Highway infrastructure and private output: evidence from static and dynamic production function models

Abstract

Much of the previous empirical literature that evaluates the relationship between public capital and productivity using a production function approach has not allowed for lagged responses of productivity to public capital. Using panel data for 48 contiguous US states over the period 1984–1997, this article demonstrates the importance of using correctly specified dynamics to examine the contribution of highway capital to state productivity. We find that the imposition of static production function models tends to overestimate the short-run effect of highways while underestimating the long-run effect. More plausible results are found when accounting for dynamic adjustments of state output and these show that both the short-run and long-run effects of highway capital are positive but fairly small, even after including positive productivity spillovers from highways located in other states.

Keywords:

• highway infrastructure
• production function
• productivity
• dynamic panel models
• spatial spillovers

Notes

Notes

1. See Shioji (2001) for a recent work that employs a dynamic panel model to estimate the productivity effects of broadly defined public capital. In this study, we demonstrate the need to explicitly consider the dynamics of output adjustment in response to increases in highway infrastructure in the modelling framework, showing that the failure to do so would yield incorrect and implausible estimates of the output effects of highways.

2. The variable H is modelled as a production shift factor since the provision of highways is external to individual firms. Assuming that technological change is Hicks-neutral means that the shift in productivity due to highway investment serves to increase the productivity of both labour and capital, but leaves the optimal combination of the factors unchanged.

3. This measure of urbanisation is as used in Carlino and Voith (1992), who analyse the effects of agglomeration economies on the state productivity in US. As argued by Graham (2007), sources of agglomeration economies are not only city size or scale, but the spatial proximity of economic activities. We have experimented with more appropriate measures of agglomerations including population density and employment density. However, there are problems of multicollinearity as both of these are found to be highly correlated with our highway density variable (r = 0.89). Given that this is not the main objective of the analysis, we use the share of population living in urban areas to control for the influence of agglomerations on state economic performance. Since such density measures are very persistent over time, their agglomeration effects could be captured by the state-specific component.

4. The Cobb–Douglas specification has some limitations. For example, it imposes the restriction of constant output elasticities of the inputs. Also, it does not provide information about whether any two inputs are complements or substitutes. Taking these limitations into account, some studies in the literature use a translog functional form for aggregate production. However, this flexible functional form involves the estimation of a large number of independent parameters. Another concern is multicollinearity due to the inclusion of many variables. We thus follow much of the empirical infrastructure research in using the simple Cobb–Douglas functional form. A key contribution of this analysis is to assess whether and how introducing dynamic components into the production function could affect the estimated impact of highway infrastructure.

5. There have been several articles that have specifically estimated the time-path of highway infrastructure impacts on regional economic activity, though outside of the production function framework. For example, see Rephann and Isserman (1994) and Chandra and Thompson (2000).

6. We use a Stata routine given by Frank Windmeijer to perform a minimum distance test of the non-linear common factor restrictions imposed in the restricted production equation (4). Based on system GMM estimates, the test rejects the appropriateness of the non-linear coefficient restrictions at the 5% level.

7. The private capital stock in a state is given by the following formula where K is private capital stock, VADD is total value added of all private industries, WS is total wages and salaries for all private industries, s indexes state, n indexes the nation and t indexes years. The term (VADD – WS) represents returns to capital that is used as a proxy for the size of private capital stocks. This procedure is similar to one outlined in Yilmaz et al. (2002). Data on VADD and WS are obtained from the BEA website (http://www.bea.gov).

8. In most of the research on this topic, highway infrastructure is measured as the monetary value of the capital stock, primarily based on the perpetual inventory method. The accuracy of the monetary stock in measuring the services provided by highway infrastructure has been subject to several criticisms, including the validity of assumptions regarding prices used to value capital stock, depreciation rates, the difference between actual government spending on infrastructure and its economic costs and estimating or benchmarking the level of capital stock for an initial year. Using physical measures of highway infrastructure avoids these difficulties.

9. The agglomeration elasticity estimates given here are not, however, directly comparable with those of Carlino and Voith (1992) and Ciccone and Hall (1996) because we have used a different definition of urbanisation.

10. The C-test is implemented under the null hypothesis that the suspect regressor can be treated as exogenous. Distributed as chi-squared with degrees of freedom equal to the number of regressors tested, the C-statistic is calculated as the difference of two Sargan statistics: one from the equation with the smaller set of instruments and the other from the equation with the larger set of instruments.

11. We also applied the C-test to examine the null hypothesis of exogeneity of the remaining variables. To perform the test, we use instruments listed in Table 4, the validity of which are again confirmed by the F-statistics from first-stage regressions and the Sargan test of overidentifying restrictions. However, the C-statistics do not reject the null hypothesis of exogeneity, given a 10% critical value of 2.71. The test statistics for ln H and Urban are, respectively, 0.292 and 1.650 in the fixed-effects specification, whereas those for ln L, ln H and Urban in the cross-section specification are 0.187, 0.269 and 0.026, respectively.

12. The C-statistics from tests of the exogeneity of labour and private capital are 4.32 and 5.35, respectively, which reject the null hypothesis at the 5% level. However, the C-test indicates that we cannot reject the null hypothesis of the exogeneity of highways and urbanisation (i.e. the C-statistics equal 1.69 and 1.66, respectively).