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The Empirical Validation of an Agent-based Model

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Abstract

The aim of this paper is to empirically validate the agent-based macroeconomic model of Gaffeo et al. [2008]. We show that the microsimulated version of the model is able to replicate actual data with a satisfactory degree of precision. From a theoretical point of view, our validation approach is made up of three different steps: a calibrated microsimulation of the model with actual data, an ex-post descriptive validation of the results, and a simple calibration exercise to ameliorate the goodness-of-fit of the model. The validation procedure of this paper has been performed using Italian data.

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Notes

  1. 1.

    In the following BAM is specifically referred to the model of Gaffeo et al. [2008].

  2. 2.

    http://econ2.econ.iastate.edu/tesfatsi/amulmark.htm.

  3. 3.

    Further developments of the model are available in Delli Gatti et al. [2011].

  4. 4.

    This is why we have omitted that part in our summary of the BAM model.

  5. 5.

    If not explicitly stated, all the values we have used in simulations are the same of Gaffeo et al. [2008] and Delli Gatti et al. [2008].

  6. 6.

    Calibration allows to ameliorate the distributional fitting by 4 percent on average. We want to stress that, even without calibration, the BAM model surprisingly obtains very good results in the validation procedure.

  7. 7.

    This value is arbitrary, as usual when defining an acceptance region. All the results for deviations of ±2 percent, ±5 percent, ±20 percent are available upon request to the corresponding author.

  8. 8.

    As in Ijiri and Simon [1977], the use of pooled distributions is possible since the yearly distributions show similar slopes.

  9. 9.

    As usual, the results for the other years available upon request.

References

  1. Alfarano, Stefano, Thomas Lux, and Friedrich Wagner . 2007. Empirical Validation of Stochastic Models of Interacting Agents. European Physical Journal B, 55: 183–187.

  2. Amaral, Luis A.N., Sergey V. Buldyrev, Shlomo Havlin, Heiko Leschhorn, Philipp Maas, Michael A. Salinger, Eugene H. Stanley, and Michael H.R. Stanley . 1997. Scaling Behavior in Economics: I. Empirical Results for Company Growth. Journal de Physique, 7: 621–633.

  3. Axelrod, Robert . 1997. Advancing the Art of Simulation in the Social Sciences, in Simulating Social Phenomena, edited by Rosario Conte, Rainer Hegselmann, Pietro Terna. Berlin: Springer-Verlag, 21–40.

  4. Axtell, Robert . 2000. Why agents? On the Varied Motivations for Agent Computing in the Social Sciences, Center on Social and Economic Dynamics Working Paper 17.

  5. Axtell, Robert . 2001. Zipf's Distribution of US Firms Sizes. Sciences, 293: 1818–1820.

  6. Axtell, Robert, Robert Axelrdod, Joshua Epstein, and Michael Cohen . 1996. Aligning Simulation Models: A Case Study and Results. Computational and Mathematical Organization Theory, 1: 123–141.

  7. Bianchi, Carlo, Pasquale Cirillo, Mauro Gallegati, and Pietro Vagliasindi . 2007. Validation in Agent-based Models: An Investigation on the CATS Model. Journal of Economic Behavior and Organization, 67: 947–964.

  8. Bianchi, Carlo, Pasquale Cirillo, Mauro Gallegati, and Pietro Vagliasindi . 2008. Validating and Calibrating ACE Models: A Case Study. Computational Economics, 30: 245–264.

  9. Bottazzi, Giulio, and Angelo Secchi . 2005. Explaining the Distribution of Firm Growth Rates. Rand Journal of Economics, 37: 234–263.

  10. Carley, Kathleen M. 1996. Validating Computational Models, Working Paper: www.econ.iastate.edu/tesfatsi/EmpVal/EmpVal.Carley.pdf.

  11. Chaouche, Ali, and Jean-Noel Bacro . 2004. Fitting the Generalized Pareto Distribution to Data. Computational Statistics and Data Analysis, 45: 787–803.

  12. Chen, Shu-Heng 2003. Agent-based Computational Macroeconomics: A Survey, In Meeting the Challenge of Social Problems via Agent-based Simulation, Post-proceedings of the Second International Workshop of Agent-based Approaches in Economic and Social Complex Systems, edited by Takao Terano, Hiroshi Deguchi and Keidi Takadama. Tokyo: Springer-Verlag, 141–170.

  13. Chen, Shu-Heng . 2005. Trends in Agent-based Computational Modeling of Macroeconomics. New Generation Computing, 23: 3–11.

  14. Cincotti, Silvano, Marco Raberto, and Andrea Teglio . 2010. Credit Money and Macroeconomic Instability in the Agent-based Model and Simulator Eurace, Economics Discussion Papers, No 2010-4. Available online at: http://www.economics-ejournal.org/economics/discussionpapers/2010-4.

  15. Cirillo, Pasquale . 2010. An Analysis of the Size Distribution of Italian Firms by Age. Physica A: Statistical Mechanics and Its Applications, 389: 459–466.

  16. Cirillo, Pasquale . 2011. About the Distribution of Wages in Italy, Submitted. Preprint available upon request.

  17. Cirillo, Pasquale, and Jürg Hüsler . 2009. On the Upper Tail of Italian Firms’ Size Distribution. Physica A: Statistical Mechanics and Its Applications, 388: 1546–1554.

  18. Dawid, Herbert, Simon Gemkow, Philipp Harting, Kordian Kabus, Klaus Wersching, and Michael Neugart . 2008. Skills, Innovation, and Growth: An Agent-based Policy Analysis. Journal of Economics and Statistics, 228: 251–275.

  19. Delli Gatti, Domenico, Corrado Di Guilmi, Edoardo Gaffeo, Gianfranco Giulioni, Mauro Gallegati, and Antonio Palestrini . 2005. A New Approach to Business Fluctuations: Heterogeneous Interacting Agents, Scaling Laws and Financial Fragility. Journal of Economic Behavior & Organization, 56: 489–512.

  20. Delli Gatti, Domenico, Edoardo Gaffeo, Mauro Gallegati, Gianfranco Giulioni, and Antonio Palestrini . 2008. Emergent Macroeconomics. Berlin: Springer-Verlag.

  21. Delli Gatti, Domenico, Edoardo Gaffeo, and Mauro Gallegati . 2010. Complex Agent-based Macroeconomics: A Manifesto for a New Paradigm. Journal of Economic Interaction and Coordination, 5: 111–135.

  22. Delli Gatti, Domenico, Saul Desiderio, Edoardo Gaffeo, Pasquale Cirillo, and Mauro Gallegati . 2011. Macroeconomics from the Bottom Up. Berlin: Springer-Verlag.

  23. Embrechts, Paul, Thomas Mikosch, and Claudia Kluppelberg . 1997. Modeling Extremal Events. Berlin: Springer-Verlag.

  24. Das, Arnab, and Bikas K. Chakrabarti . 2005. Quantum Annealing and Related Optimization Methods. Berlin: Birkäuser.

  25. Fagiolo, Giorgio, Alessio Moneta, and Paul Windrum . 2008. A Critical Guide to Empirical Validation of Agent-based Models in Economics: Methodologies, Procedures, and Open Problems. Computational Economics, 30: 195–226.

  26. Fujiwara, Yoshi . 2004. Zipf Law in Firms Bankruptcy. Physica A, 337: 219–230.

  27. Gabaix, Xavier, Paremswaran Gopikrishnan, Vasiliki Plerou, and Eugene H. Stanley . 2003. A Theory of Power Law Distributions in Financial Markets Fluctuations. Nature, 423: 267–270.

  28. Gaffeo, Edoardo, Corrado Di Guilmi, and Mauro Gallegati . 2003. Power Law Scaling in the World Income Distribution. Economics Bullettin, 15: 1–7.

  29. Gaffeo, Edoardo, Michele Catalano, Fabio Clementi, Domenico Delli Gatti, Mauro Gallegati, and Alberto Russo . 2007. Reflections on Modern Macroeconomics: Can We Travel along a Safer Road? Physica A: Statistical Mechanics and Its Applications, 382: 89–97.

  30. Gaffeo, Edoardo, Domenico Delli Gatti, Saul Desiderio, and Mauro Gallegati . 2008. Adaptive Microfoundations for Emergent Macroeconomics. Eastern Economic Journal, 34: 441–463.

  31. Gilli, Manfred, and Peter Winker . 2003. A Global Optimization Heuristic for Estimating Agent-based Models. Computational Statistics and Data Analysis, 42: 299–312.

  32. Gourieroux, Christian, and Alain Monfort . 1996. Simulation-based Econometric Methods. Oxford: Oxford University Press.

  33. Haber, Gottfried . 2008. Monetary and Fiscal Policy Analysis with an Agent-based Macroeconomic Model. Journal of Economics and Statistics, 228: 276–295.

  34. Hall, Bronwyn . 1987. The Relationship between Firm Size and Firm Growth in the US. Manufacturing Sector. Journal of Industrial Economics 35: 583–606.

  35. Ijiri, Yuji, and Simon Herbert A. 1977. Skew Distributions and the Size of Business Firms. Amsterdam: North Holland.

  36. Kaldor, Nicholas . 1965. Capital Accumulation and Economic Growth, In The Theory of Capital. Proceedings of a Conference held by the International Economic Association, edited by Friedrich August Lutz and Douglas Chalmers Hague. London: MacMillan.

  37. Kleijen, Jack P. 1995. Verification and Validation of Simulation Models. European Journal of Operations Research, 82: 145–162.

  38. Klevmarken, Anders N. 1998. Statistical Inference in Microsimulation Models: Incorporating External Information, Working Paper of Uppsala University, Department of Economics.

  39. Lovelock, James . 2000. Gaia: A New Look at Life on Earth. Oxford: Oxford University Press.

  40. McDonald, James B. 1984. Some Generalized Functions for the Size Distribution of Income. Econometrica, 52: 647–663.

  41. Okuyama, Ken, Hideki Takayasu, and Mizuno Takayasu . 1999. Zipf's Law in Income Distribution of Companies. Physica A, 269: 125–131.

  42. Prabhakar, Murthy D.N., Min Xie, and Renyan Jiang . 2003. Weibull Models. New York: Wiley.

  43. Quandt, Richard E. 1966. On the Size Distribution of Firms. American Economic Review, 56: 416–432.

  44. Ramsden, Jeremy, and Georgy Kiss-Haypal . 2000. Company Size Distribution in Different Countries. Physica A, 277: 220–227.

  45. Russo, Alberto, Michele Catalano, Edoardo Gaffeo, Mauro Gallegati, and Mauro Napolitano . 2007. Industrial Dynamics, Fiscal Policy and R&D: Evidence from a Computational Experiment. Journal of Economic Behavior and Organization, 64: 426–447.

  46. Sargent, Thomas J. 1998. Verification and Validation in Simulation Models. Proceedings of 1998 Winter Simulation Conference, 52–64.

  47. Simon, Herbert A. 1955. On a Class of Skew Distribution Functions. Biometrika, 42: 425–440.

  48. Stanley, Michael, Luis Amaral, Sergey Buldyrev, Shlomo Havling, Heiko Leshorn, Philipp Maas, Michael Salinger, and Eugene H. Stanley . 1996. Scaling Behavior in the Growth of Companies. Nature, 379: 804–806.

  49. Stiglitz, Joseph . 1989. Financial Markets and Development. Oxford Review of Economic Policy, 5: 55–68.

  50. Subbotin, Mikhail T. 1923. The Law of Frequency of Error. Mathematicheskii Sbornik, 31: 296–301.

  51. Venter, Gary . 1983. Transformed Beta and Gamma Distributions and Aggregate Losses. Proceedings of the Casualty Actuarial Society, 70: 156–193.

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Acknowledgements

The authors are grateful to the editor and to an anonymous referee for their invaluable suggestions, which have clearly ameliorated the readability and the relevance of this work.

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Cirillo, P., Gallegati, M. The Empirical Validation of an Agent-based Model. Eastern Econ J 38, 525–547 (2012). https://doi.org/10.1057/eej.2011.34

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Keywords

  • validation
  • calibration
  • agent-based models
  • goodness-of-fit
  • micro-simulation

JEL Classifications

  • H3
  • C63