## 4 The Empirical Model  
The empirical model proposed in this study, which uses a log-log specification, closely follows the study of [PERSON] and [PERSON] [19]:  
\[ \begin{split}\Delta\ln(C_{t})&=\alpha_{i}+\beta_{1} \Delta\ln(Exch\ rate)_{t}+\beta_{2}\Delta\ln(GR)_{t}+\beta_{3}\Delta\ln(GAS)_{t} \\ &+\sum_{i=1}^{n}\theta_{i}\Delta\ln(GT_{i})_{t}+\tau_{1}(D_{-}US_ {-}CRISIS)_{t}+e_{i}\end{split}  \tag{1}\]  
where the dependent variable \(C_{t}\) denotes the \(t\) month total number of pedestrian or personal vehicle crossings. In Equation (1), _Exch rate_ represents the real exchange rate variable, \(GR\) denotes the Mexican economy growth rate, \(GAS\) is the real gas price in the U.S., \(D\_US\_CRISIS\) is the dummy variable that captures economic turmoil, and \(GT_{i}\) represents the variables constructed from Google Trends that capture decision-maker' sentiments (BEMS and Imm variables). The time series was computed in logarithms for both the dependent and independent variables, except the dummy variable. Two sets of models were estimated: the first was for the entire sample of PoEs, and the second set was divided into three regions (California, Texas, and other). Endogeneity is  
Figure 3: IGAE and Real Exchange Rate from 2004 to 2020. Note: The monthly data are from 2004 to February 2020. IGAE stands for the Global Indicator of Economic Activity and is displayed on the right vertical axis. Source: Own estimations using data from INEGI and Banco de Mexico. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Pedestrians** & \begin{tabular}{c} **Personal** \\ **Vehicles** \\ \end{tabular} & **BEMS** & **Imm** & \
\begin{tabular}{c} **Real Exch.** \\ **Rate** \\ \end{tabular} & **IGAE** &
\begin{tabular}{c} **Real Gas** \\ **Price** \\ \end{tabular} \\ \hline Pedestrians & \(1\) & & & & & & \\ Personal Vehicles & \(0.65\) & \(1\) & & & & \\ BEMS & \(0.10\) & \(0.24\) & \(1\) & & & \\ Imm & \(0.26\) & \(0.50\) & \(0.41\) & \(1\) & & \\ Real Exch. Rate & \(-0.21\) & \(-0.32\) & \(-0.06\) & \(-0.47\) & \(1\) & \\ IGAE & \(-0.06\) & \(-0.28\) & \(-0.06\) & \(-0.55\) & \(0.60\) & \(1\) \\ Real Gas Price & \(-0.22\) & \(-0.40\) & \(-0.16\) & \(0.02\) & \(-0.44\) & \(-0.21\) & \(1\) \\ \hline \hline \end{tabular} Source: Own estimations.  
\end{table} 
Table 3: Correlation matrix. not expected to be a concern because exchange rates are defined in international financial markets. Therefore, border crossings from Mexico are not expected to directly affect the value of the Mexican peso. Furthermore, these border crossings can have little effect on national gas prices in the U.S. or the evolution of Mexico's national economy. The log-log specification allowed us to identify the elasticities between the pedestrian and personal vehicle crossings and the independent variables. Due to the wealth effect resulting from the currency movements, it was expected that a depreciation of the local currency would negatively affect Mexicans' propensity to cross northbound. Thus, it was anticipated that the sign of the coefficient estimated would be \(\beta_{1}<0\). When the Mexican economy expands, its residents have more resources to cross northbound to take advantage of price differences in goods and services on both sides of the border [26]. Indeed, border crossings are explained by Mexican residents' shopping trips [26,44]. Mexicans have greater resources for cross-border shopping trips near the top of the economic cycle. Thus, the coefficient of this variable was predicted to be \(\beta_{2}>0\). For decades, the government set gas prices in Mexico, with price differentials expected along the border [4,16,19]. Thus, it can be assumed that the U.S. gas price may play a role in the decision to cross the northbound border. If the U.S. gas price increases, Mexicans are less motivated to cross the border. The sign for this coefficient was expected to be \(\beta_{3}<0\).