# Measuring Efficiency and Effectiveness of Highway Management in Sustainability
## 3 Data, Methods, and Results
### Modeling Relationship between Efficiency and Effectiveness
#### 3.3.3 Estimation Routine  
We utilize the two-stage regression model approach. At the first stage, we use the fixed effects panel data model to estimate the predicted values of highway expenditure. \[y_{it}=\beta X_{it}+a_{i}+u_{it}\]  
where \(\alpha\) means the individual fixed effect and \(u\) is an error term. At the second stage, the study employs the Spatial Autoregressive Panel Model to control the geographical spatial effect among continental states. Assuming that present performance depends \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **Description** & **Data Source** \\ \hline Effectiveness indicator & Combination of road condition, mobility, and safety & Author’s computation with PCA \\ \hline Road condition & \(\frac{3\text{goal(info)}+2\text{gr/(info)}+1\text{year(false)}}{\text{total \# miles}}\) & \\ \hline Mobility & Reciprocal of Annual Average Daily Traffic & \\  & (AADT)/lane-miles & \\ \hline Safety & Reciprocal of the number of people fatally & \\  & injured/lane-miles & \\ \hline Efficiency score & Theta from DEA (Data Envelopment Analysis) & Author’s computation with DEA \\ \hline Urbanization & Population density & U.S. Census \\ \hline Automobiles per capita & Number of automobiles/population & Highway Statistics \\ \hline Drivers/driving age people & Number of drivers/population of driving age & Highway Statistics \\ \hline Maintenance expenditure per capita & Maintenance expenditure per capita & Highway Statistics \\ \hline Capital outlay per capita & Capital outlay per capita & Highway Statistics \\ \hline Highway expenditure per capita & Highway expenditure per capita & U.S. Census \\ \hline Revenue for highway per capita & Revenue for highway per capita & Highway Statistics \\ \hline Own source ratio & \(1-\) (Intergovernmental revenue/Total revenue) & U.S. Census \\ \hline Republican governor & Republican governor = 1, otherwise = 0 & NCSL, NASBO \\ \hline Divided government & 1 = governor’s party equal to the majority & NCSL, NASBO \\  & partisanship of legislature, 0 = otherwise & NCSL, NASBO \\ \hline Median voter & Median income of household & U.S. Census \\ \hline Economic condition & Unemployment rate & U.S. Census \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Variable Description and Data Source. NCSL = National Conference of State Legislatures; NASBO = National Association of State Budget Officers. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Variable** & **N** & **Mean** & **Std. Dev.** & **Min** & **Max** \\ \hline Effectiveness indicator & 528 & 0.996 & 4.015 & 0.000004 & 39.818 \\ Road condition & 528 & 2.443 & 0.242 & 1.775 & 2.971 \\ Mobility & 528 & 0.54 & 0.087 & 0.009 & 0.741 \\ Safety & 528 & 58.355 & 38.409 & 10.992 & 213.692 \\ Efficiency score & 528 & 0.687 & 0.194 & 0.161 & 1 \\ Urbanization & 528 & 192.870 & 257.903 & 5.307 & 1201.497 \\ Automobiles per capita & 528 & 0.441 & 0.079 & 0.151 & 0.641 \\ Drivers/driving age people & 528 & 894.833 & 62.973 & 704.746 & 1115.696 \\ \hline Maintenance expenditure per capita & 528 & 0.047 & 0.033 & 0.002 & 0.271 \\ Capital outlay per capita & 528 & 0.239 & 0.112 & 0.072 & 1.115 \\ Highway expenditure per capita & 528 & 0.376 & 0.151 & 0.159 & 1.579 \\ Revenue for highway per capita & 528 & 0.409 & 0.194 & 0.156 & 1.952 \\ \hline Own source ratio & 528 & 73.339 & 5.882 & 47.161 & 85.491 \\ Republican governor & 528 & 0.534 & 0.499 & 0 & 1 \\ Divided government & 528 & 0.526 & 0.499 & 0 & 1 \\ Median income of household & 528 & 46306.91 & 7965.03 & 29359 & 72483 \\ Unemployment rate & 528 & 5.198 & 1.512 & 2.3 & 11.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Descriptive Statistics. on past performance, regression models include the lagged dependent variable on the right-hand side. We set the effectiveness indicator, which is produced by the principal component analysis, as the dependent variable. In addition, the other decomposed components (road condition, mobility, and safety) are also tested as dependent variables for comparison.