers and run estimates separately. As
mentioned already, in estimating wage functions for standard workers it is inappropriate to use
potential experience and tenure at the same time; therefore, we drop tenure and its square fromthe explanatory variables. Table 9 displays the results for the pooling regression. Interestingly,
the coefficient for the interaction term for experience and population density is larger for
non-standard workers than for standard workers. Figure 2 illustrates the relationship between
potential experience and density elasticity of wages for standard and non-standard workers. For
standard workers, the peak elasticity is 0.058 at 25 years of experience and gradually decreases
thereafter. On the other hand, for non-standard workers i.e., most of whom have experienced
job changes, the peak elasticity is 0.080 at 30 years of experience; a roughly higher and later
peak. The curve is relatively steep for non-standard workers, which indicates that the
productivity enhancing effects of agglomeration becomes stronger for job-changers as work
experience accumulates.15 One plausible interpretation is that, after certain years of work
experience, superior matching through job changes dominates the effects of on-the-job
accumulation of skills. This is consistent with Wheeler (2006), who found that wage growth ispositively associated with city size and that this association is the result of faster wage growth
due to job changes rather than that experienced on a particular job. For example, the differencein the elasticities between standard and non-standard workers with 20 to 25 years of experience
is about 0.02. This figure can be interpreted as an approximation of the effects of better
matching. The different elasticities for standard workers at the time of hiring along with 20 to
25 years of experience (about 0.03) can be interpreted as an approximation of learning
effects.16
14

The population density for a city with one standard deviation larger than the average is 5,871/km2
and that of a city with one standard deviation lower is 287/km2.
15
Some part of the effects of job changes should be interpreted as the effects of spatial sorting by skills
and not the effects of better matching in large cities. This is because job changes include both intra-cityand inter-city changes.
16
Precisely, “passive sorting” cannot be ruled out because standard workers are the survivors whostayed with the firm they joined just after graduation.

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Tables 10 and 11 report the results for the subsamples of 1) small- and medium-sized firms
and 2) single establishments where the firm has only one establishment. For these subsamples,standard workers’ transfer between different locations in their career is limited. Although thedifference in the elasticities between standard and non-standard workers is somewhat smaller
than the result using a total sample, the coefficients for the interaction terms for experience anddensity are still larger for non-standard workers, confirming the existence of superior matchingeffects in densely populated cities.

5. Conclusion
This paper empirically analyzes the relationship among urban density, human capital, andwages using Japanese micro data. Specifically, we estimate wage functions including
population density as an explanatory variable by employing data from the Basic Survey on
Wage Structure from 1990 to 2009. In particular, the estimations consider interaction terms
between population density and various observable skills as well as comparisons between
standard workers with lifetime employment and non-standard workers experiencing jobchanges. These estimations are conducted to disentangle the sources of agglomeration wage
premium, such as learning through experience in densely populated regions, superior matchingof employees, and employees in large labor markets.
The major results can be summarized as follows:(1) Simple raw elasticity of nominal wages with respect to municipal population density is
about 0.08. After controlling for individual worker characteristics and firm size, thisfigure decreased to roughly 0.05. By further adjusting regional price disparities, the real
wage elasticity becomes about 0.03. This figure is comparable with those found inprevious studies.
(2) The agglomeration wage premium is larger for university graduates. This suggests that
agglomeration economies and worker skills are complementary.
(3) The wage elasticity to density increases with the tenure of workers up to around 20
years. This result indicates that human capital accumulation through learning by
experience within a firm is relatively large in establishments located in densely
populated cities.
(4) The wage elasticity to density also increases with the potential experience of workers
up to around 30 years of experience. This relationship is stronger for “non-standard
employees” who experienced job changes than “standard employees” who served at asingle firm for long time. This result suggests that, in addition to the learning effects,- 13 -

superior matching between workers and firms through labor turnover contribute to theurban wage premium.
These results highlight that working in an agglomerated region enhances worker
productivity through both rapid learning and superior matching. Under structural changes suchas a declining population and the trend toward a knowledge-based service economy, the results
suggest that forming densely populated areas by facilitating inter-regional migration ofworkers have desirable effects on both individual wages and firm productivity throughout
Japan. Although the effects of specific policies are beyond the scope of this paper, the creationof a well-functioning external labor market to enable flexible labor turnover, deregulation ofland-use restrictions in urban areas, and efficient infrastructure investment focusing on
populated areas may contribute to actualizing agglomeration economies.
The cross-sectional analysis in this paper is subjected limitations. The effects from thedifferences in unobservable skills among regions and spatial sorting of workers are noteliminated. However, it should be noted that, according to previous studies that employedpanel data, even after correcting these biases, a significant agglomeration wage premium
existed. The major purpose of this paper is not to measure accurately the size of theagglomeration economies, but to detect their difference among worker skills, although thequantitative magnitude of the wage premium found in this paper should be interpreted withdiscount.

- 14 -

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- 16 -

Table 1 Number of Sample Workers
1990
1995
2000
2005
2009
Average

Regular worker
1,258,097
1,382,724
1,258,627
1,187,773
1,193,660
1,256,176

Full-time worker
1,154,121
1,239,455
1,103,741
946,249
901,401
1,068,993

Standard worker
303,573
397,673
344,155
253,918
239,120
307,688

Table 2 Summary Statistics(1) 2009
lnwagefemaleedudum_c
edudum_uage
potexptenurelnpopdenslnhoursN
898,263901,401
901,401
901,401
901,401
901,401
901,401
885,344898,263

mean
2.963
0.318
0.145
0.294
41.01021.69911.768
6.885
5.132

sd
0.546
0.466
0.352
0.456
12.35912.93910.839
1.555
0.193

p50
2.924
0
0
0
40
21
8
6.829
5.147

max
7.815
1
1
1
99
79
66
9.871
6.178

min
-2.549
0
0
0
15
0
0
0.949
0

p50
2.944
0
0
0
20
9
7.108
5

max
8.679
1
1
1
79
66
9.928
6

min
-2.549
0
0
0
-1
0
0.785
0

(2) Pooling Five Years from 1990 to 2009lnwagefemaleedudum_c
edudum_u
potexptenurelnpopdenslnhoursN
5,327,834
5,344,967
5,344,967
5,344,967
5,344,967
5,344,967
5,147,979
5,327,834

mean
2.969
0.305
0.121
0.234
20.82511.892
7.169
5.175

sd
0.556
0.460
0.327
0.423
13.03910.4471.509
0.191- 17 -

Table 3 Estimation Results of Wage Functions

femaleedudum_c
edudum_u
potexppotexpsq
tenuretenuresq
lnpopdens_consIndustry dummies
Firm size dummies
Year dummies
Number of obs
Adj R2(1)
2009-0.2614 ***(-291.80)***
0.1348(110.87)***
0.3199(320.45)***0.0258(206.65)-0.0006 ***(-231.19)***
0.0329(257.41)-0.0003 ***(-74.26)***
0.0556(211.75)***
2.0357(925.17)yesnono882,249
0.5602(2)
2009-0.2654 ***(-309.96)***
0.1370(117.80)***0.2965(308.74)***
0.0269(225.34)-0.0006 ***(-235.43)***
0.0310(253.61)-0.0003 ***(-84.89)***0.0447(176.13)***2.3099(965.28)yes
yes
no882,2490.5986(3)pooled-0.2743 ***(-752.55)***
0.1523(294.44)***0.3055(735.99)***
0.0263(523.61)-0.0006 ***(-582.96)***
0.0353(648.65)-0.0002 ***(-167.04)***
0.0587(554.73)***
1.9849(2104.20)
yes
no
yes
5,131,475
0.6175(4)pooled-0.2783 ***(-803.99)***
0.1536(312.56)***
0.2823(711.83)***
0.0291(607.88)-0.0006 ***(-617.70)***
0.0305(585.13)-0.0002 ***(-158.30)***
0.0473(465.29)***
2.2570(2272.32)
yes
yes
yes
5,131,475
0.6552(Notes) OLS estimates with t-values in parentheses. * significant at 10%; ** significant at 5%;*** significant at 1%. Pooled regression is for five years from 1900 to 2009.

- 18 -

Table 4 Estimation Results Using Real Wages

femaleedudum_c
edudum_u
potexppotexpsq
tenuretenuresq
lnpopdens_consIndustry dummies
Firm size dummies
Year dummies
Number of obs
Adj R2

(1)

(2)

(3)

(4)

2009

2009

pooledpooled-0.2521 ***(-257.07)***
0.1318(99.87)***0.3182(295.11)***0.0268(195.32)-0.0006 ***(-215.54)***
0.0330(235.05)-0.0003 ***(-69.11)***0.0373(124.74)***
2.1519(850.09)yesnono735,179
0.5524-0.2573 ***(-273.70)***
0.1339(105.79)***
0.2949(283.46)***
0.0278(211.67)-0.0006 ***(-219.32)***
0.0312(231.61)-0.0003 ***(-78.40)***0.0264(91.08)***2.4197(887.59)yes
yes
no735,179
0.5894-0.2449 ***(-442.34)***
0.1460(198.45)***0.3162(533.73)***
0.0290(368.45)-0.0006 ***(-396.43)***
0.0329(405.86)-0.0002 ***(-101.99)***
0.0340(196.31)***2.1376(1440.91)
yes
no
yes
2,284,664
0.5762-0.2489 ***(-468.52)***
0.1471(208.32)***
0.2946(514.64)***0.0304(402.34)-0.0006 ***(-405.64)***
0.0298(381.68)-0.0002 ***(-105.49)***
0.0237(141.57)***
2.3957(1525.30)
yes
yes
yes
2,284,664
0.6103(Notes) OLS estimates with t-values in parentheses. * significant at 10%; ** significant at 5%;*** significant at 1%. Pooled regression is for three years from 2000 to 2009.

- 19 -

Table 5 Estimates for Standard Workers (1990–2009 pooled)femaleedudum_c
edudum_u
potexppotexpsq
lnpopdens_consIndustry dummies
Year dummies
Number of obs
Adj R2(1)
All standard
workers-0.1406 ***(-237.44)***
0.0925(117.26)***
0.2472(438.58)***
0.0672(926.64)-0.0009 ***(-481.01)***
0.0460(273.84)***
2.0652(1461.75)
yes
yes
1,482,772
0.7314(2)
SMEs-0.1335 ***(-138.27)***
0.0987(80.62)***0.2424(245.60)***
0.0595(492.39)-0.0009 ***(-259.17)***
0.0450(155.30)***
1.9983(858.76)yes
yes
466,368
0.7069(3)Singleestablishments-0.1244 ***(-81.73)***
0.0993(51.38)***0.2547(151.49)***0.0609(316.85)-0.0009 ***(-179.30)***
0.0476(99.96)***
1.9839(518.21)yes
yes
196,533
0.6679(Notes) OLS estimates with t-values in parentheses. * significant at 10%;** significant at 5%; *** significant at 1%.

- 20 -

Table 6 Estimation Results with the Interaction Term of Education and Density

femaleedudum_c
edudum_u
potexppotexpsq
tenuretenuresq
lnpopdens
edudum_c*lnpopdens
edudum_u*lnpopdens_consIndustry dummies
Firm size dummies
Year dummies
Number of obs
Adj R2(1)
2009-0.2622 ***(-292.50)***
0.1361(25.40)***0.2191(50.74)***0.0258(206.91)-0.0006 ***(-231.42)***
0.0328(257.13)-0.0003 ***(-73.90)***0.0514(147.07)0.0002(0.23)***
0.0141(23.85)***2.0629(772.71)yesnono882,249
0.5605(2)
2009-0.2661 ***(-310.57)***
0.1313(25.65)***0.2084(50.49)***0.0269(225.58)-0.0006 ***(-235.64)***
0.0309(253.34)-0.0003 ***(-84.53)***0.0409(121.72)0.0011(1.56)***
0.0123(21.85)***2.3343(836.93)yes
yes
no882,2490.5988(3)pooled-0.2743 ***(-751.86)***
0.1907(77.37)***0.2820(140.09)***
0.0263(523.34)-0.0006 ***(-582.71)***
0.0353(648.65)-0.0002 ***(-167.05)***
0.0587(457.17)-0.0052 ***(-15.77)***
0.0030(11.61)***1.9852(1849.35)
yes
no
yes
5,131,475
0.6176(4)pooled-0.2782 ***(-802.66)***
0.1987(84.88)***0.2846(148.82)***0.0291(607.66)-0.0006 ***(-617.45)***
0.0305(585.20)-0.0002 ***(-158.47)***
0.0481(392.08)-0.0061 ***(-19.67)-0.0004(-1.54)***2.2514(2041.04)
yes
yes
yes
5,131,475
0.6552(Notes) OLS estimates with t-values in parentheses. * significant at 10%; ** significant at 5%;*** significant at 1%. Pooled regression is for five years from 1900 to 2009.

- 21 -

Table 7 Estimation Results with the Interaction Term of Tenure and Density

femaleedudum_c
edudum_u
potexppotexpsq
tenuretenuresq
lnpopdens
tenure*lnpopdens
tenuresq*lnpopdens_consIndustry dummies
Firm size dummies
Year dummies
Number of obs
Adj R2(1)
2009-0.2607 ***(-291.11)***
0.1347(110.78)***
0.3197(320.41)***0.0256(204.89)-0.0006 ***(-229.38)***
0.0175(34.10)***0.0001(7.34)***
0.0427(90.93)***0.0022(31.09)-0.0001 ***(-25.78)***
2.1259(605.28)yesnono882,249
0.5608(2)
2009-0.2648 ***(-309.31)***
0.1368(117.68)***
0.2964(308.69)***
0.0267(223.72)-0.0006 ***(-233.81)***
0.0180(36.88)**0.0000(2.01)***
0.0340(75.57)***0.0019(27.33)***0.0000(-22.88)***
2.3842(676.10)yes
yes
no882,2490.5990(3)pooled-0.2736 ***(-750.81)***
0.1527(295.39)***0.3052(735.77)***
0.0260(516.20)-0.0006 ***(-575.65)***
0.0197(86.49)***0.0001(17.34)***0.0454(227.36)***0.0022(71.29)-0.0001 ***(-56.98)***
2.0822(1339.66)
yes
no
yes
5,131,475
0.6180(4)pooled-0.2777 ***(-802.36)***
0.1540(313.40)***0.2821(711.65)***
0.0288(600.63)-0.0006 ***(-610.77)***
0.0175(81.06)***0.0001(11.37)***
0.0360(189.70)***0.0018(62.36)***0.0000(-48.80)***
2.3388(1528.81)
yes
yes
yes
5,131,475
0.6555(Notes) OLS estimates with t-values in parentheses. * significant at 10%; ** significant at 5%;*** significant at 1%. Pooled regression is for five years from 1900 to 2009.

- 22 -

Table 8 Estimation Results with the Interaction Term of Experience and Density

femaleedudum_c
edudum_u
potexppotexpsq
tenuretenuresq
lnpopdenspotexp*lnpopdens
potexpsq*lnpopdens_consIndustry dummies
Firm size dummies
Year dummies
Number of obs
Adj R2(1)
2009-0.2591 ***(-289.17)***
0.1344(110.63)***0.3213(321.81)***0.0050(10.14)-0.0002 ***(-22.37)***
0.0328(257.32)-0.0003 ***(-74.23)***
0.0226(31.34)***0.0030(43.50)-0.0001 ***(-35.31)***2.2655(436.84)yesnono882,249
0.5614(2)
2009-0.2631 ***(-307.26)***
0.1366(117.60)***
0.2981(310.25)***
0.0063(13.45)-0.0002 ***(-22.39)***0.0310(253.58)-0.0003 ***(-84.89)***0.0120(17.33)***0.0030(45.01)***0.0000(-36.36)***2.5385(498.71)yes
yes
no882,2490.5998(3)pooled-0.2713 ***(-744.44)***
0.1537(297.70)***0.3077(741.03)***
0.0034(16.76)-0.0002 ***(-53.33)***
0.0352(647.27)-0.0003 ***(-167.75)***
0.0227(81.23)***0.0032(115.09)-0.0001 ***(-86.92)***
2.2449(1070.02)
yes
no
yes
5,131,475
0.6190(4)pooled-0.2752 ***(-795.32)***
0.1552(316.47)***0.2848(718.10)***0.0056(29.16)-0.0002 ***(-56.87)***
0.0304(584.25)-0.0002 ***(-159.67)***
0.0097(36.31)***0.0033(124.25)-0.0001 ***(-91.63)***2.5300(1239.75)
yes
yes
yes
5,131,475
0.6569(Notes) OLS estimates with t-statistics in parentheses. * significant at 10%; ** significant at 5%;*** significant at 1%. Pooled regression is for five years from 1900 to 2009.

- 23 -

Table 9 Estimates for Standard and Non-standard Workers (1990–2009 pooled)femaleedudum_c
edudum_u
potexppotexpsq
lnpopdenspotexp*lnpopdens
potexpsq*lnpopdens_consIndustry dummies
Year dummies
Number of obs
Adj R2(1)
fulltime-0.3456 ***(-811.71)***
0.1915(314.42)***0.3427(701.32)***
0.0231(97.02)-0.0004 ***(-88.57)***
0.0177(53.45)***0.0044(135.93)-0.0001 ***(-103.64)***
2.2583(911.96)yes
yes
5,131,475
0.4686(2)
standard-0.1394 ***(-235.58)***
0.0933(118.38)***
0.2476(439.52)***0.0498(135.97)-0.0006 ***(-59.92)***
0.0279(81.04)***0.0024(48.22)***0.0000(-34.49)***
2.1990(834.69)yes
yes
1,482,772
0.7321(3)
non-standard-0.3826 ***(-748.16)***
0.2225(299.04)***
0.3575(552.26)***
0.0219(69.59)-0.0004 ***(-62.58)***
0.0173(35.56)***0.0042(95.93)-0.0001 ***(-80.15)***2.2013(613.15)yes
yes
3,648,703
0.4223(Notes) OLS estimates with t-statistics in parentheses. * significant at 10%;** significant at 5%; *** significant at 1%.

Table 10 Estimation Results with the Interaction Term of Experience and Density (Small- andMedium-Sized Firms, 1990–2009 pooled)lnpopdenspotexp*lnpopdens
potexpsq*lnpopdens
Number of obs
Adj R2(1)
fulltime
0.0173***(40.28)0.0036***(89.96)-0.00006 ***(-73.53)
2,663,353
0.4413(2)
standard
0.0259***(48.81)0.0026***(31.85)-0.00004 ***(-19.78)
466,368
0.7082(3)
non-standard
0.0180***(31.80)0.0034***(69.96)-0.00006 ***(-61.14)2,196,985
0.4153(Notes) OLS estimates with t-statistics in parentheses. * significant at 10%; ** significant at 5%;*** significant at 1%. All regressions include industry dummies, year dummies, sex, education,and potential experience and its square as explanatory variables.

- 24 -

Table 11 Estimation Results with the Interaction Term of Experience and Density (Single
Establishments, 1990–2009 pooled)lnpopdenspotexp*lnpopdens
potexpsq*lnpopdens
Number of obs
Adj R2(1)
fulltime
0.0162***(25.90)0.0036***(63.88)-0.0001 ***(-52.92)
1,376,441
0.4041(2)
standard
0.0260***(31.03)0.0028***(21.34)-0.00004 ***(-10.84)
196,533
0.6700(3)
non-standard
0.0192***(24.03)0.0033***(48.01)-0.0001 ***(-41.97)
1,179,908
0.3875(Notes) OLS estimates with t-statistics in parentheses. * significant at 10%; ** significant at 5%;*** significant at 1%. All regressions include industry dummies, year dummies, sex, education,and potential experience and its square as explanatory variables.

- 25 -

Figure 1 Population Density and Experience-Wage Curve (1990–2009 pooled)
0.6

0.5

log wage

0.4

0.3

0.2

0.1

40

38

36

34

32

30

28

26

24

22

20

18

16

14

12

10

8

6

4

2

0

0.0

potential experience+1s.d.

-1s.d.

(Notes) The figure is based on the pooled regression result. The lines indicate log population
density of cities with ± one standard deviation from the mean.

Figure 2 Experience and Wage Elasticity to Density (Standard and Non-standard Workers)
0.09

wage elasticity with density

0.08
0.07
0.06

Standard
Non-standard

0.05
0.04
0.03

39

37

35

33

31

29

27

25

23

21

19

17

15

13

11

9

7

5

3

1

0.02
potential experience(Notes) The figure is based on the pooled regression results for standard and non-standard workers.

- 26 -