PL EN
RESEARCH PAPER
Firm-Size Distribution in Poland: Is Power Law Applicable?
 
More details
Hide details
1
Department of Macroeconomics, Institute of Economics, University of Lodz, Poland
 
2
Department of International Trade, Institute of Economics, University of Lodz, Poland
 
 
Submission date: 2020-08-23
 
 
Final revision date: 2021-02-13
 
 
Acceptance date: 2021-03-18
 
 
Publication date: 2021-06-29
 
 
Corresponding author
Piotr Gabrielczak   

Department of Macroeconomics, Institute of Economics, University of Lodz, Poland
 
 
GNPJE 2021;306(2):31-49
 
KEYWORDS
JEL CLASSIFICATION CODES
ABSTRACT
This article focuses on the existence of power laws in the firm-size distribution in Poland. Specifically, we empirically test whether the size distribution of companies in Poland has the characteristics of Zipf ’s law, a special case of power law observed in many different contexts in empirical economic literature. Our analysis uses 2019 data on the 2,000 largest companies in Poland as ranked by the Rzeczpospolita daily newspaper in its “Lista 2000” (Top 2,000 List). We reviewed theoretical mechanisms generating power laws and used several estimators of the power-law exponent in our empirical analysis. Our results confirm statistically significant deviations from Zipf ’s law in the firm-size distribution in Poland. We found evidence that the power law cannot satisfactorily approximate the sales-based distribution of firms.
 
REFERENCES (59)
1.
Altmann G. [2002], Zipfian linguistics, Glottometrics, 3: 19–26.
 
2.
Atkinson A. B., Piketty T., Saez E. [2011], Top Incomes in the Long Run of History, Journal of Economic Literature, 49 (1): 3–71.
 
3.
Axtell R. L. [2001], Zipf Distribution of US Firm Sizes, Science, 293 (5536): 1818–1820.
 
4.
Bak P. [1996], How Nature Works, Copernicus, New York.
 
5.
Benhabib J., Bisin A., Zhu S. [2011], The Distribution of Wealth and Fiscal Policy in Economies with Finitely Lived Agents, Econometrica, 79 (1): 123–157.
 
6.
Biswas A., Triki H., Zhou Q., Moshokoa S. P., Ullah M. Z., Belic M. [2017], Cubic – quartic optical solitons in Kerr and power law media, Optik, 144: 357–362.
 
7.
Bokányi E., Kondor D., Vattay G. [2019], Scaling in words on Twitter, Royal Society Open Science, 6 (2): 1–11.
 
8.
Bouchaud J. P., Farmer J. D., Lillo F. [2009], How Markets Slowly Digest Changes in Supply and Demand, in: K. R. Schenk-Hoppe, T. Hens, (eds.), Handbook of Financial Markets: Dynamics and Evolution: 57–160, North-Holland, Amsterdam.
 
9.
Brakman S., Garretsen H., van Marrewijk C. [2001], An Introduction to Geographical Economics, Cambridge University Press, Cambridge.
 
10.
Clough J. R., Gollings J., Loach T. V., Evans T. S. [2015], Transitive reduction of citation networks, Journal of Complex Networks, 3 (2): 189–203.
 
11.
Di Giovanni J., Levchenko A. A. [2013], Firm entry, trade, and welfare in Zipf’s world, Journal of International Economics, 89 (2): 283–296.
 
12.
Di Giovanni J., Levchenko A. A., Rancière R. [2011], Power laws in firm size and openness to trade: Measurement and implications, Journal of International Economics, 85 (1): 45–52.
 
13.
Doryń W., Stachera D. [2008], Wpływ internacjonalizacji na wyniki ekonomiczne największych polskich przedsiębiorstw przemysłowych, Gospodarka Narodowa, 11–12: 95–114.
 
14.
Edwards R., Batty M. [2015], City size: Spatial dynamics as temporal flows, Environment and Planning A, 48 (6): 1–3.
 
15.
Ellis N. C., O’Donnell M. B., Römer U. [2015], Usage-Based Language Learning, in: B. MacWhinney, W. O’Grady (eds.), The Handbook of Language Emergence: 69–87, John Wiley & Sons, Chichester.
 
16.
Gabaix X. [1999], Zipf’s law for cities: an explanation, Quarterly Journal of Economics, 114 (3): 739–767.
 
17.
Gabaix X. [2008], Power Laws, in: S. N. Durlauf, L. E. Blume (eds), The New Palgrave Dictionary of Economics, Palgrave Macmillan, London.
 
18.
Gabaix X. [2009], Power Laws in Economics and Finance, Annual Review of Economics, 1 (1): 256–293.
 
19.
Gabaix X. [2011], The Granular Origins of Aggregate Fluctuations, Econometrica, 79 (3): 733–772.
 
20.
Gabaix X. [2016], Power Laws in Economics: An Introduction, Journal of Economic Perspectives, 30 (1): 185–205.
 
21.
Gabaix X., Ibragimov R. [2011], Rank-1/2: a simple way to improve the OLS estimation of tail exponents, Journal of Business and Economic Statistics, 29 (1): 24–39.
 
22.
Gabaix X., Landier A. [2008], Why Has CEO Pay Increased So Much?, Quarterly Journal of Economics, 123 (1): 49–100.
 
23.
Gabaix X., Lasry J. M., Lions P. L., Moll B. [2016], The Dynamics of Inequality, Econometrica, 84 (6): 2071–2111.
 
24.
Gopikrishnan P., Plerou V., Nunes Amaral L. A., Meyer M., Stanley H. E. [1999], Scaling of the Distribution of Fluctuations of Financial Market Indices, Physical Review E, 60 (5): 305–316.
 
25.
Hill B. M. [1970], Zipf ’s law and prior distributions for the composition of a population, Journal of the American Statistical Association, 65 (331): 1220–1232.
 
26.
Hulten C. [1978], Growth Accounting with Intermediary Inputs, Review of Economic Studies, 45: 511–518.
 
27.
Jaworek M., Karaszewski W., Kuczmarska M. [2018], Przedsiębiorstwa z udziałem kapitału zagranicznego na tle ogółu przedsiębiorstw w Polsce w okresie 1994–2017, Przegląd Organizacji, 9: 6–14.
 
28.
Kalemli-Özcan S., Sørensen B. E., Villegas-Sanchez C., Volosovych V., Yeşiltaş S. [2019], How to Construct Nationally Representative Firm Level Data from the Orbis Global Database: New Facts and Aggregate Implications, Tinbergen Institute Discussion Paper No. TI 2015–110/ IV.
 
29.
Kromer V. [2002], Zipf´s law and its modification possibilities, Glottometrics, 5: 1–13.
 
30.
Kucera H., Francis W. N. [1967], Computational Analysis of Present-Day American English, Brown University Press, Providence.
 
31.
Kyle A. S., Obizhaeva A. A. [2019], Large Bets and Stock Market Crashes, mimeo, https://papers. ssrn.com/sol3/papers.cfm?abstract_id=2023776 (23 August 2020).
 
32.
Li W. [2002], Zipf ’s Law Everywhere, Glottometrics, 5: 14–21.
 
33.
Lotka A. J. [1926], The frequency distribution of scientific productivity, Journal of the Washington Academy of Sciences, 16 (12): 317–323.
 
34.
Lucas Jr. R. E., Moll B. [2014], Knowledge Growth and the Allocation of Time, Journal of Political Economy, 122 (1): 1–51.
 
35.
Mandelbrot B. [1982], The Fractal Geometry of Nature, W. H. Freeman, San Francisco.
 
36.
Mehri A., Lashkari S. M. [2016], Power-law regularities in human language, The European Physical Journal B, 89 (241): 1–6.
 
37.
Mitzenmacher M. [2003], A Brief History of Generative Models for Power Law and Lognormal Distributions, Internet Mathematics, 1 (2): 226–251.
 
38.
Newman M. E. J. [2005], Power laws, Pareto distributions and Zipf ’s law, Contemporary Physics, 46 (5): 323–351.
 
39.
Olmedilla M., Martinez-Torres M. R., Toral S. L. [2016], Examining the power-law distribution among eWOM communities: a characterisation approach of the Long Tail, Technology Analysis & Strategic Management, 28 (5): 601–613.
 
40.
Pareto V. [1896], Cours d’économie politique, Librairie Droz, Lausanne.
 
41.
Patience G. S., Patience C. A., Blais B., Bertrand F. [2017], Citation analysis of scientific categories, Heliyon, 3 (5): 1–24.
 
42.
Perline R. [2005], Strong, Weak and False Inverse Power Laws, Statistical Science, 20 (1): 68–88.
 
43.
Piketty T., Zucman G. [2014], Capital is Back: Wealth-Income Ratios in Rich Countries, 1700–2010, Quarterly Journal of Economics, 129 (3): 1255–1310.
 
44.
Plerou V., Gopikrishnan P., Stanley H. E. [2005], Quantifying Fluctuations in Market Liquidity: Analysis of the Bid-Ask Spread, Physical Review E, 71 (4): 1–8.
 
45.
Rosen S. [1981], The Economics of Superstars, American Economic Review, 71 (5): 845–858.
 
46.
Schroeder M. [1991], Fractals, Chaos, Power Laws, Freeman, New York.
 
47.
Serbyn M., Michailidis A. A., Abanin D. A., Papić Z. [2016], Power-Law Entanglement Spectrum in Many-Body Localized Phases, Physical Review Letters, 117: 1–6.
 
48.
Simon H. [1955], On a Class of Skew Distribution Functions, Biometrika, 42 (3–4): 425–440.
 
49.
Soo K. T. [2005], Zipf ’s Law for cities: a cross-country investigation, Regional Science and Urban Economics, 35 (3): 239–263.
 
50.
Sornette D., Knopoff L., Kagan Y. Y., Vanneste C. [1996], Rank-ordering statistics of extreme events: application to the distribution of large earthquakes, Journal of Geophysical Research, 101 (B6): 13883–13893.
 
51.
Spaide R. F. [2016], Choriocapillaris Flow Features Follow a Power Law Distribution: Implications for Characterization and Mechanisms of Disease Progression, American Journal of Ophthalmology, 170: 58–67.
 
52.
Sui J., Zheng L., Zhang X., Chen G. [2015], Mixed convection heat transfer in power law fluids over a moving conveyor along an inclined plate, International Journal of Heat and Mass Transfer, 85: 1023–1033.
 
53.
Toda A. A., Walsh K. [2015], The Double Power Law in Consumption and Implications for Testing Euler Equations, Journal of Political Economy, 123 (5): 1177–1200.
 
54.
Wang L., Du J. [2017], The diffusion of charged particles in the weakly ionized plasma with power-law kappa-distributions, Physics of Plasmas, 24 (10): 1–4.
 
55.
Welch B. L. [1947], The Generalization of ‘Student’s’ Problem when Several Different Population Variances are Involved, Biometrika, 34 (1/2): 28–35.
 
56.
White H., McCain K. W. [1989], Bibliometrics, Annual Review of Information Science Technology, 24: 119–186.
 
57.
Wyllys R. E. [1981], Empirical and theoretical bases of Zipf ’s law, Library Trends, 30 (1): 53–64.
 
58.
Yule G. U. [1925], A Mathematical Theory of Evolution. Based on the Conclusions of Dr J. C. Willis, F. R. S., Philosophical Transactions of the Royal Society of London. Series B, Containing Papers of a Biological Character, 213: 21–87.
 
59.
Zipf G. K. [1949], Human Behavior and the Principle of Least Effort: An Introduction to Human Ecology, Addison-Wesley Press Inc., Cambridge (MA).
 
eISSN:2300-5238
Journals System - logo
Scroll to top