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

Author

Listed:
  • Giulio Bottazzi

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

  • Angelo Secchi

    () (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

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.

Suggested Citation

  • Giulio Bottazzi & Angelo Secchi, 2011. "A New Class of Asymmetric Exponential Power Densities with Applications to Economics and Finance," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00642696, HAL.
  • 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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    References listed on IDEAS

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    1. 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.
    2. Alfarano, Simone & Milakovic, Mishael, 2008. "Does classical competition explain the statistical features of firm growth?," Economics Letters, Elsevier, vol. 101(3), pages 272-274, December.
    3. Giulio Bottazzi & Angelo Secchi, 2006. "Explaining the distribution of firm growth rates," RAND Journal of Economics, RAND Corporation, vol. 37(2), pages 235-256, June.
    4. 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.
    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, vol. 60(3), pages 335-341, September.
    6. 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.
    7. 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.
    8. 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.
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    Citations

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    Cited by:

    1. Thomas Brenner & Matthias Duschl, 2014. "Modelling Firm and Market Dynamics - A Flexible Model Reproducing Existing Stylized Facts," Working Papers on Innovation and Space 2014-07, Philipps University Marburg, Department of Geography.
    2. repec:bla:jtsera:v:38:y:2017:i:2:p:175-190 is not listed on IDEAS
    3. Tumlinson, Samuel E., 2015. "On the non-existence of maximum likelihood estimates for the extended exponential power distribution and its generalizations," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 111-114.
    4. Matthias Duschl & Thomas Brenner, 2013. "Characteristics of regional industry-specific employment growth rates' distributions," Papers in Regional Science, Wiley Blackwell, vol. 92(2), pages 249-270, June.
    5. Giulio Bottazzi & Angelo Secchi & Federico Tamagni, 2014. "Financial constraints and firm dynamics," Small Business Economics, Springer, vol. 42(1), pages 99-116, January.
    6. Mercedes Campi & Marco Due~nas, 2017. "Volatility and Economic Growth in the Twentieth Century," Papers 1708.06792, arXiv.org.
    7. Huber, Peter & Oberhofer, Harald & Pfaffermayr, Michael, 2017. "Who creates jobs? Econometric modeling and evidence for Austrian firm level data," European Economic Review, Elsevier, vol. 91(C), pages 57-71.
    8. repec:spr:eurasi:v:3:y:2013:i:2:d:10.14208_ebr.2013.03.02.003 is not listed on IDEAS
    9. 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, vol. 71(C), pages 955-970.
    10. Matthias Duschl & Shi-Shu Peng, 2013. "Chinese firm dynamics and the role of ownership type A conditional estimation approach of the Asymmetric Exponential Power (AEP) density," Papers on Economics and Evolution 2014-01, Philipps University Marburg, Department of Geography.
    11. Andrew Harvey & Rutger-Jan Lange, 2015. "Volatility Modeling with a Generalized t-distribution," Cambridge Working Papers in Economics 1517, Faculty of Economics, University of Cambridge.
    12. Reiner Franke, 2015. "How Fat-Tailed is US Output Growth?," Metroeconomica, Wiley Blackwell, vol. 66(2), pages 213-242, May.
    13. Matthias Duschl & Thomas Brenner, 2011. "Characteristics of Regional Industry-specific Employment Growth – Empirical Evidence for Germany," Working Papers on Innovation and Space 2011-07, Philipps University Marburg, Department of Geography.
    14. Matthias Duschl & Thomas Brenner, 2013. "Growth dynamics in regional systems of technological activities – A SVAR approach," Working Papers on Innovation and Space 2013-12, Philipps University Marburg, Department of Geography.
    15. Caterina Santi & Pietro Santoleri, 2017. "Exploring the link between innovation and growth in Chilean firms," Small Business Economics, Springer, vol. 49(2), pages 445-467, August.
    16. Ramos, Arturo, 2015. "Are the log-growth rates of city sizes normally distributed? Empirical evidence for the US," MPRA Paper 65584, University Library of Munich, Germany.
    17. Puente-Ajovin, Miguel & Ramos, Arturo, 2015. "An improvement over the normal distribution for log-growth rates of city sizes: Empirical evidence for France, Germany, Italy and Spain," MPRA Paper 67471, University Library of Munich, Germany.
    18. 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, vol. 39(C), pages 140-164.
    19. Francesco Bogliacino & Giuditta Prato & Daniel Nepelski, 2013. "Ownership Structure and R&D Orientation in ICT Groups," Eurasian Business Review, Springer;Eurasia Business and Economics Society, vol. 3(2), pages 164-178, December.

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    Keywords

    Asymmetric Exponential Power;

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