ARMAX Modelling of International Tourism Demand

One of the basic goals of tourism demand modelling is to estimate income and/or price elasticities, which can then be used in developing better informed public and private policies. The focus of econometric studies is to determine the extent to which the data support a particular theory. In reviews of empirical studies on international tourism demand and its determinants, Lim (1999, 2006) argued that the most prominent and frequently used variable in these studies is income of tourist-generating countries, which affects the ability of consumers in these countries to pay for their overseas travel. More specifically, the demand for international travel is positively related to income in the origin market. Japan has been a dominant economic power and a tourism superpower in the Asia-Pacific region. It has been the largest inbound market for many countries in the region. Figure 1 shows the real GDP and outbound travel of Japan since 1980. The purpose of this paper is to use the ARMAX model to investigate the dynamic relationship between tourism demand and real income of Japan, and to compare the findings with the single-equation model. Extensive discussion of ARMAX modelling and estimation can be found in Franses (1991) and Greene (2000). The ARMAX model is an extension of the Box-Jenkins autoregressive-moving average (ARMA) model with explanatory exogenous variables (X). Box-Jenkins (1970) models are used to capture the autoregressive moving average of past observations of tourist arrivals from Japan to Taiwan and New Zealand. While it is possible to use the autoregressive (AR) and moving average (MA) processes 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, other explanatory variables, such as real income in the origin country, have also affected the demand for international travel. [GRAPHICS] By including an income variable with a finite lag structure, the ARMAX model is used to estimate the income elasticity of tourism demand by Japan for New Zealand and Taiwan over the period 1980 to 2004. Before specifying the ARMAX model, tests and diagnostics are performed in the estimation of the Box-Jenkins models. By excluding insignificant AR and MA lags, the use of diagnostics and selection criteria would help to determine a more parsimonious model. The latter is subsequently used to undertake ARMAX modelling and estimation of the income elasticity of travel demand. After discussing the tourism movements from Japan to New Zealand and Taiwan since 1980 and characteristics of international tourists, the methodology and unit root tests for the tourism and income time series are discussed, the estimation of the single equation and ARMAX models is presented, and some concluding remarks are given. The EViews 5 econometric software package is used for the data analysis and empirical estimation.