On the robustness of the fat-tailed distribution of firm growth rates: a global sensitivity analysis

  • G. Dosi
  • M. C. Pereira
  • M. E. Virgillito
Regular Article


Firms grow and decline by relatively lumpy jumps which cannot be accounted by the cumulation of small, “atom-less”, independent shocks. Rather “big” episodes of expansion and contraction are relatively frequent. More technically, this is revealed by the fat-tailed distributions of growth rates. This applies across different levels of sectoral disaggregation, across countries, over different historical periods for which there are available data. What determines such property? In Dosi et al. (The footprint of evolutionary processes of learning and selection upon the statistical properties of industrial dynamics. Industrial and corporate change. Oxford University Press, Oxford, 2016) we implemented a simple multi-firm evolutionary simulation model, built upon the coupling of a replicator dynamic and an idiosyncratic learning process, which turns out to be able to robustly reproduce such a stylized fact. Here, we investigate, by means of a Kriging meta-model, how robust such “ubiquitousness” feature is with regard to a global exploration of the parameters space. The exercise confirms the high level of generality of the results in a statistically robust global sensitivity analysis framework.


Fat-tailed distributions Kriging meta-modeling Near-orthogonal latin hypercubes Variance-based sensitivity analysis ABMs validation 

JEL Classification

C15 C63 D21 D83 L25 



We thank Francesca Chiaromonte for helpful comments and discussions. We gratefully acknowledge the support by the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 649186 - ISIGrowth and by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), process No. 2015/09760-3.


  1. Bargigli L, Riccetti L, Russo A, Gallegati M (2016) Network calibration and metamodeling of a financial accelerator agent based model. ssrnGoogle Scholar
  2. Bottazzi G (2014) SUBBOTOOLS. Scuola Superiore Sant’Anna, PisaGoogle Scholar
  3. Bottazzi G, Secchi A (2003) A stochastic model of firm growth. Phys A Stat Mech Appl 324(1):213–219CrossRefGoogle Scholar
  4. Bottazzi G, Secchi A (2006) Explaining the distribution of firm growth rates. RAND J Econ 37(2):235–256CrossRefGoogle Scholar
  5. Bottazzi G, Cefis E, Dosi G (2002) Corporate growth and industrial structures: some evidence from the italian manufacturing industry. Indus Corp Change 11(4):705–723CrossRefGoogle Scholar
  6. Cioppa T, Lucas T (2007) Efficient nearly orthogonal and space-filling latin hypercubes. Technometrics 49(1):45–55CrossRefGoogle Scholar
  7. Dosi G (2007) Statistical regularities in the evolution of industries. A guide trough some evidence and challenges for the theory. In: Malerba F, Brusoni S (eds) Perspectives on innovation (2007), Cambridge University Press, CambridgeGoogle Scholar
  8. Dosi G, Marsili O, Orsenigo L, Salvatore R (1995) Learning, market selection and the evolution of industrial structures. Small Bus Econ 7(6):411–436CrossRefGoogle Scholar
  9. Dosi G, Nelson R, Winter S (2000) The nature and dynamics of organizational capabilities. Oxford University Press, OxfordGoogle Scholar
  10. Dosi G, Pereira M, Virgillito M (2016) The footprint of evolutionary processes of learning and selection upon the statistical properties of industrial dynamics. Industrial and corporate change. Oxford University Press, Oxford. doi: 10.1093/icc/dtw044 Google Scholar
  11. Dupuy D, Helbert C, Franco J (2015) DiceDesign and DiceEval: two R packages for design and analysis of computer experiments. J Stat Softw 65(11):1–38CrossRefGoogle Scholar
  12. Helton J, Johnson J, Sallaberry C, Storlie C (2006) Survey of sampling-based methods for uncertainty and sensitivity analysis. Reliab Eng Syst Saf 91(10):1175–1209CrossRefGoogle Scholar
  13. Ijiri Y, Simon H (1977) Skew distributions and the sizes of business firms. North-Holland, AmsterdamGoogle Scholar
  14. Iooss B, Boussouf L, Feuillard V, Marrel A (2010) Numerical studies of the metamodel fitting and validation processes. arXiv preprint arXiv:1001.1049
  15. Jeong S, Murayama M, Yamamoto K (2005) Efficient optimization design method using kriging model. J Aircr 42(2):413–420CrossRefGoogle Scholar
  16. Kleijnen JP (2009) Kriging metamodeling in simulation: a review. Eur J Oper Res 192(3):707–716CrossRefGoogle Scholar
  17. Kleijnen J, Sargent R (2000) A methodology for fitting and validating metamodels in simulation. Eur J Oper Res 120(1):14–29CrossRefGoogle Scholar
  18. Krige D (1951) A statistical approach to some basic mine valuation problems on the witwatersrand. J Chem Metall Min Soc S Afr 52(6):119–139Google Scholar
  19. Matheron G (1963) Principles of geostatistics. Econ Geol 58(8):1246–1266Google Scholar
  20. McKay M, Beckman R, Conover W (2000) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 42(1):55–61CrossRefGoogle Scholar
  21. Metcalfe JS (1998) Evolutionary economics and creative destruction. Routledge & Kegan Paul, LondonCrossRefGoogle Scholar
  22. Nelson RR, Winter SG (1982) An evolutionary theory of economic change. Belknap Press of Harvard University Press, CambridgeGoogle Scholar
  23. R Core Team (2016) R: a language and environment for statistical computing. R Foundation for Statistical Computing, ViennaGoogle Scholar
  24. Rasmussen C, Williams C (2006) Gaussian processes for machine learning. MIT Press, CambridgeGoogle Scholar
  25. Roustant O, Ginsbourger D, Deville Y (2012) Dicekriging, diceoptim: two R packages for the analysis of computer experiments by kriging-based metamodeling and optimization. J Stat Softw 51(1):1–55CrossRefGoogle Scholar
  26. Salle I, Yildizoglu M (2014) Efficient sampling and meta-modeling for computational economic models. Comput Econ 44(4):507–536CrossRefGoogle Scholar
  27. Saltelli A, Annoni P (2010) How to avoid a perfunctory sensitivity analysis. Environ Model Softw 25(12):1508–1517CrossRefGoogle Scholar
  28. Saltelli A, Tarantola S, Campolongo F (2000) Sensitivity analysis as an ingredient of modeling. Stat Sci 15(4):377–395CrossRefGoogle Scholar
  29. Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S (2008) Global sensitivity analysis: the primer. Wiley, New YorkGoogle Scholar
  30. Schumpeter J (1947) Capitalism, socialism, and democracy. Harper & Brothers Publishers, New York and LondonGoogle Scholar
  31. Silverberg G, Dosi G, Orsenigo L (1988) Innovation, diversity and diffusion: a self-organisation model. Econ J 98(393):1032–1054CrossRefGoogle Scholar
  32. Valente M (2014) LSD: laboratory for simulation development. University of L’Aquila, L’AquilaGoogle Scholar
  33. Van Beers W, Kleijnen J (2004) Kriging interpolation in simulation: a survey. In: Proceedings of the 2004 Winter Simulation Conference, 2004. IEEE, vol 1Google Scholar
  34. Wang G, Shan S (2007) Review of metamodeling techniques in support of engineering design optimization. J Mech Des 129(4):370–380CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Institute of EconomicsScuola Superiore Sant’AnnaPisaItaly
  2. 2.Institute of EconomicsUniversity of CampinasCampinasBrazil
  3. 3.Istituto di Politica Economica, Universita’ Cattolica del Sacro CuoreMilanItaly

Personalised recommendations