Modelling the non-linear effects of tourism development on emerging market economies using normal-power model

Abstract

In linear regression, a major problem arise when the response variable is bimodal. In this study, the non-linear effects of tourism development on the economic well-being of some selected emerging economies, which have bimodal features was modelled. In a linear regression model, the dependent variable follows a normal distribution, but non-linear regression, it is assumed to follow a normal-power distribution. The non-linear model was estimated by first transforming the normal-power model, which is intrinsically non-linear to linear using a simple transformation technique. The GDP per capita (response variable) is used as a proxy for measuring the economy, while international tourist arrivals (predictor variable) is used as a proxy to measure tourism development (Nigeria, Ghana, Cote D’Ivoire and Senegal). The results showed 70 per cent of the variation in GDP per Capita can be explained by the number of international tourists visiting the countries. The results of the models showed that the non-linear normal-power model outperformed the linear normal model using the log-likelihood, AIC, BIC, and MSE for the four countries. It is also true for the pooled regression. The Likelihood Ratio Test (LRT) further showed the flexibility of the non-linear model compared with the linear model since the test statistic of LRT for the selected countries 335.1018, 323.594, 312.658 and 281.415 for Nigeria, Ghana, Ivory Coast and Senegal as well as 1361.066 for the pooled regression are greater than the Chi-Square critical value of 5.991 at 2 degrees of freedom. This explained how significant the non-linear normal-power model can predict the RGDP-TOUR model as compared with the linear normal model. However, the linear model is a special case (sub-model) of the non-linear normal-power model if the parameters of the power function distribution are relaxed. It is therefore recommended that the relationship between gross domestic product per capita and international tourist arrivals is non-linear and should be fitted with normal-power regression model.