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Workinq Paper 8703

ESTIMATING THE RELATIONSHIP BETWEEN
LOCAL PUBLIC AND PRIVATE INVESTMENT

by Randall W. Eberts and Michael S. Fogarty

Randall W. Eberts i s an a s s i s t a n t v i c e
p r e s i d e n t and economist a t t h e Federal
Reserve Bank of Cleveland. Michael S.
Fogarty i s d i r e c t o r o f t h e Center f o r
.
Regional Economic Issues a t Case Western
Reserve U n i v e r s i t y i n Cleveland, Ohio. The
authors g r a t e f u l l y acknowledge t h e
assistance o f Douglas Dalenberg and Chul Soo
Park i n c o m p i l i n g t h e investment s e r i e s .
P a t r i c i a E. Beeson and Robert Schwab
provided h e l p f u l comments and suggestions.
Working Papers o f t h e Federal Reserve Bank
o f Cleveland a r e p r e l i m i n a r y m a t e r i a l s
c i r c u l a t e d t o s t i m u l a t e d i s c u s s i o n and
c r i t i c a l comment. The views s t a t e d h e r e i n
a r e those of t h e authors and n o t n e c e s s a r i l y
those o f t h e Federal Reserve Bank o f
Cleveland or t h e Board o f Governors of t h e
Federal Reserve System.

May 1987

I. introduction
Economic development has become a major concern o f many local
pol icymakers.

The most recent recession, by cutting deep into many urban

economies, has left local officials scrambling to claim what they
consider t o be their share o f the national economic expansion.

Although

competition for economic activity has considerable historical precedent,
at present regional rivalry appears t o be particularly keen as snowbelt
states fight to slow the loss o f manufacturing facilities to the southern
and western regions of the country. One o f the primary instruments
available t o local policymakers to retain, nurture and attract firms is
the formation o f public infrastructure.

Maintenance and expansion of

public infrastructure such as highways, water distribution and treatment
facilities, airports, and waterways are important factors in the decision
o f firms t o expand and locate.
The recent interest in the use of public infrastructure t o promote
economic development differs to some extent from the regional and federal
development projects of the late 1950s and 1960s.

These programs, such

as the Appalachian development effort, involved massive infusions of
money from higher levels o f government in an attempt t o provide these
regions with a critical mass o f infrastructure that would presumably
stimulate economic growth.

In contrast, infrastructure development at

the individual local level is much less ambitious.

Although federal

grants are an important financing source of some local projects, to a
large extent, local public investment is financed out o f local and state
revenues, which are under the control o f area taxpayers.

These funds are

spent o n local roads, water distribution and treatment facilities,.

school s, and other bui ldings and structures.

State and local governments

spent over 238.5 billion dollars on equipment and structures in 1978
alone, which is nearly 7 3 percent o f total government expenditures on
capital (Musgrave, 1981).
Despite the importance of these factors to businesses and local
government officials, very 1 i ttle work has been done t o explore the
relationship between private and public investment.

Investigation into

this relationship has been plagued primarily by the lack of adequate
data.

Even with recent interest in the deterioration o f the nation's

public infrastructure, estimates o f public capital stock for local areas,
which provide consistent measures across standard metropolitan
statistical areas (SMSAs), have not been made.

In addition, information

on plant location and estimates of local private capital stock is not
readily available.

In response to the lack o f data t o explore these

issues concerning local economic development, we have undertaken a
project to measure private and pub1 i c capital stocks for 52 SMSAs -from
1958-1 978.
The fundamental issue raised in this paper concerns the use and
effectiveness o f public infrastructure as a local policy instrument.

A

necessary condition for local public investment t o influence economic
development is for the formation o'f public investment t o precede the
formation o f private investment.

Obviously, the timing o f investment i s

not sufficient for public investment t o be an effective policy
instrument, since many other locational and market factors are important
in business decisions.

Nonetheless, such a sequence of events would

indicate that local areas, through either deliberate local policy o r the
desire o f local voters, actively use public outlays as an instrument t o

try to direct loca-l development.

On the other hand, if the sequence o f

events occurs in the opposite direction, it would appear that local
officials mere,ly respond t o the location o f private economic activity by
putting in place infrastructure after private investment has been made.
One could argue that the installation o f roads and sewer and water lines,
for example, may be prearranged before a business decides to locate in an
area, even though the actual construction does not occur unti 1 after the
private faci 1 i ty has been bui l t. Considering, however, the amount o f
time necessary to build structures and the fact that we are looking at
the aggregate behavior of many individuals, one would expect that over a
sufficiently long period of time the likelihood o f perfect timing andlor
foresight would be very small.
To answer the question of whether local public investment
"influences" private investment, we perform the Sims test o f "Granger
causality" for a sample of 40 SMSAs using investment data from 1904 t o
1978. Granger's definition o f causality is based upon the predictive
ability o f one series to explain another.

Granger states that X "causes"

Y if the past history o f X can be used t o predict Y more accurately than
by simply using the past history of Y.

While this definition is not in

complete accord with the notion of causality held by philosophers of
science, it has considerable appeal for examining statistical
relationships since, under certain a priori restrictions, it is
equivalent t o econometric exogenei ty.

Sargent (19761, for example, used

the Sims procedure t o test for exogeneity o f policy variables in his
macro model.

We perform the Sims test o n public and private investment

series t o test if public investment is exogenous o r if there are strong

feedbacks from private t o public investment.
The issue of exogeneity addresses a secondary area o f concern: can
public investment be considered exogenous in econometric models? One of
our goals in investigating the relationship between public and private
investment is t o determine the effect of public infrastructure on the
productivity o f urban economies. Thus, the issue o f exogeneity is
important when entering public capital stock into production functions,
private investment equations, regional economic growth models, and firm
location equations.
For now, however, we perform the Sims test o n investment series of
each of 40 SMSAs.

We then examine whether the patterns o f significant

directional relationships can be explained by various characteristics of
these local economies.

Finally, we consider the sign and magnitude of

the correlation between the t w o time series for a subsample o f the 40
SMSAs .

11.

Econometric Specification
Urban Economic Model

A simple model of the urban economy

demonstrates the relationship between private and public capital and the
possibility that the direction o f influence between the t w o investment
series may g o in either direction.

'

Public infrastructure can be viewed as both an intermediate and a
final good.

Local residents consume services from pub1 i c capital stock

as a final good; local firms use public capital stock as a factor of
production.

In both cases, public capital is not purchased directly but

i s financed by tax d o l l a r s , the amount determined w i t h i n the p o l i t i c a l
process.

The process by whi ch l o c a l pub1i c investment i n f 1uences p r i v a t e

investment and vice versa can be i l l u s t r a t e d by c o n s t r u c t i n g a simple,
export base model o f a l o c a l economy.
Pest i eau

( 1976)

S i m i l a r models are found i n

and Kanemoto (1 980).

Assume t h a t manufacturing f i r m s w i t h i n the l o c a l area purchase l o c a l
inputs ( p r i v a t e c a p i t a l , K, and labor,

L) t h a t , when combined w i t h l o c a l

p u b l i c c a p i t a l ( G I produces Q, an output t h a t i s s o l d t o a n a t i o n a l
market.

The issue o f how p u b l i c c a p i t a l enters the production f u n c t i o n

has been discussed t h e o r e t i c a l l y by Negishi (1973).

He shows t h a t p u b l i c

c a p i t a l , viewed as an unpaid f a c t o r o f production, renders the production
function homogeneous o f degree one w i t h respect t o a1 1 inputs, i n c l u d i n g
public capital.

Furthermore, he argues t h a t i f p u b l i c and p r i v a t e

c a p i t a l stock are not s u b s t i t u t e s , the higher r e n t s accruing t o firms due
t o the l e v e l o f p u b l i c c a p i t a l w i l l a t t r a c t a d d i t i o n a l f i r m s i n t o the
area.

Thus, p r i v a t e c a p i t a l investment i s a f u n c t i o n o f p u b l i c

i n f r a s t r u c t u r e investment.

These r e l a t i o n s h i p s can be shown by p o s i t i n g

a general production f u n c t i o n :

Since G i s determined exogenously, i t i s considered a quasi- fixed i n p u t .
Also, since G i s n o t a pure p u b l i c good i n the Samuelsonian sense,
congestion may occur depending upon the number o f firms t h a t use the
good.

A congestion f a c t o r could be entered i n t o the model as

where g , i s t h e amount o f services from G received by t h e i t h f i r m ,
which i s a f u n c t i o n o f the l e v e l o f t o t a l o u t p u t and a congestion
parameter (0<0<
1>

.

S i nce t h i s addi t i o n a l c h a r a c t e r i s t i c w i 11 n o t change

t h e general r e l a t i o n s h i p between p r i v a t e and p u b l i c investment, i t i s n o t
included i n t h e model.

The publicness o f t h e services from p u b l i c

c a p i t a l stock, however, may be one o f several reasons why p u b l i c and
p r i v a t e investment may n o t be s t r o n g l y c o r r e l a t e d f o r some SMSAs, if
indeed t h i s t u r n s o u t t o be the case.
Under c e r t a i n r e g u l a r i t y c o n d i t i o n s , t h e demand f o r p r i v a t e c a p i t a l
and l a b o r can be described as a f u n c t i o n of p u b l i c c a p i t a l :

(2)

K = K(w,r,Q,G)

(3)

L = L(w,r,Q,G),

and

where w i s t h e wage r a t e and r i s t h e p r i c e o f c a p i t a l .
Local income i s generated through t h e p a y r o l l of manufacturing f i r m s
i n the area.

D o l l a r s spent by manufacturing workers on l o c a l services

create a d d i t i o n a l l o c a l income according t o t h e m u l t i p l i e r 8.

Thus,

P u b l i c goods are provided through t h e p o l i t i c a l process i n which t h e
preferences o f t h e median v o t e r determine t h e l e v e l o f p u b l i c
expenditures.

Businesses do n o t have d i r e c t i n p u t i n t o t h e p o l i t i c a l

process.

Their preferences may be conveyed through lobbying efforts

directed at voters o r government officials.

Furthermore, communities

with large industrial complexes may simply have more money t o spend o n
public outlays.
At this stage, we keep the model simple and adopt a median voter
model t o determine the level of public outlays.

The utility of the

median voter is a function o f a composite private good, X ; and public
capital stock, G.

Of course, the median voter consumes other pub1 ic

serivces, but it serves our purpose t o consider only G. The median voter
maximizes uti 1 i ty, subject to a budget constraint:

(5)

max

U(X,G)

s.t. pxX+pGyG=Y,

where p, is the price of the private good, p, is the unit cost of the
public capital good, and y is the median voter's share of the cost of
the public capital good.
efficiently.

We assume that local public goods are produced

First order conditions yield a demand function for G:

Again, a congestion function could be specified as described for the
production function.

Since the income o f the median voter is a function

of the wage rate and the demand for labor by firms in the community, the
demand for publlc infrastructure is also a function o f the level of
private capital investment.

W i t h i n t h i s simple framework, the r e l a t i o n s h i p between p u b l i c and
p r i v a t e c a p i t a l may be i n e i t h e r d i r e c t i o n :

p u b l i c c a p i t a l may a c t i v e l y

i n f l u e n c e p r i v a t e c a p i t a l , o r p r i v a t e c a p i t a l may a c t i v e l y i n f l u e n c e
public capital.

That i s , G i n f l u e n c e s K d i r e c t l y through t h e p r o d u c t i o n

f u n c t i o n ; o r K i n f l u e n c e s G i n d i r e c t l y by i n f l u e n c i n g L and thus Y.
Although f i r m s and taxpayers b e n e f i t f r o m t h e s e r v i c e s they r e c e i v e
from c a p i t a l stock, p o l i c y decisions are u s u a l l y made w i t h r e g a r d t o
investment.

C a p i t a l stock i s t h e r e s u l t o f p a s t investment d e c i s i o n s .

With constant d e p r e c i a t i o n p a t t e r n s over time, the f o r m a t i o n o f c a p i t a l
stock f o l l o w s t h e t i m i n g o f investment d e c i s i o n s .

Thus, p u b l i c and

p r i v a t e investment s e r i e s a r e used t o examine the i s s u e . o f d i r e c t i o n a l
relationships.

S i m s Test

The Sims t e s t i s b a s i c a l l y a t e s t o f p r e d i c t i v e n e s s .

best, i t can t e s t Granger's s t a t i s t i c a l d e f i n i t i o n o f c a u s a l i t y .

At

A t the

l e a s t , i t can t e s t whether an optimal p r e d i c t i o n o f one s e r i e s depends
upon another.

The a b i l i t y t o t e s t a s p e c i f i c hypothesis depends upon

a p r i o r i r e s t r i c t i o n s placed on the s t r u c t u r a l equations.

This problem

w i t h " c a u s a l i t y " t e s t i n g was f i r s t r e p o r t e d by Jacobs, Learner, and Ward
(1979).

To i l l u s t r a t e t h e i r p o i n t , they consider a simple s t r u c t u r a l

model t h a t serves o u r purpose of model i n g the r e l a t i o n s h i p between
p r i v a t e and p u b l i c investment.

Consider t h e p o s s i b i l i t y t h a t p u b l i c

o u t l a y s (g) e x p l a i n p r i v a t e investment ( k ) :

and the p o s s i b i l i t y t h a t p r i v a t e investment ( k > explains p u b l i c
investment (9):

where (t-1) i s a generalized delay o f i periods and c l t and c t t
are independent, s e r i a l l y uncorrelated random variables w i t h zero means
and variances a: a:,

respectively.

The reduced form o f t h i s s t r u c t u r a l system i s

Since we are concerned about feedback from p r i v a t e t o p u b l i c
investment, we focus on three hypotheses t h a t describe the extent k
influences g:
H1:

t=Ozz=O. JLW refer t o t h i s hypothesis as "k does not cause
g," o r t h a t a p o l i c y t h a t c o n t r o l l e d k by s e l e c t i n g the e r r o r
c l t could not have any impact on the g v a r i a b l e .

Hz:

T=O. JLW refer t o t h i s as "g i s contemporaneously exogenous."

3:

tB1l+Ozl=O=nzl.
This i s the hypothesis t h a t an
optimal p r e d i c t i o n o f g does not depend on k. JLW r e f e r t o t h i s
as "k i s not informative about f u t u r e g."

As they note, H, i s o f t e n mistaken f o r the c a u s a l i t y hypothesis (HI).
Since the s t r u c t u r a l model i s not i d e n t i f i e d and none o f the parameters can
be estimated, i t I s not possible t o estimate
possible t o t e s t HI.

T

and 0 and thus not

What can be estimated i s n z l . I f i t i s

discovered that n z l is zero, then k is not informative about future.
g.

If, furthermore, one could restrict

T

t o be zero, then the finding

that n z l = O would infer that D z l is also equal t o zero--thus g is
exogenous t o the model.
JLW further show that the informativeness hypothesis ( H 3 :

n z l = O ) is not a useful indicator of simultaneous equation bias.
that is required for consistent estimates is that r=O.

All

In our

particular circumstance, it is reasonable t o assume that private and
public investment are not contemporaneously correlated.

The formation o f

public capital stock, in particular, requires a considerable amount o f
time.

Roads, highways, airports, ports, water treatment and sewer

facilities, for example, take a number of years t o build.

Add t o this a n

equally long period o f time required for private capital formation, it is
highly unlikely that over a long period of time, public and private
investment are consistently contemporaneous.
Therefore, with the a prior1 restriction that r=o, it is possible
t o interpret the results of the Sims test as a test of exogeneity.

Even

without this restriction, the Sims test indicates the ability of g t o
explain k and vice versa.
The Sims test regresses current g on past, current, and future values
o f k.

The null hypothesis that g is not informative about k is

equivalent .to.all the coefficients on the future values of k being equal.
t o zero.

Thus, the two-sided regression model is estimated:

An analogous regression of k on past and f u t u r e g i s then estimated t o
t e s t i f k i s informative about g.

Since the e r r o r term (w) w i l l

generally be s e r i a l l y correlated, use o f OLS w i l l y i e l d consistent but
i n e f f i c i e n t parameter estimates.

A generalized l e a s t squares approach o r

some o t h e r method o f p r e f i l t e r i n g t h e time series i s used.

Sims suggests

a s p e c i f i c f i l t e r (1-.75LI2 where i t i s applied t o the natural logs of
the time series.

Sims r e p o r t s t h a t t h i s i s successful i n f l a t t e n i n g the

spectral density o f most economic time series.

Sims does report,

however, t h a t h i s f i l t e r does not completely prewhiten the series.

Feige

and Pearce (1979) show t h a t the choice o f p r e f i l t e r i n g does a f f e c t the
F- statistics.

We, therefore, estimate equation (10) using the i t e r a t i v e

Cochran-Orcutt estimation technique t o c o r r e c t f o r f i r s t - o r d e r s e r i a l
correlation.
Four combinations o f r e s u l t s from the Sims t e s t are possible, and i t
i s i n s t r u c t i v e t o examine the various p o l i c i e s these r e s u l t s may imply.
F i r s t , p r i v a t e Investment may i n f l u e n c e pub1i c investment.

I n t h i s case,

p u b l i c c a p i t a l formation i s p a s s i v e l y responding t o the needs of p r i v a t e
investment.

According t o the model , as p r i v a t e investment increases,

demand f o r labor and thus p a y r o l l s a l s o increase, expanding the income of
the l o c a l economy.

With a higher income, the median voter demands a

greater amount o f p u b l i c services, i n c l u d i n g p u b l i c investment.
Consequently, p u b l i c investment does n o t appear t o be used as a
growth- stimulating p o l i c y instrument.
Second, p u b l t c investment influences p r i v a t e investment.

This case

provides t h e strongest evidence p o s s i b l e from the Sims t e s t t h a t p u b l i c
investment stimulates p r i v a t e investment.

Although o t h e r f a c t o r s . a r e

undoubtedly important in explaining private investment, the model
indicates that public investment, by yielding higher profits to local
firms, attracts additional investment into the area.
Third, the direction o f influence may g o both ways.

'

This would

indicate either that the direction o f influence switches from one time
period t o the next, possibly due t o various external events, or that
there are strong feedback effects present throughout the entire time
period.
Fourth, there is no statistical relationship between pub1 ic and
private investment.

This statement should be qualified by the

possibility that the model is misspecified.

Nonetheless, it may be the

case that decisions t o invest in the private sector and in the public
sector are totally independent. Possible examples o f this are cities
dominated by a dingle industry, such as Detroit, Rochester, o r Seattle.
Another possibility is that public investment is used as a policy
instrument, but is ineffective.

Data

111.

Annual total public outlays for central cities within 40 SMSAs were
collected for the period 1904-78 from City Finances.

Public capital

outlay is defined as direct expenditure for contract or force account
construction o f buildings, roads, and other improvements, and for
purchases o f equipment, land, and existing structures. Included as total
outlays are expenditures on
a)
b)

sanitary and storm sewers and sewage disposal facilities,
roadways, sidewalks, and all structures and improvements
necessary for their use, such as to-11 highways, bridges and
tunnel s,

C)

dl

h o s p i t a l s,
p u b l i c s e r v i c e e n t e r p r i s e s , which i n c l u d e s a i r p o r t s and p o r t s .

Annual t o t a l p r i v a t e investment f o r manufactures was c o l l e c t e d over
t h e same t i m e p e r i o d from the Census o f Manufactures and the Annual
Investment was estimated f o r SMSAs u s i ng 1977

Survey of Manufactures.
boundary d e f i n i t i o n s .

Both s e r i e s a r e converted t o constant 1967 d o l l a r s

by u s i n g t h e Engineering News-Record indexes.
One obvious d i f f i c u l t y w i t h r e l a t i n g t h e two time s e r i e s i s t h a t
p u b l i c o u t l a y s are a v a i l a b l e o n l y for c e n t r a l c i t i e s over the e n t i r e t i m e
p e r i o d , w h i l e p r i v a t e investment i s f o r the e n t i r e SMSA.
t h i s problem v a r i e s across c i t i e s and time p e r i o d s .

The s e v e r i t y o f

For instance, p r i o r

t o World War 11, c e n t r a l c i t i e s comprised most o f t h e SMSA and d e f i n i t e l y
dominated f i s c a l expenditures.

Even a f t e r World War 11, c e n t r a l c i t i e s

provided much o f the major water treatment f a c i l i t i e s and contained much
of the highway complexes.

I n r e c e n t years i n which SMSA-level

expenditures a r e a v a i l a b l e , we f i n d t h a t t h e percentage of t o t a l o u t l a y s
i n an SMSA by c e n t r a l c i t i e s v a r i e s from an average o f 30 percent t o o v e r
90 percent.

The c i t y o f Cleveland, for example, accounted f o r

approximately 28 percent o f t o t a l SMSA expenditures on p u b l i c c a p i t a l
d u r i n g 1965-81, although i t c o n t r i b u t e d c l o s e t o 90 percent of water
treatment expenditures.

New York C i t y , on t h e o t h e r hand, c o n t r i b u t e d

n e a r l y 80 p e r c e n t o f t h e t o t a l SMSA expenditures on p u b l i c i n f r a s t r u c t u r e
d u r i n g t h e same time p e r i o d .

Thus, one would expect s e r v i c e s p r o v i d e d by

c e n t r a l c i t i e s t o s p i l l over i n t o t h e r e s t of the SMSA.

here fore,

p u b l i c investment s e r i e s i s u s e f u l i n e x p l o r i n g l e a d and l a g
r e l a t i o n s h i p s between l o c a l p u b l i c and p r i v a t e investment.

the

IV.

Results
Recogni zi ng that private and pub1 ic expenditures over three-quarters

o f a century have been i nf 1 uenced by significant events and overall
structural changes in behavior, we estimate the Sims test for pre- and
post-World War I1 periods as well as for the entire 75-year period. The
analysis examines 40 SMSAs.

The plots contained in figures 1-6 are

representative of the sample of SMSAs.

Investment in public

infrastructure is characterized by cyclical upturns and downturns, which
in some cases follow the major business cycles during this century.

With

few exceptions, the older, pre-WWII cities exhibited tremendous increases
in public capital formation during the new era prosperity o f the 1920s.
This boom was followed by a severe drop in public investment during the
Great Depression.

Very little activity occurred during the austere years

of World War 11, and it was not until the capital goods boom o f the
mid-1950s that we also see a significant increase in public capital stock
formation.

Due partly to increased suburbanization and the increased

role o f the federal government in financing public infrastructure, public
investment in the latter quarter o f the century is not as large and not
as cyclical as found in the earlier period.
Even though these generalizations are applicable t o most of the
SMSAs, each SMSA exhibits some unique characteristics.

Cleveland and

Akron (figures 1 and 2 ) . for example, show strong cyclical patterns
throughout the entire time period with private investment apparently
leading public investment before WWII and public leading private after
the war.

Seattle and Portland (figures 3 and 4) reveal somewhat

different patterns.

Public investment in the early part o f the century

exceeds private investment at several points in time. Seattle
demonstrates a fairly haphazard lead-lag pattern whereas Portland's is
somewhat more regular. Atlanta (figure 5) is illustrative of several o f
the "growth" areas in which private leads public investment, particulary
during the postwar period.

Houston (figure 6) is definitely a post-WWII

city. Very little public o r private investment was made during the first
half of the century, but the second half shows tremendous private
investment that dwarfs public investment.

Sims Test Results

Results of the Sims test are meant t o be

suggestive o f the relationships that may exist between private and public
investment.

As discussed earlier, this is a test o f predictive power and

not of structural causation.

Interpretation of the results, therefore,

must be made with considerable discretion.

The results are shown in

table 1 with asterisks indicating that the null hypothesis that public
does

not influence

private investment (or private does not influence

public) is rejected at the .05 percent significance level.

When the test

is applied t o the entire time series (actually from 1916 t o 1966, since
we used 12 future and past lags), neither null hypothesis could be
rejected for 2 9 o f the 40 SMSAs. The null hypothesis that public
investment does not influence private investment was rejected for 21 of
the 40 SMSAs.

The null hypothesis that private investment does not

influence public investment was rejected for only eight SMSAs.

Stated

differently, neither hypothesis could be rejected for 16 o f the 40
SMSAs.

In addition, these results show a dominance of public investment

influencing private

investment, an important r e s u l t f o r t h e use o f p u b l i c investment as a
p o l i c y instrument.
When t h e sample was d i v i d e d i n t o pre- and post-WHII periods u s i n g
four leads and lags, t h e r e s u l t s change.

I n t h i s case, the n u l l

hypotheses c o u l d n o t be r e j e c t e d f o r o n l y seven SMSAs.

I n the pre-war

period, p r i v a t e investment i n f l u e n c e d p u b l i c investment f o r s i x SMSAs,
whereas p u b l i c i n f l u e n c e d p r i v a t e f o r 10 SMSAs.

D u r i n g t h e postwar

period, p r i v a t e investment influenced p u b l i c f o r 10 SMSAs, and p u b l i c
influenced p r i v a t e investment f o r nine SMSAs.
The dominance o f p u b l i c i n f l u e n c i n g p r i v a t e investment i s reduced
when s h o r t e r p e r i o d s o f time are considered: p u b l i c investment i n f l u e n c e d
p r i v a t e investment f o r 19 SMSAs w h i l e p r i v a t e i n f l u e n c e d p u b l i c f o r 16
SMSAs.

One reason f o r t h i s d i f f e r e n c e may be t h a t t h e f o u r f u t u r e and

past l a g s may n o t be long enough t o p i c k up t h e e f f e c t of p u b l i c on
p r i v a t e f o r some c i t i e s .

When the e n t i r e p e r i o d was used, c o e f f i c i e n t s

o f the e l e v e n t h and t w e l f t h leads were s t a t i s t i c a l l y s i g n i f i c a n t in-some
cases.

Thus, n i n e SMSAs t h a t r e j e c t e d t h e nu1 1 hypothesis t h a t pub1i c

does n o t i n f l u e n c e p r i v a t e investment when t h e 12-year l a g was used i n
the longer p e r i o d c o u l d n o t r e j e c t i t when s h o r t e r l a g s were necessary.
This problem was o f f s e t t o some e x t e n t by t h e a b i l i t y t o c o n t r o l f o r
d i f f e r e n t s t r u c t u r a l r e l a t i o n s h i p s b e f o r e and a f t e r t h e war.

For

example, seven SMSAs t h a t d i d n o t r e j e c t t h e n u l l hypothesis when the
p e r i o d spanned b o t h pre-war and postwar p e r i o d s r e j e c t e d i t when t h e t i m e
p e r i o d was d i v i d e d .

D i r e c t i o n a l R e l a t i o n s h i p s across SMSAs

I n o r d e r t o e x p l o r e whether t h e

d i r e c t i o n o f i n f l u e n c e between p u b l i c and p r i v a t e investment ( o r no

r e l a t i o n s h i p a t a l l ) d i f f e r s s y s t e m a t i c a l l y across SMSAs, we use l o g i t
a n a l y s i s t o e x p l a i n the s i g n i f i c a n t F - s t a t i s t i c s i n which the dependent
v a r i a b l e equals one i f s i g n i f i c a n t a t the .05 percent l e v e l and zero
otherwise.

The r e s u l t s are shown i n t a b l e 2.

The regional l o c a t i o n of

SMSAs were i n d i c a t e d by the WEST and SOUTH dummy variables, w i t h the r e s t
o f the country included i n the i n t e r c e p t .

The v a r i a b l e EARLY i s a

measure o f the r e l a t i v e t i m i n g o f t h e placement o f p u b l i c . i n f r a s t r u c t u r e
and the needs o f the population.

I t i s computed as the difference

between the year i n which maximum population (MAXPOPY) was reached i n the
c e n t r a l c i t y and the year i n which maximum p u b l i c c a p i t a l stock was
obtained i n the c e n t r a l c i t y .

Thus, i f p u b l i c c a p i t a l stock peaks before

population (EARLY greater than zero), then the SMSA may be considered t o
have more f o r e s i g h t i n e s t a b l i s h i n g an i n f r a s t r u c t u r e base f o r f u t u r e
economic a c t i v i t y .
The r e s u l t s show t h a t p r i v a t e investment i s more l i k e l y t o influence
p u b l i c investment f o r SMSAs located i n the South than i n the r e s t of t h e
country.

I n a d d i t i o n , the sooner p u b l i c i n f r a s t r u c t u r e i s p u t i n place

vis- a- vis the s i z e o f the population (EARLY i s p o s i t i v e ) , the more l i k e l y
p u b l i c investment w i l l i n f l u e n c e p r i v a t e investment.

Siqn and Magnitude o f the C o r r e l a t i o n between Investment Series

The

Sirns t e s t r e v e a l s s i g n i f i c a n t r e l a t i o n s h i p s between p r i v a t e and p u b l i c
investment f o r a number o f SMSAs i n the sample, b u t i t 1 s unable t o
reveal the magnitude and sign o f the c o r r e l a t i o n between pub1 l c and
p r i v a t e investment.

We estimate t h i s e f f e c t f o r t h e pre-war and postwar

periods f o r a subsample o f SMSAs using a s l i g h t l y d i f f e r e n t approach.

Because of t h e s t r o n g p o s s i b i l i t y t h a t o t h e r f a c t o r s a f f e c t investment
decisions i n b o t h t h e p r i v a t e and p u b l i c sectors, each t i m e s e r i e s was
regressed on p a s t values o f i t s e l f (Haynes and Stone, 1985).

The

r e s i d u a l s , t h u s purged o f most of t h i s extraneous influence, are used as
innovations o f each time s e r i e s .

The i n n o v a t i o n s o f p r i v a t e investment

are subsequently regressed on present and p a s t values o f innovations o f
p u b l i c investment and v i c e versa.
1-6 are shown i n t a b l e 3.

The sum o f the c o e f f i c i e n t s of l a g s

I f one considers s i x years t o be s u f f i c i e n t l y

long t o capture most of the i n f l u e n c e o f one investment on the o t h e r ,
then t h e sum can be i n t e r p r e t e d as t h e long- run e f f e c t .
The f i r s t r e s u l t t o n o t i c e i n t a b l e 3 i s t h a t a l l s t a t i s t i c a l l y
significant coefficients are positive.

Thus, an increase i n one type o f

investment b r i n g s about an increase i n investment o f t h e o t h e r type.
Second, w i t h o n l y a few exceptions, the r e l a t i o n s h i p s t h a t were found t o
be s i g n i f i c a n t u s i n g the Sims t e s t , were a l s o s t a t l s t i c a l l y s i g n i f i c a n t
i n these r e g r e s s i o n s .
Results show t h a t the long- run e f f e c t o f p r i v a t e investment on p u b l i c
investment i s always l e s s than one.

Furthermore, the e f f e c t appears t o

be much l a r g e r i n the prewar p e r i o d than i n t h e postwar period.

The

r e l a t i v e magnitudes between t h e two p e r i o d s a r e reversed f o r the long- run
e f f e c t o f p u b l i c investment on p r i v a t e investment.

However, estimates o f

$11 o f p r i v a t e investment f o r every $1 o f p u b l i c investment, as was
estimated f o r Cleveland, seems somewhat l a r g e .

These magnitudes are n o t

s u r p r i s i n g when one considers t h e r a t i o of p r i v a t e investment t o p u b l i c
investment.

D u r i n g t h e prewar period, t h e r a t i o f o r Cleveland averaged

about 3 whereas i n t h e postwar p e r i o d i t was c l o s e r t o 8.

A s discussed

earlier, these high figures may result from the fact that only central
city expend1 tures on pub1 ic outlays were avai lable.

The percentage of

total outlays by the city of Cleveland compared to the entire SMSA, for
example, is much lower during the latter period than the former.

Thus,

given the fact that the population in the city of Cleveland peaked in
1952, while the SMSA population continued to grow, one would expect the
percentage of public outlays by the city with respect to total SMSA
outlays to fall over this period.

When it is possible to find SMSA-level

data, we find that the ratio of city outlays to SMSA outlays is .25
during the 1960s and 1970s.

Akron's ratio is higher at around - 4 5 and

thus its estimated long-run effect is lower than Cleveland's.

It is

interesting to compare our results with estimates obtained using
cross-sectional data for the late 1960s and the 1970s when public outlays
by SMSAs are available.

Deno (19861, using the same private investment

estimates and the same sample of SMSAs as we used, estimated the long-run
effect to be 0.28.

V.

Concluding Remarks
The basic question addressed in this paper Is whether public outlays

influence private investment.

A precondition for public outlays to be

considered a policy instrument is that public outlays must precede
private investment. This sequence of events does not ensure, however,
that public outlays will be effective in stimulating local economic
activity.

A more complete identification of the causal links between

public outlays and private investment would require estimating a full
structural model.

We have posited a simple model of the urban economy

that relates public infrastructure and private economic activity.
Unfortunately, sufficient time-series data are not available to estimate
the structural model.
The reduced-form equations from the structural model offers another
approach t o estimating this relationship.

The Sims test is used to

estimate the direction o f influence between the two investment series.
In only seven out o f the 40 cases, d o we find no statistically
significant relationship between public outlays and private investment.
For half of the cities, public outlays influenced private investment;
for a smaller number of cities private investment preceded public
investment.
We have explored a number of factors to explain differences in the
dominant direction o f influence, but we have found only two significant
characteristics.

Private investment is more likely t o influence public

outlays in cities located in the South. One interpretation o f this
finding is that local governments in the South are less apt t o use public
funds for development purposes, especi a1 ly before World War 11. We a1 so
found that public outlays were more likely t o precede private investment
in cities in which the level of public capital stock peaked prior to the
population peak of each city.
Based on our estimated publ ic capital stock series derived from these
public outlay data, investments by central city and special district
governments have not been sufficient t o mai ntai n the publ i c capital stock
o f many cities included in the sample since the 1950s.

While this is

consistent with the declining population o f these cities during this
period, it still leaves open the question o f how much should cities -

invest i n infrastructure.

Although t h i s question obviously cannot be

answered w i t h the present a n a l y s i s , the findings i n t h i s paper do suggest
a more a c t i v e r o l e f o r i n f r a s t r u c t u r e i n r e g i o n a l growth than e x i s t i n g
research has i d e n t i f i e d .

Bibliography
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I n f r a s t r u c t u r e and t h e Formation of P r i v a t e C a p i t a l , " Unpublished
D i s s e r t a t i o n , U n i v e r s i t y o f Oregon, Department of Economics, Eugene,
Oregon, June 1986
Fei ge, Edgar L. , and Doug1as K. Pearce (1 979). "The Casual Causal
R e l a t i o n s h i p between Money and Income: Some Caveats f o r Time S e r i e s
A n a l y s i s , " The Review o f - Economics and S t a t i s t i c s v o l . LXI, no. 4
(November 1979) pp. 521-33.
'

Granger, Cl i v e W. J . " I n v e s t i g a t i n g Causal R e l a t i o n s by
Econometric Models and Cross Spectral Methods," Econometrica v o l .
37, no. 3, J u l y 1969 pp. 424-38.
Haynes, Stephen E., and Joe A . Stone (1985). "A Neglected Method of
Separating Demand and Supply i n Time Series Regression," Journal o f
Business and Economic S t a t i s t i c s v o l . 3, no. 3, J u l y 1985 pp. 238-43.
Jacobs, Rodney L., Edward E. Leamer, and Michael P. Ward (1979).
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XVII, no. 3, J u l y 1979, pp. 401-13.
Kanemoto, Yoshitsugu. " A Note on t h e Measurement o f B e n e f i t s o f P u b l i c
I n p u t s , " Canadian Journal of Economics, v o l . X I I I , no. 1 , February
1980, pp. 135-42.
Musgrave, John C. " Fixed C a p i t a l Stock Estimates i n t h e U n i t e d
States: Revised Estimates," Survey of C u r r e n t Business, v o l . 61,
no. 2, February 1981, pp. 57-68.
"The Excess o f P u b l i c E x ~ e n d i t u r e son
Negishi, Takashi.
- Industries,"
Journal o f .Pub1i c ~ c o n o m i c s , v o l . 2, no. 3, J u l y 1973,
pp. 231-40.
Pestieau, P i e r r e . " P u b l i c I n t e r m e d i a t e Goods and M a j o r i t y Voting,"
P u b l i c Finance, v o l . X X I , no. 2, 1976, pp. 209-17.
Sargent, Thomas J.
"A C l a s s i c a l Econometric Model of t h e U n i t e d
States," J o u r n a l of P o l i t i c a l Etonomy, v o l . 84, no. 2, A p r i l 1976,
pp. 207-37.
Sims, C h r i s t o p h e r A. "Money, Income and C a u s a l i t y , " American
Economic Review, v o l . L X I I , no. 4 September 1972; pp. 540-52.

U.S. Bureau of Census, C i t y Finances, 1940-1964.

, C i t y Government Finances, 1964-65 through 1980-81.

, F i n a n c i a l S t a t i s t i c s of C i t i e s , 1909-1913, 1915-1919,
1921-1 939.

, General S t a t i s t i c s of C i t i e s , 1909, 1915, 1916.
23

Table 1:

F - S t a t i s t i c o f t h e Sims Test for "Granger" Causation
between P u b l i c and P r i v a t e Investment i n Selected SMSAs,
1904-1978.

PreWWII
SMSA

A

PostWWI

B

A

B

1 904-1 978
A

B

Akron

2.49

.67

.45

7.56*

3.51*

2.57*

Atlanta

1.40

3.72'

2.23

1.87

4.27*

1.12

.73

.80

1.08

2.04

.88

1.56

1.88

2.37

2.43

2.02

4.22*

2.27*

Baltimore
Birmingham
Buffalo
Canton
Chi cago
Cincinnati
C l eve1and
Col umbu s
Dal 1as
Dayton
Denver
Detroi t
Erie
Grand Rapids
Houston

Indi anapol i s
Jersey C i t y
Kansas C i t y

Table 1 (continued)

Los Angeles

1.02

1.53

.51

.37

.73

.86

Louisville

.89

5.19*

8.48*

.81

1.49

1.79

Mernphis

.68

3.30*

2.00

-31

4.84*

.69

M i 1 waukee

2.91*

5.95*

.36

5.72*

1.30

16.08*

Minneapolis

3.54*

.83

.52

1.60

.95

18.18*

Newark

2.09

-92

1 .ll

.85

.97

6.77*

9

8

New Orleans
New York
Phi l a d e l p h i a
Pittsburgh
P o r t 1and
Readi ng
Ri chmond
Rochester
San Diego
Seattle
San Franci sco
S t . Louis
To1edo
Youngstown
Total s i g n i f i c a n t
a t .05 p e r c e n t

6

10

10

21

Note:

A: Private investment "Granger" causes public investment;
Public investment "Granger" causes private investment.
The pre-WWII period begins in 1904 and ends in 1945; the
post-WWII period begins in 1946 and ends in 1978. The
Sims Test was performed with four period leads and lags for these
two subperiods. Pub1 ic investment is total pub1 ic outlays
by central cities in each SMSA obtained from City Finances, 19041978. Private investment is investment by manufacturers within
the SMSA obtained from Annual Survey o f Manufactures and other
sources. The combined period estimation of the Sims Test was
performed with 12 period leads and lags.
The asterisk ( * ) denotes .05 significance level.
B:

Source:

Author's calculations.

Table 2:

F a c t o r s r e l a t e d t o t h e s i g n i f i c a n c e of t h e Sims Test
f o r s e l e c t e d SMSAs, 1904-1978
D i r e c t i o n o f Hypothesized "Granger" Causation

Variable

Constant

P r i v a t e t o Pub1i c

Pub1i c t o P r i v a t e

1.95 -43.44 -52.78
(6.32)
(1.37)
(1.65)

1.62
(5.21)

3.79 - 16.10 -36.30
(4.76)
(.14) (.31)

1.19
(2.32)

1.07
(1.99)

-1 -55 -2.58 -2.89 -1.30
(.91) (1.32) (1.46)
(.73)

4.47
(4.33)

West
South

-87
(1.60)

.

.73
(1.33)

Ear 1y

Maxpop
Capn

Note:

Dependent v a r i a b l e equals one ( z e r o ) i f F - s t a t i s t i c d e r i v e d from t h e
Sims t e s t i s s t a t i s t i c a l l y s i g n i f i c a n t ( i n s i g n i f i c a n t ) a t t h e 5 p e r c e n t
l e v e l . T - s t a t i s t i c s a r e i n parentheses. The v a r i a b l e WEST denotes SMSAs
i n t h e western U.S.; SOUTH denotes SMSAs i n t h e southern U.S.; w i t h t h e
n o r t h e a s t and t h e midwest included i n t h e i n t e r c e p t . The v a r i a b l e EARLY
i s t h e d i f f e r e n c e between t h e year i n which maximum p o p u l a t i o n (MAXPOPY)
was reached and t h e year i n which maximum pub1 i c c a p i t a l stock was
o b t a i n e d . MAXPOP i s t h e maximum p o p u l a t i o n o f t h e c e n t r a l c i t y i n t h e
SMSA. CAPN i s t h e maximum p u b l i c c a p i t a l stock of t h e c e n t r a l c i t y i n
t h e SMSA.

Source:

Author's calculations.

Sum o f t h e Estimated Lag D i s t r i b u t i o n s o f t h e I n f l u e n c e
of P r i v a t e Investment on P u b l i c I n v e s t m e n t and

Table 3:

P u b l i c Investment on P r i v a t e Investment f o r S e l e c t e d SMSAs

SMSA

A
.42

B

.83
(.97)

.64
(1.31)

Cl eve 1and
Houston.
P o r t 1and
(

I n d i anapol is
Pittsburgh
M i nneapol is

.94
.64)

.70
(1.19)
.21
(.94)
.52
(2.14)

.38

-.04
(.14>

A
.014

B
10.71

.29
(1.05)

2.69
( .44)

.03
(.I61

-3.67
(1.02)

.83
(1.63)
-1.66
(1.41

.83
(1.56)

( . 12)

.77

.41
(1.18)

3.96
( .56)

-15
(1.04)

(.lo)

( .70)

Dayton

1.46
(1.24)

-.20
(1.19)

Akron

.36
(1.85)

( .26)

Rochester

-29
(2.25)

.43
(.57>

Atlanta

.56
(1.18)

.92
(2.43)

Philadelphia

-77
(1.93)

( .45)

.74

.43
.27

.26

Note: Model A (B) regresses t h e i n n o v a t i o n s o f c u r r e n t p u b l i c ( p r i v a t e )
investment on i n n o v a t i o n s o f p r i v a t e ( p u b l i c ) investment w i t h l a g s 0-6.
The e s t i m a t e r e p o r t e d i n t h e t a b l e i s t h e sum of t h e c o e f f i c i e n t s o f l a g s
1-6. For each t i m e s e r i e s , i n n o v a t i o n s a r e t h e r e s i d u a l s from a
r e g r e s s i o n of t h e s e r i e s on a d l s t r l b u t e d l a g of p a s t values o u t f o u r
years.

Source:

Author's calculations.

Figure 1

Cleveland Public and Private Outlays 1904-1978
Private Investment

'

SOURCE: Author's analysis.

CI Government
- - - - - w m - m m - m -Investment
-m-wwm

Figure 2

Akron Public and Private Outlays 1904-1978
Private Investment

U Government Investment
m 1 - 1 m m 1 w m - - m w m - m - w -

150

1900

,1910

1920

SOURCE: Author's analysis.

1930

1940

1950

1960

1970

1980

Figure 3

Seattle Public and Private Outlays 1904-1978
D Government Investment

Private Investment

o

o

~

~

o

~

~

o

o

o

.

.

~

I

~

~

L

v

~

1

1

1

300
3

200 -

-

I,

I

r 'A

I

t

I

~

100 -

O

,

I

l

I

l

l

I

I(

SOURCE: Author's analysis.

1

1

1

1

(

1

1

1

1

~

1

1

1

I

1

1

1

1

1

I

1

1

1

1

I

1

Figure 4

Portland Public and Private Outlays 1904-1978
Private Investment

SOURCE: Author's analysis.

D Government Investment
o - - - o - - m - m o m m m - - m - v

Figure 5

Atlanta Public and Private Outlays 1904-1978

SOURCE: Author's analysis.

Figure 6

Houston Public and Private Outlays 1904-1978
private Investment

1900

1910

1920

SOURCE: A u t h o r ' s a n a l y s i s .

0 ~ o v e r n m e n tInvestment
---lllO1-DmOmOO1w--