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An empirical investigation of intraurban wage gradients
JOURNAL
OF URBAN
ECONOMICS
10,
50-60 (1981)
An Empirical Investigation of lntraurban Wage Gradients W. EBERTS
RANDALL Depurtment
of Economics,
University
of Oregon,
Eugene, Oregon 97403
Received November 12, 1979; revised March 14, 1980 Intraurban wage gradients have received little attention in the urban literature but have been shown theoretically to be important indicators of the spatial characteristics of urban economic activity. This study examines the spatial distribution of wages of five groups of municipal public employees in the Chicago SMSA. Negative wage gradients, significant at the 0.05 level, are found for four of the five labor groups. Results show that monthly wages decreaseon average as much as $24 per additional mile from the city center.
INTRODUCTION Empirical investigations of intraurban wage gradients have been conspicuously missing from the urban literature. The importance of wage gradients as determinants of the spatial arrangements of economic activity in urban areas and as tools in the analysis of spatial distribution has long been recognized. Moses [9] first constructed a theory of intraurban wage gradients to explain intraurban travel patterns. Later, in collaboration with Williamson, Moses [lo] used wage differentials to explain suburbanization. More recently, Mills [8] and Muth [ 1I] have incorporated wage gradients into more general models of urban spatial equilibrium. Despite these efforts, only three studies have been found in the literature which examine intraurban wage gradients empirically. This is certainly not true of urban price gradients in general. Indeed, urban rent gradients have received much attention in the last two decades. Even as early as 1973, a review article by Ball [1] catalogued no less than eleven studies of nine different cities. Additional studies have followed. The purpose of this study is to ascertain empirically the nature of intraurban wage differentials. The primary hypothesis to be tested is the correlation between the accessibility to the urban core and the wage differentials within urban labor markets. To do so, the paper is organized as follows. The first section reviews the few studies of wage gradients that have been undertaken. Section II outlines the prerequisite for the existence of wage gradients and formulates the wage gradient equation. The third section discusses the data and the appropriateness of using the Chicago labor 50 0094-I l90/8 I /040050-l I $02.00/O Copyright 0 19x1 by Academic Press. Inc All rights. of reproduction in any form reserved.
INTRAURBAN
WAGE
GRADIENT
51
market in the study. The fourth section describes the estimation results, and the fifth section contains some closing remarks. I. LITERATURE The purpose of this paper is to investigate the characteristics of intraurban wage gradients and not simply the differential wage levels found between central cities and suburbs. Numerous studies of the differential effect have emerged including works by Ehrenberg and Goldstein [4] and Wachter [17]. However, only three works exist which deal directly with the continuous spatial variation of wages within an urban labor market. The three studies strike no general consensus; the results of each differ depending on the particular labor group and metropolitan area under investigation. Segal [ 151 studied wage patterns in New York City and found positive wage gradients for some industries and negative gradients for others. His data were aggregated, and the lack of observations reduced the rigor of his analysis. Another study, conducted by the Institute of Office Management [6], looked at pay scalesof workers in the London metropolitan area. Of the groups studied, only the wages of clerical workers revealed any tendency to decrease with distance from the central business district (CBD). Like the New York City study, the London study was plagued with the problem of finding sufficient observations to conduct a rigorous analysis. Rees and Schultz [13], in their study of the Chicago labor market, found a negative wage gradient for manufacture workers. However, the wage gradient was not in relation to the Chicago CBD but to the southeast comer of the metropolitan area where heavy industry was most concentrated. Their attempts to find similar relationships between wages and employment concentration failed for other labor groups. Obviously, a major reason for the paucity of wage gradient studies is the lack of adequate data. The lack of data may also explain why none of the studies looked at features such as the relative influence of demand and supply characteristics on the wage gradient and why none have corrected for differences in the nature of firms and the labor force. Such relationships need to be explored to provide a complete description of intraurban wage gradients. II. MODEL Wage gradients result from the spatial decisions of utility-maximizing workers and the labor requirements of cost-minimizing firms. The theory of wage gradients is well documented in the literature. Muth [ 1l] presents a model of wage gradients with local employment, and White [ 181extends the model to incorporate suburban concentration of employment. Thus, only
52
RANDALL
W. EBERTS
the salient features of the model need to be highlighted here. In particular, since the intent of the study is to examine wage gradients empirically, it is important to specify correctly the effect of exogenous supply and demand conditions on the wage offers of firms as well as to take into account the differences in the nature of firms and the labor force. Before specifying the wage equation, several assumptions need to be made to insure a negative correlation between wage offers and distance of the firm from the CBD. First, the firm must behave according to some efficiency criterion so that its behavior is constrained by exogenous market conditions.’ Second, households must achieve equilibrium. Third, concentration of employment must be sufficiently large so that not all workers can live adjacent to their workplace. These assumptions lead to an hypothesized negative relationship between the wage offer and the distance from the CBD. When differences in demand characteristics between communities are considered, the wage equation is written: wit(h)
=
wO +
Plxlt(P)
+
IX k=2
P/~[~kt~ltl O(P) (1)
+
i j=l
Yj’j,(P>
+
Cir3
i = 1,...,5.
The wage of the ith labor group observed in the tth community is denoted by wi,; the distance to the CBD of the tth community is x,,; and the socioeconomic and organizational variables that affect both the supply and demand for labor are denoted by the z’s.* Since the theory provides no clues as to which functional form of the wage equation is appropriate, (1) permits the data to specify the appropriate form. Following the Box-Cox transform technique, the dependent and ‘In this study the “firms” are independent municipal governments located throughout the Chicago metropolitan area. Although efficient behavior is not well documented for the public sector, recent theoretical work by Niskanen [ 121and empirical work by the author [3] show that public agencies that follow a budgetary approach in allocating resources do indeed follow cost-minimizing behavior. *The supply and demand conditions of neighboring communities will also affect the wages in community t. This effect can be incorporated into the wage equation by entering as an explanatory variable the wages of neighboring communities weighted by their respective distances from community t. Since estimation based on techniques that deal with spatial correlation in the residuals produces insignificant results, the neighboring wage effects are deleted from (1).
INTRAURBAN
WAGE
GRADIENT
53
independent variables are written in the general form:
Jo) = (Y” - 1)/L = l0d.Y)~
A#0 x = 0,
where h takes on values between 0 and 2. The explanatory variables are entered into (1) either in a multiplicative form with distance or additively. The noninteractive terms include the distance variable and three measuresof organizational structure. Accessibility to the CBD is entered as the airline distance from community t to the CBD. Various measures of accessibility have been used in the urban rent gradient literature. Mills [7] concludes that airline distance to the CBD is the most useful, and more complex measures are not worth the cost of computing. Municipal governments in the Chicago SMSA differ in organizational structure and the relative ability and propensity to pay employees. Organizational structure may dictate the type of employees that a local government can hire. For example, the size of the community may have a limiting effect on the extent of specialized skills within the government organization. Since employees with specialized skills command higher salaries and larger cities demand greater specialization, larger cities will tend to pay higher average wages. Goldstein and Ehrenberg [5] show that the relative ability and propensity of local governments to pay higher wages are also related to the behavior of public administrators. The tenure of public administrators depends in part on their responsivenessto the demands of their constituents and employees. Administrators can increase the likelihood that demands of various groups will be satisfied by increasing the range of services offered to taxpayers, increasing compensation to employees, and improving their working conditions. All three measures require a large budget and a large organization. Thus, municipal wages should be positively related to the size of the budget and the size of the municipal government which are related to the size of the community. Workers’ characteristics may also affect the wage level. If municipal governments follow efficiency criteria, then compensation should be positively correlated with individual productivity. Satisfactory measures of productivity and skill levels are not obtainable except for the number of hours worked per week. The interactive variables reflect the effect of local supply and demand conditions on the wage gradient. Theory shows that in absolute terms excess
54
RANDALL
W. EBERTS
demand for labor decreasesthe gradient while excess supply increases the gradient. The logic of the multiplicative form can be seen by writing the coefficient of the distance variable as a linear function of community characteristics: k=2
When p, and fik have the same sign, the slope increases. Opposite signs indicate that the socioeconomic variables force the wage gradient to be flatter. Three variables are used to measure supply and demand conditions. The first is the ratio of employment of a particular labor group in each city to the supply of that labor group which resides in the same city. This ratio measures the attractive force of the community as an employment subcenter. As firms in the subcenter require more labor than can be supplied locally, they offer higher wages which causesthe wage gradient to decrease. The second variable, the rate of population change in the community, measures the excess supply of labor in an area. A better proxy of excess supply would be a measure of the change in employment demand relative to supply in each city. Unfortunately, data on firm relocations are not available for each city. A fair assumption, supported by data from other major cities, is that firms relocate at a much slower pace than households.3 A substantial change in population may cause a surplus of labor making it possible for firms to meet their labor requirements with a high proportion of local workers. Consequently, the wage offerings in these communities will be lower and the attractive force of the community will be smaller than they otherwise would be if workers had to be attracted from more distant points. The supply of workers near the firm is also affected by the ability of workers of certain income levels to live in communities that hold job opportunities for them. Firms which cannot substitute away from low skill jobs may be obliged to offer higher wages to compensate workers for higher house prices or additional commuting costs. As a result, the wage gradient will be sensitive to the per unit housing costs in a community. ‘Struyk and James [ 161have tabulated the percentage change in employment due to plant relocations for four SMSAs. They find that in a three year period on average six percent of employment change is due to relocation of firms. On the other hand, the Bureau of Census statistics show that 17%of the households in the country relocate in a single year and of these 8.3% relocate within a metropolitan area. In a five year period, the respective numbers are roughly 48% and 17%. These rough estimates show that households do move more often than firms and thus even though the rate of population change may overstate excess supply, a positive change reflects a surplus of labor in a particular city.
INTRAURBAN
55
WAGE GRADIENT
III. DATA The author has been fortunate to acquire an especially rich source of data from the Cook County Bureau of Administration. Since 1971, the Bureau in cooperation with the U.S. Civil Service Commission has conducted a semiannual survey of government salaries and fringe benefits for over 100 municipalities in the six-county Chicago metropolitan area. Five categories of noneducational municipal workers will be considered in this study: administration, clerical, police, fire and public works. The extensive collection of information on wages,supply and demand conditions, and organizational characteristics permits distance from the CBD to be included as a continuous variable. The Chicago area is well suited for a wage gradient study. It has been a laboratory for a number of previous studies including the urban density study by Muth [I 1, Chap. 91 and the land value study by Mills [7]. Both Muth and Mills find that the economic and geographic features of Chicago comply very closely with the assumptions of the model. It is most appropriate, therefore, to look at Chicago when studying intraurban wage gradients. Three features make Chicago particularly attractive. First, the Chicago area is situated on a flat, almost featureless plain. Second, the City of Chicago contains a concentration of most major types of employment which appear to be sufficiently large to meet the assumptions of the model. Table 1 shows percentages of total employment located in the City of Chicago for various labor groups. Third, the transportation system is particularly conducive to estimate wage gradients. Almost all of the major transportation TABLE 1 Percentageof Total SMSA Employment Located in City of Chicago by Labor Group Private sector0 Professional Managers and administrators Clerical and kindred workers Craftsmen, foremen Laborers Service workers Total
Public sectorh 48% 40 61 56 69 67 57
Administrators
33%
Clerical Fire Police Public Works Total
79 71 80 75 76
“Source: Census of Population, 1970, Tables 105, 118. hSource: “Regional Government Salary and Fringe Benefit Survey,”
Cook County, Bureau of Administration, July 1974.
56
RANDALL
W. EBERTS
TABLE 2 Comparison of Wage and Salary Level of Selected Private and Public Job Categories Job category File clerk A B C Typists A B Guards Laborers Auto mechanics Painters, maintenance Mechanics, maintenance
Public sector wage
Range of private sector wage
$129.50(mo.) 117.50 103.00 139.00 122.50 $ 4.46 (hr.) 4.57 6.42 6.05 5.83
$1l6.50- 146.00(mo.) 106.00- 135.50 97.00- I 15.00 126.00- 155.00 109.00- 136.50 $ 3.93-5.13 (hr.) 3.91-5.34 5.78-7.13 5.32-6.56 5.35-6.52
Sources: Public Sector wage data are obtained from “Regional Government Salary and Fringe Benefit Survey,” Cook County, Bureau of Administration, July 1974. Private sector wage data are obtained from Bureau of Labor Statistics, Chicago SMSA area survey, July 1974.
routes including the Regional Transit Authority elevated railroad lines and private commuter trains follow radial paths from the city center. Only one major expressway servescommuters who travel around the circumference of the city.4 Although public labor markets are used to estimate wage gradients, the results can be used to infer characteristics of intraurban private labor markets. Analysis of nationwide data has led Ehrenberg and Goldstein [4] to suggest that there is considerable mobility between public and private sector jobs. Evidence of intersectoral mobility in the Chicago area is found in the similarity between wage and salary levels offered by public and private employers as shown in Table 2. Comparison of wages of similar jobs reveals that public sector wage rates consistently fall within the range of private sector wages. Thus, in many respects, conclusions drawn from observations of the public sector can be extended to the private sector as well. IV. ESTIMATION
RESULTS
Even though various functional forms, including exponential, log and linear, were used to estimate the wage equations, no specification is statisti4The influence of radial transportation lines on the location of firms and households is well documented by Rock 1141.
INTRAURBAN
57
WAGE GRADIENT
tally superior to the rest. The 95% confidence interval around the optimal maximum likelihood statistic contains a wide range of functional forms for each labor group. Moreover, the estimated wage elasticities with respect to distance for each group do not vary significantly among functional forms. Therefore, only the double log and semilog specifications, both within the 95% confidence interval, will be reported here. The results are most encouraging for establishing the existence of negative wage gradients. As shown in Tables 3 and 4, four out of the five labor groups exhibit negative coefficients for the distance variable that are different from zero at the 0.05 significance level. Table 5 shows the elasticities computed about the mean under the two functional forms. These elasticities are easily translated into monetary terms and reveal that for the double log case administration monthly wages decrease on average $24 per mile, clerical $10 per mile, police $12 per mile, and public works $9 per mile. The signs of the socioeconomic coefficients are consistent with the theory although their significance levels vary among labor groups. The noninteractive explanatory variables show little statistical significance when considered TABLE 3 Regression Coefficients of the Wage Equation for Each Labor Group Estimated Using the Semilog Form (1,O) Labor groups Explanatory variables (I)
Distance from the CBD measured in airline miles (2) Per capita municipal government expenditures (3) Length of workweek (4) Population of community in 1970 (5) (Per unit housing costs) X (distance to CBD) (6) (Employment concentration) X (distance to CBD) (7) (Population change) X (distance to CBD) R’(adj.) - L,,(L
Fc)
Administration - 528.44 (2.49)“ 179.88 (1.49) - 561.04 (2.15) 139.05 (1.64) 685.12 (3.12) - 77.52 (1.69) - 8.50 (0.3I) 0.31 250.59
Clerical
Fire
Police
Public works
- 223.16 (4.16) - 18.46 (0.54) - 196.54 (0.99) - 17.04 (0.72) 279.21 (4.72) I .47 (0. IO) - 12.13 (1.61)
- 104.86 (1.48) - 156.27 (3.58) 91.93 (0.88) - 3.37 (0.11) 37.56 (0.45) 60.39 (2.98) - 21.97 (2.26)
- 240.68 (3.69) - 69.89 (1.72) - 722.19 (0.66) - 18.13 (0.65) 220.32 (2.86) 20.55 (1.10) - 12.69 (1.40)
- 198.82 (2.09) - 78.68 (1.32) - 1022.31 (1.16) - 4.41 (0.12) 70.74 (0.65) 22.83 (1.32) 41.02 (2.38)
0.30 191.22
0.33 203.52
0.27 199.99
0.22 165.59
Note. Dependent variable: Average wages of selected labor groups. “t-statistics are shown in parentheses.
58
RANDALL
W. EBERTS
TABLE 4 Regression Coefficients of the Wage Equation for Each Labor Group Estimated during the Double Log Form (0.0) Labor groups Explanatory variables ( I)
Distance from the CBD measuredin airline miles (2) Per capita municipal government expenditures (3) Length of work week (4) Population of community in 1970 (5) (Per unit housing costs) X (distance to CBD) (6) (Employment concentration) X (distance to CBD) (7) (Population change) X (distance to CBD) R’(adj.) - L,,(k
Clerical
Fire
Police
Public works
- 0.379 (2.14)” - 0.183 (1.83) - 0.397 (1.83) 0.084 (1.19) 0.470 (2.58) - 0.054 (1.41) - 0.009 (0.39)
- 0.324 (4. IS) - 0.032 (0.64) - 2.95 (1.03) - 0.025 (0.74) 0.400 (4.69) 0.002 (0.11) - 0.017 (I .60)
- 0.088 (1.54) - 0.129 (3.65) 0.089 (I .05) - 0.001 (0.05) 0.036 (0.54) 0.050 (3.05) - 0.019 (2.40)
- 0.209 (3.79) - 0.058 (1.69) - 0.669 (0.72) - 0.014 (0.59) 0.192 (2.94) 0.018 (1.12) - 0.012 (1.52)
- 0.217 (2.08) - 0.088 (1.35) - 0.987 (1.02) - 0.002 (0.04) 0.078 (0.65) 0.028 (1.47) 0.043 (2.29)
0.24 260.25
0.30 190.34
0.35 201.74
0.29 199.68
0.21 166.78
Administration
P)
Nofe. Dependent variable: Average wages of selected labor groups. “t-statistics are shown in parentheses.
TABLE 5 Elasticities of Wages with Respect to Distance Computed for Each Labor Group Using the Semilog and Double Log Forms Functional form Labor group (1) (2) (3) (4) (5)
Administration Clerical Fire Police Public works
Semilog -
0.349 0.327 0.131 0.205 0.209
Double log -
0.379 0.324 0.088 0.209 0.217
Mean wage 1510 682 II88 1176 951
Note. (1) The mean of distance is 22. (2) Elasticities computed at the mean.
INTRAURBAN
WAGE
GRADIENT
59
individually. Coefficients for only two groups are significant at the 0.05 level. The coefficients associated with the interactive variables exhibit a greater amount of explanatory power. The coefficient of the per unit housing costs is significant at the 0.05 level for two groups although the signs are mixed. The concentration of employment in each community is insignificant for all but one of the five labor groups. According to theory, the coefficient of the employment concentration variable should be positive and the population change variable should be negative. In all but one case, the signs of the coefficients follow this hypothesis although the estimate of only one labor group is significant at the 0.05 level. CONCLUSION The study shows that for the Chicago metropolitan labor market statistically significant wage gradients exist for four of the five labor groups studied. Furthermore, for the labor group which does not exhibit a statistically significant negative gradient, a zero slope is found rather than a positive slope found by previous investigators. Given these findings, it is interesting to ask why a negative wage gradient is found for some labor groups and not others. One possible explanation rests with the necessary conditions for a negative wage gradient, namely, that a sufficient degree of concentration of employment should exist to attract workers from outlying areas. However, the percentage of total SMSA employment located in the City of Chicago provides few clues since administration wages,although the least concentrated in the CBD, show a highly significant negative coefficient of distance. The fire department, on the other hand, despite a high concentration exhibits a statistically insignificant accessibility coefficient. Another possible explanation for the nonexistence of wage gradients is the influence of strong labor unions throughout the entire market. This may explain why the wages of fire department personnel, who notably have strong unions, do not vary with distance. On the other hand, the strong police unions have little effect on the negative wage gradients. Moreover, a union variable contributes nothing to the explanation of wages for any of the labor groups. Other explanations may stem from the mobility of labor between the private and public sectors and the nature of the intraurban transportation system. Only a cross-sectional analysis of many labor groups in many urban markets can adequately explain these characteristics. Many aspects of intraurban wage gradients have yet to be investigated. This study has established that negative wage gradients do exist; it is the task of future research to examine wage gradients of additional metropoli-
60
RANDALL
W. EBERTS
tan regions and wage groups to ascertain more general conditions of intraurban spatial equilibrium. ACKNOWLEDGMENTS I am grateful to Gerald Bierwag, Gerald Goldstein, W. Ed Whitelaw, Bert Steece, and a referee for a careful reading of the manuscript and helpful suggestions.
REFERENCES 1. M. J. Ball. Recent empirical work on the determinants of relative house values, Urban Srudes, 10, 213-233 (1973). 2. G. E. P. Box and D. R. Cox, An analysis of transformations, J. Roy. Statist. Sot., Ser. B, Xi. 211-243 (1964). 3. R. W. Eberts, “An Economic Analysis of Municipal Governments in a Metropolitan
Setting,” Ph.D. Dissertation, Department of Economics, Northwestern University ( 1978). 4. R. G. Ehrenberg and G. S. Goldstein, A model of public sector wage determination, J. Urhun Econ., 2, 223-245 (1975). 5. G. S. Goldstein and R. G. Ehrenberg, Executive compensation in municipalities, Southern Econ. J., 43, 937-947 (1976).
6. Institute of Office Management, “Clerical and Salaries Analysis: 1962,” Institute of Office Management, London (1962). 7. E. S. Mills, The value of urban land, in “The Quality of the Urban Environment” (H. S. Perloff, Ed.), Resources for the Future, Washington, D. C. (1969). 8. E. S. Mills, “Studies in the Structure of the Urban Economy,” Johns Hopkins Press, Baltimore (1972). 9. L. N. Moses, Towards a theory of intra-urban wage differentials and their influence on travel patterns, Pupers Proc. Reg. Sci. Assoc., 9, 52-63 (1962). IO. L. N. Moses and Harold F. Williamson, The location of economic activity in cities, Amer. Ecou. Rw., 57, 211-222 (1967).
I I R. F. Muth, “Cities and Housing,” Univ. of Chicago Press,Chicago (1969). 12. W. A. Niskanen, “Bureaucracy and Representative Government,” Aldine-Atherton, Chicago (1971). 13. A. Rees and G. P. Schultz, “Workers and Wages in an Urban Labor Market,” Univ. of Chicago Press, Chicago (1970). 14. S. M. Rock, “The Redistributive Effects of Mass Transit in the Chicago Area,” Ph.D. Dissertation, Department of Economics, Northwestern University (1975). 15. M. Segal, “Wages in the Metropolis,” Harvard Univ. Press, Cambridge, Mass. (1960). 16. R. J. Struyk and F. J. James, “Intrametropolitan Industrial Location,” Heath, Lexington, Mass. (1975). 17. M. L. Wachter, Wage determination in a local labor market: a case study of the Boston labor market, J. Humun Res., 7, 87- 103 (1972). lg. M. J. White, Firm suburbanization and urban subcenters, J. Urban Econ., 3, 232-243 (1976).
OF URBAN
ECONOMICS
10,
50-60 (1981)
An Empirical Investigation of lntraurban Wage Gradients W. EBERTS
RANDALL Depurtment
of Economics,
University
of Oregon,
Eugene, Oregon 97403
Received November 12, 1979; revised March 14, 1980 Intraurban wage gradients have received little attention in the urban literature but have been shown theoretically to be important indicators of the spatial characteristics of urban economic activity. This study examines the spatial distribution of wages of five groups of municipal public employees in the Chicago SMSA. Negative wage gradients, significant at the 0.05 level, are found for four of the five labor groups. Results show that monthly wages decreaseon average as much as $24 per additional mile from the city center.
INTRODUCTION Empirical investigations of intraurban wage gradients have been conspicuously missing from the urban literature. The importance of wage gradients as determinants of the spatial arrangements of economic activity in urban areas and as tools in the analysis of spatial distribution has long been recognized. Moses [9] first constructed a theory of intraurban wage gradients to explain intraurban travel patterns. Later, in collaboration with Williamson, Moses [lo] used wage differentials to explain suburbanization. More recently, Mills [8] and Muth [ 1I] have incorporated wage gradients into more general models of urban spatial equilibrium. Despite these efforts, only three studies have been found in the literature which examine intraurban wage gradients empirically. This is certainly not true of urban price gradients in general. Indeed, urban rent gradients have received much attention in the last two decades. Even as early as 1973, a review article by Ball [1] catalogued no less than eleven studies of nine different cities. Additional studies have followed. The purpose of this study is to ascertain empirically the nature of intraurban wage differentials. The primary hypothesis to be tested is the correlation between the accessibility to the urban core and the wage differentials within urban labor markets. To do so, the paper is organized as follows. The first section reviews the few studies of wage gradients that have been undertaken. Section II outlines the prerequisite for the existence of wage gradients and formulates the wage gradient equation. The third section discusses the data and the appropriateness of using the Chicago labor 50 0094-I l90/8 I /040050-l I $02.00/O Copyright 0 19x1 by Academic Press. Inc All rights. of reproduction in any form reserved.
INTRAURBAN
WAGE
GRADIENT
51
market in the study. The fourth section describes the estimation results, and the fifth section contains some closing remarks. I. LITERATURE The purpose of this paper is to investigate the characteristics of intraurban wage gradients and not simply the differential wage levels found between central cities and suburbs. Numerous studies of the differential effect have emerged including works by Ehrenberg and Goldstein [4] and Wachter [17]. However, only three works exist which deal directly with the continuous spatial variation of wages within an urban labor market. The three studies strike no general consensus; the results of each differ depending on the particular labor group and metropolitan area under investigation. Segal [ 151 studied wage patterns in New York City and found positive wage gradients for some industries and negative gradients for others. His data were aggregated, and the lack of observations reduced the rigor of his analysis. Another study, conducted by the Institute of Office Management [6], looked at pay scalesof workers in the London metropolitan area. Of the groups studied, only the wages of clerical workers revealed any tendency to decrease with distance from the central business district (CBD). Like the New York City study, the London study was plagued with the problem of finding sufficient observations to conduct a rigorous analysis. Rees and Schultz [13], in their study of the Chicago labor market, found a negative wage gradient for manufacture workers. However, the wage gradient was not in relation to the Chicago CBD but to the southeast comer of the metropolitan area where heavy industry was most concentrated. Their attempts to find similar relationships between wages and employment concentration failed for other labor groups. Obviously, a major reason for the paucity of wage gradient studies is the lack of adequate data. The lack of data may also explain why none of the studies looked at features such as the relative influence of demand and supply characteristics on the wage gradient and why none have corrected for differences in the nature of firms and the labor force. Such relationships need to be explored to provide a complete description of intraurban wage gradients. II. MODEL Wage gradients result from the spatial decisions of utility-maximizing workers and the labor requirements of cost-minimizing firms. The theory of wage gradients is well documented in the literature. Muth [ 1l] presents a model of wage gradients with local employment, and White [ 181extends the model to incorporate suburban concentration of employment. Thus, only
52
RANDALL
W. EBERTS
the salient features of the model need to be highlighted here. In particular, since the intent of the study is to examine wage gradients empirically, it is important to specify correctly the effect of exogenous supply and demand conditions on the wage offers of firms as well as to take into account the differences in the nature of firms and the labor force. Before specifying the wage equation, several assumptions need to be made to insure a negative correlation between wage offers and distance of the firm from the CBD. First, the firm must behave according to some efficiency criterion so that its behavior is constrained by exogenous market conditions.’ Second, households must achieve equilibrium. Third, concentration of employment must be sufficiently large so that not all workers can live adjacent to their workplace. These assumptions lead to an hypothesized negative relationship between the wage offer and the distance from the CBD. When differences in demand characteristics between communities are considered, the wage equation is written: wit(h)
=
wO +
Plxlt(P)
+
IX k=2
P/~[~kt~ltl O(P) (1)
+
i j=l
Yj’j,(P>
+
Cir3
i = 1,...,5.
The wage of the ith labor group observed in the tth community is denoted by wi,; the distance to the CBD of the tth community is x,,; and the socioeconomic and organizational variables that affect both the supply and demand for labor are denoted by the z’s.* Since the theory provides no clues as to which functional form of the wage equation is appropriate, (1) permits the data to specify the appropriate form. Following the Box-Cox transform technique, the dependent and ‘In this study the “firms” are independent municipal governments located throughout the Chicago metropolitan area. Although efficient behavior is not well documented for the public sector, recent theoretical work by Niskanen [ 121and empirical work by the author [3] show that public agencies that follow a budgetary approach in allocating resources do indeed follow cost-minimizing behavior. *The supply and demand conditions of neighboring communities will also affect the wages in community t. This effect can be incorporated into the wage equation by entering as an explanatory variable the wages of neighboring communities weighted by their respective distances from community t. Since estimation based on techniques that deal with spatial correlation in the residuals produces insignificant results, the neighboring wage effects are deleted from (1).
INTRAURBAN
WAGE
GRADIENT
53
independent variables are written in the general form:
Jo) = (Y” - 1)/L = l0d.Y)~
A#0 x = 0,
where h takes on values between 0 and 2. The explanatory variables are entered into (1) either in a multiplicative form with distance or additively. The noninteractive terms include the distance variable and three measuresof organizational structure. Accessibility to the CBD is entered as the airline distance from community t to the CBD. Various measures of accessibility have been used in the urban rent gradient literature. Mills [7] concludes that airline distance to the CBD is the most useful, and more complex measures are not worth the cost of computing. Municipal governments in the Chicago SMSA differ in organizational structure and the relative ability and propensity to pay employees. Organizational structure may dictate the type of employees that a local government can hire. For example, the size of the community may have a limiting effect on the extent of specialized skills within the government organization. Since employees with specialized skills command higher salaries and larger cities demand greater specialization, larger cities will tend to pay higher average wages. Goldstein and Ehrenberg [5] show that the relative ability and propensity of local governments to pay higher wages are also related to the behavior of public administrators. The tenure of public administrators depends in part on their responsivenessto the demands of their constituents and employees. Administrators can increase the likelihood that demands of various groups will be satisfied by increasing the range of services offered to taxpayers, increasing compensation to employees, and improving their working conditions. All three measures require a large budget and a large organization. Thus, municipal wages should be positively related to the size of the budget and the size of the municipal government which are related to the size of the community. Workers’ characteristics may also affect the wage level. If municipal governments follow efficiency criteria, then compensation should be positively correlated with individual productivity. Satisfactory measures of productivity and skill levels are not obtainable except for the number of hours worked per week. The interactive variables reflect the effect of local supply and demand conditions on the wage gradient. Theory shows that in absolute terms excess
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demand for labor decreasesthe gradient while excess supply increases the gradient. The logic of the multiplicative form can be seen by writing the coefficient of the distance variable as a linear function of community characteristics: k=2
When p, and fik have the same sign, the slope increases. Opposite signs indicate that the socioeconomic variables force the wage gradient to be flatter. Three variables are used to measure supply and demand conditions. The first is the ratio of employment of a particular labor group in each city to the supply of that labor group which resides in the same city. This ratio measures the attractive force of the community as an employment subcenter. As firms in the subcenter require more labor than can be supplied locally, they offer higher wages which causesthe wage gradient to decrease. The second variable, the rate of population change in the community, measures the excess supply of labor in an area. A better proxy of excess supply would be a measure of the change in employment demand relative to supply in each city. Unfortunately, data on firm relocations are not available for each city. A fair assumption, supported by data from other major cities, is that firms relocate at a much slower pace than households.3 A substantial change in population may cause a surplus of labor making it possible for firms to meet their labor requirements with a high proportion of local workers. Consequently, the wage offerings in these communities will be lower and the attractive force of the community will be smaller than they otherwise would be if workers had to be attracted from more distant points. The supply of workers near the firm is also affected by the ability of workers of certain income levels to live in communities that hold job opportunities for them. Firms which cannot substitute away from low skill jobs may be obliged to offer higher wages to compensate workers for higher house prices or additional commuting costs. As a result, the wage gradient will be sensitive to the per unit housing costs in a community. ‘Struyk and James [ 161have tabulated the percentage change in employment due to plant relocations for four SMSAs. They find that in a three year period on average six percent of employment change is due to relocation of firms. On the other hand, the Bureau of Census statistics show that 17%of the households in the country relocate in a single year and of these 8.3% relocate within a metropolitan area. In a five year period, the respective numbers are roughly 48% and 17%. These rough estimates show that households do move more often than firms and thus even though the rate of population change may overstate excess supply, a positive change reflects a surplus of labor in a particular city.
INTRAURBAN
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WAGE GRADIENT
III. DATA The author has been fortunate to acquire an especially rich source of data from the Cook County Bureau of Administration. Since 1971, the Bureau in cooperation with the U.S. Civil Service Commission has conducted a semiannual survey of government salaries and fringe benefits for over 100 municipalities in the six-county Chicago metropolitan area. Five categories of noneducational municipal workers will be considered in this study: administration, clerical, police, fire and public works. The extensive collection of information on wages,supply and demand conditions, and organizational characteristics permits distance from the CBD to be included as a continuous variable. The Chicago area is well suited for a wage gradient study. It has been a laboratory for a number of previous studies including the urban density study by Muth [I 1, Chap. 91 and the land value study by Mills [7]. Both Muth and Mills find that the economic and geographic features of Chicago comply very closely with the assumptions of the model. It is most appropriate, therefore, to look at Chicago when studying intraurban wage gradients. Three features make Chicago particularly attractive. First, the Chicago area is situated on a flat, almost featureless plain. Second, the City of Chicago contains a concentration of most major types of employment which appear to be sufficiently large to meet the assumptions of the model. Table 1 shows percentages of total employment located in the City of Chicago for various labor groups. Third, the transportation system is particularly conducive to estimate wage gradients. Almost all of the major transportation TABLE 1 Percentageof Total SMSA Employment Located in City of Chicago by Labor Group Private sector0 Professional Managers and administrators Clerical and kindred workers Craftsmen, foremen Laborers Service workers Total
Public sectorh 48% 40 61 56 69 67 57
Administrators
33%
Clerical Fire Police Public Works Total
79 71 80 75 76
“Source: Census of Population, 1970, Tables 105, 118. hSource: “Regional Government Salary and Fringe Benefit Survey,”
Cook County, Bureau of Administration, July 1974.
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W. EBERTS
TABLE 2 Comparison of Wage and Salary Level of Selected Private and Public Job Categories Job category File clerk A B C Typists A B Guards Laborers Auto mechanics Painters, maintenance Mechanics, maintenance
Public sector wage
Range of private sector wage
$129.50(mo.) 117.50 103.00 139.00 122.50 $ 4.46 (hr.) 4.57 6.42 6.05 5.83
$1l6.50- 146.00(mo.) 106.00- 135.50 97.00- I 15.00 126.00- 155.00 109.00- 136.50 $ 3.93-5.13 (hr.) 3.91-5.34 5.78-7.13 5.32-6.56 5.35-6.52
Sources: Public Sector wage data are obtained from “Regional Government Salary and Fringe Benefit Survey,” Cook County, Bureau of Administration, July 1974. Private sector wage data are obtained from Bureau of Labor Statistics, Chicago SMSA area survey, July 1974.
routes including the Regional Transit Authority elevated railroad lines and private commuter trains follow radial paths from the city center. Only one major expressway servescommuters who travel around the circumference of the city.4 Although public labor markets are used to estimate wage gradients, the results can be used to infer characteristics of intraurban private labor markets. Analysis of nationwide data has led Ehrenberg and Goldstein [4] to suggest that there is considerable mobility between public and private sector jobs. Evidence of intersectoral mobility in the Chicago area is found in the similarity between wage and salary levels offered by public and private employers as shown in Table 2. Comparison of wages of similar jobs reveals that public sector wage rates consistently fall within the range of private sector wages. Thus, in many respects, conclusions drawn from observations of the public sector can be extended to the private sector as well. IV. ESTIMATION
RESULTS
Even though various functional forms, including exponential, log and linear, were used to estimate the wage equations, no specification is statisti4The influence of radial transportation lines on the location of firms and households is well documented by Rock 1141.
INTRAURBAN
57
WAGE GRADIENT
tally superior to the rest. The 95% confidence interval around the optimal maximum likelihood statistic contains a wide range of functional forms for each labor group. Moreover, the estimated wage elasticities with respect to distance for each group do not vary significantly among functional forms. Therefore, only the double log and semilog specifications, both within the 95% confidence interval, will be reported here. The results are most encouraging for establishing the existence of negative wage gradients. As shown in Tables 3 and 4, four out of the five labor groups exhibit negative coefficients for the distance variable that are different from zero at the 0.05 significance level. Table 5 shows the elasticities computed about the mean under the two functional forms. These elasticities are easily translated into monetary terms and reveal that for the double log case administration monthly wages decrease on average $24 per mile, clerical $10 per mile, police $12 per mile, and public works $9 per mile. The signs of the socioeconomic coefficients are consistent with the theory although their significance levels vary among labor groups. The noninteractive explanatory variables show little statistical significance when considered TABLE 3 Regression Coefficients of the Wage Equation for Each Labor Group Estimated Using the Semilog Form (1,O) Labor groups Explanatory variables (I)
Distance from the CBD measured in airline miles (2) Per capita municipal government expenditures (3) Length of workweek (4) Population of community in 1970 (5) (Per unit housing costs) X (distance to CBD) (6) (Employment concentration) X (distance to CBD) (7) (Population change) X (distance to CBD) R’(adj.) - L,,(L
Fc)
Administration - 528.44 (2.49)“ 179.88 (1.49) - 561.04 (2.15) 139.05 (1.64) 685.12 (3.12) - 77.52 (1.69) - 8.50 (0.3I) 0.31 250.59
Clerical
Fire
Police
Public works
- 223.16 (4.16) - 18.46 (0.54) - 196.54 (0.99) - 17.04 (0.72) 279.21 (4.72) I .47 (0. IO) - 12.13 (1.61)
- 104.86 (1.48) - 156.27 (3.58) 91.93 (0.88) - 3.37 (0.11) 37.56 (0.45) 60.39 (2.98) - 21.97 (2.26)
- 240.68 (3.69) - 69.89 (1.72) - 722.19 (0.66) - 18.13 (0.65) 220.32 (2.86) 20.55 (1.10) - 12.69 (1.40)
- 198.82 (2.09) - 78.68 (1.32) - 1022.31 (1.16) - 4.41 (0.12) 70.74 (0.65) 22.83 (1.32) 41.02 (2.38)
0.30 191.22
0.33 203.52
0.27 199.99
0.22 165.59
Note. Dependent variable: Average wages of selected labor groups. “t-statistics are shown in parentheses.
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TABLE 4 Regression Coefficients of the Wage Equation for Each Labor Group Estimated during the Double Log Form (0.0) Labor groups Explanatory variables ( I)
Distance from the CBD measuredin airline miles (2) Per capita municipal government expenditures (3) Length of work week (4) Population of community in 1970 (5) (Per unit housing costs) X (distance to CBD) (6) (Employment concentration) X (distance to CBD) (7) (Population change) X (distance to CBD) R’(adj.) - L,,(k
Clerical
Fire
Police
Public works
- 0.379 (2.14)” - 0.183 (1.83) - 0.397 (1.83) 0.084 (1.19) 0.470 (2.58) - 0.054 (1.41) - 0.009 (0.39)
- 0.324 (4. IS) - 0.032 (0.64) - 2.95 (1.03) - 0.025 (0.74) 0.400 (4.69) 0.002 (0.11) - 0.017 (I .60)
- 0.088 (1.54) - 0.129 (3.65) 0.089 (I .05) - 0.001 (0.05) 0.036 (0.54) 0.050 (3.05) - 0.019 (2.40)
- 0.209 (3.79) - 0.058 (1.69) - 0.669 (0.72) - 0.014 (0.59) 0.192 (2.94) 0.018 (1.12) - 0.012 (1.52)
- 0.217 (2.08) - 0.088 (1.35) - 0.987 (1.02) - 0.002 (0.04) 0.078 (0.65) 0.028 (1.47) 0.043 (2.29)
0.24 260.25
0.30 190.34
0.35 201.74
0.29 199.68
0.21 166.78
Administration
P)
Nofe. Dependent variable: Average wages of selected labor groups. “t-statistics are shown in parentheses.
TABLE 5 Elasticities of Wages with Respect to Distance Computed for Each Labor Group Using the Semilog and Double Log Forms Functional form Labor group (1) (2) (3) (4) (5)
Administration Clerical Fire Police Public works
Semilog -
0.349 0.327 0.131 0.205 0.209
Double log -
0.379 0.324 0.088 0.209 0.217
Mean wage 1510 682 II88 1176 951
Note. (1) The mean of distance is 22. (2) Elasticities computed at the mean.
INTRAURBAN
WAGE
GRADIENT
59
individually. Coefficients for only two groups are significant at the 0.05 level. The coefficients associated with the interactive variables exhibit a greater amount of explanatory power. The coefficient of the per unit housing costs is significant at the 0.05 level for two groups although the signs are mixed. The concentration of employment in each community is insignificant for all but one of the five labor groups. According to theory, the coefficient of the employment concentration variable should be positive and the population change variable should be negative. In all but one case, the signs of the coefficients follow this hypothesis although the estimate of only one labor group is significant at the 0.05 level. CONCLUSION The study shows that for the Chicago metropolitan labor market statistically significant wage gradients exist for four of the five labor groups studied. Furthermore, for the labor group which does not exhibit a statistically significant negative gradient, a zero slope is found rather than a positive slope found by previous investigators. Given these findings, it is interesting to ask why a negative wage gradient is found for some labor groups and not others. One possible explanation rests with the necessary conditions for a negative wage gradient, namely, that a sufficient degree of concentration of employment should exist to attract workers from outlying areas. However, the percentage of total SMSA employment located in the City of Chicago provides few clues since administration wages,although the least concentrated in the CBD, show a highly significant negative coefficient of distance. The fire department, on the other hand, despite a high concentration exhibits a statistically insignificant accessibility coefficient. Another possible explanation for the nonexistence of wage gradients is the influence of strong labor unions throughout the entire market. This may explain why the wages of fire department personnel, who notably have strong unions, do not vary with distance. On the other hand, the strong police unions have little effect on the negative wage gradients. Moreover, a union variable contributes nothing to the explanation of wages for any of the labor groups. Other explanations may stem from the mobility of labor between the private and public sectors and the nature of the intraurban transportation system. Only a cross-sectional analysis of many labor groups in many urban markets can adequately explain these characteristics. Many aspects of intraurban wage gradients have yet to be investigated. This study has established that negative wage gradients do exist; it is the task of future research to examine wage gradients of additional metropoli-
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tan regions and wage groups to ascertain more general conditions of intraurban spatial equilibrium. ACKNOWLEDGMENTS I am grateful to Gerald Bierwag, Gerald Goldstein, W. Ed Whitelaw, Bert Steece, and a referee for a careful reading of the manuscript and helpful suggestions.
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Setting,” Ph.D. Dissertation, Department of Economics, Northwestern University ( 1978). 4. R. G. Ehrenberg and G. S. Goldstein, A model of public sector wage determination, J. Urhun Econ., 2, 223-245 (1975). 5. G. S. Goldstein and R. G. Ehrenberg, Executive compensation in municipalities, Southern Econ. J., 43, 937-947 (1976).
6. Institute of Office Management, “Clerical and Salaries Analysis: 1962,” Institute of Office Management, London (1962). 7. E. S. Mills, The value of urban land, in “The Quality of the Urban Environment” (H. S. Perloff, Ed.), Resources for the Future, Washington, D. C. (1969). 8. E. S. Mills, “Studies in the Structure of the Urban Economy,” Johns Hopkins Press, Baltimore (1972). 9. L. N. Moses, Towards a theory of intra-urban wage differentials and their influence on travel patterns, Pupers Proc. Reg. Sci. Assoc., 9, 52-63 (1962). IO. L. N. Moses and Harold F. Williamson, The location of economic activity in cities, Amer. Ecou. Rw., 57, 211-222 (1967).
I I R. F. Muth, “Cities and Housing,” Univ. of Chicago Press,Chicago (1969). 12. W. A. Niskanen, “Bureaucracy and Representative Government,” Aldine-Atherton, Chicago (1971). 13. A. Rees and G. P. Schultz, “Workers and Wages in an Urban Labor Market,” Univ. of Chicago Press, Chicago (1970). 14. S. M. Rock, “The Redistributive Effects of Mass Transit in the Chicago Area,” Ph.D. Dissertation, Department of Economics, Northwestern University (1975). 15. M. Segal, “Wages in the Metropolis,” Harvard Univ. Press, Cambridge, Mass. (1960). 16. R. J. Struyk and F. J. James, “Intrametropolitan Industrial Location,” Heath, Lexington, Mass. (1975). 17. M. L. Wachter, Wage determination in a local labor market: a case study of the Boston labor market, J. Humun Res., 7, 87- 103 (1972). lg. M. J. White, Firm suburbanization and urban subcenters, J. Urban Econ., 3, 232-243 (1976).