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Long-run tourism demand elasticities are important policy indicators for tourism product providers. Past tourism demand studies have mainly focused on the point estimates of demand elasticities. Although such estimates have some policymaking value, their information content is limited, as their associated sampling variability is unknown. Moreover, point estimates and their standard errors may be subject to small sample deficiencies, such as estimation biases and non-normality, which renders statistical inference for elasticity problematic. This paper presents a new statistical method called the bias-corrected bootstrap, which has been proved to provide accurate and reliable confidence intervals for demand elasticities. The method is herein employed to analyze the demand for Hong Kong tourism.

Researchers and practitioners are interested in tourism demand elasticities for two main reasons. First, these elasticities reflect the way in which tourists respond to changes in the influencing factors of tourism demand in terms of direction and magnitude. Second, they provide useful information for tourism policy formulations, as tourism providers can manipulate such determinants as the tourism price and marketing expenditure to increase demand for the tourism product/service under consideration. Tourism demand elasticities provide “unit-free” measures of the sensitivity of an explanatory variable to tourism demand, given a pre-specified functional relationship. Economic theory suggests that, subject to budgetary constraints, tourists choose to purchase particular tourism products/services from among a set of all available such products/services to maximize their utility (Song & Witt, 2000). When the price of a tourism product/service changes, tourists’ real income also changes. In addition, the price of the product/service in question, relative to the alternatives, also changes. These changes are called income and substitution effects, respectively. Thus, the income and price elasticity values derived from the demand function include both of these effects. Numerous empirical studies on tourism demand elasticity have been published since the early 1970s, including those carried out by Crouch, 1995, Li et al., 2005 and Lim, 1997. Table 1 presents a list of all those published since 2000. The general findings of these studies indicate that the income elasticities of tourism demand, especially the demand for international tourism, are generally greater than one, thus indicating that tourism is a luxury. The own price elasticity is normally negative, but the magnitudes vary considerably depending on the type of tourism (long or short haul) and the time span of the demand under consideration (long-run versus short-run). However, these studies report point estimates only. Point estimation gives a single value as an estimate of the parameter of interest, but provides no information about the degree of variability associated with it. Hence, such estimates are substantially less informative than confidence intervals. Another drawback is that point estimation provides a biased estimate of true elasticity, as elasticity is often a non-linear function of other model parameters. Table 1. Published Tourism Demand Elasticities Author(s) Source Market Destination Measured by Elasticity Income Price Sub. Price Song, Romilly, and Liu (2000) UK Australia Arrivals 2.721 -2.086 --- UK Belgium/Luxembourg Arrivals 2.162 -0.532 --- UK France Arrivals 2.123 -1.079 --- UK Germany Arrivals 2.263 -1.251 --- UK Italy Arrivals 1.739 -1.013 --- UK Netherlands Arrivals 2.488 -0.23 --- UK Greece Arrivals 2.174 -0.21 --- UK Spain Arrivals 2.199 -0.496 --- UK Irish Republic Arrivals 2.655 0.947 --- UK Switzerland Arrivals 2.028 -0.146 --- UK US Arrivals 2.003 0.16 --- Vanegas and Croes (2000) US Aruba Arrivals 1.512 -0.114 --- US Aruba Arrivals 1.485 --- --- US Aruba Arrivals 1.494 -0.123 --- US Aruba Arrivals 1.702 -0.198 --- US Aruba Arrivals 1.384 --- --- Kulendran and Witt (2001) UK Germany Arrivals 0.541 -4.001 -0.714 UK Greece Arrivals 0.608 -9.9 --- UK Netherlands Arrivals 0.727 --- --- UK Portugal Arrivals 1.821 -0.921 --- UK Spain Arrivals 0.928 -2.988 --- UK US Arrivals 1.697 --- -3.567 Greenidge (2001) US Barbados Arrivals 2.268 --- --- UK Barbados Arrivals 1.512 --- --- Canada Barbados Arrivals 3.1342 -0.184 --- Song et al. (2003) Australia Thailand Arrivals 3.518 -3.582 4.102 Japan Thailand Arrivals --- -0.709 0.772 South Korea Thailand Arrivals 2.046 --- -2.902 Singapore Thailand Arrivals --- -5.745 4 Malaysia Thailand Arrivals --- --- 4.238 UK Thailand Arrivals 4.922 -0.414 0.559 US Thailand Arrivals --- -1.619 -0.367 Song and Witt (2003) Germany South Korea Arrivals --- --- 0.75 Japan South Korea Arrivals -4.715 -0.281 3.43 UK South Korea Arrivals 3.273 -0.018 0.642 US South Korea Arrivals --- -8.776 3.362 Song et al. (2003) Australia Hong Kong Arrivals --- -0.583 0.552 Canada Hong Kong Arrivals 3.322 -1.012 --- Mainland China Hong Kong Arrivals 1.521 -0.402 1.248 France Hong Kong Arrivals 2.616 -0.436 0.663 Germany Hong Kong Arrivals 3.62 -1.389 --- Indonesia Hong Kong Arrivals 1.484 -2.885 --- India Hong Kong Arrivals 1.459 -1.059 1.209 Japan Hong Kong Arrivals 2.53 --- --- Song et al. (2003) South Korea Hong Kong Arrivals 1.704 --- --- Malaysia Hong Kong Arrivals 1.02 -0.206 --- Philippines Hong Kong Arrivals --- --- 1.657 Singapore Hong Kong Arrivals 1.316 -1.223 --- Taiwan Hong Kong Arrivals 2.14 -1.729 --- Thailand Hong Kong Arrivals 0.944 -0.911 --- UK Hong Kong Arrivals 2.096 -0.492 0.643 US Hong Kong Arrivals 1.499 -1.004 0.463 Song and Wong (2003) Australia Hong Kong Arrivals 0.233 -0.421 0.308 Canada Hong Kong Arrivals 2.907 -0.799 0.524 France Hong Kong Arrivals 2.211 -0.364 0.822 Germany Hong Kong Arrivals 1.182 -0.175 1.173 UK Hong Kong Arrivals 2.079 -0.537 0.563 US Hong Kong Arrivals 2.907 -1.013 0.301 Dritsakis (2004) UK Greece Arrivals 6.0268 --- --- Germany Greece Arrivals 2.1592 --- --- Lim (2004) South Korea Australia Arrivals 19.194 -19.68 --- Croes and Vanegas (2005) US Aruba Arrivals 2.66 -0.22 --- Venezuela Aruba Arrivals 3.86 -1.62 --- Netherlands Aruba Arrivals 6.75 -0.044 --- Li, Wong, Song, and Witt (2006) UK France Expenditure 2.817 -1.163 0.997 UK Greece Expenditure 1.834 -1.959 0.506 UK Italy Expenditure 1.935 -1.184 -0.502 UK Portugal Expenditure 1.779 -0.161 -0.725 UK Spain Expenditure 2.22 -1.23 -0.478 Mervar and Payne (2007) 15 EUM[a] Croatia Arrivals 4.8 --- --- 15 EUM Croatia Arrivals 4.91 --- --- members of EZ[b] Croatia Arrivals 3.88 --- --- members of EZ Croatia Arrivals 4.29 --- --- 25 EUM Croatia Arrivals 5 --- --- 25 EUM Croatia Arrivals 5.1 --- --- Muňoz (2007) Germany Spain Arrivals 5.4 -2.16 --- Lim, McAleer, and Min (2008a) Japan Taiwan Arrivals 2.19 --- --- Japan New Zealand Arrivals 1.4 --- --- Japan New Zealand Arrivals 0.81 --- --- Ouerfelli (2008) Germany Tunisia Arrivals 3.71 -7.47 0.43 France Tunisia Arrivals 2.77 -2.71 0.3 Italy Tunisia Arrivals 2.17 -2.43 -0.15 Italy Tunisia Arrivals 1.81 -2.39 --- UK Tunisia Arrivals 1.44 -0.93 0.003 UK Tunisia Arrivals 0.48 -0.41 0.06 Lim, Min and McAleer (2008b) Japan New Zealand Arrivals 1.4 --- --- Japan New Zealand Arrivals 1.193 --- --- Japan Taiwan Arrivals 0.4 --- --- Notes: [a]: “old” European Union members; [b]: European Zone. Table options In addition, the sampling distribution of a point elasticity estimator is likely to follow a non-normal distribution, which renders conventional statistical inference based on normal approximation problematic. Hence, with point estimates alone, it is difficult to assess whether an elasticity estimate is statistically significant or whether it truly represents elastic demand. Therefore, a confidence interval that is robust to small sample biases and non-normality and that has a prescribed level of confidence is more useful for decision-makers. The main purpose of this study is to estimate demand elasticity intervals using the bootstrapping method with a view to overcoming the problems associated with point demand elasticity estimates. The empirical analysis of these intervals is based on a dataset relevant to the demand for Hong Kong tourism. More specifically, we estimate the confidence intervals for the long-run elasticities of the demand for inbound tourism to Hong Kong with respect to its main economic determinants: income, own price and substitute price. We consider nine major inbound markets: Australia, mainland China (China), Japan, Korea, the Philippines, Singapore, Taiwan, the United Kingdom (UK) and the United States (US). Our analysis is based on the autoregressive distributed lag (ARDL) model, which is applied to each market. We employ the ARDL bounds test proposed by Pesaran, Shin, and Smith (2001) to determine the existence of a long-run relationship between tourism demand and its determinants. Once the presence of such a relationship is established, we estimate the long-run elasticities using the ARDL model. For interval estimation, we employ the bias-corrected bootstrap method developed by Kilian (1998), which Li and Maddala (1999) found to be the best means of constructing confidence intervals for long-run elasticities. It is designed to overcome the aforementioned problems of bias and non-normality in relation to elasticity estimation. This study is closely related to that carried out by Song, Wong, and Chon (2003), who modeled the demand for Hong Kong tourism and employed the ARDL model to examine the influence of income and price on the number of international tourists arriving from 16 major origin countries/regions. Although both the current study and that carried out by Song, Witt, and Li (2003) provide estimates of long-run elasticities, there are two key differences between them. First, whereas the earlier study employed annual data from 1973 to 2000 to estimate the demand models, our study makes use of quarterly data from 1985 to 2006. An updated dataset with higher sampling frequency yields richer information content, which can lead to better-quality, more accurate estimation. Seasonality is an important factor when quarterly data are used. However, demand elasticity is determined by such economic fundamentals as income and price. Hence, our ARDL model includes seasonal dummy variables and a long autoregressive (AR) term to control for both deterministic and stochastic seasonality. We thus obtain elasticity estimates free from the effects of seasonality. Second, Song et al. (2003) were concerned with point estimates, whereas the main focus of the present study is interval estimation. Our main finding is that source market income is the most important determining factor for the demand for Hong Kong tourism in the long run. Demand from long-haul markets (Australia, the UK and the US) and growing economies (China and Korea) is found to be particularly income-elastic. Overall, however, we find that this demand is not sensitive to the own and substitute prices in the long run, although there is a strong tendency in short-haul markets (Japan, Korea and the Philippines) for price to be statistically significant and often elastic. That is, the demand from Australia, Japan and Korea is inelastic to the price of Hong Kong tourism, although that from Korea and the Philippines is highly elastic to the tourism price of substitute destinations. The remainder of the paper is organized as follows. The next section presents the methodology employed in the study. Section 3 presents the background to tourism in Hong Kong, a description of the data, and the empirical results, and the final section concludes the paper.

The elasticities of demand for tourism are important measures for both academics and practitioners, as they are useful for policymaking and long-term planning. A large number of studies have estimated income and price elasticities, but their primary focus has been on point estimation, with interval estimation completely neglected. Point estimation alone is not informative, because the completely unknown sampling variability renders statistical inference about elasticity impossible. It is also well known that conventional methods of variance estimation for long-run elasticity are inaccurate and unreliable. Based on these failings, the bias-corrected bootstrap method proposed by Li and Maddala (1999) was adopted in this study, as it has been found to be the best means of constructing confidence intervals. Our analysis is based on the ARDL model, which belongs to a general class of dynamic linear models widely used in tourism demand studies. We establish the presence of a long-run relationship and then estimate long-run income and price elasticities. We find strong evidence of a long-run relationship among demand, income and prices for all nine of the source markets considered. The bias-corrected bootstrap confidence intervals obtained show that the income levels of source markets are the most important determinant of Hong Kong tourism demand in the long run. Demand from long-haul markets (Australia, the UK and the US) and growing economies (China and Korea) demonstrates a particularly high degree of elasticity to income. Overall, such demand is found not to be sensitive to the own and substitute prices of Hong Kong tourism, although we observe a strong tendency for short-haul markets to react sensitively to these prices. The results presented in this paper also clearly demonstrate that the use of the conventional confidence interval approach can provide misleading inferential outcomes on the long-run elasticity of demand. The bootstrap method provides more economically sensible results, as they are not dependent on a restrictive model or distributional assumptions. The ranges of possible income and price elasticities in the tourism literature have been obtained through meta-analysis alone; that is, they represent the collective evaluation of the point estimates reported in accumulated prior studies. Although meta-analytic results offer interesting insights, they provide no indication of whether economically sensible interval estimates of tourism demand elasticities can be obtained from an observed dataset. By adopting the bias-corrected bootstrap as a means of statistical inference, this paper represents the first attempt to provide such estimates. □