| dc.contributor.author | Gabrielczak, Piotr | |
| dc.contributor.author | Serwach, Tomasz | |
| dc.date.accessioned | 2019-09-20T07:36:41Z | |
| dc.date.available | 2019-09-20T07:36:41Z | |
| dc.date.issued | 2019-09-20 | |
| dc.identifier.uri | http://hdl.handle.net/11089/30229 | |
| dc.description.abstract | The article focuses on power laws and their growing popularity in science in general and in
economics specifically. The theoretical mechanisms responsible for their generating are reviewed.
We also empirically test whether firm-size distribution of companies in Poland has the characteristics
of the Zipf’s law – a special case of a power law. This is confirmed based on an investigation within
the sample of 2000 largest companies and a set of alternative estimators of the power law exponent. | pl_PL |
| dc.language.iso | en | pl_PL |
| dc.relation.ispartofseries | Lodz Economics Working Papers;3 | |
| dc.subject | power law | pl_PL |
| dc.subject | Zipf’s law | pl_PL |
| dc.subject | firm-size distribution | pl_PL |
| dc.subject | scaling | pl_PL |
| dc.title | Firm-size distribution in Poland – is power law applicable? | pl_PL |
| dc.type | Working Paper | pl_PL |
| dc.page.number | 1-19 | pl_PL |
| dc.contributor.authorAffiliation | University of Lodz | pl_PL |
| dc.contributor.authorAffiliation | University of Lodz | pl_PL |
| dc.references | Adamic L. A., Huberman B. A. (2002), Zipf’s law and the internet, “Glottometrics”, No. 3. | pl_PL |
| dc.references | Altmann G. (2002), Zipfian linguistics, “Glottometrics”, No. 3. | pl_PL |
| dc.references | Arshad S., Hu S., Ashraf B. N. (2018), Zipf’s law and city size distribution: A survey of the literature and future research agenda, “Physica A: Statistical Mechanics and its Applications”, Vol 492, DOI 10.1016/j.physa.2017.10.005. | pl_PL |
| dc.references | Atkinson A. B., Piketty T., Saez E. (2011), Top Incomes in the Long Run of History, “Journal of Economic Literature”, Vol. 49, No. 1, DOI 10.1257/jel.49.1.3. | pl_PL |
| dc.references | Axtell R. L. (2001), Zipf Distribution of US Firm Sizes, “Science”, Vol. 293, No. 5536, DOI 10.1126/science.1062081. | pl_PL |
| dc.references | Bak P. (1996), How Nature Works, Copernicus, New York. | pl_PL |
| dc.references | Barabasi A. L., Albert R. (1999), Emergence of scaling in random networks, “Science”, Vol. 286, No. 5439, DOI 10.1126/science.286.5439.509. | pl_PL |
| dc.references | Barford P., Bestavros A., Bradley A., Crovella M. (1999), Changes in web client access patterns: characteristics and caching implications, “World Wide Web”, Vol. 2, No. 1-2. | pl_PL |
| dc.references | Benhabib J., Bisin A., Zhu S. (2011), The Distribution of Wealth and Fiscal Policy in Economies with Finitely Lived Agents, “Econometrica” Vol. 79, No. 1, DOI 10.3982/ECTA8416. | pl_PL |
| dc.references | Biswas A., Kara A. H., Ullah M. Z., Zhou Q., Moshokoa S. P., Belic M. (2017b), Conservation laws for cubic–quartic optical solitons in Kerr and power law media, “Optik”, Vol. 145, DOI 10.1016/j.ijleo.2017.08.047. | pl_PL |
| dc.references | Biswas A., Triki H., Zhou Q., Moshokoa S. P., Ullah M. Z., Belic M. (2017a), Cubic–quartic optical solitons in Kerr and power law media, “Optik”, Vol. 144, DOI 10.1016/j.ijleo.2017.07.008. | pl_PL |
| dc.references | Bokányi E, Kondor D., Vattay G. (2019), Scaling in Words on Twitter, mimeo, https://arxiv.org/pdf/1903.04329.pdf (28.08.2019). | pl_PL |
| dc.references | Bouchaud J.-P., Farmer J. D., Lillo F. (2009), How Markets Slowly Digest Changes in Supply and Demand, in: Schenk-Hoppe K. R., Hens T. (eds.), Handbook of Financial Markets: Dynamics and Evolution, North-Holland, Amsterdam. | pl_PL |
| dc.references | Brakman, S., Garretsen, H., van Marrewijk, C. (2001), An Introduction to Geographical Economics, Cambridge University Press, Cambridge. | pl_PL |
| dc.references | Breslau L., Cao P., Fan L., Philips G., Shenker S. (1999), Web caching and Zipf-like distributions: evidence and implications, Proceedings of IEEE Infocom’99, DOI 10.1109/INFCOM.1999.749260. | pl_PL |
| dc.references | Cao Z., He Z., Johnson N. (2017), Asymmetric access to information impacts the power-law exponent in networks, mimeo, https://arxiv.org/pdf/1712.06169.pdf (28.08.2019). | pl_PL |
| dc.references | Clough J. R., Gollings J., Loach T. V., Evans T. S. (2015), Transitive reduction of citation networks, “Journal of Complex Networks”, Vol. 3, No. 2, DOI 10.1093/comnet/cnu039. | pl_PL |
| dc.references | Crovella M. E., Bestavros A. (1997), Self-similarity in world wide web traffic: evidence and possible causes, “IEEE/ACM Transactions on Networking”, Vol. 5, No. 6, DOI 10.1109/90.650143. | pl_PL |
| dc.references | Dahl G. (1979), Word Frequencies of Spoken American English, CT Verbatim, Essex. | pl_PL |
| dc.references | de Solla Price D. J. (1965), Networks of Scientific Papers, “Science”, Vol. 149, No. 3683, DOI 10.1126/science.149.3683.510. | pl_PL |
| dc.references | di Giovanni J., Levchenko A. A. (2013), Firm entry, trade, and welfare in Zipf's world, “Journal of International Economics”, Vol. 89, No. 2, DOI 10.1016/j.jinteco.2012.08.002. | pl_PL |
| dc.references | 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”, Vol. 85, No. 1, DOI 10.1016/j.jinteco.2011.05.003. | pl_PL |
| dc.references | Edwards R., Batty M. (2015), City size: Spatial dynamics as temporal flows, “Environment and Planning A”, Vol. 48, No.6, DOI 10.1177/0308518X15621634. | pl_PL |
| dc.references | Egghe L. (1991), The exact place of Zipf’s and Pareto’s law amongst the classical informetric laws, “Scientometrics”, Vol. 20, No. 1. | pl_PL |
| dc.references | Egghe L. (2000), The distribution of N-grams, “Scientometrics” 47, No. 2. | pl_PL |
| dc.references | Egghe L., Rousseau R. (1990), Introduction to Informetrics: Quantitative Methods in Library, Documentation and Information Science, Elsevier, Amsterdam-New York. | pl_PL |
| dc.references | Ellis N. C., O’Donnell M. B., Römer U. (2015), Usage-Based Language Learning, in: MacWhinney B., O’Grady W. (eds.), The Handbook of Language Emergence, John Wiley & Sons, Chichester. | pl_PL |
| dc.references | Fairthorne R. A. (1969), Empirical hyperbolic distributions (Bradford Zipf Mandelbrot) for bibliometric description and prediction, “Journal of Documentation”, Vol. 25, No. 4, DOI 10.1108/eb026481. | pl_PL |
| dc.references | Gabaix X. (1999), Zipf’s law for cities: an explanation, “Quarterly Journal of Economics”, Vol. 114, No.3. | pl_PL |
| dc.references | Gabaix X. (2008a), Power Laws, in: Durlauf S. N., Blume L. E. (eds), The New Palgrave Dictionary of Economics, Palgrave Macmillan, London. | pl_PL |
| dc.references | Gabaix X. (2008b), Power Laws in Economics and Finance, NBER Working Paper No. 14299, Cambridge (MA). | pl_PL |
| dc.references | Gabaix X. (2011), The Granular Origins of Aggregate Fluctuations, “Econometrica”, Vol. 79, No. 3, DOI 10.3982/ECTA8769. | pl_PL |
| dc.references | Gabaix X. (2016), Power Laws in Economics: An Introduction, “Journal of Economic Perspectives”, Vol. 30, No. 1, DOI 10.1257/jep.30.1.185. | pl_PL |
| dc.references | 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”, Vol. 29, No. 1, 24–39, DOI: 10.1198/jbes.2009.06157 | pl_PL |
| dc.references | Gabaix X., Landier A. (2008), Why Has CEO Pay Increased So Much?, “Quarterly Journal of Economics”, Vol. 123, No. 1, 10.1162/qjec.2008.123.1.49. | pl_PL |
| dc.references | Gabaix X., Lasry J.-M., Lions P.-L., Moll B. (2016), The Dynamics of Inequality, “Econometrica”, Vol. 84, No. 6, DOI 10.3982/ECTA13569. | pl_PL |
| dc.references | Gell-Mann M. (1994), The Quark and the Jaguar, Freeman, New York. | pl_PL |
| dc.references | Glassman S. (1994), A caching relay for the world wide web, “Computer Networks and ISDN Systems”, Vol. 27, No.2, DOI 10.1016/0169-7552(94)90130-9. | pl_PL |
| dc.references | 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”, Vol. 60, No. 5, DOI 10.1103/physreve.60.5305. | pl_PL |
| dc.references | Hackett A. P. (1967), 70 Years of Best Sellers, 1895-1965, R.R. Bowker Company, New York. | pl_PL |
| dc.references | Hertzel D. H. (1987), Bibliometrics, history of the development of ideas, In: Kent A. (ed.), Encyclopedia of Library and Information Science, Vol. 42, Suppl. 7, Marcel Dekker Inc., Basel-New York. | pl_PL |
| dc.references | Hill B. M. (1970), Zipf’s law and prior distributions for the composition of a population, “Journal of the American Statistical Association”, Vol. 65, No. 331, DOI 10.2307/2284288. | pl_PL |
| dc.references | Hřebíček L. (2002), Zipf’s law and text, “Glottometrics”, No. 3. | pl_PL |
| dc.references | Huberman B. H., Pirollo P. L. T., Pitkow J. E., Lukose R. M. (1998), Strong regularities in world wide web surfing, “Science”, Vol. 280, No. 5360, DOI 10.1126/science.280.5360.95. | pl_PL |
| dc.references | Ijiri Y., Simon H. A. (1977), Skew Distributions and the Sizes of Firms, North-Holland, Amsterdam. | pl_PL |
| dc.references | Knudsen T. (2001), Zipf’s Law for Cities and Beyond: The Case of Denmark, “American Journal of Economics and Sociology”, Vol. 60, No. 1. | pl_PL |
| dc.references | Kromer V. (2002), Zipf´s law and its modification possibilities, “Glottometrics”, No. 5. | pl_PL |
| dc.references | Kucera H., Francis W. N. (1967), Computational Analysis of Present-Day American English, Brown University Press, Providence. | pl_PL |
| dc.references | Kyle A. S., Obizhaeva A. A. (2019), Large Bets and Stock Market Crashes, mimeo, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2023776 (1.09.2019), SSRN, DOI 10.2139/ssrn.2023776. | pl_PL |
| dc.references | Li W. (2002), Zipf’s Law Everywhere, “Glottometrics”, No. 5. | pl_PL |
| dc.references | Lotka A. J. (1926), The frequency distribution of scientific productivity, “Journal of the Washington Academy of Sciences”, Vol. 16, No. 12. | pl_PL |
| dc.references | Lucas Jr. R.E., Moll B. (2014), Knowledge Growth and the Allocation of Time, “Journal of Political Economy” , Vol. 122, No. 1. | pl_PL |
| dc.references | Mandelbrot B. (1982), The Fractal Geometry of Nature, W. H. Freeman, San Francisco. | pl_PL |
| dc.references | Mehri A., Lashkari S. M. (2016), Power-law regularities in human language, “The European Physical Journal B”, Vol 89, No. 241, DOI 10.1140/epjb/e2016-70423-9. | pl_PL |
| dc.references | Mitzenmacher M. (2003), A Brief History of Generative Models for Power Law and Lognormal Distributions, “Internet Mathematics”, Vol. 1, No. 2. | pl_PL |
| dc.references | Montemurro M. A., Zanette D. H. (2002), New perspectives on Zipf’s law in linguistics: from single texts to large corpora, “Glottometrics”, No. 4. | pl_PL |
| dc.references | Newman M. E. J. (2005), Power laws, Pareto distributions and Zipf's law, “Contemporary Physics”, Vol. 46, No. 5, DOI 10.1080/00107510500052444. | pl_PL |
| dc.references | 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”, Vol. 28, No. 5, DOI 10.1080/09537325.2015.1122187. | pl_PL |
| dc.references | Osareh F. (1996a), Bibliometrics, citation analysis and co-citation analysis: a review of literature I, “Libri”, Vol. 46, No 3, DOI 10.1515/libr.1996.46.3.149. | pl_PL |
| dc.references | Osareh F. (1996b), Bibliometrics, citation analysis and co-citation analysis: a review of literature II, “Libri”, Vol. 46, No. 4, DOI 10.1515/libr.1996.46.4.217. | pl_PL |
| dc.references | Pareto V. (1896), Cours d’économie politique, Librairie Droz, Lausanne. | pl_PL |
| dc.references | Patience G. S., Patience C. A., Blais B., Bertrand F. (2017), Citation analysis of scientific categories, “Heliyon”, Vol. 3, No. 5. DOI 10.1016/j.heliyon.2017.e00300. | pl_PL |
| dc.references | Perline R. (2005), Strong, Weak and False Inverse Power Laws, “Statistical Science”, Vol. 20, No. 1, DOI 10.1214/088342304000000215. | pl_PL |
| dc.references | Piketty T., Zucman G. (2014), Capital is Back: Wealth-Income Ratios in Rich Countries, 1700–2010, “Quarterly Journal of Economics”, Vol. 129, No.3, DOI 10.1093/qje/qju018. | pl_PL |
| dc.references | Plerou V., Gopikrishnan P., Stanley H. E. (2005), Quantifying Fluctuations in Market Liquidity: Analysis of the Bid-Ask Spread, “Physical Review E”, Vol. 71, No.4, DOI 10.1103/PhysRevE.71.046131. | pl_PL |
| dc.references | Redner S. (1998), How popular is your paper? An empirical study of the citation distribution, “European Physical Journal B”, Vol. 4, No. 2. | pl_PL |
| dc.references | Rosen K. T., Resnick M. (1980), The size distribution of cities: an examination of the Pareto law and primacy, “Journal of Urban Economics”, Vol. 8, No. 2, DOI 10.1016/0094-1190(80)90043-1. | pl_PL |
| dc.references | Rosen S. (1981), The Economics of Superstars, “American Economic Review”, Vol. 71, No. 5. | pl_PL |
| dc.references | Rousseau R. (2002), George Kingsley Zipf: life, ideas, his law and informetrics, “Glottometrics”, Np. 3. | pl_PL |
| dc.references | Rousseau R., Zhang Q. (1992), Zipf’s data on the frequency of Chinese words revisited, “Scientometrics”, Vol. 24, No.2. | pl_PL |
| dc.references | Schroeder M. (1991), Fractals, Chaos, Power Laws, Freeman, New York. | pl_PL |
| dc.references | Serbyn M., Michailidis A. A., Abanin D. A., Papić Z. (2016), Power-Law Entanglement Spectrum in Many-Body Localized Phases, “Physical Review Letters”, No. 117, DOI 10.1103/PhysRevLett.117.160601. | pl_PL |
| dc.references | Silagadze Z. K. (1997), Citations and the Zipf-Mandelbrot’s law, “Complex Systems”, Vol. 11, No. 6. | pl_PL |
| dc.references | Simon H. (1955), On a Class of Skew Distribution Functions, “Biometrika”, Vol. 42, No. 3-4, DOI 10.1093/biomet/42.3-4.425. | pl_PL |
| dc.references | Soo K. T. (2005), Zipf’s Law for cities: a cross country investigation, “Regional Science and Urban Economics”, Vol. 35, No. 3, DOI 10.1016/j.regsciurbeco.2004.04.004. | pl_PL |
| dc.references | 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”, Vol. 101, No. B6, DOI 10.1029/96JB00177. | pl_PL |
| dc.references | Spaide R. F. (2016), Choriocapillaris Flow Features Follow a Power Law Distribution: Implications for Characterization and Mechanisms of Disease Progression, “American Journal of Ophthalmology”, Vol. 170, DOI 10.1016/j.ajo.2016.07.023. | pl_PL |
| dc.references | 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”, Vol. 85, DOI 10.1016/j.ijheatmasstransfer.2015.02.014. | pl_PL |
| dc.references | Toda A. A., Walsh K. (2015), The Double Power Law in Consumption and Implications for Testing Euler Equations, “Journal of Political Economy”, Vol. 123, No. 5, DOI 10.1086/682729. | pl_PL |
| dc.references | Wang L., Du J. (2017), The diffusion of charged particles in the weakly ionized plasma with power-law kappa-distributions, “Physics of Plasmas”, Vol. 24, No. 10, DOI 10.1063/1.4996775. | pl_PL |
| dc.references | White H., McCain K. W. (1989), Bibliometrics, “Annual Review of Information Science Technology”, Vol. 24. | pl_PL |
| dc.references | Wyllys R. E. (1981), Empirical and theoretical bases of Zipf’s law, “Library Trends”, Vol. 30, No. 1. | pl_PL |
| dc.references | 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”, Vol. 213. | pl_PL |
| dc.references | Zipf G. K. (1949), Human Behavior and the Principle of Least Effort: An Introduction to Human Ecology, Addison-Wesley Press Inc., Cambridge (MA). | pl_PL |
| dc.contributor.authorEmail | piotr.gabrielczak@uni.lodz.pl | pl_PL |
| dc.contributor.authorEmail | tomasz.serwach@uni.lodz.pl | pl_PL |
