Regional Science and Urban Economics 29 (1999) 445461
Location and the effect of demographic traits onearnings
a , b*Stuart A. Gabriel , Stuart S. RosenthalaDepartment of Finance and Business Economics, Marshall School of Business, University of
Southern California, Los Angeles, CA 90089-1421, USAbDepartment of Economics and Center for Policy Research, Syracuse University, Syracuse, NY,
Received 15 October 1996; received in revised form 18 January 1999; accepted 27 January 1999
With mobile workers and competitive markets, equilibrium nominal wage rates rise withthe local cost of living but fall with the value of local amenities. Earnings and wageregressions that ignore such effects may suffer from omitted variable bias because observededucation and demographic attributes affect both worker skill levels and location choice.Geographic fixed effects can be used to control for unobserved locational attributesprovided that their scope is at least as narrow as the underlying labor markets, but not sonarrow as to introduce simultaneity problems arising from the endogenous choice oflocation on the basis of income. Estimates from the 19851989 American Housing Surveysuggest that SMSA-level fixed effects control for unobserved locational attributes withoutintroducing simultaneity problems. In addition, failure to control for location leads to biasedestimates of the effect of important demographic characteristics. 1999 Elsevier ScienceB.V. All rights reserved.
Keywords: Returns to labor; Location effects; Compensating variations
JEL classification: J3; J31
*Corresponding author. Tel.: 11-213-740-6523.E-mail address: firstname.lastname@example.org (S.A. Gabriel)
0166-0462/99/$ see front matter 1999 Elsevier Science B.V. All rights reserved.PI I : S0166-0462( 99 )00008-3
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Over the years, a large number of studies have found pronounced differences inearnings across workers of different education, race, and gender [recent examplesinclude Blau and Beller (1992), Katz and Murphy (1992), and Murphy and Welch(1992)]. That literature is fundamental to the study of labor economics and hasprovided important insight into the returns to education, in addition to promptingdebate about the extent to which discrimination depresses wage rates for womenand minorities. However, most earnings studies largely fail to control for locationspecific cost of living and amenity differentials that may comprise important
1components of the workers equilibrium compensation package. In an open citymodel with mobile workers, metropolitan area wage rates must rise to offset higherhousing costs, ceteris paribus. In addition, because mobile workers choose whereto locate in part based on preferences for location specific amenities [e.g., Tiebout(1956), Hamilton (1976), and Epple and Romer (1991)], wage rates should fallwith an increase in the value of the amenities specific to a given geographically
2distinct labor market.One implication of these arguments is that a workers compensation package is
comprised of both real pecuniary and nonpecuniary earnings. Real pecuniaryearnings are given by nominal earnings deflated by a location specific cost ofliving index, whereas nonpecuniary earnings take the form of location specificamenities. It follows that with competitive markets and mobile households, inequilibrium differences in nominal earnings across similarly skilled workerssituated in geographically distinct labor markets should be offset by compensating
3variations in location specific amenity and cost of living differentials. Hence,earnings and wage regressions that omit those amenity and cost of livingdifferentials will suffer from omitted variable bias to the extent that observable
1Occasionally wage and earnings studies have included broad regional dummy variables to controlfor locational effects. However, inclusion of such variables is generally done without attention to thetradeoff between omitted variable and simultaneity bias to be discussed here, and the relationship ofthat tradeoff to the theory of compensating differentials.
2Thus, both wage rates and house prices adjust across cities in response to local amenity and fiscaldifferentials. See Henderson (1982), Roback (1982, 1988), Blomquist et al. (1988), Beeson and Eberts(1989), and Gyourko and Tracy (1989, 1991), for example.
3In an earlier paper that focuses on household commutes [Gabriel and Rosenthal (1996)], we treatcommute times as an additional component to the labor compensation package. However, commutesare excluded from the present analysis for three reasons. First, theoretical arguments by Mills andHamilton (1989) and empirical work by Ihlanfeldt (1992) suggest that the relationship betweencommutes and wage rates within cities is quite flat. Second, our data contains commute times only for1985 whereas all other variables are available for both 1985 and 1989. Thus, dropping commute timesallows us to estimate earnings regressions for both 1985 and 1989. Third, we ultimately focus on theeffect of SMSA-level locational attributes that include the set of commute opportunities available inany given SMSA.
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worker characteristics influence both the workers skill level and the workerschoice of labor market.
More generally, these arguments are part of a broader phenomena described byRosen (1986) as the theory of compensating wage differentials. In particular,wages adjust for all non-pecuniary job-specific attributes, including occupationalhazards, employment and income security, as well as locational amenities.However, while there have been many empirical attempts to examine the degree towhich wages adjust to offset differences in occupational safety and job security,treatment of locational effects has been quite limited. The limited attention tolocation may reflect, in part, the enormous data requirements should one attempt tocontrol for location through direct inclusion of individual location-specificattributes in the wage regression (see Henderson (1982), Roback (1988), Blom-
4quist et al. (1988), and Gyourko and Tracy (1991), for example). Such anapproach, however, remains open to the possibility of omitted (locational) variablebias since it is impossible to fully specify the complete set of locational attributes.For the sizable literature that focuses on the wage and earnings effects ofeducation, race, and other demographic characteristics of the worker, such omittedvariable bias may be important.
Controlling for locational effects is problematic, however, because as suggestedabove, accurate data on the value of localized amenity and cost of livingdifferentials across labor markets may not exist. Thus, direct inclusion of a longlist of observable locational attributes is at best an imperfect means of controllingfor location. As an alternative, fixed effects methods can be used to control forunobserved locational attributes if workers can be grouped into spatially distinctclusters. We show that such fixed effects models yield consistent estimates of theimpact of education and demographic traits on earnings provided that twoconditions hold: the geographic scope of the fixed effects must be at least asnarrow as the workers underlying labor markets, but not so narrow as to introducesimultaneity problems arising from the endogenous stratification of workers acrossneighborhoods on the basis of income.
These issues are explored using a unique data base from the 19851989American Housing Survey (AHS) that permits us to group workers both at thewithin-SMSA neighborhood level and at the SMSA level. Results favor the SMSAmodel and suggest that inclusion of SMSA fixed effects largely controls forunobserved locational attributes without introducing simultaneity problems. More-over, failing to control for location leads to downward biased estimates of theblack earnings deficit by roughly 6 percentage points and downward biased
4Henderson (1982), Roback (1988), Blomquist et al. (1988), and Gyourko and Tracy (1991)estimate quality-of-life differentials across metropolitan areas, where quality of life is measured bysumming the degree to which individual SMSA-level amenities are capitalized into wages and houseprices.
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estimates of the returns to males by 3 to 6 percentage points. More generally, ourfindings suggest that wage and earnings studies that seek to obtain consistentestimates of demographic effects can control for possible omitted locationalattributes by including SMSA-level dummy variables in the regression, anapproach that has modest data requirements and is easily implemented.
To clarify these and other results the paper is organized as follows. Thefollowing section describes the theoretical underpinnings of the earnings andlocation analysis. Section 3 presents the econometric model and discussesestimation procedures. Section 4 describes the data and variables. The final twosections of the paper present estimation results and concluding remarks.
2. Theoretical model
Household utility (v) is given by the sum of a systematic (V ) and anidiosyncratic (f) component,
v 5V(x , a ) 1 f (2.1)ij ij j iwhere V increases with the consumption of a privately purchased composite good(x ) and a local public good (a ) (V .0, V .0) at a diminishing rate (V ,0,ij j 1 2 11V ,0), while f is unforecastable with mean zero and finite variance. To simplify22 iexposition, we define location j as a geographically distinct labor market in whichworkers have access to the same set of labor market specific locational attributes
5and amenities. Notationally, variables that are specific to a given location aresubscripted only by j, as in a . Variables that are unique to a given householdjregardless of the location of the familys residence are subscripted only by i, as inf . Variables that are sensitive to both locational and household specific charac-iteristics are subscripted by i and j. Hence, x is double subscripted becauseijconsumption of the private composite good depends on a households endowmentand on the labor market specific price of housing and other goods (in a manner tobe clarified below).
Each worker inelastically supplies one unit of labor. Labor markets arecompetitive, and an employer at a given location varies wage rates across workersonly in response to differences in endowment that affect the workers skill level.However, employers in different geographically distinct labor markets are free tooffer different wages to similarly skilled workers. Accordingly, wage rates aregiven by y 5 y (m ), and the households budget constraint is,ij j i
5For the purposes of this paper, by definition labor market specific attributes include only thoseamenities that would affect the equilibrium supply of labor and wage in a given area. Examples of suchlabor market specific amenities include the weather, natural features, public safety, public services, andthe like.
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y (m ) 5 p x . (2.2)j i j ij
As indicated in expression (2.2), households spend all of their monetary earningson the private composite good. Note also that within a given labor market, theprice of the composite good ( p ) is constant across households and is subscriptedj
6only by j.
We adopt an open city, long run perspective, in which families are perfectlymobile (i.e., zero moving costs). Hence, households maximize Eq. (2.1) subject toEq. (2.2) by choosing where to locate from among all possible geographicallydistinct labor markets. Those decisions determine y , p , and a , while x isij j j ijobtained from the budget constraint as x 5 y (m ) /p . A spatial equilibrium isij j i jattained when workers with identical endowment obtain equal expected utilityregardless of the labor market in which they are situated. Substituting for x in theijutility function and taking expectations yields,
E[V(x ,a ) 1 f ] 5V( y (m ) /p , a ) 5 k(m ), (2.3)ij j i j i j j i
where k is the expected utility for a worker with endowment, m , and E is theiexpectations operator.
Expression (2.3) implies that the workers equilibrium compensation is apackage comprised of real pecuniary and nonpecuniary earnings: pecuniaryearnings are given by nominal wage receipts deflated by the labor market specificprice level, y (m ) /p , while nonpecuniary earnings are provided in the form ofj i jlocation specific amenities, a . Hence, in equilibrium, an increase in p or aj jdecrease in a must be offset by higher nominal wages, y , ceteris paribus.j ij
3. Econometric model
To facilitate the empirical work two simplifying assumptions are imposed. First,a workers exogenously given equilibrium level of utility is specified as a linearfunction of the workers demographic and human capital characteristics, ork(m ) 5 d b , where d includes information on age, education, gender, and race,i i d ifor example. In addition, the systematic component to a workers utility is writtenas a linear function of locational amenities and the log of the privately purchasedcomposite good, V( y (m ) /p , a ) 5 log( y ) 2 log( p ) 1 a . Substituting into (2.3)j i j j i j jand allowing for random effects associated with the idiosyncratic component toutility,
log( y ) 2 log( p ) 1 a 5 d b 1 e (3.1)ij j j i d i6The composite good is composed of goods and services whose prices may vary across geo-
graphically distinct labor markets. As such, P is the cost of living index for labor market j.j
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2where e is a mean zero normally distributed error term with variance s , and a ,i jp , and y are defined as before. Rearranging terms, (3.1) can be rewritten as,j i
log( y ) 5 log( p ) 2 a 1 d b 1 e (3.2)ij j j j d iwhich says that log wage earnings are a linear function of the labor market specificamenities and cost of living, and the workers demographic and human capitalcharacteristics.
The key to our empirical approach is to recognize that a and p are locationj jspecific fixed effects. Including dummy variables for each location yields,
log( y ) 5 g 1 d b 1 e (3.3)ij j i d ijwhere g 5log( p ) 2 a . If the geographic scope of the individual clusters definedj j jby j51, . . . , J, is at least as narrow as their underlying labor markets, then (3.3)takes into account all relevant locational effects and omitted variable bias goes tozero. This is convenient since one could never fully specify the complete vector oflabor market specific amenities nor obtain perfectly accurate measures of the costof living in a given labor market. In contrast, most previous analyses of earningsdifferentials implicitly constrain all of the g in (3.3) to be equal, and in so doingjignore the impact of location specific amenity and cost of living differentials onworker compe...