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A New Class of Asymmetric Exponential Power Densities with Applications to Economics and Finance

  • Giulio Bottazzi

    ()

    (LEM - Laboratory of Economics and Management - Sant'Anna School of Advanced Studies)

  • Angelo Secchi

    ()

    (Axe Institutions - CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS)

We introduce a new $5$-parameter family of distributions, the Asymmetric Exponential Power (AEP), able to cope with asymmetries and leptokurtosis and, at the same time, allowing for a continuous variation from non-normality to normality. We prove that the Maximum Likelihood (ML) estimates of the AEP parameters are consistent on the whole parameter space, and when sufficiently large values of the shape parameters are considered, they are also asymptotically efficient and normal. We derive the Fisher information matrix for the AEP and we show that it can be continuously extended also to the region of small shape parameters. Through numerical simulations, we find that this extension can be used to obtain a reliable value for the errors associated to ML estimates also for samples of relatively small size ($100$ observations). Moreover we show that around this sample size, the bias associated with ML estimates, although present, becomes negligible. Finally, we present a few empirical investigations, using diverse data from economics and finance, to compare the performance of AEP with respect to other, commonly used, families of distributions.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number hal-00642696.

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Date of creation: 2011
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Handle: RePEc:hal:cesptp:hal-00642696
Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00642696
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  1. Alfarano, Simone & Milaković, Mishael, 2008. "Does Classical Competition Explain the Statistical Features of Firm Growth?," Economics Working Papers 2008,03, Christian-Albrechts-University of Kiel, Department of Economics.
  2. Giulio Bottazzi & Angelo Secchi, 2006. "Explaining the distribution of firm growth rates," RAND Journal of Economics, RAND Corporation, vol. 37(2), pages 235-256, 06.
  3. DiCiccio T.J. & Monti A.C., 2004. "Inferential Aspects of the Skew Exponential Power Distribution," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 439-450, January.
  4. Canning, D. & Amaral, L. A. N. & Lee, Y. & Meyer, M. & Stanley, H. E., 1998. "Scaling the volatility of GDP growth rates," Economics Letters, Elsevier, vol. 60(3), pages 335-341, September.
  5. Giulio Bottazzi & Angelo Secchi, 2003. "Sectoral Specifities in the Dynamics of U.S. Manufacturing Firms," LEM Papers Series 2003/18, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  6. G. Bottazzi & E. Cefis & G. Dosi & A. Secchi, 2007. "Invariances and Diversities in the Patterns of Industrial Evolution: Some Evidence from Italian Manufacturing Industries," Small Business Economics, Springer, vol. 29(1), pages 137-159, June.
  7. Giulio Bottazzi, 2004. "Subbotools User's Manual," LEM Papers Series 2004/14, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  8. Carolina Castaldi & Giovanni Dosi, 2009. "The patterns of output growth of firms and countries: Scale invariances and scale specificities," Empirical Economics, Springer, vol. 37(3), pages 475-495, December.
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