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Federal Reserve Bank of Chicago

Clustering of Auto Supplier Plants in
the U.S.: GMM Spatial Logit for Large
Samples
Thomas Klier and Daniel P. McMillen

WP 2005-18

Clustering of Auto Supplier Plants in the U.S.:
GMM Spatial Logit for Large Samples
Thomas Klier
Federal Reserve Bank of Chicago
Research Department
230 S. LaSalle St.
Chicago, IL 60604
312-322-5762
tklier@frbchi.org
Daniel P. McMillen
Department of Economics (MC 144)
University of Illinois at Chicago
601 S. Morgan St.
Chicago, IL 60607
312-413-2100
mcmillen@uic.edu
May 5, 2005
JEL codes: R30, R15, L62
Key words: Spatial econometrics, clustering, plant location, auto supplier industry
Abstract
A linearized version of Pinkse and Slade’s (1998) spatial probit estimator is used
to account for the tendency of auto supplier plants to cluster together. By reducing
estimation to two steps – standard probit or logit followed by two-stage least squares –
linearization produces a model that can be estimated using large datasets. Our results
imply significant clustering among older plants. Supplier plants are more likely to be in
counties that are near assembly plants, that include interstate highways, and that are near
other counties with supplier plants. New plants show no additional tendency toward
clustering beyond that shown by older plants.
The authors thank Cole Bolton and Paul Ma for excellent research assistance.

2
1. Introduction
North American auto supplier plants have been remarkably concentrated for a
long time (Klier 2004). However, since the mid-1970s the spatial configuration of the
industry has been changing (Rubenstein 1992). Whereas the industry was concentrated
in a corridor running from Chicago to New York, it now has a north-south orientation.
The industry continues to be very spatially concentrated (Ellison and Glaeser 1997).
Using county level data, Woodward (1992) and Smith and Florida (1994) find evidence
that vertical linkages as well as the presence of highway infrastructure influence plant
location decision of Japanese plants in the United States.
In this paper, we model the location decisions of auto supplier plants using probit
models that take explicit account of the tendency for auto plants to cluster together.
Despite the rapid change in the geographic configuration of the industry, we show that
three salient features remain the same. First, Detroit remains the hub of the auto corridor,
which now extends southward to Kentucky and Tennessee with fingers reaching into
Mexico and Canada. Second, both supplier plants and assembly plants tend to cluster
together. Third, plant locations seldom stray far from the network of highways running
toward Detroit.
Spatial data increase the complexity of models of plant location decisions. We
use a logit model and county-level data: what is the probability that a plant is located in a
county given the locations of other plants and the characteristics of the county? Spatial
data typically exhibit both autocorrelation and heteroskedasticity. Autocorrelation makes
standard logit (or probit) estimates inefficient, and heteroskedasticity leads to inconsistent
estimates.

Several estimators have been proposed that are capable of producing

3
consistent estimates when data are spatially autocorrelated and heteroskedastic – Case
(1992), LeSage (2000), McMillen (1992), and Pinkse and Slade (1998). However, these
estimators become infeasible for large samples because they require the inversion of nxn
matrices, where n is the sample size.

One objective of our paper is to propose a

computationally feasible estimator for spatial discrete-choice models.
Our estimator is a linearized version of the generalized methods of moments
(GMM) estimator proposed by Pinkse and Slade (1998). Linearization allows the model
to be estimated in two steps. The first step is a standard probit or logit model, in which
spatial autocorrelation and heteroskedasticity are ignored. The second step involves twostage least squares estimates of the linearized model. The benefit of linearization is that
no matrix needs to be inverted and estimation requires only standard probit/logit models
and linear two-stage least squares. Thus, the model can be estimated even with very
large sample sizes.
Our estimator extends the literature on spatial modeling by allowing a model with
a spatially weighted dependent variable to be estimated in a discrete choice framework.
For the case of continuous dependent variables, examples of this sort of model include
Bordignon, Cerniglia, and Revelli (2003); Brett and Pinkse (2000); Brueckner (1998);
Brueckner and Saavedra (2001); Case, Rosen, and Hines (1993); Fredriksson and
Millimet (2002); Revelli (2003); and Saavedra (2000). The general model is written Y =
ρWY + Xβ + u, where Y is the dependent variable, W is the “contiguity matrix”, X is a
matrix of explanatory variables, u is an error term, and ρ and β are parameters whose
values are to be estimated. Spatial effects are present if ρ is not equal to zero: values of Y
are influenced by neighboring values of Y, where “neighbor” is defined implicitly by the

4
pre-specified entries of the contiguity matrix. For example, Brueckner (1998) finds that
California municipalities are more apt to have restrictive growth control measures if
nearby municipalities are also highly restrictive. Current estimators for this class of
spatial models are only suitable for models with continuous dependent variables. We
extend these estimators to the case where the dependent variable of interest is discrete.
Continuing with the example of growth controls, we re-interpret Y as the underlying
latent variable showing the strength of the tendency to adopt growth controls, which then
is translated into a discrete variable showing whether the municipality has measures to
control growth.
We use the spatial probit model to analyze location decisions of both old (pre1991) and new (1991-2003) auto supplier plants in the U.S. To capture the notion of
clustering, we assume that the propensity to locate a plant in a given county depends on
the propensity to locate plants in contiguous counties. Additional explanatory variables
include characteristics of the county such as the presence of an interstate highway,
distance from Detroit, population density, and crime rates.

We also include as

explanatory variables a count of the number of auto assembly plants located within 450
miles of the center of the county and the distance from there to the nearest assembly
plant.

Our results imply a strong tendency toward clustering among older plants.

Supplier plants that were opened prior to1991 are far more likely to locate near other
supplier plants and near interstate highways. They also are more likely to locate near
counties with assembly plants. New plants also tend to cluster together. However, the
focus of the industry has shifted southward. Once we control for proximity to existing
plants, new plants show no additional tendency toward concentration. The auto region

5
has shifted from an east-west to a north-south extension. It remains highly concentrated,
and Detroit continues to be its hub. Supplier plants cluster near assembly plants and
amongst each other.

2. Spatial Discrete Choice Models
The spatial model is written in matrix notation as
Y = ρWY + Xβ + ε

(1)

The nxn matrix W is the “weight matrix.” In the typical specification, Wii = 0 and

∑

n
ji =1

Wij = 1 for j ≠ i .

This specification implies that each value of the dependent

variable is a function of a group of explanatory variables, X, and a weighted average the
values of the dependent variable for nearby observations. Counties are the unit of
observation in our application. We follow common practice and impose that Wij = 1/ni
for all counties that are contiguous to county i, where ni is the number of observations
that are contiguous to county i. Under this specification, W is sometimes referred to as
the “contiguity matrix.” The coefficient ρ captures the spatial interaction effect. If ρ > 0,
then high values of Y for nearby observations increase the value for observation i. In our
formulation, ρ > 0 implies clustering: the probability of having an auto supplier plant in
a county increases if there are plants in neighboring counties. In contrast, ρ < 0 implies
dispersion as the probability decreases when there are plants in neighboring counties.
When the dependent variable is continuous, equation (1) is usually estimated by
maximum likelihood methods.

Under the assumption of normally and identically

distributed errors, the log-likelihood function is

6
−

n
n
1
((I − ρWY ) − Xβ )′ ((I − ρWY ) − Xβ ) + ln I − ρW
ln (2π ) − ln σ 2 −
2
2
2
2σ

(2)

where I − ρW is the Jacobian of the transformation from ε to Y. Common estimation
procedures are reviewed in Anselin (1988). Alternatively, Kelijian and Prucha (1998)
propose a GMM estimator for the model in which the spatial autoregressive term, WY, is
replaced by an instrumental variable, which is the predicted value from a regression of
WY on a set of instruments, Z. The GMM estimator has two advantages over maximumlikelihood estimation: (1) it does not rely on a potentially inaccurate assumption of
normally distributed errors, and (2) by relying on two-stage least squares, estimation does
not require calculating the determinants of nxn matrices. 1 The primary advantage of
maximum-likelihood estimation is the potential for efficiency.
structure of the model is rarely known.

However, the true

The specification of W is arbitrary, and

researchers often try several different specifications to figure out which one best captures
the spatial patterns evident in the data. GMM estimation is more robust than maximum
likelihood to departures from the restrictive assumptions required by the maximum
likelihood estimator.
When the dependent variable is discrete rather than continuous, maximum
likelihood estimation is problematic because the likelihood function typically involves n
integrals.

Several authors have proposed estimation procedures that maintain the

structure implied by maximum likelihood estimation for the spatial probit model. Case
(1992) assumes a special, block diagonal structure for W, which simplifies the estimation
1

Maximum-likelihood estimation can be simplified somewhat by calculating the eigenvalues of W, ωi,

since ln I − ρW =

∑

n
i =1

ln (1 − ρω i ) . After calculating ωi, no further manipulations of large matrices are

necessary. However, calculating the eigenvalues of an nxn matrix is itself problematic when the sample
size is large.

7
procedure substantially. For example, we might assume that all observations within a
state have a common spatial component: Wij = 1/ns (i≠j) for all observations in state s,
where ns is the number of observations in state s. However, this restrictive specification
does not allow the weights to decline with distance within a state. McMillen (1992) and
LeSage (2000) base their estimators directly on equations (1) and (2). McMillen uses an
EM algorithm to estimate the model under the assumption of normally distributed errors,
whereas LeSage uses a Bayesian approached based on Gibbs sampling to simulate the
probabilities. Both approaches are limited to relatively small samples because they
require the nxn matrix (I − ρW ) to be inverted in each iteration.
−1

A variant of the Pinkse and Slade (1998) GMM estimator for a spatial probit
model does not rely on the normality assumption. Their estimator is designed for a
model with spatially dependent errors:
y = Xβ + e,

(

)

e = θWe + ε = I − θW −1 ε

(3)

where ε is a vector of independently and identically distributed errors. Equation (3)
forms the basis for a probit model; the discrete variable, d, equals one if y > 0 and d = 0
−1

′
otherwise. The covariance matrix is V (e ) = ⎡(I − θW ) (I − θW )⎤ .
⎢
⎥
⎣
⎦

Thus, the model

structure implies both heteroskedasticity and autocorrelation for e unless θ = 0. Denoting
the ith diagonal element of this covariance matrix by σ i2 , the probability that di =1 is
given by Φ (X i* β ) , where X i* = X i / σ i . The generalized probit residuals are
ui =

(

(

d i − Φ X i* β

)(

(

)

Φ X i* β 1 − Φ X i* β

))

(4)

8
The GMM estimator is the value of θ that minimizes u ′ZMZ ′u , where Z is a matrix of
instruments and M is a positive-definite matrix. An interesting application of the Pinkse
and Slade estimator is found in Flores-Lagunes and Schnier (2005).
If M = (Z ′Z ) , the GMM estimator reduces to nonlinear two stage least squares.
−1

The iterative procedure has the following steps:

2.

′
Assume initial values for Γ = (β , θ ) , Γ0, and calculate u0 and the
gradient terms, G = ∂u 0 / ∂Γ .
ˆ
Regress G on Z. The predicted values are G .

3.
4.

ˆ ˆ
Construct the new estimates as Γ1 = Γ0 − G ′G
Iterate to convergence.

1.

( )

−1

ˆ
G ′u 0 .

The covariance matrix is given by

( ) [∑

ˆ ˆ
ˆ
var(Γ) = G ′G

−1

]( )

ˆ ˆ ˆ ˆ ˆ
u 2 Gi′G G ′G
i =1 i
n

−1

(5)

Note that a logit model involves no changes to this algorithm. The only difference is that
we define the probability as Pi = exp(X i* β ) / (1 + exp(X i* β )) and u i =

d i − Pi

Pi (1 − Pi )

.

This model extends readily to the spatial model. To do so, we must reinterpret
equation (1) as the underlying latent variable explaining the propensity to have d =1. As
the propensity to have d =1 increases (or decreases) for nearby observations, the
propensity increases (or decreases) for observation i also. This assumption is different
from a model in which the discrete variable d depends directly on neighboring values of d
– d = ρWd + Xβ + ε – or in which the value of the underlying variable depends on
neighboring values of d – y = ρWd + Xβ + ε .
consistent.

These models are not algebraically

9
Following this interpretation of equation (1) as the underlying latent variable for
the discrete choice model, we have
Y = ( I − ρ W ) Xβ + ( I − ρ W ) ε
−1

−1

(6)

As in the Pinkse and Slade (1998) model, the covariance matrix is given by
−1

⎡(I − ρW )′ (I − ρW )⎤ . The generalized probit error term is again given by equation (4),
⎢
⎥
⎣
⎦
but we now define the transformed value of X as X i* = H i / σ i , where H = (I − ρW ) X
−1

and σi is the square root of the ith diagonal entry of the covariance matrix.

The

estimation algorithm is unchanged. All that changes is the gradient terms. As before, we
have

⎛ ∂P ⎞
∂u i
= −⎜ *i ⎟ X i*
⎜ ∂X β ⎟
∂β
⎝ i ⎠

(7)

The gradient term for the spatial term is now:

⎤
⎛ ∂P ⎞ ⎡
X *β
∂u i
= −⎜ *i ⎟ ⎢ X i* β − i 2 Λ ii ⎥
⎜ ∂X β ⎟
∂ρ
σi
⎦
⎝ i ⎠⎣
where Λ is the nxn matrix (I − ρW ) W (I − ρW )
−1

(

)

(

)(

(

−1

( I − ρ W )− 1 .

Pi = Φ X i* β , whereas Pi = exp X i* β / 1 + exp X i* β

(8)

Under the probit model,

)) for the logit model.2

Note that Λii

= 0 ∀ i for the Pinkse and Slade (1998) version of the model, in which spatial dependence
is only present in the error terms. However, Λii ≠ 0 when the autoregressive term WY is
included as an explanatory variable. We exploit this fact in the next section to derive a
linearized version of the spatial autoregressive probit model.

(

)

For completeness, note that ∂Pi / ∂X i* β = u i u i + X i* β for the probit model, and ∂Pi / ∂X i* β = Pi (1 − Pi )
for the logit model.

2

10
3. The Linearized Spatial Probit Model
Although GMM estimation is robust to departures from the normality assumption
that is explicit in maximum likelihood estimation, the spatial probit and logit models
remain computationally burdensome. Each step of the iterative estimation procedures
requires the inversion of the nxn matrix (I-ρW). Yet the spatial model given by equation
(1) is generally viewed as an approximation. We seldom know the true structure of the
spatial dependence; what is known is that the errors tend to be correlated over space. The
models implied by equations (1) and (3) were developed for the relatively small data sets
that were common in the past. Large data sets require less restrictive models that do not
require inverting large matrices.
Since the model is already viewed as an approximation, a reasonable
simplification is to make the approximation explicit and linearize the model around a
convenient starting point (see Greene 2002). In this case, the starting point is obvious:
when ρ=0, β is estimated consistently by standard probit or logit models. And when ρ =
0, no matrices need be inverted because (I-ρW)-1 = I. The gradient terms simplify
substantially because the error terms have constant variances and X i* β = X i β . Recall
that u i =

d i − Pi

Pi (1 − Pi )

for either the logit or probit model. Linearizing this expression

′
around the initial estimates Γ0 = (β 0 , ρ 0 ) , we have u i ≈ u i0 + G0 (Γ − Γ0 ) .
vi = u i0 − G0 Γ0 + G0 Γ . Again letting M = (Z ′Z )

estimator is v′Z (Z ′Z )Z ′v .

−1

Define

, the objective function for the GMM

11
With the linearized model, estimation involves only three steps:

ˆ
1. Estimate the model by standard probit or logit. The estimated values are β 0 .
Calculate u0 and the gradient terms, G β = ∂u / ∂β and G ρ = ∂u / ∂ρ , where
⎛ ∂Pi
∂u i
= −⎜
⎜ ∂X β
ˆ
∂β
⎝ i 0

⎞
⎛
⎞
ˆ
⎟ X i and ∂u i = −⎜ ∂Pi ⎟ X i β 0 .
⎜ ∂X β ⎟
⎟
ˆ
∂ρ
⎝ i 0⎠
⎠
ˆ
ˆ
2. Regress Gβ and Gρ on Z. The predicted values are G β and G ρ .
′ˆ
ˆ
ˆ
3. Regress u 0 − G β β 0 on − G β and − G ρ . The coefficients are the estimated

values of β and ρ.
No large matrices have to be inverted in this algorithm. All it requires is standard probit
(or logit) and several linear regressions.
The algorithm is closely related to the first step of the GMM estimator for the
non-linearized model, which is a regression of u0 on

ˆ
ˆ
− G β and − G ρ . Subsequent

iterations of the full model would require calculating (I-ρW)-1. The spatial error model
approach of Pinkse and Slade (1998) is not identified under the linearization approach
because Λii in equation (8) is equal to zero when ρ = 0. However, the first term in
equation (8) allows ρ to be estimated under the spatial model. If the true structure of the
model is given by equation (1), linearization will provide accurate estimates as long as ρ
is small, and in general, the linearized model will provide a good approximation to an
underlying unknown spatial model.

12
4. Data
We base our analysis on data acquired from ELM International, a Michigan-based
vendor. Though not designed with research applications in mind, the intention behind the
ELM database is to cover the entire North American auto industry. Data are available at
the plant and company level. However, plants producing primarily for the aftermarket
are not part of the database; nor are plants that produce machine tools or raw materials,
such as steel and paint. 3
The ELM database, which provides 3,542 plant-level records, was purchased at
the end of 2003. The database includes information on a plant’s address, products,
employment, parts produced, customer(s), union status, as well as square footage.
Several operations were necessary to clean up the data. First, records were crosschecked
with state manufacturing directories to obtain information on the plant’s age. 4
Information on captive plants was obtained from Harbour (2003). We also appended
information on the nationality of the company to the record of each plant from the ELM
company-level data.

For the 150 largest supplier companies, the accuracy and

completeness of ELM’s plant listings – both the number of plants and their locations –
was crosschecked with the individual company’s website when possible.5

The

crosschecking resulted in a net addition of 335 records. Finally, the accuracy of the
employment for the largest plants (more than 2,000 employees) was also checked with
company websites or phone calls. After this preparation, the data set comprises 4,478
observations of auto supplier plants located in North America, of which 3,416 are located
3

The data include information on “captive” supplier plants, which are parts operations that assemblers own
and operate themselves, such as engine and stamping facilities.
4
Plants for which no matching records were found were contacted by phone.

13
in the U.S., 461 in Canada, and 601 in Mexico. To our knowledge, this data set contains
the most accurate description of the North American auto supplier industry currently
available. The formal analysis draws only on the U.S. data.
One of our objectives in the empirical analysis is to determine whether recent
plant location decisions differ from those of the past. Our definition of “new” is any
plant that has opened since 1991. We refer to plants that began operations before 1991 as
“existing” plants. The data is cross-sectional in nature. Hence, the age variable applies
only to surviving establishments. This focus on survivors may lead us to understate the
extent to which “old” plants are concentrated at the upper end of the auto corridor.
Within the North American auto industry, we distinguish assembly and supplier plants.
We focus on supplier plants as they represent by far the largest number of establishments
in this industry. In so doing, we are able to capture the spatial extension of this industry
quite well. Within the industry, the location of assembly plants matters as they often
represent the delivery point for a supplier’s output.
Figure 1 shows the location of existing (pre-1991) supplier plants in North
America in 2003, along with the sites of assembler plants. The dominance of the East
North Central region is striking. Detroit remains the core of the industry, with large
numbers of counties occupied by supplier plants in Ohio and Indiana, also. 6 The locus of
the industry has been moving southward over time. Though many plants are still evident
in New England and the Middle Atlantic states, the East South Central and South Atlantic
states have been adding plants recently. Very few plants are located in the western states.
Figure 2 shows the location of supplier plants that have opened since 1991. Most of the
5

We thank Jim Rubenstein for sharing his plant-level data for the 150 largest supplier companies. The 150
largest supplier companies are listed annually in the industry weekly Automotive News.

14
new plants are located along a path running south from Detroit, although a respectable
number of plants have opened in New England and the Middle Atlantic states. The
tendency of supplier plants to locate near assemblers is clear in both Figure 1 and 2.
Table 1 presents descriptive statistics for the variables used in our analysis. Of
the 3107 counties in the 48 contiguous states for which all data are available, 866
(27.87%) have plants that opened before 1990 and 245 (7.89%) have new plants. Most
new plants are located in counties that already have an existing plant: only 37 counties
have only a new plant. As shown in Figure 1 and 2, both new and existing plants are
concentrated in the East North Central, South Atlantic, and East South Central census
regions; these three regions account for more than two thirds (32.45%, 20.16%, and
16.06%, respectively) of the counties with auto supplier plants in 2003. The rotation of
the auto corridor toward a north-south corridor running from Detroit is evident in the
tendency for new plants to open up in the East North Central and East South Central
regions. In fact, counties with new plants tend to be closer to Detroit on average than
counties with existing plants – 407 miles compared to 494 miles. New supplier plants are
also closer to assembler plants on average than are the existing suppliers: the centers of
the counties in which new plants are located are 69.3 miles from the nearest assembler on
average, compared with 104.5 miles for existing plants. The number of assembler plants
within 450 miles of county centers is also higher for new plants than for existing plants –
36.547 versus 30.671. Overall, Table 1 suggests that the auto industry is re-trenching by
drawing closer to Detroit along a north-south corridor.
Our empirical strategy involves estimating separate logit models explaining
whether a county has an existing plant or a new plant. For the subset of counties that
6

For a map of plant density see Klier et al (2004)

15
have plants, we also estimate logit models explaining whether the county has a new plant.
Our explanatory variables include the regional dummy variables and distance from
Detroit. We include a dummy variable indicating whether an interstate highway runs
through the county. Auto suppliers have increasingly been using just in time inventory
systems, placing a premium on locations near highways running to assembler plants and
to Detroit. To account for the tendency to locate near assembler plants, our explanatory
variables include the distance to the nearest assembler and the count of the number of
assemblers within 450 miles (an approximate one day’s drive) from the center of the
county. We also include some characteristics of the counties – population density, the
proportion of the residents who are white, the proportion who have graduated from high
school, the proportion of the employment in the county that is in manufacturing, and
measures of the rates of violent and property crime.
We account for the tendency of supplier plants to cluster together in two ways.
First, we include the spatial lag variable WY, which is a weighted average of the
propensity for neighboring counties to have a supplier plant. The weight matrix, W, is a
contiguity matrix. We construct the matrix by setting Wij = 1/ni for counties that share a
common border, where ni is the number of observations that are contiguous to county i.
Wij = 0 for all other observations (including Wii). A positive value for this variable’s
coefficient implies a county’s probability of having a plant increases with the propensity
for neighboring counties to have plants. Our second measure of the tendency to cluster is
relevant only for new plants. For logit models explaining the probability that a county
has a new plant, we include as explanatory variables the number of existing suppliers
within 100 miles and between 100 and 450 miles of the center of the county. The results

16
for these variables will help determine whether the location decisions for new plants
simply mimic those of existing plants.

5. Logit Results
Our base model for counties with plants built prior to 1990 is shown in the first
column of results in Table 2. The estimated logit model indicates that the presence of an
interstate highway significantly increases the probability that a county will have an auto
supplier plant. The probability of having an existing plant also increases if the center of
the county is close to an assembly plant and if it is within a day’s drive from a large
number of assemblers. Not surprisingly, the probability of having an existing supplier
plant is higher if the county has a high proportion of high school graduates and if it
already has a high concentration of manufacturing employment. A somewhat surprising
result is our finding that the probability of having a plant is higher in counties with high
crime rates. This result holds even though we have controlled for the population density
in the counties. A possible explanation is that high crime rates reduce land values in a
county, and that auto plants substitute toward private security provision.

Another

possibility is that crime rates are correlated with urban locations in a way that is not
captured by the population density variable. At any rate, the positive effect of crime on
plant location is a robust result that holds up in subsequent models.
The tendency for auto supplier plants to cluster is evident in Table 2. Other
regions of the country tend to have much lower probabilities of having a plant than the
base location, the East North Central region, with significantly negative effects in the
Middle Atlantic, West North Central, South Atlantic, West South Central, and Pacific

17
regions.

Although distance from Detroit is not a significant determinant of plant

locations once other variables are taken into account, plants are much more likely to be
located near assembly plants and in counties containing interstate highways.

Since

assembly plants are clustered in the auto corridor around Detroit, supplier plants tend to
cluster together also.
The results for the linearized spatial logit model are presented in the last column
of Table 2. Instruments for the GMM estimation procedure include all of the exogenous
variables shown in Table 2. In addition, we include the weighted average of nearby
values (WX) of those variables that vary significantly over space – the presence of an
interstate highway, population density, crime rates, the proportion of employment that is
in manufacturing, and the proportions of the county’s residents that are white and who
have high school degrees. Most of the results for the spatial version of the model are
quite similar to those for the standard model. The significant changes are (1) the spatial
lag variable (WY) is highly significant, and (2) distance to the nearest assembler is no
longer a statistically significantly determinant of plant location. The positive coefficient
for WY implies that the probability that a county has an existing supplier plant increases
when neighboring counties have a high propensity to have plants also. These results
suggest that existing plants cluster together closely, even beyond the extent indicated by
the controls for regions, the presence of nearby assembly plants, highways, and other
manufacturing establishments.
Table 3 shows the estimated results for two sets of models explaining the
probability that a county has a supplier plant that has opened since 1991. The first set
omits controls for the number of existing suppliers within 100 miles and between 100 and

18
450 miles of the center of a county, while the second set includes these two variables.
Both models are estimated by standard logit and the linearized GMM spatial estimator.
We use the same instruments for the new plants models as for existing plants.
The first two columns of results in Table 3 are directly comparable to the models
estimated for existing plants. As was the case for existing plants, new supplier plants are
more likely to be located in counties that contain a stretch of interstate highway, that have
high proportion of high school graduates, that have a high proportion of their employment in manufacturing, and that have high property crime rates. In the base model, the
coefficient for distance from Detroit is significantly negative, implying that new plants
are more likely to be located closer to Detroit. However, this result disappears once we
control for the spatial autoregressive term, WY. Table 3 suggests that new plants are
somewhat less likely to be in the East North Central region, however. Controlling for
distance from Detroit, new plants are significantly more likely to be located in the East
South Central Region than in the base region surrounding Detroit.

Thus, the auto

industry is rotating toward the area south of Detroit.
The models presented in the first two columns of Table 3 suggest that the
tendency toward clustering is somewhat less pronounced for new plants than was
indicated for existing plants.

Although distance from the nearest assembler has a

significantly negative effect on the probability of having a new plants, neither this
variable nor the number of assemblers within 450 has a statistically significant effect
once we control for the spatial autoregressive term. The coefficient for the spatial
autoregressive term, WY, is statistically different from zero at the 10% level but not at the
5% level, and its value is lower than was the case for existing plants (0.355 v. 0.542).

19
However, it is possible that part of the reason for this apparent lack of explanatory power
of the variables that indicate clustering is due to the relatively small number of counties
that have new plants. Overall, the results for the first two columns of results in Table 3
suggest that the location decisions of new plants are broadly similar to those of existing
plants. New plants are more likely to locate south of Detroit, and exhibit a somewhat
smaller tendency toward clustering, but otherwise the factors that influenced the locations
of existing plants also affect new plants locations.
The last two columns of Table 3 add two variables to the models, the number of
existing suppliers within 100 miles and between 100 and 450 miles of the county. The
probability of having a new plant in a county rises significantly when older plants already
exist in the area, with a pronounced effect if there already are plants within 100 miles of
the county center. That effect diminishes in size for plants located within the larger
radius. It is, however, statistically significant. The spatial autoregressive term is no
longer statistically significant once these variables are added to the models. Though new
plants have a tendency to cluster together, the tendency simply mimics the location
pattern of existing plants. There is no increment to the clustering tendency among new
plants.
Table 4 presents logit results for the subset of counties that have either an existing
or a new plant. The dependent variable equals one if the county has a plant that has
opened since 1990.

The results directly capture the difference in location patterns

between new and old plants. New plants are more likely than old plants to be in counties
with a stretch of interstate highway. They are more likely to be in counties that are close
to assemblers. New plants are also more likely to be in counties with high property crime

20
rates, and in counties located in the East South Central, West South Central, Mountain,
and Pacific Regions. They are less likely to be in counties in the Middle Atlantic States.
Controlling for these regional fixed effects, new plants are likely to be closer to Detroit
than existing plants. With the exception of the Middle Atlantic and Mountain regional
effects, these results hold up once we control for the spatial autoregressive term. 7 The
insignificant coefficient for WY suggests again that new plants have no additional
tendency toward clustering once we control for the location of existing plants.

6. Conclusion
The spatial autoregression model is useful when individual decisions are mutually
dependent and are influenced by proximity. Do tax rates in one jurisdiction depend on
tax rates in nearby jurisdictions? Does the presence of growth controls depend on
whether neighboring municipalities have growth controls? Does the sales price of a
house depend on the prices paid for nearby homes? We show that the same class of
model is useful for identifying clustering in the location decisions of auto supplier plants
in the U.S. Does the presence of supplier plants in neighboring counties increase the
probability that a county will also have a plant? We find strong evidence of clustering
among plants that opened prior to 1991. Supplier plants are more likely to be located in
counties that are near assembly plants, in counties that contain a stretch of interstate
highway, and in counties that are near other counties with supplier plants. New plants
also tend to cluster, but there is no additional tendency toward clustering beyond that
shown by older plants.

7

The set of instruments is the same as used in previous models.

21
We extend the literature on spatial modeling in two ways. First, we extend the
standard spatial autoregression model to the case of a discrete continuous variable. Our
model is appropriate if the propensity to have a value of one for the dependent variable
depends on the propensity for nearby observations. Thus, the probability that an auto
supplier plant is located in a county depends on the underlying latent variable
determining the probability that nearby counties have assembly and/or supplier plants.
The model can be estimated using a straightforward extension of the GMM estimator
proposed by Pinkse and Slade (1998) for a spatial probit model. Our second contribution
to the literature on spatial modeling is to show how a linearized version of the GMM
approach can be used to estimate the spatial probit model when the sample size is large.
Our approach involves only three steps. The first stage is a standard probit or logit
estimator, while the second step is a standard two stage least squares estimation
procedure. The linearized model can be estimated even for very large data sets.

22
References
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yardstick competition: Property tax rates and electoral behavior in Italian cities. Journal
of Urban Economics 54, 199-217.
Brett, Craig and Joris Pinkse. 2000. The determinants of municipal tax rates in British
Columbia. Canadian Journal of Economics 33, 695-714.
Brueckner, Jan K. 1998. Testing for strategic interaction among local governments: The
case of growth controls. Journal of Urban Economics 44, 438-467.
Brueckner, Jan K. and Luz A. Saavedra. 2001. Do local governments engage in strategic
property-tax competition? National Tax Journal 54, 203-229.
Case, Anne C. 1992. Neighborhood influence and technological change. Regional
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Case, Anne C., Harvey S. Rosen, and James C. Hines. 1993. Budget spillovers and
fiscal policy interdependence: Evidence from the states. Journal of Public Economics
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manufacturing industries: A dartboard approach, Journal of Political Economy 105, 889927.
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Fredriksson, Per G. and Daniel L. Millimet. 2002. Strategic interaction and the
determinants of environmental policy across U.S. states. Journal of Urban Economics
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Greene, William H. 2002. Econometric Analysis. Upper Saddle River NJ: Prentice
Hall.
Harbour Consulting, Harbour Report, 2004 (2003).
Kelijian, Harry H. and Ingmar R. Prucha. 1998. A generalized spatial two-stage least
squares procedure for estimating a spatial autoregressive model with autoregressive
disturbances. Journal of Real Estate Finance and Economics 17, 99-121.
Klier, Thomas. 2004. Challenges to the U.S. auto industry. Chicago Fed Letter. Federal
Reserve Bank of Chicago, March.

23

LeSage, James P. 2000. Bayesian estimation of limited dependent variable spatial
autoregressive models. Geographical Analysis 32, 19-35.
McMillen, Daniel P. 1992. Probit with spatial autocorrelation. Journal of Regional
Science 32, 335-348.
Pinkse, Joris and Margaret E. Slade. 1998. Contracting in space: An application of
spatial statistics to discrete-choice models. Journal of Econometrics 85, 125-154.
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Rubenstein, James M. 1992. The Changing U.S. Auto Industry – A Geographical
Analysis. London: Routledge.
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Journal of Urban Economics 47, 248-279.
Smith, Donald and Richard Florida. 1994. Agglomeration and industrial location: An
econometric analysis of Japanese-affiliated manufacturing establishments in automotiverelated industries. Journal of Urban Economics 36, 23-41.
Woodward, Douglas. 1992. Locational determinants of Japanese manufacturing start-ups
in the United States. Southern Economic Journal 58, 690-708.

24
Table 1
Descriptive Statistics
All
Counties
Existing plant located in county (%)
New plant located in county (%)
Interstate highway (%)
Distance to nearest assembler (100 miles)
Number of assemblers within 450 miles
Existing suppliers within 100 miles
Existing suppliers,
100-450 miles
Population density
(1000s per sq. mile)
Proportion white
Proportion high school graduates
Proportion manuf. employment
Violent crime rate
(1000s)
Property crime rate
(1000s)
East North Central (%)
New England (%)
Middle Atlantic (%)
West North Central (%)
South Atlantic (%)
East South Central (%)
West South Central (%)
Mountain (%)
Pacific (%)
Distance from Detroit
(100 miles)
Number of observations

27.87
7.89
44.09
1.880
(1.799)
19.467
(17.791)
0.487
(0.911)
7.811
(7.329)
0.218
(1.434)
0.875
(0.153)
0.695
(0.103)
0.186
(0.106)
0.278
(0.320)
2.631
(1.983)
14.06
2.16
4.83
19.89
18.93
11.72
15.13
9.01
4.28
7.395
(4.365)
3107

Counties
with
Existing
Plants
100.00
24.02
63.51
1.045
(1.068)
30.671
(17.064)
1.129
(1.420)
12.129
(6.920)
0.357
(1.315)
0.884
(0.133)
0.711
(0.096)
0.245
(0.093)
0.364
(0.394)
3.283
(2.111)
33.03
3.35
7.04
10.62
20.09
15.82
6.58
1.85
1.62
4.942
(3.338)
866

Counties
with New
Plants

New or
Existing
Plants

84.90
100.00
73.47
0.693
(0.788)
36.547
(16.439)
1.815
(1.890)
14.303
(6.341)
0.418
(0.782)
0.886
(0.118)
0.714
(0.091)
0.256
(0.085)
0.409
(0.378)
3.488
(2.078)
43.27
1.63
3.67
6.12
15.92
23.27
3.67
0.41
2.04
4.073
(3.412)
245

95.90
27.13
63.34
1.041
(1.053)
30.573
(17.076)
1.110
(1.405)
12.120
(6.948)
0.347
(1.289)
0.884
(0.133)
0.709
(0.096)
0.245
(0.093)
0.362
(0.389)
3.260
(2.094)
32.45
3.32
7.09
10.63
20.16
16.06
6.76
1.77
1.77
4.978
(3.380)
903

Note. Standard deviations are in parentheses for continuous variables.

25
Table 2
Logit Models: Existing Supplier Plants
Variable
Constant

Standard Logit Spatial Logit
-8.333**
-6.166**
(0.910)
(1.059)
Interstate highway
0.725**
0.584**
(0.110)
(0.113)
Distance to nearest assembler (100 miles)
-0.183**
-0.010
(0.066)
(0.072)
Number of assemblers within 450 miles
0.035**
0.028**
(0.008)
(0.008)
Population density
-0.059
-0.061
(1000s per sq. mile)
(0.036)
(0.038)
Proportion white
0.095
0.113
(0.494)
(0.518)
Proportion high school graduates
5.330**
2.990**
(0.819)
(0.973)
Proportion manuf. employment
9.670**
6.599**
(0.698)
(0.931)
Violent crime rate
0.582**
0.472*
(1000s)
(0.245)
(0.261)
Property crime rate
0.323**
0.302**
(1000s)
(0.041)
(0.047)
New England
0.236
0.036
(0.346)
(0.329)
Middle Atlantic
-0.830**
-0.426*
(0.225)
(0.233)
West North Central
-0.546**
0.049
(0.227)
(0.268)
South Atlantic
-0.787**
-0.484**
(0.194)
(0.205)
East South Central
-0.192
0.005
(0.215)
(0.220)
West South Central
-0.853**
-0.354
(0.303)
(0.331)
Mountain
-0.851
-1.174**
(0.555)
(0.590)
Pacific
-1.403*
-1.961**
(0.788)
(0.806)
Distance from Detroit
0.014
0.094
(100 miles)
(0.058)
(0.059)
WY
0.542**
(0.101)

Notes. Standard errors are in parentheses. Significance at the 5% and 10% level is
indicated by “**” and “*”.

26
Table 3
Logit Models: New Supplier Plants
Variable
Constant
Interstate highway
Distance to nearest assembler (100
miles)
Number of assemblers within 450 miles

Standard
Logit
-6.964**
(1.576)
0.888**
(0.179)
-0.543**
(0.140)
0.016
(0.013)

Spatial
Logit
-6.029**
(1.586)
0.835**
(0.186)
-0.203
(0.231)
0.013
(0.015)

-0.058
(0.076)
0.013
(0.856)
3.910**
(1.259)
6.681**
(1.043)
0.309
(0.332)
0.296**
(0.059)
0.514
(0.650)
-0.998**
(0.397)
-0.031
(0.408)
-0.077
(0.296)
1.172**
(0.305)
0.505
(0.581)
1.889
(1.475)
4.519**
(1.552)
-0.274**
(0.108)

-0.140**
(0.055)
0.107
(0.742)
3.176**
(1.319)
5.605**
(1.205)
0.190
(0.289)
0.323**
(0.052)
0.222
(0.687)
-0.645
(0.425)
0.172
(0.435)
-0.023
(0.298)
1.095**
(0.366)
0.540
(0.506)
-1.545
(1.977)
3.263
(2.320)
-0.194
(0.159)
0.355*
(0.181)

Existing suppliers within 100 miles
Existing suppliers, 100-450 miles
Population density
(1000s per sq. mile)
Proportion white
Proportion high school graduates
Proportion manuf. employment
Violent crime rate
(1000s)
Property crime rate
(1000s)
New England
Middle Atlantic
West North Central
South Atlantic
East South Central
West South Central
Mountain
Pacific
Distance from Detroit
(100 miles)
WY

Standard
Logit
-9.474**
(1.647)
0.858**
(0.183)
-0.371**
(0.135)
-0.049*
(0.029)
0.709**
(0.129)
0.229**
(0.067)
-0.021
(0.063)
-0.765
(0.892)
3.576**
(1.298)
5.628**
(1.103)
-0.063
(0.343)
0.317**
(0.059)
1.561**
(0.697)
0.242
(0.462)
0.372
(0.418)
0.296
(0.323)
1.247**
(0.306)
0.346
(0.629)
-0.730
(1.519)
-0.125
(1.684)
0.114
(0.126)

Spatial
Logit
-9.207**
(1.980)
0.837**
(0.193)
-0.182
(0.196)
-0.046
(0.031)
0.675**
(0.198)
0.214**
(0.078)
-0.036
(0.039)
-0.612
(0.784)
3.475**
(1.347)
5.073**
(1.199)
-0.045
(0.308)
0.304**
(0.053)
1.122
(0.771)
0.219
(0.468)
0.306
(0.425)
0.218
(0.328)
1.155**
(0.354)
0.109
(0.569)
-2.152
(1.954)
-0.928
(2.016)
0.149
(0.152)
0.104
(0.195)

Notes. Standard errors are in parentheses. Significance at the 5% and 10% level is indicated by
“**” and “*”.

27

Table 4
Logit Models: New Versus Existing Plants
Variable
Constant

Standard Logit Spatial Logit
-2.078
-1.880
(1.761)
(1.740)
Interstate highway
0.595**
0.586**
(0.193)
(0.192)
Distance to nearest assembler (100 miles)
-0.443**
-0.408**
(0.152)
(0.201)
Number of assemblers within 450 miles
0.008
0.008
(0.014)
(0.016)
Population density
0.022
0.010
(1000s per sq. mile)
(0.068)
(0.048)
Proportion white
-0.280
-0.353
(1.026)
(0.923)
Proportion high school graduates
1.155
1.044
(1.401)
(1.386)
Proportion manuf. employment
1.927
1.895
(1.199)
(1.205)
Violent crime rate
-0.123
-0.131
(1000s)
(0.383)
(0.361)
Property crime rate
0.196**
0.196**
(1000s)
(0.073)
(0.070)
New England
0.337
0.448
(0.682)
(0.686)
Middle Atlantic
-0.860**
-0.739
(0.418)
(0.456)
West North Central
0.440
0.461
(0.437)
(0.454)
South Atlantic
0.429
0.426
(0.342)
(0.379)
East South Central
1.351**
1.264**
(0.338)
(0.414)
West South Central
1.196*
1.134**
(0.616)
(0.570)
Mountain
3.156**
2.947
(1.484)
(1.880)
Pacific
5.740**
5.405**
(1.661)
(2.262)
Distance from Detroit
-0.296**
-0.282*
(100 miles)
(0.114)
(0.145)
WY
0.132
(0.193)

Notes. The dependent variable equals one if the county has a new plant. The data set
includes the 903 counties that contain either a new or an existing plant. Standard errors
are in parentheses. Significance at the 5% and 10% level is indicated by “**” and “*”.

28

Figure 1
Counties with Existing Plants

29

Figure 2
Counties with New Plants

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François R. Velde

WP-03-31

Deregulation and the Relationship Between Bank CEO
Compensation and Risk-Taking
Elijah Brewer III, William Curt Hunter and William E. Jackson III

WP-03-32

4

Working Paper Series (continued)
Compatibility and Pricing with Indirect Network Effects: Evidence from ATMs
Christopher R. Knittel and Victor Stango

WP-03-33

Self-Employment as an Alternative to Unemployment
Ellen R. Rissman

WP-03-34

Where the Headquarters are – Evidence from Large Public Companies 1990-2000
Tyler Diacon and Thomas H. Klier

WP-03-35

Standing Facilities and Interbank Borrowing: Evidence from the Federal Reserve’s
New Discount Window
Craig Furfine

WP-04-01

Netting, Financial Contracts, and Banks: The Economic Implications
William J. Bergman, Robert R. Bliss, Christian A. Johnson and George G. Kaufman

WP-04-02

Real Effects of Bank Competition
Nicola Cetorelli

WP-04-03

Finance as a Barrier To Entry: Bank Competition and Industry Structure in
Local U.S. Markets?
Nicola Cetorelli and Philip E. Strahan

WP-04-04

The Dynamics of Work and Debt
Jeffrey R. Campbell and Zvi Hercowitz

WP-04-05

Fiscal Policy in the Aftermath of 9/11
Jonas Fisher and Martin Eichenbaum

WP-04-06

Merger Momentum and Investor Sentiment: The Stock Market Reaction
To Merger Announcements
Richard J. Rosen

WP-04-07

Earnings Inequality and the Business Cycle
Gadi Barlevy and Daniel Tsiddon

WP-04-08

Platform Competition in Two-Sided Markets: The Case of Payment Networks
Sujit Chakravorti and Roberto Roson

WP-04-09

Nominal Debt as a Burden on Monetary Policy
Javier Díaz-Giménez, Giorgia Giovannetti, Ramon Marimon, and Pedro Teles

WP-04-10

On the Timing of Innovation in Stochastic Schumpeterian Growth Models
Gadi Barlevy

WP-04-11

Policy Externalities: How US Antidumping Affects Japanese Exports to the EU
Chad P. Bown and Meredith A. Crowley

WP-04-12

Sibling Similarities, Differences and Economic Inequality
Bhashkar Mazumder

WP-04-13

Determinants of Business Cycle Comovement: A Robust Analysis
Marianne Baxter and Michael A. Kouparitsas

WP-04-14

5

Working Paper Series (continued)
The Occupational Assimilation of Hispanics in the U.S.: Evidence from Panel Data
Maude Toussaint-Comeau

WP-04-15

Reading, Writing, and Raisinets1: Are School Finances Contributing to Children’s Obesity?
Patricia M. Anderson and Kristin F. Butcher

WP-04-16

Learning by Observing: Information Spillovers in the Execution and Valuation
of Commercial Bank M&As
Gayle DeLong and Robert DeYoung

WP-04-17

Prospects for Immigrant-Native Wealth Assimilation:
Evidence from Financial Market Participation
Una Okonkwo Osili and Anna Paulson

WP-04-18

Individuals and Institutions: Evidence from International Migrants in the U.S.
Una Okonkwo Osili and Anna Paulson

WP-04-19

Are Technology Improvements Contractionary?
Susanto Basu, John Fernald and Miles Kimball

WP-04-20

The Minimum Wage, Restaurant Prices and Labor Market Structure
Daniel Aaronson, Eric French and James MacDonald

WP-04-21

Betcha can’t acquire just one: merger programs and compensation
Richard J. Rosen

WP-04-22

Not Working: Demographic Changes, Policy Changes,
and the Distribution of Weeks (Not) Worked
Lisa Barrow and Kristin F. Butcher

WP-04-23

The Role of Collateralized Household Debt in Macroeconomic Stabilization
Jeffrey R. Campbell and Zvi Hercowitz

WP-04-24

Advertising and Pricing at Multiple-Output Firms: Evidence from U.S. Thrift Institutions
Robert DeYoung and Evren Örs

WP-04-25

Monetary Policy with State Contingent Interest Rates
Bernardino Adão, Isabel Correia and Pedro Teles

WP-04-26

Comparing location decisions of domestic and foreign auto supplier plants
Thomas Klier, Paul Ma and Daniel P. McMillen

WP-04-27

China’s export growth and US trade policy
Chad P. Bown and Meredith A. Crowley

WP-04-28

Where do manufacturing firms locate their Headquarters?
J. Vernon Henderson and Yukako Ono

WP-04-29

Monetary Policy with Single Instrument Feedback Rules
Bernardino Adão, Isabel Correia and Pedro Teles

WP-04-30

6

Working Paper Series (continued)
Firm-Specific Capital, Nominal Rigidities and the Business Cycle
David Altig, Lawrence J. Christiano, Martin Eichenbaum and Jesper Linde

WP-05-01

Do Returns to Schooling Differ by Race and Ethnicity?
Lisa Barrow and Cecilia Elena Rouse

WP-05-02

Derivatives and Systemic Risk: Netting, Collateral, and Closeout
Robert R. Bliss and George G. Kaufman

WP-05-03

Risk Overhang and Loan Portfolio Decisions
Robert DeYoung, Anne Gron and Andrew Winton

WP-05-04

Characterizations in a random record model with a non-identically distributed initial record
Gadi Barlevy and H. N. Nagaraja

WP-05-05

Price discovery in a market under stress: the U.S. Treasury market in fall 1998
Craig H. Furfine and Eli M. Remolona

WP-05-06

Politics and Efficiency of Separating Capital and Ordinary Government Budgets
Marco Bassetto with Thomas J. Sargent

WP-05-07

Rigid Prices: Evidence from U.S. Scanner Data
Jeffrey R. Campbell and Benjamin Eden

WP-05-08

Entrepreneurship, Frictions, and Wealth
Marco Cagetti and Mariacristina De Nardi

WP-05-09

Wealth inequality: data and models
Marco Cagetti and Mariacristina De Nardi

WP-05-10

What Determines Bilateral Trade Flows?
Marianne Baxter and Michael A. Kouparitsas

WP-05-11

Intergenerational Economic Mobility in the U.S., 1940 to 2000
Daniel Aaronson and Bhashkar Mazumder

WP-05-12

Differential Mortality, Uncertain Medical Expenses, and the Saving of Elderly Singles
Mariacristina De Nardi, Eric French, and John Bailey Jones

WP-05-13

Fixed Term Employment Contracts in an Equilibrium Search Model
Fernando Alvarez and Marcelo Veracierto

WP-05-14

Causality, Causality, Causality: The View of Education Inputs and Outputs from Economics
Lisa Barrow and Cecilia Elena Rouse

WP-05-15

7

Working Paper Series (continued)
Competition in Large Markets
Jeffrey R. Campbell

WP-05-16

Why Do Firms Go Public? Evidence from the Banking Industry
Richard J. Rosen, Scott B. Smart and Chad J. Zutter

WP-05-17

Clustering of Auto Supplier Plants in the U.S.: GMM Spatial Logit for Large Samples
Thomas Klier and Daniel P. McMillen

WP-05-18

8