does public infrastructure affect regional performance?

Growth and Change Vol. 26 (Spring J99-5), pp. 204-216

Does Public Infrastructure Affect Regional Performance?

KIM ANDREWS JAMES SWANSON

ABSTRACT Docs public infrastructure affect state output'? This paper uses both a Cobb-Dough5 and a translog production function to examine the impact of public infrastructure spending on state output. Like labor and private capital, the stock of public capital is considered to be an input into the production process. The data are bascd on Alicia Munnell's work and were provided by the Federal Reserve Bank of I h t o n . Unlike many of the earlier studies employing Ordinary Leas1 Squares (OLS) techniques, this analysis employs estimating methods that take advantage of the longitudinal nature of the data set. While these methods lend support to the public capitol hypothesis, there is evidence that studies relying on OLS have reported a cocrlicicnt on public capital that is upward biased. This papcr, which controls for heterogeneity in the data, finds the coefficient on public capital to be smallcr than thal presented in previous studies. This finding has important policy implications. I t intiicatcs that while investment in public capital may have a positive impact on the private sector, this impact will be much smaller than predicted by previous studies.

Introduction c hccausc of thc link between productivity and living standards. Gcnerally, growth in productivity is associatcd with a growth in rcal wagcs and ultimatcly an improvcmcnt in living standards. The bchavior of productivity in thc U.S. has bccn thc focus of much discussion among economists. While the absolute lcvel of productivity rcmains high relative to other industrialized countries, the growth ratc of productivity in the U.S. has fallen significantly relative to nations such as Germany and Japan. It is felt that the stagnation of real wages in thc U.S. is dircclly rclated to this dcclinc in productivity.

Numerous lactors ranging from a decline in the quality of the labor force to output and productivity measurement errors have becn postulatcd as playing a rolc in this slow down. Aschaucr's work in 198% resultcd in a burgeoning

I IAYGI<S iN I'lIODLIC1TVI'I'Y AKIC A MAJOR CONCIIRh' IN ANY ECONOMY

Kim Andrews is an assistan1 professor and James Swunson is an associate prqfessor in economics at Central Missouri State University, Warrenshurg. The authors thunk Nancy Medlin for editorial assistance and three anonymous referees ,for helpful comments.

Submitted Aug. 1994, revised Feb., Apr. 1995. 0 1995 College of Business and Economics, University of Kentucky

PUBLIC INFRASTRUCTURE 205

litcraturc that bcgan to explore in more detail the impact of public capital cxpcnditurcs on productivity. It was at this time that writers noted the prccipilous dccline in productivity in the U.S. had been accoinpanicd by a decline in public capital cxpenditurcs. It is postulated that such expenditures can impact productivity through both a direct and an indirect cffcct. Thc dircct cffcct ariscs bccausc public capital cnters the production function as an input. The indircct elfcct ariscs bccausc public capital can affect the productivity of labor and privatc capital.

Thc purposc ol this paper is to cxaminc thc dircct cffcct that public capital may havc on statc output. In the following scction, wc will briefly review thc litcraturc on thc public capilal hypothesis. In the third section we present thc data and mcthodology used to estimate both the Cobb-Douglas and the translog production functions. Thc ncxt section discusses the results of this cstimation. Thc final scction prcscnts our conclusions.

Literature Review Thc most common mcthods of examining thc impact of public capital on

economic activity havc been to estimate a production function in which public capital is considcrcd to bc an input into the production proccss or to cxaminc thc impact of public capital on factor productivity. Production functions at both national and rcgional lcvels havc bccn estimated. Examples of studics using aggrcgate production functions at thc national lcvcl include Mcra (1973) and Aschauer (1989a).

llsing the assumption of constant returns to scale and ordinary least squares (OLS), Mcra uses data developed by the Japanese govcrnment to estimate Cobb- Douglas production functions for the primary, secondary, and tertiary sectors. Hc finds social capital to have a significant, positive impact on output in all three sectors.

Aschaucr ( I 98%) uses both ordinary least squares and two-stage least squarcs to cstimatc a Cobb-Douglas function for the U.S. privatc busincss scctor ovcr the 1949-1985 time period. Significant cocfficicnts of 0.39 and 0.40, rcspcclivcly show public capital to bc positivcly rclatcci lo private business sector output.

Scvcral studics havc estimated rcgional production functions. Thcsc include Mcrriman (1990), Costa ct al. (1987), Munncll (1990a), Eisncr (1991), and Garcia-Mila and McGuirc (1992). Using a joint gcncralizcd lcast squarcs procedurc, Mcrriman (1990) employs both Japancse and American data to cstimatc rcgional Lranslog production functions. Hc rinds that govcrnment capital is an importmi input into thc production proccss across sectors and mtions.

206 GROWTH AND CHANGE, SPRING 1995

Using ordinary least squares, Costa et al. (1 987) estimate a translog function for the 48 contiguous states during the 1972 time period. Functions for the manufacturing scctor, nonagriculture sector, and all scctors arc estimated. Public capital is found to contributc significantly to manufacturing output in all three sectors.

Munncll (199Oa) uses poolcd state data over the 1970-1986 time period to cstimatc a Cobb-Douglas production function. She uses the assumptions of 1 ) no constraints, 2) constant returns to scale ovcr thc private inputs, and 3 ) conslant rcturns to scalc ovcr the entire function. Employing ordinary least syuarcs, she finds that public capital, regardlcss of thc assumption uscd, is positivcly rclatcd to gross statc product. Munnell also uses ordinary lcast squares I.cchniqucs 1.0 cstimatc two translog production functions: onc which uses an aggregate public capital variable and anothcr in which public capital is disaggrcgatcd into highway stock, watcr and scwcr systems, and othcr. The aggrcgatc stock of public capital is found to be positivcly related to output as arc highway stock and watcr and scwcr systcms.

Eisncr (199 I ) makcs usc of Munncll’s (19904 data to cxamine variations in statc output duc cxclusivcly to timc differences and variations in state output duc exclusivcly 1.0 sutc diffcrcnccs. Following Munncll’s assumptions, he finds that statcs having morc public capital also have grcatcr levels of output. However, he docs not find that statcs with morc public capital in one year than anothcr have grcatcr lcvcls of output during the year in which public capital was grcater. Hc argues this rcsult is not surprising as public capital cxpenditurcs would likcly inlluencc output only aftcr scvcral periods.

Using ordinary least squares, Garcia-Mila and McGuirc (1992) estimate a Cobb-Douglas production function for thc 48 contiguous statcs ovcr the 1970- 1983 timc pcriod. W hilc finding public capital cxpcnditurcs to be positivcly rclatcd to gross state product, thcir rcsults indicatc that, relative to infrastructurc spcnding for highways, spcnding on education has a grcatcr impact on statc output.

Studics cxamining the impact of public capital on factor productivity have bccn done at thc international, national, and regional lcvels. They include work by Aschaucr (1989b), Munnell (1990b), Hultcn and Schwab (1991), Moomaw and Williams (1991), Holtz-Eakin and Schwartz (1994), and Mullcn and W i I liams (1 990).

Aschaucr (1 98%) uses ordinary least squares to cstimate labor productivity growth for thc G7 countries over the 1966-1985 timc pcriod. His cstirnatcs show tha t incrcasing public invcstmcnt by 1 pcrcent rcsulls in a 0.4 pcrccnt gain in labor productivity.


Munncll (1990b) cxamines growth in labor productivity for thc U.S. ovcr the 1949-1987 time period. Using ordinary least squares, shc finds public capital investment makes an important contribution in explaining changes in labor productivity. Munncll also examines the impact of public capital an changcs in multifactor productivity growth. She finds that much of the decline in multifactor productivity growth during the 1970s is a result of a decline in the growth of public capital.

Hulten and Schwab (1991) use sources of growth analysis to examine the impact of public capital on rcgional multifactor productivity growth in the U.S. manufacturing scctor over the 1965-1986 lime period. Their results show no significant rclationship bctwccn growth in regional public capital and growth in regional multifactor productivity.

Moomaw and Williams (1991) develop a measure of total factor productivity growth for thc manufacturing scctor of thc contiguous 48 states over the 1954- 1976 timc period. Using three-stage least squares, thcy find that govcrnment spending on transportation infrastructurc and cducation arc important in explaining both diffcrcnccs in tolal factor productivity across statcs and growth rates in to1;d factor productivity.

Holk-Eakin and Schwartj! (1994) use a neoclassical growth modcl that explicitly incorporates public infrastructurc. Thc model is estimated using a poolcd data sct for the 48 contiguous states over thc 1971-1986 time pcriod. Their cstimaks show infrastructure investmcnt having a negligible impact on annual productivity over this time period.

Mullcri and Williams (1990) examine growth rates in total factor productivity in manufacturing for 29 Standard Metropolitan Statistical Arcas over the 1963- 1966 timc period. Using both ordinary least squares and two-stagc least squares, thcy find thc coefficient on intrastructurc (in thc form of highways) to be positive; however, it is not significantly rclatcd to changcs in total factor productivity in the manufacturing scctor of urban arcas.

Therc arc several authors who criticizc studies finding a positive link bctwccn public capilal and cconomic activity. Jorgcnson (1991) and Tatoin (1991a, 1991b) arguc that studies examining the impact of public capital often ignorc thc influcncc of cncrgy priccs on productivity. Omitting energy priccs could causc cnergy-rclated productivity Iosscs to bc attributed to the dccline in the growth of public capital. These authors also arguc that production function studics omit significant time trcnds. If trcnds are important, thcir omission C ~ U S C S the coefficient on public capital to bc biascd. Finally, the data used in studics may contain variables that are not stationary. After correcting for this problem, thc impact of public capital on economic activity is found to be quitc small or cvcn insignificant.


Holtz-Eakin ( 1993) argues that cross-sectional studies generally ignore underlying differences in productivity. This results in biased and inconsistent estimates. Specifically, he contends that ignoring these underlying differences results in an upward bias of the public capital coefficient.

As the above discussion indicates, much of the literature supports the public capital hypothesis. However, because some nagging questions regarding the impact of public capital still remain, more exploration of the public capital hypothesis is in order. In the next section, we will set forth the data and methodology used to further examine the hypothesis of the direct effect of the public capital.

Data and Methodology Data on state labor usage, stale private and public capital usage, and state

output for each of the 48 contiguous states from 1970 through 1986 are used to estimate an aggregate production function. The capital stock measures are from Munncll’s (1 990a) conslruction of public and private capital stock. These data are derived by apportioning Bureau of Economic Analysis national stock estimates of various sectors among the states. The labor data are total employment on nonagricultural payrolls reported by the Burcau of Labor Statistics. Gross state product is used for the output measure. The data were made available by the Federal Reserve Bank of Boston and are more fully discussed in Munncll (1990a). An additional variable, the state uncmployment ratc, is included to control for changcs in productivity. These changcs may occur because of both cyclical and long-tcrm changes in a state’s economic activity.

Productivity within a state can be affected by the busincss cycle. The procyclical behavior of productivity is well discussed in the literature. Capacity utilization is a possiblc reason for this behavior. During a downturn in economic activity, thcrc is a tcndcncy for firms’ sales and output to decline more rapidly than their use of inputs. In the case of a fixed output such as capital, it is obvious why this occurs. In the case of labor, firms may hoard labor due to quasi fixed costs. Fay and Medoff (1985) have offered evidence of labor hoarding by firms during cyclical downturns. Hoarding is consistent with the procyclical behavior of labor productivity.

A second cxplanation of the cyclical behavior of productivity relates to the composition of output in the economy. Relative to the service sector, the manufacturing sector is very sensitive to changes in economic conditions. Because of this, the relative share of output produced by manufacturing tends to decline during periods of downturn. Productivity in the manufacturing sector is among the highest of all sectors in the economy. The decline in productivity in


the manufacturing scctor (brought about by the relatively large declinc in output during a downturn) may rcducc overall productivity in the economy.

Productivity within a state can also be affected because of long-term trends that occur as dcmographics and industry mix change. Data have consistently shown uncmploymcnt rates among minority groups to bc grcatcr than thc uncmploymcnt ratc of thc nonminority group. As the percentagc of minoritics making up thc labor force increases, the uncmploymcnt ratc can be cxpccted to risc.

In addition to the impact of changing dcmographics, structural changcs in the economy have also impacted unemployment. First, thcrc has bcen a long-tcrm shift from the goods-producing sector to the service sector. Sccond, all industries havc intcnsificd their automation and computcrization efforts. Finally, the corporate scctor in thc U.S. has gone through a pcriod of downsizing. Thcsc factors havc all contributed to increases in structural unemployment (Wcincr 1993). McGcc (1985) has provided empirical support for a link bctwecn the uncmploymcnt rate and demographics and between the uncmploymcnt ratc and industry mix.

Thus, thcrc arc rcasons to bclieve that there is a relationship between the uncmploymcnt ralc and cyclical changes in the economy’s pcrlormance. In addition, thcrc is also a relationship between the unemployment rate and long- tcrm trcnds in dcmographics and industry mix. Neithcr of these effects are likcly to bc captured by thc input variables of the aggregate production function. Thus, thc uncmploymcnt ratc is includcd in the model to control for both cyclical and long-tcrm trcnds.

Thc sccond scction notcs Holk-Eakin’s (1993) discussion of the problcm of using OLS to cstimatc longitudinal data scls. OLS ignorcs individual slate diffcrcnccs in undcrlying productivity from such things as cliinatc and rcsourcc endowincnt. Sincc states that havc above averagc cndowmcnLs tend to havc morc output and grcatcr incomcs, they typically invest morc in public capilal. Extcnding this linc of rcasoning, ignoring thc individual statc differcnccs is like omitting a rclcvant cxplanatory variable. Sincc the state spccific paramctcr is, in somc scnsc, an cstimator for the statc’s multifactor productivity, thc paramctcr estimate is most likcly to be positivc. Thus, thc bias on thc public capital paramctcr dcpcnds upon thc partial covariancc coefficient bctwccn public capital and the statc spccific paramctcr. Following Holu-Eakin’s argument, this results in upward biased OLS estimates of the public capital paramctcr.

Onc method of capluring differcnces across states is through diffcrcnccs in thc conslant tcrm in a Fixed Eflech modcl. The least squarcs dummy variablc (LSDV) modcl spccifies a scparatc dummy variablc for each statc in the OLS estimation to capture thc state specific productivity characteristics (Greene 1993).


An F test can be used to test for differences across states (underlying producli- vity effects) by using both the LSDV (unrestricted) and Lhe OLS (restricted) estimators.

Alternatively, the estimation model can specify the individual spccific constant terms as randomly distributed across states in a Random Effects model. In the Feasible Generalized Least Squares (FGLS) model, the state specific component is modelcd as part of the random disturbance and is assumed to be constant through time (Greene 1993). This model treats the individual effects as uncorrclatcd with the other regressors in the model. If this is not true, the random effects model may suffer from inconsistency due to omitted variables.

I t is possible, because of the existence of underlying productivity differences among statcs, Lhat the Fixed Effects (LSDV) and the Random ,5fecfs (FGLS) models will both prove superior to the OLS estimator. In choosing between thcsc cstimators, two lines of argument can be followed. On a theoretical level, thc fixcd elfccLs inodcl is a reasonable approach when the differences between units can bc vicwcd as parametric shift.< of thc regression function. This model might bc vicwcd as applying only to the states in thc study. Thus, if all states arc includcd, this approach would be appropriate. Alternatively, if the time pcriod is trcatcd as a random sample from all possible time periods, the random eflects model would be appropriate.

Hausman (1978) has developed a procedure that can be used to tcst for orthogonality of thc random effects and the regressors. If the individual effects are uncorrelatcd with thc other regressors in the modcl, then the LSDV and the FGLS arc consistcnt, but LSDV is inefficient. If thcrc is correlation, LSDV is consistcnt, but FGLS is not. Under the null hypothcsis of no correlation, the test statistic

is distributed chi-square with degtees of frccdom equal to the number of slope paramctcrs estimated. S’ is the estimated variance of the LSDV model. In thc following section we provide the results of estimating the Cobb-Douglas and translog production tunctions. Becausc theory docs not offer a clear choice betwcen the LSDV and FGLS methods of estimating the two models, the Hausman test is used as the basis for our choice.

PUBLIC INFRASTRUCTURE 21 1

Empirical Results We first estimated a log linear Cobb-Douglas production function of the form

InQ = I d + alnK + b i d + clnG (2)

whcre (log) output (1nQ) is regressed on thrw inputs (log) labor (Id), (log) private capital ( I N , and (log) public capital (1nG). Because each of the estimated models cvidenced autocorrelated error terms, a two-step Cochrane- Orcutt estimator was employed to improve the efficiency of the estimates. The Durbin Watson statistics reported arc after the ARl correction.

Table 1 reporLs two rcsults for the Cobb-Douglas model: one without any constraints as to returns to scalc and one with the parameters constrained to constant returns lo scalc. The OLS results are reported for comparison purposes.

[ABLE 1. COBB-DOUGLAS: 48 STATE (1 970-1 986)

Parameter

Durbin-Watson 2.0 1.9 2.0 2.0

Note: t-statistics in parentheses * [I-(a+c)]


For both versions, the F t a t rejected the OLS estimator at any level of signifi- cancc.’ Further, the Hausman test showed that thc hypothesis of no correlation could not be rcjcctcd for cither version? Thus, the random effects model is reported for both vcrsions.

The discussion will focus on the unconstrained modcl bccausc statistics indicatc that this modcl provides a better fit. Thc cocfficicnts on labor and privatc capital arc 0.62 and 0.33 respectively. If the 0.11 contribution from public capital is divided up proportionately, the result is very close to the traditional division of income between capital and labor. The coefficient on thc uncmploymcnt variable has the cxpectcd sign and is significant. Thc positive, significant cocfficicnt on public capital providcs support for the argument that public capital has a positive, direct impact on output. Calculations show the marginal product of public capital in 1986 to be approximately 0.25.

It should bc nolcd that the size of our public capital cocfficicnt is smaller than thc ccxfficicnt of 0.15 reported by Munnell (1990a). Our model, then, predicts a smaller impact of public capital on output. These results are consistent with thc hypothesis of upward bias in the public capital coefficient. This hypothcsis is further strcngthcned by comparing our results with other work in this arm. For cxamplc, depending on the sector examined, Costa et al. (1987) find the coefficient on public capital to be between 0.19 and 0.26. While Mera’s (1973) rcsults vary depcnding upon the specification used for public capital, he generally finds this coefficient to be grcatcr than the results we report. While our results do indicate a positive role for infrastructure, thcy arc lcss optimistic than the results rcportcd in earlier studies.

Clcarly thc Cobb-Douglas production function places scvcrc limitations on the structure of thc technology. A more gencral form of technology is desircd. One such form that is frcqucntly used in the literaturc is the translog production function. In addition to the advantagc of a more flexible form, this production function also allows gross substitutability in production Lo be investigated.

This rcquircs cstimation of a translog production function, where Q is gross statc product and X and Y arc inputs (labor, private capital, and public capital). As shown in cquation 3, each input in the translog production function is cxprcssed as thc diffcrcncc bctween thc natural log of the input and the natural log of thc mcan of thc input.

3 6


In this framework, the function is like a second-order Taylor series approxima- tion of an arbitrary function.

Table 2 reports the translog production function results where the dependent variablc is thc natural log of state output. The Fixed Effects model was estimated based upon the I: and Hausman tests? While the coefficient on public capital is not significant when performing the typical two-tailed test, it is significant at the 6.7 pcrcent level when a one-tailed test is performed. The squared public capital variable is not significant for either the one-tailcd or two- tailcd tests. The test of the null hypothesis that the coefficients of the public capital variables are jointly zero yielded an I; statistic of 7.88 that is significant at less than 1 percent. This suggests that public capital does contributc to gross stalc product and thus productivity. However, a with the Cobb-Douglas estimates, thc results suggest that failure to control for state specific effects tends to result in upward biased estimates of the public capital parameters.

As the results in Tables 1 and 2 show, the coefficients on the unemploymcnt variable are significant regardless of the model estimated. The size of the cocfficicnls are remarkably consistent across models. These results indicate the importance of controlling for the impact of cyclical and long-term trends on productivity. Models which do not control for these changes likely suffer from a misspecification error.

As previously statcd, another benefit of the translog is the ability to investigate the issue of substitutability and complementarity between inputs. Our results show public capital and labor to be gross substitutes and public capital and private capital to be gross complements; however, this latter result is only marginally significant. While these results are at odds with both Costa et al. (1987) and Munnell's (1990a) findings, they do support Aschauer's 1989c study. In this study, Aschauer found nonmilitary public capital stock playing a significant, positive role in determining the rate of return to private capital. This implies that policy makers may have an opportunity to use public sector investment as an engine of growth in the private sector through a "crowding in" effect.

Conclusions Estimates of aggregate production functions have generally found that public

capital contributes positively to aggregate output and productivity. However, these results have been criticized because of their reliance on OLS estimating techniques that do not control for state specific factors that may affect productivity. This study uses a panel data estimation technique that controls for these dilfercnccs. While our rcsults provide support for the public capital hypothesis, we also find that controlling for state specific effects reduces the impact of


Variable

Constant

Labor

Private capital

(Labor)'

(Private capital)'

OLS Fixed Effects Model Model

11 .Ol State Specific (804.0)

0.66 0.77 (31.5) (24.9)

0.29 0.26 (20.3) (13.1)

0.24 0.20 (6.0) (5 .6 )

(4.9) (2.5) 0.12 0.07

(Labor)( Private capital)

Public capital

(Public capital)'

-0.37 -0.27 (-7.8) (-5.3)

(7.2) (1.5) 0.13 0.04

(Labor)(Public capital)

(Private capital)(Public capital)

-0.20 -0.13 (-2.1) (-2.5)

(1.9) (1.7)

Unemployment Rate

R2

Durbin-Watson I

-0.01 -0.01 (-8.2) (-6.4)

0.995 0.998

Note: t-Statistics in parentheses


public capital on output. When using both Cobb-Douglas and translog functions, thcrc is cvidcncc of an upward bias in thc OLS paramctcr estimate of public capital. Furthcr, thc Cobb-Douglas results indicatc that constant rcturns to scale is an inappropriatc assumption when public capital is introduccd into the production function.

Whilc thc uanslog function does not show evidence of a direct effect on slatc output (whcn using thc typical two-tailed test), the joint impact of public capital on output is found to be significant. Furthcr, the uanslog results lend support to the hypothesis that public capital can have an indircct impact on output by incrcasing the marginal product of private capital. Overall, the results indicatc that public invcslmcnt may be used by policy makers as a mcans of incrcasing growth in the private sector. However, after controlling for state spccific cffccts, this impact is likely to be much smaller than that predicted by earlicr studies.

NOTES

1 . The I; statistics were 3064.8 with 4 and 764 degrees of freedom for the unconstrained model and 53.7 with 3 and 765 degrees of freedom for the constrained model.

2. The test statistics were 9.72 with 4 degrees of freedom for the unconseained model and 6.24 with 3 degrees of freedom for the constrained model.

3. The F statistic was 22.60 with 47 and 710 degrees of freedom, while the Hausman test statistic was 145.13 with 10 degrees of freedom. In both cases, the probability of observing these values, given the null hypothesis being correct, is less than 0.001.

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does public infrastructure affect regional performance?

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