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 IIistribution through a progressive adaptation technique, performing at each iteration the chi(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
Corbellini, A., Crosato, L., Ganugi, P., Mazzoli, M. (2010). Fitting Pareto II Distributions on Firm Size: Statistical Methodology and Economic Puzzles. In C.H. Skiadas (a cura di), Advances in Data Analysis Theory and Applications to Reliability and Inference, Data Mining, Bioinformatics, Lifetime Data, and Neural Networks (pp. 321-328). Springer/Birkhauser [10.1007/978-0-8176-4799-5_26].
Fitting Pareto II Distributions on Firm Size: Statistical Methodology and Economic Puzzles
CROSATO, LISA;
2010
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 IIistribution through a progressive adaptation technique, performing at each iteration the chi(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
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