# Measuring Efficiency and Effectiveness of Highway Management in Sustainability
## 4 Results: Explaining the Relationship between Efficiency and Effectiveness  
The study conducts a two-stage regression analysis. At the first stage, the highway expenditure is predicted with six explanatory variables using the fixed effects model. Table 8 reports that highway expenditure is associated with the following two factors: revenue and the median voter. The result shows one additional dollar of revenue for highway per capita increase highway expenditure per capita when holding the other variables constant. Median voter also increases highway expenditure which is consistent with prior literature [5; 6].  
Spatial regression results are reported in Table 9. Past performance is strongly and positively associated with each dependent variable. That is, one percentage change of past performance increases road condition by 0.5%, mobility by 0.95%, safety by 0.5%, and effectiveness indicator by 0.76%. Effects of the efficiency score, which is the key independent variable, are statistically significant. Since the efficiency score is calculated by data envelopment analysis that conducts a cross-sectional analysis, it cannot be used for comparing each state's efficiency over time. Rather, it represents relative dominance compared with others in each year. The regression results reveal that efficiency has a positive effect on mobility, safety, and the effectiveness indicator. Thus, it can be said that a relatively dominant state in efficiency is likely also more effective in highway management. However, the efficiency variable has a negative effect on road condition. A possible explanation of the different effect directions could be found in the concept and measurement of efficiency and road condition. Efficiency can be represented by the ratio of output to input. Road condition would depend upon frequent maintenance such as resurfacing, which requires a higher level of input.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Highway Expenditure Per Capita**} \\ \cline{2-3}  & **Coef.** & **S.E.** \\ \hline Revenue for highway per capita & 0.238 *** & 0.030 \\ Own source ratio & 0.001 & 0.001 \\ Republican governor & 0.011 & 0.007 \\ Divided government & 0.009 & 0.007 \\ Median voter & 0.01 *** & 0.001 \\ Economic condition & \(-\)0.002 & 0.003 \\ Constant & \(-\)0.030 & 0.064 \\ \hline Number of observations & 432.000 & \\ Number of groups & 48.000 & \\ Prob \textgreater{} F & 0.001 & \\ \hline \hline \end{tabular} Note: *** \(p<\) 0.01. Time-period: 11 waves (2000–2013 except 2009–2011). Forty-eight continental U.S. states.  
\end{table}
Table 8: First Stage Regression with the Fixed Effects Model.  
In terms of control variables, urbanized states with higher population densities are doing well on highway management, one percentage change of population density makes a 0.3% increase of the effectiveness indicator. The number of automobiles negatively affects effectiveness: road condition and safety. Rho represents the impact of spatial relations and shows positive effects, which means that a state is influenced by the surrounding states' highway condition and management.  
There is an interesting point regarding expenditure. Total highway expenditure predicted at the first stage has negative effects, whereas maintenance and capital outlay (investment) have positive effects on effectiveness. Particularly, maintenance expenditure is reported as having an all positive effect, though the effect on road conditions is not statistically significant. The results imply that specific direct spending on highways directly affects effectiveness, while indirect spending, such as operating expenses, does not enhance effectiveness.