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Choosing the Right Skew Normal Distribution: the Macroeconomist’ Dilemma

Wojciech Charemza (), Carlos Díaz () and Svetlana Makarova ()

No 15/08, Discussion Papers in Economics from Division of Economics, School of Business, University of Leicester

Abstract: The paper discusses the consequences of possible misspecification in fitting skew normal distributions to empirical data. It is shown, through numerical experiments, that it is easy to choose a distribution which is different from that which generated the sample, if the minimum distance criterion is used. The distributions compared are the two-piece normal, weighted skew normal and the generalized Balakrishnan skew normal distribution which covers a variety of other skew normal distributions, including the Azzalini distribution. The estimation method applied is the simulated minimum distance estimation with the Hellinger distance. It is suggested that, in case of similarity in values of distance measures obtained for different distributions, the choice should be made on the grounds of parameters’ interpretation rather than the goodness of fit. For monetary policy analysis, this suggests application of the weighted skew normal distribution, which parameters are directly interpretable as signals and outcomes of monetary decisions. This is supported by empirical evidence of fitting different skew normal distributions to the ex-post monthly inflation forecast errors for Poland, Russia, Ukraine and U.S.A., where estimations do not allow for clear distinction between the fitted distributions for Poland and U.S.A.

Keywords: Skew Normal Distributions; Ex-post Uncertainty; Inflation Forecasting; Economic Policy (search for similar items in EconPapers)
JEL-codes: E17 C46 E52 E37 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-cba, nep-cis, nep-ecm and nep-mac
Date: 2015-05
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Working Paper: Too many skew normal distributions? The practitioner’s perspective (2013) Downloads
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