*3.1. Specification Research Model*

From the literature review, this study hypothesizes that investment in tourism infrastructure such as transport and communication infrastructure, hotel and restaurant industry, and recreation facilities, will positively impact on attracting international visitors to Vietnam, while dummy variables indicate the temporary influence of special events. This relationship is shown by Equation (1) below.

$$VA\_{i,t} = f(TC\_{t\prime}HR\_{t\prime}EF\_{t\prime}Dum\_{i,t}) + \mathcal{U}\_{i,t} \tag{1}$$

where *VAi*,*<sup>t</sup>* is the visitor arrivals from source country *i* in year *t*; *TC<sup>t</sup>* is the capital invested in transport and communications infrastructure in year *t*; *HR<sup>t</sup>* is the capital invested in the hotel and restaurant industry in year *t*; *RF<sup>t</sup>* is the capital invested in recreation facilities in year *t*; *Dumi*,*<sup>t</sup>* are the dummy variables representing qualitative factors from source country *i* at time *t*; *Ui*,*<sup>t</sup>* is the disturbance term that captures all the other factors that may influence the number of visitor arrivals from source country *i* at time *t*.

The international visitor arrivals can be divided into several categories, i.e., "sightseeing tourists, business tourists and tourists of other types" (Tang 2020, p. 38) and there can be heterogeneity between them. However, because there are not enough specific data for these objects, heterogeneity between them is not considered.

This study uses regression analysis with a log-log model to estimate the impact of tourism infrastructure development investment on attracting international tourists to Vietnam. In fact, the log-log model is often used to estimate the parameters in order to evaluate the impact level of the independent variable on the dependent variable, because then the effect can be obtained directly from the coefficients (Witt and Witt 1995; Song et al. 2009). Furthermore, the natural logarithmic transformation also reduces data instability (Enders 2004; Studenmund 2006).

There are many techniques to estimate the coefficients of the factors affecting the number of visitors in order to fit the data. Initially, the ordinary least squares (OLS) technique was used commonly for both time series or panel data (such as in the study of Vanegas Sr and Croes 2000; Kulendran and Witt 2001; Lim 2004; Croes and Vanegas Sr 2005; Muñoz 2007). However, OLS regression requires the series to be stationary, otherwise it will lead to spurious regression (Granger and Newbold 1974). One of the technique considered to solve the non-stationary series problem is the cointegration test. The cointegration technique describes "the existence of an equilibrium, or stationary, relationship among two or more time-series, each of which is individually non-stationary" (Banerjee et al. 1994, p. 136). Furthermore, "cointegration techniques permit the estimation and testing of the long-run equilibrium relationships" (Lim and McAleer 2001, p. 1618; Dritsakis 2004, p. 118). Two common estimators for the technique are fully modified ordinary least squares (FMOLS) and dynamic ordinary least squares (DOLS). These estimators need to satisfy one fundamental assumption: the variables included in the models are all non-stationary at level, but stationary at first difference and cointegration of order 1. This technique has been applied in several studies which meet the qualifications (e.g., Dogru et al. 2017). However, these conditions are not always met. Moreover, according to Narayan and Narayan (2005, p. 429), "methods of cointegration are not reliable for small sample sizes". To overcome these limitations, Pesaran and Shin (1999) proposed an ARDL modeling approach. This method is superior regardless of whether the variables exhibit I(0), I(1), or a mixture of both. Song et al. (2003, p. 365) state that "one of the advantages of the general ARDL is that a modern econometric technique, known as error correction, can be readily incorporated into the modeling process". Given these advantages, the ARDL estimation technique has been widely used in recent studies (Song et al. 2003; Lee 2011; Otero-Gómez et al. 2015; Lin et al. 2015; Shafiullah et al. 2018; Kumar et al. 2020).

Based on the above analysis, the nonlinear panel ARDL approach is applied in this study. "Nonlinear ARDL model in panel form which is also a nonlinear representation of the dynamic heterogenous panel data model that is suitable for large T panels" (Salisu and Isah 2017, p. 261). The panel ARDL method also helps to estimate the long-run and short-run relationships for the general sample, as well as the short-run cross-sectional coefficients for each subject, even when the variables are non-stationary and/or show no cointegration. The nonlinear panel ARDL model used in this study is presented in the form of Equation (2) below:

The panel ARDL method also helps in estimation.

$$\begin{split} \Delta \ln \text{VA}\_{i,t} &= \mu\_{i} + \sum\_{\substack{j=1 \\ j=1}}^{q1} \theta\_{1ij} \Delta \ln \text{VA}\_{i,t-j} + \sum\_{j=0}^{q2} \theta\_{2ij} \Delta \ln \text{TC}\_{t-j} + \sum\_{j=0}^{q3} \theta\_{3ij} \ln \text{HR}\_{t-j} \\ &+ \sum\_{j=0}^{q4} \theta\_{4ij} \ln \text{RF}\_{t-j} + \varphi\_{oi} + \varphi\_{1i} \ln \text{VA}\_{i,t-1} + \varphi\_{2i} \ln \text{TC}\_{t-1} + \varphi\_{3i} \ln \text{HR}\_{t-1} \\ &+ \varphi\_{4i} \ln \text{RF}\_{t-1} + \sum\_{j=1}^{q3} \theta\_{1j} + \varepsilon\_{i,t} \\ &i = 1,2,\dots, \text{N}; \ t = 1,2,\dots, T \end{split} \tag{2}$$

where *µ<sup>i</sup>* is the group-specific effect; *i* is the source country; *t* is the number of periods (year); −1 < *ϕ*<sup>1</sup> < 0 is the error correction term's coefficient; *εi*,*<sup>t</sup>* is the error term; is the first difference operator; j is the lag order decided by the Akaike Information Criterion (AIC); ln is the natural logarithm. For each cross-section, the long-term slope (elasticity) of capital investment in transport and communications infrastructure, the hotel and restaurant industry, and recreation facilities is calculated as − *ϕ*2*<sup>i</sup> ϕ*1*<sup>i</sup>* , − *ϕ*3*<sup>i</sup> ϕ*1*<sup>i</sup>* ,− *ϕ*4*<sup>i</sup> ϕ*1*<sup>i</sup>* , respectively, and with the expectation of a positive coefficient. Therefore, the short-term estimate of capital investment in transport and communications infrastructure, the hotel and restaurant industry, and recreation facilities are *ϑ*2*ij*, *ϑ*3*ij*, *ϑ*4*ij*, respectively. where *μ<sup>i</sup>* is the group-specific effect; *i* is the source country; *t* is the number of periods (year); −1 < ߮<sup>ଵ</sup> < 0 is the error correction term's coefficient; ߝ,௧ is the error term; is the first difference operator; j is the lag order decided by the Akaike Information Criterion (AIC); ln is the natural logarithm. For each cross-section, the long-term slope (elasticity) of capital investment in transport and communications infrastructure, the hotel and restaurant industry, and recreation facilities is calculated as − ఝమ ఝభ , − ఝయ ఝభ , − ఝర ఝభ , respectively, and with the expectation of a positive coefficient. Therefore, the short-term estimate of capital investment in transport and communications infrastructure, the hotel and restaurant industry, and recreation facilities are ߴଶ, ߴଷ, ߴସ, respectively.

+ ି௧ܥ݈݊ܶ∆ଶߴ

݈ܸ݊ܣ,௧ିଵ + ߮ଶ

ଷ

ୀ

ି௧ܴܪ݈݊ଷߴ

݈݊ܪܴ௧ିଵ

(2)

݈݊ܶܥ௧ିଵ + ߮ଷ

*Economies* **2021**, *9*, x FOR PEER REVIEW 7 of 20

+ ି௧,ܣ݈ܸ݊∆ଵߴ

݈ܴ݊ܨ௧ିଵ + ݑܦ݉,௧ + ,௧

*i* = 1, 2, …*N*; *t* = 1, 2, … *T*

ଶ

ୀ

ߴସ݈ܴ݊ܨ௧ି + ߮ + ߮ଵ

#### *3.2. Data 3.2. Data*

+ ߤ = ௧,ܣ݈ܸ݊∆

ଵ

ୀଵ

+ ସ

+ ߮<sup>ସ</sup>

ୀ

The measurement of tourist attraction to Vietnam in this study is based on international tourist arrivals, as used by many previous studies to measure tourism demand (Khadaroo and Seetanah 2007a; Seetanah and Khadaroo 2009; Seetanah et al. 2011; Mandi´c et al. 2018). The international visitor arrivals were collected from the ten largest source markets and the remaining markets for 25 years (1995–2019) to form panel data with 275 observations (N = 11 and T = 25). Data on international visitors to Vietnam by source countries in the period 1995–2018 were collected from the VNAT. The ten countries with the most significant number of visitors to Vietnam in the period 1995–2019 are China, Korea, Japan, the United States (US), Malaysia, Australia, the United Kingdom (UK), Singapore, France, and Germany, respectively. These ten source countries accounted for 70.08% of total visitor arrivals to Vietnam from 1995–2019 (Figure 1). The measurement of tourist attraction to Vietnam in this study is based on international tourist arrivals, as used by many previous studies to measure tourism demand (Khadaroo and Seetanah 2007a; Seetanah and Khadaroo 2009; Seetanah et al. 2011; Mandić et al. 2018). The international visitor arrivals were collected from the ten largest source markets and the remaining markets for 25 years (1995–2019) to form panel data with 275 observations (N = 11 and T = 25). Data on international visitors to Vietnam by source countries in the period 1995–2018 were collected from the VNAT. The ten countries with the most significant number of visitors to Vietnam in the period 1995–2019 are China, Korea, Japan, the United States (US), Malaysia, Australia, the United Kingdom (UK), Singapore, France, and Germany, respectively. These ten source countries accounted for 70.08% of total visitor arrivals to Vietnam from 1995–2019 (Figure 1).

**Figure 1.** Visitors from ten major international markets in the period 1995–2019. **Figure 1.** Visitors from ten major international markets in the period 1995–2019.

The data series covers 25 years from 1995–2019 and the summary of variables used in the model is described in Table 1 below. The data series covers 25 years from 1995–2019 and the summary of variables used in the model is described in Table 1 below.


**Table 1.** Summary of variables used in the model.

Note: Data on social investment capital is converted to fixed prices; the original year was 1994.

TC

Transport and communications infrastructure

rant industry

HR Hotel and restau-

RF Recreation facilities

According to the GSO of Vietnam, the investment capital of the activities in Table 1 for the period 1995–2009 are based on the original year, 1994. However, from 2010–2019 the fixed price is for 2010. Therefore, the fixed price of 2010–2019 is converted to the original year price by the conversion coefficient of the original year 2010 to the original year 1994 according to the Equation (3) below. inal year price by the conversion coefficient of the original year 2010 to the original year 1994 according to the Equation (3) below. Conversion coefficient of the original Value in year n at the 2010 price (3)

According to the GSO of Vietnam, the investment capital of the activities in Table 1 for the period 1995–2009 are based on the original year, 1994. However, from 2010–2019 the fixed price is for 2010. Therefore, the fixed price of 2010–2019 is converted to the orig-

Conversion coefficient of the original year 2010 to the original year, 1994 = Value in year n at the 2010 price Value in 2010 based on the original 1994 price (3) year 2010 to the original year, 1994 = Value in 2010 based on the original 1994 price Source: Vietnam Ministry of Planning and Investment (2012).

communications GSO of Vietnam

WTO) and VNAT

GSO of Vietnam

GDO of Vietnam
