Arturo Ramos, Till Massing, Atushi Ishikawa, Shouji Fujimoto, Takayuki Mizuno
arXiv 20 Jan 2023 · General Economics
arXiv:2301.09438 · PDF · DOI · OpenAlex · Extracted main text
We study 17 different statistical distributions for sizes obtained {}from the classical and recent literature to describe a relevant variable in the social sciences and Economics, namely the firms' sales distribution in six countries over an ample period. We find that the best results are obtained with mixtures of lognormal (LN), loglogistic (LL), and log Student's $t$ (LSt) distributions. The single lognormal, in turn, is strongly not selected. We then find that the whole firm size distribution is better described by a mixture, and there exist subgroups of firms. Depending on the method of measurement, the best fitting distribution cannot be defined by a single one, but as a mixture of at least three distributions or even four or five. We assess a full sample analysis, an in-sample and out-of-sample analysis, and a doubly truncated sample analysis. We also provide the formulation of the preferred models as solutions of the Fokker--Planck or forward Kolmogorov equation.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | McLachlan, G. and Peel, D (2003) Finite mixture models | 1.000 | 6 | 4 | 100% |
| 2 | Peña, G., Puente-Ajovń, M., Ramos, A., and Sanz-Gracia, F (2022) Log-growth rates of $CO_2$: An empirical analysis self | 1.000 | 5 | 3 | 100% |
| 3 | Campolieti, M. and Ramos, A (2021) The distribution of strike size: Empirical evidence from Europe and North America in the 19th and 20th centuries self | 0.928 | 4 | 4 | 100% |
| 4 | Puente-Ajovń, M., Ramos, A., and Sanz-Gracia, F (2020) Is there a universal parametric city size distribution? Empirical evidence for 70 countries self | 0.928 | 4 | 3 | 100% |
| 5 | Gualandi, S. and Toscani, G (2019) Size distribution of cities: A kinetic explanation | 0.843 | 3 | 3 | 100% |
| 6 | Gualandi, S. and Toscani, G (2019) Human behavior and lognormal distribution. A kinetic description | 0.843 | 3 | 3 | 100% |
| 7 | Kwong, H. S. and Nadarajah, S (2019) A note on Pareto tails and lognormal body of US cities size distribution | 0.843 | 3 | 3 | 100% |
| 8 | Puente-Ajovń, M., Ramos, A., Sanz-Gracia, F., and Arribas-Bel, D (2020) How sensitive is city size distribution to the definition of city? The case of Spain self | 0.843 | 3 | 3 | 100% |
| 9 | Su, H.-L (2019) On the city size distribution: A finite mixture interpretation | 0.843 | 3 | 3 | 100% |
| 10 | Fiori, A. M (2020) On firm size distribution: statistical models, mechanisms, and empirical evidence | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 89 scored citations.