Measuring the effect of the misery index on international tourist departures: Empirical evidence from Mexico

Sánchez López, Fernando Article Measuring the effect of the misery index on international tourist departures: Empirical evidence from Mexico Economies Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Sánchez López, Fernando (2022) : Measuring the effect of the misery index on international tourist departures: Empirical evidence from Mexico, Economies, ISSN 2227-7099, MDPI, Basel, Vol. 10, Iss. 4, pp. 1-16, https://doi.org/10.3390/economies10040081 This Version is available at: https://hdl.handle.net/10419/328381 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Economies 10: 81. https:// doi.org/10.3390/economies10040081 Academic Editors: Angeliki N. Menegaki and Aleksander Panasiuk Received: 16 February 2022 Accepted: 17 March 2022 Published: 1 April 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). economies Article Measuring the Effect of the Misery Index on International Tourist Departures: Empirical Evidence from Mexico Fernando Sánchez López Instituto de Investigaciones Económicas, Universidad Nacional Autónoma de México, Ciudad de México 04510, Mexico; fer[email protected] Abstract: Tourism’s capacity to alleviate poverty is one of the most important subjects in tourism studies, as tourism is capable of boosting economic growth and generating employment. On the other hand, it is known that lack of income and unemployment have negative effects on outbound tourism; however, the relationship between outbound tourism and poverty has been understudied. In this paper, we compute a vector autoregressive (VAR) model to analyze the relationship between tourist departures from Mexico and a modified misery index to measure the effect of the loss of well-being, measured in terms of this index, on the number of outbound tourists. The results indicate that increases in the misery index have negative effects on the number of outbound tourists. Conversely, there is no statistically significant effect of tourist departures on the misery index. The results also suggest that the depreciation of the national currency exerts a positive effect on the misery index. Finally, based on the historical decomposition analysis, it was verified that the misery index was not closely related to outbound tourism during the first COVID-19 wave. Keywords: international tourism; Okun’s misery index; outbound tourism; poverty; unrestricted VAR 1. Introduction Inbound tourism is considered a main driver of economic growth. The tourism-led growth hypothesis, according to Rasool et al. (2021), is directly founded on the exportled growth hypothesis, which claims that economic growth can be boosted not only by way of increasing labor and capital but also by means of furthering exports. According to Hipsher (2017) , tourism is a labor-intensive sector that benefits those with low levels of skill and education. According to Sharma and Thapar (2016), tourism is among the most lucrative nontechnology-based economic sectors, particularly in developing nations, as these types of countries frequently confront problems such as lack of capital, lack of employment opportunities, and poverty. Since tourism is considered to make an important contribution to economic growth, besides being recognized as an employment-generating sector, Weinz and Servoz (2013) consider it to have important potential for poverty reduction. Conversely, outbound tourism spending is cataloged as an import for the country of origin, so its value is compared with the country’s export value (Mehran and Olya 2019). In this sense, outbound tourism, following Seetaram (2010), is considered to largely affect the economy in the opposite direction of inbound tourism in terms of economic growth and employment creation. This study aims to investigate the relationship between the misery index and tourist departures in Mexico. To achieve this goal, we computed an unrestricted vector autoregressive (VAR) model, which considers the compensated misery index (CMI), the multilateral real exchange rate, and the number of outbound tourists as endogenous variables. The main results of this model suggest, on the one hand, that the number of outbound tourists is diminished by increases in the CMI but, on the other hand, that tourist departures do not have a statistically Economies 2022,10, 81. https://doi.org/10.3390/economies10040081 https://www.mdpi.com/journal/economies Economies 2022,10, 81 2 of 16 significant effect on the CMI. In addition, the results show that, during the first wave of the COVID-19 pandemic, the CMI and tourist departures were not closely related. We believe that this article contributes to the existing literature in the following ways. First, to the best of our knowledge, this is the first study documenting the relationship between poverty, in terms of the CMI, and tourist departures, as this subject has been traditionally studied from the perspective of inbound or domestic tourism. Second, this document contributes to closing the gap between studies on outbound and inbound tourism. In the same vein, we consider that it will be of interest to policymakers and tourism managers, as it provides statistical evidence that the misery index helps explain decreases in outbound tourism demand, and also that tourist departures have not had a statistically significant impact on the loss of well-being measured in terms of this index during the study period. The remainder of this paper is organized as follows. In Section 2, we present the literature review, which is divided into two subsections: we first present a detailed literature review on the discomfort economic index and then review the links between outbound tourism and the misery index. Section 3is also divided into two subsections, as we present the data and their sources and the VAR empirical design. In Section 4, we present the econometric results. Finally, in Section 5, the discussion and conclusions are presented. 2. Literature Review 2.1. Discomfort Economic Index In its original form, according to Lechman (2009), Okun’s misery index (MI) is calculated by simply adding the unemployment rate (U)to the inflation rate (π): MI =U+π(1) The expression in Equation (1) was initially named the “discomfort economic index” (Lechman 2009). In 1980, U.S. President Ronald Reagan renamed it “the economic misery index” in “deriding” the previous U.S. president, Jimmy Carter (Lovell and Tien 2000). Okun’s misery index probably constituted the first attempt to measure a population’s economic malaise in a single number (Cohen et al. 2014). It was conceived to measure the loss in general welfare and as an objective method to quantify economic malaise (Lechman 2009) . In fact, this index endeavors to summarize the most evident costs for society, as unemployment prevents people from earning an income, whereas high inflation rates increase the cost of living by reducing purchasing power (Riascos 2009). Most of the criticisms of the discomfort economic index are due to its simplicity, as it embodies an oversimplification of the socioeconomic problems affecting society (Lovell and Tien 2000; Riascos 2009). In fact, it is considered a simplified version of the social preference function over inflation and unemployment (loss function), as the loss function differs from the misery index in both its functional form and weights (Welsch 2007). Given that Okun’s misery index considers only two macroeconomic indicators, according to Lovell and Tien (2000), it can be regarded as a “crude (dis)utility function”. Lovell and Tien argue that Okun implicitly supposed that the indifference curves describing people’s preferences for unemployment and inflation are straight lines with a slope equal to −1, implying that citizens’ aversion to such economic indicators is identical. However, Winkelmann and Winkelmann (1998) found that unemployment has a strong negative impact on life satisfaction, claiming that non-pecuniary costs of unemployment are higher than pecuniary costs. Di Tella et al. (2001) demonstrated that unemploymenthas more negative effects on reported well-being than inflation, indicating that Okun’s misery index underweights the discontent generated by joblessness. Additionally, Asher et al. (1993) consider that variations in MI are policy-related, but it is not easy to attribute them to specific policy actions. Despite the criticisms of its simplicity, Okun’s misery index is frequently used to examine social welfare (Riascos 2009). In fact, Grabia (2011) considers that such an index establishes a kind of poverty index due to the effects of unemployment and inflation on average citizens’ standards of living. Moreover, according to Riascos (2009), Okun’s misery Economies 2022,10, 81 3 of 16 index, as a poverty measure, should be considered an objective indicator, as it does not take into account the socioeconomic perception that persons or households have of themselves. Additionally, Riascos proposed including the MI among the monetary approaches to measure poverty, as monetary indicators of poverty are based on income’s capacity to guarantee the satisfaction of basic life conditions. Nonetheless, it is very important to mention that, according to Lechman (2009), MI is not a perfect measure of poverty, but its fluctuations reflect “changes in society’s economic performance”. Additionally, this index has been applied in a vast number of ways; for example, Yang and Lester (1999) found that, in the case of the United States, Okun’s misery index is related to the number of suicides. In the case of Iran, Piraee and Barzegar (2011) found a long-term relationship between the misery index and economic crimes such as embezzlement, bribery, forgery, and drawing counterfeit checks. Özcan and Açıkalın (2015) found that in the case of Turkey, there is a relationship between lottery gambling and the misery index, arguing that people are more prompted to bet in lottery games during economic crises. Similarly, in the case of Turkey, Akçay (2017) found that the MI has a positive impact on remittance flows in both the short and long term. Wang et al. (2019) provided empirical evidence on the negative effects of the MI on economic growth in Pakistan. There have also been numerous modifications to Okun’s misery index; for example, MacRae (1977) proposed that the loss of votes for the incumbent political party is a quadratic function of unemployment and inflation. Barro (1999) developed the so-called Barro misery index (BMI), which incorporates the interest rate and GDP; Barro argues that increases in the long-term interest rate and economic growth below the average also contribute to misery. Lovell and Tien (2000) suggest using the absolute value of the inflation rate; they consider that the effects of deflation are as “painful” as those of inflation. Ramoni-Perazzi and Orlandoni-Merli (2013) recommended adding employment in the informal sector to the measure, since joining this sector is frequently an immediate response by workers to subsistence problems, making informality a form of hidden unemployment to some extent. Cohen et al. (2014) developed a dynamic misery index using the expectation-augmented Phillips curve and Okun’s law. Murphy (2016) elaborated on a state misery index for the United States using data on regional pricing parities. Based on the BMI, Hortalàand Rey (2011) calculated a “compensated misery index” by subtracting the economic growth rate . y from Okun’s original misery index, as shown in Equation (2): CMI =MI −. y(2) It is important to mention that Gaddo (2011) uses a similar specification of the misery index, simply calling it “modified Okun”. In this document, we use the abbreviation CMI to denote the expression in Equation (2) in reference to the name utilized by Hortalàand Rey (2011). In this document, based on the idea that the MI represents a type of poverty index, we study the impact of CMI on Mexico’s international outbound tourism to approximate the effect of poverty on the decision to travel abroad. The CMI was selected among the different specifications of the misery index because the empirical findings suggest that all three CMI components are tourism-related, as will be discussed in the following subsection. 2.2. Outbound Tourism and Compensated Misery Index According to the World Bank (2021), “International outbound tourists are the number of departures that people make from their country of usual residence to any other country for any purpose other than a remunerated activity in the country visited”. From an accounting perspective, international outbound tourists’ spending is classified as an import (Boullón 2009;Seetaram 2010), and income is among the main determinants of the import level (Sosa 2001). Moreover, tourism behaves as a luxury good (Álvarez 1996; Smeral 2003), which implies, by definition, that its income elasticity of demand will be greater than unity when income rises by 1% (Varian 1999). Economies 2022,10, 81 4 of 16 Economic crises have a profound effect on the tourism sector since, as mentioned by Ramírez (1994), tourism is sustained by three basic factors: available time, desire to travel, and economic resources. According to Álvarez (1996), during phases of economic decline, tourism demand, measured as tourist spending, decreases more than proportionally with respect to the fall in the income level. In general, countries with important proportions of outbound tourists have a high income level, as well as an adequate income distribution (Ascanio 2012). Effectively, the income level is likely to determine a strict upper limit for tourism demand, whereas the lack of a certain level of wealth prevents individuals or households from acquiring superior goods (Kim et al. 2012). Moreover, traveling abroad for tourism purposes usually takes place once basic needs have been met (Ascanio 2012;Panosso and Lohmann 2012). Concerning unemployment, Sánchez (2019) provided empirical evidence of a bidirectional relationship between tourism GDP growth and the unemployment rate; on the one hand, tourism GDP growth helps reduce the unemployment rate, but on the other, increases in the unemployment rate diminish the growth of tourism GDP. Alegre et al. (2019) found that high levels of unemployment increase the probability of not going on vacations, as unemployment represents an indicator of the current economic situation, in addition to influencing future expectations of income and employment. Inflation deteriorates the purchasing power of a currency; such deterioration can incline consumers toward basic goods and services, thus postponing the decision to travel for tourism purposes, as well as the acquisition of other non-essential goods and services (Dominé2014). However, tourism purchases are usually made in advance of their actual consumption; therefore, past values of prices and exchange rates are better at explaining tourism demand than current values (Stabler et al. 2009). On the other hand, since outbound tourism is regarded as a form of import, its effects on the economy are considered to be the opposite of those generated by inbound tourism in terms of economic growth, the reduction of unemployment, and the generation of foreign currencies (Seetaram 2010). However, outbound tourists also contribute to the economy as they spend money in their residence country when preparing to travel; this often includes spending on airlines, passports, and travel agencies (Dahdá2003). In Figure 1, we summarize the main effects of each CMI component on the consumption of luxury goods and, by extension, on outbound tourism. Economies 2022, 10, x FOR PEER REVIEW 5 of 17 Figure 1. CMI and tourism. 3. Materials and Methods 3.1. Data and Sources To conduct this study, we used time-series data from the second quarter of 2000 to the second quarter of 2020 and retrieved the CMI calculated by Sánchez (2021). We also obtained the real exchange rate (RER) index with respect to 111 countries (year base 1990) (Banco de México 2020b) and Mexico’s international outbound tourists (T) in thousands of people (Banco de México 2020a). Since Sánchez (2021) reports the CMI as quarterly frequency data, we averaged the real exchange rate index into quarterly data. For its part, the number of outbound tourists was aggregated into quarterly data. We seasonally adjusted both of these series by applying the Census X12 filter, a technique that permits easier identification of trends and atypical data in the series (Pindyck and Rubinfeld 2001) in addition to removing calendar effects (Chatfield 2003). To avoid finding spurious results when computing the VAR model, we applied the breakpoint unit root test to the series (Table 1), since traditional unit root tests could fail in the presence of structural changes (Glynn et al. 2007). Table 1. Breakpoint unit root tests, 2000Q2–2020Q2. Series Innovation Outlier Additive Outlier A B C D A B C D ln  −1.499 −3.823 −3.877 −3.195 −1.812 −3.296 −4.282 −6.443 *** ln  −2.594 −3.676 −3.562 −3.460 −2.646 −3.733 −3.664 −3.376  −5.476 *** −5.520 *** −5.425 ** −5.576 *** −5.586 *** −5.520 *** −5.795 *** −6.986 ***  󰇗 −10.94 *** −10.87 *** −10.96 *** −10.06 *** −14.24 *** −11.75 *** −11.08 *** −13.25 ***  󰇗 −8.396 *** −8.335 *** −8.270 *** −8.465 *** −8.837 *** −8.835 *** −8.659 *** −8.634 *** Note: A: intercept only; B: trend and intercept (intercept); C: trend and intercept (trend and intercept); D: trend and intercept (trend); lag length: Schwarz criterion; max. lags = 8; breakpoint selection: Dickey-Fuller min-t; ** and *** denote rejection of the unit root hypothesis at the 5% and 1% significance levels, respectively; symbolization: 󰇗=∆ln, 󰇗 =∆ln. Figure 1. CMI and tourism. Economies 2022,10, 81 5 of 16 It is important to mention that in this literature review we did not find any research on the effect of poverty on international tourist departures. Conversely, there are various studies on the effect of tourism on poverty alleviation in different countries, such as Kenya (Njoya and Seetaram 2018), Mexico (Garza-Rodriguez 2019), and South Africa (Saayman et al. 2012). 3. Materials and Methods 3.1. Data and Sources To conduct this study, we used time-series data from the second quarter of 2000 to the second quarter of 2020 and retrieved the CMI calculated by Sánchez (2021). We also obtained the real exchange rate (RER) index with respect to 111 countries (year base 1990) (Banco de México 2020b) and Mexico’s international outbound tourists (T) in thousands of people (Banco de México 2020a). Since Sánchez (2021) reports the CMI as quarterly frequency data, we averaged the real exchange rate index into quarterly data. For its part, the number of outbound tourists was aggregated into quarterly data. We seasonally adjusted both of these series by applying the Census X12 filter, a technique that permits easier identification of trends and atypical data in the series (Pindyck and Rubinfeld 2001) in addition to removing calendar effects (Chatfield 2003). To avoid finding spurious results when computing the VAR model, we applied the breakpoint unit root test to the series (Table 1), since traditional unit root tests could fail in the presence of structural changes (Glynn et al. 2007). Table 1. Breakpoint unit root tests, 2000Q2–2020Q2. Series Innovation Outlier Additive Outlier A B C D A B C D ln T−1.499 −3.823 −3.877 −3.195 −1.812 −3.296 −4.282 −6.443 *** ln RER −2.594 −3.676 −3.562 −3.460 −2.646 −3.733 −3.664 −3.376 CMI −5.476 *** −5.520 *** −5.425 ** −5.576 *** −5.586 *** −5.520 *** −5.795 *** −6.986 *** . t−10.94 *** −10.87 *** −10.96 *** −10.06 *** −14.24 *** −11.75 *** −11.08 *** −13.25 *** . rer −8.396 *** −8.335 *** −8.270 *** −8.465 *** −8.837 *** −8.835 *** −8.659 *** −8.634 *** Note: A: intercept only; B: trend and intercept (intercept); C: trend and intercept (trend and intercept); D: trend and intercept (trend); lag length: Schwarz criterion; max. lags = 8; breakpoint selection: Dickey-Fuller min-t; ** and *** denote rejection of the unit root hypothesis at the 5% and 1% significance levels, respectively; symbolization: . t=∆ln T,. rer =∆ln RER. The results of such tests indicate that the CMI is an I(0) series, whereas the multilateral real exchange rate is an I(1) series, and the number of outbound tourists mostly behaves as an I(1) series (Table 1). To avoid obtaining spurious results through the VAR model, in addition to the CMI we used the stationary series . t and . rer , which represent the first difference of ln T and ln RER , respectively. Since all three variables in the model are stationary (Table 1), following Enders (2015), there is no need to test for cointegration. Since the CMI, by definition, is the difference between the MI and the GDP growth rate, as shown in Equation (2), this variable is not properly a series in levels; therefore, it was considered adequate to conduct this study by using differentiated series, and computing a VAR model in differences. Economies 2022,10, 81 6 of 16 3.2. Empirical Design A VAR (p) model including three endogenous variables, two exogenous variables, and a constant, can be written as a system of equations, as shown in Equation (3): . rer =∝1+ p ∑ i=1β1i . rert−i+ p ∑ i=1θ1iCMIt−i+ p ∑ i=1γ1i . tt−i+ϑ1δAt +µ1δBt +e1t CMI =∝2+ p ∑ i=1β2i . rert−i+ p ∑ i=1θ2iCMIt−i+ p ∑ i=1γ2i . tt−i+ϑ2δAt +µ2δBt +e2t . t=∝3+ p ∑ i=1β3i . rert−i+ p ∑ i=1θ3iCMIt−i+ p ∑ i=1γ3i . tt−i+ϑ3δAt +µ3δBt +e3t (3) where δA is a dummy variable defined to capture the effect of the first COVID-19 wave. COVID19 was declared a pandemic on 11 March 2020 by the World Health Organization (2020). Following Sáenz (2021), Mexico began to apply sanitary and social distancing measures on 23 March 2020. During the second quarter of 2020, according to Cota (2020), Mexico experienced the greatest registered fall in its GDP as a result of the COVID-19 lockdowns. Meanwhile, δB helps the model to adequately simulate the main breaks in the series; that is, the particular periods where the model overestimated or underestimated the series. δAt =(1t=2020Q2 0Otherwise (4) δBt =       1i f t =2001Q3;2007Q2; 2009Q3; 2013Q3;2014Q1 −1i f t =2001Q4;2002Q3; 2003Q1; 2007Q1;2010Q3; 2017Q1;2018Q3; 2020Q1 0Otherwise (5) According to Catalán(n.d.), VAR models permit a better understanding of the relations among a set of variables, and, as they are specified without imposing restrictions on the parameters, its specification is more flexible in comparison to other models. Nonetheless, according to Jaramillo (2009), there are several criticisms of VAR models, which are nonparsimonious representations of a time-series vector, leading to problems with degrees of freedom, overfitting, and multicollinearity. To tackle these eventualities, we first estimated the optimal value for p by using the traditional information criteria: sequential modified LR test statistic (LR), final prediction error (FPE), Akaike (AIC), Schwarz (SIC), and Hannan–Quinn (HQ). As we used quarterly data, we allowed a maximum of six lags when performing this test (Table 2). Table 2. VAR lag order selection criteria. Lag LR FPE AIC SIC HQ 0 NA 5.26 ×10−6−3.641207 −3.360982 * −3.529422 1 34.13363 4.07 ×10−6−3.899929 −3.339480 −3.676359 * 2 17.30131 3.99 ×10−6*−3.922859 * −3.082187 −3.587505 3 10.65644 4.30 ×10−6−3.851494 −2.730598 −3.404355 4 4.865500 5.09 ×10−6−3.690717 −2.289596 −3.131793 5 19.23276 * 4.67 ×10−6−3.790916 −2.109571 −3.120207 6 8.597716 5.16 ×10−6−3.709894 −1.748325 −2.927400 Note: * indicates lag order selected by the criterion. According to the FPE and AIC, the optimal number of lags in this model was p= 2, whereas the rest of the criteria differed in their number of lags (Table 2). Accordingly, the VAR(2)was computed. Concerning multicollinearity, since each equation in a VAR can be individually computed as an ordinary least squares regression (Gujarati and Porter 2009), we computed the variance inflation factors (VIF) to test for multicollinearity. Economies 2022,10, 81 7 of 16 Finally, the econometric analysis in this study was conducted by means of an unrestricted VAR model, as we have not found empirical or theoretical evidence concerning the relationship between the CMI and the real exchange rate and, as mentioned by Gottschalk (2001) , restrictions in a model should not be imposed in the absence of an adequate theoretical framework. 4. Econometric Results To test the impact of the CMI on Mexican outbound tourism, we performed a VAR (2) , the results of which are summarized in Table 3. Table 3. VAR model. Variable . rer CMI . t . rert−10.017232 7.781535 0.178309 [0.14549] [2.45109] [1.71666] . rert−20.010501 −0.287187 −0.274804 [0.08629] [−0.08804] [−2.57475] CMIt−17.37×10−50.439408 −0.012036 [0.01658] [3.68698] [−3.08665] CMIt−2 −0.002146 0.165540 0.002851 [−0.51739] [1.48898] [0.78369] . tt−1 −0.021513 −2.248327 −0.220603 [−0.24778] [−0.96606] [−2.89716] . tt−2 −0.116459 3.366115 −0.203880 [−1.32859] [1.43263] [−2.65214] Intercept 0.014092 1.759171 0.054928 [0.63756] [2.96921] [2.83364] δAt 0.144122 18.23392 −1.777181 [3.22700] [15.2312] [−45.3734] δBt −0.005807 −0.518049 0.115389 [−0.48615] [−1.61796] [11.0148] R20.190572 0.820348 0.971770 Adjusted R20.096725 0.799518 0.968497 F-statistic 2.030669 39.38440 296.8990 Note: [ ] t-statistic. After computing the VAR, we verified that it satisfied the correct specification tests at the 5% significance level (Table 4). The full serial correlation tests are presented in Table A1 in Appendix A. Table 4. VAR joint correct specification tests. Test Statistic Probability Doornik–Hansen Normality Test: Skewness 6.9977 0.0720 Kurtosis 3.5516 0.3141 Jarque–Bera 10.549 0.1033 Serial Correlation LM test (Rao F-statistic): No serial correlation at lag h (12) 1.7071 0.0915 No serial correlation at lags 1 to h (12) 1.1366 0.2630 White heteroskedasticity test (no cross terms) 102.89 0.1665 White heteroskedasticity test (cross terms) 226.55 0.2975 Note: Tests at the 5% significance level. Economies 2022,10, 81 8 of 16 To complement the tests in Table 4, we verified that the model fulfills the stability condition (Figure A1), and, by means of the VIF, we verified that the variables in the model were moderately correlated (Table A2). Because the model was computed using the differentiated series . t and . rer , as a final test for the unrestricted VAR, we tested the model’s capacity to recover the information of these two series in levels, besides correctly simulating the CMI. The results are shown in Figure 2. Economies 2022, 10, x FOR PEER REVIEW 8 of 17 After computing the VAR, we verified that it satisfied the correct specification tests at the 5% significance level (Table 4). The full serial correlation tests are presented in Table A1 in Appendix A. Table 4. VAR joint correct specification tests. Test Statistic Probability Doornik–Hansen Normality Test: Skewness 6.9977 0.0720 Kurtosis 3.5516 0.3141 Jarque–Bera 10.549 0.1033 Serial Correlation LM test (Rao F-statistic): No serial correlation at lag h (12) 1.7071 0.0915 No serial correlation at lags 1 to h (12) 1.1366 0.2630 White heteroskedasticity test (no cross terms) 102.89 0.1665 White heteroskedasticity test (cross terms) 226.55 0.2975 Note: Tests at the 5% significance level. To complement the tests in Table 4, we verified that the model fulfills the stability condition (Figure A1), and, by means of the VIF, we verified that the variables in the model were moderately correlated (Table A2). Because the model was computed using the differentiated series 󰇗 and 󰇗, as a final test for the unrestricted VAR, we tested the model’s capacity to recover the information of these two series in levels, besides correctly simulating the CMI. The results are shown in Figure 2. 50 60 70 80 90 100 110 02 04 06 08 10 12 14 16 18 20 Multilateral Real Exchange Rate Multilateral Real Exchange Rate (Simulation) 0 4 8 12 16 20 24 02 04 06 08 10 12 14 16 18 20 Compensated Misery Index Compensated Misery Index (Simulation) 0 1000 2000 3000 4000 5000 6000 02 04 06 08 10 12 14 16 18 20 International Outbound Tourists International Outbound Tourists (Simulation) Figure 2. Unrestricted VAR simulation (Broyden’s algorithm). As shown in Figure 2, the model satisfactorily simulates the outbound tourism series and identifies the impact of the international financial crisis on the CMI. Additionally, Figure 2 shows that in all three cases the model adequately simulates the second quarter of 2020, which corresponds to the first wave of the COVID-19 pandemic, consistent with the fact that  presents the highest t-statistic in all three VAR equations (Table 3). These two facts highlight the importance of introducing dummy variables into the model. To analyze the model results, we first present a generalized impulse response analysis (Figure 3). The results show that there is no statistically significant response of the multilateral real exchange rate to a shock in the misery index (Figure 3a). Equally, this analysis shows that the multilateral real exchange rate is not significantly affected by shocks in Mexican outbound tourism (Figure 3b). Concerning the misery index, the impulse response analysis illustrates that it is positively affected by the depreciation of the Mexican peso; this effect is statistically significant during the second period and becomes statistically insignificant during the subFigure 2. Unrestricted VAR simulation (Broyden’s algorithm). As shown in Figure 2, the model satisfactorily simulates the outbound tourism series and identifies the impact of the international financial crisis on the CMI. Additionally, Figure 2shows that in all three cases the model adequately simulates the second quarter of 2020, which corresponds to the first wave of the COVID-19 pandemic, consistent with the fact that δAt presents the highest t-statistic in all three VAR equations (Table 3). These two facts highlight the importance of introducing dummy variables into the model. To analyze the model results, we first present a generalized impulse response analysis (Figure 3). The results show that there is no statistically significant response of the multilateral real exchange rate to a shock in the misery index (Figure 3a). Equally, this analysis shows that the multilateral real exchange rate is not significantly affected by shocks in Mexican outbound tourism (Figure 3b). Concerning the misery index, the impulse response analysis illustrates that it is positively affected by the depreciation of the Mexican peso; this effect is statistically significant during the second period and becomes statistically insignificant during the subsequent periods (Figure 3c). Conversely, an increase in the number of outbound tourists did not significantly affect the CMI (Figure 3d). In the case of outbound tourists, a depreciation of the Mexican peso reduces the number of tourist departures; such an effect is statistically significant during the third period (Figure 3e). Equally, increases in the CMI diminish the number of outbound tourists; this negative effect is statistically significant only during the second period (Figure 3f). To gain more statistical evidence supporting the impulse response analysis, we performed the Granger causality test (Table 5). According to the results in Table 5, outbound tourists and CMI do not Granger-cause the multilateral real exchange rate. However, this test, congruent with the impulse response analysis, shows a barely significant relationship at the 5% significance level from the real exchange rate to the CMI. In contrast, the results in Table 5show that outbound tourism does not Granger-cause CMI, whereas the multilateral real exchange rate and CMI have statistically significant effects on outbound tourism at the 5% and 1% significance levels, respectively. As a second method to analyze the model’s results, we performed a variance decomposition analysis (Table 6). 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