Modelling income effects on long and short haul international travel from Japan

Transcription

1 Tourism Management 29 (2008) Modelling income effects on long and short haul international travel from Japan Christine Lim a,b,, Jennifer C.H. Min c, Michael McAleer d a Department of Tourism and Hospitality Management, University of Waikato, Private Bag 3105, Hamilton, New Zealand b Nanyang Business School, Nanyang Technological University, Singapore c International Business Department, Ming Chuan University, 250 Chung Shan N. Road, Section 5,Taipei 111, Taiwan, ROC d School of Economics and Commerce, University of Western Australia, Australia Received 10 June 2007; accepted 14 February 2008 Abstract International travel and tourism are among the most dynamic sectors in the modern economy. The phenomenal growth in international tourist arrivals has significantly outpaced global economic growth over the previous five decades, with particularly strong growth in the Asia and Pacific regions. Among other factors, changes in aircraft technology, economic prosperity and international air service liberalization in the late 1970s have contributed to the growth in the Japanese long haul outbound travel demand. The prolonged economic recession in Japan in the 1990s has changed Japanese outbound tourist preferences for travel to short haul destinations. Income in the origin country is arguably the most widely used explanatory variable in the extant empirical tourism demand literature. This paper examines the dynamic relationship between travel demand and real income in Japan using linear and nonlinear models in order to distinguish between travel demand to Taiwan and New Zealand, which are two short and long haul markets for Japan. The empirical findings that New Zealand has a higher income elasticity of demand as compared with Taiwan should be useful for tourism authorities in developing better informed policies and to manage tourism resources efficiently in destination marketing. r 2008 Elsevier Ltd. All rights reserved. Keywords: Japanese travel demand; Income elasticity; Long and short haul markets; Linear and nonlinear models 1. Introduction The significant growth of international travel demand is indicative of tourism as one of the most dynamic economic sectors and social activities of the past century. This is evident in the phenomenal growth of international arrivals, from 25 million tourists in 1950 to a record high of 808 million in 2005, which has significantly outpaced global economic growth, as measured by real Gross Domestic Product. During this period, tourism development and growth were particularly strong in the Asia and Pacific regions, which experienced 13% growth rate per annum, Corresponding author at: Department of Tourism and Hospitality Management, University of Waikato, Private Bag 3105, Hamilton, New Zealand. Tel.: ; fax: addresses: clim@waikato.ac.nz (C. Lim), jennifer_min.tw@yahoo.com.tw (J.C.H. Min), michael.mcaleer@gmail.com (M. McAleer). compared with an average annual growth rate of 6.5% worldwide (World Tourism Organization, 2006a). International tourism rebounded strongly in 2004 and 2005, after two years of negative growth in 2001 and 2003 due to a depressed worldwide economy and SARS, respectively. Notwithstanding the downturn in international tourism in the recent past, international receipts still represented about 6% of total world exports and 30% of service exports in 2003 (World Tourism Organization, 2006b). The Japanese outbound travel market has experienced a similar pattern during the same period. In particular, the setbacks were related to fears of terrorism and diseases after the events of September 11, 2001 in the USA, and the SARS and bird flu outbreaks in These events have caused negative growth of 9% and 20% in 2001 and 2003, respectively, in Japanese international travel demand. The global tourism industry continued to experience above average growth in 2006, despite concerns over /$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi: /j.tourman

2 1100 ARTICLE IN PRESS C. Lim et al. / Tourism Management 29 (2008) political conflicts, terrorism, bird-flu pandemic and rising oil prices. Strong growth in Asia and Pacific regions has been boosted by emerging market such as India, as well the recovery of destinations like Thailand and the Maldives from the impact of the December 2004 tsunami in the Indian Ocean (Carlsen, 2006; Rittichainuwat, 2006). France has remained as the world s top tourist destination in 2006, attracting 78 million tourists, in spite of growing competition from other popular destination such as Spain. Changes in aircraft technology, economic prosperity and international air service liberalization in the late 1970s, have contributed to the growth in the Japanese long haul travel demand for the USA, Australia and New Zealand. Moreover, the Japanese government removed all overseas travel restrictions in 1964 to coincide with the hosting of the Tokyo Olympic Games. Numerous major factors and socioeconomic reforms have subsequently contributed to the emergence of Japan as a leading tourist-generating country in the world since the 1980s. They include the lifting of foreign exchange controls, rapid population growth due to the postwar baby boom, a significant appreciation of the yen in the 1980s and early 1990s, strong economic growth, and lifestyle changes. Land and stock prices in Japan appreciated by between 70- and 100-fold from the mid-1950s to the late-1980s. Japanese tourists have a reputation for being big spenders, and this has made Japan an attractive market for many destinations (Choy, 1998; Morris, 1991; Murphy & Williams, 1999; Nozawa, 1992). As Japan has been a dominant outbound market in international tourism in terms of tourist arrivals and expenditures, considerable research has been undertaken to examine the patterns of Japanese outbound travel (Lim & McAleer, 2005; Mak, Carlile, & Dai, 2005; Polunin, 1989; Sakai, Brown, & Mak, 2000; Tokuhisa, 1980; Wang & Lim, 2005), and the characteristics of Japanese travellers (Ahmed & Krohn, 1992; Balaz & Mitsutake, 1998; Cha, McCleary, & Uysal, 1995; Heung, Qu, & Chu, 2001; Holtzman, Murthy, & Gordon, 1991; Iverson, 1997a; Lang, O Leary, & Morrison, 1993; March, 1997a; Pinhey & Iverson, 1994; Sage, 1985). Moreover, several studies have been undertaken to compare Japanese tourist behaviour with that of tourists from other nations (Chen, 2000; Dybka, 1988; Iverson, 1997b; March, 1997b; Mihalik, Uysal, & Pan, 1993). Although Japan had been in a severe economic recession since the mid-1990s following three decades of prosperity, it was ranked fourth in the world on international tourism expenditures in , after Germany, USA and UK (World Tourism Organization, 2006c). The economic malaise in Japan has changed Japanese outbound tourist preferences in recent years for travel to short-haul destinations, which are closer to Japan, and hence cheaper. This has benefited countries in the Asia and Pacific regions, such as Taiwan. The purpose of this paper is to use the ARMAX model to investigate the dynamic relationship between tourism demand and real income of Japan over time. We analyse Japan s international travel demand for New Zealand and Taiwan, which represent two of Japan s long- and short-haul markets, respectively. A basic goal of tourism demand modelling is to estimate income elasticity that can be used in developing more accurate, and hence better informed, policies. The focus of econometric studies is to determine the extent to which the data support a particular theory. More specifically, the ARMAX model, which embodies both econometric and time series analyses, will be used to test the economic theory that the demand for international travel is positively related to income in the origin market. Japan has been the most important inbound market for Taiwan, and it is New Zealand s largest Asian tourist source market. Since 1980, the average annual tourist arrivals from Japan to New Zealand and Taiwan represent about 9% and 41% of total Japanese resident departures, respectively. Besides facing intense competition from many Asian destinations due to the entry of budget airlines and cheaper airfares since 2002, the increase in the strength of the New Zealand dollar, due primarily to high interest rates, has caused a continual decline in Japanese tourist arrivals to New Zealand (see Fig. 1). Since 2005, there has been a marked appreciation in the NZ dollar against most major currencies. Additionally, the exchange rate has caused lower tourist spending in New Zealand. According to Lin (1990), geographical proximity, being the second closest neighbour after Korea, and similar cultural values have significant impacts on intra-regional travel demand by Japan for Taiwan. Taiwan was a former colony of Japan from 1895 to 1945 prior to the Kuo-Ming Ton (KMT) Party s flight to Taiwan from China to exercise its sovereignty. Since the 1990s, tourist flows from Japan have suffered several setbacks due to a series of political events, economic/financial and natural disasters (for instance, the 1995 economic recession in Japan, rising tension in cross-straits relations between Taiwan and China in 1995/1996, and the Asian financial crisis in 1997/1998). However, it was the 1999 earthquake in Taiwan, and SARS outbreak in 2003, which had the most far-reaching consequences on Japanese inbound arrivals to Taiwan (see Fig. 2). The plan of the remainder of the paper is as follows. Section 2 discusses the methodology to be adopted to analyse the time series data. Unit root tests for the tourism time series data and estimation of the optimal autoregressive moving average (ARMA) models are presented in Sections 3 and 4, respectively. In Section 5, the unit root test procedure is applied to the real GDP of Japan before estimating the ARMAX model. The rolling estimation approach is used to determine the long run income elasticity of travel demand in Section 6 and examine the stability of the parameter estimates over time. Some concluding remarks are given in Section 7, with suggestions for further application of this framework. The EViews

3 C. Lim et al. / Tourism Management 29 (2008) % change in JP tourist to NZ Japan GDP % change in JP tourist to NZ q1 1985q1 1990q1 1995q1 2000q1 2005q1 time Japan GDP Fig. 1. Japan real GDP (billion of JPY) and annual percentage change in tourist arrivals from Japan to New Zealand. 200 % change in JP tourist to TW Japan GDP % change in JP tourist to TW Japan GDP q1 1985q1 1990q1 1995q1 2000q1 2005q1 time... Fig. 2. Japan real GDP (billion of JPY) and annual percentage change in tourist arrivals from Japan to Taiwan. 5 software package is used for the data analysis, empirical estimation and calculation of the diagnostic checks. 2. Methodology Box and Jenkins (1970) models are often used to analyse the time series behaviour of tourist arrivals. The former consists of two simple and useful models, namely the auto regressive (AR) and moving average (MA) models. While it is possible to use the AR and MA processes alone to capture the current pattern of tourist arrivals from a particular market based on its own past arrivals and the random error from previous periods, explanatory variables such as real income in the origin country, tourism prices and transportation costs, have also affected demand for international travel. In a review of empirical studies on international tourism demand and its determinants, Lim (1999, 2006), Song and Witt (2000) argued that the variety of explanatory factors used is undoubtedly very large. Nonetheless, the most prominent and frequently used variable in these studies is the income of tourist-generating countries, which affects the ability of consumers in these countries to pay for their overseas travel. However, these studies have not examined any possible differences in income effects of long and short haul travel demand. By including an income variable with a finite lag structure, we can use the ARMAX model to estimate the income elasticity of tourism demand by Japan for New Zealand and Taiwan for the period Furthermore, international travel is a luxury good such that the income elasticity of demand is greater than one. Our procedure prescribes treating the theory as a prior, and we propose an ARMAX framework in which the theory is represented through a specific model. Specification and estimation of such a model are discussed extensively in, among others, Franses (1991) and Greene (2000).

4 1102 ARTICLE IN PRESS C. Lim et al. / Tourism Management 29 (2008) The ARMAX model is an extension of the ARMA model with explanatory exogenous variables (X). It has been used to analyse the dynamic relationship between variables in economics, marketing, and other areas of the physical and social sciences (see, for example, Franses, 1991; Wu, Lin, Tiao, & Cho, 2005). Previous research in tourism has used the ARMAX model to examine the impact of terrorism on tourism, and to forecast tourism revenues. Akal (2004) applied the ARMAX model to forecast Turkey s international tourism revenues for the post-2001 economic crisis with international visitors as the explanatory variable. In Sloboda (2003), the ARMAX model is used to assess the effects of terrorism on tourism with tourist receipts and terrorist incidents as the dependent and explanatory variables, respectively. Both of these studies have used annual data with few observations to estimate the impacts of the explanatory variables on the dependent variable. Furthermore, these studies did not conduct the Wald test of parametric restrictions to obtain parsimonious models. In the analysis of international tourism demand by Japan for New Zealand and Taiwan, tourist arrivals from the origin and real GDP of Japan are chosen as the proxies for international travel demand and real income of Japan, respectively. The sample period under consideration is because of the limited availability of quarterly observations on GDP obtained from the EconData Time Series Databases. Other sources provided observations beyond 2004 but the dataset are less extensive, and are not compatible with the income observations from EconData. Real GDP is measured by GDP (expenditure) deflated by CPI at 2000 constant prices. Japanese tourist arrival data to New Zealand and Taiwan are obtained from New Zealand Department of Statistics ( ), and Taiwan Tourism Bureau ( ), respectively. The seasonally unadjusted quarterly data are expressed in logarithms to capture multiplicative time series effects. It is possible to apply the logarithmic transformation to the variables since they have only positive values. Furthermore, this would allow us to examine how economic agents would react to relative rather than absolute changes in income, that is, the percentage change in travel demand as a result of a one percent change in real income. 3. Unit root tests Examination of Fig. 3 suggests that log tourist arrivals from Japan to New Zealand and Taiwan appear to be nonstationary and contain a deterministic or stochastic trend, or both. If the trend is deterministic (stochastic), the series will (will not) revert to a long run trend line, innovation shocks have diminishing (permanent) effects, and the forecast variance is constant (increases) for longer horizons. If the trend is deterministic, the time series is trend stationary. By removing the trend component of the series (known as de-trending the data), the detrended series would be stationary. If the trend is stochastic, the series is Log Tourist Arrivals Log Tourist Arrivals Year Year Fig. 3. Logarithm of short-term tourist arrivals from Japan, said to contain a unit root. By taking first differences, the differenced series would be stationary. Standard augmented Dickey Fuller (ADF) tests for unit root are used, under the null hypothesis of a stochastic trend (or a unit root) against the alternative of a deterministic trend (or trend stationary). The ADF test equation is given as follows: Dy t ¼ a þ dt þ by t 1 þ Xk i¼1 c i Dy t i þ u t, (1) where y t is the natural logarithm of tourist arrivals from Japan to New Zealand or from Japan to Taiwan at time t, t is a deterministic time trend, Dy t i is the lagged first difference to accommodate (possibly) serially correlated error processes, u t is an independently and identically distributed error term, a, d, b and c are parameters to be estimated.

5 C. Lim et al. / Tourism Management 29 (2008) Table 1 ADF and Philip Perron test statistics Log tourist arrivals from Japan to: ADF Without trend With trend Philip Perron Without trend With trend New Zealand (ln z) Taiwan (ltw) Table 2 Unit root tests ADF lag length ADF statistic (A) ln z ltw (B) dlnz dltw The ADF tests for a unit root are used for both logarithmic tourist arrival series over the full sample period. Note that the ADF tests of the unit root null hypothesis correspond to the following one-sided test: H 0 : b ¼ 0, H 1 : bo0. The deterministic time trend is included in the auxiliary regression equation (1) because the reported ADF statistics, with and without a deterministic trend, are substantially different for both series, and for New Zealand in particular (see Table 1). Additionally, the ADF test results are confirmed by the Philip Perron test and the coefficient of the time trend is significant at the 5% level. As the test is performed as the t-test on b, it needs to be mentioned that the t-ratio of the OLS estimate of b does not have an asymptotic standard normal distribution. Instead, the null hypothesis of a unit root is based on the t-statistic using simulated critical values (Dickey & Fuller, 1981). An initial lag length of 4 is selected for k and the order is sequentially reduced until a significant lag length is obtained. The results of the ADF unit root tests are presented in Table 2(A). When the ADF test statistics are compared with the critical values from the nonstandard Dickey Fuller distribution with trend, the former for Japanese tourist arrivals to New Zealand and Taiwan are both greater than the critical value of Thus, the null hypothesis of a unit root is not rejected at the 5% significance level, implying that the series are nonstationary. By taking first differences of the logarithm of tourist arrivals, the ADF tests show that the null hypothesis of a unit root is clearly rejected. The ADF statistics for both series are less than the critical value of 2.89, as shown in Table 2(B). Thus the first differences of the logarithmic tourist arrivals are stationary. Tourist arrivals in first differences are presented in Fig. 4, where it is clear that the series do not contain a stochastic trend. However, there may be some unexplained volatility in the log first difference series (see McAleer, 2005 for further details). 4. ARIMA models for tourist arrivals Since the ADF test procedures show that the logarithmic tourist arrival series are integrated of order one, I(1), whereas the first differenced series are integrated of order zero, I(0), the latter is used to estimate the Box Jenkins models. The autoregressive moving average, or ARMA(p,q), model is given below: y t ¼ a þ b 1 y t 1 þ b 2 y t 2 þþb p y t p þ u t þ y 1 u t 1 þþy q u t q, (2) where y t ; y t 1 ;...; y t p represent the current and lagged tourist arrivals, p is the lag length of the AR error term, and q is the lag length of the MA error term. The series is described by an AR integrated MA model or ARIMA(p,d,q) when y t is replaced by D d 1 y t. Since the process is integrated of order 1 (d ¼ 1), a sensible strategy for estimating ARIMA(p,1,q) models with values for p and q from 0 to 4, is to start with small p and q and increase to larger values. Only models with statistically significant AR and MA coefficients are selected, ensuring that the estimated residuals do not have serial correlation at the (say) 5% significance level. As for the latter, we use the Breusch Godfrey Lagrange multiplier test of serial correlation, LM(SC). It can be used to test for higher-order ARMA errors, and is applicable in the presence of lagged dependent variables. Using the Lagrange multiplier test, if the computed F statistic exceeds the critical value given by F 2,86 (.05) ¼ 3.15, this leads to the rejection of the null hypothesis of no serial correlation. Table 3 presents the results of the various ARIMA models for the logarithms of tourist arrivals from Japan to New Zealand and to Taiwan. Two competing ARIMA models, namely ARIMA(2,1,4) and ARIMA(3,1,3), have been identified for New Zealand for different orders of p and q. While incorporating additional lags for a model will tend to reduce the residual sum of squares, there is a trade-off between the degrees of freedom and the power of the test. A parsimonious model is generally preferred in the literature. The two most commonly used model selection criteria are the Akaike Information Criterion (AIC) and the Schwarz Bayesian Criterion (SBC), with the decision to base the model choice being to select the model for which the appropriate criterion is smallest. These selection criteria favour both ARIMA models as they have the same AIC and SBC values. The two optimal models for New Zealand are given as follows (with absolute t-ratios in parentheses).

6 1104 C. Lim et al. / Tourism Management 29 (2008) New Zealand Model 1: ð1 þ 0:97L 2 Þð1 LÞ ln z t ¼ 0:003 þ ð1 0:76L þ 1:07L 2 0:91L 3 þ 0:58L 4 Þ^ t : ð40:7þ ð3:33þ ð8:68þ ð15:1þ ð15:4þ ð6:54þ New Zealand Model 2: ð1 þ 0:97L þ 0:88L 2 þ 0:90L 3 Þ ð1 LÞ ln z t ¼ 0:003 þ ð1 þ 0:38L þ 0:33L 3 Þ^ t : ð22:9þ ð17:4þ ð23:3þ ð3:54þ ð3:56þ ð3:21þ Only one ARIMA model, namely ARIMA(4,1,4), has been identified as optimal for Taiwan, as follows (with absolute t-ratios in parentheses): ð1 þ 0:64L þ 0:60L 2 þ 0:54L 3 0:38L 4 Þ ð1 LÞltw t ¼ 0:0003 ð1 0:99L 4 Þ^ t : ð14:6þ ð10:8þ ð9:88þ ð6:77þ ð2:98þ ð27:7þ 0.12 Furthermore, the computed F statistics for the LM(SC) test are all less than the critical value. Thus, the null hypothesis of no serial correlation is not be rejected for these models ARIMAX model According to Franses (1991), the ARMAX regression is an extension of ARIMA modelling. The ARMAX model has lagged dependent and explanatory variables, and a MA disturbance. We assume a simple model of tourism demand, whereby tourist arrivals are a function of the real income at the origin. It is argued that current tourist arrivals are affected by the current income and income with Year Table 3 ARIMA models for tourist arrivals from Japan to two destinations Variable Coefficient t-statistic AIC/SBC LM(SC) (A) New Zealand C AIC ¼ 5.44 F ¼ 1.95 AR(2) SBC ¼ 5.28 p ¼ 0.15 MA(1) MA(2) MA(3) MA(4) C AIC ¼ 5.44 F ¼ 2.29 AR(1) SBC ¼ 5.28 p ¼ 0.11 AR(2) AR(3) MA(1) MA(3) Year Fig. 4. Log first difference of short-term tourist arrivals from Japan, (B) Taiwan C AIC ¼ 5.27 F ¼ 1.34 AR(1) SBC ¼ 5.11 p ¼ 0.27 AR(2) AR(3) AR(4) MA(4)

7 C. Lim et al. / Tourism Management 29 (2008) a one-period lag. An extension of Eq. (2) to include a single explanatory (income) variable leads to the following singleequation ARMAX model: y t ¼ a þ b 1 y t 1 þþb p y t p þ f 0 x t þ f 1 x t 1 þ u t y 1 u t 1 y q u t q, (3) where x t ; x t 1 are the current and one-period lagged real income in the origin country, respectively. Eq. (3) is also known as an ARIMAX model and can accommodate more than one explanatory variable if the lag structure for each variable is finite. We assume there is no feedback from y t to x t, and that the errors are independently and identically distributed, with zero mean, constant variance and zero covariance. Before the ARIMAX model is used to estimate the relationship between income and travel demand by Japan, the explanatory variable must also be tested for stationarity. The ADF test procedures are applied to the real GDP of Japan (in logarithms) for the presence of unit roots, and the time series is appropriately differenced to achieve stationarity. The deterministic trend term (t) is retained in the test regression because the ADF t-statistics with and without trend are substantially different. It is also found that the ADF test statistic of 0.32 is greater than the critical value of 3.46 at the 5% level, and this is obtained at a significant lag length of 3. Therefore, the null hypothesis of a unit root cannot be rejected, which implies that the real GDP series of Japan are nonstationary. Taking the first difference of the logarithm of real GDP and applying the ADF test procedures to the transformed series, a more negative test statistic of 4.01 than the critical value of 2.89 is obtained at a significant lag length of 2. This suggests that the differenced series is stationary and follows an I(0) process, or is integrated of order zero, whereas the logarithm of real GDP is integrated of order one, I(1). Hence, the first difference of the logarithm of real GDP will be used in the ARIMAX model to estimate the income elasticity of travel demand by Japan. Eq. (3) can be rewritten as y t ð1 b 1 L b p L p Þ¼a þðf 0 þ f 1 LÞx t þu t ð1 y 1 L y q L q Þ, (4) where L is the lag operator. From (4), we can write a y t ¼ ð1 b 1 L b p L p Þ þ ðf 0 þ f 1 LÞ ð1 b 1 L b p L p Þ x t þ ð1 y 1L y q L q Þ ð1 b 1 L b p L p Þ u t. Hence, the total impact of a change in x on y is given by the ratio of the lag polynomials for the dependent and explanatory variables. Fig. 4 shows substantial seasonality in tourist arrivals even though the ADF tests of the first differenced series reject the null hypothesis of a unit root. In order not to over-difference the series (for instance, by performing seasonal differencing), three seasonal dummy variables are included in the ARIMAX regression to account for seasonal effects. It can also be seen in Fig. 4 that tourist arrivals were affected by SARS in 2003, particularly for Taiwan (World Health Organization, 2003). To account for this shock, a dummy variable, SARS_DUM, which takes the value 1 for 2003:2 and zero for other quarters, is included in the ARIMAX model for Taiwan. The model selection procedure results in the following specifications: y t ¼ a þ b 1 y t 1 þþb p y t p þ f 0 x t þ f 1 x t 1 þ d 1 D 1t þ d 2 D 2t þ d 3 D 3t þ u t y 1 u t 1 y q u t q ðnew ZealandÞ, Table 4 Initial regression estimates of ARIMAX Models, Dependent variable: y t Regressor New Zealand Model 1 New Zealand Model 2 Taiwan Coefficient t-statistic Coefficient t-statistic Coefficient t-statistic y t y t y t y t x i D D D SARS u t u t u t u t Constant

8 1106 C. Lim et al. / Tourism Management 29 (2008) y t ¼ a þ b 1 y t 1 þþb p y t p þ f 0 x t þ f 1 x t 1 þ d 1 D 1t þ d 2 D 2t þ d 3 D 3t þ d 4 SARS þ u t y 1 u t 1 y q u t q ðtaiwanþ. The initial regression of the ARIMAX models for New Zealand and Taiwan are given in Table 4. Not all the seasonal dummy variables are significant at the 5% level. Moreover, SARS did not have a significant negative impact on Japanese tourist arrivals to Taiwan. The Lagrange multiplier tests, LM(SC), show that the errors are not serially correlated at the 5% level. Estimation of a regression model is usually not the final stage of a model evaluation process (see, for example, McAleer, 1994). While lagged variables that are not significant at the 5% level are excluded from the final model, it is possible to obtain more parsimonious models by also excluding the exogeneous variables which are not significant. The Wald test is performed regarding the coefficient restriction(s) specified by the null hypothesis. Specifically, the null is assessed by the F-statistic for testing whether the coefficients of the seasonal and/or SARS dummy variables to be excluded from the ARIMAX models are zero. EViews also reports a chi-square statistic (with associated p-value) which is equal to the F-statistic times the number of restrictions. If there is only one Table 5 Wald test of coefficient restriction Test statistic Value df Probability (A) Initial ARIMAX Model 1 for New Zealand F-statistic (1,85) Chi-square (B) Initial ARIMAX Model 2 for New Zealand F-statistic (2,84) Chi-square (C) Initial ARIMAX Model for Taiwan F-statistic (2,82) Chi-square restriction, as in the case of the ARIMAX model 1 for New Zealand, the F-statistic and chi-square statistic are identical. The coefficient restrictions in the ARIMAX model for Taiwan and ARIMAX model 2 for New Zealand are that some parameters are equal to zero. In Table 5, the p-values of both statistics indicate that the null hypothesis is not rejected, and the associated variable(s) can be excluded from the regression equations. The ARIMAX models for New Zealand and Taiwan are re-estimated and the results of the final models are presented in Table 6. All the models in the table show that the short run income elasticities of travel demand are positive and significant. However, only the elasticity estimates for New Zealand are greater than 1.0, which suggests that international travel is a luxury good. It is worth noting that the estimates of the MA parameters in New Zealand s model 2 are not significant, so that an ARIX model is appropriate. However, there are MA disturbances in both Taiwan s model and New Zealand s model 1, such that these models become nonlinear (see, for example, Greene, 2000). A two-stage least squares procedure involving the use of instrumental Table 7 Estimates of nonlinear ARIMAX Model using two-stage least squares, Dependent variable: y t Regressor New Zealand Model 1 Taiwan Coefficient t-statistic Coefficient t-statistic y t y t y t x t D D u t u t Constant Table 6 Final regression estimates of ARIMAX Models, Dependent variable: y t Regressor New Zealand Model 1 New Zealand Model 2 Taiwan Coefficient t-statistic Coefficient t-statistic Coefficient t-statistic y t y t y t x t D D u t u t Constant

9 C. Lim et al. / Tourism Management 29 (2008) variables is appropriate. The instrumental variables for these models are the lags of real income. Table 7 shows the nonlinear regression ARIMAX models for New Zealand model 1 and Taiwan, respectively. Japanese international travel demand for Taiwan has become income elastic and significant. Since the income elasticity estimate for New Zealand s model 1 is not significant, this model will not be used to obtain the long run income elasticity of Japanese outbound travel demand for New Zealand in the next section. 6. Income stability The rolling estimation approach for the ARIMAX model will be used to analyse the stability of international travel demand due to changes in real income over time. Since Japan was in a recession for around two years prior to the Asian currency crisis in 1997, the rolling estimates for tourism demand will start from the first quarter of 1998 to the second quarter of 2004 for both New Zealand and Taiwan. The resulting rolling estimates of the real income elasticity are given in Table 8. Only the long run elasticity estimates for New Zealand are consistently significant at the 5% level. The estimates have increased over time, from Table 8 Income elasticity of travel demand using rolling estimation, Sample period Quarter New Zealand Model Taiwan Model Denotes 5% significance level. Denotes 10% significance level to a maximum of On the contrary, the income elasticity of travel demand for Taiwan is only positive and significant during the SARS epidemic, and also in Conclusion This paper analysed the impact of changes in income on Japanese outbound travel using an ARIMAX dynamic regression model. The model is developed in two stages and it is evaluated with an extensive set of testing and diagnostic checks for model adequacy, including tests of unit roots, parametric restrictions and serial correlation. Initially, the lag structures of tourism time series models for New Zealand and Taiwan are determined. The procedures for testing stationarity and the orders of integration of variables using the augmented Dickey Fuller (ADF) test were discussed. Tests and diagnostics were performed in estimating Box Jenkins ARIMA models to capture the auto regressive (AR) and moving average (MA) components of past observations in the tourist arrivals and their shocks to Taiwan and New Zealand from Japan. Following three decades of prosperity and unprecedented growth, Japan experienced a major economic slowdown in the 1990s. The ARIMAX models for international tourism demand analysis were specified to determine the possible impacts of a change in the real income of Japan on its dynamic tourism demand. The income variable was also tested and transformed appropriately to obtain a stationary process. Additional variables, namely seasonal and SARS dummy variables, were also included in the estimation of the ARIMAX model. Restrictions were imposed on the insignificant estimates of the initial ARIMAX model in order to obtain more parsimonious models. It was postulated that tourism demand, as measured by tourist arrivals, is positively related to the income at the origin. Parsimonious ARIMAX models were used to obtain the long run income elasticity of international travel demand. The income elasticity of demand estimates for New Zealand and Taiwan ranged from 1.50 to In particular, the restricted ARIX model for New Zealand confirmed the importance of changes in income on the Japanese demand for long haul travel. However, the income elasticities are not particularly significant for short haul travel to Taiwan in the long run. While the empirical results support theoretical expectations, the insights gained attest to the importance of managing tourism resources efficiently in destination marketing. Since the effect of changes in income on international travel demand is not uniform across markets, host countries which placed considerable resources to increase visitor numbers can do so sensibly with short haul markets in which the relative influence of income is not significant. In terms of policy implications for long haul markets, tourism resource management in destination marketing is not optimized when these markets are experiencing prolonged economic decline or sluggishness,

10 1108 ARTICLE IN PRESS C. Lim et al. / Tourism Management 29 (2008) or face the prospect of long term economic slowdown. It is not surprising that, even though New Zealand has increased its marketing expenditures in recent years, there has been minimal success in revitalizing the Japanese tourism source market. Hence, tourism managers should try to maximize returns by examining the income effects on long and short haul travel, and allocating their marketing resources carefully. Destination tourism policy makers and suppliers of tourism activities are also interested in forecasting tourism demand. Since the late 1980s, numerous empirical tourism studies have used the ARIMA model for forecasting as it can capture the time series behaviour of the variable based on its own past history. However, a model that captures the evolution of historical patterns of tourist arrivals to a destination, and the behavioural relationship with related economic variables, such as income, tourism prices and exchange rates, might be more appealing and useful for forecasting purposes. The ARIMAX model, which embodies both econometric and time series analyses, focuses on both the ARIMA and regression components. This approach is particularly useful in forecasting tourism demand because it can also incorporate the future influence of changes in related variables on travel demand. An additional insight that has been gained from this research is the inappropriate use of linear single equation models which have significant MA components. The ARIMAX models not only capture the dynamic relationships between time series variables and permit testing of economic theoretic concepts as related to travel demand, but they can also inform the appropriate use of single equation models. For tourism managers to have a greater understanding of the various tourist source markets, as well as to make long run forecasts for effective tourism planning, it is imperative to use appropriate models to analyse tourism demand. It is worth mentioning that the price variable has not been included in the ARIMAX model because of data unavailability or incompatibility. Frequently used proxies for the tourism price variable include the tourist price index, CPI of the origin and destination, exchange rate and/or real exchange rate. Tourist price indices are typically unavailable. The CPI ratio is not a satisfactory measure as it does not reflect the prices of goods which tourists actually purchase, because the expenditure pattern of a tourist is quite different from that of the average household (see Lim, 2006). According to Song and Witt (2000), potential tourists tend to measure the costs of goods and services in the destination in terms of their own currency. However, it is not possible to construct the exchange rate of the New Zealand dollar in terms of the Japanese yen because of the liberalization of the financial sector and floating of the New Zealand dollar on international markets in The same reasoning applies to the use of the real exchange rate variable for New Zealand. However, the real exchange rate for New Zealand from 1985 to 2004 is I(0). The exchange rate of the Taiwan dollar in terms of Japanese yen and the real exchange rate variables are both I(0). Including I(0) variables in the ARIMAX model does not affect the cointegration relationship with the I(1) variables, namely tourist arrivals and real income variables. Ignoring this issue, we find that the estimated real exchange rates in the ARIMAX model are not significant at the 5% level for New Zealand and Taiwan (the results are available on request). Transportation costs are usually measured by the price of air travel. This is problematic due to the unavailability of airfare data (proxy for transportation costs), particularly special fares for economy class, which include excursion and promotional fares. Theoretically, if the model has excluded a relevant explanatory price variable, the misspecification would cause the estimated income elasticity to be biased downward. Consider y ¼ tourist arrivals, x ¼ income and z ¼ price, such that the ARMAX model is given as follows: y ¼ a þ bx þ gz þ u where b40 and go0. If z is omitted from the model by setting gamma ¼ 0 incorrectly, then OLS or nonlinear least squares will lead to the standard omitted variables bias result, namely: Eð^bÞ ¼b þ g covðx; zþ=varðxþ ¼b þ bias. As it is likely that cov(x,z)40, it follows that biaso0, such that the OLS estimator of b will be biased downward, that is, Eð^bÞob. Acknowledgements The authors are grateful to the editor and three anonymous reviewers for helpful comments and suggestions. The first author wishes to acknowledge the financial and research support of the Waikato Management School, University of Waikato and the Nanyang Business School, Nanyang Technological University. The third author wishes to acknowledge the financial support of the Australian Research Council. References Ahmed, Z. U., & Krohn, F. B. (1992). Understanding the unique consumer behavior of Japanese tourists. Journal of Travel & Tourism Marketing, 3(1), Akal, M. (2004). Forecasting Turkey s tourism revenues by ARMAX model. Tourism Management, 25(5), Balaz, V., & Mitsutake, M. (1998). Japanese tourists in transition countries of Central Europe: Present behavior and future trends. Tourism Management, 19(5), Box, G. E. P., & Jenkins, G. M. (1970). Time series analysis, forecasting and control. San Francisco: Holden Day. Carlsen, J. (2006). Post-tsunami tourism strategies for the Maldives. Tourism Review International, 10(1/2), Cha, S., McCleary, K. W., & Uysal, M. (1995). Travel motivations of Japanese overseas travelers: A factor-cluster segmentation approach. Journal of Travel Research, 34(1), Chen, J. S. (2000). Cross-cultural differences in travel information acquisition among tourists from three Pacific-rim countries. Journal of Hospitality & Tourism Research, 24(2),

11 C. Lim et al. / Tourism Management 29 (2008) Choy, D. J. L. (1998). Changing trends in Asia-Pacific tourism. Tourism Management, 19(4), Dickey, D., & Fuller, W. (1981). Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica, 49, Dybka, J. (1988). Overseas travel to Canada: New research on the perceptions and preferences of the pleasure travel market. Journal of Travel Research, 26(4), Franses, P. H. (1991). Primary demand for beer in the Netherlands: An application of ARMAX model specification. Journal of Marketing Research, 28(2), Greene, W. H. (2000). Econometric analysis (3rd ed.). New Jersey: Prentice-Hall. Heung, V. C. S., Qu, H., & Chu, R. (2001). The relationship between vacation factors and socio-demographic and traveling characteristics: The case of Japanese leisure travelers. Tourism Management, 22(3), Holtzman, W. L., Murthy, B., & Gordon, J. C. (1991). Cultural bridging with the Japanese. Cornell Hotel and Restaurant Administration Quarterly, 32(3), Iverson, T. J. (1997a). Japanese visitors to Guam: Lessons from experience. Journal of Travel & Tourism Marketing, 6(1), Iverson, T. J. (1997b). Decision timing: A comparison of Korean and Japanese travelers. International Journal of Hospitality Management, 16(2), Lang, C. T., O Leary, J. T., & Morrison, A. M. (1993). Activity segmentation of Japanese female overseas travelers. Journal of Travel & Tourism Marketing, 2(4), Lim, C. (1999). A meta-analytic review of international tourism demand. Journal of Travel Research, 37(3), Lim, C. (2006). A survey of tourism demand modelling practice: Issues and implications. In L. Dwyer, & P. Forsyth (Eds.), International handbook on tourism economics (pp ). UK: Edward Elgar Publishing. Lim, C., & McAleer, M. (2005). Analyzing the behavioral trends in tourist arrivals from Japan to Australia. Journal of Travel Research, 43(4), Lin, M. (1990). Taiwan: Magnet for Japanese tourists. Cornell Hotel and Restaurant Administration Quarterly, 31(1), Mak, J., Carlile, L., & Dai, S. (2005). Impact of population aging on Japanese international travel to Journal of Travel Research, 44(2), March, R. (1997a). An exploratory study of buyer supplier relationships in international tourism: The case of Japanese wholesalers and Australian suppliers. Journal of Travel & Tourism Marketing, 6(1), March, R. (1997b). Diversity in Asian outbound travel industries: A comparison between Indonesia, Thailand, Taiwan, South Korea and Japan. International Journal of Hospitality Management, 16(2), McAleer, M. (1994). Sherlock Holmes and the search for truth: A diagnostic tale. Journal of Economic Surveys, 8(4), (reprinted in L. Oxley et al. (Eds.), Surveys in econometrics (pp ). Oxford: Blackwell). McAleer, M. (2005). Automated inference and learning in modeling financial volatility. Econometric Theory, 21(1), Mihalik, B. J., Uysal, M., & Pan, M. C. (1993). A comparison of information sources used by vacationing Germans and Japanese. Hospitality Research Journal, 18(3), Morris, S. (1991). Japanese travel to Europe. EIU Travel and Tourism Analyst, 3, Murphy, A., & Williams, P. W. (1999). Attracting Japanese tourists into the rural hinterland: Implications for rural development and planning. Tourism Management, 20(4), New Zealand Department of Statistics ( ). Monthly tourist arrivals. Wellington. Nozawa, H. (1992). A marketing analysis of Japanese outbound travel. Tourism Management, 13(2), Pinhey, T. K., & Iverson, T. J. (1994). Safety concerns of Japanese visitors to Guam. Journal of Travel & Tourism Marketing, 3(2), Polunin, I. (1989). Japanese travel boom. Tourism Management, 10(1), 4 8. Rittichainuwat (2006). Tsunami recovery: A case study of Thailand s tourism. Cornell Hotel and Restaurant Administration Quarterly, 47(4), Sage, C. (1985). Concerning the Japanese market. Tourism Management, 7(4), Sakai, M., Brown, J., & Mak, J. (2000). Population aging and Japanese international travel in the 21st century. Journal of Travel Research, 38(3), Sloboda, B. W. (2003). Assessing the effects of terrorism on tourism by use of time series methods. Tourism Economics, 9(2), Song, H., & Witt, S. F. (2000). Tourism demand modelling and forecasting: Modern econometric approaches. Amsterdam: Pergamon. Tokuhisa, T. (1980). Tourism within, from and to Japan. International Social Science Journal, 32(1), Taiwan Tourism Bureau ( ). Monthly report on tourism. Taipei: Tourism Bureau. Wang, Y., & Lim, C. (2005). Assessing forecasting models for outbound Japanese travellers to Australia and China. Journal of Applied Economics and Management, 3(2), World Health Organization (2003). World health organization issues emergency travel advisory. Retrieved 15 September 2006, from / World Tourism Organization (2006a). Historical perspective of world tourism. Retrieved 1 October 2006, from / facts/menu.htmls. World Tourism Organization. (2006b). Tourism highlights 2005 edition. Madrid: World Tourism Organization. World Tourism Organization (2006c). UNWTO world tourism barometer. Retrieved 6 November 2006, from / menu.htmls. Wu, C. S., Lin, J. L., Tiao, G. C., & Cho, D. D. (2005). Is money demand in Taiwan stable? Economic Modelling, 22(2),