On the distributional aspects of urban growth

Journal of Urban Economics 55 (2004) 371–397 www.elsevier.com/locate/jue

On the distributional aspects of urban growth Christopher H. Wheeler Department of Economics, Tulane University, 206 Tilton Hall, New Orleans, LA 70118, USA Received 17 March 2003; revised 10 October 2003

Abstract Although many theories of urban growth have broad implications regarding the dynamics of wage inequality, little empirical work has explored the issue. This paper studies the relationship between the growth of three measures of economic activity—population, employment, and per capita income—and a variety of wage-dispersion measures across a sample of US metropolitan areas between 1970 and 1990. Overall, the results indicate a negative association between the two: cities experiencing more rapid growth also tend to witness smaller increases (or larger decreases) in their inequality. Such findings offer some support to theories stressing growth-mechanisms which equalize productivity across workers.  2003 Elsevier Inc. All rights reserved. Keywords: Urban growth; Wage inequality; Earnings distributions; Convergence

1. Introduction As emphasized recently by Krugman [29], one of the most striking features of the geographic distribution of economic activity in the US is concentration: that is, the vast majority of the country’s population—in fact, as of 1990, more than 75 percent (US Bureau of the Census [39])—resides in a metropolitan area. Perhaps for this reason, a large literature has emerged in the past several decades studying the nature and causes of the urban growth process.1 To date, of course, much of this research effort has focused on two primary issues: first, the determinants of growth (e.g. Ioannides [25], Eaton and Eckstein [16], Black and E-mail address: [email protected]. 1 Studies of growth in cities have also, undoubtedly, been motivated by recent advances in the theory of

economic growth (e.g. Barro and Sala-i-Martin [7], Aghion and Howitt [4]) which, in many cases, stress mechanisms that are likely to be especially pronounced in local geographic markets (e.g. Lucas [30]). 0094-1190/$ – see front matter  2003 Elsevier Inc. All rights reserved. doi:10.1016/j.jue.2003.10.005

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Henderson [10] provide theoretical treatments; Glaeser et al. [20,21], Simon and Nardinelli [36] offer empirical evidence); and second (by extension), the implications of that growth for aggregate or average measures of productivity (e.g. Carlino and Voith [13], Ciccone and Hall [14], and Glaeser and Mare [22]). Unfortunately, little work has bothered to consider questions pertaining to the distributional aspects of the process. That is, while cities with certain initial characteristics may grow faster, thus experiencing more substantial increases in their average levels of productivity, how does growth influence the distribution of productivity (i.e. inequality) across a city’s inhabitants? Other than being a matter of interest in and of itself, the answer, I believe, may also offer further insight into the mechanisms driving city-level growth. After all, many theories do (in light of recent empirical evidence) have implications regarding the dynamics of earnings inequality which are not all necessarily the same. Several recent studies, for example, contend that urban growth is driven by human capital accumulation (e.g. Eaton and Eckstein [16], Black and Henderson [10]), the basic idea of which is straightforward. Human capital, presumably, increases productivity which leads to an expansion of a city’s equilibrium level of population or employment. This expansion, in turn, fuels greater human capital accumulation through a positive externality, and the process continues. As support for this hypothesis, Black and Henderson [10] report evidence of a strong positive association between education levels (given by the fraction of the population that is college-educated) and resident population across US metropolitan areas during the latter half of the 20th century. Additional evidence that human capital fuels growth among US cities has been reported by, among others, Glaeser et al. [21] and Simon and Nardinelli [36]. Why, then, should growth have any influence on inequality? A recent paper by Moretti [32] studying the social return to human capital indicates that greater city-level human capital (i.e. education) tends to boost the wages of less-educated workers relative to their more-educated counterparts. In particular, he finds that a 1 percent increase in a city’s share of college-educated workers increases the wages of high school dropouts, high school graduates, and college graduates by, respectively, 1.9, 1.6, and 0.4 percent. Based on this evidence, if urban growth is indeed the product of human capital accumulation, one might expect to see wage dispersion decline as cities expand due to a fall in between-educationgroup earnings gaps. Additionally, while urban areas in the US tend to exhibit balanced growth in the sense that there is little evidence of any growth-size relationship, there have been substantial differences in the average rates at which metropolitan areas have grown over the past several decades (Glaeser et al. [21]). In particular, cities in the South and West regions of the United States have grown faster, on average, than cities in either the Midwest or Northeast. This result can be seen in the first three sets of rows in Table 1, which report average growth rates of three variables—population, employment, and real per capita income—for a sample of 275 metropolitan statistical areas and consolidated metropolitan area statistical areas between 1970 and 1990.2 With the exception of per capita income

2 These figures are derived from the sources discussed in Section 2.

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Table 1 Average metropolitan area growth and inequality change by region Region Population 1970–1980 Population 1980–1990 Employment 1970–1980 Employment 1980–1990 Per capita income 1970–1980 Per capita income 1980–1990 Overall 90–10 wage differential 1970–1980 Overall 90–10 wage differential 1980–1990

West

Midwest

Northeast

South

0.28 (0.12) 0.18 (0.12) 0.47 (0.13) 0.23 (0.14) 0.27 (0.06) 0.1 (0.09) 0.11 (0.12) 0.2 (0.12)

0.07 (0.06) 0.03 (0.08) 0.21 (0.1) 0.1 (0.09) 0.25 (0.06) 0.11 (0.05) 0.16 (0.05) 0.25 (0.13)

0.04 (0.09) 0.04 (0.07) 0.15 (0.11) 0.12 (0.08) 0.18 (0.04) 0.23 (0.09) 0.18 (0.06) 0.17 (0.14)

0.21 (0.15) 0.13 (0.14) 0.37 (0.15) 0.2 (0.17) 0.3 (0.07) 0.15 (0.1) 0.08 (0.1) 0.22 (0.12)

Notes. Growth calculations are based on 49 metropolitan areas in the West, 70 in the Midwest, 36 in the Northeast, and 120 in the South for each year. 1970–1980 inequality calculations are based on 18 metropolitan areas in the West, 26 in the Midwest, 22 in the Northeast, and 37 in the South. 1980–1990 inequality calculations are based on 36 metropolitan areas in the West, 56 in the Midwest, 29 in the Northeast, and 90 in the South. Standard deviations are reported in parentheses.

in the 1980s, each variable exhibited faster average growth among western and southern cities than among cities in either the Midwest or Northeast. To be sure, this pattern likely reflects the well-established movement of the US population toward the West and South, which, aside from preferences for a warmer climate, has been attributed to the relatively low cost of labor in these two regions (Wheat [40]). A significant part of urban growth in the US over this time period, therefore, may be linked to rising labor demand in cities with low initial levels of wages as producers seeking cheap labor moved in. The result of such a shift, of course, would be to increase those wages as employment grows, thereby producing a convergence of wage rates across regions (Blanchard and Katz [11]). Whether this rise in labor demand leads to an increase or decrease in the dispersion of wages within cities, however, is not clear cut. If producers relocate primarily to take advantage of low-cost unskilled labor, for example, growth may produce a narrowing of the level of inequality as low-skill wages catch up to high-skill wages. An increase in the relative demand for skilled labor, on the other hand, would accomplish just the opposite by further increasing the skill premium. In light of the recent rise in the relative demand for skills throughout the US labor market (e.g. Katz and Murphy [11]), one might expect this latter effect to have been more important in the past few decades. Finally, cities have long been conjectured to be the centers of technological advance. As is well known, work by Marshall [31] and Jacobs [26] suggests that the free flow of information and ideas within urban areas spurs innovation. Evidence reported by

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Harrison et al. [23]—who find that producers in large, diverse urban markets are more likely to adopt new production technologies than producers situated elsewhere—and Feldman and Audretsch [17]—who show that diverse urban markets tend to spur greater product innovation than smaller, more homogeneous areas—certainly comports with this hypothesis. Because urban diversity has also been linked to the expansion of employment in many city industries (Glaeser et al. [20]), innovation may, therefore, be an important mechanism driving the growth of metropolitan areas. The connection between growth and inequality, then, would depend on the nature of the technological advance. In particular, given that many researchers have argued that innovation over the last several decades has been skill-biased (e.g. Acemoglu [1], Aghion [3]), one might expect, a priori, to see more rapidly growing cities exhibit especially large increases in wage inequality during this period.3 This paper offers some descriptive evidence on the connection between the growth of three measures of economic activity—population, employment, and real per capita income—and three measures of wage inequality—overall, residual, and between-education-group—across a sample of US metropolitan areas over the years 1970, 1980, and 1990.4 In general, the evidence reveals a negative association between the two sets of variables: cities that exhibit faster growth also tend to experience smaller increases (or larger decreases) in their levels of wage dispersion. The results are particularly strong when considering overall inequality, defined as the difference between the 90th and 10th percentiles of the log weekly wage distribution, which is significantly correlated with each measure of economic growth. This basic finding can be seen, at least casually, by comparing the final two rows in Table 1 with the growth rates listed above. Although the relationship is far from exact, there is a general tendency for regions with more rapidly growing cities to experience smaller changes in overall inequality during this time period. Statistically, formal estimates suggest that a 10 percentage point increase in a city’s rate of population or employment growth, for example, is accompanied by a 3 to 5 percentage point decrease, approximately, in the 90–10 wage gap. The estimated effect of per capita income growth is even stronger, implying a 5 to 11 percentage point drop in inequality given a 10 percentage point increase in growth. Results are somewhat more mixed when I consider two of the components underlying this overall measure: between-education-group inequality, captured by differences in the estimated coefficients on a set of education dummies from city-specific regressions of wages on education and experience, and within-group (i.e. ‘residual’) inequality, defined as 90–10 differences in the residuals from these regressions. Although negatively associated with all three measures of growth, the between-education-group measures are particularly correlated with changes in per capita income, whereas residual inequality tends to be more strongly associated with population changes. Employment growth, by contrast, appears to have a fairly significant tie to both measures of inequality. 3 This implication, of course, is analogous to the one drawn from the migration hypothesis just described. 4 Although somewhat short when considering patterns of economic growth, this sample time frame does cover

the period on which most previous studies of US wage inequality have focused. Extension of the analysis to longer time horizons is left to future work.

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As suggested below, this result may reflect differences in the nature of each type of growth. In particular, whatever elements underlie per capita income growth also seem to reduce overall wage dispersion primarily through a between-skill-group channel. Growth in population, on the other hand, appears to be the result of mechanisms that reduce wage dispersion predominantly within skill groups. Employment growth, then, appears to involve aspects of each type. The balance of the paper proceeds as follows. The next section provides a short description of the data. Section 3 documents the estimated effects of city-level growth on overall, residual, and between-education-group inequality. Section 4 then takes up the issue of convergence: in particular, whether there is any evidence that the urban growth process has brought US metropolitan areas to a common level of wage inequality. The final section offers some concluding remarks, including a brief discussion of the implications of the findings for the theories mentioned above.

2. Data The data used in the analysis are drawn from two primary sources. Individual-level observations on worker earnings are taken from three Integrated Public Use Microdata Series (IPUMS) Census extracts compiled by Ruggles and Sobek [35]: the 1970 1 Percent (Form 2) Metro Sample, the 1980 1 Percent Metro Sample, and the 1990 1 Percent Metro Sample.5 Information on specific metropolitan areas for these same three years is derived from the 1972 County and City Databook and the 1998 USA Counties on CD-ROM (US Bureau of the Census [38,39]). Samples of individuals from the Census are constructed using selection criteria that has become fairly standard in the wage inequality literature (e.g. Katz and Murphy [28], Juhn et al. [27]). In particular, I examine only white males between the ages of 18 and 65, who worked at least 14 weeks in the previous year, were not in school at the time of the survey, and earned at least 67 dollars per week (in 1982 dollars). Doing so limits the sample to individuals with a reasonably strong attachment to the labor force. Throughout the paper, a worker’s wage is defined as his weekly wage and salary earnings.6 Topcoded wage and salary earnings are imputed as 1.5 times the topcode for both 1970 and 1980, and as 210,000 dollars for the 1990 sample.7 These figures are converted to real terms using the Personal Consumer Expenditure Chain-Type Price Index of the National Income and Product Accounts. 5 Because the 1990 sample is weighted, I use the IPUMS person weights in the calculation of all statistics using this sample. 6 The 1970 Census codes weeks worked in interval form. Therefore, I estimate weeks worked for individuals in this year using the mean of the average weeks worked figures derived for the corresponding weeks worked and education categories (no high school, some high school, high school, some college, college degree or more) in the 1980 and 1990 samples. 7 This procedure mimics previous studies of wage earnings using these Census data (e.g. Autor et al. [5], Acemoglu and Angrist [2]).

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The basic geographic unit of analysis is the metropolitan statistical area (MSA) or consolidated metropolitan statistical area (CMSA) if an MSA is part of a CMSA. Although somewhat larger than one what might envision by a local labor market, the use of CMSAs greatly facilitates the construction of metropolitan areas with consistent definitions over time.8 In particular, because geographic definitions do change from year to year, individuals assigned to one metropolitan area (within a CMSA) in the 1970 Census would, in some instances, be assigned to another (within the same CMSA) in 1980 or 1990. Aggregating MSAs to the CMSA level helps to circumvent this problem. Although there are 275 such metropolitan areas in the US, a total of 103 MSAs and CMSAs are identified in the 1970 Census sample, 220 in the 1980 sample, 226 in the 1990 sample. The majority of the variables at the metropolitan area level are constructed from data reported at the county level. Among the principal quantities used are total resident population, total employment, per capita money income,9 the percentage of the adult population (i.e. of age 25 or older) with at least a college degree, the percentage of total employment in manufacturing, the unemployment rate, population density, and employment density. Densities are calculated as the ratio of city-level population or employment to total city-level land area (in square miles).10 While, in practice, two of these variables—the college and manufacturing fractions— could be estimated from the IPUMS samples, I utilize the measures reported in the CCDB and USA Counties data files because they are based on more complete samples and, thus, ought to involve less error.11 I did, for the sake of comparison, construct estimates of these two variables from the IPUMS samples—using all workers between the ages of 18 and 65 with positive wage and salary earnings—and repeated the analysis described below.12 The results from doing so were very similar to those reported here.13 To account for their potential influence on wage inequality, two additional variables are constructed for each metropolitan area: the percentage of the population that is foreignborn and the percentage of the workforce that belongs to a union. The ‘foreign-born rate’ 8 Metropolitan area definitions as of 1995, given by the USA Counties dataset, are used throughout. Individual observations from the Census are matched to these areas using the metropolitan area codes—the county-level composition of which appears in the documentation of Ruggles and Sobek [35]—reported in the IPUMS. As an additional note, I use the terms ‘city’ and ‘metropolitan area’ interchangeably throughout the paper for expositional purposes. 9 This variable is constructed by dividing total money income—income received by persons 15 years of age or older from wages and salaries, self-employment, and various transfers (e.g. Social Security, public assistance)— by the resident population. For additional details, see US Bureau of the Census [38,39]. As with the Census wage data, I convert per capita income into real terms using the NIPA consumer expenditure deflator. 10 Qualitatively similar results are obtained when a city’s density is computed as a population- or employmentweighted average of its constituent county-level densities. I report evidence using the unweighted measures because they make better instruments in terms of both relevance and ‘exogeneity’ (see Section 3.2). 11 These two particular quantities are derived originally from Summary Tape File 3C of the US Census of Population and Housing. Documentation regarding the sampling procedures can be found at http://www.census. gov/td/stf3/contents.html. 12 The samples used to estimate these quantities from the IPUMS data consisted of 452,134 individuals for 1970, 672,182 for 1980, and 723,706 for 1990. 13 Given that the correlations between the IPUMS-based and county-based variables were quite high—0.95 for education, 0.97 for manufacturing activity—this conclusion is not surprising.

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is derived rather simply from the Census extracts based on responses to the place-of-birth question. The ‘unionization rate’ is calculated from data provided by Hirsch et al. [24] who report unionization rates for US states. Metropolitan area-level unionization rates are imputed as weighted averages of the state-level rates taken across all states in which each metropolitan area is situated. The weights in this case are given by the fraction of each city’s population residing in each constituent state. Summary statistics for each year’s set of metropolitan areas appear in Table 2. In general, they confirm many well-established patterns for this time frame. Most notably, educational attainment and wage dispersion have risen; unionization rates and the extent of manufacturing in total employment have fallen.

3. Evidence 3.1. Baseline results: overall inequality Consider the following characterization of earnings in a city economy. Let the wage of p the worker situated at percentile p in city c at time t, wct , be given as follows:
p p p p wct = exp µc + δt + φ p log(Nct ) + γ p Zct + ct (1) p

where µc is a time-invariant constant specific to percentile p of city c, designed to capture the average characteristics (e.g. human capital, skill, ability) of the workers situated at this p city-percentile;14 δt is a time effect common to all workers at this percentile in year t; Nct is the size (i.e. population, employment, or per capita income) of city c at time t; p Zct is a vector of additional city-level covariates influencing labor earnings; and ct is a city-time-percentile specific residual. A common measure of ‘overall’ wage inequality for a given city economy—the difference between the 90th and 10th percentiles of its log wage distribution—then follows as
10 
90 
90 
90 
90  10 − log wct = µc − µ10 + φ − φ 10 log(Nct ) log wct c + δt − δt
90  
10 − ct (2) + γ 90 − γ 10 Zct + ct which, because I am interested in estimating the effects of changes in log(Nct ) (i.e. the city’s rate of growth) on wage dispersion and not on the individual wage percentiles themselves, can be written more compactly as
90 
10  (3) log wct − log wct = µc + δt + φ log(Nct ) + γ Zct + ct . Taking (10-year) differences then yields the following expression relating the change in a city’s overall inequality to its rate of growth:

90 
10     log wct − log wct = δt + φ  log(Nct ) + γ [Zct ] + ct (4) 14 Note, the underlying assumption here is not that workers situated at each city-percentile are necessarily

the same over time. These fixed effects are merely intended to capture any (unspecified) characteristics that are actually shared by workers at a particular city-percentile in different years.

378

Variable

1970 Mean

St. dev.

1980 Min.

Max.

Mean

St. dev.

1990 Min.

Max.

Mean

St. dev.

Min.

Max.

Overall 90–10 diff. 1.23 0.19 0.88 1.86 1.34 0.13 0.94 1.83 1.57 0.13 1.11 1.89 Residual 90–10 diff. 0.97 0.1 0.76 1.26 1.08 0.1 0.72 1.49 1.21 0.1 0.95 1.47 College–some college diff. 0.29 0.07 0.14 0.47 0.26 0.1 -0.09 0.58 0.35 0.1 -0.07 0.64 College–high school diff. 0.42 0.08 0.19 0.61 0.36 0.1 0.06 0.62 0.5 0.11 0.005 0.84 College–some high school diff. 0.55 0.09 0.33 0.76 0.51 0.11 0.17 0.94 0.69 0.17 0.13 1.23 College–no high school diff. 0.67 0.13 0.4 0.97 0.61 0.19 0.09 1.12 0.84 0.26 -0.24 1.84 Population 1319330 2276973 245045 17884092 780879.6 1709195 100376 17260490 851909.5 1862459 106470 17830586 Employment 512328.5 905919.5 77690 7151902 345834.1 766863.2 34724 7530683 406188.8 905355.2 37189 8567713 Per capita income 7366 913 5548.2 9756.1 8928.9 1150.2 5132.5 14400.5 10255.2 1750.2 5138.1 17030.6 College rate 0.109 0.028 0.05 0.231 0.159 0.047 0.077 0.347 0.194 0.058 0.095 0.365 Manufacturing rate 0.257 0.105 0.049 0.461 0.217 0.092 0.032 0.522 0.171 0.073 0.036 0.463 Union rate 0.257 0.095 0.088 0.417 0.211 0.084 0.06 0.349 0.146 0.068 0.046 0.294 Foreign rate 0.046 0.042 0.002 0.212 0.044 0.048 0.002 0.304 0.062 0.07 0.003 0.398 Unemployment rate 0.042 0.014 0.021 0.082 0.067 0.022 0.022 0.149 0.064 0.019 0.031 0.143 Individual observations 2158.6 3679.7 343 26745 1410.9 3029.4 149 30005 1425.4 3116.2 141 30132 Notes. Statistics based on 103 metropolitan areas for 1970, 220 for 1980, 226 for 1990. ‘Individual observations’ reports the number of workers per city identified in the Census.

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Table 2 Summary statistics

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which provides the basic equation to be estimated. To do so, three specifications are considered in which the vector of ‘non-size’ regressors, Zct , takes various forms. These three are then further augmented with region dummies to assess the robustness of the estimated coefficients to geographic differences in the rates at which inequality has changed.15 In each instance, estimation proceeds by generalized/weighted least squares (GLS) whereby each city-year observation on the change in inequality is weighted by the average number of individual observations used in its calculation (e.g. the 1970–1980 observation on a particular city is weighted by the average of the number of observations from the 1970 and 1980 samples for that city). As suggested by Moretti [32], this type of weighting scheme provides a simple correction for differences in the precision with which the dependent variable is measured across observations.16 Additionally, standard errors are adjusted to account for any remaining heteroskedasticity and the within-city correlation structure implied by the differenced residuals, ct . Results appear in panels A (for population growth), B (for employment growth), and C (for per capita income growth) of Table 3. The estimates reveal several findings of interest. First, they provide some support for the idea that declining unionization has contributed to greater wage dispersion in recent decades (e.g. Fortin and Lemieux [18]). In all three tables of results, the estimated coefficients are negative and, in two instances, statistically non-zero at conventional levels (i.e. at least 10 percent). Table 3 Overall inequality and GLS estimates Specification Variable

I

II

III

I

−0.23*** (0.08) –

−0.31*** (0.08) −1.24** (0.61) 0.005 (0.34) −0.34 (0.22) 0.79*** (0.29) 0.29 (0.47) No 0.26

−0.33*** (0.08) –

Change in manufacturing rate

–

−0.23*** (0.07) −1.25** (0.62) –

Change in union rate

–

–

Change in foreign rate

–

–

Change in unemployment rate

–

–

A. Population growth Change in college rate

Region effects? R2

No 0.18

No 0.21

–

II −0.3*** (0.09) −0.9* (0.53) –

–

–

–

–

–

–

Yes 0.24

Yes 0.26

III −0.33*** (0.1) −0.92 (0.56) −0.19 (0.32) −0.17 (0.24) 0.65*** (0.24) 0.48 (0.48) Yes 0.29

(continued on next page) 15 A list of Census regions and their constituent states appears in Appendix A. Because metropolitan areas, in some cases, run across state boundaries, some have parts in different regions. This occurs for seven cities in my sample. To handle these observations, I assign each city to the region in which the majority of the city’s total population resides. 16 Unweighted regressions, as it turns out, generate results that are very similar to those reported here.

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Table 3 (continued) Specification Variable B. Employment growth Change in college rate

I

II

III

I

II

III

−0.26***

−0.25***

−0.36***

−0.39***

−0.38***

(0.06) −0.94 (0.63) –

(0.07) −0.85 (0.58) 0.22 (0.32) −0.36* (0.2) 0.81*** (0.27) −0.24 (0.48) No 0.31

(0.07) –

Yes 0.31

Yes 0.31

−0.4*** (0.09) −0.42 (0.54) −0.04 (0.31) −0.2 (0.22) 0.66*** (0.24) −0.13 (0.5) Yes 0.34

−0.67*** (0.08) 0.85 (0.66) −0.82*** (0.27) −0.37* (0.19) 0.55* (0.28) 0.04 (0.3) No 0.36

−0.52*** (0.08) – –

−0.59*** (0.09) 0.76 (0.63) –

–

–

–

–

–

–

(0.06) –

Change in manufacturing rate

–

Change in union rate

–

–

Change in foreign rate

–

–

Change in unemployment rate

–

–

Region effects? R2

No 0.23

No 0.25

−0.55*** (0.1) –

Change in manufacturing rate

–

−0.65*** (0.1) 0.96 (0.66) –

Change in union rate

–

–

Change in foreign rate

–

–

Change in unemployment rate

–

–

C. Per capita income growth Change in college rate

Region effects? R2

No 0.29

No 0.3

–

(0.07) −0.26 (0.51) –

–

–

–

–

–

–

Yes 0.33

Yes 0.34

−0.63*** (0.08) 0.76 (0.65) −0.64** (0.26) −0.24 (0.2) 0.61** (0.25) 0.15 (0.32) Yes 0.38

Note. Dependent variable is change in 90–10 log weekly wage differential. All specifications also include a constant and a dummy for the 1970–1980 period. Heteroskedasticity-consistent standard errors, adjusted for within-metropolitan area correlation, are reported in parentheses. Regressions are weighted by the number of city-level observations used in the wage percentile calculations. 314 observations (103 for 1970–1980, 211 for 1980–1990). * Significantly different from zero at 10% level. ** Idem., 5%. *** Idem., 1%.

Second, I find that earnings inequality is strongly associated with changes in the percentage of the population born outside of the United States. Indeed, regardless of the measure of growth being considered, the coefficient on the foreign-born rate is positive and statistically significant. Such a result, I should add, is not inconsistent with the evidence surveyed by Topel [37] regarding immigration and inequality. In particular, while much of the evidence he describes suggests that native US workers do not experience significant wage decreases in response to rising immigration, recent immigrant cohorts do. The findings here may be reflecting this effect.

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Third, the results do show some evidence supporting the notion that increases in earnings inequality can be linked to a decrease in manufacturing’s presence in total employment. Four of the six estimated coefficients are negative, although only those appearing in the per capita income growth equations are significant. Fourth, evidence on the effects of the business cycle, as captured by the local unemployment rate, tends to be weak in these data. Although mostly positive, as one might expect given previous results on the cyclicality of inequality (e.g. see Blank and Blinder [12] for a survey), none of the coefficients on the unemployment rate are statistically different from zero. Fifth, the effects of education, given by the change in the percentage of the population having completed college, are mostly insignificant and somewhat mixed in sign. In particular, the coefficients are negative in the population and employment growth specifications, positive in the income growth specifications. This result, I would suggest, should not be taken to imply that inequality is unrelated to human capital accumulation. It may simply be the product of the high degree of correlation between education and growth (particularly per capita income growth) in these data.17 Indeed, when the growth rates are not included in specifications II and III, the estimated coefficient on the change in the college rate becomes significantly negative.18 Among the strongest and most robust results, as it happens, are the estimated growth effects. All of the coefficients on each measure of metropolitan growth are statistically negative and suggestive of economically meaningful magnitudes. Based on the longest specification (III), for example, the estimates suggest that a 10 percentage point increase in population or employment growth—approximately, a one standard deviation increase— corresponds to, roughly, a 3 to 4 percentage point decrease in the difference between the 90th and 10th percentiles of the log weekly wage distribution. The implied connection is even stronger for per capita income growth: a 10 percentage point rise in growth is accompanied by a 6 to 7 percentage point drop in inequality. These marginal associations are depicted graphically in Figs. 1a–c.19 Such results, I should add, also emerge (more or less) when CMSAs are dropped from the sample, and the analysis is performed using MSAs only.20 Coefficient estimates (standard errors) on the growth of population, employment, and per capita income from specification III for this smaller sample are, respectively, −0.12 (0.09), −0.2 (0.09), and −0.48 (0.14) without region effects; −0.07 (0.1), −0.17 (0.09), and −0.42 (0.14) with region effects. While these estimates are somewhat smaller in magnitude than those reported in panels A–C of Table 3—thereby suggesting an important role for CMSAs in the findings—they still suggest the same qualitative inequality-growth relationship. 17 Using the 314 city–year observations in the sample, the correlations between the change in the college rate

and population, employment, and per capita income growth are, respectively, 0.16, 0.37, and 0.69. 18 Specifically, the coefficients (standard errors) for specifications II and III without region effects are −1.24 (0.64) and −1.3 (0.68). With region effects they are −1.22 (0.57) and −1.2 (0.62). 19 The figures are constructed by plotting the residual from the estimation of specification III (with region effects) in which growth has been dropped against each growth rate. The fitted lines represent predicted values from regressions of this residual on each growth rate. 20 Doing so reduces the sample size from 314 to 272 (i.e. there are 21 CMSAs observed over two decades).

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(a)

(b)

(c) Fig. 1. Inequality and (a) population growth, (b) employment growth, and (c) per capita income growth.

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The results also hold up to different specifications of inequality, particularly measures that capture differences between the upper end of the wage distribution and the lower end. For example, using a city’s overall 75–25 wage differential as the dependent variable in specification III (region dummies included) instead of the 90–10 difference produces coefficients (standard errors) on population growth, employment growth, and per capita income growth of −0.19 (0.05), −0.24 (0.05), and −0.46 (0.09). Results for inequality between the top and middle of the wage distribution, by contrast, are somewhat weaker. Coefficients (standard errors) using the 90–50 differential in specification III (again, with region effects included) are, respectively, −0.05 (0.04), −0.07 (0.03), and −0.18 (0.04). This pattern suggests that, while growth is negatively associated with inequality defined in a variety of ways, much of this association seems to be driven by movement at the bottom end of the wage distribution. This basic finding, incidentally, is consistent with the results discussed in the next section. 3.2. Robustness: instrumental variable estimates One econometric issue not addressed in the estimation strategy just described is the potential endogeneity of growth with respect to changing inequality. Given that a vast literature has emerged in the past decade stressing this particular aspect of the growth process (e.g. see Benabou [8] for a survey), the results reported above would exhibit some degree of bias were growth a function of inequality. The nature of any such bias in an urban growth context, however, is not, a priori, clear. On the one hand, higher inequality may serve to slow a city’s growth, particularly if economic agents view it negatively. Many individuals, for example, may wish to live in relatively homogeneous localities and, thus, seek to avoid cities perceived to have strong economic divisions. In such an instance, high inequality should stand as an impediment to subsequent expansion in population, employment, and income. On the other hand, high inequality may have exactly the opposite effect and enhance growth, especially if it is associated with low ‘bottom-end’ wages. Indeed, because firms are free to move, high inequality cities may tend to attract employers looking for relatively low-wage workers, thus spurring a city’s subsequent rate of growth. As demonstrated below, the evidence tends to support this second hypothesis—high inequality is associated with faster growth. This result suggests that any bias associated with an endogenous rate of growth in these data is likely positive, implying that the negative coefficients reported in panels A–C of Table 3 are, if anything, actually somewhat closer to zero than the ‘true’ parameter values. To see this point, consider the results from basic growth regressions in which 10-year growth rates of population, employment, and per capita income are expressed as linear functions of three initial characteristics—the proportion of the population with at least a college degree, the manufacturing share in total employment, and the unemployment rate— and the initial overall 90–10 wage differential.21 In each case, I find a significantly positive 21 These three additional variables are included to account for the results established by Glaeser et al. [21]

on city-level growth. Not including them, incidentally, produces qualitatively similar findings with respect to the coefficients on initial inequality.

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coefficient on initial inequality: without region effects in the regressions, the coefficients (standard errors) for population, employment, and per capita income growth are 0.3 (0.1), 0.34 (0.09), and 0.14 (0.07); with region effects added, 0.12 (0.05), 0.18 (0.07), and 0.16 (0.05). If there is a feedback from inequality to growth, therefore, these data indicate that it is likely positive: higher inequality tends to spur growth, not hinder it. Interestingly, the data also show that this relationship is driven almost entirely by variation in the 10th percentile across cities. Consider Table 4, which reports results from the same growth regressions just described, but in which the 90–10 wage differential is replaced by initial values of the 90th and 10th percentiles entered separately. The results are quite clear: growth rates vary much more with respect to initial values of the 10th percentile than the 90th. In fact, across all three measures, we see that urban growth tends to rise significantly in cities with particularly low levels of ‘bottom-end’ wages, but does not respond much to variation in the value of ‘top-end’ wages. Because high-inequality cities also tend to have relatively low bottom-end wages cross-sectionally, the result that inequality spurs growth naturally follows.22 The first column of Table 5 shows a similar result for changes in a city’s overall 90–10 wage difference. Estimates from a regression of the change in overall inequality on initial values of the 90th and 10th percentiles indicate that inequality responds to cross-sectional differences in the level of bottom-end wages, not top-end wages. What is more, the data Table 4 Determinants of urban growth: overall wage percentiles Population growth Variable 10th percentile 90th percentile College rate Manufacturing rate Unemployment rate Region effects? R2

Employment growth

I

II

−0.34***

−0.17***

I −0.4***

(0.1) 0.07 (0.21) 0.28 (0.39) −0.49*** (0.16) −1.01** (0.51) No 0.48

(0.06) 0.02 (0.06) −0.11 (0.3) −0.28** (0.12) −1.61*** (0.45) Yes 0.68

(0.08) −0.01 (0.21) 0.86* (0.44) −0.52*** (0.15) 0.23 (0.57) No 0.52

Per capita income growth II

−0.27*** (0.06) −0.04 (−0.08) 0.69* (0.36) −0.28** (0.14) 0.04 (0.5) Yes 0.65

I −0.18** (0.08) 0.02 (0.09) 0.86*** (0.19) 0.23** (0.1) 0.1 (0.38) No 0.16

II −0.23*** (0.07) 0.02 (0.05) 1.24*** (0.28) 0.22*** (0.08) 0.86* (0.49) Yes 0.26

Notes. GLS estimates. Dependent variable is 10-year growth rate of population, employment, or per capita income. Regressors are given by initial values of the variables listed in the first column. Each specification also includes a constant and a dummy for 1970–1980 time period. See notes to Table 3. * Significantly different from zero at 10% level. ** Idem., 5%. *** Idem., 1%.

22 As noted in the concluding section, this finding is particularly supportive of a model in which urban growth is driven by the location decisions of producers who seek cheap ‘bottom-end’ labor.

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Table 5 Dynamic properties of inequality Dependent variable Variable Change in 90–10 differential Initial 10th percentile Initial 90th percentile R2

Change in 90–10 differential

Change in 10th percentile

–

−1.03*** (0.06) –

0.37*** (0.07) −0.04 (0.14) 0.4

Change in 90th percentile −0.035 (0.06) –

–

–

0.67

0.06

Notes. See Table 4. *** Significant at the 1% level.

also indicate that changes in city-level 90–10 wage differentials operate primarily through changes in the 10th percentile, not the 90th. This can be seen in the last two columns of Table 5 which report coefficients from regressions of the change in each wage percentile on the contemporaneous change in the 90–10 difference. Quite simply, the 10th percentile changes dramatically with inequality; the 90th changes little. The picture emerging from this evidence, then, ought to be apparent. Cities with high initial inequality levels experience relatively rapid growth in population, employment, and per capita income. This growth, in turn, reduces inequality, as the bottom end of the wage distribution rises, thereby impeding future growth. Thus, in an equation describing the change in inequality as a function of growth, any stochastic element decreasing inequality should also lead to lower growth since growth appears to follow from high inequality. The sign of the bias in the GLS estimates reported in Table 3, therefore, ought to be positive (i.e. toward zero).23 Given that, in spite of this bias, GLS still points to a significantly negative connection between growth and inequality, the conclusion drawn above is reinforced. Nevertheless, to address this issue, I turn now to the estimation of Eq. (4) by two-stage least squares (2SLS). As instruments for population and employment growth, I use the logarithms of initial population and employment densities. Again, while it is well known that city-level growth is largely uncorrelated with initial size (e.g. Eaton and Eckstein [16]), the data used here suggest that growth is, by contrast, significantly related to initial density. A regression of population growth on log initial population density, for instance, produces a coefficient (standard error) of −0.07 (0.008) with an R 2 of 0.27. For employment, the results are similar: −0.08 (0.008) with an R 2 of 0.23.24 As an instrument for per capita income growth, I utilize initial log per capita income which, as is well known from the 23 Notice, this very same feedback mechanism ought to generate a negative bias in an equation expressing growth as a function of inequality. Based on the results established thus far, any positive shock increasing a city’s growth rate ought to decrease its level of inequality. Hence, the covariance between inequality (the regressor) and the random component of growth (the residual) will be negative. 24 The coefficients on initial density, incidentally, remain significantly negative when these regressions are augmented with time and region effects. To see that these data reproduce the commonly found result of little association between growth and initial size, regressions of population and employment growth on initial log levels

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literature on growth convergence, is negatively associated with subsequent growth: the estimated coefficient (standard error) is −0.09 (0.06) with an R 2 of 0.03. Do these variables constitute valid instruments? Based on the rule-of-thumb suggested by Nelson and Startz [33], the first-stage results certainly indicate that all three are sufficiently relevant. Moreover, initial levels of density and income are unlikely to be endogenous with respect to subsequent changes in inequality. Of course, one could still argue that these instruments might be flawed in the sense that they might actually be the ‘true’ determinants of changing inequality, which, as it so happens, also drive rates of growth. That is, initial density and income might simply be omitted, relevant regressors whose direct effects on inequality would be assigned to the growth rates they cause. Such an argument, however, would imply that, when each instrument is added to the GLS specifications described above, the coefficients on growth should be driven to zero. To the contrary, when I do so, I find that the coefficients on growth remain strongly negative in all specifications, whereas initial density and per capita income enter much less significantly.25 Such evidence suggests that these variables are indeed reasonable instruments. Results appear in Table 6. As above, all regressions are weighted by the average number of city-level observations used in the percentile calculations. Two aspects of the estimates are particularly noteworthy. First, as in Table 3, all of the coefficient estimates are negative. Here, however, the magnitudes are somewhat larger, suggesting that the GLS estimates are indeed biased toward zero. For example, whereas the previous estimates from specification III indicated that, in response to a 10 percentage point increase in either population or employment growth, inequality dropped by between 3 and 4 percentage points (6 to 7 percentage points for per capita income growth), the 2SLS estimates imply a 4 to 5 percentage point drop in inequality (9 to 11 percentage points for per capita income). Second, although quite a bit noisier than the GLS results, all but two of the coefficients— those from the shortest of the three specifications (I) using per capita income growth—are statistically significant at conventional levels. Thus, the basic conclusion drawn above, that urban growth reduces earnings inequality, remains. 3.3. Between- vs. within-group components To what extent, then, does this ‘growth-induced’ decline in overall inequality stem from a narrowing of the gap between workers of different skill groups as opposed to a reduction in the gap between workers belonging to the same group? In this section, I explore this

produce coefficients (standard errors) of, respectively, −0.019 (0.013) and −0.02 (0.013). Neither is statistically different from zero at 10 percent significance. 25 For example, estimating the longest specification (III with region effects), the coefficients (standard errors) on population, employment, and per capita income growth are −0.29 (0.1), −0.37 (0.09), and −0.52 (0.09). Those on initial log population density, log employment density, and log per capita income, by contrast, are 0.01 (0.01), 0.007 (0.01), 0.15 (0.09). Moreover, when the growth rates are dropped from the regressions, each of these coefficients rises substantially: 0.026 (0.012), 0.031 (0.012), 0.34 (0.09), further suggesting that any influence these variables have on inequality operates through growth.

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Table 6 Overall inequality and 2SLS estimates Specification Variable

I

II

III

−0.21*** (0.08) –

−0.72* (0.43) –

I

II

III

–

−0.85*** (0.29) −0.32 (0.6) –

–

–

–

–

–

–

Yes

Yes

−0.49** (0.23) −0.77 (0.53) −0.04 (0.39) −0.14 (0.24) 0.75*** (0.26) 0.5 (0.5) Yes

Change in manufacturing rate

–

−0.35*** (0.06) −1.26** (0.64) –

Change in union rate

–

–

Change in foreign rate

–

–

Change in unemployment rate

–

–

No

No

−0.36*** (0.12) −1.23** (0.6) 0.1 (0.43) −0.33 (0.22) 0.84*** (0.3) 0.29 (0.47) No

−0.21***

−0.31***

−0.35***

−0.77**

(0.05) −0.87 (0.62) –

(0.36) –

A. Population growth Change in college rate

Region effects? B. Employment growth

Change in manufacturing rate

–

Change in union rate

–

–

Change in foreign rate

–

–

Change in unemployment rate

–

–

No

No

(0.1) −0.86 (0.56) 0.21 (0.4) −0.36* (0.2) 0.81*** (0.27) −0.23 (0.54) No

−1.34***

−1.08***

(0.36) 3.3*** (1.18) –

(0.23) 2.2** (0.95) −0.89*** (0.26) −0.32* (0.2) 0.67*** (0.25) −0.11 (0.28) No

Change in college rate

Region effects? C. Per capita income growth Change in college rate

(0.07) –

−4.5 (3.7) –

Change in manufacturing rate

–

Change in union rate

–

–

Change in foreign rate

–

–

Change in unemployment rate

–

–

No

No

Region effects?

–

−0.62*** (0.16) 0.37 (0.59) –

–

–

–

–

–

–

Yes

Yes

–

−1.18*** (0.31) 2.7** (1.2) –

–

–

–

–

–

–

Yes

Yes

−8.1 (20.7) –

−0.49*** (0.17) −0.23 (0.55) 0.06 (0.37) −0.19 (0.22) 0.71*** (0.25) −0.27 (0.61) Yes −0.94*** (0.25) 1.75 (1.1) −0.73*** (0.27) −0.24 (0.2) 0.7*** (0.26) −0.005 (0.32) Yes

Notes. Dependent variable is change in 90–10 log weekly wage differential. Log initial per capita income instruments for (A) population growth, (B) employment growth, and (C) per capita income growth. All specifications also include a constant and a dummy for the 1970–1980 period. Heteroskedasticity-consistent standard errors, adjusted for within-metropolitan area correlation, are reported in parentheses. Regressions are weighted by the number of city-level observations used in the wage percentile calculations. * Significantly different from zero at 10% level. ** Idem., 5%. *** Idem., 1%.

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issue using the following two-step procedure. In the first, I estimate a regression in which log weekly wages for individual i, in city c, at time t is expressed as log(wict ) = βct Xict +

5 

j

j

θct Eict + ξict

(5)

j =1

where Xict is a vector of personal characteristics consisting of an indicator for marital status and a fourth-order polynomial in potential experience;26 the five E j terms represent educational attainment dummies ((1) no high school, (2) some high school, (3) high school, (4) some college, (5) college degree or more); and ξict is a person-city-time-specific residual. All parameters are allowed to vary by both metropolitan area and year. Between-skill-group inequality, which for my purposes I define in a between-educationgroup sense, are based upon the five θ terms, which capture the average weekly wage earnings for individuals of a given educational group in a particular city–year, conditional on a flexible polynomial in experience. Given these estimates, I construct four betweeneducation-group premia: college–some college (θˆct5 − θˆct4 ), college–high school (θˆct5 − θˆct3 ), college–some high school (θˆct5 − θˆct2 ), college–no high school (θˆct5 − θˆct1 ). Within-group (i.e. residual) inequality is then computed as the difference between the 90th and 10th percentiles of the distribution of residuals, ξˆict . With these estimates in hand, each is modeled statistically in a manner analogous to that for overall inequality; thus,
5 j j j j θˆct − θˆct = µc + δt + φ j log(Nct ) + γ j Zct + ct , j = 1, . . . , 4 (6) for each of the four between-education-group quantities, and
90  ξˆct − ξˆct10 = µc + δt + φ log(Nct ) + γ Zct + ct

(7)

for the residual measure. As before, estimation proceeds using 10-year differences to eliminate the city-specific intercepts, µc . The results appear in Table 7 (for the between-education-group measures) and Table 8 (for the within-group measure). For the sake of parsimony, the tables only report the ˆ from the longest specification of regressors, III (with estimated growth coefficients, φ, changes in college, manufacturing, unionization, foreign-born, and unemployment rates included), both with and without region effects. Each is estimated by GLS and 2SLS, where, again, initial log densities and initial log per capita income instrument for rates of growth. Consider, first, the results pertaining to the four between-education-group measures given in Table 7. Although they are not as uniformly significant as those reported for overall inequality, I do find, interestingly, that all of the coefficients are negative. Thus, the evidence does suggest an inverse connection between growth, broadly speaking, and between-skill-group inequality. 26 Potential experience is estimated as the maximum of (age minus years of education minus 6) and 0. Because

the 1990 Census does not code educational attainment as years of schooling completed for all individuals, I impute years of education for individuals in this year using Table 5 of Park [34].

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Table 7 Relative education returns and growth Differential

Population growth

College– no high school

−0.12 (0.1) −0.24** (0.1) −0.14 (0.15) −0.49** (0.24) −0.04 (0.06) −0.1 (0.08) −0.11 (0.09) −0.29* (0.17) −0.07 (0.06) −0.12* (0.07) −0.11 (0.09) −0.25* (0.14) −0.02 (0.05) −0.05 (0.06) −0.11 (0.08) −0.23 (0.14)

College– some high school

College– high school

College– some college

Employment growth

Per capita income growth

Region effects?

Estimation method

−0.19** (0.09) −0.31*** (0.1) −0.15 (0.13) −0.45** (0.19) −0.09* (0.05) −0.17** (0.07) −0.11 (0.08) −0.28** (0.13) −0.1** (0.05) −0.16*** (0.06) −0.11 (0.08) −0.23** (0.12) −0.05 (0.05) −0.08 (0.06) −0.11 (0.07) −0.21* (0.12)

−0.79*** (0.11) −0.78*** (0.11) −1.15*** (0.29) −1.16*** (0.3) −0.45*** (0.06) −0.46*** (0.06) −0.57*** (0.14) −0.67*** (0.17) −0.45*** (0.05) −0.46*** (0.05) −0.48*** (0.12) −0.57*** (0.13) −0.27*** (0.06) −0.28*** (0.06) −0.26** (0.1) −0.34*** (0.11)

No

GLS

Yes

GLS

No

2SLS

Yes

2SLS

No

GLS

Yes

GLS

No

2SLS

Yes

2SLS

No

GLS

Yes

GLS

No

2SLS

Yes

2SLS

No

GLS

Yes

GLS

No

2SLS

Yes

2SLS

Notes. Coefficients on growth from estimation of specification III (which includes college, manufacturing, unionization, foreign-born, and unemployment rates in differences as well as a dummy for the 1970–1980 period). Dependent variable is change in relative education premium. Heteroskedasticity-consistent standard errors, adjusted for within-metropolitan area correlation, are reported in parentheses. Regressions are weighted by the number of city-level observations used in the education return calculations. * Significantly different from zero at 10% level. ** Idem., 5%. *** Idem., 1%.

The strongest results, notably, emerge when per capita income growth is considered. All of the 16 coefficients on that variable are statistically different from zero at conventional levels. What is more, the implied correlations are actually quite sizable: a 10 percentage point increase in per capita income growth is associated with a 3 percentage point drop in the college–some college differential; a 4 to 7 percentage point drop in either the college–

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Table 8 Residual inequality and growth Estimation method

Region effects?

Population growth

Employment growth

GLS

No

GLS

Yes

2SLS

No

2SLS

Yes

−0.13*** (0.04) −0.13*** (0.04) −0.23*** (0.07) −0.34*** (0.13)

−0.13*** (0.03) −0.13*** (0.04) −0.21*** (0.06) −0.3*** (0.11)

Per capita income growth −0.09 (0.08) −0.05 (0.08) −0.41** (0.17) −0.31* (0.17)

Notes. Dependent variable is change in 90–10 residual log wage differential. See also Notes Table 7. * Significantly different from zero at 10% level. ** Idem., 5%. *** Idem., 1%.

high school or college–some high school differential; and an 8 to 12 percentage point decrease in the college–no high school gap. Between the two remaining growth measures, employment growth appears to be the more relevant variable for explaining changes in between-education-group inequality. Of the 16 coefficients, 10 are statistically non-zero at 10 percent significance, and among these, the magnitudes are fairly consistent, suggesting a 1 to 4 percentage point drop in the between-education-group gaps given a 10 percentage point increase in growth. Changes in population, for the most part, do not appear to have a particularly strong connection to most of the between-education-group gaps, as only five of the coefficients are significant. The within-group results, on the other hand, produce a very different pattern. Indeed, while all of the estimated growth effects on inequality are negative here too, the strongest results emerge from increases in population and employment. Looking at Table 8, we can see that each of the coefficients on these two series is significantly negative: the magnitudes, in this case, suggest that our benchmark 10 percentage point rise in growth is accompanied by a 1 to 3 percentage point decrease in the residual 90–10 wage difference. The estimated connection between the change in residual inequality and per capita income growth, on the other hand, is noticeably weaker. While all four coefficients in the table are negative, only the two instrumental variable estimates are statistically non-negligible. In light of the strong connection between overall inequality and each of the three growth measures reported above, such results are quite intuitive, at least from a purely mechanical point of view. If much of the association between growth and overall inequality is manifested in the prices of observable characteristics like education, little will be left for unobserved elements. If not, the inequality-growth relationship will be driven primarily by unobservables. Among the three growth measures considered, per capita income seems to correspond to the first pattern, population the second. Employment growth appears to incorporate elements of both. Although such an explanation is certainly reasonable, is there an economic rationale that accounts for this discrepancy between the channels through which different measures of growth influence inequality? A complete answer, of course, is beyond the scope of the

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present analysis, but may relate to differences in the mechanisms driving each measure of growth. To be sure, although all three growth measures are positively related to one another, they are far from perfectly correlated.27 Whatever mechanisms drive income growth may influence inequality predominantly through a between-group channel: lifting lower wage/skill groups relative to higher wage/skill groups. The mechanisms driving population growth, on the other hand, may instead serve to decrease inequality primarily within skill groups. Employment growth, then, may be the product of both types of elements. Because the urban growth literature has, for the most part, not addressed different types of city-level growth (e.g. population vs. per capita income), further inquiry into this issue, I would suggest, is certainly warranted.

4. Convergence Given that the evidence documented thus far shows that urban growth (broadly defined) is associated with decreasing inequality—whether it be overall, between-education-group, or residual—a related question concerning convergence naturally arises. In particular, since previous evidence has revealed that regional patterns of growth have led to convergence in per capita incomes (Barro and Sala-i-Martin [6]) and wages (Blanchard and Katz [11]) across US states, as well as some degree of convergence in income distributions across regions (Bishop et al. [9]), has urban growth generated any evidence of convergence in city-level inequality measures? This section examines this question with respect to two different notions of convergence.28 4.1. β-convergence The first notion, ‘β-convergence,’ implies that, if we are to see cities with different levels of inequality converge to a common level, there will be a negative association between initial inequality and the magnitude of its subsequent change. Thus, in a regression of the change in inequality on the initial level of inequality:
10 
10  
90 

90  − log wct = α + δt + β log wct  log wct −1 − log wct −1 + ct for overall wage differentials,
  j j j j  θˆct5 − θˆct = α j + δt + β j θˆct5 −1 − θˆct −1 + ct ,

j = 1, . . . , 4

for the relative education premia, and   
 ξˆct90 − ξˆct10 = α + δt + β ξˆct90−1 − ξˆct10−1 + ct for the residual measure, we should find significantly negative values for each of the β parameters. 27 Pairwise correlations among the three growth rate series in my sample are 0.93 for employment and population, 0.58 for employment and per capita income, 0.35 for population and per capita income. 28 The question of whether there has been convergence in inequality levels across economies has also been raised by Benabou [8]. Although his discussion focuses primarily on the distributional dynamics of incomes and not wage earnings, the results here can still be interpreted as evidence on this matter.

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Two sets of results—one from regressions which include region effects and one from those that do not—appear in Table 9. Notice, in addition to each of the six measures of wage inequality (overall and residual 90–10 differences, four college premia), I have also reported β-convergence results for each of the individual components of these measures. Overall, the evidence is quite strong: each of the six wage dispersion variables shows some tendency to converge to a common level. With the exception of the college–no high school wage differential when region effects are excluded from the regression, all of the estimated coefficients are significantly negative. Table 9 Evidence on β-convergence Coefficient on initial level Change in Overall 90–10 differential Overall 90th percentile Overall 10th percentile Residual 90–10 differential Residual 90th percentile Residual 10th percentile College–some college premium College–high school premium College–some high school premium College–no high school premium College return Some college return High school return Some high school return No high school return

Without region effects

With region effects

−0.3*** (0.09) 0.03 (0.07) −0.42*** (0.04) −0.19*** (0.06) −0.16** (0.07) −0.27*** (0.06) −0.65*** (0.05) −0.42*** (0.06) −0.34*** (0.07) −0.14 (0.09) −0.62*** (0.05) −0.68*** (0.06) −0.74*** (0.08) −0.75*** (0.09) −0.56*** (0.1)

−0.4*** (0.08) 0.03 (0.04) −0.53*** (0.07) −0.2*** (0.08) −0.2** (0.08) −0.29*** (0.08) −0.71*** (0.06) −0.49*** (0.07) −0.41*** (0.11) −0.21*** (0.07) −0.62*** (0.07) −0.71*** (0.1) −0.82*** (0.12) −0.9*** (0.12) −0.79*** (0.11)

Notes. Estimated coefficients from regressions of changes on initial values. All regressions include a constant and a time dummy for the 1970–1980 period. Heteroskedasticity-consistent standard errors, adjusted for withinmetropolitan area correlation, are reported in parentheses. Regressions are weighted by the number of city-level observations used in the wage percentile/education return calculations. * Significantly different from zero at 10% level. ** Idem., 5%. *** Idem., 1%.

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Moreover, the individual pieces help to provide some idea as to how this process has worked. Consider, for example, the convergence result for overall inequality. Based on the estimates for the 90th and 10th percentiles taken individually, it is evident that any convergence in this measure of dispersion has been driven by adjustment at the bottom end of the distribution: low 10th percentiles ‘catching up’ to high 10th percentiles. Little, by contrast, has happened among the 90th percentile. Although not nearly as striking as this particular finding, the remainder of the results suggest a qualitatively similar pattern: returns among individuals at the lower ends of the wage distribution show somewhat stronger β-convergence than those at higher ends. 4.2. σ -convergence The second notion of convergence, ‘σ -convergence,’ implies that, if cities are converging to a common level of inequality, the cross-sectional standard deviation of inequality levels should be decreasing over time. Although this concept is quite similar to that of βconvergence, important differences exist between the two notions (e.g. Durlauf and Quah [15] provide a discussion). As shown below, the data examined here demonstrate one such difference. Table 10 reports the estimated standard deviations for each of the inequality measures between 1970 and 1990. As with the results on β-convergence, I have also included results for each of the constituent pieces. Furthermore, to maintain a balanced panel of cities, the standard deviations are calculated using the 103 metropolitan areas that are identified in each of the three years.

Table 10 Evidence on σ -convergence Year Variable

1970

1980

1990

Overall 90–10 differential Overall 90th percentile Overall 10th percentile Residual 90–10 differential Residual 90th percentile Residual 10th percentile College–some college premium College–high school premium College–some high school premium College–no high school premium College return Some college return High school return Some high school return No high school return

0.159 0.105 0.177 0.087 0.039 0.05 0.052 0.06 0.074 0.1 0.143 0.158 0.16 0.157 0.174

0.124 0.093 0.124 0.078 0.039 0.042 0.051 0.068 0.084 0.15 0.09 0.104 0.11 0.114 0.158

0.133 0.139 0.141 0.094 0.046 0.051 0.046 0.067 0.098 0.18 0.145 0.148 0.139 0.153 0.189

Notes. Standard deviations. Sample limited to set of 103 metropolitan areas identified in all three years. Calculations are weighted by the number of city-level observations used in the wage percentile/education return calculations.

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Table 11 Rank correlations and changes Rank correlation Variable Overall 90–10 differential Overall 90th percentile Overall 10th percentile Residual 90–10 differential Residual 90th percentile Residual 10th percentile College–some college premium College–high school premium College–some high school premium College–no high school premium College return Some college return High school return Some high school return No high school return

1970–1980

1980–1990

0.9 0.75 0.87 0.74 0.72 0.65 0.22 0.58 0.62 0.66 0.23 0.37 0.48 0.47 0.62

0.67 0.79 0.56 0.71 0.71 0.61 0.29 0.52 0.43 0.57 0.26 0.33 0.24 0.17 0.44

Average change 1970–1980 10.2 (8.9) 14.9 (15.1) 11.6 (9.5) 16.0 (14.6) 17.2 (14.4) 18.8 (16.6) 28.7 (23.7) 21.2 (17.4) 20.1 (16.6) 19.8 (14.7) 29.7 (22.2) 25.7 (21.5) 23.2 (19.6) 23.3 (20.2) 20.5 (16)

1980–1990 18.7 (15.6) 14.7 (12.8) 21.7 (17.5) 16.6 (15.4) 16.8 (15.1) 19.6 (17.7) 27.8 (22) 21.8 (19.5) 24.8 (19.7) 20.4 (18.6) 29.8 (20.7) 28.8 (19.2) 30.3 (20.7) 31.5 (21.9) 24.6 (19.9)

Notes. Sample limited to set of 103 metropolitan areas identified in all three years. ‘Average change’ reports the average absolute value of the change in ranks between years (standard deviation in parentheses).

What the standard deviations reveal is a general lack of σ -convergence among these variables. Although there is some evidence that the cross-sectional standard deviation of certain measures (e.g. the overall and residual differentials and percentiles, the absolute education returns) declined between 1970 and 1980, they rose again during the 1980s. Thus, although the evidence on β-convergence is fairly significant, there has not been a corresponding reduction in cross-sectional dispersion over the entire sample period. Again, given the difference in these two notions of convergence, this result is not altogether unreasonable. It may, for instance, reflect the fact that, while the β-convergence process moved these measures closer together during the 1970s, it served to separate them during the 1980s as cities ‘overshot’ one another. To see this point, consider the figures reported in Table 11. Listed in the first two columns are rank correlations (i.e. correlations of a city’s cross-sectional rank in one year with its cross-sectional rank in another) of each of the measures in Tables 9 and 10 between adjacent years. Although positive, many of the correlations are actually rather low, particularly when considering the 1980–1990 period. This result suggests that the cross-sectional distribution of each variable exhibited some degree of churning: some cities moved up in rank, others fell. The next two columns of the table provide further evidence on the extent of this churning by reporting the average absolute value of a city’s change in rank between adjacent years. For example, between 1970 and 1980, cities in this sample moved, on average, 10.2 places in the rank-ordering with respect to the overall 90–10 wage differential. Between 1980 and 1990, they moved nearly 19 places on average. Given that there are only 103 cities used to calculate these figures, the fact that the average change in rank is quite large—on the order of 15 to 30 places in most instances—suggests an overshooting dynamic.

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5. Concluding comments Although researchers have long been interested in characterizing the urban growth process, surprisingly little work has explored how growth and inequality at the city level are related. This paper has offered evidence on the link between three measures of growth and three measures of wage dispersion across a sample of US metropolitan areas between 1970 and 1990. While there are some differences in the strength of the relationship across the various growth-inequality pairs, the basic conclusion is clear: growth reduces inequality. In light of such evidence, we are left with the following question: which theories of urban growth described in the Introduction are consistent with this result? Theories based upon human capital accumulation, I would argue, are certainly consistent with a negative growth-inequality connection. Again, while previous research has established an important role for human capital in explaining growth by regressing city-level growth rates on initial values of education, the evidence here yields a similar conclusion from a different angle. Building on Moretti’s [32] insights regarding the social return to human capital across individuals of different skill/education groups, if human capital acquisition drives urban growth, growth should be negatively associated with wage dispersion. Such an implication is borne out by the data. Of course, to the extent that human capital’s influence on wage dispersion is manifested primarily in the reduction of between-skill-group gaps, the evidence also suggests that human capital acquisition may be a relatively more important feature of growth in per capita income than growth in either employment or population. The results are also compatible with a migration-based model in which growth is driven by the location of producers seeking cheap labor. This process implies, quite simply, that employers flock to cities with relatively low wages, thereby increasing the demand for labor and, thus, equilibrium earnings in these markets. This particular interpretation, incidentally, is also suggested by Glaeser et al. [20] with respect to their findings on the nature of cityindustry growth. There is, however, one additional facet to this story implied by the results reported here. Assuming that urban growth patterns are driven by the location decisions of mobile firms, the results on overall inequality suggest that producers have been drawn to cities with low values of wages at the bottom end of the wage distribution, not low values at the top (recall Table 4). Indeed, none of the three growth measures considered here is significantly related to the magnitude of a city’s 90th wage percentile. Much of the convergence in average wage levels documented in other work, therefore, may have been driven by the cross-sectional dynamics of the lower tails of the country’s regional wage distributions. To the extent that innovation has been skill-biased in recent decades, the idea that technological change drives urban growth, therefore, is not consistent with the findings. This conclusion, however, should not be taken to imply that innovation is an unimportant aspect of city economies. To be sure, given the concentration of educated workers in urban areas (e.g. Glaeser [19]), as well as the propensity of producers in large, diverse markets to innovate, one would expect to see skill-biased innovation occurring primarily in metropolitan areas. Additional evidence gleaned from the three Census extracts certainly supports this idea. In particular, using the 103 metropolitan areas identified in both 1970 and 1990 in this

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sample, overall 90–10 wage differentials grew by 40.9 percentage points among cities in the West, 46.5 percentage points in the Midwest, 38.9 percentage points in the Northeast, and 30.4 percentage points in the South. The corresponding figures calculated across individuals living outside of metropolitan areas in these regions were, respectively, 19, 28, 26, and 12 percentage points. Thus, it appears that rising wage inequality has been, to a significant degree, an urban phenomenon. At the same time, however, the evidence also indicates that, while cities as a whole may have experienced particularly large increases in earnings inequality between 1970 and 1990, the growth process itself has served as a mitigating factor.

Acknowledgments I thank Jan Brueckner and two anonymous referees for their comments and suggestions. All errors, naturally, are my own.

Appendix A. Composition of US Census regions West:

Washington, Oregon, California, Nevada, Idaho, Montana, Wyoming, Utah, Colorado, Arizona, New Mexico, Alaska, Hawaii. Midwest: North Dakota, South Dakota, Nebraska, Kansas, Minnesota, Iowa, Missouri, Wisconsin, Illinois, Michigan, Indiana, Ohio. Northeast: Maine, Vermont, New Hampshire, Massachusetts, Rhode Island, Connecticut, New York, Pennsylvania, New Jersey. South: Texas, Oklahoma, Arkansas, Louisiana, Kentucky, Tennessee, Mississippi, Alabama, West Virginia, Delaware, Maryland, District of Columbia, Virginia, North Carolina, South Carolina, Georgia, Florida.

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