Complexity and scaling laws in economics
Scaling laws (also called power laws) have been found in a variety of contexts in finance, in economics, and in other social sciences. The idea is exemplified by the Pareto principle, that was famously proposed by management consultant Joseph Juran and is named for economist Vilfredo Pareto: It states that about 20% of the population own about 80% of the wealth. More generally, there is an exponential relationship with a negative exponent (hence, falling) between the frequency (population share) and the property (wealth). While there is some variation, the scaling relation continues to hold with remarkable stability across time periods, countries, regions, and aggregation levels. Similar scaling relations have been found in financial market returns, in firm sizes, in the sizes of population centers, in productivity data, in some social and economic networks (co-patenting networks, inter-banking networks, travel networks, spread of epidemics, etc.). The seminar will explore some of these cases in detail. It will also consider how the emergence of such scaling laws can be explained and what implications they have for economics, economic policy, and business.
Organisation and Examination
Organisation:
Students will write a term paper and present it at the end of the term. Topics will be assigned at the beginning of the term. There will be a presentation session over one or two days (depending on the number of participants) at the end of term. Students will be assigned a supervisor and are expected to stay in touch with the supervisor while working on the term paper.
Examination:
There will be no examination. Students will write a term paper and present it in the course.
Topics and Literature
General literature: Theory of scaling laws
Bak, P., Tang, C., and Wiesenfeld, K. (1988). Self-organized criticality. Physical Review A, 38(1):364–374.
Clauset, A., Shalizi, C. R., and Newman, M. E. J. (2009). Power-law distributions in empirical data. SIAM Review, 51(4):661–703.
Farmer, J. D. and Geanakoplos, J. (2008). Power laws in economics and elsewhere. Working Paper, Santa Fe Institute. Available online: http://tuvalu.santafe.edu/ jdf/papers/powerlaw3.pdf
Frank, S. A. (2009). The common patterns of nature. Journal of Evolutionary Biology, 22(8):1563–1585.
Gerlach, M. and Altmann, E. G. (2019). Testing statistical laws in complex systems. Phys. Rev. Lett., 122:168301.
Newman, M. E. J. (2005). Power laws, Pareto distributions and Zipf’s law. Contemporary Physics, 46(5):323–351.
Nolan, J. P. (2019). Stable distributions - models for heavy tailed data. Unfinished manuscript. http://fs2.american.edu/jpnolan/www/stable/chap1.pdf
Scaling laws in wealth and income
Di Guilmi, C., Gaffeo, E., and Gallegati, M. (2003). Power law scaling in world income distribution. Economics Bulletin.
Hegyi, G., Néda, Z., and Augusta Santos, M. (2007). Wealth distribution and pareto’s law in the hungarian medieval society. Physica A: Statistical Mechanics and its Applications, 380:271–277.
Mandelbrot, B. (1960). The pareto-levy law and the distribution of income. International Economic Review, 1(2):79–106.
Pareto, V. (1897). The new theories of economics. Journal of Political Economy, 5(4):485–502.
Scaling laws in finance
Bouchaud, J.-P. and Potters, M. (2003). Theory of financial risk and derivative pricing: from statistical physics to risk management. Cambridge University Press, Cambridge. (Chapter 1)
Gabaix, X., Gopikrishnan, P., Plerou, V., and Stanley, H. E. (2003). A theory of power-law distributions in financial market fluctuations. Nature, 423:267–270.
Lux, T. and Alfarano, S. (2016). Financial power laws: Empirical evidence, models, and mechanisms. Chaos, Solitons & Fractals, 88:3–18.
Mandelbrot, B. (1963). The variation of certain speculative prices. The Journal of Business, 36(4):394–419.
Mandelbrot, B. B. and Hudson, R. L. (2004). The (mis)behavior of markets. Basic Books, New York, NY.
Scaling laws and fragility of financial markets
Battiston, S., Puliga, M., Kaushik, R., Tasca, P., and Caldarelli, G. (2012). Debtrank: Too central to fail? financial networks, the fed and systemic risk. Scientific reports, 2:541.
Delli Gatti, D., Di Guilmi, C., Gaffeo, E., Giulioni, G., Gallegati, M., and Palestrini, A. (2005). A new approach to business fluctuations: heterogeneous interacting agents, scaling laws and financial fragility. Journal of Economic Behavior & Organization, 56(4):489–512. Festschrift in honor of Richard H. Day.
Mandelbrot, B. B. and Hudson, R. L. (2004). The (mis)behavior of markets. Basic Books, New York, NY.
Taleb, N. N. and Tapiero, C. S. (2010). Risk externalities and too big to fail. Physica A: Statistical Mechanics and its Applications, 389(17):3503–3507.
Scaling laws in firm populations
Axtell, R. L. (2001). Zipf distribution of U.S. firm sizes. Science, 293(5536):1818–1820.
Bottazzi, G. and Secchi, A. (2006). Explaining the distribution of firm growth rates. The RAND Journal of Economics, 37(2):235–256.
Gabaix, X. (2011). The granular origins of aggregate fluctuations. Econometrica, 79(3):733–772.
Ijiri, Y. and Simon, H. A. (1977). Skew distributions and the sizes of business firms, volume 24. North Holland, Amsterdam.
Schwarzkopf, Y., Axtell, R., and Farmer, J. D. (2010). An explanation of universality in growth fluctuations. SSRN working paper http://ssrn.com/abstract=1597504.
Yang, J., Heinrich, T., Winkler, J., Lafond, F., Koutroumpis, P., and Farmer, J. D. (2019). Measuring productivity dispersion:
a parametric approach using the lévy alpha-stable distribution. Working Paper, Oxford Martin School, University of Oxford, arXiv preprint arXiv:1910.05219, https://www.oxfordmartin.ox.ac.uk/publications/measuring-productivity-dispersion-a-parametric-approach-using-the-l%C3%A9vy-alpha-stable-distribution/
Scaling laws in economic networks
Barabási, A.-L. and Albert, R. (1999). Emergence of scaling in random networks. Science, 286(5439):509–512.
Battiston, S., Puliga, M., Kaushik, R., Tasca, P., and Caldarelli, G. (2012). Debtrank: Too central to fail? financial networks, the fed and systemic risk. Scientific reports, 2:541.
Newman, M. E. J. (2003). The structure and function of complex networks. SIAM Review, 45(2):167–256.
Souma, W., Fujiwara, Y., and Aoyama, H. (2003). Complex networks and economics. Physica A: Statistical Mechanics and its Applications, 324(1-2):396–401. Proceedings of the International Econophysics Conference.
Scaling laws in urban spaces
Bettencourt, L. M., Samaniego, H., and Youn, H. (2014). Professional diversity and the productivity of cities. Scientific reports, 4:5393.
Bettencourt, L. M. A., Lobo, J., and Youn, H. (2013). The hypothesis of urban scaling: formalization, implications and challenges. Online at: http://arxiv.org/abs/1301.5919
Gabaix, X. (1999). Zipf’s law for cities: An explanation. The Quarterly Journal of Economics, 114(3):739–767.
Levy, M. (2009). Gibrat’s law for (all) cities: Comment. American Economic Review, 99(4):1672–75.
Scaling laws in innovation and technology
Lafond, F. (2014). The size of patent categories: Uspto 1976-2006. UNU-MERIT Working Papers, (060). https://cris.maastrichtuniversity.nl/en/publications/the-size-of-patent-categories-uspto-1976-2006
O’Neale, D. R. J. and Hendy, S. C. (2012). Power law distributions of patents as indicators of innovation. PLOS ONE, 7(12):1–9.
Silverberg, G. and Verspagen, B. (2007). The size distribution of innovations revisited: An application of extreme value statistics to citation and value measures of patent significance. Journal of Econometrics, 139(2):318–339.