Fitting probability distributions to economic growth: a maximum likelihood approach

The growth rate of the gross domestic product (GDP) usually carries heteroscedasticity, asymmetry and fat-tails. In this study three important and significantly heteroscedastic GDP series are examined. A Normal, normal-mixture, normal-asymmetric Laplace distribution and a Student's t-Asymmetric Laplace (TAL) distribution mixture are considered for distributional fit comparison of GDP growth series after removing heteroscedasticity. The parameters of the distributions have been estimated using maximum likelihood method. Based on the results of different accuracy measures, goodness-of-fit tests and plots, we find out that in the case of asymmetric, heteroscedastic and highly leptokurtic data the TAL-distribution fits better than the alternatives. In the case of asymmetric, heteroscedastic but less leptokurtic data the NM fit is superior. Furthermore, a simulation study has been carried out to obtain standard errors for the estimated parameters. The results of this study might be used in e.g. density forecasting of GDP growth series or to compare different economies.