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A new class of asymmetric exponential power densities with applications to economics and finance

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  • Giulio Bottazzi
  • Angelo Secchi

Abstract

We introduce a new five-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. Copyright 2011 The Author 2011. Published by Oxford University Press on behalf of Associazione ICC. All rights reserved., Oxford University Press.

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Bibliographic Info

Article provided by Oxford University Press in its journal Industrial and Corporate Change.

Volume (Year): 20 (2011)
Issue (Month): 4 (August)
Pages: 991-1030

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Handle: RePEc:oup:indcch:v:20:y:2011:i:4:p:991-1030

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  1. 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, Springer, vol. 29(1), pages 137-159, June.
  2. DiCiccio T.J. & Monti A.C., 2004. "Inferential Aspects of the Skew Exponential Power Distribution," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 99, pages 439-450, January.
  3. Giulio Bottazzi & Angelo Secchi, 2006. "Explaining the distribution of firm growth rates," RAND Journal of Economics, RAND Corporation, RAND Corporation, vol. 37(2), pages 235-256, 06.
  4. Alfarano, Simone & Milakovic, Mishael, 2008. "Does classical competition explain the statistical features of firm growth?," Economics Letters, Elsevier, Elsevier, vol. 101(3), pages 272-274, December.
  5. Canning, D. & Amaral, L. A. N. & Lee, Y. & Meyer, M. & Stanley, H. E., 1998. "Scaling the volatility of GDP growth rates," Economics Letters, Elsevier, Elsevier, vol. 60(3), pages 335-341, September.
  6. Giulio Bottazzi & Angelo Secchi, 2003. "Sectoral Specifities in the Dynamics of U.S. Manufacturing Firms," LEM Papers Series, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy 2003/18, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  7. Giulio Bottazzi, 2004. "Subbotools User's Manual," LEM Papers Series, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy 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, Springer, vol. 37(3), pages 475-495, December.
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Cited by:
  1. Matthias Duschl & Thomas Brenner, 2013. "Growth dynamics in regional systems of technological activities – A SVAR approach," Working Papers on Innovation and Space, Philipps University Marburg, Department of Geography 2013-12, Philipps University Marburg, Department of Geography.
  2. Asquith, William H., 2014. "Parameter estimation for the 4-parameter Asymmetric Exponential Power distribution by the method of L-moments using R," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 71(C), pages 955-970.
  3. Matthias Duschl & Thomas Brenner, 2011. "Characteristics of Regional Industry-specific Employment Growth – Empirical Evidence for Germany," Working Papers on Innovation and Space, Philipps University Marburg, Department of Geography 2011-07, Philipps University Marburg, Department of Geography.
  4. Giulio Bottazzi & Angelo Secchi & Federico Tamagni, 2010. "Financial Constraints and Firm Dynamics," Discussion Papers, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy 2010/99, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
  5. Lunardi, José T. & Miccichè, Salvatore & Lillo, Fabrizio & Mantegna, Rosario N. & Gallegati, Mauro, 2014. "Do firms share the same functional form of their growth rate distribution? A statistical test," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 39(C), pages 140-164.

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