## 7 Empirical Results and Interpretation  
The coefficient estimation result of the specified OLS model in Table 4 reveals some interesting stories about the outer-inner city complementary (or substitute) relation between \"Outdoor Activities\" in the 11 national parks and \"Gaming Industry\" in Las Vegas. Furthermore, the estimation results show the effects of four other critical factors under consideration in this study: 'COVID-19 Infections', 'Policy Responses to Pandemic', 'Vacination Trajectories', and 'Social Interaction.' \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variables** & **Mean** & **Std. Deviation** & **N** \\ \hline ln.TRV\_11 NP & 14.5775436 & 0.46204036 & 126 \\ AR\_12 & 14.5519478 & 0.47641431 & 126 \\ ln.AutoMH\_AVG & 11.6006090 & 0.12517300 & 126 \\ CV\_D\_In\_GRev & 2.50357012 & 6.61740760 & 126 \\ ln.Gaming\_Rev\_LV & 20.4135598 & 0.65577507 & 126 \\ Winter & 0.25 & 0.437 & 126 \\ Peak\_S & 0.41 & 0.494 & 126 \\ Pos\_Rate & 0.009352085 & 0.028429146 & 126 \\ Vacc\_1\_Rate & 0.01189 & 0.066734 & 126 \\ NP\_P\_Csd & 0.02 & 0.153 & 126 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Descriptive Statistics of Variables. The coefficient of the key variable for the outer-inner city complementary relation, i.e., \"In.Gaming_Rev_LV\", is 0.132 and statistically significant at 0.1%-level. A 1% increase of monthly gaming revenue in Las Vegas for the entire 126-month study period (roughly $7.887 million) increased the monthly visitation to the 11 NPs by 0.132% (roughly 3109 more visitors per month). This finding proves the presence of the outer-inner city complementary relation between \"Outdoor Activities\" in the 11 national parks and the \"Gaming Industry\" in Las Vegas for the entire 126-month study period. However, this complementarity relation was not found in the pandemic period for the 16-month period (from March 2020 to June 2021). The coefficient for \"CV_D_In.GRev\" is negative (\(-0.01\)) and statistically significant only at 10%-level. This indicates the presence of substitution effects between the inner-city tourism resources in Las Vegas and the outer-city tourism resources among the 11 national parks. A possible explanation can be that, in contrast to the pre-pandemic period, the visitors to the inner-city (Las Vegas) had substituted the indoor gaming (gamble) activities for outdoor tourism resources (national parks for outdoor activities) in the outer-city. The visitors to the 11 national parks did not spend enough time indoor gaming activities in Las Vegas (inner-city); instead, they bypassed it for healthier outdoor activities with a low risk of exposure to COVID-19. As a result, the complementary relation for all time periods turned into a substitution relation trading the indoor gaming for the outdoor activities in national parks. Among the COVID-19 pandemic factors, the coefficient for \"Pos_Rate\" appears to be positive, unlike the expectation, at 1.228 but not significant at a 5%-level. Though not significant, the coefficient may indicate that an increased positivity rate of COVID-19 tests in the U.S. may make people seek safer and healthier outdoor activities (e.g., visiting the 11 NPs). However, the positive (or encouraging) marginal effect (for the outdoor activities) of the increased risk from COVID-19 was not strong enough due to the uncertainty in the pandemic. How one recognizes the trade-off between benefit from outdoor activities in pandemic and cost of potential exposure to risks may vary significantly by individuals. On the other hand, the coefficient for \"Vacc_1_Rate\" is 0.507 and statistically significant at 10%-level. A 1% increase in vaccination rates (the % share of people who received at least one shot out of the total U.S. population) for the entire 126-month study period (roughly 3.3 million more people becoming vaccinated in the U.S.) increased the monthly visitation to the 11 NPs by 0.507% (roughly 11,939 more visitors per month). This shows the positive marginal effect of increased vaccination rates on the national park visitations.