## 6 Modelling Experiments  
In order to test our 'deconcentrated tourism concentration' hypothesis--based on the Galaxy structure in Figure 1, this paper specified a linear regression model (OLS model) with 126 monthly visitors to the 11 nearest National Parks to Las Vegas within 460 miles (7.5 h of driving distance) as a dependent variable. The specified model tests the outer-inner city complementary (or substitutes) relation between \"Outdoor Activities\" in the 11 national parks and the \"Gaming Industry\" in Las Vegas, the gateway city to the 11 national parks for most visitors. Other variables include (1) COVID-19 infection (positivity rate) and vaccination (vaccination rate) variables; (2) policy response variable \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variables** & **Description** & **Data Source** \\ \hline In.TRV\_11 NP & L.N. of monthly visitors to all 11 National Parks & NPS 1 \\  & (combined) & NPS 1 \\ AR\_12 & Lag of In.TRV\_11 NP by 12 months (same month a year & NPS 1 \\  & & ago) \\ In.AutoMH\_AVG & LN of monthly traffic volume to Las Vegas through & LVCVA 2 \\  & Major Highways & \\ CV\_D\_In.GRev & LN of gaming revenue in Las Vegas for pandemic & \\  & period & LVCVA 2 \\ In.Gaming\_Rev\_LV & LN of gaming revenue in Las Vegas for all times & LVCVA 2 \\ Winter & Dummy for the winter season & N/A \\ Peak\_S & Dummy for peak months for NP (May, June, July, & N/A \\  & August, and September) & \\ Pos\_Rate & Monthly positivity rate of COVID-19 tests in the U.S. & CDC 3 \\  & (in \%) & CDC 3 \\ Vacc\_1\_Rate & Monthly \% share of population who receives at least 1 & CDC 3 \\  & COVID vaccine & \\ NP\_P\_Csd & Dummy for the months with partially closed national & NPS1 \\ \hline \hline \end{tabular} 1 NPS—National Park Service. 2 LVCVA—Las Vegas Convention and Visitor Authority. 3 CDC—Center for Disease Control.  
\end{table} 
Table 2: Variable Description for Model Specification with Raw Data Source. (Dummy for partial National Park closure); (3) social interaction variable (average daily traffic on major highways to/from Las Vegas Metro); (4) control variables for seasonality (AR (12), a Dummy for peak season, and a Dummy for winter). \[Y=\beta_{o}+X\beta+\varepsilon \tag{1}\]  
where, \(Y\): monthly visitors to the 11 nearest National Parks to Las Vegas; \(\beta_{o}\): constant term; \(\beta\): coefficient vector (9 \(\times\) 1 vector) to be estimated; \(\varepsilon\): iid error term; \(X\): independent variable vector (9 \(\times\) 1 vector), as listed in Table 2.  
Descriptive statistics are summarized in Table 3. The average number of monthly visitors to the 11 National Parks (NPs) for the 126-month period (from January 2011 to June 2021) is 2,354,802 (2.355 million monthly visitors). In contrast, the average monthly visitors for the recent 42-month period (from January 2018 to June 2021) is 7.0% higher at 2,520,688 (2.521 million monthly visitors), even with the monthly average loss of 638,340 visitors during the COVID-19 pandemic (from March 2020 to June 2021) compared to the monthly visitation in 2019. The most significant net loss in the monthly visitation to the 11 NPs was found in April 2020, when nine NPs were either partially or fully closed, followed by May 2020 and June 2020 when the fully or partially closed NPs started to open again to the public. The average monthly gaming revenue in Las Vegas for the 126 months (from January 2011 to June 2021) is $788,771,825 ($788.8 million monthly revenue from gaming activities in Las Vegas). In contrast, the average monthly gaming revenue for the recent 42-month period (from January 2018 to June 2021) is 2.7% lower at $767,209,929 ($767.2 million monthly revenue from gaming activities in Las Vegas), with the monthly average loss of $364.0 million gaming revenue for the 12 consecutive months during the COVID-19 pandemic (from March 2020 to February 2021) compared to the monthly revenues in 2019.