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Abstract

This study extends the literature on the permanent or transitory nature of shocks to per capita tourist arrivals along several dimensions. First, the study evaluates the nature of shocks to per capita tourist arrivals for a global panel of 129 countries. Second, unlike previous studies, we jointly estimate structural changes that represent either abrupt breaks or as a Fourier approximation of smooth breaks along with introducing a factor structure to test for the presence of unit roots in per capita tourist arrivals. Third, contrary to previous studies, our results show that rejection of the null hypothesis of a unit root in per capita tourist arrivals is quite limited compared to other unit root tests that fail to account for cross-correlations. Policy implications of the findings are also discussed.

Keywords

Permanent shocks transitory shocks tourist arrivals structural changes cross-correlation PANIC panel C12 C23 F31

Introduction

The United Nations World Tourism Organization noted a 4% increase in international tourist arrivals, reaching 1.5 billion in 2019. However, we observed a decline of 74% globally due to the onset of the COVID-19 pandemic in the first quarter of 2020 alone. Even the first quarter of 2021 witnessed a decrease of 83%.¹ The emergence of the COVID-19 virus, the rapid development of a vaccine, and the recurring mutations of the virus have generated a great deal of uncertainty about its global impact, particularly in the tourism sector. While tourism researchers understand the susceptibility of the tourism sector to exogenous shocks and the subsequent negative impact of such shocks, the question remains whether shocks to tourist arrivals are permanent or transitory. This question is even more relevant in light of the global economic repercussions of the recent COVID-19 pandemic (Payne et al., 2022b, among others).

Indeed, international tourism contributes significantly to the balance of payments for destination countries through foreign exchange earnings and government revenues (UNWTO, 2020). As such, examining the effects of shocks on international tourist arrivals that impact the flow of foreign exchange earnings and tourism revenues is important for the sustainability of a country’s tourism and hospitality sector. In this regard, we evaluate the permanent or transitory nature of shocks through panel unit root tests that simultaneously recognize structural breaks and common factors. Yucel (2021) notes that country-specific shocks occurring in a country may lead to spillover effects on international tourist arrivals in other countries. Hence, the panel framework proposed in this study allows for the interdependence between tourist arrivals in various countries. If tourist arrivals follow a unit root process, then shocks to tourist arrivals will have a permanent impact as tourist arrivals will not return to their original trend. On the other hand, if tourist arrivals are stationary, shocks will have a transitory impact. As for the policy implications, if an adverse shock is considered transitory, the need for a policy response is less likely, whereas an adverse shock viewed as permanent in nature will more likely require an offsetting policy response.

This study extends the research on the second-generation panel unit root and stationarity tests to determine the permanent or transitory nature of shocks to tourist arrivals by Lee et al. (2014), Yang et al. (2014), Solarin (2015), Dash et al. (2017), Xie et al. (2018), Kyophilvaong et al. (2019), Yucel (2021), and Payne and Nazlioglu (2022) on several fronts. First, as the literature review will show, this study will be the largest multi-country examination of a global panel of 129 countries. Second, we employ a new panel unit root test that allows for both structural breaks and cross-sectional dependence (i.e. common factors) simultaneously. The presence of cross-sectional dependence due to unobservable common factors or spatial spillover effects is a serious consideration in the estimation and the validity of inferences drawn from panel data models (Baltagi and Pirotte, 2010). Studies by Pesaran (2006), Bai (2009), among others, suggest using factor structures associated with the error terms to appropriately model such cross-sectional dependence. Likewise, the absence of structural breaks within the modeling framework may lead to inconsistent estimation and invalid inferences. As noted by Bai (2010), Baltagi et al. (2016), and Baltagi et al. (2017), standard panel estimators may be biased when not appropriately accounting for cross-correlations and structural breaks. To address these concerns, we employ new panel unit root tests that utilize either the two break tests of Lee and Strazicich (2003b) or the Fourier approximation of Enders and Lee (2012a,b) to capture smooth breaks alongside the PANIC procedure of Bai and Ng (2004) within a factor structure to account for cross-correlations. Finally, this new test is compared to several unit root tests with and without structural breaks and/or cross-correlations to gauge the sensitivity of the results.

Section 2 provides an overview of the literature on the unit root properties of tourist arrivals, expenditures, and receipts. Section 3 describes the methodology and data while Section 4 presents the empirical results with discussion. Concluding remarks are given in Section 5.

Literature review

The literature on the time series behavior of tourist arrivals, expenditures, and receipts with respect to the extent to which shocks are permanent or transitory has emerged in recent years. While several studies have evaluated the degree of persistence through fractional integration models, we focus our review of the literature on those studies utilizing unit root and stationarity tests with and without structural breaks and/or cross-sectional dependence.² Table 1 displays a summary table of the literature utilizing unit root/stationarity tests in regards to tourist arrivals, expenditures, and receipts.

Table 1.

Summary of empirical studies (Chronological order).

Author(s)	Time frame	Country coverage	Unit root and stationarity tests	Main findings
Au et al. (2005)	1981–2001 Annual	Tourist arrivals to Hong Kong from 36 countries	Dickey and Fuller (1979, 1981) test	Dickey and Fuller (1979, 1981) test reveals stationarity of tourist arrivals for 12 countries and non-stationarity for 24 countries.
Bhattacharya and Narayan (2005)	1980–1999 Annual	Visitor arrivals to India from 10 countries	Dickey and Fuller (1979, 1981), Maddala and Wu (1999), and Im et al. (2003) tests	Dickey and Fuller (1979, 1981) test reveals stationarity of visitor arrivals from two of the 10 countries while Maddala and Wu (1999) and Im et al. (2003) tests support stationarity for the panel of countries.
Narayan (2005a)	1970–2002 Annual	Real tourism expenditures in Fiji	Zivot and Andrews (1992) and Lumsdaine and Papell (1997) tests	Zivot and Andrews (1992) and Lumsdaine and Papell (1997) tests with structural breaks reveal stationarity of real tourism expenditures.
Narayan (2005b)	1970–2002 Annual	Tourism expenditure in Fiji	Dickey and Fuller (1979, 1981), Vogelsang (1997), and Vogelsang and Perron (1998) tests	Dickey and Fuller (1979, 1981) test reveals non-stationarity of tourism expenditures, but Vogelsang (1997) and Vogelsang and Perron (1998) tests with structural breaks support stationarity.
Narayan (2005c)	1970–2002 Annual	Visitor arrivals to Fiji from three countries	Dickey and Fuller (1979, 1981), Phillips and Perron (1988), Kwiatkowski et al. (1992), and Sen (2003) tests	Dickey and Fuller (1979, 1981), Phillips and Perron (1988), and Kwiatkowski et al. (1992) tests reveal non-stationarity of visitor arrivals while the Sen (2003) test with structural breaks supports stationarity.
Chu et al. (2008)	1969–2004 Annual	Visitor arrivals to Taiwan from 22 countries	Dickey and Fuller (1979, 1981), Phillips and Perron (1988), Kwiatkowski et al. (1992), Elliott et al. (1996), Ng and Perron (2001), and Breuer et al. (2001) tests	Dickey and Fuller (1979, 1981), Phillips and Perron (1988), Kwiatkowski et al. (1992), Elliott et al. (1996), and Ng and Perron (2001) tests reveal non-stationarity of visitor arrivals for the majority of countries while the Breuer et al. (2001) test supports stationarity for 10 of the 22 countries.
Narayan (2008)	1991:1–2003:9 Monthly	Visitor arrivals to Australia from 28 countries	Lee and Strazicich (2003a,b) and Im et al. (2003) tests	Lee and Strazicich (2003a,b) tests without structural breaks reveal stationarity of visitor arrivals for eight of the 28 countries, with one structural break stationarity for 13 of the 28 countries, and with two structural breaks stationarity for 25 of the 28 countries. The LM panel unit root test with structural breaks and Im et al. (2003) test supports stationarity for the panel of countries.
Narayan and Prasad (2008)	1991:1–2003:9 Monthly	Visitor arrivals to Australia from 20 countries to include eight Asian countries and G7 countries	Seemingly unrelated regresssion Dickey and Fuller (1979, 1981), Taylor and Sarno (1998), and Im et al. (2005) tests	Seemingly unrelated regresssion Dickey and Fuller (1979, 1981) and Taylor and Sarno (1998) tests reveal stationarity of visitor arrivals for the panel of 20 countries and G7 countries, but non-stationarity for the eight country Asian panel. Im et al. (2005) test with structural breaks supports stationarity for all three country panels.
Lean and Smyth (2009)	1995:1–2005:12 Monthly	International visitor arrivals to Malaysia from 10 countries	Lee and Strazicich (2003a,b) test	Lee and Strazicich (2003a,b) test with one break in the intercept reveals stationarity of international visitor arrivals for six of the 10 countries, with breaks in the intercept and slope stationarity for nine of the 10 countries, and with two breaks stationarity for all 10 countries.
Lee (2009)	2004:1–2007:9 Monthly	Tourist arrivals to Singapore from 12 countries	Joint Dickey and Fuller (1979, 1981) and Kwiatkowski et al. (1992) tests	Except for India, Malaysia, and United States, the joint Dickey and Fuller (1979, 1981) and Kwiatkowski et al. (1992) test reveals stationarity of tourist arrivals for the other nine countries.
Lorde et al. (2009)	1956–2005 Annual	International tourist arrivals to Barbados from four countries and regions	Dickey and Fuller (1979, 1981), Hylleberg et al. (1990), Kwiatkowski et al. (1992), Breitung (2000), Hadri (2000), Levin et al. (2002), and Im et al. (2003) tests	Dickey and Fuller (1979, 1981) and Kwiatkowski et al. (1992) tests reveal non-stationarity of international tourist arrivals while Hylleberg et al. (1990) test documents seasonal unit roots. Breitung (2000), Hadri (2000), Levin et al. (2002), and Im et al. (2003) tests support non-stationarity for the panel of countries.
Smyth et al. (2009)	1983:1–2005:12 Monthly	International visitor arrivals to Bali in Indonesia from 11 countries	Dickey and Fuller (1979, 1981), Phillips and Perron (1988), Kwiatkowski et al. (1992), Elliott et al. (1996), and Im et al. (2005) tests	Dickey and Fuller (1979, 1981), Phillips and Perron (1988), Kwiatkowski et al. (1992), and Elliott et al. (1996) tests reveal non-stationarity of international visitor arrivals. Im et al. (2005) test with structural breaks supports stationarity for the panel of countries.
Tang and Wong (2009)	2003:1–2007:12 Monthly	International visitor arrivals to Cambodia from 16 countries categorized by five regions	Dickey and Fuller (1979, 1981), Lanne et al. (2002), Saikkonen and Lutkepohl (2002) tests	With the exception of Indonesia, Dickey and Fuller (1979, 1981) tests reveal non-stationarity of international visitor arrivals whereas Lanne et al. (2002) and Saikkonen and Lutkepohl (2002) tests with structural breaks support stationarity.
Lee (2011)	1978:1–2010:6 Monthly	Visitor arrivals to Singapore from seven countries	Zivot and Andrews (1992) test	Zivot and Andrews (1992) test with structural breaks reveals non-stationarity of visitor arrivals for all seven countries.
Saleh et al. (2011)	1988–2007 Annual	International tourist arrivals to Thailand from 10 countries	Lee and Strazicich (2003a,b) and Im et al. (2005) tests	Lee and Strazicich (2003a,b) test with structural breaks reveals stationarity of international tourist arrivals for all 10 countries and Im et al. (2005) test with structural breaks supports stationarity for the panel of countries.
Bassil et al. (2014)	2008:1–2013:12 Monthly	International visitor arrivals to Lebanon from 15 countries (including expatriate Lebanese)	Lee and Strazicich (2003a,b) and Im et al. (2005) tests	Lee and Strazicich (2003a,b) test with one and two structural breaks reveals stationarity of international visitor arrivals for all 15 countries while Im et al. (2005) test with one and two structural breaks supports stationarity for the panel of countries.
Chu et al. (2014)	1995–2010 Annual	Visitor arrivals to China from 18 countries	Maddala and Wu (1999), Breuer et al. (2001), Hadri (2000), Levin et al. (2002), and Im et al. (2003) tests	Maddala and Wu (1999), Hadri (2000), Levin et al. (2002), and Im et al. (2003) panel unit root tests reveal non-stationarity of visitor arrivals for all 18 countries while the Breuer et al. (2001) test supports non-stationarity for 13 of the 18 countries.
Lee et al. (2014)	1970–2010 Annual	Tourist arrivals to Taiwan from six countries and regions	Maddala and Wu (1999), Levin et al. (2002), Choi (2002), Im et al. (2003), Bai and Ng (2004), Moon and Perron (2004), Pesaran (2007), Ucar and Omay (2009), and Chang (2002) tests	Maddala and Wu (1999), Levin et al. (2002), Im et al. (2003), Moon and Perron (2004), and Pesaran (2007) tests reveal stationarity of tourist arrivals for the panel of countries and regions. Choi (2002), Bai and Ng (2004), and Chang (2002) tests support non-stationarity for the panel of countries and regions. Ucar and Omay (2009) test with Fourier function for gradual breaks and sequential panel selection method supports stationarity with the exception of South Korea.
Tan and Tan (2014)	1994:1–2011:6 Monthly	International tourist arrivals to Singapore from 20 countries	Carrion-i-Silvetre et al. (2005) test	Carrion-i-Silvetre et al. (2005) test with structural breaks reveals stationarity of international tourist arrivals for individual countries and the panel of countries.
Yang et al. (2014)	1970–2011 Annual	Tourist arrivals to Taiwan from six countries and regions	Kwiatkowski et al. (1992) and Carrion-i-Silvestre et al. (2005) tests with Fourier function	Kwiatkowski et al. (1992) test with structural breaks and Fourier function reveals stationarity of tourist arrivals with the exception of South Korea and Europe while Carrion-i-Silvestre et al. (2005) test with Fourier function for graduate breaks supports stationarity for the panel of countries and regions.
Solarin (2015)	2001:1–2013:10 Monthly	International tourist arrivals to Sarawak in Mayalsia from 10 countries	Wu and Lee (2009) test	Wu and Lee (2009) test reveals stationarity of international tourist arrivals for all 10 countries.
Debeoglu (2016)	1996–2014 Annual	Visitor arrivals to Turkey from 15 countries	Dickey and Fuller (1979, 1981) and Im et al. (2003) test	Dickey and Fuller (1979, 1981) test reveals stationarity of visitor arrivals for seven of the 15 countries while Im et al. (2003) test supports stationarity for the panel of countries.
Solarin (2016)	1990:1–2012:12 Monthly	International tourist arrivals to Mauritius from 16 countries	Lee and Strazicich (2003a,b) and Kruse (2011) tests	Kruse (2011) non-linearity test reveals stationarity of international tourist arrivals for 15 of the 16 countries while Lee and Strazicich (2003a,b) test with structural breaks supports stationarity (linearity test) in Malagasy Republic.
Dash et al. (2017)	2001–2013 for Brazil, Russia, and India and 2000–2013 for China Annual	Tourist arrivals to Brazil, Russia, India, and China	Choi (2006), Pesaran (2007), Demetrescu and Hanck (2012), and Im et al. (2005) tests	Choi (2006) test reveals stationarity of tourist arrivals for Brazil and Russia panels and non-stationarity for India and China panels. Pesaran (2007) test supports non-stationarity for Brazil, Russia, and India panels and stationarity for China panel. Demestrescu and Hanck (2012) tests find stationarity for Brazil, Russia, and India panels while non-stationarity for China panel. Im et al. (2005) test with structural breaks shows stationarity for Brazil, Russia, India, and China panels.
Tiwari et al. (2018)	1981–2012 Annual	Foreign tourist arrivals to India from 17 countries	Kwiatkowski et al. (1992), DeJong et al. (2007), Xiao and Lima (2007), and Narayan and Popp (2010) tests	Kwiatkowski et al. (1992), DeJong et al. (2007), and Xiao and Lima (2007) tests reveal non-stationarity of foreign tourist arrivals while the Narayan and Popp (2010) test with structural breaks supports stationarity for eight of the 17 countries.
Valadkhani and O’Mahony (2018)	1991:1–2014:4 Monthly	Tourist arrivals to Australia from 53 countries	Dickey and Fuller (1979, 1981), Phillips and Perron (1988), Kwiatkowski et al. (1992), and Zivot and Andrews (1992) tests	Dickey and Fuller (1979, 1981) test reveals stationarity in tourist arrivals for 29 countries, Phillips and Perron (1988) test stationarity in 4 countries, Kwiatkowski et al. (1992) test stationarity in 48 countries, and Zivot and Andrews (1992) test with structural break stationarity in 50 countries.
Xie et al. (2018)	1981–2012 Annual	Foreign tourist arrivals to India from 17 countries	Carrion-i-Silvetre et al. (2005), Carrion-i-Silvestre et al. (2009), and Bahmani-Oskoee et al. (2014) with Fourier function tests	Carrion-i-Silvestre et al. (2005) and Carrion-i-Silvestre et al. (2009) tests with structural breaks reveal mixed evidence on stationarity of foreign tourist arrivals. Bahmani-Oskoee et al. (2014) test with Fourier function for gradual breaks supports stationarity for 12 of the 17 countries.
Charles et al. (2019)	1981–2015 Annual	Total tourist arrivals to La Reunion, tourist arrivals to La Reunion disaggregated by major source markets, and tourist arrivals to La Reunion disaggregated by visiting motivations	Elliott et al. (1996), Perron and Yabu (2009), and Kerjriwal and Perron (2010) tests	Elliott et al. (1996), Perron and Yabu (2009), and Kerjriwal and Perron (2010) tests reveal stationarity with structural breaks across the various measures of tourist arrivals with the exception of European tourist arrivals and business visitation.
Kyophilavong et al. (2019)	1995–2014 Annual	Tourist arrivals to Laos from four regions	Moon and Perron (2004), Choi (2006), Pesaran (2007), and Demetrescu and Hanck (2012) tests	Moon and Perron (2004) and Choi (2006) tests reveal stationarity of tourist arrivals while the Pesaran (2007) and Demetrescu and Hanck (2012) tests support non-stationarity of tourist arrivals for the non-ASEAN region and stationarity for the Asia and Pacific, ASEAN, and European regions.
Baig and Hussain (2020)	2007:1–2017:9 Monthly	Domestic and foreign tourist arrivals to Gilgit-Baltistan in Pakistan	Dickey and Fuller (1979, 1981), Kwaitkowski et al. (1992), and Lee and Strazicich (2003a,b) tests	Dickey and Fuller (1979, 1981) and Kwaitkowski et al. (1992) tests reveal stationarity of both domestic and foreign tourist arrivals. Lee and Strazicich (2003a,b) tests with structural breaks support stationarity as well.
Yucel (2021)	1995–2018 Annual	International tourist arrivals to the 20-most visited countries	Breuer et al. (2002), Smith et al. (2004), Im et al. (2005), Pesaran (2007), Hadri and Kurozumi (2012), Nazlioglu and Karul (2017), and Lee and Tieslau (2019) tests	With the exception of Hadri and Kurozumi (2012) test, Breuer et al. (2002), Smith et al. (2004), and Pesaran (2007) tests reveal non-stationarity of international tourist arrivals for the panel of countries while the Im et al. (2005) and Lee and Tieslau (2019) tests with structural breaks show stationarity. Nazlioglu and Karul (2017) tests with Fourier function for gradual breaks supports stationarity as well.
Payne and Nazlioglu (2022)	1995–2019 Annual	Per capita tourism expenditures and receipts for 63 countries	Nazlioglu and Karul (2017) and Nazlioglu et al. (2021) tests	Nazlioglu and Karul (2017) and Nazlioglu et al. (2021) panel tests reveal non-stationarity. Tests of stationarity with a common factor structure without structural breaks at the individual country level support non-stationarity in 24 and 26 countries with respect to per capita tourism expenditures and receipts, respectively. With inclusion of a Fourier function for gradual breaks and the common factor structure show non-stationarity in 48 and 54 countries with respect to per capita tourism expenditures and receipts, respectively.

A great deal of the research to date has focused on the Asia-Pacific Rim region. Narayan (2005a) employs the Zivot and Andrews (1992) and Lumsdaine and Papell (1997) unit root tests with structural breaks to examine the stationarity of real tourism expenditures in Fiji. The structural breaks identify the military coup in 1987, but the null hypothesis of a unit root is rejected to suggest the military coup was only a temporary shock. In a related study, Narayan (2005b) finds non-stationarity of tourism expenditures in Fiji; however, the Vogelsang (1997) structural break test and Vogelsang and Perron’s (1998) unit root test confirm a structural break with the 1987 military coup and the stationarity of tourism expenditures. Narayan (2005c) deploys Sen’s (2003) unit root test with structural breaks alongside the augmented Dickey and Fuller (1979, 1981) and Phillips and Perron (1988) unit root tests, as well as the Kwiatkowski et al. (1992) stationarity test to examine visitor arrivals from Australia, New Zealand, and the U.S. to Fiji. The results indicate that visitor arrivals follow a stationary process once structural breaks are introduced.

Through the seemingly unrelated regression Dickey and Fuller (1979, 1981) and augmented Dickey-Fuller (MADF) tests of Taylor and Sarno (1998), Narayan and Prasad (2008) show that tourist arrivals to Australia from a panel of 20 tourist source markets and G7 countries, respectively, are stationary, which is not the case for a panel of eight Asian countries. However, when using the Im et al. (2005) panel unit root tests with structural breaks, they find that all three country panels are stationary. In another study, Narayan (2008) uses univariate and panel unit root tests with respect to visitor arrivals to Australia from 28 tourist source markets. The results from the univariate Lagrange multiplier (LM) tests of Lee and Strazicich (2003a, 2003b) indicate that when structural breaks are not allowed for the null hypothesis of a unit root is rejected for eight of the 28 countries. But, when one structural break is considered the null hypothesis is rejected for 13 of the 28 countries, and with two structural breaks the null hypothesis is rejected for 25 of the 28 countries. The panel LM version of the test, including one and two structural breaks, based on the panel test of Im et al. (2003) reveals that visitor arrivals are stationary. Valadkhani and O’Mahony (2018) undertake a much larger study of tourist arrivals from 53 countries to Australia. The augmented Dickey and Fuller (1979,1981) and Phillips and Perron (1988) unit root tests show that tourist arrivals are non-stationarity for most countries. On the other hand, the Kwiatkowski et al. (1992) test identifies tourist arrivals from 48 of the 53 countries as stationary, while the Zivot and Andrews (1992) test finds stationarity in 50 of the 53 countries.

In addition to the research on Australia, a number of studies investigate tourist arrivals to Singapore. Lee (2009) tests the stationarity of tourist arrivals to Singapore from 12 major source markets using the joint augmented Dickey and Fuller (1979, 1981) and Kwiatkowski et al. (1992) test to discover that tourist arrivals except from India, Malaysia, and the U.S. are stationary. Lee (2011) employs the Zivot and Andrews (1992) unit root test with one structural break for visitor arrivals from China, Australia, India, Japan, the U.K., South Korea, and the U.S. to Singapore. The results fail to reject the null hypothesis of a unit root, lending support for the permanent nature of shocks. Tan and Tan (2014) apply the Carrion-i-Silvestre et al. (2005) panel stationarity test with structural breaks to examine tourist arrivals to Singapore from 20 major source markets to find the shocks to tourists arrivals are temporary.

Several studies evaluate tourist arrivals in the case of Malaysia. Lean and Smyth (2009) utilize the Lee and Strazicich (2003a, 2003b) one and two structural break unit root tests for visitor arrivals to Malaysia from the top 10 tourist source markets to show that tourist arrivals from all countries are stationary with allowance for two structural breaks. Using the Wu and Lee (2009) unit root test with allowance for both non-linearity and cross-sectional dependence, Solarin (2015) examines the tourist arrivals from the 10 major source markets to the community of Sarawak on the island of Borneo in Malaysia to discover that shocks to tourist arrivals are transitory.

A number of studies also examine the time series behavior of tourist arrivals to Taiwan. Chu et al. (2008) investigate tourist arrivals from 22 countries to Taiwan using a battery of univariate unit root and stationarity tests to reveal the non-stationarity of visitor arrivals. In contrast, the Breuer et al. (2001) panel SURADF unit root test identifies the stationarity of tourist arrivals from 10 of the 22 countries. Lee et al. (2014) employ a variety of first- and second-generation unit root tests to determine the stationarity of tourist arrivals to Taiwan from six countries and regions. While the panel tests of Maddala and Wu (1999), Levin et al. (2002), Im et al. (2003), Moon and Perron (2004), and Pesaran (2007) support stationarity, the tests by Choi (2002), Bai and Ng (2004), and Chang (2002) provide evidence of non-stationarity. Further results show that the Ucar and Omay (2009) non-linear panel unit root test, which combines the non-linear framework of Kapetanios et al. (2003) and the panel unit root procedure of Im et al. (2003) with the sequential panel selection method of Chortareas and Kapetanios (2009), also support stationarity in tourist arrivals with the exception of South Korea. Yang et al. (2014) utilize the panel stationarity tests of Carrion-i-Silvestre et al. (2005) with a non-linear Fourier function and individual Kwiatkowski et al. (1992) stationarity tests with allowance for sharp and smooth breaks to test the stationarity of tourist arrivals from Japan, Southeast Asia, Hong Kong and Macao, the U.S., South Korea, and Europe to Taiwan. Their results show stationarity of tourist arrivals for the overall panel of countries and regions; however, on an individual basis tourist arrivals are non-stationary in the case of South Korea and Europe.

Bhattacharya and Narayan (2005) apply the augmented Dickey and Fuller (1979, 1981) unit root test to find the stationarity of visitor arrivals to India for two of the 10 major source markets while the panel unit root tests of Maddala and Wu (1999) and Im et al. (2003) reject the null hypothesis of a unit root for the panel of countries. Tiwari et al. (2018) investigate the stationarity of foreign tourist arrivals to India from 17 major source markets using several unit root and stationarity tests. When using the Kwiatkowski et al. (1992), DeJong et al. (2007), and Xiao and Lima (2007) tests, the results show the non-stationarity of foreign tourist arrivals. However, the Narayan and Popp (2010) unit root test with structural breaks favors the stationarity of foreign tourist arrivals in eight of the 17 countries examined. Xie et al. (2018) apply Carrion-i-Silvestre et al. (2005) and Carrion-i-Silvestre et al. (2009) panel stationarity tests to find mixed results on the stationarity of foreign tourist arrivals from 17 countries to India. Further analysis using the Bahmani-Oskooee et al. (2014) test with a Fourier function supports stationarity in 12 of the 17 countries.

In addition, there have been several other studies of international tourist arrivals to Asian countries. Using visitor arrival data from 18 countries to China, Chu et al. (2014) discover that the panel unit root tests of Levin et al. (2002), Im et al. (2003), Maddala and Wu (1999), and Hadri (2000) fail to reject the null hypothesis of a unit root in all the countries. However, the Breuer et al. (2001) panel SURADF test fails to reject the null hypothesis of a unit root for only 13 of the 18 countries (Indonesia, Malaysia, Philippines, Singapore, Korea, Thailand, U.K, Germany, France, Italy, Portugal, Sweden, and Switzerland).

Au et al. (2005) use the augmented Dickey and Fuller (1979, 1981) unit root test to evaluate tourist arrivals from 36 countries to Hong Kong to find that only tourist arrivals from 12 countries exhibit stationary behavior. Smyth et al. (2009) examine the impact of terrorist incidents on tourist arrivals to Bali based on univariate and panel unit root/stationarity tests. Results from the augmented Dickey and Fuller (1979, 1981), Phillips and Perron (1988), Kwiatkowski et al. (1992), and Elliott et al. (1996) tests indicate the presence of a unit root in tourist arrivals. However, the Im et al. (2005) panel unit root test with structural breaks rejects the null hypothesis of a unit root.

Tang and Wong (2009) explore the impact of the SARS epidemic on international visitor arrivals from five geographical regions (ASEAN, Asia and Oceania, Europe, and the Americas) to Cambodia. With the exception of Indonesia, the augmented Dickey and Fuller (1979, 1981) unit root test reveals that visitor arrivals to Cambodia are non-stationary, while the tests of Lanne et al. (2002) and Saikkonen and Lutkepohl (2002) with structural breaks demonstrate stationarity. Saleh et al. (2011) examine the time series behavior of tourist arrivals from 10 countries to Thailand using the Lee and Strazicich (2003a, 2003b) univariate unit root tests with structural breaks and the Im et al. (2005) panel unit root tests with structural breaks. Both the univariate and panel unit root tests reject the null hypothesis of a unit root.

Kyophilavong et al. (2019) apply second-generation panel unit root tests with allowance for cross-sectional dependence to evaluate the stationarity of tourist arrivals to Laos from four regions. The findings from the Moon and Perron (2004) and Choi (2006) tests support stationarity, whereas the Pesaran (2007) and Demestrescu and Hanck (2012) tests provide evidence to the contrary for the non-ASEAN region. Baig and Hussain (2020) investigate domestic and foreign tourist arrivals to the Gilgit-Baltistan region in northern Pakistan. The results from the augmented Dickey and Fuller (1979, 1981) and Kwiatkowski et al. (1992) tests support stationarity. Also, the Lee and Strazicich (2003a, 2003b) unit root tests with structural breaks confirm stationarity.

In addition to the numerous studies related to Asia-Pacific Rim countries, a number of other country studies have been undertaken. Lorde et al. (2009) test the stationarity of tourist arrivals from the U.S., U.K, Canada, and other minor markets to Barbados using the augmented Dickey and Fuller (1979, 1981) unit root test and Kwaitkowski et al. (1992) stationarity test to demonstrate the non-stationarity of tourist arrivals. The panel unit root tests of Breitung (2000), Hadri (2000), Levin et al. (2002), and Im et al. (2003) reveal that exogenous shocks will have permanent effects on tourist arrivals to Barbados. Bassil et al. (2014) evaluate international visitor arrivals from Yemen, Kuwait, Qatar, Algeria, Bahrain, Oman, United Arab Emirates, Tunisia, Egypt, Jordan, Morocco, Syria, Iraq, Saudi Arabia, and expatriate Lebanese to Lebanon using the Lee and Strazicich (2003a, 2003b) univariate unit root tests and Im et al. (2005) panel unit root test with structural breaks to show that tourist arrivals are stationary.

Dedeoglu (2016) utilizes the augmented Dickey and Fuller (1979, 1981) unit root test and the panel unit root test of Im et al. (2003) to investigate the stationarity of tourist arrivals from 15 major source markets to Turkey. The null hypothesis of a unit root is rejected for Germany, Netherlands, France, the U.S., Georgia, Romania, and Syria, while the Im et al. (2003) panel unit root test rejects the null hypothesis of a unit root for the panel of countries. Solarin (2016) applies the Kruse (2011) non-linear unit root test to examine the 16 major tourism source markets to Mauritius to find that international tourist arrivals are stationary in 15 of the 16 countries; however, the linear unit root test of Lee and Strazicich (2003a, 2003b) supports stationarity for tourist arrivals from the Malagasy Republic. Charles et al. (2019) use data on total tourist arrivals, disaggregated tourist arrivals by major source markets, and tourist arrivals disaggregated by visitor motivations to the French island of La Reunion. Charles et al. (2019) implement the structural break tests of Perron and Yabu (2009) and Kejriwal and Perron (2010), then applies the Elliott et al. (1996) unit root tests to discover, with the exception of European tourist arrivals and business visitation, the transitory effect of external shocks.

Dash et al. (2017) use several panel unit root tests to yield mixed results with respect to the stationarity of tourist arrivals to BRIC countries. Choi (2006) tests reveal stationarity of tourist arrivals to Brazil and Russia; stationarity for China from Pesaran (2007) tests, and stationarity for Brazil, Russia, and India based on the tests from Demestrescu and Hanck (2012). The Im et al. (2005) panel unit root tests with structural breaks demonstrate stationarity for all four country panels. Yucel (2021) evaluates the top 20 tourist destinations in the world to determine through first- and second-generation panel unit root tests whether shocks to tourist arrivals are permanent or transitory. With the exception of the Hadri and Kurozumi (2012) test, the Breuer et al. (2002), Smith et al. (2004), and Pesaran (2007) second-generation panel unit root tests without structural breaks fail to reject the null hypothesis of a unit root. However, the LM panel unit root tests of Im et al. (2005) and Lee and Tieslau (2019) with structural breaks reject the null hypothesis of a unit root. Upon further evaluation of the results from the Fourier panel KPSS test of Nazlioglu and Karul (2017), the null hypothesis of stationarity is not rejected, irrespective of the Fourier frequency. Finally, Payne and Nazlioglu (2022) examine the stationarity of per capita tourism expenditures and receipts for a panel of 63 countries using several panel stationarity tests by Nazlioglu and Karul (2017) and Nazlioglu et al. (2021). Their findings reveal that the introduction of a common factor structure without structural breaks rejects the null hypothesis of stationarity for per capita tourism expenditures and receipts, respectively in less than half of the countries. However, the inclusion of a Fourier function with smooth breaks along with the common factor structure substantially increases the number of rejections of the null hypothesis of stationarity to more than 75% of the countries.

Methodology and data

While controlling for the effects of structural breaks is important, equally relevant is the cross-sectional dependence in per capita tourist arrivals. Indeed, we observe significant comovements among per capita tourist arrivals across countries. The cross-correlations in per capita tourist arrivals will likely reflect common shocks that can drive the comovements in the per capita tourist arrivals across countries. For instance, the diffusion of technological advances across countries, the synchronization of international business cycles, the interdependence of global supply chains, the global financial crisis of 2007–2009, and the more recent COVID-19 pandemic phenomenon are all sources of increased cross-correlations in per capita tourist arrivals (Payne and Lee, 2022; Payne and Nazlioglu, 2022).

A number of unit root tests have been considered to address the issue of cross-sectional dependence. The PANIC (panel analysis of non-stationarity in idiosyncratic and common components) procedure of Bai and Ng (2004) is a popular procedure to control the effects of comovements. The PANIC procedure is a generalized approach to treating comovements as a systemic component of a variable’s cross-sectional behavior. If cross-sectional dependence exists among the panel of per capita tourist arrivals by country, it is directly relevant to non-stationarity.

All tests utilizing the PANIC procedure impose an initial factor structure via the popular principal component analysis (PCA). The general PCA factor structure can be defined by

Y_{i t} = Λ_{i}^{'} F_{t} + e_{i t}

(1)

where

Y_{i t} = {[Y_{1 t}, . ., Y_{N t}]}^{'}

denotes the panel data;

F_{t}

is a

k \times 1

vector of latent factors that captures commonalities across N countries;

Λ_{i}

denotes the associated factor loadings of each individual i and

Λ = [Λ_{1}, . . Λ_{N}]

; and

e_{i t} = {[e_{1 t}, . ., e_{N t}]}^{'}

are the error terms. The estimated factor matrix

{\hat{F}}_{t}

is obtained as the eigenvectors corresponding to the first k largest eigenvalues of the square matrix

Y Y^{'}

multiplied by

T^{1 / 2}

. Then, the factor loadings can be given as

\hat{Λ} = Y^{'} {\hat{F}}_{t} / T

The focus of our analysis is to employ unit root tests that jointly allow for structural breaks in a factor structure to test the null hypothesis of a unit root in per capita tourist arrivals.³ To this end, we first employ the Lagrange multiplier (LM) unit root tests of Lee and Strazicich (2003b) with two structural breaks along with the Bai and Ng (2004) PANIC procedure. The LM tests are more convenient than the augmented Dickey-Fuller (1979, 1981) unit root tests when we allow for structural breaks. Thus, we can simultaneously allow for two structural breaks and cross-correlations in a factor structure. As noted by Payne et al. (2022a), the motivation of using the LM tests of Lee and Strazicich (2003b) is that they do not exhibit spurious rejections under the null hypothesis and allow for breaks under both the null and alternative hypotheses. Also, the LM tests exhibit good size properties under strong serial correlations based on the augmented version. Thus, we consider the following model:

y_{t} = δ^{'} Z_{t} + e_{t}, e_{t} = β e_{t - 1} + ɛ_{t}, t = 1, . ., T .

(2)

where

Z_{t}

contains exogenous variables. The unit root null hypothesis is

β = 1

. The level-shift or “crash” model is given with

Z_{t} = {[1, D_{1 t}, . ., D_{R t}]}^{'}

, where

D_{j t} = 1

for

t \geq T_{B j} + 1

, j = 1,.., R, and 0.0 otherwise, and

T_{B j}

represents for the time period of the j-th break. The trend break model is denoted by

Z_{t} = {[1, D_{1 t}, . ., D_{R t}, D T_{1 t}^{*}, . ., D T_{R t}^{*},]}^{'}

, where

D T_{j t}^{*} = t - T_{B j}

for

t \geq T_{B j} + 1

, and 0.0 otherwise. Using the LM (score) principle, the null restriction

β = 1

is imposed and the first step regression in differences is given as

∆ y_{t} = δ^{'} ∆ Z_{t} + u_{t} .

, where

δ = {[δ_{1 i}, δ_{2 i}, δ_{3 i}, δ_{4 i}]}^{'}

i = 1, \dots, R

. The following regression,

∆ y_{t} = δ^{'} ∆ Z_{t} + \emptyset {\tilde{S}}_{t - 1} + e_{t}

, where

{\tilde{S}}_{t} = y_{t} - \tilde{ψ} - Z_{t} \tilde{δ}

is used to obtain the unit root test statistics. Here,

\tilde{δ}

is the coefficient in the regression of

∆ y_{t}

∆ Z_{t}

, and

\tilde{ψ}

is the restricted MLE of

ψ

with

\tilde{ψ} = y_{1} - Z_{1} \tilde{δ}

. Meng et al. (2013) consider a transformation procedure that makes the resulting test invariant to the locations of breaks. The response surface function estimates for these LM unit root tests with breaks is provided by Nazlioglu and Lee (2020).⁴

Our task is to allow for a factor structure in the above testing procedure in which consideration is given for a panel model with an alternative data generating process as follows.

y_{i t} = δ^{'} Z_{i t} + π_{i} F_{t} + e_{i t}, e_{i, t} = β e_{i, t - 1} + ϵ_{i t}, i = 1, . . N; t = 1, . ., T .

(3)

where

F_{t}

is an

r \times 1

vector which represents the unobserved common factors and

π_{i}

denotes factor loadings that represent the responses of each cross-section unit to the common factors. In light of the challenges of estimating the factor terms with other parameters within a linear framework, the iterative procedure for joint estimation is adopted by Payne et al. (2022a) and Payne and Lee (2022).

To control for structural breaks, we also consider an alternative procedure using a Fourier function. The LM tests with breaks employ dummy variables that require estimating the number of breaks, locations, and break types. While the models using dummy variables may work well in the cases of sharp or abrupt breaks when the relevant information is readily available, they do not work well in the cases of smooth or gradual breaks. As such, we adopt the PANIC-Fourier tests of Nazlioglu et al. (2022) and Payne and Lee (2022), who consider the LM version of the PANIC tests while allowing for a Fourier function. For these tests, the following Fourier function is used to model multiple non-linear breaks of unknown forms.

d_{i t} = a_{i} + b_{i} t + \sum_{k = 1}^{m_{i}} c_{i k} \sin (\frac{2 π k t}{T}) + \sum_{k = 1}^{m_{i}} d_{i k} \cos (\frac{2 π k t}{T}) .

(4)

where m_i represents the Fourier frequency for each cross-sectional unit, whereby we consider different results using a different number of cumulative frequencies with m_i = 1, 2, and 3. The advantages of using the Fourier function are discussed in Enders and Lee (2012a, 2012b). In particular, the task of estimating the number of breaks and their locations is diverted to estimating a parsimonious frequency parameter. Then, we replace the dummy variables included in Z_t of equation (2), and use the iterative procedure to estimate the parameters in the model and the test statistics.⁵

Annual data on international tourist arrivals and the population for 129 countries over the period 1995–2019 was obtained from the World Bank Development Indicators. The variable of interest in our analysis is per capita tourist arrivals, defined as international tourist arrivals divided by the population.⁶ Table 2 displays the summary statistics associated with each country in our global panel. A quick perusal of Table 2 highlights the relative magnitude of tourism to a country’s population as the averages of per capita tourist arrivals are quite high for small island countries. The average per capita tourist arrivals range from 0.0046 in Ethiopia to 83.6523 in San Marino. As a measure of relative dispersion, the coefficient of variation ranges from 0.0609 in Luxembourg to 1.2617 in Bhutan. Moreover, the coefficient of variation for such small island countries as Aruba, Bahamas, Cayman Islands, among others, is relatively lower than other countries.

Table 2.

Summary statistics of per capita tourist arrivals.

Countries	Mean	STD	CV	Min	Max
Albania	0.7139	0.6973	0.9767	0.0378	2.2444
Algeria	0.0445	0.0166	0.3742	0.0181	0.0717
Angola	0.0104	0.0074	0.7115	0.0006	0.0250
Antigua & Barbuda	8.9418	1.3961	0.1561	6.5092	11.1271
Argentina	0.1163	0.0381	0.3274	0.0657	0.1679
Armenia	0.2109	0.1958	0.9287	0.0037	0.6404
Aruba	13.9569	2.3984	0.1718	10.3804	18.3520
Australia	0.2727	0.0454	0.1664	0.2062	0.3732
Austria	2.6288	0.4462	0.1697	2.0892	3.5906
Azerbaijan	0.1674	0.0891	0.5325	0.0121	0.3162
Bahamas	14.6436	1.9524	0.1333	11.5210	18.6143
Bahrain	6.5237	1.4040	0.2152	3.4355	9.6320
Bangladesh	0.0015	0.0005	0.3475	0.0007	0.0032
Barbados	3.9853	0.3671	0.0921	3.3656	4.7307
Belgium	0.6628	0.0615	0.0928	0.5485	0.8132
Belize	2.9282	1.0481	0.3579	1.3029	4.8062
Bermuda	9.2256	1.2715	0.1378	7.3275	12.5952
Bhutan	0.1013	0.1279	1.2617	0.0090	0.4141
Bolivia	0.0626	0.0214	0.3411	0.0368	0.1076
Brazil	0.0265	0.0051	0.1931	0.0123	0.0318
British Virgin Islands	12.7073	1.7650	0.1389	6.4440	14.8197
Bulgaria	1.0729	0.3448	0.3213	0.6024	1.7994
Burkina Faso	0.0132	0.0040	0.3000	0.0070	0.0203
Cabo Verde	0.6105	0.4121	0.6751	0.0725	1.3783
Cambodia	0.1616	0.1262	0.7808	0.0194	0.4010
Canada	1.0809	0.3381	0.3128	0.7174	1.6136
Cayman Islands	35.3578	4.1237	0.1166	28.7154	45.3200
China	0.0844	0.0227	0.2695	0.0385	0.1155
Colombia	0.0448	0.0247	0.5522	0.0161	0.0900
Comoros	0.0368	0.0104	0.2828	0.0168	0.0530
Costa Rica	0.4676	0.1378	0.2948	0.2588	0.6669
Croatia	10.2972	3.1534	0.3062	3.4848	14.7644
Cuba	0.2196	0.0946	0.4308	0.0684	0.4156
Curacao	4.9119	1.6619	0.3383	2.6451	8.2126
Cyprus	2.6050	0.3552	0.1364	2.1583	3.4349
Dominica	4.9402	1.5633	0.3164	2.7783	8.5818
Dominican Republic	0.4623	0.1327	0.2870	0.2310	0.7105
Ecuador	0.0718	0.0284	0.3950	0.0384	0.1484
Egypt	0.1012	0.0359	0.3551	0.0503	0.1780
Ethiopia	0.0046	0.0025	0.5473	0.0018	0.0088
Finland	0.5566	0.1152	0.2070	0.3364	0.7806
Gambia	0.1013	0.0691	0.6826	0.0399	0.2637
Georgia	0.6297	0.6872	1.0912	0.0182	2.0768
Germany	0.3065	0.0982	0.3203	0.1818	0.4761
Grenada	3.7165	0.5781	0.1556	2.6149	4.7466
Guam	8.0691	1.0561	0.1309	5.7696	9.9644
Guatemala	0.0962	0.0294	0.3057	0.0494	0.1542
Guyana	0.1981	0.0853	0.4303	0.0876	0.4024
Haiti	0.0754	0.0256	0.3390	0.0426	0.1198
Hong Kong	4.5649	2.5644	0.5618	1.5526	8.7435
Hungary	4.0805	0.9361	0.2294	2.8135	6.2835
Iceland	2.4311	1.9612	0.8067	0.7889	7.0537
India	0.0053	0.0037	0.6943	0.0022	0.0131
Indonesia	0.0309	0.0117	0.3781	0.0203	0.0595
Iran	0.0392	0.0258	0.6571	0.0074	0.1098
Ireland	1.7721	0.2349	0.1325	1.3351	2.2448
Italy	1.2005	0.1722	0.1434	0.9800	1.5972
Jamaica	1.0236	0.2426	0.2370	0.6915	1.4716
Japan	0.0838	0.0707	0.8439	0.0267	0.2525
Jordan	0.7566	0.2231	0.2949	0.4434	1.1124
Kenya	0.0346	0.0055	0.1583	0.0247	0.0469
Korea, republic	0.1715	0.0833	0.4859	0.0809	0.3385
Kuwait	1.4865	0.3991	0.2685	0.8986	2.0564
Lao PDR	0.3239	0.2206	0.6810	0.0714	0.6948
Latvia	2.1118	1.1993	0.5679	0.6571	4.3588
Lebanon	0.2397	0.0717	0.2990	0.1174	0.4377
Lesotho	0.2553	0.1678	0.6573	0.1101	0.5764
Liechtenstein	1.7930	0.2760	0.1539	1.4081	2.5802
Luxembourg	1.8318	0.1116	0.0609	1.5879	2.0048
Macao SA	38.8312	14.7419	0.3796	16.9645	61.5290
Malaysia	0.6603	0.2233	0.3382	0.2510	0.9187
Maldives	2.0599	0.5844	0.2837	1.2359	3.2074
Mali	0.0095	0.0019	0.1974	0.0044	0.0135
Malta	4.3684	1.1005	0.2519	2.9560	6.9813
Mauritius	0.7231	0.2118	0.2929	0.3893	1.1310
Mexico	0.8532	0.1320	0.1547	0.6544	1.0685
Moldova	0.0241	0.0171	0.7100	0.0048	0.0653
Monaco	8.4684	0.7123	0.0841	7.0903	9.5006
Mongolia	0.1363	0.0601	0.4409	0.0306	0.2263
Morocco	0.2304	0.0834	0.3621	0.1019	0.3594
Myanmar	0.0271	0.0255	0.9414	0.0044	0.0889
Namibia	0.5017	0.1166	0.2324	0.2586	0.6694
Nepal	0.0224	0.0083	0.3708	0.0111	0.0418
Netherlands	0.6970	0.1921	0.2757	0.4237	1.1605
New Calendonia	1.2052	0.5951	0.4938	0.6187	2.3204
New Zealand	0.5687	0.1207	0.2123	0.3836	0.7873
Nicaragua	0.1656	0.0602	0.3633	0.0733	0.3067
Niger	0.0053	0.0015	0.2916	0.0032	0.0082
North Mariana Islands	0.1462	0.0902	0.6169	0.0487	0.3650
Northern Macedonia	9.0650	2.4162	0.2665	6.3133	15.4889
Norway	0.8663	0.1683	0.1942	0.6134	1.1848
Palau	4.8793	1.7803	0.3649	2.7849	9.1707
Panama	0.3948	0.1725	0.4369	0.1522	0.6433
Paraguay	0.9007	0.7618	0.8458	0.4518	3.2821
Philippines	0.0385	0.0149	0.3875	0.0226	0.0764
Poland	1.8888	0.3350	0.1773	1.3271	2.3315
Portugal	1.0345	0.2851	0.2756	0.6093	1.6696
Puerto Rico	1.2605	0.1296	0.1028	1.1035	1.5440
Romania	0.3561	0.1298	0.3645	0.2146	0.6615
Russia	0.1585	0.0362	0.2281	0.0694	0.2341
San Marino	83.6523	27.2702	0.3260	55.4700	129.9132
Seychelles	2.3056	0.8720	0.3782	1.5277	4.3841
Singapore	2.2996	0.5338	0.2321	1.4890	3.3516
Sint Maarten	50.2347	10.0527	0.2001	32.5126	66.3925
Slovenia	0.9985	0.5335	0.5343	0.3679	2.2515
South Africa	0.1901	0.0570	0.3000	0.1130	0.2690
Spain	2.0570	0.3567	0.1734	1.3206	2.6769
Sri Lanka	0.0478	0.0318	0.6645	0.0172	0.1163
St. Kitts & Nevis	11.2583	6.4019	0.5686	4.0497	24.3716
St. Lucia	4.8845	0.9806	0.2007	2.7711	6.6741
St. Vincent & Grenadines	2.3044	0.4594	0.1994	1.8412	3.5445
Sweden	0.6092	0.2960	0.4858	0.2617	1.2997
Tanzania	0.0183	0.0046	0.2532	0.0099	0.0267
Thailand	0.2650	0.1456	0.5495	0.1169	0.5733
Togo	0.0299	0.0241	0.8080	0.0112	0.1084
Tonga	0.5736	0.1693	0.2952	0.3001	0.8995
Trinidad & Tobago	0.3533	0.0468	0.1324	0.2248	0.4100
Tunisia	0.5891	0.1043	0.1770	0.4192	0.8063
Turkey	0.3481	0.1630	0.4681	0.1202	0.6202
Ukraine	0.3636	0.1442	0.3965	0.1189	0.6232
United Kingdom	0.4958	0.0702	0.1417	0.3863	0.6219
United States	0.4205	0.1467	0.3488	0.2140	0.6139
Uruguay	0.7717	0.2175	0.2819	0.4071	1.2277
Uzbekistan	0.0461	0.0468	1.0155	0.0040	0.2010
Vanuatu	0.8235	0.3132	0.3803	0.4382	1.3911
Vietnam	0.0612	0.0457	0.7460	0.0180	0.1867
Virgin Islands	21.8223	2.8711	0.1316	16.1476	26.0841
Zambia	0.0522	0.0137	0.2619	0.0179	0.0717
Zimbabwe	0.1615	0.0238	0.1473	0.1146	0.2045

Note: STD denotes the standard deviation. CV is the ratio of STD over the mean. Min and Max are the minimum and maximum values of per capita tourist arrivals in each country.

Empirical results and discussion

To begin with, we evaluate the results using the Lagrange Multiplier (LM) unit root tests of Schmidt and Phillips (1992), without either structural breaks or cross-correlations. Also, to determine the net effects of cross-correlations and breaks, we consider the LM tests without breaks but with a factor structure, as well as the LM tests with breaks but without a factor structure. Table 3 presents the summary of these test results.

Table 3.

Results of the benchmark tests.

Countries	No break No factor			No break With factor			Dummy trend breaks No factor
	Schmidt & Phillips (1992)			New test			Lee & Strazicich (2003b)
	LM	pval	lag	PANIC-LM	pval	lag	LM	pval	brk1	brk2
Albania	−0.48	1.00	1	−1.08	1.00	1	−13.61 ^a	0.00	2006	2010
Algeria	−2.47	0.18	1	−0.60	1.00	4	−9.37 ^a	0.00	2004	2013
Angola	−1.59	0.67	1	−1.30	0.81	0	−7.98 ^a	0.00	2003	2010
Antigua & Barbuda	1.70	1.00	0	−1.64	0.81	3	−5.55 ^b	0.03	2005	2012
Argentina	1.62	1.00	0	−1.75	0.52	0	−22.91 ^a	0.00	2007	2015
Armenia	−0.69	1.00	1	−0.77	0.99	5	−6.00 ^b	0.02	2006	2013
Aruba	−0.71	1.00	0	−2.62	0.12	0	−7.14 ^a	0.00	2003	2012
Australia	−1.81	0.52	1	−1.00	0.96	0	−6.43 ^a	0.01	2006	2009
Austria	1.11	1.00	0	−0.45	1.00	5	−6.55 ^a	0.01	2006	2012
Azerbaijan	−2.85 ^c	0.09	1	−1.82	0.47	0	−7.31 ^a	0.00	2007	2012
Bahamas	−2.44	0.19	1	−1.48	0.88	2	−6.96 ^a	0.00	2004	2008
Bahrain	3.22	1.00	0	−3.85 ^a	0.01	0	−16.91 ^a	0.00	2008	2014
Bangladesh	−0.41	1.00	0	−1.63	0.60	0	−10.17 ^a	0.00	2005	2010
Barbados	2.56	1.00	0	−1.62	0.60	0	−6.78 ^a	0.00	2003	2008
Belgium	0.66	1.00	0	−1.80	0.71	2	−9.07 ^a	0.00	2002	2013
Belize	−2.85 ^c	0.09	1	−1.96	0.61	1	−7.65 ^a	0.00	2003	2014
Bermuda	−2.72	0.12	1	−1.43	0.73	0	−11.41 ^a	0.00	2003	2013
Bhutan	−0.80	0.99	1	−1.29	0.94	5	−10.81 ^a	0.00	2006	2014
Bolivia	0.12	1.00	0	−0.27	1.00	5	−8.55 ^a	0.00	2006	2014
Brazil	1.97	1.00	0	−1.42	0.74	0	−9.54 ^a	0.00	2004	2013
British Virgin Islands	−3.70 ^a	0.01	1	−2.58	0.13	0	−10.60 ^a	0.00	2007	2015
Bulgaria	0.06	1.00	0	−1.80	0.49	0	−5.79 ^b	0.02	2003	2011
Burkina Faso	0.25	1.00	0	−1.35	0.78	0	−12.79 ^a	0.00	2004	2010
Cabo Verde	−2.58	0.15	1	−1.91	0.68	5	−6.92 ^a	0.00	2004	2010
Cambodia	−1.06	0.95	1	−1.09	1.00	1	−5.15 ^b	0.05	2002	2006
Canada	−1.68	0.61	1	−3.47 ^c	0.08	4	−5.91 ^a	0.01	2005	2013
Cayman Islands	0.52	1.00	0	−1.85	0.45	0	−9.50 ^a	0.00	2003	2011
China	3.33	1.00	0	−1.45	0.90	2	−10.87 ^a	0.00	2002	2009
Colombia	−0.08	1.00	0	−2.59	0.12	0	−8.02 ^a	0.00	2003	2013
Comoros	−1.18	0.94	0	−1.16	0.90	0	−9.89 ^a	0.00	2004	2011
Costa Rica	4.53	1.00	0	−2.82 ^c	0.08	0	−10.41 ^a	0.00	2005	2012
Croatia	−1.37	0.82	1	−1.90	0.64	1	−15.30 ^a	0.00	2006	2013
Cuba	−3.09 ^c	0.06	1	−3.13	0.16	5	−8.41 ^a	0.00	2007	2014
Curacao	−4.42 ^a	0.00	1	−0.62	1.00	3	−6.63 ^a	0.01	2010	2013
Cyprus	−2.13	0.32	1	−3.15	0.15	5	−9.45 ^a	0.00	2004	2010
Dominica	1.34	1.00	0	−1.82	0.48	0	−5.11 ^b	0.05	2004	2011
Dominican Republic	−2.17	0.31	1	−2.35	0.40	3	−8.43 ^a	0.00	2002	2007
Ecuador	−0.71	1.00	0	−0.61	1.00	3	−15.92 ^a	0.00	2010	2015
Egypt	1.22	1.00	0	−2.82	0.23	5	−9.99 ^a	0.00	2009	2013
Ethiopia	−1.42	0.79	1	−1.39	0.91	1	−7.10 ^a	0.00	2004	2012
Finland	1.85	1.00	0	−1.71	0.54	0	−15.19 ^a	0.00	2002	2010
Gambia	−0.41	1.00	0	−2.20	0.50	4	−12.49 ^a	0.00	2009	2012
Georgia	−1.46	0.77	1	−2.14	0.56	5	−20.44 ^a	0.00	2004	2009
Germany	2.37	1.00	0	−2.72	0.27	5	−9.03 ^a	0.00	2006	2012
Grenada	−2.80 ^c	0.10	1	−2.87	0.19	1	−10.11 ^a	0.00	2003	2009
Guam	−1.55	0.73	0	−2.23	0.51	5	−8.06 ^a	0.00	2009	2013
Guatemala	0.83	1.00	0	−1.70	0.55	0	−8.69 ^a	0.00	2006	2012
Guyana	−0.12	1.00	0	−0.72	0.99	5	−5.29 ^b	0.04	2002	2012
Haiti	1.47	1.00	0	−2.43	0.18	0	−5.55 ^b	0.03	2003	2015
Hong Kong	2.14	1.00	0	−1.96	0.61	1	−5.95 ^a	0.01	2010	2015
Hungary	−0.97	0.97	1	−0.04	1.00	4	−9.30 ^a	0.00	2009	2013
Iceland	−4.57 ^a	0.00	1	−2.48	0.33	2	−26.51 ^a	0.00	2009	2014
India	0.09	1.00	0	−1.82	0.72	5	−24.90 ^a	0.00	2002	2011
Indonesia	−1.75	0.56	1	−0.88	0.99	5	−6.20 ^a	0.01	2004	2014
Iran	−2.05	0.37	1	−1.10	0.98	5	−26.12 ^a	0.00	2005	2015
Ireland	−1.99	0.41	1	−1.66	0.80	1	−7.63 ^a	0.00	2006	2015
Italy	−2.06	0.36	1	−4.44 ^b	0.02	5	−7.15 ^a	0.00	2003	2011
Jamaica	0.88	1.00	0	−2.73 ^c	0.10	0	−6.35 ^a	0.01	2007	2013
Japan	−1.67	0.62	1	−0.61	1.00	4	−20.40 ^a	0.00	2003	2008
Jordan	0.44	1.00	0	−1.73	0.76	2	−5.21 ^b	0.04	2004	2010
Kenya	−0.85	1.00	0	−0.20	1.00	5	−9.98 ^a	0.00	2005	2012
Korea, republic	−1.30	0.86	1	−0.99	0.99	5	−14.84 ^a	0.00	2008	2014
Kuwait	−1.74	0.57	1	−4.24 ^b	0.03	5	−9.90 ^a	0.00	2009	2015
Lao PDR	1.74	1.00	0	−4.72 ^a	0.01	5	−7.21 ^a	0.00	2005	2010
Latvia	0.48	1.00	0	−2.20	0.26	0	−6.67 ^a	0.01	2003	2009
Lebanon	−3.26 ^b	0.04	1	−1.87	0.66	1	−10.45 ^a	0.00	2003	2011
Lesotho	−0.09	1.00	0	−3.05	0.17	5	−21.08 ^a	0.00	2004	2011
Liechtenstein	−2.17	0.31	1	−1.60	0.62	0	−9.40 ^a	0.00	2004	2012
Luxembourg	1.22	1.00	0	−3.58 ^c	0.06	3	−7.33 ^a	0.00	2007	2014
Macao SA	1.26	1.00	0	−1.75	0.75	3	−6.08 ^a	0.01	2005	2012
Malaysia	2.10	1.00	0	−1.26	0.84	0	−10.11 ^a	0.00	2003	2012
Maldives	−0.88	1.00	0	−2.77 ^c	0.09	0	−10.10 ^a	0.00	2002	2008
Mali	1.53	1.00	0	−1.76	0.74	3	−6.30 ^a	0.01	2002	2015
Malta	0.65	1.00	0	−1.58	0.63	0	−10.14 ^a	0.00	2006	2015
Mauritius	2.38	1.00	0	−1.66	0.80	4	−8.66 ^a	0.00	2006	2015
Mexico	−0.92	1.00	0	−4.06 ^b	0.03	2	−10.48 ^a	0.00	2005	2010
Moldova	−1.82	0.51	1	−2.63	0.28	4	−6.46 ^a	0.01	2003	2011
Monaco	−2.94 ^c	0.07	1	−1.46	0.71	0	−8.99 ^a	0.00	2003	2011
Mongolia	2.40	1.00	0	−1.64	0.59	0	−10.36 ^a	0.00	2005	2011
Morocco	5.24	1.00	0	−1.78	0.51	0	−5.33 ^b	0.04	2002	2006
Myanmar	−0.69	1.00	0	−1.91	0.66	4	−46.88 ^a	0.00	2010	2013
Namibia	−1.76	0.55	1	−1.67	0.80	2	−10.23 ^a	0.00	2004	2009
Nepal	−0.75	1.00	0	−1.91	0.65	3	−8.71 ^a	0.00	2004	2012
Netherlands	−1.67	0.62	1	−1.56	0.84	1	−6.87 ^a	0.00	2005	2014
New Calendonia	−1.88	0.48	1	−2.64	0.30	5	−9.69 ^a	0.00	2007	2010
New Zealand	−2.31	0.24	1	−1.96	0.61	1	−7.10 ^a	0.00	2003	2009
Nicaragua	3.05	1.00	0	−3.34 ^b	0.02	0	−12.44 ^a	0.00	2003	2015
Niger	−1.50	0.76	0	−2.02	0.34	0	−5.60 ^b	0.02	2007	2015
North Mariana Islands	0.26	1.00	0	−1.33	0.80	0	−8.72 ^a	0.00	2007	2015
Northern Macedonia	−2.06	0.39	0	−1.56	0.64	0	−7.68 ^a	0.00	2005	2014
Norway	1.24	1.00	0	−3.79 ^b	0.05	1	−7.23 ^a	0.00	2003	2013
Palau	1.02	1.00	0	−2.04	0.61	5	−7.47 ^a	0.00	2005	2012
Panama	3.65	1.00	0	−2.50	0.34	4	−7.21 ^a	0.00	2004	2012
Paraguay	−0.69	1.00	1	−0.63	1.00	1	−12.42 ^a	0.00	2002	2012
Philippines	−1.42	0.79	1	0.46	1.00	5	−11.50 ^a	0.00	2009	2012
Poland	−2.42	0.20	1	−2.26	0.45	1	−20.51 ^a	0.00	2007	2012
Portugal	0.21	1.00	0	−2.07	0.60	5	−9.75 ^a	0.00	2004	2014
Puerto Rico	−0.46	1.00	0	−1.94	0.63	2	−6.54 ^a	0.01	2006	2015
Romania	−2.10	0.34	1	−3.66 ^c	0.07	5	−14.21 ^a	0.00	2003	2008
Russia	1.70	1.00	0	−3.78 ^b	0.05	2	−5.60 ^b	0.02	2006	2013
San Marino	−2.90 ^c	0.09	0	−2.11	0.30	0	−11.14 ^a	0.00	2002	2008
Seychelles	−1.09	0.95	1	−1.59	0.83	5	−6.02 ^b	0.02	2003	2014
Singapore	−0.98	1.00	0	−1.73	0.53	0	−6.82 ^a	0.00	2005	2008
Sint Maarten	1.85	1.00	0	−2.00	0.35	0	−9.50 ^a	0.00	2002	2007
Slovenia	−1.66	0.62	1	−0.99	0.96	0	−9.26 ^a	0.00	2006	2015
South Africa	2.75	1.00	0	−1.29	0.82	0	−8.11 ^a	0.00	2008	2013
Spain	−1.64	0.63	1	−2.49	0.33	3	−9.05 ^a	0.00	2002	2009
Sri Lanka	−1.97	0.41	1	−2.05	0.56	1	−9.62 ^a	0.00	2004	2015
St. Kitts & Nevis	0.70	1.00	0	−3.10 ^b	0.04	0	−8.37 ^a	0.00	2003	2012
St. Lucia	2.37	1.00	0	−1.25	0.85	0	−8.03 ^a	0.00	2003	2015
St. Vincent & Grenadines	−0.14	1.00	0	−2.46	0.34	3	−7.80 ^a	0.00	2002	2009
Sweden	1.46	1.00	0	−2.14	0.28	0	−13.97 ^s	0.00	2008	2013
Tanzania	2.19	1.00	0	−2.36	0.20	0	−8.10 ^s	0.00	2002	2011
Thailand	0.99	1.00	0	−2.12	0.57	5	−7.61 ^a	0.00	2008	2011
Togo	−0.51	1.00	0	−1.69	0.56	0	−10.48 ^a	0.00	2005	2009
Tonga	−0.67	1.00	0	−2.82 ^c	0.08	0	−5.59 ^b	0.02	2005	2010
Trinidad & Tobago	1.48	1.00	0	−1.48	0.88	3	−9.97 ^a	0.00	2005	2011
Tunisia	0.14	1.00	0	−2.72 ^c	0.10	0	−11.35 ^a	0.00	2008	2013
Turkey	0.83	1.00	0	−0.46	1.00	3	−20.92 ^a	0.00	2004	2013
Ukraine	1.49	1.00	0	−2.23	0.51	5	−11.65 ^a	0.00	2005	2011
United Kingdom	−2.95 ^c	0.07	1	−4.23 ^b	0.02	2	−6.07 ^a	0.01	2004	2007
United States	0.84	1.00	0	−1.90	0.42	0	−28.09 ^a	0.00	2003	2010
Uruguay	0.05	1.00	0	−1.99	0.36	0	−4.94 ^c	0.06	2006	2009
Uzbekistan	−2.80 ^c	0.10	1	−1.29	0.98	1	−6.97 ^a	0.00	2003	2013
Vanuatu	1.10	1.00	0	−2.16	0.52	4	−6.90 ^a	0.00	2007	2013
Vietnam	−1.36	0.83	1	−1.37	0.92	1	−9.47 ^a	0.00	2007	2012
Virgin Islands	1.91	1.00	0	−2.02	0.35	0	−8.45 ^a	0.00	2005	2014
Zambia	2.13	1.00	0	−1.41	0.74	0	−6.78 ^a	0.00	2002	2009
Zimbabwe	2.15	1.00	0	−0.78	0.99	5	−8.05 ^a	0.00	2005	2009
# rejections		12			18			129
# factors		n/a			5			n/a

Note: Total counts show the number of rejections at least the 10% significance level. The p-values are obtained from the response surface estimates provided in Nazlioglu and Lee (2020). The maximum number of lags is set to 5, and the number of augmented lags k is determined by the general-to-specific approach based on the statistical significance of the lagged dependent variate at the 10% level of significance. The number of factors is estimated based on the panel information criterion (ICp) of Bai and Ng (2002) using a maximum of 5 factors. The Gauss codes for finding the critical values and computing the p-values are provided at the website: https://sites.google.com/site/junsoolee/codes. Significance levels: 1%(a), 5%(b), and 10%(c) and denoted in boldface type.

With respect to the Schmidt and Phillips (1992) unit root tests without structural breaks or cross-correlations shown in Table 3, we find that at least the 10% significance level only 12 of the 129 countries (Azerbaijan, Belize, British Virgin Islands, Cuba, Curacao, Genada, Iceland, Lebanon, Monaco, San Marino, United Kingdom, and Uzbekistan) reject the null hypothesis of a unit root. Thus, we find little evidence of stationarity in per capita tourist arrivals when there is no allowance for either structural breaks or cross-correlations.

Given the results from the Schmidt and Phillips (1992) unit root test, we next allow for a factor structure following Bai and Ng (2004) in the use of principal component analysis (PCA) to examine the degree of comovements among per capita tourist arrivals. We find that the first principal component (PC) explains about 93.3% of the variation of all per capita tourist arrivals in the global panel, while the second PC accounts for 6.1%. This principal component analysis explains a relatively high degree of comovement.

With the introduction of a factor structure through the new PANIC-LM unit root test, the number of rejections at least the 10% significance level increased to 18 of the 129 countries (Bahrain, Canada, Costa Rica, Italy, Jamaica, Kuwait, Lao PDR, Luxembourg, Maldives, Mexico, Nicaragua, Norway, Romania, Russia, St. Kitts & Nevis, Tonga, Tunisia, and United Kingdom). However, when we employ the Lee and Strazicich (2003b) LM unit root tests with two trend structural breaks without a factor structure, the null hypothesis is rejected at least the 10% significance level for all 129 countries. Though some of the structural breaks may be more country-specific in origin, a vast majority of the structural break dates coincide with the 2002–2004 SARS epidemic originating in Asia along with the onset and subsequent recovery from the global financial crisis.

Next, we formally examine the results from the new LM unit root tests, which incorporate the PANIC common factor structure into the Lee and Strazicich (2003b) unit root tests with two-level and two-trend structural break models, respectively as displayed in Table 4. The null hypothesis of a unit root is rejected at least the 10% significance level for 30 countries based on the level break tests and 13 countries for the trend break tests. Thus, the null hypothesis of a unit root is rejected far less than the Lee and Strazicich (2003b) unit root tests with breaks and without allowance for cross-correlations.

Table 4.

Test results with breaks and factors.

Countries	Dummy breaks, with factor								Smooth breaks, with factor
	Two level breaks				Two trend breaks				Fourier (m = estimated)
	LM	pval	brk1	brk2	LM	pval	brk1	brk2	LM	pval	m	lag
Albania	−8.99 ^a	0.00	2009	2012	−3.69	0.23	2007	2012	−2.42	1.00	3	2
Algeria	−0.75	1.00	2006	2010	−1.79	0.61	2002	2012	−4.71	0.37	3	0
Angola	−2.96 ^b	0.05	2005	2012	−3.64	0.34	2005	2012	−2.14	0.96	1	5
Antigua & Barbuda	−1.00	0.98	2007	2009	−4.61	0.13	2003	2009	−4.33	0.66	3	3
Argentina	−1.08	0.76	2006	2009	−0.56	0.83	2003	2009	−2.67	0.26	0	3
Armenia	−2.60 ^c	0.10	2006	2011	−2.78	0.63	2003	2011	−5.08	0.32	3	5
Aruba	−0.78	0.85	2002	2012	−2.31	0.50	2002	2012	−3.16	1.00	3	2
Australia	−1.72	0.60	2002	2008	−3.53	0.26	2003	2011	−4.56	0.50	3	5
Austria	−0.42	0.96	2008	2011	5.74	1.00	2005	2008	−1.00	1.00	2	5
Azerbaijan	−2.76 ^c	0.09	2004	2007	−3.73	0.29	2003	2007	−3.49	0.94	3	5
Bahamas	0.00	1.00	2004	2007	−1.70	0.63	2003	2008	−4.27	0.65	3	5
Bahrain	−1.88	0.50	2002	2010	1.70	0.99	2007	2010	−3.48	0.98	3	2
Bangladesh	−2.59 ^c	0.09	2004	2008	−1.52	0.66	2007	2010	−4.18	0.69	3	4
Barbados	2.40	1.00	2003	2006	−2.86	0.66	2003	2006	−9.93 ^a	0.00	0	4
Belgium	−1.89	0.37	2002	2008	−24.4 ^a	0.00	2002	2008	−2.51	1.00	3	1
Belize	−2.82 ^c	0.10	2002	2004	−0.82	0.79	2003	2006	−3.13	0.14	0	4
Bermuda	0.14	0.97	2005	2007	2.44	1.00	2004	2007	−3.16 ^b	0.03	0	0
Bhutan	−4.46 ^a	0.00	2008	2011	−0.99	0.76	2008	2012	−0.87	1.00	2	5
Bolivia	0.57	1.00	2002	2008	−2.33	0.87	2002	2012	−4.46	0.55	3	5
Brazil	−3.49 ^b	0.02	2005	2008	−1.86	0.59	2004	2009	−4.18	0.75	3	2
British Virgin Islands	−3.51 ^b	0.02	2004	2008	−4.03	0.21	2006	2009	−4.93	0.37	3	5
Bulgaria	0.62	0.99	2003	2008	0.71	0.96	2002	2008	−2.40	0.95	1	2
Burkina Faso	−2.05	0.26	2003	2010	−11.9 ^a	0.00	2003	2007	−3.48	0.57	1	2
Cabo Verde	−2.01	0.41	2008	2010	−3.36	0.29	2004	2010	−5.51	0.14	3	0
Cambodia	2.29	1.00	2002	2011	−2.18	0.68	2003	2011	−3.10	0.96	3	0
Canada	−3.02 ^b	0.04	2002	2005	−0.89	0.78	2002	2008	−1.64	0.59	0	0
Cayman Islands	−2.03	0.40	2003	2006	−4.39	0.14	2003	2010	−1.76	0.75	0	4
China	−1.77	0.40	2003	2012	−3.12	0.33	2002	2005	−0.77	1.00	3	4
Colombia	0.22	0.99	2005	2009	−1.25	0.88	2005	2009	−2.20	1.00	2	3
Comoros	0.24	0.98	2006	2008	−3.19	0.32	2006	2009	−4.93	0.42	3	2
Costa Rica	−0.77	0.85	2003	2008	0.58	0.95	2002	2008	−3.58	0.95	3	3
Croatia	−1.28	0.74	2008	2011	−4.83	0.11	2007	2012	−3.97	0.69	3	0
Cuba	−2.42	0.13	2005	2012	−5.74 ^b	0.04	2004	2007	−3.50	0.94	3	5
Curacao	−1.76	0.44	2003	2009	−4.66 ^c	0.10	2003	2009	−5.20	0.22	3	0
Cyprus	−2.47	0.12	2002	2008	−3.05	0.34	2008	2012	−1.59	1.00	3	5
Dominica	−2.23	0.30	2003	2010	−3.75	0.30	2003	2010	−3.84	0.39	2	0
Dominican Republic	−6.14 ^a	0.00	2002	2008	0.36	0.93	2002	2012	−5.58	0.20	3	5
Ecuador	−1.25	0.89	2005	2008	−1.96	0.57	2007	2011	−2.19	1.00	3	5
Egypt	−1.87	0.50	2006	2010	−2.13	0.53	2002	2010	−5.46	0.23	3	5
Ethiopia	−3.41 ^b	0.02	2005	2008	−2.77	0.40	2005	2012	−9.53 ^a	0.01	3	5
Finland	−0.95	0.95	2002	2012	3.96	1.00	2008	2012	−3.50	0.94	3	5
Gambia	−2.02	0.27	2007	2009	−4.18	0.17	2006	2009	−4.54	0.51	3	5
Georgia	−4.96 ^a	0.00	2002	2011	−7.82 ^a	0.01	2008	2011	−2.53	1.00	3	4
Germany	−2.08	0.25	2005	2008	−3.34	0.29	2002	2008	−3.17	1.00	3	2
Grenada	−2.39	0.23	2005	2011	−4.25	0.16	2003	2011	−5.15	0.30	3	5
Guam	−0.98	0.79	2003	2011	−1.88	0.76	2003	2008	−1.22	1.00	3	1
Guatemala	−1.46	0.77	2003	2008	−1.14	0.90	2003	2008	−4.69 ^a	0.01	0	2
Guyana	0.80	1.00	2002	2006	−1.59	0.65	2003	2010	−2.25	0.99	2	0
Haiti	−0.96	0.99	2003	2006	−0.82	1.00	2003	2006	−6.16	0.12	3	4
Hong Kong	−2.41	0.20	2003	2011	−3.89	0.23	2003	2012	−5.75 ^c	0.07	2	2
Hungary	−1.08	0.76	2004	2011	−2.78	0.39	2002	2012	−4.10	0.72	2	4
Iceland	−2.88 ^b	0.05	2009	2011	−0.09	0.98	2002	2010	−6.04 ^a	0.00	0	4
India	−0.51	1.00	2005	2009	−0.93	0.77	2002	2012	−2.71	0.99	3	5
Indonesia	1.72	1.00	2002	2004	−1.53	0.66	2002	2011	−0.25	1.00	0	0
Iran	−3.09 ^b	0.04	2006	2009	−3.56	0.26	2005	2008	−4.41	0.57	3	5
Ireland	−3.42 ^b	0.02	2008	2012	−3.86	0.21	2008	2012	−3.94	0.83	3	3
Italy	−1.24	0.89	2003	2005	−4.22	0.16	2003	2012	−4.24 ^b	0.03	0	5
Jamaica	−1.55	0.58	2002	2005	−2.27	0.50	2005	2010	−3.82 ^a	0.01	0	0
Japan	−11.3	0.00	2008	2010	−5.94 ^b	0.04	2003	2010	−3.73	0.45	1	4
Jordan	−2.13	0.35	2003	2010	−0.02	0.90	2003	2010	−4.33	0.57	2	4
Kenya	−4.44 ^a	0.00	2007	2012	−9.17 ^a	0.00	2002	2007	−2.34	0.21	0	0
Korea, republic	0.05	1.00	2002	2005	−3.46	0.39	2003	2006	−3.18	0.97	3	5
Kuwait	−1.76	0.45	2003	2006	−3.69	0.23	2002	2007	−4.28	0.73	2	5
Lao PDR	−0.42	0.91	2009	2011	−3.05	0.34	2002	2012	−1.09	1.00	3	4
Latvia	−0.55	1.00	2005	2008	−0.74	0.80	2002	2008	−3.66	0.95	2	4
Lebanon	−3.36 ^b	0.03	2008	2010	−3.94	0.24	2006	2010	−3.29	0.93	3	0
Lesotho	−2.91 ^b	0.05	2003	2009	−1.78	0.78	2007	2010	−5.10	0.32	3	5
Liechten	−0.42	1.00	2006	2008	−2.41	0.62	2006	2012	−2.22	0.47	0	2
Luxembourg	−1.77	0.40	2007	2010	−2.88	0.37	2007	2010	−3.09	1.00	3	2
Macao SA	−1.41	0.80	2003	2007	−0.15	0.88	2003	2007	−0.88	0.98	0	0
Malaysia	0.96	1.00	2003	2006	−7.66 ^a	0.01	2003	2008	−3.62	0.92	3	5
Maldives	−2.46	0.20	2004	2008	−1.23	0.72	2004	2007	−2.85	0.20	0	3
Mali	−3.14	0.04	2008	2011	−1.82	0.77	2008	2011	−4.76	0.44	3	4
Malta	−1.07	0.94	2003	2008	−2.41	0.47	2003	2008	−2.44	1.00	3	5
Mauritius	−0.39	0.92	2006	2008	−2.63	0.43	2005	2008	−11.7 ^a	0.00	3	5
Mexico	−1.29	0.87	2002	2010	−0.69	0.81	2004	2010	−6.25 ^c	0.10	3	5
Moldova	0.17	1.00	2003	2008	−2.73	0.71	2003	2008	−2.41	0.42	0	5
Monaco	−0.96	0.80	2002	2008	−2.67	0.54	2002	2008	−4.80	0.47	3	2
Mongolia	4.14	1.00	2003	2012	−2.20	0.52	2003	2012	−4.20	0.74	3	2
Morocco	−1.42	0.61	2006	2009	−2.79	0.39	2002	2010	−2.54	1.00	2	3
Myanmar	1.89	1.00	2007	2012	−3.86	0.21	2002	2012	−1.78	1.00	3	3
Namibia	−6.17 ^a	0.00	2003	2005	−0.31	0.86	2003	2006	−3.16	1.00	3	2
Nepal	−1.97	0.33	2006	2010	0.21	0.92	2002	2007	−3.90	0.72	3	0
Netherlands	−2.65	0.12	2002	2007	1.55	1.00	2007	2012	−4.69	0.50	3	3
New Caledonia	−0.54	0.90	2010	2012	−6.77 ^a	0.01	2008	2012	−3.79 ^b	0.05	0	3
New Zealand	−3.21 ^b	0.04	2003	2011	0.88	0.97	2003	2011	−5.40 ^b	0.02	1	5
Nicaragua	−3.23 ^b	0.04	2005	2009	−3.24	0.48	2002	2007	−3.10	0.96	3	0
Niger	−0.59	0.99	2007	2012	0.07	0.91	2007	2012	−4.39	0.63	3	3
North Mariana Islands	−1.70	0.43	2008	2012	−0.94	0.77	2004	2009	−5.90	0.17	3	2
Northern Macedonia	−1.15	0.73	2003	2011	0.95	0.97	2003	2011	−4.33	0.56	2	3
Norway	−4.23 ^a	0.00	2003	2011	−0.88	0.78	2008	2011	−2.55	0.99	3	5
Palau	−1.44	0.78	2003	2010	−3.42	0.28	2003	2010	−5.30	0.28	3	4
Panama	−1.74	0.59	2006	2010	−1.69	0.63	2006	2010	−7.29 ^b	0.04	3	4
Paraguay	−0.97	0.80	2005	2012	−0.30	0.98	2002	2006	−4.65 ^a	0.01	0	3
Philippines	2.25	1.00	2002	2008	−2.09	0.92	2003	2008	−5.67 ^a	0.01	1	5
Poland	−1.72	0.42	2008	2011	0.95	0.97	2003	2008	−3.41	0.99	3	1
Portugal	−1.96	0.30	2003	2006	−0.80	0.79	2006	2011	−4.66	0.34	2	3
Puerto Rico	−2.15	0.34	2003	2008	−0.20	0.87	2008	2012	−7.85 ^b	0.03	3	4
Romania	0.03	1.00	2006	2008	−0.11	0.89	2005	2008	−5.84 ^a	0.00	0	5
Russia	−1.67	0.63	2008	2012	−1.27	0.88	2002	2012	−5.51 ^a	0.00	0	3
San Marino	−0.75	1.00	2002	2004	−3.77	0.28	2004	2011	−0.21	1.00	3	0
Seychell	−0.67	1.00	2002	2007	−3.76	0.22	2003	2012	−3.21	0.67	1	5
Singapor	−0.99	0.98	2003	2010	−3.72	0.29	2003	2009	−2.81	0.99	3	0
Sint Maarten	−0.27	0.93	2003	2009	−4.22	0.16	2008	2011	1.01	1.00	0	0
Slovenia	−0.41	1.00	2004	2008	−6.36 ^b	0.03	2008	2012	−3.06	0.75	1	5
South Africa	−2.03	0.40	2005	2009	−1.11	0.90	2009	2012	−3.89	0.90	3	2
Spain	−2.20	0.29	2008	2011	0.40	0.94	2005	2008	−3.95	0.82	3	3
Sri Lanka	−0.52	1.00	2010	2012	0.29	0.93	2008	2012	−3.74	0.93	2	2
St. Kitts & Nevis	−1.84	0.52	2003	2007	−2.65	0.42	2003	2007	−2.92	1.00	3	2
St. Lucia	−1.19	0.90	2003	2006	−1.96	0.57	2003	2006	−2.14	1.00	3	0
St. Vincent & Grenadines	−1.90	0.33	2007	2009	−7.96 ^a	0.01	2007	2012	−2.31	0.22	0	0
Sweden	0.14	1.00	2010	2012	−0.73	0.80	2007	2010	−2.63	0.99	3	5
Tanzania	−1.49	0.62	2008	2011	−1.25	0.72	2008	2011	−4.24	0.57	3	0
Thailand	−8.88 ^a	0.00	2010	2012	−1.48	0.95	2008	2012	−2.55	0.99	3	5
Togo	−4.40 ^a	0.00	2007	2011	−5.81 ^b	0.05	2007	2011	−3.72 ^b	0.05	0	2
Tonga	−3.21 ^b	0.03	2005	2011	0.21	1.00	2006	2011	−3.38	0.90	3	0
Trinidad &Tobago	0.47	0.99	2007	2009	0.90	0.97	2007	2012	−2.16	1.00	3	3
Tunisia	−1.91	0.32	2003	2010	−2.31	0.49	2003	2010	−4.59	0.41	3	0
Turkey	−5.64 ^a	0.00	2006	2008	−1.58	0.65	2002	2009	−4.44	0.56	3	5
Ukraine	−13.2 ^a	0.00	2006	2008	−3.69	0.23	2008	2011	−3.50	0.98	3	2
United Kingdom	0.21	0.97	2003	2005	−4.40	0.14	2002	2006	−4.52	0.59	3	2
United States	−2.20	0.31	2005	2011	−2.32	0.64	2005	2011	−6.24 ^c	0.10	3	5
Uruguay	−2.21	0.30	2007	2010	−0.20	0.88	2003	2010	−4.60	0.41	3	0
Uzbekistan	−1.24	0.88	2002	2008	−0.23	0.98	2005	2009	−2.51	0.89	1	5
Vanuatu	−2.62 ^c	0.10	2007	2011	0.11	0.91	2004	2012	−2.92	0.99	3	4
Vietnam	−0.58	1.00	2002	2008	−2.35	0.49	2008	2012	−1.87	1.00	2	1
Virgin Islands	−1.40	0.62	2003	2009	−1.57	0.65	2008	2011	−3.37	0.98	3	3
Zambia	−1.52	0.72	2002	2008	−2.99	0.35	2002	2007	−9.68 ^a	0.00	0	5
Zimbabwe	−1.84	0.46	2005	2011	−5.85 ^b	0.05	2007	2011	−6.96 ^c	0.06	3	5
# rejections		30				13				22
# factors		5				5				5

See the footnote of Table 3.

Recognizing the possibility that structural breaks do not follow an abrupt change, but a gradual process, we utilize the Fourier function to investigate the global trend of per capita tourist arrivals. In Figure 1, we present the plot of the estimated global Fourier function. When the Fourier breaks are allowed, which models structural breaks as a gradual process along with a factor structure, the number of rejections is 22 of the 129 countries. We find that the inclusion of structural breaks and cross-correlations through the PANIC common structure within the new LM unit root test results in a much lower number of rejections of the null hypothesis of a unit root in per capita tourist arrivals. Thus, these findings are dramatically different from the Lee and Strazicich (2003b) unit root tests that allows for endogenous structural breaks and the absence of cross-correlations. Indeed, the incorporation of the PANIC common structure in the Lee and Strazicich (2003b) unit root test with endogenous structural breaks illustrates that the number of rejections of the null hypothesis is reduced considerably. In summary, the evidence of stationarity in per capita tourist arrivals is not as robust as standard unit root tests would suggest, as it likely that shocks to per capita tourist arrivals are more permanent in nature, thereby requiring an offsetting policy response to restore per capita tourist arrivals to their original trend.

Figure 1.

Plots of the estimated global Fourier function and the time means. Note: The smooth curve is the plot of the estimated global Fourier function of the per capita tourist arrivals. The red line depicts the time means of data in a given year.

Our results run counter in many respects to the previous studies using second-generation panel tests that incorporate cross-sectional dependence and/or structural breaks. The majority of the studies using second-generation panel unit root/stationarity tests by Lee et al. (2014), Yang et al. (2014), Solarin (2015), Dash et al. (2017), Xie et al. (2018), Kyophilavong et al. (2019), and Yucel (2021) provide support for the stationarity of tourist arrivals. Payne and Nazlioglu (2022) propose an alternative panel stationarity test that includes both structural breaks and common factors in the examination of per capita tourism expenditures and receipts to generally find non-stationarity of both tourism measures. Rather than use a panel stationarity test framework, as in Payne and Nazlioglu (2022), our analysis jointly estimates a Lagrange multiplier panel unit root test with allowance for structural changes that represent either abrupt breaks or as a Fourier approximation of smooth breaks along with introducing a factor structure to capture cross-sectional dependence. Second, unlike previous studies that test for structural breaks and cross-sectional dependence and find support for stationarity, our study reveals very limited support for stationarity in tourist arrivals. Third, our results reiterate the importance of simultaneously modeling both structural breaks and cross-correlations in per capita tourist arrivals across countries to ensure consistent estimation and validity of inferences drawn.

Concluding remarks

It has been well established, as evident from the COVID-19 pandemic, that the tourism and hospitality industry is susceptible to exogenous shocks and the subsequent negative impact of such shocks. The contribution of this study rests with the realization that shocks to tourist arrivals have repercussions with respect to the balance of payments for destination countries through foreign exchange earnings and tourism revenues. In response, our study extends the existing literature on testing the permanent or transitory nature of shocks to per capita tourist arrivals on several fronts. Unlike the majority of previous studies, our study scales tourist arrivals by the population of the tourist destination country to gauge the relative magnitude of the tourist flows. Second, our analysis serves as the largest multi-country study to date in the examination of a global panel of 129 countries. Finally, our study introduces new panel unit root tests that simultaneously model structural breaks (both sharp and smooth breaks) and a common factor structure. In this regard, the two break tests of Lee and Strazicich (2003b) and the Fourier approximation to capture smooth breaks of Enders and Lee (2012a, 2012b) are employed in tandem with the PANIC procedure of Bai and Ng (2004) in a factor structure to account for cross-correlations.

Our findings indicate that rejection of the null hypothesis of unit root is quite limited once cross-correlations are accounted for in a simultaneous fashion with structural breaks when compared to other unit root tests that fail to account for cross-correlations. This result is contrary to the majority of the previous studies that suggest tourist arrivals follow a stationary process. With the recent COVID-19 pandemic serving as a case in point, understanding the transmission of shocks in the tourism and hospitality sector is important in terms of modeling and forecasting of tourist flows and the possible need for policy intervention in the event shocks occur. Such policy discussions should also include the assessment of risk mitigation strategies, and for those countries heavily dependent on the tourism sector to explore avenues to diversify their economic base and export orientation in order to minimize the influence of adverse shocks impacting the tourism and hospitality sector and the overall economy.

Future research can extend the methodological approach of simultaneously modeling a common factor structure with structural breaks to test for unit root processes in other tourism indicators and over an expanded time horizon that incorporates the various phases of the COVID-19 pandemic.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

James E Payne

Notes

Author biographies

James E. Payne, PhD in Economics from Florida State University, serves as the Dean of the College of Business Administration at The University of Texas at El Paso and holds the Paul L. Foster and Alejandra de la Vega Foster Distinguished Chair in International Business. Dr. Payne has authored over 270 peer-reviewed journal articles and serves on the editorial board member for a number of academic journals.

Junsoo Lee, PhD in Economics from Michigan State University, serves as the William White McDonald Family Distinguished Faculty Fellow at The University of Alabama. Dr. Lee’s research interests include time series econometrics, non-linear models, and applied econometrics. His published articles include the Review of Economics and Statistics, International Economic Review, Econometric Theory, Journal of Applied Econometrics, Economics Letters, Journal of Money, Credit and Banking, Oxford Bulletin of Economics and Statistics, Journal of Time Series Analysis, Journal of Environmental Economics and Management, Journal of Health Economics, and Studies in Nonlinear Dynamics and Econometrics. Dr. Lee also serves as an Associate Editor for the Journal of Empirical Finance, Economic Modelling, and the Journal of Economics and Finance.

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Global perspective on the permanent or transitory nature of shocks to tourist arrivals: Evidence from new unit root tests with structural breaks and factors

Abstract

Keywords

Introduction

Literature review

Methodology and data

Empirical results and discussion

Concluding remarks

Footnotes

Declaration of conflicting interests

Funding

ORCID iD

Notes

Author biographies

References