On the probability distribution of economic growth

Abstract

Three important and significantly heteroscedastic gross domestic product series are studied. Omnipresent heteroscedasticity is removed and the distributions of the series are then compared to normal, normal mixture and normal–asymmetric Laplace (NAL) distributions. NAL represents a skewed and leptokurtic distribution, which is in line with the Aghion and Howitt [1] model for economic growth, based on Schumpeter's idea of creative destruction. Statistical properties of the NAL distributions are provided and it is shown that NAL fits the data better than the alternatives.

Keywords:

• The Aghion–Howitt model
• asymmetric innovations
• mixed normal–asymmetric Laplace distribution
• kernel density estimation
• method of moments estimation

Acknowledgements

This research was supported by the Department of Statistics at Stockholm University, Royal Swedish Academy of Sciences, the International Institute of Forecasters and by the Societas Scientiarum Fennica. We gratefully acknowledge helpful comments from Daniel Thorburn of Stockholm University, Mattias Villani of the Swedish Riksbank and from Roy Batchelor of Cass Business School, London. Parts of this paper have been presented at the International Symposium on Forecasting in 2007 and 2008 and also at various other venues. We are grateful for the many suggestions from seminar participants. The authors also like to thank three anonymous referees and the editor for very valuable suggestions and comments that improved the article considerably.

Notes

This could also be studied using regime-switching models, but given the few observations, we did not pursue this idea.

Consists of Canada (1961–2007), France (1978–2007), Germany (1991–2007), Italy (1980–2007), Japan (1980–2007), UK (1960–2007) and USA (1960–2007). Volume national data are scaled up/down to 2000 price levels and the G7 series is calculated as their sum.

The kernel density estimate is defined as

• where h is the bandwidth and K(·) is the kernel function. In this study, we have used the Gaussian kernel, , and the Silverman 29 “Rule of Thumb” bandwidth
  which is considered to be optimal when data are close to normal.

We tried to make use of the fifth moment, but in none of the series did it even at a 10% significance level differ from zero. For convenience, also the fifth moment is included in Appendix.

Defined as .