Wage Adjustment in Local Labor Markets: Do the

Wage Rates in all Industries Adjust?

Michael K. Lettau

Office of Economic Research

Bureau of Labor Statistics

May 1994

Abstract

Previous research finds that an increase in a local area's labor demand

increases the area's total employment and average wage rate relative to U.S.

total employment and the U.S. average wage rate. This paper extends previous

research by exploring heterogeneity within an area's labor market. Using

employment and average hourly earnings estimates for U.S metropolitan areas,

disaggregated by industry, I test whether an increase in an area's overall

labor demand increases the wage rate of an industry with constant labor demand

located in the area. And, if so, does employment for the industry in the area

decrease?

I find that an increase in an area's overall labor demand increases the

average hourly earnings of an industry with constant labor demand located in

the area, although the industry's employment in the area only slightly

decreases or actually increases. Under the structure of a model in which all

industries compete for the area's pool of workers, this suggests that an

area's labor demand is quite inelastic.

This paper is based on Chapters 3 and 4 of my doctoral thesis submitted

to the College of Letters and Sciences, University of Wisconsin-Madison,

October 1993. I thank Glen Cain, Arthur Goldberger, John Kennan, James

Walker, the participants of the UW-Madison Labor Workshop, the members of the

BLS Office of Economic Research, and especially John Shea for many comments.

The views expressed are those of the author and do not reflect the policies of

the BLS or the views of other BLS staff members.
1

I. Introduction and Overview

Labor market models with costless factor and product mobility predict

that wage rates will be the same in all metropolitan areas of the United

States. If the wage rate were higher in a particular area, workers would move

to the area to increase their utility and firms would move out of the area to

increase their profits. The area's wage rate would fall to the level in other

areas.1 However, it is costly for both labor and firms to move. Short-run

mobility costs are likely to prevent wages from adjusting immediately,

allowing an area's wage rate to diverge from the U.S. wage rate in the short

run.

Several empirical studies find that an increase in an area's labor

demand increases the area's wage rate relative to the U.S. wage rate. Topel

(1986), Bartik (1991), Eberts and Stone (1992), and Blanchard and Katz (1992)

are all examples. Bartik and Eberts and Stone use data for U.S. metropolitan

areas. Topel and Blanchard and Katz use U.S. state data. The labor

demand/labor supply diagram in Figure 1 gives a grossly simplified summary of

these studies. Let n.j equal log employment in area j differenced from U.S.

log employment. Let w.j equal the log average wage rate in area j differenced

from the U.S. log average wage rate.2

 

1See Rosen (1979) and Roback (1982) for an explanation of why wage rates may

vary across areas in the long run.

2Section AI of the appendix summarizes this paper's notation.
2

The studies estimate the response of n.j and w.j to a shift in labor demand

from LD.j to LD.j'. In general, they find that an area's elasticity of labor

supply is between 2.0 and 5.0. That is, an increase in the area's labor

demand increases both an area's employment and its wage rate. The percent

increase in employment tends to exceed the percent increase in the wage rate,

which suggests that LS.j in Figure 1 is fairly elastic.

This paper extends the work in previous studies by exploring

heterogeneity within an area's labor market. Previous studies typically use

an area's total employment, an estimate of an area's average wage rate, and a

single instrument for an area's labor demand to estimate the area's elasticity

of labor supply. Consequently, their results imply that an increase in an

area's labor demand increases the area's total employment and average wage

rate.3 However, does an increase in an area's average wage rate represent an

increase in wage rates among all firms and individuals located in the area?

When an area's overall labor demand increases, the labor demand curves of all

 

3This is a bit overstated. Eberts and Stone (1992) also use employment and

average wage rates for areas divided into good-producing and service-producing

sectors. Blanchard and Katz (1992) also use average wage rates in

manufacturing for U.S. states. And Bartik (1991) uses several estimates for

areas' wage rates, including estimates for quantiles of areas' wage rates.
3

industries in the area undoubtedly do not increase uniformly. Do the wage

rates of all industries in the area increase uniformly or do the wage rates of

some industries diverge from the wage rates of others? And how does an

increase in an area's labor demand affect employment among industries in the

area? As a concrete example, between 1980 and 1986, average hourly earnings

increased by 18% in Akron, Ohio. In Denver, Colorado, average hourly earnings

increased by 38%.4 Both Akron and Denver had firms in the furniture

manufacturing industry in 1980. Did the wage rate of workers from Akron

furniture manufacturing firms increase by 18% from 1980 to 1986 while the wage

rate of workers from Denver furniture manufacturing firms increased by 38%?

If so, did employment in Denver furniture manufacturing firms grow at a slower

rate than employment in Akron furniture manufacturing firms?

This paper considers two alternative answers to these questions. Both

are extreme cases. I will refer to the first case as the area model. In the

area model, the wage rates of all industries in an area increase uniformly

with an increase in the area's overall labor demand. Figure 2 shows the

effect of an increase in labor demand for industry i=I while labor demand for

other industries in area j remains constant. N.j equals total employment in

area j, Nij equals employment for industry i in area j, and Wj equals the

wage rate in area j.

 

4Average hourly earnings growth in nominal terms; calculated using data

described in Section III.
4

As shown in panel [2], the labor demand curve for industry i=I shifts to the

upper right from LDij to LDij'. The labor demand curve for area j is the sum

of the labor demand curves across industries in area j, so an increase in

labor demand for industry i increases area j's overall labor demand. As shown

in panel [1], area j's labor demand curve shifts to the upper right from LD.j

to LD.j', although the increase is proportionally smaller than the increase in

labor demand for industry i=I in area j. The wage rate in area j increases

from Wj to Wj' and total employment increases from N.j to N.j'. For industry

i=I, employment increases from Nij to Nij'. For the other industries in area

j, as shown in panel [3], employment decreases from Nij to Nij'. An increase

in labor demand for industry i=I acts as a negative labor supply shock for

other industries located in area j.

However, suppose industries' wage rates in an area do not increase

uniformly with an increase in the area's labor demand. At the other extreme,

which I will refer to as the alternative model, suppose the wage rate of an

industry in an area is not affected by the labor demand of other industries

located in the same area. Figure 3 shows the effect of an increase in labor

demand for industry i=I while labor demand for other industries in area j
5

remains constant. Wij equals the wage rate for industry i in area j, and W.j

equals the average wage rate in area j.

As shown in panel [2], the increase in labor demand increases employment and

the wage rate of industry i in area j. In panel [3], however, employment and

the wage rate of other industries in the area are not affected. Total

employment and the average wage rate in area j increase, as shown in panel

[1], which is substantively the same as panel [1] from Figure 2. However,

unlike panel [1] from Figure 2, the change in area j's average wage rate does

not represent the change in any industry's wage rate in area j. The change in

an area's average wage rate is merely the aggregate of the change in each

industry's wage rate.

The empirical work in previous studies is largely analogous to

estimating the slope of the labor supply curve in panels [1] of Figures 2 and

3. In contrast, by using employment and average hourly earnings estimates for

166 U.S. metropolitan areas disaggregated by 37 2-digit (SIC) industries, this

paper tests whether employment and wage rate movement among industries in a
6

metropolitan area is consistent with the diagrams in panels [2] and [3] of

Figure 2 or consistent with the diagrams in panels [2] and [3] of Figure 3.

I use an industry's U.S. employment and U.S. average hourly earnings to

instrument for the industry's labor demand in a metropolitan area. Thus, the

empirical test is the following. For an industry with constant U.S.

employment and constant U.S. average hourly earnings, does the industry's

average hourly earnings in a metropolitan area increase with an increase in

the U.S. employment and U.S. average hourly earnings of other industries

located in the same area? In other words, for an industry with constant labor

demand, does the industry's average hourly earnings in an area increase with

an increase in the area's overall labor demand? And, if so, does the

industry's employment in the area decrease, following the prediction of panel

[3] from Figure 2?

The empirical results are summarized as follows.

• The average hourly earnings of an industry with constant labor demand

increases with an increase in labor demand among other industries located

in the same area. However, the average hourly earnings of all industries

in an area do not increase uniformly with an increase in the area's overall

labor demand.

• The magnitude of the increase in an industry's average hourly earnings in an

area, given an increase in labor demand among other industries located in

the same area, depends on the similarity of the industries' distribution of

occupations.

• Even though the average hourly earnings of an industry with constant labor

demand increases with an increase in the area's overall labor demand,

employment for the industry only slightly decreases or actually increases.

Under the structure of the area model shown in Figure 2, this suggests that

an area's labor demand is quite inelastic.

 The remainder of the paper is organized as follows. Section II

summarizes the specification used for the empirical work in Section IV.

Section III briefly describes the data used for the empirical work. Section

IV presents the empirical results. Section V summarizes.
7

II. Empirical Specification

The empirical work in Section IV consists of estimating the parameters

for two sets of regression equations: equations (1) and (2) and equations (3)

and (4).

(1) (N.jt-N.jt-1)/N.jt-1 = τ1t + Θ11ZNjt + Θ12ZWjt + v1.jt

(2) W.jt-W.jt-1 = τ2t + Θ21ZNjt + Θ22ZWjt + v2.jt

(3) (Nijt-Nijt-1)/Nijt-1 = τ3t + Θ31[(Ni.t-Ni.t-1)/Ni.t-1] + Θ32(Wi.t-Wi.t-1) + Θ33ZNjt

+ Θ34ZWjt + v1ijt

(4) Wijt-Wijt-1 = τ4t + Θ41[(Ni.t-Ni.t-1)/Ni.t-1] + Θ42(Wi.t-Wi.t-1) + Θ43ZNjt

+ Θ44ZWjt + v2ijt

where: Nijt = employment for industry i in area j in year t.

 Wijt = average hourly earnings for industry i in area j in year t.

 N.jt = total employment in area j in year t.

 W.jt = average hourly earnings in area j in year t.

 Ni.t = U.S. employment for industry i in year t.

 Wi.t = U.S. average hourly earnings for industry i in year t.

 ZNjt = Σi(Nijt-1/N.jt-1)[(Ni.t-Ni.t-1)/Ni.t-1]

 ZWjt = Σi(Nijt-1/N.jt-1)(Wi.t-Wi.t-1)

In equations (1) and (2), the percent change in an area's total employment and

the change in an area's average hourly earnings are regressed on instruments

for the change in the area's overall labor demand. In equations (3) and (4),

the percent change in employment and the change in average hourly earnings for

an industry in an area are regressed on instruments for the change in the

industry's labor demand and instruments for the change in the area's overall
8

labor demand. The Θ parameters are coefficients for the labor demand

instruments. The τ parameters are year-varying intercept terms.

In equations (1) through (4), the percent change in an industry's U.S.

employment and the change in an industry's U.S. average hourly earnings

instrument for the change in the industry's labor demand in an area.5

Analogously, the average percent change in industries' U.S. employment and the

average change in industries' U.S. average hourly earnings instrument for the

change in an area's overall labor demand, where the averages are weighted by

the area's mix of industries in the previous year. That is,

[(Ni.t-Ni.t-1)/Ni.t-1] and (Wi.t-Wi.t-1) instrument for the change in industry i's

labor demand in area j, while ZNjt and ZWjt instrument for the change in area

j's overall labor demand.6

The specifications in equations (1) through (4) are based on the two

models of an area's labor market. Figure 2 demonstrates the area model.

Figure 3 demonstrates the alternative model. Section AII of the Appendix

presents the two models in detail. In this section, however, I only summarize

the models' predictions, as they merely formalize the intuition in Figures 2

 

5The specifications in equations (1) through (4) are based on the models of an

area's labor market presented in Section AII of the Appendix. The models

assume that the change in labor demand for an industry in an area has a

component that is common to the industry across all areas, while the change in

labor supply for an industry in an area has no component that is common to the

industry across all areas. With these and the models' other assumptions, the

percent change in an industry's U.S. employment and the change in an

industry's U.S. average hourly earnings are valid instruments for the change

in the industry's labor demand in an area.

6Bartik (1991) and Blanchard and Katz (1992) use a similar instrument. A

potential problem with using the industry's proportion of the area's total

employment in the previous year to calculate the instruments for the change in

an area's overall labor demand is that, in equation (3), Nijt-1 is used to

calculate the dependent variable and two of the independent variables: ZNjt

and ZWjt. This could lead to spurious correlation. However, I experimented

with using the industry's proportion of the area's total employment in the

current year, as well as the industry's proportion of the area's total

employment over multiyear periods. The results were not sensitive.
9

and 3. In the area model, all industries compete for an area's pool of

workers, thereby determining the area's wage rate. An increase in an area's

overall labor demand increases the wage rates of industries in the area

uniformly. Thus, the change in the wage rate for an industry in an area is

determined by the change in labor demand among all industries in the area, not

by the change in labor demand for any single industry. In contrast, in the

alternative model, each area/industry combination is a separate labor market.

Employment and the wage rate for an industry in an area is determined by labor

demand for the industry alone. Labor demand among other industries located in

the same area is not relevant.

The following lists the area and alternative models' predictions for the

parameters in equations (1) through (4).

Area Model Alternative Model

(Figure 2) (Figure 3)

Labor Demand Predicted Restricted Predicted Restricted

Eq. Instrument Coef. sign coefficent sign coefficent

(1) ZNjt Θ11 + [ηs/(ηd+ηs)] + [ηs/(ηd+ηs)]

ZWjt Θ12 + [ηdηs/(ηd+ηs)] + [ηdηs/(ηd+ηs)]

(2) ZNjt Θ21 + [1/(ηd+ηs)] + [1/(ηd+ηs)]

ZWjt Θ22 + [ηd/(ηd+ηs)] + [ηd/(ηd+ηs)]

(3) (Ni.t-Ni.t-1)/Ni.t-1 Θ31 +1+ [ηs/(ηd+ηs)]

Wi.t-Wi.t-1 Θ32 + ηd + [ηdηs/(ηd+ηs)]

ZNjt Θ33 - -[ηd/(ηd+ηs)] 0 0

ZWjt Θ34 - -ηd[ηd/(ηd+ηs)] 0 0

(4) (Ni.t-Ni.t-1)/Ni.t-1 Θ41 00+ [1/(ηd+ηs)]

Wi.t-Wi.t-1 Θ42 00+ [ηd/(ηd+ηs)]

ZNjt Θ43 + [1/(ηd+ηs)] 0 0

ZWjt Θ44 + [ηd/(ηd+ηs)] 0 0

Note: When all the models' restrictions are imposed, the τ parameters from

equations (1) through (4) are functions of ηd, ηs, and a year-specific shock

to labor supply that is common to all areas, defined as πt.
10

When all the models' restrictions are imposed, the Θ coefficients are

functions of the slopes of the labor demand and labor supply curves shown in

Figures 2 and 3. The labor demand slope is defined as -ηd. (Thus, a positive

value for ηd implies a downward-sloping labor demand curve.) The labor supply

slope is defined as ηs. The models assume that the labor demand and labor

supply slopes apply to all industries and areas. Also note that ηd and ηs are

semi-elasticities; that is, they equal the percent change in employment with

respect to a unit change in the wage rate.7

Section AII of the Appendix derives the restricted coefficients.

However, their form is readily apparent from Figures 2 and 3. As panels [1]

of Figures 2 and 3 suggest, the area and alternative models imply the same

restrictions for equations (1) and (2). Thus, the interpretation of the

parameter estimates for equations (1) and (2) is the same following either

model. I concentrate on the models' restriction that both Θ11/Θ21 and Θ12/Θ22

equal ηs. That is, because both ZNjt and ZWjt instrument for shifts in an

area's overall labor demand curve, their coefficients from the total

employment equation divided by their coefficients from the average wage rate

equation equal the slope of an area's labor supply curve.

In contrast, as panels [2] and [3] from Figures 2 and 3 suggest, the

area and alternative models imply different restrictions for equations (3) and

(4). Following the area model's intuition in Figure 2, the change in the wage

rate for an industry in an area is determined by the change in the area's

overall labor demand. Thus, the area model implies that the coefficients for

ZNjt and ZWjt in equation (4) are positive. Moreover, once the effect of a

 

7I use the percent change in employment and the level change in average hourly

earnings to be consistent with the labor market models in Section AII. The

results are the same qualitatively when I use the log change for both

employment and average hourly earnings.
11

change in an industry's labor demand is accounted for in the change in an

area's overall labor demand, it has no further effect on the expected change

in the industry's wage rate in the area. Thus, the area model implies that

the coefficients for [(Ni.t-Ni.t-1)/Ni.t-1] and (Wi.t-Wi.t-1) in equation (4) are

zero. That is, because an increase in an area's overall labor demand

increases the wage rates of all industries in the area uniformly, the change

in an area's average wage rate represents the change in each industry's wage

rate in the area. Thus, under the area model's assumptions, equation (4) is

identical to equation (2), although I add an extra residual to equation (4) to

account for idiosyncratic movement in an individual industry's wage rate.

For equation (3), the area model implies that the expected change in

employment for an industry in an area is a function of both the change in the

industry's labor demand and the change in the area's overall labor demand.

Therefore, under the area model's assumptions, the instruments for the change

in an individual industry's labor demand combine with the instruments for the

change in an area's overall labor demand to identify the labor demand

parameter ηd. That is, holding labor demand for an industry constant, an

increase in an area's overall labor demand moves the industry's employment and

wage rate in the area to the upper left along a downward-sloping labor demand

curve, as panel [3] of Figure 2 demonstrates.

In contrast to the area model, the alternative model assumes that each

industry in an area is a separate labor market. That is, the change in

employment and the wage rate for an industry in an area is a function of the

change in labor demand for the industry alone. Moreover, the change in an

area's total employment and average wage rate is merely the aggregate of the

change in employment and the wage rate for individual industries located in
12

the area. Thus, the restricted coefficients in equation (3) and (4) equal the

restricted coefficients in equation (1) and (2) under the alternative model's

assumptions.

The empirical work in Section VI is based primarily on the area model,

although the alternative model provides alternative hypotheses. I estimate

equations (1) and (2) and equations (3) and (4) as seemingly-unrelated

regression systems. I estimate the parameters in both their linear form and

imposing all the area model's restrictions. I use the procedure suggested by

White (1980) to calculate asymptotic standard errors for the estimated

parameters. Consequently, for equations (1) and (2), the standard error

estimates are consistent under general forms of heteroskedasticity for v1.jt

and v2.jt and general forms of correlation between v1.jt and v2.jt for

observations from the same area and year. Similarly, for equations (3) and

(4), the standard error estimates are consistent under general forms of

heteroskedasticity among the v1ijt's and the v2ijt's, general forms of

correlation among the v1ijt's and the v2ijt's for observations from the same

area and year but different industries, and general forms of correlation

between v1ijt and v2ijt for observations from the same area and year but

different industries.

III. Data

I combine payroll and employment data from County Business Patterns

(CBP) with hours worked data from the March Current Population Survey (CPS) to

estimate employment and average hourly earnings for 166 U.S. metropolitan

areas (MSAs), broken down by 37 2-digit (SIC) industries. Likewise, I combine

CBP data with CPS data to estimate U.S. employment and U.S. average hourly
13

earnings by 2-digit industry. The data run annually from 1974 through 1990,

although the effective sample runs from 1975 through 1990 because the

variables are first differenced. I convert average hourly earnings from all

years to first-quarter 1990 dollars using the national Consumer Price Index

for urban workers, though I make no adjustment for price-level differences

among metropolitan areas. Lettau (1993) describes the data set in detail.

IV. Regression results

A. MSA results

In the first set of regressions, I estimate the parameters for equations

(1) and (2), so the dependent variables are the percent change in an MSA's

total employment and the change in an MSA's average hourly earnings. MSA j's

total employment for year t equals the sum of employment across industries in

area j for year t.

(5) N.jt = ΣiNijt

MSA j's average hourly earnings for year t equals the mean of average hourly

earnings across industries in area j for year t, weighted by each industry's

employment.

 (6) W.jt = Σi(Nijt/N.jt)Wijt

As mentioned in Section I, previous studies typically use an area's total

employment and an area's average wage rate to estimate the response of an

area's employment and wage rate to a shift in labor demand. Therefore, the
14

first set of regression results are comparable to results from previous

studies. They provide the natural starting point. Table 1 shows descriptive

statistics for the variables used to estimate equations (1) and (2).

The top half of Table 2 shows parameter estimates for equations (1) and

(2) when none of the models' restrictions are imposed. The dependent variable

in column 1 is (N.jt-N.jt-1)/N.jt-1. The dependent variable in column 2 is

W.jt-W.jt-1. Year dummy variables, ZNjt, and ZWjt are the explanatory variables.

Column 3 shows the implied estimate for an area's labor supply elasticity,

which equals the coefficient estimate from the employment equation divided by

the coefficient estimate from the wage rate equation, multiplied by 10, the

approximate sample mean of W.jt. According to both the area and the

alternative models, the two labor demand instruments should give similar

estimates for the elasticity of an area's labor supply. The elasticity

estimates differ greatly however. The employment instrument gives a positive

estimate of 3.172. The wage rate instrument gives a negative estimate of

-0.096. The null hypothesis that Θ11/Θ21 equals Θ12/Θ22 is rejected with 99%

confidence. Previous studies generally use an area's employment to instrument

for shifts in the area's labor demand, so the labor supply elasticity estimate

based on the coefficient estimates for ZNjt is more comparable to estimates

reported previously. An elasticity estimate slightly above 3.0 is in line

with previous estimates, which are between 2.0 and 5.0.8

The bottom of Table 2 shows parameter estimates when I impose the

models' restrictions. I estimate ηd, ηs, and πt using nonlinear least-

 

8With ZWjt excluded as an explanatory variable, the coefficient estimates for

ZNjt give a labor supply elasticity estimate of 2.908.
15

squares.9 The estimate of ηs implies an estimate for an area's labor supply

elasticity of 1.380, about halfway between the separate estimates given by

ZNjt and ZWjt. If preference is given to ZNjt for measuring an area's labor

demand, the labor supply elasticity estimate of 3.172 corroborates results

from previous studies. However, if both labor demand instruments are assumed

equally valid in identifying an area's labor supply elasticity, the results in

Table 2 provide conflicting evidence. The coefficient estimates for ZWjt

suggest that an area's labor supply elasticity is near zero.

The estimate of ηd implies a low elasticity of labor demand for an area,

about 0.192. However, in equations (1) and (2), ηd is identified through

functional form assumptions only. No variable instruments for shifts in an

area's labor supply. Consequently, I make no inference from the estimate for

ηd in Table 2.

B. Individual Industry Results

In the second set of regressions, I estimate the parameters for

equations (3) and (4). The dependent variables are the percent change in an

industry's employment in an MSA and the change in an industry's average hourly

earnings in an MSA. Table 3 shows descriptive statistics. For 387

observations (0.5% of total observations), the average hourly earnings change

is less than -5.0 or greater than 5.0. I omit these observations as outliers.

The parameter estimates do not appear sensitive to the threshold for outliers.

Columns 1 and 2 of Table 4 show parameter estimates for equations (3)

and (4) when Θ41 and Θ42 from equation (4) are restricted to equal zero. None

of the area model's other restrictions are imposed however. The dependent

 

9The null hypothesis that the τ and Θ parameters from equations (1) and (2)

are the functions of ηd, ηs, and πt implied by the area and alternative models

is rejected with 99% confidence.
16

variable in column 1 is the percent change in an industry's employment in an

MSA. The dependent variable in column 2 is the change in an industry's

average hourly earnings in an MSA. For the equation (3), the area model

implies that the coefficient for (Ni.t-Ni.t-1)/Ni.t-1 equals 1.0, the coefficient

for Wi.t-Wi.t-1 is positive, and the coefficients for ZNjt and ZWjt are negative.

The coefficient estimate for (Ni.t-Ni.t-1)/Ni.t-1 in column 1 is fairly close to

1.0 at 0.838, and the coefficient estimate for Wi.t-Wi.t-1 is positive though

small in magnitude at 0.011. However, contrary to the area model's

prediction, the coefficient estimate for ZNjt in column 1 is positive and

statistically significant at 1.428. The area model implies that, holding

labor demand for an industry constant, an increase in an area's overall labor

demand decreases employment for the industry in the area, as panel [3] of

Figure 2 demonstrates. The size of the decrease depends on the slope of the

industry's labor demand curve. However, the positive coefficient estimate for

ZNjt suggests that, for an industry with constant labor demand, employment

increases with an increase in the area's overall labor demand rather than

decreases. Under the structure of the area model, this suggests that an

industry's labor demand curve slopes upward rather than downward. The

alternative model implies that, holding labor demand for an industry constant,

an increase in an area's overall labor demand does not affect employment for

the industry in the area, so the positive coefficient estimate for ZNjt also

contradicts the alternative model. Consistent with the area model, the

coefficient estimate for ZWjt in column 1 is negative at -0.032, though not

statistically significant.

For equation (4), the area model implies that the coefficients for ZNjt

and ZWjt are positive. Consistent with the area model's prediction, the
17

coefficient estimates for ZNjt and ZWjt in column 2 of Table 4 are positive and

statistically significant. However, they are only about a third the magnitude

of the coefficient estimates when the dependent variable is the change in an

area's average hourly earnings, shown in column 2 of Table 2. According to

the area model, the only difference between the change in an industry's wage

rate in an area and the change in an area's average wage rate is the extra

residual added to equation (4). The τ and Θ parameters in equations (2) and

(4) are the same. In other words, because an increase in an area's labor

demand increases the wage rates of all industries in the area uniformly, the

expected increase in the wage rate for an industry in an area equals the

expected increase in the area's average wage rate. Accordingly, the

coefficient estimates in column 2 of Table 4 should be similar to the

coefficient estimates in column 2 of Table 2. However, the parameter

estimates in Tables 2 and 4 imply that, with an increase in an area's labor

demand, the expected increase in the area's average hourly earnings is about

three times greater than the expected increase in the average hourly earnings

of an industry in the area. This suggests that the wage rates of all

industries in an area do not increase uniformly with an increase in the area's

labor demand.

Columns 3 and 4 of Table 4 show parameter estimates for equations (3)

and (4) under no restrictions. This specification incorporates the

predictions of both the area and the alternative models. The coefficient

estimates in column 3 differ slightly from the coefficient estimates in column

1 because I estimate equations (3) and (4) as a regression system. The

coefficient estimates for ZNjt and ZWjt in column 4 are similar to the

coefficient estimates in column 2; that is, the coefficient estimates for ZNjt
18

and ZWjt do not change much when (Ni.t-Ni.t-1)/Ni.t-1 and Wi.t-Wi.t-1 are included as

explanatory variables. Consistent with the area model and contrary to the

alternative model, the positive coefficient estimates for ZNjt and ZWjt in

column 4 suggest that, for an industry with constant labor demand, an increase

in an area's labor demand increases the industry's average hourly earnings in

the area. However, contrary to the area model and consistent with the

alternative model, the coefficient estimate for Wi.t-Wi.t-1 in column 4 is

positive and significant, which implies that Wi.t-Wi.t-1 contributes to the

expected change in industry i's average hourly earnings in area j beyond its

contribution to ZWjt. This suggests that, if an industry's labor demand

increases while labor demand for other industries in an area remains constant,

the industry's wage rate in the area will diverge from the wage rates of other

industries in the area. The joint hypothesis that Θ41 and Θ42 equal zero is

rejected against the alternative that they do not zero with 99% confidence.

Surprisingly, however, the coefficient estimate for (Ni.t-Ni.t-1)/Ni.t-1 in

column 4 is negative. The area model implies a zero coefficient while the

alternative model implies a positive coefficient, so the negative coefficient

estimate of -0.594 for (Ni.t-Ni.t-1)/Ni.t-1 contradicts both models.

The unrestricted parameter estimates in Table 4 provide some support for

the area model and some support for the alternative model, while the negative

coefficient estimate for (Ni.t-Ni.t-1)/Ni.t-1 in column (4) contradicts both

models. Nonetheless, the top half of Table 5 shows parameter estimates for

equations (3) and (4) with the area model's restrictions imposed on the τ and

Θ parameter estimates.10 The alternative model implies different

 

10The null hypothesis that the τ and Θ parameters from equations (3) and (4)

are the functions of ηd, ηs, and πt implied by the area model is rejected with

99% confidence.
19

restrictions, so the estimates for ηd, ηs, and πt in Table 5 are not valid

under the alternative model's assumptions. The estimates for ηd and ηs imply

the values for the linear coefficients in equations (3) and (4) shown in the

bottom half of the table.

Under the area model's assumptions, variation in labor demand shifts

among industries in an area identifies the slope of the area's labor demand

curve. Thus, observable variables identify ηd, rather than solely functional

form assumptions. The estimate of ηd implies that an area's elasticity of

labor demand equals 0.126. To see why the elasticity estimate is so low,

again consider the coefficient estimates in columns 1 and 2 of Table 4, where

Θ41 and Θ42 are restricted to equal zero but the area model's other

restriction are not imposed. The coefficient estimates for ZNjt and ZWjt in

the wage rate equation are positive, so an increase in an area's labor demand

increases the average hourly earnings of an industry in the area. In the

employment equation, the coefficient estimate for ZWjt is negative but small

in magnitude while the coefficient estimate for ZNjt is positive. Thus, for an

industry with constant labor demand, an increase in an area's overall labor

demand increases the industry's average hourly earnings in the area and only

slightly decreases or actually increases the industry's employment in the

area. Under the area model's structure, this translates into a very steep

slope for an industry's labor demand curve. All industries in an area are

assumed to have the same labor demand parameter ηd, so an industry's labor

demand elasticity in an area equals the area's labor demand elasticity.

Therefore, under the area model's assumptions, the results in Table 5 suggest

that an area's labor demand is very inelastic at 0.126.
20

The estimate for an area's elasticity of labor supply in Table 5 is

3.180, about twice the magnitude of the estimate from the MSA regressions in

Table 2. However, with employment and average hourly earnings broken down by

industry and metropolitan area, ηs is identified largely through functional

form assumptions. Consequently, I emphasize the labor supply elasticity

estimate in Table 2, which is valid under either the area or the alternative

model's assumptions.

C. Extensions

Equations (1) through (4) are based on the area and alternative models,

which are static and extremely simple. Therefore, in this subsection, I

modify the empirical specification of equations (3) and (4) to account for

some of the models' limitations.

1. Local Demand Spillovers

In both the area and alternative models, I assume that there is no cost

to trading a good in an area in which it is not produced. However, if a good

is costly to trade where it is not produced, the price of the good is likely

to differ among areas. Moreover, local demand for the good may be tied to the

area's employment or average wage rate, resulting in the industry's labor

demand in an area being correlated with the area's overall labor demand. For

example, output from the Eating and Drinking industry may be supplied

exclusively to the area in which it is produced. As a consequence, the change

in U.S. employment and U.S. average hourly earnings for other industries in

the area may better predict the change in Eating and Drinking's labor demand

in the area than does the change in Eating and Drinking's U.S. employment or

U.S. average hourly earnings. In terms of equation (3), v1ijt may be

correlated with ZNjt and ZWjt for industries that supply their output primarily
21

to area j. This may explain why the coefficient estimates for ZNjt in columns

1 and 3 of Table 4 are positive, contrary to either model's prediction.

To mitigate the bias, Tables 6 and 7 show parameter estimates for

equations (3) and (4) when only observations from mining and manufacturing

industries are used, on the assumption that mining and manufacturing

industries primarily supply their output to a national market, so demand for

goods produced by these industries is not tied to a single area's employment

or average wage rate. I continue to use employment and average hourly

earnings from all industries to calculate ZNjt and ZWjt.

The parameter estimates in Table 6 are fairly similar to the parameter

estimates in Table 4 however. In fact, the coefficient estimates for ZNjt in

columns 1 and 3 of Table 6 remain positive and are larger in magnitude than

the estimates in columns 1 and 3 of Table 4. Table 7 shows parameter

estimates when I impose all the area model's restrictions. The labor demand

elasticity estimate of 0.040 is even closer to zero than the labor demand

elasticity estimate in Table 5, when observations from all industries are

used.

2. Occupation Similarity of Industries

In the area model, an increase in labor demand for any industry in an

area increases the wage rate of all industries in the area equally. In the

alternative model, a change in labor demand for an industry in an area does

not affect the wage rates of other industries in the area. Reality is

probably between the two extremes. The degree to which an industry's labor

demand affects the wage rates of other industries in the area likely depends

on the degree to which the industries demand workers with similar skills.
22

Thus, I next introduce measures of the similarity of occupations between

industries into equations (3) and (4).

Rewrite equations (3) and (4) as follows. The instruments for an area's

overall labor demand are redefined to include measures of the similarity of

the occupation distribution between industries. (For clarity, I use a

subscript k rather than an italic i when summing across industries.)

(7) (Nijt-Nijt-1)/Nijt-1 = τ3t + Θ31[(Ni.t-Ni.t-1)/Ni.t-1] + Θ32(Wi.t-Wi.t-1) + Θ33ZNijt

+ Θ34ZWijt + u3ijt

(8) Wijt-Wijt-1 = τ4t + Θ41[(Ni.t-Ni.t-1)/Ni.t-1] + Θ42(Wi.t-Wi.t-1) + Θ43ZNijt

+ Θ44ZWijt + u4ijt

where: ZNijt = Σkωikjt[(Nk.t-Nk.t-1)/Nk.t-1]

 ZWijt = Σkωikjt(Wk.t-Wk.t-1)

 ωikjt = [(Nkjt-1/N.jt-1)(Sikt)α]/{Σk[(Nkjt-1/N.jt-1)(Sikt)α]}, so

Σkωikjt = 1 for all i,j,t

 Sikt = Similarity of occupation distribution between industry i and

industry k for year t

Equations (7) and (8) differ from equations (3) and (4) in that two weights

are used to calculate the change in an area's overall labor demand. In

previous regressions, the change in an area's overall labor demand equaled the

weighted average of the change in each industry's labor demand, weighted by

the industry's proportion of the area's total employment in the previous year,

shown as ZNjt and ZWjt in equations (1) through (4). In equations (7) and (8),

however, I add a second weight: (Sikt)α. Sikt measures the similarity of the

distribution of occupations between industry i and industry k for year t.

Sikt ranges from zero to one. Sikt equals zero if the two industries employ no
23

workers from the same occupation; Sikt equals one if the two industries have

the same distribution of occupations, such as when i equals k. I use March

CPS data on workers' industry and occupation to calculate Sikt for each year

and industry combination. The parameter α is estimated with the τ and θ

parameters. Section AIII of the appendix describes of how Sikt is calculated.

When α equals zero, equations (7) and (8) reduce to equations (3) and

(4). When α is greater than zero, however, ZNijt and ZWijt are labeled more

properly as instruments for labor demand in area j that is relevant to

industry i. In equations (7) and (8), the expected change in an industry's

employment and average hourly earnings given an increase in labor demand for

another industry located in the same area depends on two factors: the other

industry's proportion of the area's total employment and whether the other

industry tends to employ workers from similar occupations. Because industries

differ in the similarity of their distribution of occupations, ZNijt and ZWijt

differ among industries in an area.

 Table 8 shows parameter estimates for equations (7) and (8). The

dependent variable in column 1 is the percent change in employment for an

industry in an area. The dependent variable in column 2 is the change in the

average hourly earnings for an industry in an area. The estimate for the

occupation similarity parameter α is allowed to differ between the two

equations. For equations (7), including the occupation similarity measure has

almost no effect on the parameter estimates. The estimate for α is small in

magnitude at 0.038 and not statistically significant. The coefficient

estimates for the Θ parameters are similar to the estimates in column 3 of

Table 4. However, the estimate of α for equation (8) in column 2 is large in

magnitude at 1.081 and statistically significant, which suggests that the
24

expected change in an industry's average hourly earnings in an area given an

increase in labor demand for other industries in the area depends on the

similarity of the industries' distribution of occupations.

Table 9 shows descriptive statistics for (Sikt)α evaluated at the two

estimates of α. The estimate of α from the employment equation is close to

zero, so (Sikt)α is estimated to be close to one regardless of the value of

Sikt. However, (Sikt)α evaluated at the estimate of α from the wage rate

equation takes on a much wider range of values. Consider the following

example. The maximum value of Sikt across all years and industry combinations

(when k does not equal i) is 0.965 for Electrical Machinery/Industrial

Machinery in 1990. The value of Sikt for Electrical Machinery/Education in

1990 is 0.501, which is near the median across all years and industries.

Under the specification in equation (8), the estimate of 1.081 for α implies

that an increase in labor demand for Electrical Machinery in area j has about

twice the effect on the average hourly earnings of Industrial Machinery

workers in area j as on Education workers in area j; that is,

(0.965/0.501)1.081 = 2.031. Conversely, the estimate of 0.038 for α from the

employment equation suggests that an increase in labor demand for Electrical

Machinery in area j has about the same effect on employment for Industrial

Machinery workers in area j as on employment of Education workers in area j;

that is, (0.965/0.501)0.038 = 1.025.

Considering the results from previous regressions, the discrepancy

between the two estimates for α is not surprising. Previous results suggest

that there is little or no tendency for employment of an industry with

constant labor demand to decrease with an increase with an area's overall

labor demand, even though the industry's average hourly earnings tends to
25

increase. Therefore, it is not surprising that the effect of an increase in

an industry's labor demand on another industry's employment in an area is not

related to the similarity of the two industries' distribution of occupations,

whereas the effect on the other industry's average hourly earnings is related

to the similarity of the two industries' distributions of occupations.11

3. Lagged Adjustment

Eberts and Stone (1992) and Blanchard and Katz (1992) find that,

although both an area's total employment and average wage rate increase with

an increase in the area's labor demand, the increase is not simultaneous. The

increase in an area's total employment tends to peak a few years before the

increase in an area's average wage rate peaks. The regression results so far

consider only contemporaneous relations between the dependent variables and

the labor demand instruments.

In Tables 10 and 11, I add two lagged values of the labor demand

instruments to the MSA and the Individual Industry regressions. The sample

runs from 1977 to 1990. For comparison, columns 1 and 2 of the tables show

regression results for the same period but with the lagged labor demand

instruments excluded. A full interpretation of the coefficient estimates for

the lagged instruments requires a dynamic model of areas' labor markets, which

is beyond this paper. Rather, I include these results to examine whether

significant comovement between the dependent variables and the labor demand

instruments is missed by looking only at contemporaneous relations.

 

11The residual standard deviations (the standard deviation of the residuals

from regressions on year dummy variables) of ZNijt and ZWijt from equation (8)

are 58% and 36% higher than the residual standard deviations of ZNjt and ZWjt

from equation (4). Consequently, the magnitude of the coefficient estimates

for ZNijt and ZWijt in column 2 of Table 8 are not directly comparable to the

magnitude of the coefficient estimates for ZNjt and ZWjt in column 4 of Table

4.
26

In general, in both Tables 10 and 11, the coefficient estimates for the

lagged labor demand instruments are either not statistically significant or

statistically significant but small in magnitude compared to the coefficient

estimates for the contemporaneous labor demand instruments. That is,

contemporaneous labor demand instruments appear to pick up most of the

comovement between the dependent variables and the labor demand instruments.

However, notable exceptions are the coefficient estimates for lagged values of

ZWjt (the area labor demand instrument based on U.S. industries' average

hourly earnings), particularly when the dependent variable is either the

percent change in an MSA's total employment or the percent change in an

industry's employment in an MSA. In column 1 of both Tables 10 and 11, the

coefficient estimate for ZWjt is not statistically significant. In column 3

of Tables 10 and 11, however, the coefficient estimates for ZWjt, ZWjt-1, and

ZWjt-2 are negative, statistically significant, and larger in magnitude than

the coefficient estimate for ZWjt in column 1.

The similarity between the coefficient estimates in column 3 of Tables

10 and 11 contradicts the prediction of the area model. The negative

coefficient estimates for ZWjt, ZWjt-1, and ZWjt-2 in column 3 of Table 11 are

consistent with the area model's prediction that the coefficient for ZWjt is

negative. Moreover, they contradict the conclusion, based on the results in

Tables 4 and 5, that competition for labor among industries in an area does

not decrease employment for an industry with constant labor demand. However,

the coefficient estimate for ZNjt in column 3 of Table 11 remains positive, as

are the coefficient estimates ZNjt-1 and ZNjt-2. Also, the area model predicts a

positive coefficient for ZWjt in equation (2). Therefore, the negative

coefficient estimates for ZWjt, ZWjt-1, and ZWjt-2 in column 3 of Table 10 are
27

not consistent with ZWjt, ZWjt-1, and ZWjt-2 instrumenting for an area's labor

demand.

V. Summary

This paper extends the empirical literature on the response of an area's

labor market to a shift in labor demand by exploring heterogeneity within an

area's labor market. Two contrary models, which Figures 2 and 3 demonstrate,

provide the framework for the paper's empirical results. In the area model,

labor demand conditions from all industries in an area jointly determine the

area's wage rate and each industry's employment. Conversely, in the

alternative model, an industry's employment and wage rate in an area are not

affected by labor demand for other industries located in the same area. I

estimate the models' parameters using employment and average hourly earnings

for 166 U.S. metropolitan areas, disaggregated by 37 industries.

I present two sets of regression results. In the first set, the unit of

observation is an MSA. In the second set, the unit of observation is an

industry in an MSA. From the first set of regressions, the labor demand

instrument based on industries' U.S. employment implies that an area's

elasticity of labor supply is slightly above 3.0, which corroborates estimates

from previous research. However, the labor demand instrument based on

industries' U.S. average hourly earnings implies that an area's elasticity of

labor supply is near zero.

Results from the second set of regressions follow neither the area model

nor the alternative model completely. Consistent with the area model, the

parameter estimates suggest that an increase in an area's overall labor demand

increases the average hourly earnings of an industry with constant labor
28

demand located in the area. Consistent with the alternative model, however,

the results also suggest that all industries' average hourly earnings in an

area do not increase uniformly with an increase in the area's overall labor

demand. Moreover, extending the regressions to include measures of the

similarity of occupations between industries suggests that the magnitude of

the increase in an industry's average hourly earnings, given an increase in

labor demand for other industries located in the same area, is larger the more

similar the industries' distributions of occupations.

The results also suggest that, for an industry with constant labor

demand, an increase in an area's overall labor demand only slightly decreases

or actually increases the industry's employment in the area, even though the

increase in the area's overall labor demand increases the industry's average

hourly earnings. Under the area model's structure, this translates into a

very inelastic estimate of 0.124 for an area's labor demand elasticity. In

other words, there is little evidence that competition for labor among

industries in an area causes a stagnant industry in the area to reduce its

employment,12 even though the stagnant industry tends to increase its wage

rate. A caveat to this conclusion, however, is that the evidence is more

conflicting when the regressions are extended to include lagged values of the

labor demand instruments. Contemporaneous and lagged instruments for an

area's overall labor demand based on industries' U.S. average hourly earnings

suggest that employment for an industry with constant labor demand does

decrease with an increase in the area's overall labor demand, although

 

12Gleaser et al. (1992) find that growth in a U.S. city's four largest

industries between 1956 and 1987 had a positive effect on growth in the city's

employment between 1956 and 1987 outside the city's four largest industries.

They interpet this result as support for urbanization externalities and

aggregate demand spillovers among industries in an city and against the

crowding out of industries from a city.
29

contemporaneous and lagged instruments for an area's overall labor demand

based on industries' U.S. employment continue to suggest that employment for

an industry with constant labor demand increases with an increase in the

area's overall labor demand.
30

References

Bartik, Timothy J. Who Benefits from State and Local Economic

Development Policies? W.E. Upjohn Institute, 1991.

Blanchard, Olivier J. and Lawrence F. Katz. "Regional Evolutions." Brookings

Papers on Economic Activity, no. 1, 1992: 1-75.

Chamberlain, Gary. "Multivariate Regression Models for Panel Data." Journal

of Econometrics, vol. 18 no. 1, January 1982: 5-46.

Duncan, Otis D. and Beverly Duncan. "A Methodological Analysis of Segregation

Indexes." American Sociological Review, vol. 20 no. 2, April 1955:

210-217.

Eberts, Randall W. and Joe A. Stone. Wage and Employment Adjustment in Local

Labor Markets. W.E. Upjohn Institute, 1992.

Employment and Earnings, vol. 36 no. 5. U.S. Department of Labor, Bureau of

Labor Statistics, Washington, DC: May 1989.

Glaeser, Edward L., Hedi D. Kallal, Jose A. Scheinkman, and Andrei Shleifer.

"Growth in Cities." Journal of Political Economy, vol. 100 no. 6,

December 1992: 1126-1152.

Goldberger, Arthur S. A Course in Econometrics. Harvard University Press,

Cambridge, MA: 1991.

Krueger, Alan B. and Lawrence H. Summers. "Efficiency Wages and the InterIndustry Wage Structure." Econometrica, vol. 56 no. 2, March 1988:

259-293.

Lettau, Michael K. "Regional Variation in Labor Market Outcomes:

Compensating Differences, Industry Location, and Wage Adjustment."

Unpublished Doctoral Thesis, University of Wisconsin-Madison, October

1993.

Roback, Jennifer. "Wages, Rents, and the Quality of Life." Journal of

Political Economy, vol. 90 no. 6, December 1982: 1257-1278.

Rosen, Sherwin. "Wage-based Indexes of Urban Quality of Life," in Current

Issues in Urban Economics, Mieszkowski and Straszheim eds., 1979: 74-

104.

Topel, Robert. "Local Labor Markets." Journal of Political Economy, vol. 94

no. 3 pt. 2, 1986: S111-S143.

White, Halbert. "A Heteroskedasticity-Consistent Covariance Matrix

Estimator and a Direct Test for Heteroskedasticity."

Econometrica, vol. 48 no. 4, May 1980: 817-838.
Table 1

Descriptive Statistics for Variables used in MSA Regressions,

Data from County Business Patterns and the CPS, 1974-90

______________________________________________________________________________

Number of

Observations Mean

Standard

Deviation Minimum Maximum

 _____________________________________________________________

N.jt 2,656 355,524 462,204 31,258 3,745,160

W.jt 2,656 10.075 1.324 6.303 16.911

(N.jt-N.jt-1)/N.jt-1 2,656 0.029 0.050 -0.256 0.251

W.jt-W.jt-1 2,656 -0.066 0.343 -3.820 2.064

ZNjt 2,656 0.026 0.032 -0.086 0.096

ZWjt 2,656 -0.026 0.153 -0.438 0.470

Deviation from year mean

(N.jt-N.jt-1)/N.jt-1 2,656 0.000 0.038 -0.300 0.269

W.jt-W.jt-1 2,656 0.000 0.325 -3.726 2.270

ZNjt 2,656 0.000 0.006 -0.048 0.030

ZWjt 2,656 0.000 0.041 -0.438 0.258

______________________________________________________________________________

Notes: The subscript j indexes for MSAs, and t indexes for years. The unit

of observation is an MSA. Variables under the heading "deviation from year

mean" are residuals from a regression on year dummy variables.
Table 2

Parameter Estimates from MSA Regressions,

Data from County Business Patterns and the CPS, 1974-90

________________________________________________________________________

 [1] [2] [3]

________________________________________________________________________

Linear coefficient estimates

(N.jt-N.jt-1)/N.jt-1 W.jt-W.jt-1

Labor Supply

 Elasticity

________________ _________ ____________

ZNjt 1.982 ** 6.249 ** 3.172 **

 (0.134) (1.105) (0.580)

ZWjt -0.018 1.911 ** -0.096

 (0.022) (0.191) (0.116)

Year dummies included yes yes

R2 0.48 0.17

Observations 2,656 2,656

Parameter estimates under restrictions of the area or alternative model

Labor demand elasticity: ηd x 10 0.192 **

 (0.091)

Labor supply elasticity: ηS x 10 1.380 **

 (0.300)

πt estimated yes

Observations 2,656

________________________________________________________________________

Notes: Asymptotic standard errors are in parentheses; ** indicates

significance at 5%. The subscript j indexes for MSAs, and t indexes for

years. The unit of observation is an MSA.
Table 3

Descriptive Statistics for Variables used in Individual Industry Regressions,

Data from County Business Patterns and the CPS, 1974-90

______________________________________________________________________________

Number of

Observations Mean

Standard

Deviation Minimum Maximum

 _____________________________________________________________

Nijt 77,036 11,006 25,416 3 578,409

Wijt 77,036 10.064 3.307 1.953 37.630

(Nijt-Nijt-1)/Nijt-1 77,036 0.036 0.186 -0.912 8.236

Wijt-Wijt-1 77,036 -0.045 0.911 -4.983 4.996

(Ni.t-Ni.t-1)/Ni.t-1 77,036 0.019 0.054 -0.288 0.274

Wi.t-Wi.t-1 77,036 -0.030 0.397 -1.899 2.002

ZNjt 77,036 0.026 0.032 -0.086 0.096

ZWjt 77,036 -0.026 0.153 -0.438 0.470

Deviation from year mean

(N.jt-N.jt-1)/N.jt-1 77,036 0.000 0.183 -0.949 8.206

W.jt-W.jt-1 77,036 0.000 0.901 -5.196 5.224

(Ni.t-Ni.t-1)/Ni.t-1 77,036 0.000 0.043 -0.333 0.323

Wi.t-Wi.t-1 77,036 0.000 0.363 -1.710 2.035

ZNjt 77,036 0.000 0.006 -0.048 0.030

ZWjt 77,036 0.000 0.040 -0.438 0.259

______________________________________________________________________________

Notes: The subscript j indexes for MSAs, i indexes for industries, and t

indexes for years. The unit of observation is an industry in an MSA.

Variables under the heading "deviation from year mean" are residuals from a

regression on year dummy variables.
Table 4

Parameter Estimates from Individual Industry Regressions,

Data from County Business Patterns and the CPS, 1974-90

______________________________________________________________________________

 [1] [2] [3] [4]

______________________________________________________________________________

Linear coefficient estimates

(Nijt-Nijt-1)/Nijt-1 Wijt-Wijt-1 (Nijt-Nijt-1)/Nijt-1 Wijt-Wijt-1

________________ ________ ________________ _________

(Ni.t-Ni.t-1)/Ni.t-1 0.838 ** -- 0.850 ** -0.594 **

 (0.018) (0.018) (0.091)

Wi.t-Wi.t-1 0.011 ** -- -0.001 0.566 **

 (0.002) (0.002) (0.011)

ZNjt 1.428 ** 2.252 ** 1.430 ** 2.199 **

 (0.142) (0.588) (0.142) (0.586)

ZWjt -0.032 0.636 ** -0.032 0.617 **

 (0.026) (0.092) (0.026) (0.091)

Year dummies included yes yes yes yes

R2 -- -- 0.08 0.07

Observations 77,036 77,036 77,036 77,036

______________________________________________________________________________

Notes: Asymptotic standard errors in parentheses; ** indicates significance

at 5%. The subscript j indexes for MSAs, i indexes for industries, and t

indexes for years. The unit of observation is an industry in an MSA.
Table 5

Parameter Estimates from Individual Industry Regressions,

Data from County Business Patterns and the CPS, 1974-90

________________________________________________________________________

Parameter estimates under restrictions of the area model

Labor demand elasticity: ηd x 10 0.126 **

 (0.020)

Labor supply elasticity: ηs x 10 3.180 **

 (0.674)

πt estimated yes

Observations 77,036

Linear coefficients implied by parameter estimates

(Nijt-Nijt-1)/Nijt-1 Wijt-Wijt-1

________________ ________

(Ni.t-Ni.t-1)/Ni.t-1 1.000 0.000

Wi.t-Wi.t-1 0.013 0.000

ZNjt -0.038 3.025

ZWjt -0.000 0.038

________________________________________________________________________

Notes: Asymptotic standard errors are in parentheses; ** indicates

significance at 5%. The subscript j indexes for MSAs, i indexes for

industries, and t indexes for years. The unit of observation is an industry

in an MSA.
Table 6

Parameter Estimates from Individual Industry Regressions,

Data from County Business Patterns and the CPS, 1974-90,

Mining and Manufacturing Industries Only

______________________________________________________________________________

 [1] [2] [3] [4]

______________________________________________________________________________

Linear coefficient estimates

(Nijt-Nijt-1)/Nijt-1 Wijt-Wijt-1 (Nijt-Nijt-1)/Nijt-1 Wijt-Wijt-1

________________ ________ ________________ _________

(Ni.t-Ni.t-1)/Ni.t-1 0.862 ** -- 0.879 ** -0.862 **

 (0.035) (0.035) (0.173)

Wi.t-Wi.t-1 0.004 -- -0.004 0.468 **

 (0.004) (0.004) (0.021)

ZNjt 2.081 ** 1.498 2.081 ** 1.488

 (0.239) (1.107) (0.239) (1.104)

ZWjt -0.057 1.033 ** -0.056 0.968 **

 (0.042) (0.173) (0.042) (0.171)

Year dummies included yes yes yes yes

R2 -- -- 0.07 0.04

Observations 34,855 34,855 34,855 34,855

______________________________________________________________________________

Notes: Asymptotic standard errors in parentheses; ** indicates significance

at 5%. The subscript j indexes for MSAs, i indexes for industries, and t

indexes for years. The unit of observation is an industry in an MSA.
Table 7

Parameter Estimates from Individual Industry Regressions,

Data from County Business Patterns and the CPS, 1974-90,

Mining and Manufacturing Industries Only

________________________________________________________________________

Parameter estimates under restrictions of the area model

Labor demand elasticity: ηd x 10 0.040

 (0.035)

Labor supply elasticity: ηs x 10 3.722 **

 (1.647)

πt estimated yes

Observations 34,855

Linear coefficients implied by parameter estimates

(Nijt-Nijt-1)/Nijt-1 Wijt-Wijt-1

________________ ________

(Ni.t-Ni.t-1)/Ni.t-1 1.000 0.000

Wi.t-Wi.t-1 0.004 0.000

ZNjt -0.011 2.658

ZWjt -0.000 0.011

________________________________________________________________________

Notes: Asymptotic standard errors are in parentheses; ** indicates

significance at 5%. The subscript j indexes for MSAs, i indexes for

industries, and t indexes for years. The unit of observation is an industry

in an MSA.
Table 8

Parameter Estimates from Individual Industry Regressions,

Data from County Business Patterns and the CPS, 1974-90,

Measure of Occupation Similarity Included

______________________________________________________________________________

 [1] [2]

______________________________________________________________________________

Linear coefficient estimates

(Nijt-Nijt-1)/Nijt-1 Wijt-Wijt-1

________________ _________

(Ni.t-Ni.t-1)/Ni.t-1 0.846 ** -0.768 **

 (0.024) (0.113)

Wi.t-Wi.t-1 -0.001 0.540 **

 (0.002) (0.014)

ZNijt 1.424 ** 1.723 **

 (0.142) (0.458)

ZWijt -0.032 0.583 **

 (0.026) (0.085)

Occupation Similarity 0.038 1.081 **

Parameter: α (0.094) (0.209)

Year dummies included yes yes

R2 0.08 0.07

Observations 77,036 77,036

______________________________________________________________________________

Notes: Asymptotic standard errors in parentheses; ** indicates significance

at 5%. The subscript j indexes for MSAs, i indexes for industries, and t

indexes for years. The unit of observation is an industry in an MSA.
Table 9

Descriptive Statistics for Occupation Similarity Measure,

using Results from Individual Industry Regressions,

Data from County Business Patterns and the CPS, 1974-90

______________________________________________________________________________

 ^ ^

 (Sikt)α

 from (Sikt)α

 from

 employment avg. hourly

 equation, earnings equation,

 ^ ^ (α = 0.038) (α = 1.081)

______________________________________________________________________________

No. of Obs. 11,248 11,248

Mean 0.973 0.514

Std 0.017 0.229

Quartiles

 Min 0.902 0.054 Eating & Drinking/Social Services, 1975

 25th 0.916 0.332 Hotels/Tobacco, 1985

 Median 0.974 0.480 Construction/Elec. Machinery, 1989

 75th 0.987 0.685 Elec. Machinery/Primary Metals, 1979

 Max (<1) 0.999 0.962 Elec. Machinery/Ind. Machinery, 1990

CDF  ---

 Cumulative Distribution Functions

x

F(x)

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

______________________________________________________________________________

Notes: Sikt calculated using CPS data from 1975 through 1990. Statistics are

for all years pooled together.
Table 10

Parameter Estimates from MSA regressions,

Data from County Business Patterns and the CPS, 1974-90

______________________________________________________________________________

 [1] [2] [3] [4]

______________________________________________________________________________

(Nijt-Nijt-1)/Nijt-1 Wijt-Wijt-1 (Nijt-Nijt-1)/Nijt-1 Wijt-Wijt-1

________________ ________ ________________ _________

ZNjt 2.098 ** 6.969 ** 1.824 ** 8.185 **

 (0.140) (1.314) (0.174) (1.751)

ZNjt-1 -- -- 0.177 -3.547 *

 (0.159) (1.814)

ZNjt-2 -- -- 0.313 ** 1.456

 (0.133) (1.445)

ZWjt -0.030 1.840 ** -0.037 * 1.861 **

 (0.023) (0.205) (0.022) (0.205)

ZWjt-1 -- -- -0.052 ** 0.450 **

 (0.026) (0.187)

ZWjt-2 -- -- -0.050 ** -0.428 *

 (0.019) (0.223)

Year dummies included yes yes yes yes

R2 0.45 0.18 0.46 0.19

Observations 2,324 2,324 2,324 2,324

______________________________________________________________________________

Notes: Asymptotic standard errors in parentheses; * indicates significance at

10%, ** indicates significance at 5%. The subscript j indexes for MSAs and t

indexes for years. The unit of observation is an MSA.
Table 11

Parameter Estimates from Individual Industry Regressions,

Data from County Business Patterns and the CPS, 1974-90

______________________________________________________________________________

 [1] [2] [3] [4]

______________________________________________________________________________

(Nijt-Nijt-1)/Nijt-1 Wijt-Wijt-1 (Nijt-Nijt-1)/Nijt-1 Wijt-Wijt-1

________________ ________ ________________ _________

(Ni.t-Ni.t-1)/Ni.t-1 0.839 ** -0.417 ** 0.868 ** -0.508 **

 (0.019) (0.106) (0.023) (0.121)

(Ni.t-1-Ni.t-2)/Ni.t-2 -- -- 0.002 0.137

 (0.024) (0.119)

(Ni.t-2-Ni.t-3)/Ni.t-3 -- -- -0.077 ** 0.131

 (0.020) (0.098)

Wi.t-Wi.t-1 -0.002 0.540 ** -0.001 0.539 **

 (0.002) (0.012) (0.002) (0.012)

Wi.t-1-Wi.t-2 -- -- 0.001 0.013

 (0.002) (0.011)

Wi.t-2-Wi.t-3 -- -- 0.003 * 0.004

 (0.002) (0.011)

ZNjt 1.471 ** 2.622 ** 1.189 ** 3.106 **

 (0.157) (0.647) (0.178) (0.743)

ZNjt-1 -- -- 0.401 ** -0.678

 (0.148) (0.671)

ZNjt-2 -- -- 0.110 0.040

 (0.111) (0.513)

ZWjt -0.035 0.596 ** -0.046 * 0.623 **

 (0.026) (0.097) (0.025) (0.098)

ZWjt-1 -- -- -0.039 * 0.247 **

 (0.021) (0.087)

ZWjt-2 -- -- -0.063 ** 0.168 **

 (0.017) (0.085)

Year dummies included yes yes yes yes

R2 0.07 0.07 0.07 0.07

Observations 66,190 66,190 66,190 66,190

______________________________________________________________________________

Notes: Asymptotic standard errors in parentheses; * indicates significance at

10%, ** indicates significance at 5%. The subscript j indexes for MSAs, i

indexes for industries, and t indexes for years. The unit of observation is

an industry in an MSA.
Appendix

AI. Notation

In this paper, employment and wage rates are disaggregated by industry

and area. The subscript i indexes for industries and j indexes for areas.

For example, Nij equals employment for industry i in area j. When employment

or wage rates are aggregated across industries or areas, the corresponding

subscript is replaced by an italic subscript in the summation and a .

subscript in the sum. For example, the sum of employment across industries in

area j is expressed as N.j = ΣiNij. I drop the . subscript, however, when I

assume explicitly that the aggregate quantity is the same in all industries or

areas. For example, when all industries in area j are assumed to pay the same

wage rate, Wj equals the wage rate in area j. When all industries in area j

are not assumed to pay the same wage rate, Wij equals the wage rate for

industry i in area j and W.j equals the average wage rate in area j.

AII. Models of an Area's Labor Market

A. Area Model

1. Labor Demand

Let metropolitan areas contain a positive number of firms from

industries i = 1 ... I. Metropolitan areas are indexed by j = 1 ... J. The

number of industries is finite while the number of areas approaches infinity.

Within an industry, firms are homogeneous, so technology is the same for firms

from the same industry regardless of where they are located. Each industry

produces one good, so i indexes for goods as well as for industries. Goods

are traded without cost, so the price of each good is the same in all areas.

Assume that firms are fixed in their location and that factors of

production other than labor are fixed in the short run. The short-run

production function for a firm from industry i in area j has a quadratic form.

(A1) xij = φinij - (2ηd)-1nij

2, ηd > 0.

where: xij = output for a firm from industry i in area j

 nij = employment for a firm from industry i in area j
I treat φi as a random variable with a mean equal to φ0, φ0 > 0; φi accounts

for labor demand conditions specific to firms from industry i. The labor

demand parameter ηd applies to firms from all industries and areas.

Assume that workers are homogeneous and can move among firms and

industries without cost, so firms from all industries in an area pay the same

wage rate. Setting the marginal product of labor equal to a firm's product

wage rate gives the labor demand curve for a firm from industry i in area j.

(A2) nij = ηdφi - ηd(Wj/Pi)

where: Wj = wage rate in area j

 Pi = price of good i.

Labor demand for industry i in area j equals the number of firms from industry

i in area j multiplied by labor demand for a firm from industry i in area j.

(A3) Nij = qijnij

 = ηdqijφi - ηdqij(Wj/Pi)

where: Nij = employment for industry i in area j

 qij = number of firms from industry i in area j

The number of firms from industry i in area j is assumed to be uncorrelated

with the random variable φi.

Labor demand in area j equals the sum of Nij across industries.

(A4) N.j = ΣiNij

 = ηdΣiqijφi - ηdWjΣiqij(1/Pi)

where: N.j = employment in area j

2. Labor Supply
Consider individual m living in area j. The individual maximizes

utility by choosing how much of each good to consume and whether or not to

work. Assume that individual m's utility function has the following form.

(A5) Um = ΣiCim - ψmDm

where: Um = utility for individual m

 Cim = individual m's consumption of good i

 Dm = 1 if individual m works, 0 otherwise.

Utility is linear in all goods. Individuals value all goods equally.

Individual m's disutility from working equals ψm. The individual maximizes

equation (A5) subject to his or her budget constraint.

(A6) Max Um s.t. ΣiPiCim = Ym + WjDm

where: Ym = individual m's non labor income

Because utility is linear in all goods, each good's demand curve is perfectly

elastic. A change in a good's production function does not affect the good's

price; preferences alone determine the price of each good. Individuals value

all goods equally, so the price of each good can be set equal to one.

Individual m from area j works if Wj is greater than ψm. Labor supply

for area j equals the number of individuals who choose to work at a given

value of Wj. Assume that, among individuals in area j, ψm follows a uniform

distribution between νj and b+νj. The random variable νj accounts for labor

supply conditions that are specific to area j. Let the mean of νj equal ν0,

ν0>0. Assume that νj is uncorrelated across areas, and assume that νj is

uncorrelated with the number of firms from industry i in area j.

Define Lj as the number of individuals living in area j, and assume that

Lj is large for all j. Labor supply in area j equals the following.

(A7) N.j = LjPr[Dm=1]

 = (1/b)LjWj - (1/b)Ljνj
3. Equilibrium

Area j's equilibrium wage rate is found by setting area j's labor demand

equal to area j's labor supply. Define q.j as the total number of firms in

area j.

(A8) q.j = Σiqij

where: q.j = Number of firms in area j

To simplify the model's solution, assume that firms and individuals are

allocated to areas such that the ratio of the number of firms in an area to

the number of individuals living in the area is the same for all areas. That

is, assume q.j/Lj equals a constant λ for all j. Factors of production other

than labor are fixed, so the number of firms in an area proxies for the

quantity of an area's non-labor factors of production. Thus, I assume that

the ratio of an area's non labor factors of production to the area's

population is the same for all areas. Setting equation (A7) equal to equation

(A4) gives the wage rate for area j.

(A9) Wj = [ηd/(ηd+ηs)]Σi(qij/q.j)φi + [ηs/(ηd+ηs)]νj

where: ηs = (λb)-1

In equation (A4), the slope of an area's labor demand curve, ηdq.j, depends on

the total number of firms in area j. Similarly, in equation (A7), the slope

of an area's labor supply curve, (1/b)Lj, depends on the number of individuals

living in area j. However, with the assumption that q.j/Lj equals λ in all

areas, the rescaled labor supply parameter ηs is constant across areas.

The average value of φi across firms, Σi(qij/q.j)φi, determines area j's

wage rate. Plugging the wage rate from equation (A9) into equation (A4) gives

employment for area j, expressed in equation (A10) as a ratio to the number of

firms in area j.

(A10) N.j/q.j = [ηdηs/(ηd+ηs)]Σi(qij/q.j)φi - [ηdηs/(ηd+ηs)]νj
All firms in area j pay the same wage rate, so the solution for Wj gives

employment for industry i in area j, expressed in equation (A11) as a ratio to

the number of firms from industry i in area j.

(A11) Nij/qij = ηdφi - ηd[ηd/(ηd+ηs)]Σi(qij/q.j)φi - [ηdηs/(ηd+ηs)]νj

The results in equations (A9), (A10), and (A11) match the intuition from

Figure 2. Average labor demand among industries in an area determines the

area's wage rate and total employment. A combination of an industry's labor

demand and average labor demand among industries in an area determines

employment for the industry in the area.

Aggregate employment for industry i equals the sum of employment in

industry i across areas.

(A12) Ni. = ΣjNij

where: Ni. = employment for industry i

Define qi. as the total number of firms from industry i.

(A13) qi. = Σjqij

The number of areas is assumed to approach infinity. Assume further that the

number of firms for an industry in any one area is small relative to total

number of the firms for the industry. More formally, assume that Σj(qij/qi.)2

approaches zero as the number of areas approaches infinity for all i. Then,

from equation (A11), aggregate employment for industry i equals the following,

expressed as a ratio to the number of firms from industry i.

(A14) Ni./qi. = ηdφi - ηd[ηd/(ηd+ηs)]Σj(qij/qi.)[Σi(qij/q.j)φi] - [ηdηs/(ηd+ηs)]ν0

For all industries, Σj(qij/qi.)νj equals ν0. However, because the number of

industries is finite, Σj(qij/qi.)[Σi(qij/q.j)φi] will not equal φ0. Let Wi.

equal the average wage across firms from industry i.
(A15) Wi. = [ηd/(ηd+ηs)]Σj(qij/qi.)[Σi(qij/q.j)φi] + [ηs/(ηd+ηs)]ν0

Equations (A14) and (A15) imply the following.

(A16) φi = (ηd)-1(Ni./qi.) + Wi.

Under the model's assumptions, an industry's labor demand shock φi can be

expressed as a linear function of Ni./qi. and Wi.. Thus, for the empirical

work in Section IV, an industry's U.S. employment and U.S. average hourly

earnings instrument for the industry's labor demand in a metropolitan area.

4. Empirical Specification

To estimate the area model's parameters, structure must be placed on the

time paths of technology (labor demand) and preferences (labor supply). For

the area model, replace φi from equation (A1) with φijt, where t indexes for

time periods. Assume that φijt-φijt-1 is the sum of three random variables;

(A17) φijt-φijt-1 = εt + εit + εijt

εt is common to all industries in all areas, εit is common to an industry in

all areas, and εijt is unique to an industry in an area. To identify the

model's parameters, assume the expected value of εijt is zero and that εijt is

uncorrelated with εt and εit for all i, j, and t. Also, assume there is no

correlation among the εijt's for observations from different areas or for

observations from the same area but different time periods. The εijt's may be

correlated for observations from the same area and time period but different

industries.

Replace νj from equation (A7) with νjt, where νjt-νjt-1 is the sum of two

random variables;

(A18) νjt-νjt-1 = πt + πjt

πt is common to all areas, while πjt is unique to an area. Assume the expected

value of πjt is zero and that πjt is uncorrelated with πt for all j. Also

assume that there is no correlation among the πjt's.
With the assumptions in equations (A17) and (A18), plus the results from

equations (A10), (A9), (A11), and (A16), the area model implies the following.

(A19)(N.jt-N.jt-1)/q.j = -[ηdηs/(ηd+ηs)]πt + [ηs/(ηd+ηs)]Σi(qij/q.j)[(Ni.t-Ni.t-1)/qi.]

+ [ηdηs/(ηd+ηs)]Σi(qij/q.j)(Wi.t-Wi.t-1) + u1.jt

where: u1.jt = [ηdηs/(ηd+ηs)]Σi(qij/q.j)εijt - [ηdηs/(ηd+ηs)]πjt

(A20) Wjt-Wjt-1 = [ηs/(ηd+ηs)]πt + [1/(ηd+ηs)]Σi(qij/q.j)[(Ni.t-Ni.t-1)/qi.]

+ [ηd/(ηd+ηs)]Σi(qij/q.j)(Wi.t-Wi.t-1) + u2jt

where: u2jt = [ηd/(ηd+ηs)]Σi(qij/q.j)εijt + [ηs/(ηd+ηs)]πjt

(A21) (Nijt-Nijt-1)/qij = -[ηdηs/(ηd+ηs)]πt + (Ni.t-Ni.t-1)/qi. + ηd(Wi.t-Wi.t-1)

- [ηd/(ηd+ηs)]Σi(qij/q.j)[(Ni.t-Ni.t-1)/qi.] -

ηd[ηd/(ηd+ηs)]Σi(qij/q.j)(Wi.t-Wi.t-1) + u1ijt

where: u1ijt = ηdεijt - ηd[ηd/(ηd+ηs)]Σi(qij/q.j)εijt - [ηdηs/(ηd+ηs)]πjt

Also, for estimation, I relax the area model's restriction that all industries

in an area pay the same wage rate by adding a second residual to equation

(A20).

(A22) Wijt-Wijt-1 = [ηs/(ηd+ηs)]πt + [1/(ηd+ηs)]Σi(qij/q.j)[(Ni.t-Ni.t-1)/qi.]

+ [ηd/(ηd+ηs)]Σi(qij/q.j)(Wi.t-Wi.t-1) + (u2ijt+ξijt)

Assume the expected value of ξijt is zero and that there is no correlation

among the ξijt's for observations from different areas or for observations from

the same area but different time periods. The ξijt's may be correlated for

observations from the same area and time period but different industries.

 In equations (A19) through (A22), I scale employment changes by the

number of firms in the industry and/or the area. For the empirical work,

however, I divide the change in employment by the previous period's employment

rather than by the number of firms; that is, I use (Nijt-Nijt-1)/Nijt-1 rather

than (Nijt-Nijt-1)/qij, etc. Scaling employment changes by the previous period's

employment has at least two advantages. First, the model is not rich enough

to explain variation in the average size of firms across industries. Scaling

employment changes by the previous period's employment rather than by the
number of firms abstracts from differences in average firm size among

industries and areas. Second, because employment changes are expressed in

percent terms, the models' parameters become semi-elasticities. Consequently,

ηs multiplied by an area's wage rate equals the area's elasticity of labor

supply, and ηd multiplied by an area's wage rate equals the area's elasticity

of labor demand. Moreover, because ηd is constant across industries, ηd

multiplied by an industry's wage rate in an area equals the elasticity of

labor demand for the industry in the area. I also replace Σi(qij/q.j)(⋅) with

Σi(Nijt-1/N.jt-1)(⋅).

Equations (A19) through (A22) are rewritten in a more general form as

equations (1) through (4) in Section II, with employment changes are scaled by

the previous period's employment.

B. Alternative Model

The setup for the alternative model is much the same as the setup for

the area model. However, I assume additionally that industry-specific human

capital ties an individual to a particular industry, so wage rates may vary

among industries in an area.

1. Labor Demand

The labor demand setup for the alternative model is the same as for the

area model. Labor demand for industry i in area j equals the following.

(A23) Nij = ηdqijφi - ηdqij(Wij/Pi)

where: Wij = wage rate for industry i in area j

2. Labor Supply

Individual m's utility function again has the following form.

(A24) Um = ΣiCim - ψmDm

The individual maximizes equation (A24) subject to his or her budget

constraint.

(A25) Max Um s.t. ΣiPiCim = Ym + WijDm
Individual m from area j works in industry i if Wij is greater than ψm.

Labor supply for industry i in area j equals the number of individuals who

choose to work at a given value of Wij. Assume that, among individuals in

area j tied to industry i, ψm follows a uniform distribution between νij and

b+νij. The random variable νij accounts for labor supply conditions that are

specific to industry i in area j. Let the mean of νij equal ν0, ν0>0, and

assume that νij is uncorrelated for industry/area combinations from different

areas. Define Lij as the number of individuals living in area j tied to

industry i, and assume that Lij is large for all i,j. Labor supply for

industry i in area j equals the following.

(A26) Nij = LijPr[Dm=1]

 = (1/b)LijWij - (1/b)Lijνij

3. Equilibrium

Under the alternative model's assumptions, setting labor demand equal to

labor supply for industry i in area j gives the wage rate for industry i in

area j. Assume that firms and individuals are allocated to industries and

areas such that the ratio of the number of firms from industry i in area j to

the number of individuals living in area j and tied to industry i is the same

for all industry/area combinations. That is, qij/Lij equals a constant λ for

all i,j. Setting equation (A23) equal to (A26) gives the wage rate for

industry i in area j.

(A27) Wij = [ηd/(ηd+ηs)]φi + [ηs/(ηd+ηs)]νij

where: ηs = (λb)-1

Plugging the wage rate from equation (A27) into equation (A23) gives

employment for industry i in area j, expressed in equation (A28) as a ratio to

the number of firms from industry i in area j.

(A28) Nij/qij = [ηdηs/(ηd+ηs)]φi - [ηdηs/(ηd+ηs)]νij
The average wage rate and total employment for area j equal the

following. Employment for area j is expressed as a ratio to the number of

firms in area j.

(A29) W.j = [ηd/(ηd+ηs)]Σi(qij/q.j)φi + [ηs/(ηd+ηs)]Σi(qij/q.j)νij

(A30) N.j/q.j = [ηdηs/(ηd+ηs)]Σi(qij/q.j)φi - [ηdηs/(ηd+ηs)]Σi(qij/q.j)νij

Equations (A29) and (A30) are virtually identical to equations (A9) and (A10).

However, equations (A27) and (A28) differ substantively from equations (A9)

and (A11). In the alternative model, each industry/area combination is a

separate labor market. Industry i's employment and wage rate in area j are

functions of labor demand only for industry i. Labor demand for other

industries in the area is not relevant.

Aggregate employment for industry i equals the following, expressed as a

ratio to the number of firms from industry i.

(A31) Ni./qi. = [ηdηs/(ηd+ηs)]φi - [ηdηs/(ηd+ηs)]Σj(qij/qi.)νij

The average wage rate among firms from industry i equals the following.

(A32) Wi. = [ηd/(ηd+ηs)]φi + [ηs/(ηd+ηs)]Σj(qij/qi.)νij

Equations (A9) and (A10) imply the following.

(A33) φi = (ηd)-1(Ni./qi.) + Wi.

Equation (A33) is identical equation (A16). They restate industry i's labor

demand curve. Note, however, that the alternative model implies that Wi. and

Ni./qi. are perfectly correlated, so the labor demand shock φi could

alternatively be expressed as a linear function of either Wi. and Ni./qi..

The empirical work in Section IV is based primarily on the area model.

Further, the empirical measures of industry's national employment and national

wage rate will not correlate perfectly. Therefore, for the empirical work in

Section IV, I use both an industry's national employment and an industry's
national average hourly earnings to instrument for the industry's labor

demand.

4. Empirical Specification

Replace φi from equation (A23) with φijt, and assume that φijt-φijt-1 is the

sum of three random variables;

(A34) φijt-φijt-1 = εt + εit + εijt

Replace νij from equation (A26) with νijt, where νijt-νijt-1 is the sum of two

random variables;

(A35) νijt-νijt-1 = πt + πijt

With the assumptions in equations (A34) and (A35), plus the results from

equations (A30), (A29), (A28), and (A27), the alternative model implies the

following.

(A36)(N.jt-N.jt-1)/q.j = -[ηdηs/(ηd+ηs)]πt + [ηs/(ηd+ηs)]Σi(qij/q.j)[(Ni.t-Ni.t-1)/qi.]

+ [ηdηs/(ηd+ηs)]Σi(qij/q.j)(Wi.t-Wi.t-1) + u3.jt

where: u3.jt = [ηdηs/(ηd+ηs)]Σi(qij/q.j)εijt - [ηdηs/(ηd+ηs)]Σi(qij/q.j)πijt

(A37) W.jt-W.jt-1 = [ηs/(ηd+ηs)]πt + [1/(ηd+ηs)]Σi(qij/q.j)[(Ni.t-Ni.t-1)/qi.]

+ [ηd/(ηd+ηs)]Σi(qij/q.j)(Wi.t-Wi.t-1) + u4.jt

where: u4.jt = [ηd/(ηd+ηs)]Σi(qij/q.j)εijt + [ηs/(ηd+ηs)]Σi(qij/q.j)πijt

(A38) (Nijt-Nijt-1/qij) = -[ηdηs/(ηd+ηs)]πt + [ηs/(ηd+ηs)][(Ni.t-Ni.t-1)/qi.]

+ [ηdηs/(ηd+ηs)](Wi.t-Wi.t-1) + u3ijt

where: u3ijt = [ηdηs/(ηd+ηs)]εijt - [ηdηs/(ηd+ηs)]πijt

(A39) Wijt-Wijt-1 = [ηs/(ηd+ηs)]πt + [1/(ηd+ηs)][(Ni.t-Ni.t-1)/qi.]

+ [ηd/(ηd+ηs)](Wi.t-Wi.t-1) + u4ijt

where: u4ijt = [ηd/(ηd+ηs)]εijt + [ηs/(ηd+ηs)]πijt

With employment changes scaled by the previous period's employment and

Σi(qij/q.j)(⋅) replaced with Σi(Nijt-1/N.jt-1)(⋅), the general specification in
equations (1) through (4) from Sections II captures the alternative model's

predictions in equations (A36) through (A39).

AIII. Occupation Similarity Measure

Sikt equals one minus a segregation index discussed by Duncan and Duncan

(1955). It is defined as follows.

(A40) Sikt = 1 - (0.5)Σo|fiot - fkot|

where: fiot = Proportion of industry i employment in occupation o in year t.

 fkot = Proportion of industry k employment in occupation o in year t.

Sikt ranges from zero to one. Sikt equals zero when the two industries employ

no workers from the same occupation. Sikt equals one when the two industries

have identical occupation distributions, such as when i equals k. I use March

CPS surveys from 1975 through 1990 to calculate fiot. The samples include

private workers who report a current industry and current occupation. The

following lists the occupations. The occupation breakdowns change slightly

between 1982 and 1983.

1975-1982 1983-1990

1. Professionals 1. Executives and Managers

2. Managers and Administrators 2. Professionals

3. Sales workers 3. Technicians

4. Clerical workers 4. Sales workers

5. Protective Service workers 5. Administrative support workers

6. Other service workers 6. Protective service workers

7. Craft and kindred workers 7. Other service workers

8. Transportation operatives 8. Precision production and craft

9. Other operatives workers

10. Laborers 9. Machine Operators

10. Transportation Occupations

11. Handlers and Laborers