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DOES PUBLIC CAPITAL CROW D OUT PRIVATE CAPITAL?
David Aschauer
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D o e s Public Capital C r o w d
O u t Private Capital?
I. Introduction
David Aschauer*
This paper is an empirical investigation into the effects of government
spending on private investment from a neoclassical perspective. The central
focus of the paper is on the question: does higher public capital accumu
lation “crowd out” private investment in plant and equipment?
On
neoclassical grounds, the answer to this question is seen to depend upon
two fundamental, opposing forces. On the one hand, higher public invest
ment raises the national rate of capital accumulation above the level chosen
(in a presumed rational fashion) by private sector agents; thus, public cap
ital spending may crowd out private expenditures on capital goods on an
e x a n te basis as individuals seek to reestablish an optimal intertemporal
allocation of resources. On the other hand, public capital—particularly
infrastructure capital such as highways, water systems, sewers, and
airports—is likely to bear a complementary relationship with private capital
in the private production technology. Thus, higher public investment may
raise the marginal productivity of private capital and, thereby, “crowd in”
private investment. Isolating these separate effects will allow: (1) a test of
the appropriateness of the equilibrium approach to fiscal policy (the former
effect); (2) information on the productivity of public capital (the latter ef
fect); and (3) a resolution to the query of whether or not public capital
spending can affect the national capital stock to a substantive degree.
The earliest conventional macroeconomic analyses of the effect of public
spending— specifically, public capital expenditures—on private investment
emphasized an e x p o s t crowding out via the effect of fiscal policy on interest
rates; to the extent that an increase in the level of public expenditure cre
ated an excess demand for current resources, interest rates would rise and
reduce the level of private capital spending. In classical, full-employment
models of the economy, the reduction in private investment per unit of
public spending would be equal to
- i r!(ir + cr)
(1)
where ir and cr measure the sensitivity of private investment and consump
tion to a change in interest rates. In the extreme of a perfectly inelastic
* David Aschauer is a Senior Economist at the Chicago Federal Reserve Bank.
A previous version of this paper was presented at the Board of Governors and the
Western Economic Association Meetings.
FRB CH ICAGO Staff Memoranda
1
private savings schedule (cr = 0), higher public spending would crowd out
private investment on a one-to-one basis; given some elasticity of savings;
however, part of the burden of higher public spending would fall on the
present as the rise in interest rates induced a reduction in the current level
of consumption spending.1 A t the opposite end of the spectrum, Keynesian
models of the “sticky price” variety predicted a smaller negative effect of
government spending on private capital accumulation as the interest sensi
tivity of money demand allowed a rise in output to be compatible with
money market equilibrium and, therefore, less of a need for a higher level
of interest rates to reestablish goods market equilibrium. In this case, the
effect on private investment is given by
- i ri l ( i r + cr + ( m * s v) lm v)]
(2)
where m n rriy are the sensitivities of money demand to interest rates and in
come and sy is the marginal propensity to save out of income. In the ex
treme case of infinitely interest sensitive money demand— the “liquidity
trap”—interest rates would not rise pursuant to a rise in government
spending and consequently there would be no effect on the level of private
investment.
Indeed, the advent of accelerator (and, subsequently, flexible accelerator)
theories of private investment led to the conclusion that fiscal policy, by
stimulating aggregate demand and output, might “crowd in” capital
spending by firms. Given the previous level of output, investment would
be crowded in given that
I mr I %
-
\ h I * my > 0
(3 )
as in this case any negative effect on investment arising from a rise in in
terest rates would be dominated by the positive effect operating through a
higher level of output and the consequent need for expanded capacity.2'3
Later discussion centered on the implications of changes in wealth associ
ated with government debt issuance and, thereby, on consumption and as
set demand. Assuming that the higher public expenditure is debt financed
and that expansions of public debt raise wealth, both consumption and
money demand were argued to rise. As the former effect tends to stimulate
production but the latter effect to raise interest rates, their net impact on
output and private investment would be ambiguous, a point discussed by
Silber (1970). Blinder and Solow (1973) took such wealth effects as the
starting point for their analysis of the effects of fiscal policies, but focused
on the requirement that the budget be balanced in long-run equilibrium.
In such an environment, bond-financed government spending was neces
sarily stimulative since a rise in income was required to finance interest
payments on the higher level of public debt.
FRB CH ICAGO Staff Memoranda
2
A dramatically different analysis o f crowding out was pursued by David
and Scadding (1974), in which they emphasized the possibility o f an e x a n te
crowding out o f private by public expenditure. Specifically, they argued
that a rise in government bond issuance crowded out an equal amount of
private investment because deficit finance is regarded as public investment
and the latter substitutes for private capital spending. Tax-financed gov
ernment spending, on the other hand, was taken as government consump
tion and to crowd out an equivalent amount of private consumption. Thus,
fiscal policy was seen as having no effect on the level of aggregate demand.
O f course, this argument is consistent with an “ultrarational” consumer
only if public capital expenditures are, as a rule, debt financed.
More recently, Barro (1974) offered the possibility that the method of fi
nance of public expenditure—whether by debt or taxes—is irrelevant to ag
gregate economic outcomes. As is now well known, this analysis involves
private savings acting as a buffer against changes in the financial position
of the public sector; a bond-financed tax cut (of a lump-sum variety) pro
motes an equal e x a n te rise in private savings to match the implicit future
tax liability with the result that interest rates, output, and the price level
are left unaffected. The crucial point, however, is that to the extent that
this “equivalence” between public finance methods holds, it makes sense to
concentrate on the real aspects of fiscal policy—the temporal pattern of
government purchases, changes in distortional tax rates, and—as in the
current paper—alterations in the composition of public spending as poten
tially powerful channels of influence on the private sector economy.
The question of the degree to which public debt issuance is offset by private
savings has been addressed by numerous authors. Boskin (1987), Feldstein
(1982), Modigliani and Sterling (1986), and Poterba and Summers (1987),
to name a few, present results that indicate private consumption is indeed
stimulated by changes in the mix of tax and debt finance of government
spending. On the opposite side, however, are papers by Aschauer (1985),
Kochin (1974), Kormendi (1982), Seater (1982), Seater and Mariano (1985),
and Tanner (1978, 1979). Other authors have studied the impact of gov
ernment financial decisions on interest rates. While Hoelscher (1987) finds
a positive effect of government bond issuance on long-term interest rates,
Dwyer (1982), Evans (1985, 1986, 1987), and Plosser (1982, 1987) have
found either no statistical relationship between debt finance and asset re
turns or, in some cases, even an inverse one. Given the diversity of these
results, it seems supportable to maintain the position that real aspects of
fiscal policy may easily be as important for aggregate macroeconomic out
comes as the decision regarding the means of finance of public expenditure.
Ahmed (1987) and Barro (1981, 1987) have emphasized the importance of
the temporal intensity of government spending for output, interest rates,
and the trade balance. Starting from the perspective of the permanent in-
FRB CH ICAGO Staff Memoranda
3
come hypothesis, a transitory rise in government spending creates an excess
demand for contemporary goods and services; thus, some combination of
a rise in output (Barro 1981), a surge in interest rates (Barro 1987), and a
current account deficit (Ahmed 1987) is required to reestablish equilibrium.
A more persistent rise in government purchases, however, is to lead to a
drain on wealth and a substantial loss in effective permanent income, a fall
in consumption and leisure and, finally, much more limited impacts on
output, asset prices, and the current account position in the international
balance of payments.
This paper follows this line of reasoning by focusing on the relationship
between various forms of government spending—nonmilitary and military
investment as well as government “consumption”—and private investment.
The next section sketches out the primary theoretical considerations. Sec
tion III provides estimates of a parsimoniously specified model of invest
ment, the rate of return to private capital, and public expenditure variables.
Section IV illustrates the interactions captured by the estimated model with
some fiscal policy simulations.
II. A Neoclassical Analysis
The theoretical analysis which follows assumes a competitive economy
populated by similar, infinitely lived individuals.
The discussion is
heuristic; for detail the reader is referred to Arrow and Kurz (1970),
Aschauer (1988a), Aschauer and Greenwood (1983), and Barro (1988).4
The relationship between private investment and public spending which
holds in general equilibrium may be expressed as
i =
i ( 4
ig,
(4)
cg)
where i — private investment, <j> = the marginal product of private capital,
i 8 = public investment or capital account expenditure, and c g = government
consumption or current account spending. Here, a rise in the marginal
product of private capital raises the level of private investment as individ
uals respond to the higher marginal return to future production by post
poning consumption, raising savings, and, in equilibrium, increasing capital
accumulation.
A unit increase in public investment, given the rate of return to private
capital, will change private investment by the amount
- 1 - (m
p c l4 > )* {fkg
-
4>)
(5)
where m p c = marginal propensity to consume out of wealth and f kg =
marginal product of public capital in private production.5 In this formu
lation, higher public investment will crowd out an equivalent amount of
private investment if there is no impact on wealth of such a change in public
FRB CH ICAGO Staff Memoranda
4
expenditure. A rise in public investment, in this case, would raise the na
tional rate of capital accumulation over the optimal level chosen by private
sector agents; in response, there would be a reduction in private savings and
investment to return national investment to its former position.
However, given that the public capital stock is at a level such that the
marginal products of private and public capital are not equated, a change
in public investment—and a marginal change in the public capital
stock—will affect the wealth o f the private sector agents. Suppose that the
public capital stock is “too low” so that f kg > </>. In such a situation, an
increase in public investment and equal crowding out of private investment
would raise future output, creating a positive future income effect. Con
sumers, in response to the improved allocation of resources, would raise
current consumption and lower savings, with the result of a further decline
in private capital accumulation.
The impact of public consumption spending on private investment depends
on three considerations, namely: the extent to which the public sector goods
and services substitute for their private sector counterparts; the persistence
of the expenditure change; and the time profile of the marginal propensity
to consume out of wealth. Let a change in current public consumption
expenditure be followed by a change in future such purchases equal to a
times the current change. Hence if the current shock is transitory, a = 0
while if permanent, a = 1. Then the effect of a one unit increase in public
consumption spending on private investment is given by
~ ((1 - ugc - f g j l ^ i m p c 1 — a * m p c )
(6)
where ugr = marginal rate of substitution of public for private consumption
goods and services, fgc = marginal product of public current account
spending in private production, and m p c f = marginal propensity to con
sume in the future out of wealth.
Clearly, if ugc + f gc = 1 there is no effect of a change in the level of public
current account spending on the agent’s effective intertemporal consump
tion opportunities and private investment is left unaltered. The higher
public expenditure crowds out private consumption spending and directly
expands production to a degree such as to leave the intertemporal allo
cation of resources and thereby, private savings and investment
undisturbed.
However, available empirical evidence suggests that public spending sub
stitutes poorly for private consumption. Kormendi (1983) and Aschauer
(1985) obtain estimates of ugc in the range (.2, .4). The evidence also indi
cates that public expenditure may have a relatively minor direct effect on
production. On the basis of British data Ahmed (1986) uncovers an esti-
/ RB CH ICAGO Staff Memoranda
5
mate of f gc of .39 while Aschauer (1988c) finds no discernable impact of
public current account spending on total factor productivity. Accordingly,
a rise in the level of government consumption would be expected to reduce
the agent’s effective consumption possibilities and potentially induce a
change in private investment as the agent reallocates the “burden” of the
public sector expansion intertemporally.
Assuming 0 < ugc + f gc < 1, consider the case where the rise in public con
sumption is permanent, a = 1. Private investment will be unaltered if the
time profile of the aggregate marginal propensity to consume is flat since
the average agent would choose to bear the implied negative wealth effect
equally over time. On the other hand, if the agent’s marginal propensity
to consume profile has an upward (downward) tilt, private investment will
fall (rise) as he chooses to bear a relatively large proportion of the wealth
effect in the future (present).
Finally, assuming that 0 < ugc + f gc < 1 and m p c = m pd\ but the change in
public consumption spending is to some extent transitory, we have the im
pact on investment given by
- (1 - ugc - f gc) * ( 1 - a )l( 1 + </>)
(7)
so that a rise in public spending induces less than an equal decline in private
investment.
Thus, on net, a rise in public consumption expenditure may have a negative
impact on private capital accumulation, the effect being more probable (a)
the more transitory is the rise in public purchases and/or (b) the less the
publicly provided goods substitute for private consumption and yield direct
productive benefits.
The marginal product of private capital is given by the expression
<f>
=/*(*,
C8 )
(8)
where k = private capital stock, k 8 = public capital stock, and c8 = public
spending on current account.
A distinctive feature of public
capital—particularly infrastructure capital such as streets and highways,
sewers, water systems, airports, and the like—is that it is likely to bear a
complementary relationship to private capital. Specifically, a higher level
of public capital of this type is expected to raise the marginal productivity
of private capital, or f k kg > 0. Further, it would be reasonable to argue that
military capital would have a smaller effect on the productivity of private
capital. A rise in public spending on nondurables and services more likely
has an ambiguous effect on the marginal product of private capital. While
the current expenses of maintaining a police force and fire departments may
lead to a higher rate of return to capital, expenditures on regulatory insti-
FRB CH ICAGO Staff Memoranda
6
tutions and pollution control no doubt depress the return to capital as firms
are forced to seek less (private) cost-effective methods of production.
Hence, along neoclassical lines a rise in public investment expenditure has
an ambiguous effect on private investment. On the one hand, to the extent
that public and private capital stocks are substitutable for one another in
the private production technology, higher public investment crowds out an
equivalent amount of private capital spending. On the other hand, the fact
of government provision leads to a presumption that public capital yields
substantial external effects by raising the productivity of private factors of
production. Depending on their relative potency, the interaction of these
two forces could result in either a decrease or increase in private capital
expenditures.
The empirical analysis below seeks to evaluate the appropriateness of the
neoclassical approach to the crowding out of public expenditure by un
scrambling these conflicting effects of government spending on private in
vestment. Specifically, it attempts to provide answers to the following
questions: (1) Does a higher public capital stock—of either nonmilitary or
military goods raise the marginal product of private capital? (2) Given any
effect of public capital accumulation on the return to private capital, does
higher public investment crowd out private investment? (3) Does higher
government consumption expenditure raise the marginal product of capital?
Crowd out private investment? (4) What is the total impact of public capital
expenditure on the level of private investment?
III. Empirical Analysis
The empirical analysis focuses on the effect of public expenditure on private
investment and the rate of return to private capital. The private investment
series is net fixed investment in nonresidential equipment and structures and
is obtained from F i x e d R e p r o d u c ib le T a n g ib le W e a lth in the U n ite d S t a t e s
1 9 2 5 - 8 5 .6 This annual series is computed along “perpetual inventory” lines
by subtracting cumulative depreciation from the gross capital stock (cu
mulative gross investment minus discarded capital) in order to obtain the
net capital stock. The net capital stock is valued in current, as opposed to
historical prices and thus is a measure of the replacement value of the pri
vate nonresidential capital stock. The accuracy of this procedure, however,
depends crucially on (a) the chosen depreciation methodology—straightline, double-declining balance, etc.—and (b) the useful service lives em
ployed for depreciation purposes. The particular series used in this paper
is computed using straight-line depreciation over 85 percent of the service
lives published in Bulletin F of the Treasury Department. This specific
methodology lies behind most of the net investment series published in the
fRB CHICAGO Staff Memoranda
7
“National Income and Product Accounts” and elsewhere in the Survey o f
Current Business.
The rate of return variable is computed as the ratio of net (of depreciation)
corporate profits plus net interest expenses to the total value of the net
capital stock (net stock of equipment and structures plus inventories plus
land). Corporate profits and net interest are obtained from various issues
of the Survey o f Current Business, the net capital stock from F ixed Repro
ducible Tangible Wealth in the United States, and inventories and land from
the Flow o f Funds of the Federal Reserve System. As computed, this vari
able measures the rate of return on nonfinancial corporate capital since the
net o f depreciation corporate profits series published in the Survey o f C ur
rent Business presently is restricted to that legal category.
The public investment series consists of federal, state, and local expendi
tures on equipment and structures. Both nonmilitary and military capital
will be considered in turn. Depreciation of this form of capital to derive a
net capital stock series is based on comparisons with similar private capital,
data from governmental agencies on actual service lives, and on the as
sumptions made by Goldsmith in a study on corporate stock ownership by
institutional investors.
Two other variables will enter the empirical analysis as well. Government
consumption or current account spending is measured by subtracting the
net public investment series from total purchases of goods and services by
all levels of government, the latter variable being taken from the Survey o f
Current Business. The capacity utilization rate of the manufacturing sector
is from the Federal Reserve Bulletin.
Sample statistics for these variables over the period 1953 to 1986 are pre
sented in Table 1. The flow expenditure variables are measured relative to
the net private capital stock series to reduce the potential for a
heteroscedastic error structure. Note, in particular, that on average public
net investment was more than 50 percent as large as private investment (1.9
percent compared to 3.4 percent of the net private capital stock, or 1.6 and
3.0 percent of gross national investment, respectively) while being charac
terized by nearly the same amount of volatility, with a standard deviation
of 0.9 percent as opposed to 1.1 percent of the net private capital stock.
Further, the maximum value of public net investment, 4.0 percent (attained
in 1953) is roughly two-thirds as large as the maximum value for private
net investment, 5.7 percent of net private capital (achieved in 1966).
Finally, on average net public investment accounted for roughly 6.7 percent
of total government expenditures on goods and services.
Public consumption expenditures amounted, on average, to 24.6 percent
of net private capital and varied from a low of 19.4 percent in 1979 to a
FRB CH ICAGO Staff Memoranda
8
high of 35.4 percent in 1953. During the recent period 1981-86, this vari
able has averaged 19.9 percent of the stock of private capital. The potential
importance of the public expenditure variables for private investment in an
intertemporal setting seems clear from these statistics.
A parsimonious empirical model capable of capturing the relationships of
interest is composed of the following two equations:
1=
Cq -b
1)
+ 6*2 * <f> -f c3* i g +
</> = c4 + c 5* t + c6 * ln k -f c*7* ln k g 4- c%*cu + e 2
(9)
where t = time. Ink = natural logarithm of the net private capital stock,
Ink* = natural logarithm of the net public capital stock, and cu = capacity
utilization rate.7 The neoclassical model sketched out above implies
c2 > 0 , 63 < 0 (and close to a value of — 1 given a public capital stock near
its optimal level), c*6 < 0 (given f k k < 0), and c7 > 0 (given f k kg > 0). A rise
in the capacity utilization rate would be expected to raise the marginal
product of capital if movements in the former variable were due to either
demand-side or technological shocks, so cH > 0 .
The reduced form of the structural model is given by
/ = b0 + b x* i{ — 1) + b 2* t + b i^ ln k -f b4 * ln k g
~b b $ *c u + bfr* ft ~h zq
(j)
(1 0 )
— b2 + b%*t + b9 *ln k + b ]{)* ln k g + b u * c u + u2 .
Estimation of the reduced form is undertaken by full information maximum
likelihood methods to take into account the over-identifying restrictions
implicit in the structural model. Specifically, these latter restrictions dictate
that the stocks of private and public capital and the capacity utilization rate
do not exert influence on the level of private investment apart from that
operating on the marginal product of private capital. This will be the case
provided that in the initial equilibrium the marginal utility of consumption
is constant across time, the marginal product of capital equals the subjec
tive rate of time preference, and movements in the capacity utilization rate
do not invoke significant wealth effects.8 However, it is to be emphasized
that the more appropriate interpretation to give to the results of statistical
tests involving these cross-equation restrictions is simply in terms of as
sessing the adequacy of the structural model in explaining the data rather
than a direct test of an exactly specified theoretical model.
Table 2 provides estimates of the model. On all counts, the neoclassical
approach to the crowding out of private by public investment spending
appears to gain support. Consider first the results relating to private in-
FRB CH ICAGO Staff Memoranda
9
vestment expenditure. Private capital accumulation responds positively to
an increase in the rate o f return to capital, with a one standard deviation
rise in the latter variable (.019) inducing roughly a one and one third
standard deviation rise in private investment (.015). In dollar terms, in
1986 a one percentage point increase in the return to capital would have
been expected to bring forth some 29 billion (1982) dollars in additional
private capital expenditures. More dramatically from the perspective of the
validity of the neoclassical approach, however, is that the point estimate
o f the impact o f public nonmilitary capital spending on private capital ac
cumulation equals — .99. This coefficient is determined fairly precisely,
with a 95 percent confidence interval given by ( — 1.32, - .66). The adjusted
coefficient of determination is high and the value of the Durbin h statistic
does not allow a rejection of the null hypothesis of an absence of serial
correlation in the estimated residuals of the investment equation.
The rate of return to private capital responds negatively to the net private
capital stock and positively to the net public capital stock. A one percent
increase in the private capital stock is estimated to lower the return to pri
vate capital by 27 basis points while a one percent rise in the public stock
of nonmilitary equipment and structures is expected to increase the rate of
return by 9 basis points. The latter estimate has a 95 percent confidence
interval of (.07, .11). Again, the coefficient of determination is high and the
value of the Durbin-Watson statistic does not indicate the presence of
strong serial correlation.
It is interesting to note that the estimated rate of return equation includes
a positive and statistically significant time trend, given the private and
public capital stocks and the capacity utilization rate. There has been a
concern in the literature about a “falling rate of profit’' over the last fifteen
or twenty years. An ocular inspection of the data probably would lead one
to conclude that indeed the rate of return to private capital has trended
downward throughout the post-Korean War period. Feldstein and Sum
mers (1977), however, argued that the apparent slump in the profitability
o f nonfinancial corporate profit was in fact an illusion arising from a failure
to take account of serial correlation and the low levels of capacity utiliza
tion during the 1970s.
Table 3 contains ordinary least squares regressions (with and without cor
rections for first order serial correlation) of the rate of return on various
sets of explanatory variables. Equations (1) and (2) of Table 3 contain the
same regressions run by Feldstein and Summers (1977) where the list of
explanatory variables is restricted to time and the capacity utilization rate.
On the basis of a sample including the latter half of the 1970s and the first
seven years of the 1980s, one would now have to conclude that the rate of
profit had indeed fallen regardless of the effects of generally lower capacity
utilization and serial correlation in the residuals of the estimated equation.
FRB CH ICAGO Staff Memoranda
10
Equations (3) and (4) of Table 4, however, reveal an interesting result in
this regard. Allowing the stocks o f private and public capital in the list of
explanatory variables for the rate of return to capital reverses the sign of
the time coefficient. This implies, in turn, that the basic cause of the falling
rate of profit captured in the first two equations o f Table 3 is to be found
in the relative behavior of the net capital stocks over the period in question;
while both the net public (nonmilitary) and private capital stocks rose
without interruption, the ratio of public to private capital stocks climbed
until 1968, peaking at .58, and then continuously tumbled to .44 in 1986.
As discussed previously, the presence of a set of cross-equation restrictions
provides a test of the adequacy of the specification of the structural model.
Specifically, we may estimate the reduced form in an unrestricted fashion
and calculate the statistic s = N * ( I V c I/ 1 V u |), where N = sample size and
V c, V u — estimated variance-covariance matrix of the constrained and un
constrained systems, respectively. This statistic is distributed as a chisquare variable with degrees of freedom equal to the number of
over-identifying restrictions implied by the structural model. In the present
case, s takes on a value of 5.96, well below the 95 percent critical point of
the chi-square distribution with 3 degrees of freedom, 7.81.
An implication compatible with the neoclassical notion of quantities re
sponding to price movements, then, is that it is not possible to reject at
usual significance levels the hypothesis that the level of private investment
is unaffected by the capacity utilization rate over and above the influence
the latter variable has on the rate of return to private capital.
Table 4 contains estimates of the separate effects of nonmilitary and mili
tary investment on private investment as well as of the stocks of these two
forms of capital on the return to private capital. The point estimate of the
impact of military capital accumulation on private investment spending is
such that a one dollar increase in purchases of military equipment and
structures depresses investment by a mere 8 cents; furthermore, there is no
statistical basis for rejecting the hypothesis of zero crowding out of private
capital spending. The neoclassical interpretation of this result is that pri
vate agents take such spending as a poor substitute for private capital, and
as such, as a drain on wealth; consequently, military capital expenditures
work to crowd out consumption as opposed to investment.9
The results of Table 4 also indicate that the stock of military capital has
no statistically discernable impact on the productivity of private capital.
Even taking the point estimate of .02 as valid suggests that the influence
of nonmilitary capital on the return to private capital is four times as large
as that of military capital.
FRB CH ICAGO Staff Memoranda
11
Table 5 presents the effects of public consumption expenditure on the level
of private investment and the return to nonfmancial corporate capital.
Note first that public consumption carries only marginal explanatory power
for the level of private capital accumulation and for the return to capital.
Indeed, accepting the point estimates at face value leads to the conclusion
that public investment and capital are of much greater statistical and
quantitative importance to an explanation of movements in the endogenous
variables. Note also that the point estimate of the coefficient on public
nonmilitary investment is reduced substantially in absolute value from the
value in Table 2 of .99 to .72, while its associated standard error increases
from .17 to .21. This appears to be due to the strong collinearity between
public nonmilitary investment and public consumption expenditure; the
simple correlation coefficient between these two variables equals .88 while
that between public nonmilitary and military investment is equal to - . 1 5 .
The conclusions to be drawn from the empirical analysis are that public
nonmilitary capital—much more than military capital or government
consumption—has substantial explanatory power for the level of private
investment in equipment and structures as well as for the average return to
private capital. While higher investment by the government sector crowds
out private investment nearly one-to-one given the return to capital, it also
works to raise the productivity o f capital which, in turn, crowds in private
investment. In the following section, simulations are employed to illustrate
the total impact of public capital expenditures on private investment.
IV. Public Investment, Private Investment, a n d
the Rate of Return
An historical simulation over the sample period 1953 to 1986 was carried
out for the estimated model of Table 2 above. Figures 1 and 2 contain the
results of this exercise. Overall, the simple model appears to describe gen
eral movements in the level of private investment and the rate of return
reasonably well. The root mean square simulation errors are .003 for the
private investment variable (which has a sample mean of .034) and .007 for
the rate of return to nonfmancial corporate capital (mean .093). The root
mean square percentage errors are 1.59 percent for private capital accu
mulation and 1.25 percent for the rate of return. As can be seen, the model
tracks the data well, capturing nearly all of the qualitative movements in
both investment and the return to capital.
Figures 3 and 4 illustrate the effects of raising the level of nonmilitary
public investment during the years between 1970 and 1986 from its actual
level to the average level attained during the earlier period 1953 to 1969,
2.5 percent of the net private capital stock. Although the model is simple
and ignores interactions between public investment and other aspects of the
FRB CH ICAGO Staff Memoranda
12
economy, the results of this experiment are nonetheless illuminating. The
immediate effect of higher public capital spending is to lower the level of
private investment by nearly the same amount since the positive effect on
the rate of return, and thereby on private expenditures on plant and
equipment, arises in subsequent periods. The crowding out is even more
severe in the second year of the higher public investment as the direct effect
of the public investment on private investment plus the effect due to the
lower level of private investment in 1970 overwhelm the mitigating effect
on the rate of return. After this point, however, the gap between the actual
level of investment and the simulated level begins to dissipate as the rate
of return is permanently raised above its actual level, as shown in Figure
4. Indeed, in 1985 the simulated level of private investment (.028 of net
private capital) is roughly equal to the actual level (.030).
Figure 5 shows the effect of the higher public investment spending on the
national level of productive investment (i.e., private investment plus public
nonmilitary investment). For the first four years, the simulated national
investment rate is lower than the actual rate; in all subsequent years the
former exceeds the latter as the raised rate of return to capital—due to both
the higher public capital stock as well as the lower private capital
stock—stimulates additional private investment. In 1985 the experimental
national investment rate is 5.3 percent of private capital as opposed to the
historical value of 3.5 percent. Interestingly, visual inspection of the simu
lated rate of return and national investment levels leads one to the conclu
sion that the public investment policy would have brought both variables
much closer to attaining the same average values as were achieved in the
earlier portion of the sample period; indeed, the simulated national invest
ment level and rate of return average 5.6 percent of the private capital stock
and 9.8 percent, respectively, compared to the actual averages over 1953 to
1969 of 6.3 and 10.7 and over 1970 to 1986 of 4.9 and 7.9. Given the va
lidity of the estimated model, it appears that public investment can have
significant effects on the national level of investment, the national capital
stock, and the profitability of private capital.
V. Conclusion
The United States has experienced a broad shift in public investment levels
over the last thirty-five years. During the period 1953 to 1969 public non
military capital accumulation averaged 1.5 percent of gross national prod
uct while during the subsequent years 1970 to 1986 the percentage of total
output devoted to this purpose has fallen to a mere 0.4. Among other
groups, the National Commission on Public Works Improvement has re
commended that annual spending on infrastructure double, from $45
billion to $90 billion, by the end of this century. Clearly, then, an impor
tant question is the extent to which such additional public capital accumu-
FRB CH ICAGO Staff Memoranda
13
lation would crowd out private investment and, thereby, mitigate the
impact of the public sector initiative on the national investment rate.
This paper has provided a preliminary, suggestive answer to this question.
A t a superficial level, an increase in public investment may be expected to
reduce private investment nearly one-to-one as the private sector utilizes the
public capital for its required purposes rather than expand private capacity.
A t a somewhat deeper level, however, a distinctive feature of public
infrastructure capital is that it complements private capital in the pro
duction and distribution of private goods and services. Thus, public in
vestment might be thought to raise private investment as the former raises
the profitability of private capital stocks. The empirical results show that
while both channels appear to be operating, the net effect of a rise in public
investment expenditure is likely to be a relatively small fall in private in
vestment. Consequently, the national level of investment is lifted; public
investment policy by no means appears to be “neutral" in its effects on the
real economy.
Footnotes
1 In the alternative extreme case of a perfectly interest elastic investment demand
schedule, higher public expenditure would crowd out private capital accumulation
on a one-to-one basis.
Carlson and Spencer (1975) refer to this as a
“Knightian” case since, according to their interpretation of Knightian capital
theory, “we should expect no diminishing returns from investment.”
2 This is a “static” model formulation as in the textbook treatment of Brajnson
(1972).
3 Among others, Robert Eisner (1986) holds strongly to the view that government
deficits “crowd in” private investment. In his words, subsequent to public debt
issuance, “business will be able to produce more to meet our demand for more
bread today, and build a new bakery now, as well, to meet our demand for more
bread tomorrow.”
4 For a critical view and theoretical discussion, see Bernheim (1987).
5 This calculation is made on the basis of a two-period model, where the
“future” has been aggregated into a single composite period. Work effort is taken
to be perfectly inelastically supplied and normalized to unity.
b John Musgrave of the Bureau of Economic Analysis, Department of Commerce,
has been very helpful in providing unpublished data.
FRB CH ICAGO Staff Memoranda
14
7 In preliminary regressions, neither time nor a lagged rate of return to capital
were statistically significant in the investment and rate of return equations, re
spectively; in any case, entering these variables does not alter the conclusions of
the analysis. Further, relating the rate of return to capital-labor ratios yields
similar results.
8 For a rise in the initial capital stocks to have no effect on private investment
given the rate of return to private capital requires, in the two period model, u =
( o /p ) * u f , where uf is the second derivative of the utility function evaluated at the
future level of consumption.
9 This assumes that shifts in military investment are permanent. If the sample
period over which the empirical work was to be undertaken were to include years
in which defense spending (particularly on capital goods) was extraordinarily high,
it would be necessary to consider the implications of the temporary nature of such
expenditures. For example, one would expect on neoclassical grounds that the
large investment in military equipment and structures during World War II
(reaching 22 percent of the private capital stock in 1943) would have been re
garded as largely temporary and hence that it would have impinged dramatically
on private saving and investment. In the sample period 1953-86, however, net
military investment ranged only between .3 and .6 of one percent of the private
capital stock.
FRB CH ICAGO Staff Memoranda
15
References
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Open Economy,” Journal o f M o n e ta r y E con o m ics Vol. 17, pp. 197-224.
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E con om ic R eview Vol. 75, pp. 117-127.
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____ ________ _ , 1988c, “Is Public Expenditure Productive?” Federal Re
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______________ and Jeremy Greenwood, 1985, “Macroeconomic Effects of
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Barro, Robert J., 1981, “Output Effects of Government Purchases,” Journal o f
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_________ _____ , 1987, “Government Spending, Interest Rates, Prices, and
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______________ , 1988, “The Neoclassical Approach to Fiscal Policy,” Uni
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and Evidence,” N B E R M a c ro ec o n o m ic s Annual, pp. 263-304.
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Boskin, Michael J., 1987, “Concepts and Measures of Federal Deficits and Debt
and Their Impact on Economic Activity,” N B E R W orking P aper 2332.
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Carlson, Keith M. and Roger W. Spencer, 1975, “Crowding Out and Its
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FRB C H I C A G O Staff M e m o r a n d a
16
David, Paul A. and John L. Scadding, 1974, “Private Savings: Ultrarationality,
Aggregation, and ’Denison’s Law’,” J o u r n a l o f P o l i t i c a l E c o n o m y Vol. 82,
pp. 225-50.
E c o n o m ic
R e p o rt
o f
th e
P re s id e n t,
1987, Washington D.C.: U.S. Government
Printing Office.
Eisner, Robert, 1986,
H ow
R e a l Is
th e F e d e r a l D e f ic it ?
New York: The Free Press.
Evans, Paul, 1985, “Do Large Deficits Produce High Interst Rates?”
E c o n o m i c R e v i e w Vol. 75, pp. 68-87.
A m e ric a n
______________ , 1986, “Do Deficits Raise Nominal Interest Rates? Evi
dence from Six Industrial Countries.” University of Houston. Mimeo.
______________ , 1987, “ Interest Rates and Expected Future Budget Deficits
in the United States,” J o u r n a l o f P o l i t i c a l E c o n o m y Vol. 95, pp. 34-58.
Feldstein, Martin S., 1982, “Government Deficits and Aggregate Demand,”
J o u r n a l o f M o n e t a r y E c o n o m i c s Vol. 9, pp. 1-20.
______________ and Lawrence Summers, 1977, “ Is the Rate of Profit Fall
ing?” B r o o k i n g s P a p e r s o n E c o n o m i c A c t i v i t y Vol. 1, pp. 211-227.
R e s e r v e B u l l e t i n , Washington D.C.:
Reserve System, Various Issues.
Fe d era l
F ix e d
R e p ro d u c ib le
T a n g ib le
W e a lth
in
Board of Governors of the Federal
th e
U n ite d
S ta te s
1 9 2 5 -8 5
,
1987,
Washington D.C.: Department of Commerce.
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n a l o f M o n e y , C r e d i t , a n d B a n k i n g Vol. 18, pp. 1-17.
Kochin, Levis A, 1974, “Are Future Taxes Anticipated by Consumers?”
o f M o n e y , C r e d i t , a n d B a n k i n g Vol. 6, pp. 385-394.
Jo u r
Jo u rn a l
Kormendi, Roger C., 1983, “Government Debt, Government Spending, and Pri
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FRB CH ICAGO Staff Memoranda
17
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Journal o f M o n e ta r y E con o m ics Vol. 9, pp. 325-352.
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______________ and Roberto S. Mariano, 1985, “New Tests of the Life Cycle
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FRB CH ICAGO Staff Memoranda
18
Table 1
Sample Statistics
1953-86
mean
.034
.019
.246
.093
i
i9
c9
4>
NOTE:
standard
deviation
.011
.009
.039
.019
maximum
minimum
.057
.040
.354
.130
.013
.006
.194
.056
/ = net private nonresidential fixed investment relative
to net private nonresidential fixed capital stock
jg = net public nonresidential fixed investment relative
to net private nonresidential fixed capital stock
c9= total government consumption spending, defined as
total government purchases of goods and services minus
net public nonresidential fixed investment, relative to net
private nonresidential fixed capital stock
(f> = rate of return to private nonfinancial corporate capital
FRB C H I C A G O Staff M e m o r a n d a
19
Table 2
f — C-j
4* C
(f) — Cg 4 - Cg
Cl
=
C2
=
c3
~
C4 =
c5 ~
C6 =
C1
~
CS ~
C9 =
-.0 4 ( -6.16)
.60 (9.65)
.79 (8.79)
-.9 9 ( -5.66)
2.52 (5.80)
.63 (5.76)
-.2 7 ( -7 .34 )
.09 (8.24)
.19 (8.45)
2 /(
—
t 4~ C j
1)
4~ C 3 *
Ink
4* C4 *
4~ C q *
Ink^
4 - Q -j
4~ C q *
c u
/
R2
SER
D-h
=
=
J
.921
.003
.70
5 .6 6 (E (-6 ))
Vc
R2
SER
D-W
-I-
&2
l
.872
.007
=1.49
-
-
-2 .4 0 (E (-7 ))
=
3 .5 6 (E (-5 ))
N* log( | Vc | / 1Vu | ) = 5.96
NOTE:
/
d>
19
Ink
Inks
t
cu
R2
SER
D-h
D-W
/ RB CH ICAGO Staff Memoranda
See Table 1
See Table 1
See Table 1
natural logarithm of net private
nonresidential capital stock
natural logarithm of net public nonmilitary
nonresidential capital stock
time* 1 0 0
capacity utilization rate in manufacturing
adjusted coefficent of determination
standard error of regression
Durbin h statistic
Durbin-Watson statistic
20
Table 3
Dependent Variable = </>
const
__
Ink
Ink9
cu
.22
2.73
(4.36)
-.2 9
.70
(4.16) (-5 .3 3 )
.09
(4.75)
2.96
(3.22)
.75
-.31
(3.05) ( “ 3.70)
(3.08)
-.0 7
-.0 9
(-3 .2 6 ) ( -4.38)
-.0 5
- . 1 0
( - 1 -2 1 ) ( -3 .05 )
_
_
-
.10
_
(8.78)
.20
(6.17)
.24
(7.27)
.19
(4.49)
P
R2
SER
D-W
.885
.006
1.46
.889
.006
1.84
.776
.009
1.02
.845
.007
1.82
.32
(1.43)
_
.57
( 2 .8 6 )
NOTE; p = first order autocorrelation coefficient.
FRB CH ICAGO Staff Memoranda
21
Table 4
/= c,
0 = c6 +
Cl =
c2 =
c3 =
CA ~
c5 =
C1 ~
Os =
C9 ~
C10 =
cn =
-.0 4 (-5 .8 1 )
.57 (9.06)
.81 (8.36)
- 1 . 0 2 (-5 .49 )
-.0 8 (-.4 8 )
1.74 (2.24)
.48 (2.41)
-.2 4 (-5 .3 1 )
.09 (6.82)
.02
(1 0 2 )
.19 (8.37)
NOTE:
+
Cq * In k
+
c3 ln k 9
+
c^0 * /n k 9m
+
_/_
R2
=
SER =
D-h =
A
.918
.003
.66
6.09(E(- -6))
Vc =
N*
cu *c u + e2
l
.871
R2
SER
D-W
= .007
= 1.52
-6))
5))
log( | VC\I\V“ \) = 6.67
igm = net military investment relative to net
private nonresidential capital
!nkgm = natural logarithm of net military capital stock
FRB CH ICAGO Staff Memoranda
c7 * t
+ c4*i9 + c5*i9m + e!
uu 1X1
CO r^
CO CO
CO
=
+ c2*/( - 1 )4- c 3 *4>
22
Table 5
i
— C<j
4" C 2* /( —1) + C3 *(j) + C4 */ + Cg*C 4* 6-j
(p = Cq 4- c7*f 4- C o * Ink 4- c$*!nk9 4- c^q C9 4C1 =
c2 =
c3 =
C4 —
Cg —
Cq =
c7 =
c8 =
c9 =
c1 0 =
c-n =
-.0 3 (-2 .8 7 )
.56 (8.89)
.81 (7.96)
- .72 (-3 .2 9 )
-.0 7 (-1 .5 8 )
2.00 (3.84)
.51 (3.95)
-.2 2 (-4 .6 9 )
.08 (5.25)
.05
( .89)
.19 (7.75)
-JL
R2
SER
D-h
= .922
= .003
- .86
5,83(E( - 6 ))
^*cu 4- e2
JL
R2
SER
D-W
= .865
= .007
=1.52
8 .8 9 (E (-7 ))
Vc=
3 .8 4 (E (-5 ))
N* log(| Vc \l\ Va \) = 7.81
NOTE: c? = See Table 1
FR8 CH ICAGO Staff Memoranda
23
FIGURE 1
H I S T O R I C A L S I M U L A T I O N FOR P R I V A T E I N V E ST M E N T
A c tu al
i i i i Si m u ] a t e d
FIGURE 2
HISTORICAL SIMULATION FOR RETURN TO PRIVATE CAPITAL
Actual
i i i i Si m u ] a t e d
FIGURE 3
S I M U L A T E D E F F E C T O F A N I N C R E A S E IN P U B L I C I N V E S T M E N T
ON P R I V A T E INVESTMENT
Actual
iii
Si Mill a t e d
FIGURE 4
SIMULATED EFFECT OF AN INCREASE IN PUBLIC INVESTMENT
ON RETURN TO PRIVATE CAPITAL
Actual
fiii
Sinulatecl
FIGURE 5
SIMULATED EFFECT OF AN INCREASE IN PUBLIC INVESTMENT
ON NATIONAL INVESTMENT
Actual
iiii
Similated
@FedFRASER