Productivity effects of public capital maintenance: evidence from U.S. states.
Kalyvitis, Sarantis ; Vella, Eugenia
I. INTRODUCTION
The potential role of government expenditure on public
infrastructure in boosting economic activity has received much attention
in academic and policy circles. (1) In the United States during the
recent Great Recession, public spending on infrastructure projects has
been a major component of the 2009-2019 stimulus package.
The American Recovery and Reinvestment Act allocates $105.3 billion
to infrastructure investment, of which $66.1 billion is directed to
transportation and water infrastructure. Early literature (e.g.,
Aschauer 1989; Munnell 1990a, 1990b) found very large returns from
infrastructure investment, whereas subsequent studies, pointing out a
number of econometric issues, failed to estimate a significantly
positive impact on output, a finding that has come to be known as the
"public capital productivity puzzle" (Baltagi and Pinnoi 1995;
Evans and Karras 1994; Garcia-Mila, McGuire, and Porter 1996;
Holtz-Eakin 1994). Another strand of research has investigated the
extent to which productivity benefits extend beyond the narrow confines
of each state's borders, for instance, through
manufacturer-supplier networks, reduction of travel time, and logistics
costs (Boarnet 1998; Boisso, Grosskopf, and Hayes 2000; Cohen and Paul
2004; Holtz-Eakin and Schwartz 1995; Pereira and Andraz 2004; Sloboda
and Yao 2008). (2)
Even though the literature on the U.S. public
infrastructure-productivity nexus is extensive, it has not taken into
account the operation and maintenance (O&M) spending, which is
required for the repair and safe operation of the existing
infrastructure stock. The nationwide figures provided by the
Congressional Budget Office (2010) report for public spending on
transportation and water infrastructure over the period 1956-2007 show
that "a little more than half of total spending for such
infrastructure has been used for operation and maintenance." (3)
State and local governments (SLGs) account for close to 90% of O&M
expenditures, while a significant share of capital expenditures by SLGs
is financed by federal grants and loan subsidies (close to 50% before
the mid-1980s and about one-third since then) according to the
Congressional Budget Office (2007, 2010). Moreover, since the late 1970s
real infrastructure spending by SLGs has been growing at a faster annual
rate than the corresponding federal outlays and has accounted for about
75% of total public-sector spending on infrastructure.
These stylized facts provide strong motivation for an empirical
assessment of the productivity impact of O&M outlays by SLGs in
addition to the widely explored, traditional effect of capital spending.
The aim of this study is to explore empirically the direct and
spillover effects of O&M spending on total factor productivity (TFP)
growth among the 48 contiguous U.S. states. We use a new state-level
dataset for capital and O&M spending on water and transportation
infrastructure, which we have assembled for the period 1978-2000 based
on the Census Bureau's SLG Finances series. The budgetary nature of
the dataset stands in contrast to the approach typically followed in the
literature, which has mainly used (often controversial) estimates of
public capital stocks, and allows us to pursue a topic left unexplored
in previous studies, namely an assessment of the productivity impacts of
O&M outlays and a comparison of them with the corresponding ones for
capital spending. Our econometric analysis employs a semiparametric
varying-coefficient specification, which offers observation-specific
estimates of output elasticities, in line with recent developments in
the literature that have emphasized the importance of parameter
heterogeneity and nonlinearities in the growth process (see, e.g.,
Henderson, Papageorgiou, and Parmeter 2012; Masanjala and Papageorgiou
2004).
Our empirical findings indicate, first, that interstate spillovers
are significantly positive and exceed within-state impacts for O&M
(and capital) spending, implying that there is a substantial wedge
between the aggregate and own-state rates of return. Second, the
spillover effect of O&M spending is found to be much higher (up to
eight times on average) than the corresponding impact of capital
spending. These results remain highly robust when we take an alternative
approach via local generalized method of moments (GMM) estimation to
address concerns about potential endogeneity. We further robustify
inference through a battery of sensitivity tests, including an
alternative measurement of the spillover variables.
Our article is close in spirit to Henderson and Kumbhakar (2006),
who attributed the "public capital productivity puzzle" to
neglected nonlinearities in the production process and recovered
statistically significant returns to public capital via a nonparametric
approach, yet without considering the potential spillover effects of
public spending. (4) Notably, there is only scant evidence on the
productive impact of public spending on capital maintenance.
Kalaitzidakis and Kalyvitis (2005) have used nationwide data from the
Canadian "Capital and Repair Expenditures" survey and have
found that Canada would benefit from a fall in total expenditures on
both public capital and maintenance and that the aggregate share of
maintenance in total expenditures should be lower. Other studies
examining the role of O&M spending (e.g., Ghosh and Gregoriou 2008;
Tanzi and Davoodi 1997) have confirmed that capital maintenance is an
important determinant of growth, but have used only proxies due to the
lack of reliable and consistent data. More recently, Kalyvitis and Vella
(2011) have estimated, using national-level data from the Congressional
Budget Office (2007), a negative effect of federal infrastructure
outlays on infrastructure and a positive one of state and local outlays
(particularly O&M) (5) In none of these studies are the spillover
effects of public capital maintenance taken into account. This article
complements and extends this literature by offering a state-level
analysis of the productive impacts of public capital maintenance, which
highlights the interregional productivity spillovers of O&M outlays
among U.S. states, in comparison to the standard capital outlays
employed in related studies.
Our finding that the interregional spillover effects of
infrastructure expenditures can be higher than the direct ones may not
appear so surprising, given that the financing cost and the associated
distortive consequences of taxation are borne by other states in this
case. (6) But how can one explain the differences in the magnitudes of
the spillover effects between capital and O&M outlays? A possible
explanation may be related to the lack of central intervention by the
federal government in the case of O&M spending, because O&M is
almost exclusively locally financed, whereas federal grants account for
a significant share of state and local capital spending on
infrastructure. The main conclusion thus is that the failure to
internalize the spillovers associated with O&M spending through
central intervention may suggest an underprovision of it in the U.S.
states during the period under investigation, because SLGs might be
"too small to think big enough," creating a collective action
problem. Given the central importance of infrastructure spending in
fiscal stimulus packages and the discussion on the potential efficacy,
need for, and impact of a National Infrastructure Bank, these results
appear to have timely policy implications.
The results presented here corroborate recent evidence on the
importance of spillover effects on growth and trade from fiscal policies
(see, e.g., Auerbach and Gorodnichenko 2013; Beetsma and Giuliodori
2011; Hebous and Zimmermann 2013). The empirical findings from these
studies suggest that, apart from the traditional domestic multiplier
effect, fiscal policy generates non-negligible secondary effects on
growth across countries as well. Our evidence on the impacts of public
infrastructure spending across U.S. states further highlights the
potential interdependence of macroeconomic policies and emphasizes the
need to assess these linkages in order to design better-targeted
measures for enhancing national productivity.
The rest of the article is organized as follows. Section II
outlines the methodology, Section III describes the data and Section IV
presents the estimation results along with a variety of robustness
checks. Finally, Section V concludes the article.
II. METHODOLOGY
In this section, we sketch out the main elements of our empirical
analysis, namely some theoretical base with respect to the productive
impact of public O&M spending, our empirical specification, and the
estimation approaches taken.
A. Theoretical Foundations for the Productive Impact of Public
O&M Spending
While the rationale regarding the capital component is
straightforward, because capital expenditure directly adds new capacity
to the existing infrastructure network, the channel through which
O&M expenditures can contribute to private production deserves some
comment. Public O&M spending serves two purposes: first, it counters
depreciation (see, e.g., Agenor 2009; Dioikitopoulos and Kalyvitis 2008;
Kalaitzidakis and Kalyvitis 2004; Rioja 2003); second, it affects the
service flow of the existing stock and in a production function should
be multiplied by the service flow of the existing stock to get an
effective service flow (in the same way that electricity expenditures
can be entered multiplicatively with capital to proxy for utilization).
In what follows, we relate both types of infrastructure expenditure
to productivity rather than just the infrastructure capital stock as is
usually done in the literature. This approach is taken here for two
reasons. First, conventional estimates of infrastructure stocks are
based on constant depreciation schemes, that is unrelated to maintenance
spending, and neglect the strand of literature mentioned above. Second,
our main purpose is to disentangle the productive impacts of the two
types of infrastructure outlays on a comparative basis, which would not
be possible using measures of public capital stocks instead of flows.
Our empirical setup therefore relies on Barro (1990)-style models
with government spending as an input to the production process.
Devarajan et al. (1996) further specified two types of government
spending-one more productive than the other-as production inputs and, in
a similar spirit, Pinnoi (1994) in his empirical study separated the
effect of services from highways and streets in the production function
into capital and maintenance outlays. More recently, Hashimzade and
Myles (2010) have developed a multicountry extension of the Barro model
of productive public expenditure to account for the presence of
infrastructural externalities between countries in the production
function.
B. The Empirical Model
We work in a standard growth-accounting framework by assuming a
general production function with the following inputs: capital, K,
labor, L, own-state capital and O&M spending, G and M, and capital
and O&M spending by other states, [S.sub.G] and [S.sub.M]:
(1) Y = F(K, LG, M,[S.sub.G], [S.sub.M], t)
where t is a time trend generally interpreted in this literature as
an exogenous technology index and [S.sub.G] and [S.sub.M] form
transboundary spillover indices. (7)
More specifically, we assume that states N = {1, 2, ..., n} belong
to a network. Let [[phi].sub.ij] be a relationship between two states i
and j. The interpretation of such links may be attributed, for instance,
to trade between them. It is assumed first that [[phi].sub.ij] > 0 if
there is a link from node j to node i and [[phi].sub.ij] = 0 otherwise,
second, that [[phi].sub.ij] [not equal to] [[phi].sub.ij], and third,
that [[phi].sub.ii] = 0 (directed and weighted network). This notation
allows us to represent the network with an adjacency matrix, [PHI], of
which the ijth entry is [[phi].sub.ij] and the main diagonal contains
zeros. (8) The two spatial externality variables are then defined by a
summary statistic of the capital and O&M spending of a state's
neighbors in the network, that is the aggregate measures of the outlays
by all neighboring states linked to region i:
(2) [S.sub.Git] [equivalent to] [N.summation over (j=1)]
[[phi].sub.ij] [Y.sub.it]/[Y.sub.jt] [G.sub.jt]
(3) [S.sub.Mit] [equivalent to] [N.summation over (j=1)]
[[phi].sub.ij] [Y.sub.it]/[Y.sub.jt][M.sub.jt].
The presence of the output multiplicative factor in Equations (2)
and (3) is justified by the fact that a state j with a high level of
economic activity, presumably constitutes overly large portions of the
spillovers, [S.sub.Git] and [S.sub.Mit], for a small state i. Thus, by
multiplying region j's spending by the ratio of state i's
output to its own output, which is a relatively small number, the size
effects in the measures of [S.sub.G] and [S.sub.M] are neutralized (see
Cohen and Paul 2004).
Differentiating Equation (1) with respect to time, dividing by Y,
and rearranging terms yields:
(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where the [theta]'s correspond to output elasticities and
[??]/A is the exogenous rate of technological progress.
Next, we define a Tornqvist index of TFP growth, based on the
private factors, K and L, to discretely approximate the left-hand side
of Equation (1). According to the definition of this index, the growth
rates are equal to the difference in the natural logarithms of
successive observations of the components and the weights are equal to
the mean of the factor shares of the components in the corresponding
pair of years:
(5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and i =
1, ..., N denotes the state and t = 1, ..., T denotes the year, given
that the output elasticities of capital and labor equal the observed
income shares, [s.sub.YK] and [s.sub.YL], in a perfectly competitive
environment.
In order to account for the potential impact of the relative size
of the two spending components, in the right-hand side of Equation (1)
we model the unobserved contributions of capital and O&M
expenditures as unknown functions of the O&M share in total
own-state spending ("O&M share" henceforth), that is
[[theta].sub.G](Z), [[theta].sub.M](Z),[MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII], (Z), where Z [equivalent to] M/(G + M). Given
that capital and O&M outlays are imperfect substitutes, the
"O&M share" is expected to have a nonlinear relationship
with growth (see Figure 1 in Kalaitzidakis and Kalyvitis 2005), and is
therefore treated here as a source of potential parameter heterogeneity.
This approach will also allow us to evaluate how the output elasticities
of infrastructure outlays change when the composition between capital
and O&M expenditures is altered and which range of the existing
"O&M shares" among states is associated with the highest
elasticities.
Combining all the above, yields our estimated equation:
(6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where the exogenous rate of technological progress is modeled as a
function of state-specific dummy variables, [D.sub.i], and a time trend,
capturing respectively idiosyncratic and time-related exogenous shifts
in technology. Equation (6) allows the growth of both own-state and
other states' spending on infrastructure capital and O&M to
influence TFP growth nonlinearly by introducing heterogeneity in the
marginal effects. (9)
C. Estimation Approach
The estimation approach we follow is based on the semiparametric
smooth-coefficient model (SSCM) proposed by Li et al. (2002) as a
flexible specification for studying a general regression relationship
with varying coefficients (see, e.g., Cai, Fan, and Li 2000a, 2000b; Fan
and Zhang 1999). The SSCM lets the marginal effect of the variable(s) of
interest be an unknown function of an observable covariate and hence
introduces parameter heterogeneity. This specification traces
nonlinearities in the estimated relationships, offering the advantage of
more flexibility in functional form than parametric counterparts, as the
coefficient functions are unspecified. Furthermore, by allowing
coefficients to depend on other variables it does not suffer from the
"curse of dimensionality" problem to the extent of a purely
nonparametric specification, which also typically requires larger sample
sizes. Li et al. (2002) illustrated the application of the SSCM by
estimating the production function of the nonmetal-mineral-manufacturing
industry in China. More recent applications include for example Chou,
Liu, and Huang (2004), Stengos and Zacharias (2006). and Jansen et al.
(2008).
Owing to the presence of the linear part. Equation (6) forms a
partially linear varying-coefficient specification, in which the growth
of both own-state and other states' spending on infrastructure
capital and O&M is allowed to influence TFP growth nonlinearly by
introducing heterogeneity in the marginal effects. We employ a standard
kernel density estimator with Gaussian kernel and choose the bandwidth
using cross validation. The three-step process we follow is described in
detail in Appendix B (see also Chou, Liu, and Huang 2004).
One issue of concern that may arise when estimating Equation (6) is
related to the presence of the spillover variables. Specifically, if
each state government knows that the expenditures of other states can
matter for their own productivity, then one might expect that these
productivity spillovers can induce strategic interactions ("budget
spillovers") among localities (see, e.g., Baicker 2005; Case,
Hines, and Rosen 1993), which would lead to endogeneity problems in the
estimation. To overcome this hazard, we also augment the analysis with a
local generalized method of moments (LGMM) estimation, proposed in a
dynamic panel data context by Tran and Tsionas (2010). LGMM can be
considered as an extension to the Li et al. (2002) model by allowing for
some or all the regressors to be correlated with the error term and for
the possibility that the latter is serially correlated. (10) Following
the literature discussing the choice of optimal instruments in the
context of semiparametric panel data models (see Baltagi and Li 2002;
Tran and Tsionas 2010), we use density-weighted kernel estimates of
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] as instruments for
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], given that the
"O&M share," [Z.sub.it], should mainly be related to
factors such as the age of the infrastructure stock, demographic trends,
weather conditions, natural events, and geography, which are viewed as
exogenous. Furthermore, to mitigate the effects of possible
cross-sectional dependence we transform all the individual series of the
data into deviations from their cross-section means at each point in
time t, which is a standard procedure for samples with a relatively
small time dimension. (11)
III. DATA
Our sample covers the 48 contiguous U.S. states over the period
1978-2000, with a total of 1,104 observations. (12) A brief description
of the data (measured in millions of 2,000 U.S. dollars) follows;
further details about the data sources and the method of construction of
all the variables used in the estimations are provided in Appendix A.
We obtain data on SLG expenditures from the "Rex-Dac"
database, which is an internal file of the U.S. Census Bureau. This
database is an archive of nearly all the data collected in the periodic
censuses of governments and annual surveys of government finances since
1977 (plus 1972). (13) Following the classification in the Congressional
Budget Office (2010) report, for O&M and capital expenditures on
water and transportation infrastructure, M and G, we consider data on
"current operations" and "capital outlay"
respectively, for the following five infrastructure types: aviation,
highways and roads, mass transit, water supply and wastewater treatment,
and water transportation, which also cover the core sectors of public
infrastructure routinely used in the related literature. "Current
operations" comprises direct expenditure for remuneration of
officers/employees and for supplies, materials, and contractual services
except for capital outlay. It also includes repair and maintenance
services to maintain required standards of compliance for the intended
use. "Capital outlays," on the other hand, are costs
associated with: (a) construction, that is production, additions,
replacements, or major structural alterations to fixed works, (b)
purchase of land, existing structures, and equipment. Capital
expenditures include purchases of new assets as well as major
improvements/alterations to existing assets. (14)
Spillover variables for each state, [S.sub.G] and [S.sub.M], are
constructed as weighted sums of capital and O&M infrastructure
spending in other states given by Equations (2) and (3). Following Cohen
and Paul (2004), different states are weighted, first, by commodity
flows across states to reflect different degrees of interstate
dependence and, second, by information on the relative sizes of
state-level economic activity. This weighting scheme is justified by the
fact that a state with a high level of economic activity, such as New
York, presumably constitutes large portions of [S.sub.G] and [S.sub.M]
for a relatively small state, such as Rhode Island. Thus, by multiplying
New York's infrastructure spending by the ratio of Rhode
Island's gross state product to its own gross state product, which
is a relatively small number, the size effects in the construction of
[S.sub.G] and [S.sub.M] for Rhode Island are neutralized. The weight
that each state j has on state i in [S.sub.G] and [S.sub.M] is proxied
by the share of the value of goods shipped from state i to state j,
[[alpha].sub.ij], in the total value of goods shipped from state i to
all other states, [summation over (i[not equal to]j)] [[alpha].sub.ij],
that is [[phi].sub.ij] [equivalent to] [[alpha].sub.ij]/ [summation over
(i[not equal to]j)] [[alpha].sub.ij]. The above weighting strategy aims
to capture the different degrees of economic ties and geographic
connections between states by avoiding the oversimplifying assumption
that each dollar spent by other states has equal interregional spillover
effects on any targeted state. (15) In Subsection B we test the
sensitivity of our results to these weights by employing an alternative
computation of the spillover variables, which maintains only the
information on the relative economic activity in the weighting
procedure. Further, we show that our results hold for a sample of
highway data because this weighting scheme was first applied in the case
of highways (see Cohen and Paul 2004).
Finally, to construct the state-by-year TFP index we use data on
output, capital, and labor for the private nonfarm sector. Output, Y, is
defined as the real gross domestic product (GDP), and labor, L, is
defined as the total number of workers. Estimates of state-level capital
stocks, K, are from Garofalo and Yamarik (2002).
Table A1 presents the data averages by state for the TFP-growth
index (our dependent variable) and for the regressors used in the
estimations. On average, TFP increased over the 1978-2000 period in all
states. Connecticut and Massachusetts experienced the largest
productivity growth rates of about 1.8% and 1.7%, respectively, whereas,
at the opposite end of the scale, the productivity-growth rate for
Montana was close to zero. Between 1978 and 2000 capital spending grew
positively in most states at a mean rate of 1.8%. For nine states
(Illinois, Louisiana, Maine, Maryland, Montana, New Hampshire, North
Dakota, Vermont, and West Virginia) the average growth rates of capital
expenditures were negative. In contrast, O&M spending grew
positively in all the states at a mean rate of around 2.9%. Table A1
also reports the average level of the "O&M share," which
shows considerable variability across states, ranging from 35% (Wyoming)
to 65% (Michigan), and exhibits the highest standard deviation (6.25%)
of all the variables used in our baseline specification.
IV. ESTIMATION RESULTS
In this section, we present our empirical findings for the
semiparametric model outlined in Section II by focusing on the output
elasticities estimated with respect to own-state capital and O&M
outlays, as well as capital and O&M outlays by other states,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], respectively. We
also perform a variety of checks to address potential concerns about the
robustness of our results.
A. Main Findings
As a benchmark, we initially estimate the model treating the
[theta]'s as constants, that is by assuming that the estimated
relationships are linear. The first column of Table 1 gives the results
from a specification that does not account for spillover effects. As can
be readily seen, we obtain statistically insignificant estimates for the
output elasticities of both capital and O&M outlays on public
infrastructure. This result is in line with the existing literature on
the "public capital productivity puzzle" in the United States,
which has stated that once either state or both state and time effects
are controlled for, the resulting estimates of the marginal productivity
of public capital are not significantly different from zero (see, among
others, Baltagi and Pinnoi 1995; Garcia-Mila, McGuire, and Porter 1996;
Holtz-Eakin 1994). In the second column of Table 1. we run a similar
linear regression but accounting for spillover effects. We again obtain
insignificant estimates for both intrastate effects, whereas the
coefficients for the corresponding cross-state spillover effects turn
out to be positive and statistically significant.
Given that neglected nonlinearities can be important in assessing
the productive impact of public infrastructure (e.g., Henderson and
Kumbhakar 2006), we next proceed to semiparametric estimation of
Equation (6). The estimated coefficients are observation-specific,
meaning that output elasticities with respect to capital and O&M
spending are derived for each state and time period. We depict the
semiparametric smooth coefficients along with the upper and lower limit
of the 95% bootstrap confidence interval in Figure 1. For comparison
purposes, we also plot the estimated parameters from the parametric
linear specification (depicted by the dashed lines). The effects from
the semiparametric regression are estimated conditional upon the
"O&M share" and the graphs clearly suggest that the
functions are nonconstant in the range of the state variable, exhibiting
nonlinear patterns. (16)
In detail. Figure 1A and B plots pointwise estimates of the output
elasticities with respect to states' own capital and O&M
outlays, [[theta].sub.G] ([Z.sub.it]) and [[theta].sub.M] ([Z.sub.it]),
respectively. Both graphs indicate that the estimated elasticities are
positive for a range of medium-to-high (exceeding 50%) levels of the
"O&M share" and are maximized when the "O&M
share" is around 55%-60%. The general picture appears to point
toward the existence of "output elasticity hills" for
intrastate infrastructure outlays, in line with the nonlinearities and
the "growth hills" for U.S. state expenditures found by Bania,
Gray, and Stone (2007) based on Barro-style models. Figure 1C and D
similarly plots output elasticities with respect to capital and O&M
outlays by other states, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN
ASCII], respectively, and shows that both cross-state spillover effects
are positive for all sample points. In addition, the plotted results
indicate that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
initially decline and then start to increase above a certain level of
the "O&M share," with these convex relationships implying
that for low and high levels of the "O&M share" the
productivity spillover effects are relatively higher. Overall, the
graphical analysis suggests that for medium levels of the "O&M
share" within-state effects appear positive and cross-state
spillover impacts take their lowest values, whereas for lower/higher
levels of the "O&M share" within-state effects are
negative and spillover effects take their highest values. This evidence
appears to imply substitutability between own-state infrastructure
outlays and other states' outlays.
To examine the effects by state, we calculate the average output
elasticities for each state, along with the corresponding standard
errors. The results are reported in Table 2, in which states are grouped
into broad census regions to allow for a comparative regional analysis.
The state-specific estimates indicate that the elasticities of own-state
O&M spending lie between -0.027 (Nebraska) and 0.0004 (New York),
whereas the corresponding elasticities of capital spending range between
-0.022 (Wyoming) and 0.0034 (Indiana). Figure 2 offers the corresponding
geographical representation. Darker colors on the maps represent larger
values for the estimated elasticities. Higher intrastate effects of
public infrastructure spending are found mostly in the states located in
the Midwest and Northeast (e.g., Indiana, Ohio, New York). This is in
line with the finding in the public infrastructure literature that
productivity effects are larger in the "snowbelt" states (see,
e.g., Aschauer 2001; Hulten and Schwab 1991). On the other hand,
interstate spillover effects are more pronounced in the
"sunbelt" states and, in particular, in the West and South
(e.g., California, Georgia, New Mexico, Texas), which generally consist
of more agricultural and sparsely populated regions.
[FIGURE 1 OMITTED]
The general picture is summarized by the means of the
observation-specific elasticities, which are statistically significant
and amount to -0.017 and -0.002 for O&M and capital expenditures,
respectively, implying that, ceteris paribus, a 1% increase in O&M
(capital) spending corresponds, on average, to a 0.017% (0.002%) fall in
output. (17) In contrast, the output elasticities of other states'
expenditures are much greater in magnitude, ranging from 0.37 (Missouri)
to 0.46 (Michigan) for O&M spending, and are always statistically
significant. The corresponding effects of capital spending are also
positive and statistically significant, but are much lower in magnitude,
ranging from 0.033 (Ohio) to 0.095 (Wyoming). Our estimates imply that a
1 % increase in O&M (capital) spending by other states corresponds,
on average, to a 0.39% (0.046%) increase in output.
Furthermore, in Table 3 we present the results from a LGMM
estimation with cross-sectional demeaned data, which accounts for the
possibility of strategic interactions among local governments that would
lead to endogeneity problems in our regression. We find that the
estimated magnitudes are very close to our baseline estimation:
intrastate effects turn out to be small (-0.0008 and 0.0095 for capital
and O&M, on average), whereas spillover effects are much larger
(0.087 and 0.337 for capital and O&M, respectively). Because the two
approaches yield very similar results, we feel confident that our
baseline specification does not suffer from endogeneity bias and hence
in the rest of the empirical analysis we will focus on the baseline
approach.
[FIGURE 2 OMITTED]
In summary, two broad conclusions can be drawn from the empirical
findings presented in this section. First, productivity spillovers of
O&M (and capital) outlays by other states are significantly positive
and exceed the corresponding impacts of within-state outlays. Second,
the spillover effect of O&M spending, for which no previous
comparable estimates exist in the literature, is found to be much higher
(on average up to eight times) than the corresponding spillover impact
of capital spending.
Our results for the low (and in some cases negative) intrastate
effects of infrastructure expenditures may naturally raise the question
of why state governments commit to these expenditures, which is not new.
however, in the "public capital productivity puzzle"
literature. From a fiscal federalism perspective, a possible explanation
might be that a large proportion of this expenditure on infrastructure
is financed by the federal government through matching grants and loan
subsidies to states and localities. As mentioned in the Introduction,
the nationwide data available show that this share ranged between 30%
and 50% over the period considered.
Furthermore, the negative (and relatively small) estimates for the
direct effects of a state's own O&M expenditures on state-level
productivity should be taken with caution, as has already been pointed
out in the literature. As Carlino and Inman (2013) state, locally
financed outlays by lower tier governments are often viewed as
ineffective for enhancing local productivity, as any benefits accrue to
all the states in the union, whereas tax costs remain the responsibility
of the deficit-creating jurisdiction. Evans and Karras (1994), who have
also estimated a negative impact of government capital on state-level
productivity, argue that "Even if government activities cost more
than they contribute to state-level private output, they may still be
underprovided because government activities may also contribute direct
nonmarket consumption services." (18) In our context, public
capital maintenance may be underprovided because government
infrastructure expenditures contribute also to other states'
private output, as indicated by the large spillover effects.
But how can one explain the particularly high estimates for the
impact of the O&M spillover? A key factor might be associated with
the fact that O&M is almost exclusively locally financed. As a
result, a given state can enjoy the productivity gains from the better
maintained infrastructure network in neighboring states without
participating in the cost, which is not the case for capital spending
cofinanced through federal grants from local contributions. Hashimzade
and Myles (2010) show theoretically that in the presence of positive
infrastructure externalities among economies, the provision of
infrastructure will be inefficiently low unless there is intervention by
a supranational body to coordinate the policies of the individual
governments by internalizing the externality. In our context, the lack
of intervention by the central government to share the cost of local
maintenance policies may therefore suggest the possibility of
underprovision.
B. Sensitivity Analysis
To assess the robustness of our main findings, we perform a battery
of sensitivity tests. First, we attempt to control for the influence of
other variables that may affect state productivity growth (see Reed
2009) to ensure that our results do not suffer from omitted-variables
bias. We therefore include in the linear part of Equation (6) the state
unemployment rate to account for cyclical effects, as well as the
following public-sector variables: "federal employees"
(defined as the log of the number of federal employees per capita),
"S&L employees" (defined as the log of the number of state
and local employees per capita), "federal revenue" (defined as
the intergovernmental revenue received by SLGs from the federal
government as a share of personal income), and "tax burden"
(defined as total state and local tax revenues as a share of personal
income). Additionally, we control for various characteristics of the
population with the following variables: "working population"
(defined as the percentage of the population between 20 and 64 years of
age), "non-White" (defined as the percentage of the population
that is non-White), and "female" (defined as the percentage of
the population that is female). The estimation results, reported in
column (2) of Table 4, show no significant change in the average
coefficients. Moreover, the coefficients on the additional controls
generally have the expected signs, with those on "working
population," "federal employees," "S&L
employees," and "federal revenue" being statistically
significant.19
Another robustness check is then to use a more general coefficient
function that includes a second state variable, namely the share of
other states' O&M spending in the sum of the two spillover
indices, SM/(SG + SM). The average coefficients presented in column (3)
of Table 4, remain practically unchanged.
Further, we drop the commodity flow weights in the computation of
the spillover variables and keep only the information on relative
economic activity to investigate whether our results are driven by the
use of these weights. The estimation results, reported in column (4),
demonstrate that the estimates obtained are again not substantially
different from our baseline findings (reported in column [ 1 ]).
Finally, we run the regression for a subsample consisting of
highway-spending data. We focus on highways and roads for two reasons.
First, they form the largest component of transportation infrastructure,
which is believed to make the economy more efficient by reducing the
amount of time and energy necessary to cover distances between firms,
consumers, and employees.
Given their network characteristics, they have so far dominated the
literature investigating the spillover effects question in the context
of public infrastructure (e.g., Boarnet 1998; Cohen and Paul 2004;
Holtz-Eakin and Schwartz 1995). More recently, in the context of the
literature on government spending multipliers, Leduc and Wilson (2013)
find that shocks to federal highway funding positively affect local GDP
and calculate average multipliers, which are close to 2, over 10-year
horizons. Second, some cost-benefit studies have emphasized the
productive impacts of maintenance expenditures on highways, yet without
taking into account their spillover effects.20 To assess the
significance of our results for O&M spending on highways, we report
in column (5) of Table 4 the estimates obtained by running the
regression for highways and streets. Our main findings continue to hold,
with the output elasticity of O&M spending by other states being
somewhat lower but still considerably higher than the corresponding
effect of capital spending.
V. CONCLUDING REMARKS
Based on a novel set of data for the 48 contiguous U.S. states over
the period 1978-2000, this article has aimed to disentangle the
productivity impacts of capital and O&M spending on public
infrastructure by explicitly accounting for cross-state spillover
effects. To this end, we have used a semiparametric smooth-coefficient
approach to account for potential nonlinearities and parameter
heterogeneity. Our findings have documented that interstate spillover
impacts are significantly positive and exceed direct impacts for both
types of spending. Importantly, the cross-state spillover effect of
O&M outlays was estimated to be considerably high. These results
were found to be robust to a battery of sensitivity tests, including for
the endogeneity of public spending.
Our findings yield policy conclusions that are relevant for the
debate over state and local infrastructure spending. In particular, they
highlight the lack of intervention by the federal government in the case
of O&M spending as a potential key factor associated with
underprovision for it in the presence of infrastructural externalities
among states. In this vein, the increased need for federal aid to states
for maintenance expenditures, which has largely been ignored until now,
is a key message to policymakers that naturally arises in this context.
Another notable implication is that, given the suboptimal provision for
infrastructure at the state level and the constraints on public
resources, state governments should turn to alternative sources of
funding to meet the financing gap. To this end, the concept of
public-private partnerships, which are joint ventures between a
government entity and the private sector, can be a convenient way to
increase the provision of public services at the local level. These
partnerships can enhance public infrastructure through joint ownership
with domestic or international firms and, at the same time, provide
opportunities for local firms through subcontracting, with emphasis
placed on maintenance activities. Also, given that spillovers accrue to
neighboring states with relatively higher economic activity, local
authorities could explore the possibility of joint initiatives across
states at the regional level. In this context, fiscal coordination among
neighboring states, financed on the basis of expected benefits through
the spillovers assessed, can increase public capital expenditure and
aggregate productivity.
By answering some empirical questions unresolved up to now, this
study has opened the door to new research issues. For instance, the
article has not investigated politicoeconomic factors that shape
infrastructure policy (see, e.g., Cadot, Roller, and Stephan 2006;
Kemmerling and Stephan 2002). Further work in this area could therefore
look into political factors as determinants of state and local
infrastructure spending, and of its allocation between capital and
O&M. Second, in the presence of the positive productivity spillover
effects found here, a natural question that arises is whether states
respond to increased capital and O&M spending in neighboring states
by decreasing their own outlays ("budget spillovers") or
engage in expenditure competition to attract new economic activity (see,
e.g., Taylor 1992). We leave these topics for future research. Capital
and O&M Spending on Public Infrastructure
To construct capital spending data on water and transportation
infrastructure at the state level, we used the following series from the
"Rex-Dac" database: "Air Trans-Cap Outlay" from
Table Rex 2 for aviation, "Total Highways-Cap Out" from Table
Rex 3 for highways and roads, "Sewerage-Cap Outlay" and
"Water Util-Cap Outlay" from Table Rex 5 for water supply and
wastewater treatment, "Water Trans-Cap Outlay" from Table Rex
5 for water transportation, and "Transit Util-Cap Outlay" from
Table Rex 5 for mass transit. Similarly, to construct O&M spending
data on water and transportation infrastructure we used the following
series: "Air Trans-Current Oper (E01)," "Total
Highways-Cur Op," "Sewerage-Current Oper (E80),"
"Water Util-Cur Oper (E91)," "Water Trans-Cur Oper
(E87)," and "Transit Util-Cur Oper (E94)." The estimates
for G and M were obtained by summing the respective expenditure amounts
for the above infrastructure components. Data series were adusted to
express spending in real (or constant) dollars.
Spillovers of Capital and O&M Spending on Public Infrastructure
The data on the value of goods shipped from state of origin to
state of destination, used for constructing the relevant weights, come
from the 1993 and 1997 Commodity Flows Surveys, U.S. Bureau of
Transportation Statistics.
Output
Real GDP by state for the private nonfarm sector comes from the
Bureau of Economic Analysis (BEA). The series was discontinued in 1997
due to the industry classification system change from Standard
Industrial Classification (SIC) to North American Industry
Classification System (NAICS). To calculate output growth rates, we
exploited both versions of the data for 1997 to be consistent with
industry definitions.
Labor
Private nonfarm employment as a measure of labor was obtained from
the BEA.
Income Shares of Labor and Capital
Labor income shares, [s.sub.YL], were calculated at the U.S. state
level following the procedure proposed by Gollin (2002). First, the wage
and salary income of employees was imputed as labor income. Then the
average labor income of employees was calculated and the same average
labor income was imputed to the self-employed. The sum of the measured
labor income of employees and the imputed labor income of the
self-employed was used as a measure of total labor income. Dividing
total labor income by total income provided an estimate of the labor
income share at the state level. State-level data on total income,
employees' wages, and the income of the self-employed for the
private nonfarm business sector are available from the BEA. Given the
share of labor, the share of capital, sYK, was then determined
residually as 1 - [s.sub.YL].
ABBREVIATIONS
BEA: Bureau of Economic Analysis
LGMM: Local Generalized Method of Moments
NAICS: North American Industry Classification System
O&M: Operation and Maintenance
SIC: Standard Industrial Classification
SLGs: State and Local Governments
SSCM: Smooth-Coefficient Model
TFP: Total Factor Productivity
doi: 10.1111/ecin.12136
Online Early publication August 26, 2014
APPENDIX B: SEMIPARAMETRIC SSCM
Our estimated equation can be written more concisely as:
(A1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and
[u.sub.it] is the error term that satisfies E ([u.sub.it]\[W.sub.it],
[X.sub.it], [Z.sub.it]) = 0.
For the estimation we follow a three-step process (see also Chou,
Liu, and Huang 2004). In the first step, all coefficients are assumed to
be smoothing functions of [Z.sub.it] and are estimated by applying a
local least-squares method with a kernel weight function:
(A2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where X[W.sub.s] [equivalent to] ([W.sub.s], [X.sub.s])', k
(.) is a kernel function and h is the smoothing parameter (bandwidth).
We use a standard normal (Gaussian) kernel [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII] and choose the bandwidth via cross validation.
Unlike Equation (A1), the estimator [??]([Z.sub.it]) in Equation (A2)
depends on [Z.sub.it] in the first step, ignoring the fact that a is a
vector of constant coefficients. Subtracting [X'.sub.it] [??]
([Z.sub.it]) from both sides of Equation (A1) yields:
(A3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [[epsilon].sub.it] [equivalent to] [X'.sub.it] ([beta]
([Z.sub.it]) - [??]([Z.sub.it]) + [u.sub.it]. The next stage is to run a
least-squares regression of Equation (A3):
(A4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
The final step is to use the second-stage linear part estimates,
[??], to redefine the dependent variable in Equation (A1), and return to
the simple smooth-coefficient environment of Li et al. (2002).
Subtracting [W'.sub.it] [??] from both sides of Equation (A1), we
get:
(A5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [v.sub.it] [equivalent to] [W'.sub.it] ([alpha] - [??])
+ [u.sub.it]. The smooth-coefficient functions can then be estimated, as
proposed by Li et al. (2002), using a local least-squares method similar
to the first step:
(A6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
For details on the consistency and asymptotic normality of [??]
([Z.sub.it]), see also Li and Racine (2007).
TABLE A1
Data Averages by State (%, 1978-2000)
Growth Rate of
Total Factor
Productivity Own-State Spending
State (TFP) Capital (G) O&M (AT)
Alabama (AL) 0.75 1.25 2.20
Arizona (AZ) 0.98 4.34 5.71
Arkansas (AR) 0.69 0.56 2.22
California (CA) 1.17 4.01 4.39
Colorado (CO) 0.93 2.10 4.37
Connecticut (CT) 1.79 3.02 1.94
Delaware (DE) 1.42 2.49 2.78
Florida (FL) 1.04 3.10 5.44
Georgia (GA) 1.33 2.84 3.19
Idaho (ID) 0.96 0.65 3.45
Illinois (IL) 0.88 -0.08 2.49
Indiana (IN) 0.65 1.11 2.63
Iowa (IA) 0.68 1.31 0.95
Kansas (KS) 0.51 1.10 3.53
Kentucky (KY) 0.26 1.60 2.77
Louisiana (LA) 0.45 -0.35 1.82
Maine (ME) 0.89 -0.50 1.69
Maryland (MD) 0.89 -0.58 3.46
Massachusetts (MA) 1.71 5.30 1.54
Michigan (MI) 0.16 0.77 2.57
Minnesota (MN) 0.97 1.93 2.05
Mississippi (MS) 0.79 0.58 1.94
Missouri (MO) 0.73 1.50 2.90
Montana (MT) 0.005 -1.15 1.43
Nebraska (NE) 0.80 0.73 1.29
Nevada (NV) 0.75 7.21 6.39
New Hampshire (NH) 1.53 -1.52 2.35
New Jersey (NJ) 1.22 2.26 3.71
New Mexico (NM) 0.83 2.80 5.20
New York (NY) 1.20 2.89 1.49
North Carolina (NC) 1.24 2.33 5.16
North Dakota (ND) 0.24 -0.19 1.09
Ohio (OH) 0.61 1.82 2.09
Oklahoma (OK) 0.15 2.52 2.24
Oregon (OR) 0.80 2.46 2.13
Pennsylvania (PA) 0.96 0.96 1.99
Rhode Island (RI) 1.56 1.27 2.30
South Carolina (SC) 1.11 5.27 4.13
South Dakota (SD) 1.08 2.47 1.00
Tennessee (TN) 0.90 2.37 2.05
Texas (TX) 0.52 3.09 3.99
Utah (UT) 0.61 3.87 5.18
Vermont (VT) 1.13 -0.46 3.41
Virginia (VA) 1.28 0.73 4.10
Washington (WA) 0.95 2.82 3.29
West Virginia (WV) 0.34 -0.19 0.94
Wisconsin (WI) 0.55 3.04 1.49
Wyoming (WY) 0.17 1.94 2.62
Mean 0.86 1.82 2.86
Std. Dev. 0.41 1.76 1.37
Growth Rate of Level of
Output O&M Share
Spilllovers Share in Total
Capital O&M of Labor Spending
State (Sc) (%) (Syz.) MKG + M)
Alabama (AL) 1.38 2.44 63.67 52.65
Arizona (AZ) 4.94 5.68 66.05 41.76
Arkansas (AR) 1.73 2.78 64.32 55.00
California (CA) 2.94 3.73 68.95 61.82
Colorado (CO) 3.78 4.70 72.92 50.09
Connecticut (CT) 2.94 3.09 68.68 50.49
Delaware (DE) 3.01 3.78 73.65 48.70
Florida (FL) 3.69 4.54 59.73 47.22
Georgia (GA) 3.65 4.80 69.79 41.99
Idaho (ID) 2.55 3.32 64.48 44.58
Illinois (IL) 1.32 2.11 69.09 57.57
Indiana (IN) 1.14 2.26 69.67 54.78
Iowa (IA) 0.55 1.62 63.47 49.61
Kansas (KS) 1.45 2.37 64.25 51.48
Kentucky (KY) 0.74 1.83 64.98 44.42
Louisiana (LA) 0.51 1.62 63.57 47.00
Maine (ME) 1.89 2.18 66.57 60.07
Maryland (MD) 1.95 3.21 58.44 51.07
Massachusetts (MA) 2.45 3.35 72.44 50.06
Michigan (MI) 0.70 1.60 71.02 65.15
Minnesota (MN) 2.44 3.10 71.49 49.04
Mississippi (MS) 1.05 2.17 58.83 50.40
Missouri (MO) 1.22 2.45 69.89 51.92
Montana (MT) 0.48 1.11 60.97 44.34
Nebraska (NE) 1.51 2.41 65.37 45.63
Nevada (NV) 5.48 6.31 72.65 41.06
New Hampshire (NH) 4.22 4.14 64.84 61.30
New Jersey (NJ) 2.47 2.82 64.62 55.77
New Mexico (NM) 2.28 3.23 61.61 50.51
New York (NY) 1.63 2.57 68.01 58.22
North Carolina (NC) 2.97 3.83 68.57 50.07
North Dakota (ND) 0.55 0.85 61.13 48.11
Ohio (OH) 0.74 1.85 69.78 54.09
Oklahoma (OK) 0.87 2.00 64.46 50.18
Oregon (OR) 2.17 3.04 68.10 53.01
Pennsylvania (PA) 0.97 1.82 66.38 63.64
Rhode Island (RI) 2.54 2.04 64.25 50.27
South Carolina (SC) 2.26 3.51 64.84 51.14
South Dakota (SD) 2.15 2.78 58.29 48.14
Tennessee (TN) 2.25 3.43 69.67 45.02
Texas (TX) 2.68 3.77 70.92 46.78
Utah (UT) 3.35 4.36 69.99 45.44
Vermont (VT) 2.83 2.88 68.51 64.08
Virginia (VA) 2.92 4.04 62.80 52.11
Washington (WA) 3.12 3.97 67.65 49.05
West Virginia (WV) -0.85 0.25 61.88 49.96
Wisconsin (WI) 1.28 2.37 67.12 55.77
Wyoming (WY) 0.12 1.18 63.65 35.66
Mean 2.06 2.90 66.29 50.96
Std. Dev. 1.28 1.22 4.00 6.25
TABLE A2
Average Output Elasticities by State in the
Absence of Spillovers, 1978-2000
[[theta].sub.M]
State [[theta].sub.G] ([Z.sup.it])
Northeast
Maine 0.0106 0.0144
(ME) (0.0006) (0.0055)
New Hampshire 0.0098 0.0006
(NH) (0.0006) (0.0066)
Vermont 0.0119 -0.0012
(VT) (0.0009) (0.0083)
Massachusetts 0.0057 0.0104
(MA) (0.0014) (0.0019)
Rhode Island 0.0055 0.0108
(RI) (0.0013) (0.0022)
Connecticut 0.0063 0.0111
(CT) (0.0013) (0.0023)
New York 0.0114 0.0253
(NY) (0.0003) (0.0008)
Pennsylvania 0.0088 0.0131
(PA) (0.0004) (0.0047)
New Jersey 0.0103 0.0204
(NJ) (0.0004) (0.0019)
Midwest
Wisconsin 0.0104 0.0210
(WI) (0.0006) (0.0019)
Michigan 0.0086 -0.0092
(MI) (0.0006) (0.0063)
Illinois 0.0107 0.0233
(IL) (0.0005) (0.0015)
Indiana 0.0106 0.0198
(IN) (0.0006) (0.0016)
Ohio 0.0102 0.0177
(OH) (0.0006) (0.0018)
North Dakota 0.0037 0.0059
(ND) (0.0011) (0.0018)
South Dakota 0.0043 0.0049
(SD) (0.0009) (0.0010)
Nebraska 0.0006 0.0025
(NE) (0.0009) (0.0008)
Kansas 0.0075 0.0109
(KS) (0.0008) (0.0018)
Minnesota 0.0050 0.0060
(MN) (0.0008) (0.0010)
Iowa 0.0059 0.0060
(IA) (0.0006) (0.0010)
Missouri 0.0085 0.0119
(MO) (0.0007) (0.0014)
South
Delaware 0.0044 0.0093
(DE) (0.0014) (0.0023)
Maryland 0.0044 0.0107
(MD) (0.0012) (0.0027)
Virginia 0.0078 0.0144
(VA) (0.0012) (0.0022)
West Virginia 0.0046 0.0107
(WV) (0.0014) (0.0025)
North Carolina 0.0057 0.0102
(NC) (0.0012) (0.0022)
South Carolina 0.0063 0.0118
(SC) (0.0012) (0.0022)
Georgia -0.0015 0.0002
(GA) (0.0008) (0.0005)
Florida 0.0022 0.0068
(FL) (0.0014) (0.0022)
Kentucky 0.0029 0.0027
(KY) (0.0012) (0.0009)
Northeast
Tennessee -0.0001 0.0013
(TN) (0.0008) (0.0003)
Mississippi 0.0066 0.0082
(MS) (0.0008) (0.0013)
Alabama 0.0090 0.0142
(AL) (0.0008) (0.0018)
Oklahoma 0.0064 0.0080
(OK) (0.0008) (0.0015)
Texas 0.0034 0.0054
(TX) (0.0012) (0.0016)
Arkansas 0.0098 0.0187
(AR) (0.0006) (0.0019)
Louisiana 0.0035 0.0055
(LA) (0.0012) (0.0016)
West
Idaho -0.0004 0.0032
(ID) (0.0013) (0.0019)
Montana -0.00002 0.0009
(MT) (0.0009) (0.0007)
Wyoming 0.0042 -0.0020
(WY) (0.0024) (0.0006)
Nevada -0.0021 -0.0008
(NV) (0.0011) (0.0006)
Utah 0.0015 0.0020
(UT) (0.0010) (0.0009)
Colorado 0.0060 0.0097
(CO) (0.0012) (0.0019)
Arizona 0.0015 0.0010
(AZ) (0.0013) (0.0013)
New Mexico 0.0014 0.0023
(NM) (0.0014) (0.0027)
Washington 0.0052 0.0067
(WA) (0.0010) (0.0013)
Oregon 0.0092 0.0145
(OR) (0.0006) (0.0016)
California 0.0096 0.0245
(CA) (0.0003) (0.0011)
Note: See Table 2 of the article.
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(1.) See Gramlich (1994), Sturm, Kuper, and de Haan (1998), and
Romp and de Haan (2007) for literature surveys.
(2.) Hulten and Schwab (1997, 157) offer some typical examples:
"... an interstate highway in Illinois does offer some benefits to
the residents of other states, a sewage treatment plant in Maryland that
reduces water pollution in the Chesapeake Bay benefits people in a wide
region." Note that the possibility of public capital having
negative spillovers because economic activity may be drawn to the zone
with the infrastructure investment and away from otherwise equivalent
areas has also been theorized in the literature (see Boarnet 1998).
(3.) Transportation and water infrastructure has typically been the
focus of the public capital productivity literature following Munnell
(1990b), with the main components analyzed including highways and
streets, water and sewer facilities, and other buildings and structures.
(4.) Earlier results by Fernald (1999) also underscored the
existence of nonlinearities in the production function. In a similar
vein, Aschauer (1999) found that, while linear estimates of production
functions deliver an infrastructure effect that disappears when state
effects are introduced, allowing for nonlinearity delivers robust
effects. In addition, Duggal, Saltzman, and Klein (1999) specified a
technological growth rate as a nonlinear function of infrastructure and
demonstrated that the impact of infrastructure on the U.S. economy is
not constant. More recently, Egert, Kozluk, and Sutherland (2009) have
used threshold models in a Bayesian-averaging framework and find that
the growth impact of infrastructure investment is highly nonlinear,
varying across Organization for Economic Co-operation and Development
(OECD) countries and over time. Similarly, Candelon et al. (2013) find
strong threshold effects in the relationship between output and public
capital using a Panel-Smooth-Threshold model.
(5.) Earlier evidence on the productivity impact of public capital
maintenance in the United States comes mainly from case studies or
cost-benefit analyses concentrated on highways. An exception is Pinnoi
(1994), who provided production function estimates suggesting that state
and local expenditures on highway maintenance are productive with
respect to the private and nonagricultural nonmanufacturing sectors. See
Section IV for more details on studies with data for highways.
(6.) See also Carlino and Inman (2013) for similar interregional
effects of American Recovery and Reinvestment Act actions on U.S.
employment.
(7.) Holtz-Eakin and Schwartz (1995) and Sloboda and Yao (2008)
include spillover variables in production functions, while Cohen and
Paul (2004) include a similar spillover index of highway stocks as an
input to a cost function. In a different context, the literature that
views innovation efforts as a major source of technological progress has
extensively studied the effects of international R&D spillovers on
productivity growth (see, e.g., the seminal paper by Coe and Helpman
1995).
(8.) If the network is undirected, then the matrix [PHI] is
symmetric ([[phi].sub.ij] = [[phi].sub.ij]). If the network is
unweighted, then [[phi].sub.ij] = 1 if there is a link between nodes i
and j. As described in the next section, we proxy [[phi].sub.ij] with
data on commodity flows across states to account for different degrees
of interstate dependence.
(9.) Notice that defining TFP based on the private factors (the
well-known Solow residual) and relating it to government services, which
dates back to Aschauer (1989) and Hulten and Schwab (1991). allows us
here to obtain a more parsimonious--in terms of number of
parameters--specification than in the case of the corresponding
production function. Note also that in our model we include government
capital and O&M spending as additional production inputs, which
implies that [g.sub.TFP] represents a biased index of technological
change that will be affected by changes in the growth rates of G, M,
[S.sub.G], [S.sub.M]. Cost-function specifications have also been used
in the literature, but in a limited number of studies, because
historical price data is typically available only for manufacturing
firms.
(10.) By including the lagged dependent variable as a regressor,
this specification also accounts for the dynamic nature of TFP growth.
Note that we have investigated the possibility of serial correlation in
our baseline estimation, but the corresponding coefficient did not turn
out to be statistically significant.
(11.) Spatial econometrics (see, e.g., Anselin 1988) have been
widely employed in the literature to deal with spatial interactions.
However, given the complexity of nonparametric estimation methods,
spatial approaches have been used in this framework to a very limited
extent so far.
(12.) In line with the literature, Alaska, Hawaii, and the District
of Columbia are excluded from the sample.
(13.) The database of 1,300 finance items is spread across eight
data tables. Data become available annually from 1977 onwards, while
there are no state-level statistics available for local governments
(i.e., counties, municipalities, townships, special districts and school
districts) for 2001 and 2003, because the corresponding surveys were
redesigned to provide only national estimates. This restricts our sample
to the period 1978-2000.
(14.) For a detailed description of what exactly constitutes the
two main spending categories, see U.S. Census Bureau, Government Finance
and Employment Classification Manual, Table 5.1: "Description of
Character and Object Categories" (source: http://www2.census.gov/
govs/pubs/classification/2006_classification_manual.pdf). For a
definition of each type of infrastructure, see Appendix B of
Congressional Budget Office (2010).
(15.) Preliminary estimations were performed simply using equal
weights in the construction of [S.sub.G] and [S.sub.M]. The output
elasticities of own-spending were found to be positive, but small
(amounting on average to 0.010 and 0.006 for G and M, respectively),
whereas the output elasticities of spending by other states were found
to be negative (amounting on average to -0.011 and -0.082 for [S.sub.G]
and [S.sub.M]). However, we believe these initial estimates, which
differ substantially from the results reported below, can be very
misleading as they fail to account for the different degrees of economic
and geographic interrelations between states. Because no corresponding
time series is available for the commodity flows data, we use an average
of the data for 1993 and 1997. which also eliminates potential
endogeneity concerns (see Cohen and Paul 2004).
(16.) We have also estimated the model parametrically by specifying
the varying coefficients as a second-degree polynomial of [Z.sub.it]
(based on the graphs). The coefficients on the quadratic terms turned
out to be statistically significant for [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII], with t statistics -1.89, 2.50 and 2.30,
respectively, which indicates that the use of the SSCM is justified.
(17.) Negative estimates for the productivity effect of public
capital have been previously reported in the literature
(see, e.g., Evans and Karras 1994; Holtz-Eakin and Schwartz 1995).
In addition, Pinnoi (1994) has estimated negative output elasticities
with respect to highway capital outlay and maintenance for some sectors
of economic activity and U.S. regions. Positive, but small, mean effects
(0.006 and 0.009 for capital and O&M. respectively) were estimated
without including the spillover variables. The detailed results by state
are presented in Tables A1 and A2.
(18.) In Blinder's (1990) words: "If my car and my back
absorb fewer shocks from potholes, I am surely better-off; but GNP may
even decline as a result of fewer car repairs and doctor's
bills."
(19.) A correlation matrix of the additional controls is available
upon request. Data are obtained from the Census Bureau's
"Rex-Dac" database for all public-sector variables, from the
Bureau of Labor Statistics. Local Area Unemployment Statistics for the
state-level unemployment rate, and from Pjesky (2006) for the population
characteristics, available until 1999. We have also experimented with
other control variables, like the size of the population and the degree
of expenditure decentralization, but they turned out to be statistically
insignificant. Finally, using the shares of total earnings earned in
federal, state and local governments instead of the number of federal,
state and local employees produced essentially the same results.
(20.) For instance, Congressional Budget Office (1988) has
indicated that the return to projects designed to maintain the average
condition of the federal highway system could be as high as 30%-40%. In
a similar vein, there has been some evidence, based on data from the
Federal Highway Administration, suggesting that beyond a certain point
maintenance and management of existing infrastructure become more
attractive than investment in additional capacity; for instance,
road-resurfacing projects have cost-benefit ratios that are nearly
double compared with projects that add new lanes (Congressional Budget
Office 1998).
SARANTIS KALYVITIS and EUGENIA VELLA *
* We are grateful to T. Stengos for sharing his Gauss routines and
for many constructive discussions. The code for local GMM estimation was
provided by M. Delis. We have also benefited from comments and
suggestions by J. Caballe, E. Dinopoulos, E. Dioikitopoulos, L.
Gambetti, S. Gnocchi, Y. Karavias, A. Kourtellos, N. Musick, V.
Sarantides, A. Sole Olle, A. Zervou, and seminar participants at the
Royal Economic Society 2012 PhD Meeting, the Royal Economic Society 2011
Conference, the 8th Conference on Research on Economic Theory and
Econometrics, Universitat Autonoma de Barcelona, and Universitat de
Barcelona. Financial support under the Operational Program
"Education and Lifelong Learning" of the National Strategic
Reference Framework-Research Funding Program "Heracleitus It"
and the Max Weber Postdoctoral Programme at the EUI is acknowledged by
E.V.
Kalyvitis: Professor, Department of International and European
Economic Studies, Athens University of Economics and Business, Athens
10434, Greece. Phone +30 2108203151, Fax +30 2108214122, E-mail
skalyvitis@aueb.gr
Vella: Research Fellow, Max Weber Postdoctoral Programme, European
University Institute, 50014 Fiesole Firenze, Italy. Phone +39 055
4685681, Fax +39 055 4685902, E-mail eugenia.vella@eui.eu
TABLE 1
Parameter Estimates of the Linear Model
Independent Without With
Variable Spillovers Spillovers
Year trend 0.0005 0.0007
(0.0001) (0.0001)
Growth of capital 0.005 -0.004
spending ([DELTA] ln G) (0.004) (0.005)
Growth of O&M spending 0.008 -0.016
([DELTA] ln M) (0.009) (0.011)
Growth of capital spillover -- 0.052 (0.012)
([DELTA] lnSc)
Growth of O&M spillover -- 0.411 (0.035)
([DELTA] ln SM)
[R.sup.2] 0.047 0.436
No. of observations 1,104 1.104
Notes: Estimation method is ordinary least squares (OLS)
and standard errors are reported in parentheses. The dependent
variable is TFP growth and regressions include a constant,
a time trend, and state dummies.
TABLE 2
Average Output Elasticities by State,
1978-2000 (Semiparametric Estimates)
State [[theta] [[theta] [MATHE- [MATHE-
.sub.G] .sub.M] MATICAL MATICAL
([Z.sub. ([Z.sub. EXPRESSION EXPRESSION
it]) it]) NOT REPRO- NOT REPRO-
DUCIBLE IN DUCIBLE IN
ASCII] ASCII]
Northeast
Maine 0.0009 -0.007 0.046 0.409
(ME) (0.001) (0.003) (0.004) (0.009)
New Hampshire -0.0008 -0.017 0.059 0.427
(NH) (0.001) (0.004) (0.006) (0.012)
Vermont -0.0003 -0.015 0.058 0.438
(VT) (0.001) (0.004) (0.006) (0.012)
Massachusetts -0.0007 -0.016 0.040 0.376
(MA) (0.001) (0.002) (0.003) (0.002)
Rhode Island -0.0017 -0.016 0.042 0.382
(RI) (0.001) (0.003) (0.003) (0.003)
Connecticut -0.0007 -0.015 0.040 0.377
(CT) (0.001) (0.003) (0.003) (0.002)
New York 0.0031 0.0004 0.037 0.388
(NY) (0.001) (0.001) (0.001) (0.004)
Pennsylvania -0.0021 -0.010 0.059 0.438
(PA) (0.001) (0.003) (0.004) (0.007)
New Jersey 0.0026 -0.005 0.035 0.379
(NJ) (0.0004) (0.002) (0.001) (0.003)
Midwest
Wisconsin 0.0027 -0.005 0.035 0.380
(WI) (0.001) (0.002) (0.001) (0.003)
Michigan -0.0037 -0.025 0.074 0.461
(MI) (0.001) (0.003) (0.005) (0.010)
Illinois 0.0025 -0.002 0.038 0.388
(IL) (0.001) (0.002) (0.001) (0.004)
Indiana 0.0034 -0.006 0.033 0.374
(IN) (0.001) (0.002) (0.001) (0.002)
Ohio 0.0031 -0.008 0.033 0.372
(OH) (0.001) (0.002) (0.001) (0.001)
North Dakota -0.0038 -0.021 0.045 0.382
(ND) (0.001) (0.002) (0.003) (0.003)
South Dakota -0.0026 -0.023 0.040 0.377
(SD) (0.001) (0.001) (0.003) (0.002)
Nebraska -0.0055 -0.027 0.046 0.384
(NE) (0.001) (0.001) (0.002) (0.002)
Kansas 0.0006 -0.017 0.035 0.373
(KS) (0.001) (0.002) (0.001) (0.002)
Minnesota -0.0016 -0.023 0.037 0.375
(MN) (0.001) (0.001) (0.001) (0.002)
Iowa -0.0011 -0.023 0.036 0.373
(IA) (0.001) (0.001) (0.001) (0.001)
Missouri 0.0017 -0.015 0.033 0.370
(MO) (0.001) (0.002) (0.001) (0.001)
South Delaware -0.0032 -0.016 0.046 0.382
(DE) (0.002) (0.003) (0.004) (0.003)
Maryland -0.0037 -0.016 0.047 0.393
(MD) (0.001) (0.003) (0.003) (0.004)
Virginia 0.0010 -0.012 0.037 0.376
(VA) (0.001) (0.003) (0.002) (0.002)
West Virginia -0.0029 -0.014 0.046 0.385
(WV) (0.001) (0.003) (0.003) (0.003)
North Carolina -0.0012 -0.017 0.040 0.378
(NC) (0.001) (0.003) (0.002) (0.002)
South Carolina -0.0006 -0.016 0.039 0.380
(SC) (0.001) (0.003) (0.002) (0.003)
Georgia -0.0101 -0.025 0.061 0.392
(GA) (0.001) (0.001) (0.004) (0.002)
Florida -0.0042 -0.019 0.047 0.383
(FL) (0.001) (0.003) (0.003) (0.002)
Kentucky -0.0082 -0.026 0.055 0.389
(KY) (0.002) (0.001) (0.006) (0.004)
Tennessee -0.0062 -0.028 0.048 0.385
(TN) (0.001) (0.001) (0.002) (0.001)
Mississippi -0.0001 -0.020 0.035 0.372
(MS) (0.001) (0.002) (0.001) (0.001)
Alabama 0.0021 -0.013 0.034 0.371
(AL) (0.001) (0.002) (0.001) (0.001)
Oklahoma -0.0004 -0.021 0.036 0.374
(OK) (0.001) (0.002) (0.001) (0.001)
Texas -0.0044 -0.020 0.047 0.381
(TX) (0.002) (0.002) (0.004) (0.003)
Arkansas 0.0023 -0.008 0.035 0.379
(AR) (0.001) (0.002) (0.001) (0.003)
Louisiana -0.0044 -0.022 0.046 0.382
(LA) (0.002) (0.002) (0.004) (0.003)
West
Idaho -0.0068 -0.020 0.054 0.386
(ID) (0.001) (0.002) (0.003) (0.002)
Montana -0.0071 -0.026 0.052 0.385
(MT) (0.001) (0.001) (0.003) (0.002)
Wyoming -0.0220 -0.022 0.096 0.414
(WY) (0.002) (0.001) (0.006) (0.006)
Nevada -0.0113 -0.023 0.065 0.393
(NV) (0.001) (0.001) (0.004) (0.003)
Utah -0.0060 -0.025 0.049 0.383
(UT) (0.001) (0.001) (0.004) (0.002)
Colorado -0.0007 -0.017 0.039 0.375
(CO) (0.001) (0.002) (0.002) (0.002)
Arizona -0.0111 -0.020 0.067 0.391
(AZ) (0.002) (0.001) (0.006) (0.004)
New Mexico -0.0070 -0.020 0.062 0.411
(NM) (0.001) (0.002) (0.004) (0.008)
Washington -0.0016 -0.021 0.039 0.375
(WA) (0.001) (0.002) (0.002) (0.002)
Oregon 0.0023 -0.012 0.033 0.371
(OR) (0.001) (0.002) (0.001) (0.002)
California -0.0004 -0.002 0.047 0.417
(CA) (0.001) (0.001) (0.002) (0.004)
Notes: Estimation method is partially linear semiparamet-
ric smooth-coefficient approach. See also Table 1.
TABLE 3
Descriptive Statistics of the Estimated Coefficients,
LGMM with Demeaned Data
Independent Variable Mean Std Dev Variance
Lagged TFP growth -0.0133 0.1259 0.0159
([g.sub.TFP.sub.it-1])
Growth of capital -0.0008 0.0136 0.0002
spending ([DELTA] ln G)
Growth of O&M spending 0.0095 0.0448 0.0020
([DELTA] ln M)
Growth of capital spillover 0.0871 0.0812 0.0066
([DELTA] lnSG)
Growth of O&M spillover 0.3371 0.2048 0.0420
([DELTA] lnSM)
No. of observations 1.008
Independent Variable Minimum Maximum
Lagged TFP growth -0.3171 0.1981
([g.sub.TFP.sub.it-1])
Growth of capital -0.0254 0.0197
spending ([DELTA] ln G)
Growth of O&M spending -0.1227 0.0857
([DELTA] ln M)
Growth of capital spillover -0.1066 0.2988
([DELTA] lnSG)
Growth of O&M spillover 0.1210 0.8467
([DELTA] lnSM)
No. of observations
Notes: The dependent variable is TFP growth. Details on the
instruments are provided in Section II.
TABLE 4
Baseline Results and Sensitivity Analysis
Independent Variable (1) (2) (3)
Nonlinear part:
average coefficients
Growth of capital spending -0.002 -0.003 -0.004
([DELTA] In G) (0.00021) (0.00021) (0.00027)
Growth of O&M spending -0.017 -0.021 -0.019
([DELTA] In M) (0.00038) (0.00047) (0.00050)
Growth of capital spillover 0.046 0.050 0.056
([DELTA] ln [S.sub.c]) (0.00059) (0.00060) (0.00099)
Growth of O&M spillover 0.388 0.375 0.361
([DELTA] ln [S.sub.M]) (0.00085) (0.00074) (0.00154)
Linear part Year trend 0.0007 0.0012 0.0006
Unemployment rate (0.00008) (0.0002) (0.00008)
-0.001
Federal employees (0.039)
0.651
State and local employees (0.201)
-1.240
Federal revenue (0.260)
0.372
Tax burden (0.139)
-0.051
Working population (0.085)
0.267
Non-White (0.084)
0.026
Female (0.031)
-0.006
No. of observations 1,104 (0.331) 1,104
1.056
Independent Variable (4) (5)
Nonlinear part:
average coefficients
Growth of capital spending -0.008 -0.007
([DELTA] In G) (0.00021) (0.00032)
Growth of O&M spending -0.029 -0.016
([DELTA] In M) (0.00056) (0.00032)
Growth of capital spillover 0.083 0.049
([DELTA] ln [S.sub.c]) (0.00051) (0.00083)
Growth of O&M spillover 0.354 0.291
([DELTA] ln [S.sub.M]) (0.00121) (0.00099)
Linear part Year trend 0.0003 0.0003
Unemployment rate (0.00008) (0.00009)
Federal employees
State and local employees
Federal revenue
Tax burden
Working population
Non-White
Female
No. of observations 1,104 1,104
Notes: The table presents coefficients obtained from the
estimation of Equation (6). Column (1) reports the baseline
results. In column (2) a number of variables are employed as
additional controls. In column (3) a second state variable
is used, namely the O&M share in the sum of the two
spillover indices. In column (4) the spillover variables
included in the regression have been computed by weighting
different states only with information on relative economic
activity. In column (5) the regression is run for highways
and roads. The dependent variable is TFP growth. All
regressions include a constant and state dummies. Standard
errors are reported in parenthesis.
