Abstract
We propose here a new implementation of the forward search, which is a powerful general method usually suitable for detecting extreme observations and for determining their effect on fitted models (Atkinson and Riani, 2000). Through the forward search we iteratively fit the Pareto II distribution to firm size data. In particular, a threshold is fixed to the fit of the Pareto II distribution through a progressive adaptation technique, performing at each iteration the χ 2 test to check for the acceptance of the null hypothesis. Yearly Zipf-plots of the truncated empirical distribution with superimposed theoretical Pareto II distribution highlight the adherence of the estimates to data for different size ranges. Possible economic interpretations of the results are then provided, referring in particular to the role of the stock market in shaping firm size distribution and to the firm size effect (Banz, 1981; Reingaum, 1981). More in general, we discuss possible implications of introducing our methodology in macroeconomic models.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arnold, B. (1983). Pareto Distributions. International Co-operative, Fairland, ME.
Atkinson, A. C. and Riani, M. (2000). Robust Diagnostic Regression Analysis. Springer-Verlag, New York.
Axtell, R. (2001). Zipf distribution of U.S. firm sizes. Science, 293: 1818–1820.
Banz, R. (1981). The relationship between return and market value of common stock. Journal of Financial Economics, 9: 3–18.
Benartzi, S. and Thaler, R.H. (1995). Myopic loss aversion and the equity premium puzzle. Quarterly Journal of Economics, CX: 73–92.
Blinder, A (1986). A skeptical note on the new econometrics, in Prices, Competition and Equilibrium, Preston, M.H. and Quandt, R.E., Eds., P. Allan, London, pp. 73–83.
Crosato, L. and Ganugi, P. (2007). Statistical regularity of firm size distribution: The Pareto IV and truncated Yule for Italian SCI manufacturing. Statistical Methods and Applications, 16(1): 85–115.
D’Addario (2003). Monetary Theory and Policy. MIT Press, Cambridge, MA.
Forni, M. and Lippi, M. (1997). Aggregation and the microfoundation of Dynamic Macroeconomics. Oxford University Press USA.
Gibrat, R. (1931). Les Inégalités Economiques. Librairie du Recueil Survey, Paris.
Hart, P.E. and Oulton, N. (1997). Zipf and the size distribution of firms. Applied Economics Letters, 4(4): 205–206.
Hart, P.E. and Prais, S.J. (1956). The analysis of business concentration: A statistical approach. Journal of the Royal Statistical Society, Series A, 119: 150–191.
Ijiri, Y. and Simon, H.A. (1977). Skew Distributions and the Sizes of Business Firms. North-Holland, Amsterdam.
Kahneman, D. (1994). New challenges to the rationality assumption. Journal of Institutional and Theoretical Economics, 150: 18–36.
Kahneman, D. and Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, XLVII: 263–91.
Kleiber, C. and Kotz, S. (2003). Statistical Size Distributions in Economics and Actuarial Sciences. Wiley, New York.
Pareto, V. (1897). Cours d’Economie Politique. Lausanne, Swisse.
Quandt, R.E. (1966). On the size distribution of firms. American Economic Review, 3: 416–432.
Reingaum, J. (1981). Misspecification of capital asset pricing: Empirical anomalies based on earning yields and market value. Journal of Financial Economics, 9: 19–46.
Shafir, E., Diamond, P., and Tversky, A. (1997). Money illusion. Quarterly Journal of Economics, CXII: 341–374.
Stanley, M.H.R., Buldyrev, S.V., Havlin, S., Mantegna, R.N., Salinger, M.A., and Stanley, H.E. (1995). Zipf plots and the size distribution of firms. Economics Letters, 49: 453–457.
Steindl, J. (1965). Random Processes and the Growth of Firms. Griffin, London.
Walsh, C. (2003). Monetary Theory and Policy. MIT Press, Cambridge, MA.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Birkhäuser Boston
About this chapter
Cite this chapter
Corbellini, A., Crosato, L., Ganugi, P., Mazzoli, M. (2010). Fitting Pareto II Distributions on Firm Size: Statistical Methodology and Economic Puzzles. In: Skiadas, C. (eds) Advances in Data Analysis. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4799-5_26
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4799-5_26
Published:
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4798-8
Online ISBN: 978-0-8176-4799-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)