Fitting probability distributions to economic growth: a maximum likelihood approach

ABSTRACT

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.

KEYWORDS:

• Normal
• normal-mixture
• normal-asymmetric Laplace
• Student's t-asymmetric Laplace
• maximum likelihood estimation

Acknowledgments

The authors would like to thank the referees for their valuable comments which have led to improvements in the final revision.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. The Kernel estimate is defined as $\hat{f}(y,h)=\frac{1}{nh}\sum _{i=1}^{n}k\left(\frac{y-y_i}{h}\right),$ where $k(\cdot )$ is the Kernel function and h is the bandwidth parameter. In this study, we have used the Gaussian Kernel, and the Silverman [50] Rule of Thumb bandwidth $\hat{h}={\left(\frac{4{\hat{\sigma }}^5}{3n}\right)}^{1/5}\approx 1.059\hat{\sigma }{n}^{-1/5},$ which is considered to be optimal when data are close to normal as the case here.