Market Potential, Increasing Returns, and Geographic Concentration

Gordon H. Hanson*
University of California, San Diego
and National Bureau of Economic Research
September 2004

Abstract. In this paper, I examine the spatial correlation between wages and consumer purchasing
power across U.S. counties to see whether regional demand linkages contribute to spatial
agglomeration. First, I estimate a simple market-potential function, in which wages are associatedwith proximity to consumer markets. Second, I estimate an augmented market-potential function
derived from the Krugman model of economic geography, parameter estimates for which reflect theimportance of scale economies and transport costs. The estimation results suggest that demand
linkages between regions are strong and growing over time, but quite limited in geographic scope.
JEL Classification: F12, R12.
Key words: Spatial agglomeration, market potential, increasing returns, transport costs.

*

IR/PS 0519, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0519;
phone: 858-822-5087; fax: 858-534-3939; email: gohanson@ucsd.edu.

I. Introduction
In this paper, I examine changes in the spatial distribution of economic activity in the UnitedStates to see what they reveal about the strength of product-market linkages between regions. The
starting point for the exercise is the idea that the level of economic activity in a location isconditioned by that location's access to markets for its goods. I attempt to show that market access –as opposed to the fixed characteristics of locations – provides a useful way to characterize the forcesthat contribute to the geographic concentration of economic activity.
There is a large theoretical literature on spatial agglomeration. Krugman (1991) explains
city formation through the interaction of transport costs and firm-level scale economies.1 Fujita,
Krugman, and Venables (1999) show that in a broad class of models scale economies and transport
costs combine to create spatial demand linkages that contribute to agglomeration. Firms are drawn
to cities by the possibility of serving large local markets from a few plants at low transport cost.
Congestion costs limit the degree of geographic concentration.
This idea is related to Harris' (1954) influential market-potential function, which states thatthe demand for goods produced in a location is the sum of purchasing power in other locations,weighted by transport costs. In its early form, the market-potential function was ad hoc. Fujita,
Krugman, and Venables (1999) reinvigorate the market-potential concept by showing how it can bederived from formal spatial models. In its modern version, the market-potential function states that
nominal wages are higher near concentrations of consumer and industrial demand.

1

This work builds on a large body of theoretical literature. See Fujita and Thisse (1996), Ottaviano and Puga (1997),

and Fujita, Krugman, and Venables (1999) for surveys of previous research.

1

Recently, there has been a burst in empirical research on economic geography.2 One strandof literature examines whether production or exports tend to concentrate near large national orregional markets, as would be consistent with Krugman’s (1980) home-market effect (Davis andWeinstein 1999 and 2003; Head and Reis 2001; Hanson and Xiang 2004). A second strand
examines how technology diffuses across space and how this in turn affects trade and industry
location (Eaton and Kortum 1999 and 2002; Keller 2002). A third strand, and the one most related
to this paper, examines whether incomes are higher in countries or regions with access to larger
markets for their goods, as would be consistent with recent economic geography models (Hanson
1996 and 1997; Redding and Venables 2004; Head and Mayer 2004).3
To assess the importance of market access, I examine the spatial correlation of wages andconsumer purchasing power across U.S. counties from 1970 to 1990. I first estimate Harris' marketpotential function. In this specification, which resembles a spatial labor-demand function, nominal
wages are increasing in consumer income in surrounding locations and decreasing in transport costs
to these locations. The estimation results indicate how far demand linkages extend across space andhow income shocks in one location affect other locations. I then estimate an augmented marketpotential function, based on Helpman’s (1998) extension of Krugman (1991). This specification,
which nests the simple market-potential function, interacts consumer purchasing power with othervariables and gives structural interpretations to the regression coefficients. The structural parametersreflect the magnitude of scale economies and transport costs.
This paper shares with Redding and Venables (2004) an estimation strategy that uses the2

See Head and Mayer (2003) and Overman, Redding, and Venables (2003) for surveys of this literature.

3

On spatial interactions see Eaton and Eckstein (1997), Eaton and Dekle (1999), and Dobkins and Ioannides (2001).

2

spatial variation in earnings to identify the structural parameters of a geography model. The two
papers differ in several important respects. While Redding and Venables use cross-country data, I
use cross-county data for a single country. Comparing my results to theirs allows one to see how thestrength of spatial interactions changes as one moves from very small to very large geographic units.
A second difference is that while their estimation uses data on cross-country trade flows, myanalysis uses no trade data whatsoever.4 This provides consistency check on the empiricalapplication of geography models in that it shows how results change as we switch the basis for
estimation from the spatial covariation in average incomes and trade flows (the RV approach) to thespatial covariation in wages and consumer purchasing power (my approach).
One problem for the empirical analysis is that the available measure of wages is averageannual earnings per worker, which vary across locations in part because worker characteristics varyacross locations. Cross-region variation in worker characteristics may reflect regional characteristics
that are constant over the sample period, which can be removed by controlling for fixed location
effects. Cross-region variation in worker characteristics may also reflect unobserved shocks towages in a location that are correlated with changes in demand for locally produced goods, creating
a possible source of simultaneity bias. I address this problem by instrumenting for changes inmarket potential using historical data on county population growth.
A second problem is that there are forces besides market access that contribute to spatial
agglomeration. Agents may be drawn to regions with pleasant weather or other amenities (Roback
1982, Beeson and Eberts 1989). Additionally, human capital spillovers may make agglomerated
regions attractive places to work (Rauch 1993; Black and Henderson 1999). To see how these4

A third difference is that Redding and Venables allow both households and firms to consume industrial products.

3

additional factors might influence the estimation, I compare results with and without controlling for
local supplies of human capital and exogenous amenities. As this approach may not control for all
factors behind geographic concentration, I address issues of interpretation in the text.

II. Theory
A. The Krugman Model
Recent theoretical work on economic geography attributes spatial agglomeration to productmarket linkages between regions. A precursor to this approach is Harris' (1954) market-potentialfunction, which equates the potential demand for goods and services produced in a location with thatlocation's proximity to consumer markets, or
MP j = ∑ Yk e

−d jk

(1)

k ∈K

where MPj is the market potential for location j, Yk is income in location k, and djk is distance
between j and k. While early work simply asserted the existence of equation (1), recent theory
derives a structural relationship similar to (1) from general-equilibrium spatial models.
I present the basic structure of the Krugman (1991) model, referring to Helpman's (1998)
extension which is more tractable for empirical work.5 All consumers have identical Cobb-Douglas
preferences over two bundles of goods, traded (manufacturing) goods and housing services,
U = Cmµ Ch1-µ5(2)

In Krugman (1991), there is an agricultural sector in place of the housing sector, where agricultural goods areproduced under constant returns by immobile farm labor. The Helpman model, by introducing a nontraded good,
generates a smoother, more realistic spatial distribution of production. See also Puga (1999).

4

µ is the share of expenditure on manufactures, Ch is the quantity of housing services consumed, and
Cm is a composite of symmetric manufacturing product varieties given by
σ−1 σ
Cm = [∑ c i σ ] σ−1
i
n

(3)

where σ is the elasticity of substitution between any pair of varieties and n is the number of varieties.
There are increasing returns in production of each manufacturing variety such that
Lim = a + bx i(4)where a and b are constants, Lim is labor used in variety i, and xi is the quantity of i produced. In
equilibrium each variety is produced by a single monopolistically competitive firm and the f.o.b.
price for each variety is a constant markup over marginal cost, which depends on the wage, w.
There are J regions and L laborers, where laborers are perfectly mobile between regions.
The stock of housing in region j is assumed to be fixed at Hj. Ownership of the housing stock is
assumed to be symmetric across individuals such that each laborer owns share 1/L of the housing
stock in each of the J regions. With iceberg transport costs in shipping goods between regions, thec.i.f. price of good i produced by region j and sold in region k is
Pijk = Pij eτd jk(5)

where Pij is the f.o.b. price of good i produced in region j, τ is the unit transportation cost, and djk isthe distance between j and k.

The solution to the model is well known (Helpman 1998; Fujita,

Krugman, and Venables 1999). For certain parameter values, manufacturing concentrates spatially.
Firms desire to be in a region with high employment to serve a large local consumer market at lowtransport cost without duplicating fixed production costs. The costs of being in a large market are
higher wages, resulting from high housing costs associated with local congestion.

5

To develop the intuition behind the market-potential function, it is useful to derive thedemand for traded goods produced in some region j. Let Cijk be the quantity of good i that region kpurchases from region j. Given CES utility over traded goods, the symmetry of traded goods intechnology and preferences, and the equilibrium condition on the constant markup of prices overmarginal cost ( Pij =σbw j ), total sales of manufacturing goods by region j areσ −1
σ∑ ∑ Pijk C ijk = n j ∑ µYk [ σ − 1 bw jek iτd jk 1− σ]kTkσ −1(6)where Tk is the CES price index for manufacturing goods available in region k. Under zero profits
manufacturing sales in region j equal wages paid to labor in j. The wage bill in j thus equals wjnjaσ.6
I then obtain a modified market-potential function (Fujita, Krugman, and Venables 1999),
w j = θ[∑ Yk e

− τ(σ −1)d jkkTkσ −1 ]1 / σ(7)where θ is a function of fixed parameters. Wages in a location are increasing in the income ofsurrounding locations, decreasing in transport costs to these locations, and increasing the price ofcompeting traded goods in these locations.
Following similar logic, the price index for traded goods in region j can be written as1στdT j = [∑ n k (bw k e jk )1− σ ]1− σ
σ −1
k

(8)

Equation (8) captures market equilibrium for traded goods. The price index for these goods is higher
where a larger fraction of goods must be imported from distant locations.
6

The wage bill in region j equals wjLimjnj, where Lmj is employment in production of manufacturing good i in j. By

zero profits, which fixes x=(σ-1)a/b, and the symmetry in technology across regions, Limj=aσ.

6Beyond equations (7) and (8), there are three additional equilibrium conditions. Equilibrium
condition three is that real wages are equalized across regions,wjw= 1-µ k µ ,
1-µ µ
Pj Tj
Pk Tk

∀ j≠ k(9)where Pj is the housing price in j. Equilibrium condition four is that regional income equals income
derived from labor and housing,Y j = n j w j aσ +1 - µ n jaσ∑ n k w k aσ, ∀ j
L k
µ

(10)

And equilibrium condition five is that housing payments equal housing expenditure,
P j H j = (1 − µ) Y j , ∀ j(11)

By its simplicity, the Krugman model ignores many features of production and consumption which
may influence industry location. My strategy is to examine whether such simple models are
informative about the spatial distribution of economic activity.

B. Model Specification

Following the logic of new economic geography models, I make nominal wages thedependent variable. In the first specification, I apply Harris’ market-potential function in (1) directly
by relating nominal wages in a location to income in other locations, weighted by distance:log(w jt ) = α 0 + α1 log(∑ Ykt eα 2 d jk ) + ε jt

(12)

k

where t is the time period, wjt is the nominal wage in region j, α0, α1, and α2, are parameters tobe estimated, and εjt is an error term discussed below. While (12) is not derived from an explicit
model, its simplicity makes it a useful baseline model for assessing demand linkages between

7regions. In (12), wages in a location reflect the demand for goods produced in that location,
where consumer demand is determined by transport costs and the spatial distribution of income.
The second specification I estimate is taken from the equilibrium conditions of the Krugman
model, including the modified market-potential function in (7). Given limited spatial data on prices
for traded goods (Tj), I cannot simultaneously estimate all of the model's structural equations. My
approach is to derive an estimating equation by combining (7), (9), and (11), which yields thefollowing augmented market-potential function:log(w jt ) = β + σ −1 log(∑k

σ(µ −1) +1 (σ −1)(1− µ) σ −1
Ykt µH kt µw ktµ e - τ(σ -1) d jk ) + η jt

(13)

where β is a function of fixed parameters and ηjt is an error term discussed below. The parameters tobe estimated are σ, the elasticity of substitution between traded goods (which we expect to exceed
unity); µ, the expenditure share on traded goods (which we expect to be between zero and one); andτ, the transportation cost of shipping one unit of a good a unit distance (which we expect to bepositive, such that transport costs are increasing in distance).
Equation (13) embodies three equilibrium conditions: the market-potential function in (7),real-wage equalization across regions in (9), and regional housing market equilibrium in (11). Since
I do not incorporate two equilibrium conditions, equations (8) and (10), estimating (13) cannot be
considered a full-information application of the Krugman model. Equation (13) differs from (12) by
the inclusion of the price index for traded goods, which is(1− σ)(µ −1) (σ −1)(1− µ ) σ −1
σ −1
Tkt
= γYkt µ
H kt µw ktµwhere γ is a constant. The key difference, then, between (12) and (13) is that the latter controls for8the regional variation in the price of traded goods while the former does not.
To interpret (13), note that for region j higher income in nearby regions raises demand for
traded goods produced in j (as long as σ(µ-1)<1), and higher wages in nearby regions raise therelative price of traded goods produced in these regions, which increases their demand for goods
produced in j. Higher production of traded goods in j raises the region’s demand for labor and its
nominal wages and housing prices. Larger housing stocks in nearby regions imply lower housing
prices and higher employment in these regions and so higher demand for traded goods.

III. Data and Estimation Issues
A. Data Sources

I take counties in the continental United States as the geographic unit of analysis. The datarequired are wages, employment, income, and housing stocks. County-level data on annual labor
compensation and employment are available from the U.S. Bureau of Economic Analysis (BEA).
The BEA tabulates both earnings and employment on a place of work basis. I use earnings andemployment data for wage and salary workers. I measure income by total personal income, which is
total income received by households and non-corporate businesses. I measure the housing stock as
total housing units, from the U.S. Census of Population and Housing. The time period for the
analysis is 1970, 1980, and 1990. Table 1 gives summary statistics on the variables.

B. The Spatial Distribution of Employment and Wages

In this section, I present data on wages and employment in U.S. counties. Wages areaverage annual earnings per worker for wage and salary workers. Employment is average annual
employment of wage and salary workers per square kilometer. Variables are expressed relative to9

weighted averages for the continental United States.
As is well known, employment is spatially concentrated around cities and wages are
relatively high near these areas of dense economic activity.7 Employment densities in the mosturbanized counties, which account for 5.4% of all counties, range from 6 to 2,237 times the U.S.
average (in New York county). Surrounding major cities are regions with moderate employment
densities, from 1.5 to 6 times the U.S. average. Over two-thirds of counties, mostly in farm andmountain states, have very low employment densities, only 0.2 to 0.6 times the U.S. average. That
employment density declines as one moves away from large consumption masses is consistent with
the idea that market access influences industry location.
Figure 1 shows the log change in county employment relative to the log change in U.S.
employment for 1970-1990. Since 1970, there has been a sizable shift in employment from thenortheast and midwest to the southeast and west, as discussed in Blanchard and Katz (1992).
Interestingly, employment change in both high and low-growth regions is far from uniform. For
instance, east and south Texas have high relative growth, but west and north Texas show relative
declines, and while most counties in plains states have low relative growth, the Twin Cities region
has high relative growth. As employment relocates to the south and west, it appears to concentratein certain pockets, leaving other areas untouched.
Figure 2 shows the log change in county wages relative to the log change in U.S. wages
between 1970 and 1990. Counties with high relative-wage growth are overwhelmingly concentrated
in the southeast. Most counties in the northern midwest and the northeast, with the exception of theAtlantic seaboard, have relative-wage declines. Comparing Figures 1 and 2, the geographic expanse
7

For the spatial density of U.S. employment and wage levels, see http://irpshome.ucsd.edu/faculty/gohanson/.

10

of relative-wage growth in the southeast appears to be larger than the geographic expanse of relativeemployment growth in the region, suggesting that employment growth in high-activity counties puts
upward pressure on wages in neighboring counties.

C. Estimation Issues

A first estimation issue relates to the geographic unit of analysis. More geographicallydisaggregated data reduces measurement error, but too much detail creates computational problems.
The expressions in (12) and (13) are summed over all locations. Specifying the independent
variables in (12) and (13) at the county level would create summation expressions with over 3,000
terms for each observation. Instead, I group surrounding counties within concentric distance bands
and then aggregate the independent variables across counties within each band. For distances of 0 to1000 km., the bands have a width of 100 km. (0-100 km., 100-200 km., etc.); for distances of 10002000 km. the bands have a width of 200 km.; and for distances above 2000 km. counties are treatedas a single unit. I calculate the set of 16 concentric-ring aggregates for all counties in the sample.
Distance to each aggregate is for the mid-point of the band.
A second estimation issue relates to heterogeneity in workers across regions. While thedesired county wage measure is for a worker with some constant level of skill, the available wage
measure is annual compensation per worker averaged across workers in a county. Let wjt be theaverage wage in county j at time t and let w*jt be the constant-skill wage in county j. Variation in theconstant skill wage, w*jt, across locations reflects true regional variation in nominal wages, due intheory to spatial variation in industry location. However, variation in country average wages, wjt,
may be due either to regional variation in w*jt or to regional variation in worker characteristics. To

11capture how measurement error in wages may affect the estimation, suppose that the deviation in thelog average wage from the log constant-skill wage can be written as,
log(w jt ) − log(w *jt ) = ω j + ν jt

(14)

The first component, ωj, is the mean deviation between the county average and constant-skill wages,
and the second component, νjt, is the period-specific deviation, assumed to be iid.
The mean deviation in wages may reflect regional differences that vary little over time, suchas the availability of agricultural land, access to railroads and highways, the presence of universities,
or proximity to state or national seats of government. If certain characteristics attract both industrial
firms and more-skilled labor, then any correlation between wages and the market-potential index
found in the data may be a byproduct of a correlation between the summation expressions in (12)and (13) and ωj. For instance, university towns may have relatively large supplies of skilled workers(because college graduates tend to look for jobs near their place of education) and relatively large
concentrations of production (because students and faculty are a captive local market). The temporalpermanence of major population centers suggests that fixed regional characteristics are likely to beimportant in the location of economic activity. To remove the mean deviation in the average wage
from the constant-skill wage from the estimation, I take time differences of the estimating equations,which produces the following specification for (13),∆ log(w j ) = σ−1[log(∑
k

log(∑
k

σ(µ −1) +1 (σ −1)(µ −1) σ −1
Ykt µ H kt µ
w ktµ e-τ(σ-1)d jk )−σ(µ −1) +1 (σ −1)(µ −1) σ −1
Ykt −1µ H kt −1 µw ktµ−1 e-τ(σ-1)d jk )] + ∆ν jt

The corresponding time-differenced expression for (12) is analogous.

12

.

(15)

The remaining error term, ∆νjt, is the change in the deviation of county average wages fromcounty constant-skill wages. There may be concern that this error term is correlated with the change
in the summation expression in (15). This would be the case, for instance, if counties thatexperience growth in demand for locally produced traded goods tend to attract workers with above
average skills. To account for possible correlation between the error term and the change in the
regressor function, I use a GMM estimator, in which I instrument for the regressor function using
historical data on county population growth, where these values are lagged by ten years or more. In
the estimation of equation (15) for the time period 1970-1980, the instruments I use are own-county
and neighboring-county population growth over the periods 1930-1940, 1940-1950, and 1950-1960.
Instruments for 1980-1990 are analogous. If county population growth reflects secular trends
associated with long-run shifts in regional economic activity, then past growth rates for counties andtheir neighbors will help predict future growth in market potential.
A third estimation issue is that other factors that influence spatial agglomeration, such as
supplies of exogenous amenities (e.g. Roback 1982) or localized human-capital externalities (e.g.
Rauch 1993), may also influence the spatial distribution of nominal wages. I deal with this issue by
including two sets of control variables in the estimation: changes in the shares of the working age
population in a county by gender, age, and educational attainment; and indicators of exogenous
amenities available in the county. An appendix describes the wage regressions. Following previous
literature (e.g. Roback 1982), the measures of exogenous amenities I use are heating-degree days,
cooling-degree days, average possible sunshine, average wind speed, average relative humidity,
average precipitation, whether the county borders the sea coast, whether the county borders a greatlake, and territorial water area in the county. By regressing county average wage growth on county

13education, the specification captures the impact of both individual education and average county
education on wages, which implicitly controls for human-capital externalities across workers withina county (Rauch 1993). As many of the control variables are difficult to obtain for 1970, I include
them in regressions for 1980 and 1990 only.
Other factors, such as technological spillovers, may also contribute to spatial agglomeration.
One difficulty in controlling for this type of spillover is that it is possible to replicate some of theresults of the Krugman model by replacing scale economies at the firm level with scale economies at
the industry or region level, as would arise from spillovers between adjacent firms (Helpman 1998).
Using external economies to explain spatial agglomeration has a long history in urban economics(Fujita and Thisse 1996). In these models, spillovers tend to be assumed rather than derived. Part of
the appeal of the Krugman model is that pecuniary externalities arise endogenously. While
spillovers between firms could certainly contribute to spatial agglomeration, the absence of
microfoundations for this explanation perhaps makes it less compelling.
To summarize the estimation strategy, step one is to estimate a baseline, simple marketpotential function in time-difference form. Step two is to estimate the augmented market-potentialfunction based on the Krugman model in equation (15). This model nests the simple marketpotential function, which permits a test of which model better fits the data.

IV. Estimation Results

The sample is 3,075 counties in the continental United States. The dependent variable in all
specifications is the log change in average annual earnings for wage and salary workers. The
independent variables are aggregates or averages across counties within concentric distance bands

14whose center is the county on which the observation is taken. All specifications are in timedifferenced form for either 1970-1980 or 1980-1990. The base specification for the augmented
market-potential function is equation (15), which written in reduced form is,ααα∆ log(w j ) = α 0 + α1[log(∑ Ykt3 w αkt4 H αkt5 eα 2 d jk ) − log(∑ Ykt3−1 w αkt4−1H kt5−1 eα 2 d jk )] + ∆ν jt (15’)
kk

The variables in the regressor function are personal income (Yk), distance in thousands of kilometers(djk), the housing stock (Hk), and average annual earnings for wage and salary workers (wk). Thebase specification for the simple market-potential function is equation (15’), with the coefficient on
income (α3) constrained to be one and coefficients on wages (α4) and housing stocks (α5)
constrained to be zero. I perform the estimation by either nonlinear least squares or GMM.

A. The Simple Market-Potential Function

Columns (1) and (2) of Table 2 show coefficient estimates for the simple market-potentialfunction. The coefficient α1 is the effect of the market-potential index on wages in a given county.
Consistent with the market-access hypothesis, the coefficient is positive and precisely estimated inboth time periods. Higher consumer demand appears to be associated with higher nominal wages ina given county. The coefficient α2 is the effect of distance from consumer markets on wages ingiven county. Also consistent with the market-access hypothesis, the coefficient is negative andprecisely estimated. Greater distance to consumer markets reduces nominal wages in a location.
The effects of both market potential and distance appear to rise over time.
Table 2 also shows the sensitivity of the results to sample restrictions. I first examine
whether the presence of high-population counties in the estimation affects the results. Highpopulation counties, which are located in major urban areas, may be subject to greater measurement15

error in wages since urban areas tend to exhibit wider variation in worker skills. In columns (3) and(4) of Table 2, I exclude all counties with greater than 0.05% of the U.S. population. Coefficientestimates in columns (3) and (4) are very similar to those in columns (1) and (2).
The distance coefficients suggest that counties beyond 1000 km. carry a weight of zero in theestimation.8 In columns (5) and (6) of Table 2, I redefine the summation expressions in equation(15) to exclude counties beyond 1000 km. from the county on which an observation is taken. The
coefficient estimates in columns (5) and (6) are very similar to those in columns (1) and (2),suggesting that market potential is determined largely by economic activity in nearby regions. In
unreported results, I found that estimation results are affected only when we begin to exclude
counties within 800 km. of a given county.
Next, I examine the effects of adding controls for human capital and exogenous amenities.
Columns (7)-(9) report regressions with these controls included for the 1980-90 time period.
Coefficient estimates for these variables from the regression in column (7) are reported in an
appendix. Comparing columns (7)-(9) with columns (2), (4), and (6), we see that while thecoefficient on distance is unchanged by the addition of the control variables, the coefficient on themarket-potential index falls in magnitude. This suggests market potential may be positively
correlated with variables associated with higher average county wages, such as average educationand experience. In other words, workers with higher observed levels of skill appear to be attracted
to locations with strong consumer demand growth. This may help explain Rauch’s (1993) findingthat wages are higher in cities where average education is higher and Ciccone and Hall’s (1996)
finding that regional labor productivity is higher where the density of employment is higher.
8

From column (1) of Table 2, the implied weight on income for a county 1000 kilometers away is e-5.5=0.004.

16

In unreported results, I performed additional checks on the robustness of the findings. First,
I estimated the simple market-potential function separately for eight geographic regions. This
controls for western states, whose large land areas and low population densities may create differing
regional demand linkages. Second, I estimated equation (17) using a more flexible specification of
distance and transport costs. I replace the function eαd, which for negative α and positive d will be
convex for all values of d, with the function 1/[1+(ρd)2], which depending on the value of ρ may
have both convex and concave regions in d. Third, I aggregated counties by state rather than byconcentric rings. These approaches all produce results that are similar to those in Tables 2 and 3.
For all specifications, α1 and α2 rise in absolute value over time, which suggests that theeffects of both consumer purchasing power in other locations and distance to other locations havebecome more important. To help interpret the results, I calculate the predicted change in wages for acounty associated with an increase in the county’s market-potential index of 10%, where I assume
that this increase in the index is concentrated at a single point in space. I then see how the predicted
county wage change varies as we increase the distance of the point at which the shock is presumed
to occur. Formally, the predicted wage change is given by,
⎡ ⎛
⎞
⎛
⎞⎤
ˆ
ˆ
ˆ
ˆ
∆ ln ŵ = αˆ 1 ⎢ln⎜⎜ (1 + 0.1 * e α 2D )∑ Yk e α 2d k ⎟⎟ − ln⎜⎜ ∑ Yk e α 2d k ⎟⎟⎥ = αˆ 1 ln(1 + 0.1 * e α 2D ) (16)
⎢⎣ ⎝
k
⎠
⎝k
⎠⎥⎦

where ∆ ln ŵ is the predicted change in county wages, α̂1 and α̂ 2 are estimated coefficients, and D
is the distance from a county to the location of the shock.
Figure 3a plots equation (16) using coefficient estimates from columns (1) and (2) of Table
2. The strength of local demand linkages appears to have increased over time. A nearby shock(within 8 km.) that increases the market-potential index by 10% increases wages by 2.6%, using17coefficient estimates for 1970-1980 in column (1), and by 3.7%, using coefficient estimates for
1980-1990 in column (2). The impact of the shock falls off quickly with distance, and more so whenusing the 1980-1990 coefficients than when using the 1970-1980 coefficients. This suggests thatimportance of proximity to markets for wages has also increased over time.
These results on demand linkages between regions are roughly consistent with other work on
the attenuation of agglomeration effects across space. Adams and Jaffe (1996) examine thecorrelation between a firm’s R&D and productivity levels in the firm’s outlying plants. While firm
R&D is positively correlated with plant total factor productivity, this effect is much stronger forplants that are closer to the firm’s R&D facilities. For plants beyond 100 miles of R&D labs, theeffect of R&D on productivity is only 10-30% as strong.
To summarize the findings of this section, nominal wages are strongly, positively correlatedwith the distance-weighted sum of personal income in surrounding regions. These results are
consistent with Harris’ (1954) formulation of a market-potential function.

B. The Augmented Market-Potential Function

Table 3 reports nonlinear least squares estimation results for the augmented market-potentialfunction in equation (15’).9 The dependent variable remains the log change in earnings of wage andsalary workers. I report both the reduced-form regression coefficient estimates and the values of thestructural parameters implied by these estimates.
Consider first the coefficient estimates in columns (1) and (2). It is again the case that9

I impose restrictions on the reduced-form parameters implied by (15).

Relaxing these restrictions slightly

improves the fit of the regression. Structural parameters derived from the two sets of regressions are similar.

18the coefficient on the market-potential index, α1, is positive and precisely estimated and that thecoefficient on distance, α2, is negative and precisely estimated. In comparing these coefficientestimates to those for the simple market-potential function in Table 2, we see that in Table 3 theeffect of market potential is smaller and the effect of distance is larger. The additional variablesin the augmented market-potential function, the housing stock and wages, enter with positive
exponents, and the exponent on total personal income is positive but smaller than unity.
Comparing values of the Schwarz Criterion in Tables 2 and 3, we see that the augmented marketpotential function improves the fit of the regression in all cases. Table 3 also reports the resultsof a Wald test on the hypothesis that the data support the coefficient constraints imposed by thesimple market-potential function (i.e., that α3 equals one and that α4 and α5 equal zero). I reject
this hypothesis at any level of significance. The reduced-form effects of personal income,wages, and housing on market potential are broadly consistent with the Krugman model. Higher
personal income, higher wages, and higher housing stocks in surrounding locations are all
associated with higher wages in a given country.
Columns (3) and (4) of Table 3 report estimation results for low-population counties, which,as in Tables 2 and 3, are very similar to those for the full sample. Columns (5) and (6) report results
including controls for human capital and exogenous amenities for the 1980-90 time period. These
results are qualitatively similar to those without controls, though distance effects appear to besmaller in absolute value once additional controls are included in the regression. An appendix
reports coefficient estimates on these variables for the regression in column (5).
Consider next to the structural parameters implied by the reduced-form coefficient estimates,
which can be derived by comparing equations (15) and (15’) (see note 17). Consistent with theory,19

estimates of σ, the elasticity of substitution, are greater than 1, and range in value between 4.9 and7.6. This is roughly in line with other estimates of the elasticity of substitution based on gravity-typemodels of international trade (Head and Mayer 2003). Recent estimates of σ in the empiricalliterature are concentrated between 4.0 and 9.0 (e.g. Feenstra 1994, Head and Ries 2000). The lower
is the value of σ, the lower in absolute value is the own-price elasticity of demand for any individual
good and the more imperfectly competitive is the market for that good. By profit-maximization,
σ/(σ - 1) equals the ratio of price to marginal cost. The implied price-cost margins range from 1.15

to 1.25 and are precisely estimated in all cases. In equilibrium, price equals average cost, in whichcase a value of σ/(σ - 1) greater than one indicates production of traded goods is subject to scaleeconomies.
Also consistent with theory, estimates of µ, the expenditure share on traded goods, arebetween 0 and 1. However, with a mean expenditure share on housing in the United States ofapproximately 0.20, estimated values for µ of 0.91 to 0.97 may seem too high. This may suggestthat the stark categorization of goods as either traded consumables or housing services is too
restrictive. Estimated values of τ, unit transport costs, suggest, counterintuitively, that transportation
costs have risen over time. However, it is difficult to evaluate the net effect of this change from the
distance parameter alone, as other parameters also change over time. Below, I examine spatial
decay functions implied by these coefficient estimates.
In Table 4, I re-estimate the regressions in columns (1), (3), and (5) of Table 3 by GMM.
The instruments are lagged own-county log population growth and lagged values of log population
growth in surrounding counting. Since the coefficient estimates are somewhat sensitive to the
choice of instruments, I report two sets of estimates, one for a narrow set of instruments (lagged

20

population growth in the own county and immediately surrounding counties) and another for abroader set of instruments (lagged population growth in the own county, immediately surrounding
counties, and more-distant counties). Based on tests of overidentifying restrictions, in all regressions
I fail to reject the hypothesis that the instruments are uncorrelated with the errors at conventional
levels of significance. For both time periods, the GMM estimates of both the reduced-form
regression coefficients and the structural parameters are qualitatively similar to those in Table 3. We
again reject the parameter constraints imposed by the simple market-potential function. Comparedto Table 3, GMM estimates of σ and µ tend to be smaller and of τ tend to be larger. Adding controls
for exogenous amenities and human capital, as shown in columns (5) and (6), reduces the precisionof the parameter estimates somewhat.
To see what the parameters imply about demand linkages between regions, I use parameter
estimates from Tables 3 and 4 to calculate the effect of a shock that increases the augmented marketpotential index by 10%. Since the shock is again defined as a percentage change in the marketpotential index (though now it the augmented form), I can again use equation (16) to describe how
the effect of this shock on wages varies with distance from its source.
Figure 3b plots equation (16) using coefficient estimates from columns (1) and (2) of Table
3. The results for the two time periods are similar. Changes in the market-potential index affectwages only if they occur within 200 km. These effects are substantially smaller than those based on
the simple market-potential function in Figure 3a. Figure 3c plots equation (16) using GMM
coefficient estimates from columns (1) and (2) of Table 4. Results for the two time periods are again
similar, though in the later period the effects of the shock fall off more quickly with distance.
Comparing Figures 3c and 3b, demand linkages between regions are much larger for the GMM

21estimates than for the nonlinear least squares estimates. In nonlinear least squares, the effects ofmeasurement error may be leading to downward bias in the estimates of demand linkages between
regions. Comparing Figures 3c and 3a, demand linkages between regions are smaller for theaugmented market-potential function than for the simple market-potential function. While the two
figures show similar effects of a nearby shock, in Figure 3c these effects fall off quickly with
distance and are effectively zero once the location of the shock is beyond 400 km.
In unreported results, I performed additional checks on the sensitivity of the regression
results. These include dropping high-population counties from the sample, dropping distant county
aggregates from the summation expressions in (15’), estimating the augmented market-potentialfunction for each region separately, using a more flexible distance function (as described in IV.A),
and aggregating counties in the regressor function by state rather than by concentric distance bands.
Results for these regressions are similar to those reported in Tables 3 and 4.
I also have estimated an augmented market-potential function based on a strict version of
Krugman (1991), in which each region has an immobile agricultural labor force but no housing
sector. This specification produces estimates of σ and τ that are qualitatively similar to those in
Tables 3 and 4, but estimates of µ that are implausibly large. In all regressions, the data reject thestrict of the Krugman model in favor of Helpman’s (1998) extension of this model.

V. Discussion

In this paper, I use data on U.S. counties to estimate nonlinear models of spatial economic
relationships. Recent theoretical work attributes the geographic concentration of economic activity
to product-market linkages between regions that result from scale economies and transport costs.

22

My findings are broadly consistent with this hypothesis.
One contribution of the paper is the estimation of a simple market-potential function basedon Harris (1954). I find that regional variation in wages is associated with proximity to large
markets. While estimated demand linkages between regions are strong, they are limited in
geographic scope. A second contribution of the paper is estimation of an augmented marketpotential function based on Krugman’s (1991) model of economic geography. This model has beenvery influential in theoretical research, and has begun to receive greater attention in empirical work.
Estimates of the model’s parameters are broadly consistent with theory. The data reject the simple
market-potential function in favor of the augmented market-potential.
My findings, of course, do not rule out the possibility that other factors also contribute tospatial agglomeration. I show that the estimation results are not qualitatively affected by introducing
controls for human capital externalities or exogenous amenities or by instrumenting for theaugmented market-potential function. But there are other factors, such as technology spillovers, forwhich I do not control and which could have important effects on industry location.
Several aspects of the empirical results raise questions about the usefulness of the Krugman
model for characterizing economic geography. Most importantly, estimated trade costs are large invalue and rise in magnitude over time. In Figures 3a-3c, the magnitude of these costs implies thatdemand linkages between regions are very weak for regions separated by more than 1000 km.
Sizable trade between distant regions suggests that actual trade costs may in fact be much lower.
Also, available evidence suggests that communication costs and some types of transportation costs
have been falling steadily over time (Cairncross, 1997). However, in defense of the results, theestimated increase in trade costs could reflect the ongoing secular shift in economic activity from23

low-trade-cost manufacturing to high-trade-cost services.
Some of the concerns about the empirical results could conceivably be remedied throughgeneralizing the Krugman model, such as by introducing more heterogeneity in industry production
and trade costs or by allowing for other motivations for spatial agglomeration. Recent work in trade
theory (e.g. Eaton and Kortum 2002) allows for substantial industry heterogeneity. That the model
has some explanatory power, despite its simplicity, is perhaps testimony to the importance of
product-market linkages for the spatial distribution of economic activity.
The results of this paper relate to other work on the spatial demand linkages posited by new
economic geography models. Redding and Venables (2004) evaluate such demand linkages, which
they term market access, by estimating the cross-country correlation between per capita income andproximity to import demand, where the latter is constructed from estimated parameters of a gravity
model of trade. They find that market access is positively correlated with per capita income, whichcorresponds to my finding that county wage growth is positively correlated with growth in acounty’s market-potential index. Thus, demand linkages appear to be strongly associated withwages whether one looks across countries or across regions inside countries.
While my approach is complementary to Redding-Venables, each has distinct advantages.
An advantage of Redding-Venables is that by starting with a gravity model they are able to accountfor the importance of proximity to both import demand and export supply, thus permitting bothconsumers and firms to be sources of industrial demand. Advantages of my approach are that I am
able to characterize the spatial distribution of economy activity at a highly disaggregated level and to
uncover the model’s structural parameters. If sufficiently disaggregated data on intraregional trade
within countries were available, it should be possible to combine these two approaches.

24Appendix: Estimation Results for Wage Controls
This table reports coefficient estimates on additional wage controls included in the regressions reported incolumn (7) of Table 2 and column (5) of Table 3. These same wage controls are also included in columns(8)-(9) of Table 2, column (6) of Table 3, and columns (5)-(6) of Table 4. I do not report results on thewage controls for these additional regressions, but they are very similar to those shown below. In each
regression, the wage controls enter linearly. The wage controls include four sets of regressors: the 19801990 change in the share of the county population 16-64 years old by age category (20-24, 25-34, 35-44,
45-54, and 55-64); the 1980-1990 change in the share of the county population 25 years and older byyears of schooling attained (9-11, 12, 13-15, 16 plus); average climate measures for the airport that isnearest to the county (average percent possible sunshine, average wind speed, average annual heating
degree days, average annual cooling degree days, average humidity, average annual precipitation, andinland water area); and dummy variables for whether the county borders the sea coast or borders a one of
the Great Lakes. County demographic data are from the U.S. Census of Population and Housing (takenfrom the USA Counties 1996 CD ROM) and climate measures are taken from the Statistical Abstract of
the United States, 1996 (Washington, DC: U.S. Department of Commerce, 1996).

Change in Share of Population
Aged 20-24
Aged 25-34
Aged 35-44
Aged 45-54
Aged 55-64
Male
9-11 Years of Schooling
12 Years of Schooling
13-15 Years of Schooling16+ Years of Schooling
Log % Possible Sunshine
Log Average Wind Speed
Log Heating Degree Days
Log Cooling Degree Days
Log Average Humidity
Log Average Precipitation
Log Inland Water Area
Equals One if County
Borders Coast
Borders Great Lake

Table 2, Column (7)Coefficient St. Error

Table 3, Column (5)Coefficient St. Error

0.260
0.430
-0.480-0.057-0.4230.191-0.086
0.032
0.153
0.487
0.198
-0.0320.009-0.041
0.002
0.073-0.004(0.140)(0.072)(0.396)(0.420)(0.121)(0.213)(0.077)(0.053)(0.083)(0.121)(0.024)(0.003)(0.006)(0.006)(0.019)(0.009)(0.009)

0.237
0.440
-1.0710.469-0.347
0.128
0.046
0.099
0.045
0.412
0.198
-0.0060.029-0.0150.055
0.049-0.003(0.138)(0.072)(0.387)(0.410)(0.116)(0.212)(0.078)(0.052)(0.083)(0.119)(0.026)(0.004)(0.008)(0.006)(0.018)(0.010)(0.001)-0.002-0.017(0.008)(0.007)-0.020-0.008(0.007)(0.007)25

I thank Steve Bronars, Keith Head, Wolfgang Keller, Gerald Oettinger, Diego Puga, Shinichi
Sakata, Matt Slaughter, Dan Trefler, David Weinstein, and seminar participants at the CEPR,
NBER, the University of Michigan, NYU, Princeton, the University of Texas, and the World Bankfor helpful comments and the National Science Foundation for financial support. Shu-yi Tsai,
Keenan Dworak-Fisher, and Zeeshan Ali provided excellent research assistance.
References

Adams, J., Jaffe, A., 1996. Bounding the effects of R&D: an investigation using matchedestablishment-firm data. Rand Journal of Economics 27, 700-721.
Beeson, P., Eberts, R., 1989. Identifying productivity and amenity effects in interurban wage
differentials. Review of Economics and Statistics 71, 443-452.
Black, D., Henderson, V., 1999. The theory of urban growth. Journal of Political Economy 107,252-284.

Blanchard, O., Katz, L., 1992. Regional evolutions. Brookings Papers on Economic Activity 1, 175.
Cairncross, F., 1997. The Death of Distance. Harvard Business School Press, Boston.
Ciccone, A., Hall, R., 1996. Productivity and the density of economic activity. American
Economic Review 86, 54-70.
Davis, D.R., Weinstein, D.E., 1999. Economic geography and regional production structure: anempirical investigation. European Economic Review 43, 379-407.
Davis, D.R., Weinstein, D.E., 2003. Market access, economic geography and comparativeadvantage: an empirical assessment. Journal of International Economics 59, 1-24.
Dekle, R., Eaton, J., 1999. Agglomeration and land rents: evidence from the prefectures. Journalof Urban Economics 46, 200-214.
Dobkins, L.H., Ioannides, Y., 2001. Spatial interactions among U.S. cities. Regional Science and26

Urban Economics 31, 701-731.
Eaton, J., Eckstein, Z., 1997. Cities and growth: theory and evidence from France and Japan.
Regional Science and Urban Economics 27, 443-474.
Eaton, J., Kortum, S., 1999. International technology diffusion: theory and measurement.
International Economic Review 40, 537-570.
Eaton, J., Kortum, S., 2002. Technology, geography, and trade. Econometrica 70, 1741-1779.
Feenstra, R.C., 1994. New product varieties and the measurement of international prices.
American Economic Review 84, 157-177.
Fujita, M., Krugman, P., Venables, A., 1999. The Spatial Economy: Cities, Regions, andInternational Trade. MIT Press, Cambridge.
Fujita, M., Thisse, J.F., 1996. Economics of agglomeration. Journal of the Japanese andInternational Economies 10, 339-378.
Hanson, G., 1996. Localization economies, vertical organization, and trade. American Economic
Review 86, 1266-1278.
Hanson, G., 1997. Increasing returns, trade, and the regional structure of wages. Economic
Journal 107, 113-133.
Hanson, G., Xiang, C., 2004. The home-market effect and bilateral trade patterns. American
Economic Review, forthcoming.
Harris, C.D., 1954. The market as a factor in the localization of industry in the United States.
Annals of the Association of American Geographers 44, 315-348.
Head, K., Mayer, T., 2003. The empirics of agglomeration and trade. Mimeo, University of
British Columbia.

27

Head, K., Mayer, T., 2004. Market potential and the location of Japanese investment in theEuropean Union. Review of Economics and Statistics, forthcoming.
Head, K., Ries, J., 2001. Increasing returns versus national product differentiation as an
explanation for the pattern of US-Canada trade. American Economic Review 91, 858-76.
Helpman, E., 1998. The size of regions, in: Pines, D., Sadka, E, Zilcha, I. (Eds.), Topics in Public
Economics. Cambridge University Press, Cambridge, pp. 33-54.
Keller, W., 2002. Geographic localization of international technology diffusion. American
Economic Review 92, 120-142.
Krugman, P., 1980. Scale economies, product differentiation, and the pattern of trade. American
Economic Review 70, 950-959.
Krugman, P., 1991. Increasing returns and economic geography. Journal of Political Economy 99,
483-499.
Ottaviano, G.I.P., Puga, D., 1997. Agglomeration in a global economy: a survey. Mimeo, LSE.
Overman, H.G., Redding, S, Venables, A., 2003. Economic geography: a survey of empirics, in:
Choi, E.K., Harrigan, J. (Eds.), Handbook of International Trade, Blackwell, Malden, pp. 353-387.
Puga, D., 1999. The rise and fall of regional inequalities. European Economic Review 43, 303334.
Rauch, J.E., 1993. Productivity gains from geographic concentration of human capital: evidence
from the cities. Journal of Urban Economics 34, 380-400.
Redding, S., Venables, A., 2004. Economic geography and international inequality. Journal ofInternational Economics 62, 53-82.
Roback, J., 1982. Wages, rents, and the quality of life. Journal of Political Economy 90, 1257-78.

28

Table 1: Variable Means for U.S. Counties(Standard Errors)

Wage

Employment

Employ.
Density

Personal
IncomeHousing
Stock

1970

17.42
(3.82)

25,509(109,896)

39.50(682.5)

897,454(3,785,338)

28,650(98,307)

1980

17.66
(3.74)

31,610(124,967)

41.59(608.4)

1,156,639(4,409,183)

27,717(90,900)

1990

17.29
(3.70)

38,041(146,679)47.03(649.4)

1,501,171(5,720,714)

27,467(87,394)

Variable Definitions:
Wage

Average annual labor earnings (thousand of 1990 dollars) for wage andsalary workers (Regional Economic Information System (REIS), U.S.BEA).

Employment

Average annual employment of wage and salary workers (REIS).

Employment
Density

Employment per square kilometer.

Personal Income

Total personal income (thousands of 1990 dollars) (REIS).

Housing Stock

Total housing units (U.S. Census of Population and Housing).

Distance

Distance from a county to the mid point of a concentric distance band (not reported
in the table above).

The Sample is 3,075 counties in the continental United States. County definitions are those for 1980. Each
independent city in Virginia is combined with the surrounding county.

29

Table 2: Estimation of the Simple Market-Potential Function

Time Period

1970-80(1)

1980-90(2)

1970-80(3)

1980-90(4)

1970-80(5)

1980-90(6)

1980-90(7)

1980-90(8)

1980-90(9)(α1) Market Potential

0.283(0.017)0.432(0.017)0.283(0.016)0.414(0.019)0.280(0.015)0.432(0.017)0.254(0.021)

0.239(0.022)0.254(0.021)(α2) Distance-5.465(0.746)-13.809(0.964)-5.465(0.718)-13.796(1.067)-5.534(0.721)-13.807(0.934)-15.352(1.796)-16.359(2.118)-15.352(1.796)

Adj. R2
Log Likelihood
Schwarz Criterion
Counties
Distance Bands
Wage Controls

0.117-16939.8-16951.8
All
All
No

0.236
-16747.2-16759.1
All
All
No

0.117
-16393.8-16951.8
Low Pop.
All
No

0.208
-14760.1-14771.9
Low Pop.
All
No

0.117
-16940.0-16952.0All<1000 kmNo

0.236
-16747.2-16759.2
All<1000 kmNo

0.362
-16474.7-16566.4
All
All
Yes

0.320
-14556.6-14646.8
Low Pop.
All
Yes

0.362
-16474.7-16566.4
All<1000 km
Yes

The full sample is 3,075 counties in the continental United States; the low-population sample is counties in the continental United States with lessthan 0.05% of the U.S. population. The dependent variable is the log change in average annual earnings for wage and salary workers. The
estimating equation for the simple market-potential function is equation (15), with α3 constrained to be one and α4 and α5 constrained to be
zero. Columns (5) and (6) exclude from the market-potential function county aggregates beyond 1000 km. from the county on which anobservation is taken. Columns (7)-(9) add controls for county average education levels, demographic characteristics, climate and other factors.
See the Appendix for the coefficient estimates on these variables (for column 7) and for more details on the wage controls. Heteroskedasticityconsistent standard errors are in parentheses. Parameters are estimated by nonlinear least squares. The Schwarz Criterion is ln(L)-k*ln(N)/2,
where L is the value of likelihood function, N is the number of observations, and k is the number of regression parameters. Coefficient estimates
for the constant term are not shown. See Table 1 for variable definitions.

30

Table 3: Estimation of the Augmented Market-Potential Function (Krugman Model)
Time PeriodMarket Potential
Distance
Personal Income
Wages
Housing Stock
Implied Valuesστµσ/(σ-1)σ(1-µ)

Adj. R2
Log Likelihood
Schwarz Criterion
Wald Test (p value)Counties
Wage Controls

1970-80(1)
0.132(0.022)-12.993(1.071)0.394(0.076)
7.202(1.271)0.606(0.076)

1980-90(2)
0.152(0.020)-17.907(0.906)0.802(0.068)5.760(0.823)0.198(0.068)1970-80(3)0.132(0.258)-11.580(1.006)0.381(0.095)6.997(1.439)0.619(0.095)1980-90(4)
0.147(0.021)-17.561(0.953)0.805(0.084)5.974(0.953)0.196(0.084)1980-90(5)0.203(0.056)-6.430(0.520)0.931(0.128)4.004(1.313)0.069(0.128)1980-90(6)
0.203(0.056)-6.429(0.520)0.931(0.128)4.006(1.314)0.068(0.128)7.597(1.250)1.970(0.328)0.916(0.015)1.152(0.029)0.639(0.072)6.562(0.838)3.219(0.416)0.956(0.013)1.180(0.030)0.226(0.075)7.377(1.402)1.816(0.351)0.911(0.018)1.157(0.034)0.653(0.089)6.779(0.973)3.039(0.440)0.967(0.016)1.173(0.029)0.221(0.094)4.935(1.372)1.634(0.523)
0.982(0.035)1.254(0.089)0.085(0.158)4.937(1.372)1.633(0.523)0.983(0.035)1.254(0.089)0.084(0.158)0.256-16698.1-16714.0
0.000
All
No

0.347
-16576.9-16592.9
0.000
All
No

0.217
-14699.4-14715.0
0.000
Low Pop.
No

0.296-14662.2-14677.9
0.000
Low Pop.
No

0.376-16479.9-16575.5
0.001
All
Yes

0.376
-14573.0-14667.1
0.001
Low Pop.
Yes

The estimating equation for the augmented market-potential function is (15’). Heteroskedasticityconsistent standard errors are in parentheses. Parameters are estimated by nonlinear least squares. The
Wald test statistic (p value) is for the hypothesis that α3=1, α4=0, and α5=0. Columns (5) and (6) include
additional wage controls in the estimation (see notes to Table 2). The Appendix shows coefficientestimates on these controls for the regression in column (5). The reported structural parameters are:σ = the elasticity of substitution between any pair of traded goods.
µ = the share of expenditure on traded goods.
τ = transportation costs (for units of 1000 km.).
σ/(σ-1) = ratio of price to marginal cost.
σ(1-µ) = stability condition for the spatial distribution of economic activity.

31

Table 4: GMM Estimation Results for the Augmented Market-Potential Function

Time Period

1970-80(1)

1980-90(2)

1970-80(3)

1980-90(4)

1980-90(5)

1980-90(6)(α1) Market Potential

0.487(0.119)-11.163(2.081)0.120(0.046)1.934(0.519)0.880(0.046)0.393(0.164)-15.400(2.054)0.664(0.138)1.882(0.957)0.336(0.138)0.492(0.119)-11.145(2.082)0.121(0.046)1.908(0.509)0.879(0.046)0.488(0.207)-16.597(3.312)0.615(0.127)1.435(0.770)0.385(0.127)0.467(0.372)-16.175(3.453)0.834(0.338)1.306(1.398)0.166(0.338)0.573(0.271)-15.108(2.366)0.754(0.169)0.992(0.703)0.246(0.169)2.053(0.500)10.593(5.585)0.545(0.113)1.934(0.519)0.935(0.025)2.546(1.064)9.964(7.129)0.821(0.154)1.647(0.446)0.456(0.210)2.028(0.490)10.836(5.737)0.539(0.114)1.972(0.463)0.935(0.025)2.050(0.869)15.800(14.901)
0.732
0.218
1.950
(0.787)0.550(0.221)2.140(1.705)14.188(18.875)
0.873(0.385)1.877(1.312)0.272(0.614)1.745(0.827)20.272(20.626)0.752(0.317)2.341(1.488)0.433(0.359)

0.160
0.000
0.343
Narrow
No

0.314
0.000
0.200
Narrow
No

0.159
0.000
0.254
Broad
No

0.298
0.000
0.167
Broad
No

0.327
0.015
0.206
Narrow
Yes

0.309
0.002
0.327
Broad
Yes

(α2) Distance(α3) Personal Income(α4) Wages(α5) Housing Stock
Implied Valuesστµσ/(σ-1)σ(1-µ)

Adj. R2
Wald Test (p value)
Chi-Square (p value)
Instrument Set
Wages Controls

Parameters are estimated by GMM. The narrow set of instruments is 10, 20, 30, and 40 year lagged
values of country population growth in the own county and in immediately surrounding counties; thebroad set of instruments adds to this set similar lagged values of more-distant-county population growth.
The Chi-Square test statistic (p value) is for a test of overidentifying restrictions on the instruments.
Heteroskedasticity-consistent standard errors are in parentheses. Columns (5) and (6) include additional
wage controls in the estimation (see notes to Table 2 and Appendix). See notes to Table 3 for additional
details on the estimation.

32

Figure 1: Log Change in Employment Relative to U.S., 1970-1990

Log Employment Change-1.4 - -0.2
(973)
-0.2 - 0(901)
0 - 0.4(917)
0.4 - 2.5(287)

Figure 2: Log Change in Average Wage Relative to U.S., 1970-1990

Log Wage Change-0.7 - -0.1
(624)
-0.1 - 0(1033)
0 - 0.15(1091)
0.15 - 1(330)

Figure 3: Spatial Decay of Predicted Wage Changes(a)Simple Market Potential Function(Nonlinear Least Squares, Table 2)
1980-90 (Table 2, Col. 2)

1970-80 (Table 3, Col. 1)

.04

.04

.035

.035

Predicted Change in Log Wages

Predicted Change in Log Wages

1970-80 (Table 2, Col. 1)(b) Augmented Market Potential Function(Nonlinear Least Squares, Table 3)

.03

.025

.02

.015

.01

.005

.025

.02

.015

.01

0

0

200

400
Distance in Km. from Shock1970-80 (Table 4, Col. 1)

600

800

1980-90 (Table 4, Col. 2).04

Predicted Change in Log Wages

.03

.005

0

.035

.03

.025

.02

.015

.01

.005

0

0

(c)

1980-90 (Table 3, Col. 2)

200

400
Distance in Km. from Shock600

Augmented Market Potential Function(GMM, Table 4)

800

0

200

400
Distance in Km. from Shock

600

800