## 7 Empirical Results and Interpretation
More people might have felt more comfortable and safer for open outdoor activities with the increasing vaccinations in the USA. The policy variable against the COVID-19 pandemic in this study is a dummy for national park closures. If there have been any partial closures among these national parks, it will have a value of one for the dummy, otherwise zero. Unlike our expectation, the coefficient for \"NP_P_Csd\", the dummy for partial park closures, is positive, at 0.159, but \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Variables**} & \multicolumn{3}{c}{**Coefficients**} & \multirow{2}{*}{**t**} & \multirow{2}{*}{**Sig.**} & \multicolumn{2}{c}{**Collinearity Statistics**} \\ \cline{2-2} \cline{5-8}  & & & & **Std. Error** & & **Tolerance** & **VIF** \\ \hline (Constant) & \(-9.964\) & *** & 1.583 & \(-6.295\) & \(<\)0.001 & & \\ AR\_12 & 0.323 & *** & 0.060 & 5.380 & \(<\)0.001 & 0.161 & 6.217 \\ ln.AutoMH\_AVG & 1.477 & *** & 0.174 & 8.511 & \(<\)0.001 & 0.278 & 3.594 \\ CV\_D\_In.Grev & \(-0.010\) & * & 0.005 & \(-1.841\) & 0.068 & 0.107 & 9.339 \\ In.Gaming\_Rev\_LV & 0.132 & *** & 0.034 & 3.897 & \(<\)0.001 & 0.266 & 3.764 \\ Winter & \(-0.252\) & *** & 0.040 & \(-6.346\) & \(<\)0.001 & 0.437 & 2.287 \\ Peak\_S & 0.196 & *** & 0.037 & 5.262 & \(<\)0.001 & 0.389 & 2.573 \\ Pos\_Rate & 1.228 & & 1.266 & 0.970 & 0.334 & 0.101 & 9.872 \\ Vacc\_1\_Rate & 0.507 & * & 0.275 & 1.842 & 0.068 & 0.389 & 2.571 \\ NP\_P\_Csd & 0.159 & & 0.161 & 0.991 & 0.324 & 0.216 & 4.624 \\ \hline \hline \end{tabular}  
* Significant codes: ***\(-0.0\), *\(-0.1\).  
\end{table} 
Table 4: Estimation Results. statistically not significant at a 5%-level. Only five national parks have been completely shut down, while four other national parks had partial closures that mainly limited the total number of visitors. However, out of 126 months in this study, the partial closures happened for only three months (March 2020 to May 2020). Consequently, policy measures that limit the visitation to national parks do not show the negative (or discouraging) marginal effect on the National Park visitations (Outdoor activities). Increased social interaction proxied by the monthly traffic volume to Las Vegas through major highways strongly impacts national park visitations. The coefficient for \"In.AutoMH_AVG\" is 1.477 and statistically significant at a 0.1%-level. A 1% increase of average daily traffic from/to Las Vegas via major highways (indicator for social interaction through traffic flows) for the 126-month study period (roughly 1100 more vehicles from/to Las Vegas via major highways) increased the monthly visitation to the 11 NPs by 1.477% (roughly 34,780 more visitors per month). This proves that Las Vegas serves as a gateway city (inner) to these national parks (outer areas for outdoor activities). The social interaction (or regional interaction) proxied by the traffic volume indicates the complementary (substitute) relation between the visitation to (or possibly through) the gateway city, Las Vegas, and the outer national parks. Among the seasonality control variables, two variables, \"Winter\" and \"AR_12\", are statistically significant with expected signs. The coefficient for \"Winter\" is \(-0.252\) and statistically significant at a 0.1%-level, indicating that compared to the non-winter season, the monthly visitation to the 11 NPs is lower by 0.252%. That is, roughly 5934 fewer monthly visitors in the winter season (December through February) than in the non-winter nine months (March through November). Additionally, the coefficient for \"AR_12\" is 0.323 and statistically significant at a 0.1%-level. This is an autoregressive term to control positive serial autocorrelation. A 1% increase of monthly visitation in the same month a year ago increased the monthly visitation to the 11 NPs by 0.323% (roughly 7606 more visitors per month). This is evidence for the presence of strong and positive serial autocorrelation in the National Park visitations (Outdoor activities).