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1 SMART CITIES: QUALITY OF LIFE, PRODUCTIVITY, AND THE GROWTH EFFECTS OF HUMAN CAPITAL Jesse M. Shapiro* Abstract —From 1940 to 1990, a 10% increase in a metropolitan area’s for example, Simon & Nardinelli, 2002), and it has received concentration of college-educated residents was associated with a 0.8% some support from the work of Rauch (1993) and Moretti increase in subsequent employment growth. Instrumental variables esti- (2003), who show that, conditional on observable worker mates support a causal relationship between college graduates and em- ployment growth, but show no evidence of an effect of high school characteristics, wages are higher in high-human-capital cit- graduates. Using data on growth in wages, rents, and house values, I ies. In contrast, however, Acemoglu and Angrist (2000) find, calibrate a neoclassical city growth model and find that roughly 60% of using an instrumental variables approach, that the external the employment growth effect of college graduates is due to enhanced productivity growth, the rest being caused by growth in the quality of life. effects of human capital at the state level are relatively This finding contrasts with the common argument that human capital 4 small. generates employment growth in urban areas solely through changes in The final explanation is that areas with more-educated productivity. populations experience more rapid growth in the quality of I. Introduction life. This might occur because more-educated individuals spur the growth of consumption amenities in cities in which ROM 1940 to 1990, a 10% increase in a metropolitan they reside, or because their influence on the political F area’s concentration of human capital was associated process leads to desirable outcomes such as reductions in with a 0.8% increase in the area’s employment growth. A crime and pollution. substantial body of literature confirms this correlation be- In this paper, I attempt to distinguish among these three tween human capital and local area employment (or popu- explanations of the positive relationship between human 1 Little is known, however, about the under- lation) growth. capital and local-area employment growth. To address the lying causes of this relationship. omitted variables issue, I instrument for an area’s human As I show more formally in the next section, essentially capital concentration using the presence of land-grant insti- three explanations are possible for the relationship between tutions (Moretti, 2004) and compulsory schooling laws human capital and city employment growth. The first is (Acemoglu & Angrist, 2000). To separate the remaining omitted variable bias: some feature or features of an area explanations, I develop and calibrate a simple neoclassical that are correlated with both human capital and employment growth model using data on growth in wages and rents to growth have been left out of the regression. Although past determine what share of the overall employment growth research has tended to find that including broad sets of effect of human capital is due to productivity growth, and controls does not eliminate the positive correlation between what share is due to improvements in the quality of life. population or employment growth and human capital (Glae- Instrumental variables estimates support the presence of a ser, Scheinkman, & Shleifer, 1995; Glaeser & Shapiro, causal effect of concentrations of college graduates on 2003a), concerns remain about the causal interpretation of employment growth, but show no evidence of a similar 2 this association. effect for high school graduates. Though not conclusive, The next hypothesis is that a highly educated population these results serve to lessen concerns about omitted vari- generates greater local productivity growth, perhaps ables and especially reverse causality. To separate the influ- through knowledge spillovers (Lucas, 1988) or pecuniary ences of productivity and quality of life, I use Census data 3 A externalities arising from job search (Acemoglu, 1996). from 1940 through 1990 to show that metropolitan areas number of researchers have adopted this explanation (see, richer in skilled residents tend to experience faster growth in (hedonically adjusted) wages, rental prices, and house val- Received for publication June 23, 2003. Revision accepted for publica- ues, with the effect on rents and house values much larger tion August 9, 2005. * University of Chicago. than the effect on wages. A calibration of a simple city I am grateful to Edward Glaeser, Claudia Goldin, Matthew Kahn, Kevin growth model based on this evidence suggests that roughly M. Murphy, Chris Rohlfs, Philipp Schnabl, two anonymous referees and 60% of the effect of college graduates on employment Daron Acemoglu, the editor, for helpful comments. Daron Acemoglu and Joshua Angrist generously provided their data on compulsory schooling growth is due to productivity; the rest comes from the laws. Raven Saks provided data from the Wharton Land Use Control relationship between concentrations of skill and growth in Survey. I thank the Institute for Humane Studies, the Center for Basic the quality of life. This conclusion is robust to a number of Research in the Social Sciences, the Chiles Foundation, and the National Science Foundation for financial support. alternative specifications, including direct controls for im- 1 See, for example, Glaeser, Scheinkman, and Shleifer (1995); Simon portant determinants of area growth, and allowance for key (1998); Simon and Nardinelli (2002); Simon (2004); and Glaeser and model parameters to vary with the human capital distribu- Shapiro (2003a). 2 For example, residents with high human capital may seek out areas in tion. which quality of life is rising, leading to a simultaneity bias. See, for example, Kahn (2000) and Cullen and Levitt (1999). 3 4 Lange and Topel (forthcoming) review the existing literature on the Black and Henderson (1999) develop a model of endogenous urban growth that embeds local effects of human capital accumulation. social returns to human capital. The Review of Economics and Statistics, May 2006, 88(2): 324-335 2006 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology ©

2 325 SMART CITIES I also test for a connection between human capital and These equilibrium conditions hold equally well in a several direct measures of quality of life. Though prelimi- dynamic context. If a city experiences relative growth in its nary, this exercise suggests the effect may be operating productivity, then it should experience growth in both wages through the expansion of consumer amenities such as bars and land prices; if it experiences growth in quality of life, and restaurants (Glaeser, Kolko, & Saiz, 2001) rather than this will tend to be reflected in land price growth. In a more through the political process. general model in which firms use land as an input to The organization of the paper is as follows. Section II production, these equilibrium conditions must be modified presents a simple model of city growth and illustrates the somewhat, but it remains possible to identify changes in three possible explanations for the relationship between productive and consumption amenities using data on wages human capital and metropolitan area employment growth. and land prices in a set of locations. Section III describes the Census data I use to conduct the To see these results formally, consider an economy with estimation, as well as the land-grant and compulsory- {1,2, . . ., }, each endowed with a set of locations i  I schooling instruments. Section IV presents ordinary least A location-specific productivity and quality of life, denoted i Q and , respectively. Firms produce a homogeneous good squares and instrumental variables estimates of the relation- i sold on a world market at the numeraire price of 1 using a ship between human capital and growth in employment, f L, R ( AF  Y constant-returns-to-scale production function ), wages, and housing costs, and provides a calibration of the f where R L denotes the quantity of labor and the quantity of model in section II. Section V relates human capital to more land used in production. Input markets are competitive, and direct measures of the change in quality of life, and section firms face a constant per-unit marginal cost given by the VI concludes. W ( C function ,P A and P )/ are the prices of labor , where W i i i i i Spatial equilibrium requires that this i. and land in location II. Estimating Framework marginal cost be equal to unity at all locations, so that our first equilibrium condition is given by In this section I develop a simple neoclassical model of city growth, and use it to illustrate three hypotheses about C  W P (1)   A , i i i the correlation between growth and human capital. The model is based on Roback’s (1982) formulation, which has for all i. been used extensively to generate city-level rankings of c  Consumers have preferences given by U U Q, X, R ( ), quality of life and to infer the value to consumers and firms c where R is the quantity of goods consumed and X is the 5 Most of various local public goods or city characteristics. quantity of land consumed. This utility function implies an studies have exploited the cross-sectional implications of ( indirect utility function V Q ,P ,W ) which, in equilibrium, i i i the Roback model; here I will place the model in a more must be constant across locations. Our second condition is 6 dynamic context. therefore Before presenting the formal model, it will be helpful to discuss the intuition behind it. Consider a world of identical  V  Q (2) ,  , W  U P i i i firms and households choosing among a set of locations. Each location is endowed with a productive amenity (which  for all i and some constant U To close the model, I will . enters the production function) and a consumption amenity suppose that P f 0, that is, that there  )  (  f ), with L (  i i (which enters the utility function). Suppose that households is an increasing supply price of housing. consume only land and a traded good and that firms use only A Allow Q to change exogenously over time. We can and i i labor as an input. Let us first consider equilibrium in totally differentiate the equilibrium conditions (1) and (2) as production, which requires that all firms be indifferent follows: between locations. In equilibrium, wages must be higher in more productive locations, because otherwise firms would dA dP dW i i i move into those locations and bid up the price of labor. In ,  C  C P W dt dt dt order for households to be indifferent between more and (3) less productive locations, land prices must be higher in more  dU dW dP dQ i i i productive places, because wages will be higher in those V .  V  V  P W Q dt dt dt dt locations. Land prices must also capitalize consumption amenities; that is, land will be more expensive in more Let k and k be the shares of land and labor in the firm’s R L pleasant locations. s cost function, let be the share of land in the household’s R budget, and let lowercase letters denote natural logarithms 5 See, for example, Blomquist, Berger, and Hoehn (1988); Gyourko and  dU Tracy (1991); Cragg and Kahn (1997); and Black (1999).  0. Then we can of variables. I will normalize 6 Roback’s model’s implications for growth have been addressed before. dt For example, Glaeser, Scheinkman, and Shleifer (1995) use a parametric rearrange the above conditions to yield expressions for the example of the more general model to make inferences about the causes changes in wages and land rents: of city growth.

3 326 THE REVIEW OF ECONOMICS AND STATISTICS where 1 1 dq dp da V Q i i i Q   ,   k dt dt W dt V k W L R  s (4) R k L 1 1 1 l a q ε ε (8) .  ε     1 t , 1  t , i i i 1  t , k k  L R k R s  R k L dq 1 V k Q da s dw i i L i R Q   . k V k dt dt k dt W R W R L s s   R R k k Suppose that a positive correlation is observed between L L H human capital and subsequent employment growth i,t Additionally, given the assumed supply curve of land, -  l . Equation (7) illustrates the three possible explana 1  i,t be the elasticity of land rents with respect to local  letting tions for such a correlation: employment, employment growth can be written as 1 dq 1 1 V da Q dl 1. Omitted variables bias. A positive relationship be- Q i i i   . (5)   H tween could arise if H is correlated and  l i,t i,t i,t 1  V k  dt dt k dt W L R W s  R - with some omitted component of X and that omit , i,t k L ted city characteristic is itself a cause of rapid em- ployment growth. For example, if highly educated These conditions must hold for all cities i. Changes in land rents will capitalize growth in produc- individuals tend to concentrate in cities with better tivity and in the quality of life, scaled by the importance of weather, and city growth is affected by the weather, land in the firm and household budgets. Changes in wages a correlation between human capital and employ- will reflect productivity growth, less a correction to com- ment growth could arise. pensate firms for changes in land prices. In the limiting case If high human capital is asso- Productivity growth. 2. in which firms use no land in the production process, wage ciated with more rapid productivity growth, that is, if a growth will directly capitalize productivity growth. The 0, then human capital will be positively  H i,t above equations therefore suggest a framework for evalu- correlated with subsequent employment growth ating the extent to which quality of life and productivity  l . i,t  1 growth are associated with a given correlate of employment 3. Growth in the quality of life. Suppose that cities with growth. higher concentrations of human capital experience denote the concentration of H To see this formally, let i,t faster growth in the quality of life; that is, suppose t, at time i human capital in city X and let be a vector of i,t q that  0. Then human capital and employment other city characteristics. Suppose that growth will covary positively. V Q Q q q q q  H   , ε  X  1 i i , t t , i t , t i ,  1 To address hypothesis 1, I employ an instrumental V W W (6) variables approach using both the presence of land-grant a a a  a X H   ε ,  colleges and universities (Moretti, 2004) and compulsory t  1 i , t i , i t , i , t  1 schooling laws (Acemoglu & Angrist, 2000) To evaluate 7 Suppose further that the shocks where  denotes changes. the relative importance of hypotheses 2 and 3, I directly 8 q a Then, by ε X and H. ε and are drawn independently of a q estimate the parameters relating human capital , and equation (5) above, we have to growth in productivity and quality of life, respectively. Given data (possibly noisy) on changes in land prices and 1 1   l wages for a panel of cities, by equation (4) we can write t 1  , i k  R s  R k (7) L V Q 1 1 Q p  q   a  ,   p   1 1 i i , t 1  1 t 1 , i , t   1  , i t l q a a q k k V W W L R X    ε  H ,       t , i , t i , t  1 i  s k k R L L k L 7 This specification assumes, of course, that the effects of human capital (9) are linear, which need not be the case. In unreported regressions I find no evidence of nonlinearities in the effect of human capital on employment k growth, but I do find evidence of convex effects of human capital on the R growth of wages and land rents. Q V k s 1 Q L R 8 w The shocks are not assumed to be identically distributed, however, nor q  a  ,     w  , i 1 t , t  1 i t  , 1 i  t 1 i , are they assumed to be drawn independently over time or independently W V k k k L R R W q a ε of one another. That is, I will allow for the possibility that and ε are s s   R R k k L L heteroskedastic, serially correlated, and correlated with one another.

4 327 SMART CITIES p w where are measurement errors in price and wage and imperfectly substitutable varieties (for example, skilled and growth, respectively, and are assumed to be independent of unskilled), then there will be additional equilibrium condi- 9 Rearranging equation (9), we have  a and  q. tions that determine the spatial distribution of wages for the two groups, and the estimates from equation (10) would be a a a k H  X  k  ε  w  p  interpretable as a weighted average of productivity growth i , t  1  R , i i t t i , 1 L t , i , t  1 affecting each group. Different groups may also choose p w  , k k  R L , t   t , i 1 1 i different consumption bundles, leading to heterogeneity in (10) the values of the share parameters discussed above. If shares q q q s  w  H p ε    X  t i i t , R , t  1 i i , t  1 , t 1  , i are correlated with human capital, this could introduce bias in estimates that assume homogeneous shares. In section IV p w .  s  R i  1 1 t , ,  t i C, I discuss the sensitivity of the results to relaxing the assumption that firm and household budget shares are iden- k Given values of , ,k ,s it is thus possible to use data on R R L tical across locations. a q growth in wages and land prices to estimate and , and thus to determine the relative importance of productivity and quality of life in explaining the relationship between III. Data Description human capital and city employment growth. The advantage of a reduced-form approach such as the A. Measuring Wages, Rents, and Human Capital one presented above is that it makes possible the use of To form the basic panel of metropolitan areas, I extract price measures to estimate the underlying relationship be- from the IPUMS database (Ruggles & Sobeck, 1997) all tween human capital and growth in productivity and the prime-age (25 to 55) white males living in Census-defined quality of life. The disadvantage of this approach, however, metropolitan areas in the years 1940, 1970, 1980, and is that it necessarily suppresses the mechanism underlying 10 My measure of total employment in a given metro- 1990. the connection between human capital and growth in pro- politan area in a given year is a count of the total number of ductivity and quality of life. For example, the model as 11 I construct an prime-age white males in the sample. formulated does not distinguish meaningfully between tech- area-level employment growth measure for each time period nological (Lucas, 1988) and pecuniary (Acemoglu, 1996) as the log change in employment. I standardize this to be a externalities from human capital, nor does it identify the ten-year growth rate in the 1940–1970 period. channel through which human capital might create con- I construct the wage series as follows. I restrict attention sumer amenities. In section V, I provide evidence on these 12 To to white prime-age males living in metropolitan areas. channels, using several direct measures of quality of life. construct a wage estimate, I divide total wage and salary The model also has several more specific limitations. income for each individual by total annual hours worked, First, in reality households consume locally produced ser- imputed from the categorical variables on weeks and hours vices as well as traded goods, and the prices of these 13 I then regress the log of worked available in the microdata. services are determined in part by local labor market con- the wage for each individual on a dummy for each metro- ditions. In a simple representative-household formulation, politan area, age and its square, and dummies for veteran each household is neither a net seller nor a net buyer of status, marital status, educational attainment, industry cate- services, so incorporating services into the framework 14 All regressions include gory, and occupational category. above would make little difference to my conclusions about dummies for missing values of marital and veteran status; the importance of productivity and quality-of-life growth. In observations with missing values of other variables were a more realistic model with heterogeneity in how much time dropped. I estimate separate regressions for each Census each household buys and sells in the service market, an increase in productivity could penalize net buyers of ser- 10 In many cases, the set of counties that make up an area grows larger vices by raising the local wage. The presence of such a force over time. Because the public-use sample of the Census does not directly would lead me to overstate the role of productivity in identify counties, it is not possible to directly construct county groupings determining the growth effects of human capital, for it that are consistent over time. In section IV C I show that my results are robust to examining only those areas whose definitions did not change would mean that an increase in wages partially represents an over the relevant period. increase in the cost of living, and would therefore capitalize 11 I have used person-level sample weights wherever appropriate in quality-of-life improvements more than is reflected in the constructing my measures of employment, human capital, and other metropolitan area characteristics. equations (10). 12 Because nearly all prime-age white males are in the labor force, The model also ignores heterogeneity in labor and hous- restricting attention to this group helps to limit concerns arising from ing markets that may be important in determining equilib- differences across metropolitan areas in which types of workers choose to participate in the labor market, which could otherwise create a composi- rium factor prices. For example, if workers come in multiple tion bias (Solon, Barsky, & Parker, 1994). 13 In all cases I used the midpoint of the categorical range as the point q a 9 p w estimate. and ε and are ε As with , it will not be necessary to assume that 14 homoskedastic, independent over time, or drawn independently of one Further details on the controls used are available in section 1 of the another. appendix.

5 328 THE REVIEW OF ECONOMICS AND STATISTICS OWEST L IGHEST AND 1.—H ABLE T AGE AND R ENTAL P RICE F IXED W for each year. The controls for housing characteristics I FFECTS , 1990 E employ are dummies for commercial use status, acreage of A. Wage Fixed Effects property, availability of kitchen or cooking facilities, num- ber of rooms, type of plumbing, year built, number of units Stamford, CT Highest 0.60 0.55 Norwalk, CT in structure, water source, type of sewage disposal, and Danbury, CT 0.41 17 To construct the house value series, number of bedrooms. 0.39 New York-Northeastern, NJ 0.38 Bridgeport, CT I perform an identical procedure using the log of reported house values for all owner-occupied dwellings. 0.11 Lowest Alexandria, LA 0.12 Laredo, TX Though the rankings of rental prices shown in table 1 0.13 Bryan-College Station, TX seem sensible, changes in unmeasured characteristics of the McAllen-Edinburg-Pharr-Mission, TX 0.18 Brownsville-Harlingen-San Benito, TX 0.22 housing stock may cause difficulties in determining the effects of human capital on land prices. As a check on the B. Rental Price Fixed Effects potential magnitude of such a problem, I obtained the Office Highest 0.77 San Jose, CA of Federal Housing Enterprise Oversight’s (OFHEO) house 0.73 Stamford, CT price index (HPI) for metropolitan areas for the years 0.69 Santa Cruz, CA 0.66 Ventura-Oxnard-Simi Valley, CA 1980–1990 (Calhoun, 1996). This index is based on a repeat 0.66 Norwalk, CT sales methodology (Case & Shiller, 1989), and thus takes Lowest 0.58 Dothan, AL advantage of the fact that the correlation between the 0.60 Florence, SC growth in house prices and changes in unobservable dwell- 0.64 Danville, VA Anniston, AL 0.66 ing characteristics will tend to be smaller when examining Johnstown, PA 0.66 multiple transactions at the same address. For the 119 Notes: Wage fixed effects reflect coefficients from metropolitan area dummies in a regression of metropolitan areas for which both the growth rate of the HPI log(wage) on these dummies and controls for observable worker characteristics. Rental price fixed effects reflect coefficients from metropolitan area dummies in a regression of log(monthly contract rent) on these and the change in estimated rental price residuals are avail- dummies and controls for observable housing characteristics. See section III of text for details. able, the correlation between these two measures is 0.83. The correlation between the 1980–1990 growth rate of the year so as to avoid unnecessary restrictions on the coeffi- HPI and the 1980–1990 change in the estimated house value cients. 18 residual is 0.92. Such strong correlations across alternative For each year I extract the coefficients on the metropol- measures reinforce the view that unmeasured housing char- itan area dummies to be used as estimates of local differ- acteristics do not play a major role in determining the 15 Naturally, these estimates are only as good ences in wages. growth rates in my measures of the implicit price of land. as the controls—sorting on omitted characteristics will in- As a measure of the concentration of human capital in a troduce bias. However, as table 1 illustrates, the estimates metropolitan area, I calculate the sample shares of prime- generally seem sensible. Moreover, for the purposes of age white males who have a high school diploma only, some studying growth the changes in these price coefficients are college, and a college degree or higher. more important than their levels—and growth rates in wage residuals will at least be purged of time-invariant differ- ences in the characteristics of local workers. B. Land-Grant Colleges and Universities The Census contains data on the value of owner-occupied housing units as well as on the rental price of renter- The federal Morrill Act of 1862 granted large parcels of occupied units. As it is not clear a priori which market is land to each state in the Union (with the size of the parcel preferable as a means of measuring differences in the proportional to the state’s number of Congressional repre- implicit price of land, I use both types of data. In contrast to sentatives) in order to fund the creation of colleges instruct- 19 the labor market sample, I do not restrict to units occupied ing in agriculture, engineering, and other subjects. An- by prime-age white males, on the view that housing prices other act in 1890 extended the so-called land-grant for different demographic groups will be tied together by provision to 16 southern states (Christy, Williamson, and market forces. To construct the rental price series, I regress Williamson, 1992). I follow Moretti (2004) in using Nev- the log of reported monthly contract rents on dummies for ins’s (1962) appendix to code a binary variable indicating metropolitan areas as well as a set of controls for dwelling 16 (Data on these characteristics are not avail- characteristics. 17 Section 2 of the appendix contains additional details about the controls able for 1940, but results on rents are robust to excluding the used. These controls were available for all years (except 1940) and therefore permit me to construct a consistent series. See also the supple- 1940–1970 time period.) I run these regressions separately mental appendix available in Shapiro (2005). 18 Both correlation coefficients are statistically significant at the 0.01% 15 level. The correlation between the change in the rent residual and the The use of metropolitan area dummies to measure local wage and change in the house value residual during the 1980–1990 period is 0.82. price differences is related to the approach taken by Gabriel and Rosenthal 19 (2004). James (1910) argues that, though the bill was introduced by Senator 16 Justin Morrill of Vermont, credit for its passage belongs to the Illinois Monthly contract rent includes utilities only if they are a specified part College professor Jonathan B. Turner. of the rental contract.

6 329 SMART CITIES REA A ETROPOLITAN M NSTITUTIONS AND T RANT -G AND 2.—L ABLE I whether a metropolitan area contains a land-grant institu- APITAL C UMAN H tion. Wilcoxon Occupational Human Capital Index Consistent with the intention to spread these universities Rank-Sum evenly across the states, the geographic distribution of -Value Difference Year p Land-Grant No Land-Grant land-grant universities is quite even. For example, among 1850 0.0579 (7) 0.0612 (2) 0.0034 0.7697 the 251 metropolitan areas in my 1980 sample, 12% of 0.0001 1860 0.0599 (10) 0.0600 (5) 0.9025 Northeastern metropolitan areas, 16% of Midwestern met- 0.0003 1870 0.0630 (15) 0.0633 (6) 0.8763 0.0026 1880 0.0687 (20) 0.0713 (7) 0.9559 ropolitan areas, 15% of Southern metropolitan areas, and 0.0712 (48) 0.0109 0.5730 0.0821 (13) 1900 15% of Western metropolitan areas contain a land-grant 0.0844 (13) 0.1173 1910 0.0749 (70) 0.0096 chi college or university. (A Pearson’s -squared test of inde- 0.0043 0.0783 (17) 0.0740 (89) 1920 0.3414 1940 0.0844 (112) 0.1010 (20) 0.0166 0.0006 pendence fails to reject the null hypothesis that land-grant 0.0000 0.0234 0.1176 (22) 0.0942 (122) 1950 colleges and universities are distributed independently of 0.0261 1970 0.1355 (96) 0.1616 (21) 0.0000 Census region.) 1980 0.1455 (235) 0.1862 (37) 0.0432 0.0000 Moretti (2004) reports that the demographic characteris- Notes: Number of observations in cell in parentheses. Land-grant classification based on Nevins (1962). Occupational human capital index is constructed by matching each primeage white male in the tics of metropolitan areas with and without land-grant col- Census public-use file with the share of prime-age white males in 1950 in the individual’s occupation with a college degree or higher, and then averaging by metropolitan area and year. leges or universities are similar in most respects. He also reports that the presence of a land-grant institution is asso- ciated with higher shares of college graduates, but lower capital distributions between the two categories of metro- shares of individuals with high school diplomas and some politan areas. From 1900 to 1920, when these institutions college. These facts seem consistent with the view that the had been established but rates of college graduation were presence of a land-grant school causes higher rates of still relatively low, the differences are moderate. The differ- college attainment, and not vice versa. ences are largest in the sample period of 1940–1980, when In 1980, 35% of prime-age white males in metropolitan rates of college attendance were highest and thus the scope areas with a land-grant school were college graduates, for the impact of land-grant schools greatest. The fact that 20 versus 25% in areas without a land-grant school. A more the correlation between occupational distribution and the direct check on the validity of the presence of land-grant presence of a land-grant college or university arose only schools as an instrument for the current distribution of after these institutions could have played a significant causal human capital is to ask whether this correlation existed role supports the exogeneity of land-grant status with re- before land-grant institutions were of significant size. The spect to preexisting differences among metropolitan areas. Census, however, did not begin asking directly about edu- cational attainment until 1940, by which time the land-grant C. Compulsory Schooling Laws schools were already of significant size (Bowman, 1962). Coincident with the rise of high school completion in the To circumvent this problem, I have constructed a human first half of the twentieth century was a significant tighten- capital index based on the distribution of occupations within ing of regulations concerning compulsory school attendance a metropolitan area. Using Census public-use samples of and child labor. Acemoglu and Angrist (2000) have shown prime-age white males from 1850 through 1980, I follow that changes in these laws at the state level had a significant Simon and Nardinelli (2002) in assigning to each individual impact on the educational attainment of those born in in the sample the percentage of individuals in the same 21 In as much as changes in these laws are affected states. occupation in 1950 with a college degree or higher. By plausibly exogenous with respect to subsequent labor and averaging this variable by metropolitan area I obtain an housing market conditions, they provide a candidate instru- occupational human capital measure for each metropolitan ment for concentrations of high school graduates in metro- area in each year. politan areas from 1940 through 1990. Table 2 shows the difference in this human capital index I have obtained Acemoglu and Angrist’s (2000) coding of between land-grant and non-land-grant metropolitan areas both compulsory attendance and child labor laws for the by year from 1850 through 1980. During the 1850–1880 1914–1965 period. Because these laws vary along many period, when many land-grant institutions had not yet been dimensions, I follow Acemoglu and Angrist (2000) in established, there is essentially no difference in the human adopting two summary measures: the minimum years of CL schooling required before leaving school ( ), and the 20 This effect is too large to be accounted for solely by the presence of minimum years in school required before work is permitted graduates of land-grant institutions themselves. But these schools may 22 well have effects that exceed their size. For example, Bowman (1962) I then create dummies for four categories of each of ). ( CA notes that “The comparatively high rate of college attendance in the rural areas of the western states contrasts dramatically with the lag of rural 21 regions in most parts of the world. This lends support to other evidence See also Goldin and Katz (2003), who argue that roughly 5% of the that the land-grant institutions sold higher education to a public much increase in high school enrollment from 1910 to 1939 is attributable to larger than that represented in their own enrollments.” Consistent with this compulsory schooling laws (CSLs). 22 view, I find that the effect of land-grant schools on college graduation rates is defined as “the larger of schooling required before dropping out CL is largest in the Midwest. and the difference between the minimum dropout age and the maximum

7 330 THE REVIEW OF ECONOMICS AND STATISTICS ABLE 3.—H UMAN C APITAL AND G ROWTH T These regressions reveal a number of important facts. First, they confirm the usual finding that cities with greater Dependent Variable Is Growth in concentrations of human capital experience more rapid Employment Wage Rental Price House Value growth in employment. A 10% increase in the share of 0.0786 0.0664 0.0160 log(share college 0.0714 college-educated residents is associated with an increase in (0.0081) (0.0247) educated) (0.0126) (0.0176) the employment growth rate of roughly 0.8%. Initial level of: 0.0345 Employment A second important pattern is that growth in wages, rents, (0.0097) and house values tends to be higher in cities with greater Wage 0.2347 concentrations of college-educated residents. A 10% in- (0.0274) Rental price 0.0382 crease in the share of college-educated residents corre- (0.0242) sponds to a 0.2% increase in wage growth and a 0.7% House value 0.0244 increase in the growth of rental prices and house values, all (0.0401) statistically significant. Note also that the effect of human 2 0.2333 R 0.0581 0.2306 0.0888 capital on the land price measures is more than 3 times as N 495 495 495 495 large as the effect on growth in wages. Notes: Table shows coefficient in regression of dependent variable on the log of the percentage of prime-age white males with a college degree in the metropolitan area. Wage, rent, and house value growth are measured as the growth in metropolitan area fixed effects from hedonic regressions as described in section III of the text. Regressions include time period dummies. Standard errors have been adjusted for B. Calibration of Growth Model serial correlation within metropolitan areas. These reduced-form facts suggest that growth in quality these variables: 6 years and under, 7 years, 8 years, and 9 of life may be playing an important role in the relationship 8 years and under, 9 years, 10 years, CL; years and over for between human capital and employment growth, because Acemoglu and Angrist (2000) CA. and 11 years and over for growth in land prices seems generally to be more sensitive argue that these categorizations efficiently capture the most to the share of college-educated residents than growth in relevant variation in state laws during this time period. wages. For a more quantitative evaluation of the relative Given these definitions, I assign each prime-age white importance of quality of life and productivity in explaining CL male in the 1940–1990 Census public-use samples to a the human-capital–employment-growth relationship, we category according to the laws prevailing category and CA will need to estimate the equations (10). For this we require in his state of birth when he was of age 14. I then calculate ), land’s share of output values for labor’s share of output ( k L for each metropolitan-area–year the share of prime-age ( k ), and the share of land in the household budget ( s ). R R white males in each category. This results in eight variables, Existing evidence on factor shares suggests values of two of which are linearly dependent, which measure the 23 More controversial is the share k  0.75 and k 0.10.  R L variation in the exposure of prime-age white males in each s of land in the household budget ( ), for which prior studies R area and year to different CSLs. When metropolitan area have traditionally used a value of approximately 0.05 fixed effects are included in a specification, these variables (Roback, 1982). This is a good approximation to the literal capture changes over time in the share of prime-age white share of land in the budget, but is likely to be far too small males exposed to each type of CSL regime, and thus provide to approximate the concept required by theory. The reason is variation useful in identifying the effects of high school that the model in section II assumes that all goods other than graduates on local area growth. land are traded on a national market and therefore display is s no local price variation. In a more realistic framework, R IV. Results not merely the household budget share of land per se, but rather the share in the household budget of all goods that are A. Baseline Specification s produced using local land as an input. In other words, R Table 3 reports coefficients from ordinary least squares should capture the importance of all cost-of-living differ- (OLS) regressions of employment, wage, rental price, and ences between locations, because all of these costs matter in house value growth on the log of the percentage of college equilibrating utility levels across cities. graduates for the 1940–1990 panel. Data on wages, rents, In section 3 of the appendix, I estimate the effect of a 1% and house values come from metropolitan area fixed effects increase in the implicit price of land on the price of a market in hedonic regressions of prices on worker or housing unit basket of goods and services, using both cross-sectional data characteristics as described in the previous section, and are and evidence on price changes over time. These estimates therefore not correlated with observable differences in 23 worker or housing unit quality. Dummies for time period are Krueger (1999) estimates that labor’s total share of output (including the return to human capital) is roughly 0.75; Poterba (1998) also places it included in all specifications, and standard errors are ad- k at between 70% and 80% of national income. I will therefore use  L justed for correlation of the errors within metropolitan areas. 0.75. Poterba (1998) reports a corporate capital income share of around 10% that, combined with a labor share of approximately three-fourths, k places an upper bound of around 0.15 on CA enrollment age.” is defined as “the larger of schooling required before I will set .  0.10, which k R R receiving a work permit and the difference between the minimum work is close to the upper bound and, if anything, seems likely to cause me to age and the maximum enrollment age” (Acemoglu & Angrist, 2000). overstate the productivity effects of human capital.

8 331 SMART CITIES RODUCTIVITY AND THE P ROWTH IN G T C UMAN 4.—H ABLE APITAL AND suggest a preferred value of s of approximately 0.32, with R UALITY OF Q IFE L a lower bound of approximately 0.22. I will report results Productivity for both values to address the sensitivity of my findings to Share of 24 s alternative values of . R Growth Effect, Effect of Human Capital As I showed in section 1, regressions of 1 on Growth in a ˆ Share of k L Measure of Land in k w  k   p L i,t  1 1  R i,t 1 Land Productivity, Budget, Quality of a q ˆ ˆ  a q ˆ ˆ and Prices s Life, k R L s w p   Rents 0.0209 0.0172 0.62 .32 1 i,t  i,t 1  R (0.0061) (0.0069) on the log of the share of college graduates will yield estimates .22 Rents 0.0209 0.0070 0.80 a q a ˆ (0.0065) (0.0069) of the parameters . These estimates, denoted and and 0.0214 0.0229 House .32 0.59 q ˆ - capture the effect of human capital on growth in produc , (0.0061) values (0.0072) tivity and the quality of life, respectively. Because the total House 0.72 0.0116 0.0229 .22 values (0.0060) (0.0072) effect of human capital on employment growth is equal to q a k Notes: Table shows coefficients in regression of p  w  and s k  p w on   1 L  1  i,t  1 R i,t  1 R i,t i,t  [see equation (7)], the fraction of the employ- 1/ k L the log of the share of prime-age white males in the metropolitan area with a college degree. All ment growth effect that is due to productivity growth can be k calculations use 0.10. I measure i as the change in metropolitan area k 0.75 and  ’s  w   R i,t L 1 log(wage) fixed effect from time t t  1, as described in section III;  p to is measured similarly, using  1 i,t q a a ˆ ˆ ˆ estimated as / /  k .  k  / data on rents and house values. All regressions include time period dummies. All standard errors have L L been adjusted for serial correlation within metropolitan areas. Table 4 shows the results of this exercise. When s is 0.32, R the estimates indicate that roughly 60% of the overall employ- ment growth effect of human capital is attributed to produc- January temperature, mean July temperature, and average tivity growth. This finding is not sensitive to the choice of 26 Most studies of local area annual inches of precipitation. measure for land price. These findings suggest that though tech- growth in the post-World War II period have found these to nological or pecuniary externalities may play an important role in be strong and robust predictors of population growth the employment growth effects of human capital, consumption (Rappaport, 2004). Examining the sensitivity of the results amenities are a significant component as well. Even for s  R to these controls therefore helps identify whether the 0.22, around one-quarter of the total employment growth effect 25 employment-growth–human-capital relationship might arise is attributed to growth in local quality of life. simply because highly educated residents select growing Overall, then, my findings indicate an important role of locations, rather than directly affecting growth. Overall, the quality of life in driving the relationship between the share results from this specification line up extremely closely with of college-educated residents in a metropolitan area and the those in the baseline, and the implied productivity share area’s subsequent employment growth. Whereas prior work rises only slightly, to 0.67. has tended to emphasize productive externalities from hu- The third row of the table shows results using data from man capital, this evidence suggests there may be important 1970–1990, in which lagged employment growth rates are consumption externalities as well. included as controls. The point estimate of the effect of human capital on employment growth is similar to the C. Robustness baseline, but is much less precisely estimated. This is In this section, I examine the robustness of my results to unsurprising, for employment growth is highly serially a number of alternative specifications. Row (2) of table 5 correlated, so that including lagged growth rates removes repeats the baseline OLS specification controlling for mean much of the variation in the dependent variable. For wage and rent growth, which display much lower degrees of serial 24 correlation, inclusion of lagged growth rates increases To address concerns about systematic heterogeneity in the parameter s , I have reestimated the models in appendix section 3, allowing the share R somewhat the estimated effects of human capital. Because of land in the budget to depend on whether a metropolitan area has an the estimated effect on wage growth increases more than the above-median share of college graduates. The difference in estimated land effect on rent growth, the calculated productivity share rises shares between high- and low-human-capital locations is not statistically significant, and the productivity share estimated from specifications (not to approximately 0.8. Even this estimate, however, implies shown) allowing for heterogeneous land shares is roughly 0.69. Evidence an important role for growth in quality of life. 1998 database from 1977 data on manufacturing from the USA Counties To address the issue of changes in the composition of also shows no systematic relationship between human capital concentra- tions and proxies for k and k . R L metropolitan areas over time, in the fourth row I present 25 Because I measure wages rather than total compensation, it is possible results for the subsample of metropolitan-area–year pairs in for my results to understate the productivity effect if growth in nonwage which the definition of the metropolitan area does not compensation is much more correlated with human capital levels than growth in wages is. Assuming conservatively that nonwage compensation change during the time period. Although the smaller sample represented 10% of total compensation during my sample period (Long & Scott, 1982), I calculate that the growth in nonwage compensation would 26 have to be more than 4 times as responsive to initial levels of human - Weather data are from the County and City Data Book (U.S. Depart capital as the growth in wages in order to attribute all of the effect of ment of Commerce, 1994). Central cities were matched to metropolitan human capital to productivity growth. areas as in Glaeser and Shapiro (2003a).

9 332 THE REVIEW OF ECONOMICS AND STATISTICS ABLE 5.—A LTERNATIVE S PECIFICATIONS * T Dependent variable is growth in Productivity N Employment Wage Rental Price Share Specification (1) Baseline 0.0786 0.0160 495 0.0664 0.62 (0.0081) (0.0247) (0.0126) (2) Weather controls 0.67 0.0500 0.0163 0.0561 495 (0.0226) (0.0084) (0.0120) 247 (3) Lag growth controls 0.83 0.0639 0.0329 0.1270 (0.0155) (0.0293) (0.0606) 0.0260 0.0748 297 0.0307 0.69 (4) No change in area definition (0.0274) (0.0128) (0.0196) (5) IV with land-grant status 0.1708 495 0.0237 0.1184 0.55 (0.0964) (0.0219) (0.0501) *Independent variable: log(share college-educated). Notes: Table shows coefficient in regression of dependent variable on the log of the percentage of prime-age white males with a college degree in the met ropolitan area. Wage, rent, and house value growth are measured as the growth in metropolitan area fixed effects from hedonic regressions as described in section III of the text. Regressions include time pe riod dummies. Standard errors have been adjusted for serial correlation within metropolitan areas. All calculations use k 0.10, and 1994. Land-grant classification based on Nevins (1962). County and City Data Book, 0.32. Data on weather taken from the  0.75, k s   R L R 28 Relative to size leads to larger standard errors (and a smaller point human capital levels across metropolitan areas. estimate) for the employment growth effect, the wage and the baseline OLS results, the 2SLS results tend to show rent growth coefficients are similar to the baseline specifi- larger (although less precisely estimated) growth effects of cation, and lead to an implied productivity share only human capital. For example, a 10% increase in the share of slightly higher than in the baseline. Controlling directly for residents who are college-educated is now estimated to the growth in the number of counties composing the met- increase employment growth by approximately 1.7%, as ropolitan area also yields results similar to those of the against 0.8% in the baseline OLS specification. The esti- 27 baseline (regression not shown). mated effects of human capital on wage and rent growth are larger in similar proportion, so that the implied productivity D. Instrumental Variables Estimates share of the growth effect remains similar to the baseline estimate. The previous subsections present correlational evidence Although I have argued that land-grant institutions have a on the connection between human capital and local area causal effect on the skill distribution in an area, it is of growth. The evidence confirms the finding of prior studies course possible that their effects on local labor and housing that human capital is positively related to employment markets occur through other, more direct channels, and not growth, and provides further indication that much of this exclusively through their effect on the concentration of effect operates through increases in the quality of life, rather human capital. For example, universities purchase land and than productivity. Although these facts seem robust to a labor, thereby making themselves direct (and sometimes number of controls and alternative specifications, concerns large) participants in these markets. The fact that I examine may still remain about the causal interpretation of my growth rates, rather than levels, of employment, wages, and estimates. Of primary concern is the possibility that skilled rents should help to reduce the effects of these other chan- residents seek out growing or soon to be growing areas, nels, as long as they are nearly fixed over time. Additionally, which would lead to a reverse-causality confound in my estimates. In this subsection I examine instrumental vari- because land-grant institutions were placed well in advance ables (IV) estimates of the growth effects of human capital, of the time period under study, the 2SLS strategy should at instrumenting with the presence of land-grant institutions as least serve to alleviate concerns about simultaneity bias in Moretti (2004) and CSLs as in Acemoglu and Angrist arising from skilled residents’ desire to live in places that (2000). will grow in the future. On the whole, then, it seems Row (5) of table 5 presents results from a 2SLS estima- reassuring that the 2SLS estimates suggest a productivity tion in which land-grant status is used to instrument for the share very similar to that obtained using the OLS specifi- log of the share college-educated. As I argue in section III B cations discussed above. above, land-grant institutions seem to be distributed evenly In Table 6 I estimate the growth effect of those with a over different regions of the United States and do not appear high school degree or more, instrumenting with CSLs as to have been placed in relation to preexisting differences in 28 The first-stage estimates from this specification show a large and 27 statistically strong effect of land-grant institutions on the share of residents In additional specifications reported in the supplemental appendix who are college-educated. In a regression of log(share college-educated) [available in Shapiro (2005)]. I show that the implied productivity share is on the land-grant status dummy, the land-grant coefficient is 0.3105 with similar for metropolitan areas with and without significant supply restric- a standard error of 0.0522. An F -test of the null hypothesis that land-grant tions on housing. I also show that both the employment growth effect and 0.001 status has no effect on log(share college-educated) rejects with  p the productivity share are higher for manufacturing-intensive areas, pos- -statistic is sufficient to rule out any F -statistic of 34.61. This F and an sibly due to pecuniary externalities of the sort discussed in Acemoglu significant weak-instruments bias (Stock & Yogo, 2002). (1996).

10 333 SMART CITIES NSTRUMENTAL STIMATES E ARIABLES -V 6.—I ABLE T log(Share with HS or More) Employment Growth Wage Growth Rental Price Growth House Value Growth (1) (3) Minimum Years (4) (2) (5) 0.2404 0.3939 0.1317 0.1950 log(share with (0.4341) HS or more) (0.0687) (0.1347) (0.2237) Minimum Years of Schooling Required before Leaving School ( CL ): 0.2366 9 (0.1311) 0.4642 10 (0.2143) 0.2149 11 (0.1621) Minimum Years in School Required before Work Is Permitted ( ): CA 0.0524 7 (0.1367) 0.1204 (0.1692) 8 0.0384 9 (0.1949) F — -statistic 3.87 — — — 495 N 495 495 495 495 Notes: Wage, rent, and house value growth are measured as the growth in metropolitan area fixed effects from hedonic regressions as described in sectio n III of the text. CSLs coded as in Acemoglu and Angrist (2000). F -statistic is test statistic from a test of the null hypothesis that the coefficients on the CL and CA dummies are jointly significant. Regressions include time period dummies and metropolitan area dummies. Growth regressions include initial levels of employment, wages, rents, and house values, respectively, as controls. Standard errors have been adju sted for serial correlation within metropolitan areas. coded by Acemoglu and Angrist (2000). These specifica- the area. In this section, I conduct a preliminary investiga- tions include metropolitan area fixed effects, so identifica- tion of two candidate explanations for this relationship. tion comes from changes over time in the exposure of First, concentrations of skilled residents may encourage prime-age white males to CSLs. As column (1) shows, the the growth of consumer services, such as restaurants and bars, first stage estimates generally confirm that these laws affect which then make an area more attractive to potential migrants. the human capital distribution, although the coefficients are In line with this hypothesis, Glaeser, Kolko, and Saiz (2001) less monotonic and precise than those reported in Acemoglu show evidence that cities with superior markets for goods and 31 and Angrist (2000). This nonmonotonicity, coupled with a services experience more rapid population growth. small F -statistic, suggests caution is needed in the interpre- Second, highly educated households may act, through the 29 tation of these estimates. political system or privately, to improve the local quality of The 2SLS estimates show no statistically significant ef- life. Moreover, better-educated households are more likely fect of high school graduates on growth in employment, to be homeowners, and some evidence exists to suggest that wages, or rents, consistent with the prior literature’s empha- homeowners make greater investments in their local com- sis on college graduates as a determinant of urban growth in munities (Glaeser & Shapiro, 2003b). 30 Though the confidence the post-World War II period. To distinguish between these hypotheses, I have collected intervals on the growth effects of human capital are large, data on direct measures of quality of life from several the point estimates are largely negative, and thus provide no sources. First, from the USA Counties 1998 database, I have evidence for significant productivity (or quality-of-life) ex- obtained data for 222 of the metropolitan areas in my 1980 ternalities from high school graduates, consistent with the sample on the number of restaurants per capita in 1977 and findings of Acemoglu and Angrist (2000). 1992, and the number of FBI-defined serious crimes per 32 Second, using the public-use capita in 1980 and 1990. V. Direct Indicators of the Quality of Life sample of the Census, I have computed the share of indi- viduals aged 16 to 19 in 1980 and 1990 who are neither high The results presented in the previous section provide school graduates nor currently in school. I will treat this preliminary support for a causal interpretation of the rela- variable as a proxy for the share of high school dropouts in tionship between the concentration of college graduates in a an area and hence as a loose measure of the quality of public metropolitan area and subsequent growth in quality of life in schools. Finally, I have obtained, for 74 of the metropolitan areas in my sample, a count of the number of days in 1980 29 F -statistic, it is not possible to reject the presence of Given the small a weak-instruments bias (Stock & Yogo, 2002). 31 30 Although the human capital measure includes those with a college See also George and Waldfogel (2003), who show evidence of degree, existing evidence and unreported specifications indicate that the economies of scale in catering to consumers’ varying tastes. 32 effect of CSLs is predominantly to move individuals from the no-high- Counties were matched to metropolitan areas as in Glaeser and school category to the high-school category. Shapiro (2003a).

11 334 THE REVIEW OF ECONOMICS AND STATISTICS ABLE 7.—S OURCES OF THE E FFECT OF H UMAN C APITAL ON Q UALITY OF L IFE T Land-Grant Difference N No Land-Grant 1980–1990 Change in: 0.2682 222 0.0594 0.3275 (1) log(restaurants per capita) (0.0085) (0.0212) (0.0187) (2) log(serious crimes per capita) 0.0363 222 0.0549 0.0913 (0.0377) (0.0335) (0.0150) (3) High school dropout rate 0.0404 0.0396 0.0008 252 (0.0077) (0.0029) (0.0032) 74 (4) log(no. days air quality index  100) 0.1929 0.3616 0.1687 (0.2973) (0.1755) (0.3795) a are from the USA Counties Notes: Change in log(restaurants per capita) is from 1977 to 1992. Data on restaurants per capita and the number of FBI-defined serious crimes per capit 1998 database (U.S. Department of Commerce, 1998), with counties matched to metropolitan areas as in Glaeser and Shapiro (2003a). High school dropout rate is the share of individual s ages 16 to 19 in 1980 and 1990 who are neither high school graduates nor in school, calculated from Census public-use samples. Data on air quality is a count of the number of days in 1980 and 1990 that the Environ mental Protection Agency’s air quality index exceeded 100, taken from http://www.epa.gov/airtrends/factbook.html. and 1990 that the Environmental Protection Agency’s air ate through “consumer city” amenities such as bars and 33 quality index exceeded 100, indicating poor air quality. restaurants, rather than from more politically mediated area In Table 7, I compare mean 1980–1990 growth rates in attributes such as crime, schools, and pollution. these variables between land-grant and non-land-grant met- REFERENCES ropolitan areas. 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The controls used in the 1970, 1980, and 1990 of Kansas City Research working paper no. 03–07 (2004). samples are dummies for the following housing characteristics [additional Rauch, James E., “Productivity Gains from Geographic Concentration of details in supplemental appendix available in Shapiro (2005)]: commercial Human Capital: Evidence from the Cities,” Journal of Urban use status; acreage of property; availability of kitchen or cooking facili- 34 (1993), 380–400. Economics ties; number of rooms; type of plumbing; year built; number of units in Journal of Roback, Jennifer, “Wages, Rents, and the Quality of Life,” structure; water source; type of sewage disposal; number of bedrooms. Political Economy 90:6 (1982), 1257–1278. Ruggles, Stephen, and Matthew Sobeck, Integrated Public Use Microdata s 3. Calibrating the Household Share of Land ( ) R (Minneapolis: Historical Census Projects, Uni- Series: Version 2.0 versity of Minnesota, 1997). The share of land in the budget, s , ought to capture the share of R Shapiro, Jesse M., “Smart Cities: Quality of Life, Productivity, and the household expenditures that go to nontraded goods. Put differently, it no. working paper Growth Effects of Human Capital,” NBER should reflect the elasticity of the household’s expenditure function with 11615 (2005). respect to the price of land. It is this elasticity that determines the utility Simon, Curtis J., “Human Capital and Metropolitan Employment consequences of a 1% increase in the price of land. In this subsection, I Growth,” Journal of Urban Economics 43 (March 1998), 223–243. attempt to infer this elasticity by estimating the effect of an increase in the Simon, Curtis J., “Industrial Reallocation across U.S. Cities, 1977–97,” price of land on the price of a representative basket of goods. [Additional Journal of Urban Economics 56:1 (2004), 119–143. details and regression tables are in a supplemental appendix available in and Clark Nardinelli, “Human Capital and the Rise of American Shapiro (2005).] Cities, 1900–1990,” Regional Science and Urban Economics 32 My first set of estimates comes from ACCRA’s cost-of-living index for (2002), 59–96. U.S. cities for the first quarter of 2000. This index is constructed by Solon, Gary, Robert Barsky, and Jonathan A. Parker, “Measuring the obtaining prices for a basket of goods, and aggregating these to form a Cyclicality of Real Wages: How Important Is Composition Bias?” composite score for each city. I am able to match 64 metropolitan areas in Quarterly Journal of Economics 109:1 (1994), 1–25. my 1990 sample to ACCRA cities, and will use these 64 areas to study the Stock, James H., and Motohiro Yogo, “Testing for Weak Instruments in no. 284 technical working paper Linear IV Regression,” NBER relationship between land prices and the price of a representative basket of (2002). goods and services. Using this data set, I find that a 1% increase in the U.S. Department of Commerce, Bureau of the Census, County and City price of land increases the overall price of goods and services by 0.32% Data Book (Washington, DC: U.S. Bureau of the Census, 1994). after adjusting for measurement error in the independent variable, with an USA Counties (Washington, DC: U.S. Department of Commerce, 1998). unadjusted elasticity of approximately 0.28. s My second set of estimates of comes from the consumer price index R (CPI). The CPI is calculated at the metropolitan area level for 24 of the APPENDIX areas in my sample, and for some of these is measured repeatedly throughout the sample period. Regressions of the growth in the CPI on the growth in measured land prices yield an elasticity of 0.32 after allowing 1. Measuring Local Area Wages for measurement error, and an estimate of 0.22 if measurement error is not taken into account. (It is necessary to use growth rates rather than levels In order to measure relative wage levels in metropolitan areas at time because the CPI is only comparable within an area over time, not across on t I regress the log wage of all prime-age males in the sample at time t, different areas within a given time period.) Overall, then, the evidence dummies for metropolitan areas and a set of controls. These controls are from several different approaches seems consistent with a value of s of age in years, the square of age in years, and dummies for categories of the R approximately 0.32, and probably not lower than 0.22. In section 3 of the following worker characteristics [additional details in supplemental appendix available in Shapiro (2005)]. main text, I report results for both of these values.

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