Theory of Zipf's law and beyond

Lecture Notes in Economics and Mathematical Systems

Volumn 632, Issue , 2010, Pages 1-170

  Saichev, Alexander ^a   Sornette, Didier ^b   Malevergne, Yannick ^c,d  

^a LOBACHEVSKY STATE UNIVERSITY OF NIZHNY NOVGOROD   (Russian Federation)

^b ETH ZURICH   (Switzerland)

^c UNIVERSITÉ JEAN MONNET   (France)

^d EMLYON BUSINESS SCHOOL   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79960100669     PISSN: 00758442     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-642-02946-2_1     Document Type: Article

References (112)

1. Abramovitz E, Stegun IA (1964) Handbook of Mathematical Functions (New York: Dover publications)
2. Adamic LA, Huberman BA (2000) The nature of markets in the World Wide Web. Q J Electron Commer 1:5-12
3. Adamic LA, Huberman BA (2002) Zipf's law and the Internet. Glottometrics 3:143-150
4. Aldous DJ (1999) Deterministic and stochastic models for coalescence (aggregation and coagulation): a review of the mean-field theory for probabilists. Bernoulli 5(1):3-48
5. Almus M, Nerlinger E (2000) Testing Gibrats law for young firms - empirical results for West Germany. Small Bus Econ 15:1-12
6. Aoyama H, Fujiwara Y, Souma W (2004) In: Takayasu H (eds) Proceedings of Second Nikkei Symposium on Econophysics. Springer, Tokyo
7. Audretsch D (1995) Innovation, growth and survival. Int J Ind Organ 13:441-457
8. Audretsch D, Santarelli E, Vivarelli M(1999) Start-up size and industrial dynamics: some evidence from Italian manufacturing. Int J Ind Organ 17:965-983
9. Axtell RL (2001) Zipf distribution of US firm sizes. Science 293:1818-1820
10. Barabasi A-L, Albert R (1999) Emergence of scaling in random networks. Science 286:509-512
11. Barabasi A-L, Albert R (2002) Statistical mechanics of complex networks. Rev Mod Phys 74: 47-97
12. Bartelsman E, Scarpetta S, Schivardi F (2003) Comparative analysis of firm demographics and survival: micro-level evidence for the OECD countries. OECD Economics Department Working Papers, No. 348. OECD. doi:10.1787/010021066480
13. Bateman G, Erdelyi A (1954) Tables of integral transforms, vol I. McGraw-Hill, New York
14. Becchetti L, Trovato G (2002) The determinants of growth for small and medium sized firms. The role of the availability of external finance. Small Bus Econ 19(4):291-306
15. Bingham NH, Goldie CM, Teugels JL (1987) Regular variation. Cambridge University Press, Cambridge
16. Blank A, Solomon S (2000) Power laws in cities population, financial markets and internet sites (scaling in systems with a variable number of com-ponents). Physica A 287(1-2):279-288
17. Bonaccorsi Di Patti E, Dell'Ariccia G (2004) Bank competition and firm creation. J Money Credit Banking 36:225-251
18. Borodin AN, Salminen P (2002) Handbook of Brownian motion - facts and formulae. Birkhäuser, Basel
19. Bottazzi G, Dosi G, Lippi M, Pammolli F, Riccaboni M (2001) Innovation and corporate growth in the evolution of the drug industry. Int J Ind Organ 19:1161-1187
20. Breaslau L, Cao P, Pan L, Phillips G, Shenker S (1999) Web caching and Zipf-like distributions: evidence and implications. IEEE INFOCOM'99, vol 1, pp 126-134
21. Brixy U, Grotz R (2007) Regional patterns and determinants of birth and survival of new firms in Western Germany. Entrepreneurship Reg Dev 19(4):293-312
22. Buldyrev SV, Pammolli F, Riccaboni M, Yamasaki K, Fu DF, Matia K, Stanley HE (2007a) Generalized preferential attachment model for business firms growth rates: II. Mathematical treatment. Eur Phys J B 57:131-138
23. Buldyrev SV, Growiec J, Pammolli F, Riccaboni M, Stanley HE (2007b) The growth of business firms: facts and theory. J Eur Econ Assoc 5(2-3):574-584
24. Cabral LMB, Mata J (2003) On the evolution of the firm size distribution: facts and theory. Am Econ Rev 93(4):1075-1090
25. Calvo JL (2006) Testing Gibrat's law for small, young and innovating firms. Small Bus Econ 26:117-123
26. Clauset A, Erwin DH (2008) The evolution and distribution of species body size. Science 321(5887):399-401
27. Daley DJ, Vere-Jones D (2007) An introduction to the theory of point processes. Springer, Berlin
28. Daniel G, Sornette D, Wohrmann P (2008) Look-ahead benchmark bias in portfolio performance evaluation. J Portfolio Manage Fall 2009. http://arXiv.org/abs/0810.1922
29. de Wit G (2005) Firm size distributions: an overview of steady-state distributions resulting from firm dynamics models. Int J Ind Organ 23:423-450
30. Duchin R, Levy M (2008) Portfolio optimization and the distribution of firm size. Working paper. http://papers.ssrn.com/sol3/papers.cfm?abstractid=1146308
31. Dunne T, Roberts MJ, Samuelson L (1988) Patterns of firm entry and exit in US manufacturing industries. RAND J Econ 19(4):495-515
32. Dunne T, Roberts MJ, Samuelson L (1989) The growth and failure of US manufacturing plants. Q J Econ 104(4):671-698
33. Eeckhout J (2004) Gibrat's law for (all) cities. Am Econ Rev 94(5):1429-1451
34. Eckhout J (2009) Gibrats law for (all) cities: Reply, American Economic Review 99:1676-1683.
35. Embrechts P, Kluppelberg C, Mikosch T (1997) Modelling extremal events. Springer, Berlin
36. Fama EF, French KR (1993) Common risk factors in the returns on stocks and bonds. J Finance Econ 33:3-56
37. Fama EF, French KR (1995) Size and book-to-market factors in earnings and returns. J Finance 50:131-155
38. Feller W(1966) An introduction to probability theory and its applications, vol II. Wiley, New York
39. Fu D, Pammolli F, Buldyrev SV, Riccaboni M, Matia K, Yamasaki K, Stanley HE (2005) The growth of business firms: theoretical framework and empirical evidence. Proc Natl Acad Sci USA 102:18801-18806
40. Fujiwara Y (2004) Zipf law in firms bankruptcy. Physica A 337(1-2):219-230
41. Fujiwara Y, Di Guilmi C, Aoyama H, Gallegati M, Souma W (2004a) Do Pareto-Zipf and Gibrat laws hold true? An analysis with European firms. Physica A 335:197-216
42. Fujiwara Y, Aoyamac H, Di Guilmib C, Soumaa W, Gallegati M (2004b) Gibrat and Pareto-Zipf revisited with European firms. Physica A 344(1-2):112-116
43. Furusawa C, Kaneko K (2003) Zipf's law in gene expression. Phys Rev Lett 90:088102
44. Gabaix X (1999) Zipf's law for cities: an explanation. Q J Econ 114:739-767
45. Gabaix X (2005) The granular origins of aggregate fluctuations. Working paper. MIT and NBER
46. Gaffeo E, Gallegati M, Palestrini A (2003) On the size distribution of firms. Additional evidence from the G7 countries. Physica A 324:117-123
47. Galbraith JK (1997) The great crash, 1929. Houghton Mifflin, Boston
48. Glassman S (1994) A caching relay for the World Wide Web. Comput Netw ISDN Syst 27(2): 165-173
49. Gur Y, Nowak A, Rakocy K, Solomon S (2008) Microscopic study reveals the singular origins of growth (preprint). e-print at arXiv:0803.2201
50. Harhoff D, Stahl K, Woywode M (1998) Legal form, growth and exit for West German firms -results for manufacturing, construction, trade and service industries. J Ind Econ 46:453-488
51. Ijri Y, Simon HA (1977) Skew distributions and the sizes of business firms. North-Holland, New York
52. Ioannides YM, Gabaix X (2003) The evoluation of city size distributions. In: Henderson JV, Thisse J-F (eds) Handbook of urban and regional economics. North-Holland, Amsterdam
53. Kaizoji T, Iyetomi H, Ikeda Y (2006) Re-examination of the size distribution of firms. Evol Inst Econ Rev 2(2):183-198
54. Karatzas I, Shreve S (1991) Brownian motion and stochastic calculus, 2nd edn. Springer, Berlin
55. Karlin S, Taylor HM (1975) A first course in stochastic processes, vol I. Academic, New York
56. Kindleberger CP (2000) Manias, panics, and crashes: a history of financial crises, 4th edn. Wiley, New York
57. Kitov I (2009) What is the best firm size to invest? http://papers.ssrn.com/sol3/papers.cfm?abstractid=1351731
58. Knaup AE (2005) Survival and longevity in the business employment dynamics data. Mon Labor Rev 2005(May):50-56
59. Kong JS, Sarshar N, Roychowdhury VP (2008) Experience versus talent shapes the structure of the Web. Proc Natl Acad Sci USA 105(37):13724-13729
60. Krugman P (1996) The self-organizing economy. Blackwell, Oxford
61. Lee Y, Amaral LAN, Canning D, Meyer M, Stanley HE (1998) Universal features in the growth dynamics of complex organizations. Phys Rev Lett 81:3275-3278
62. Levy M(2009) Gibrats law for (all) cities: Comment, American Economic Review 99:1672-1675.
63. Levy M, Solomon S (1996) Power laws are logarithmic Boltzmann laws. Int J Mod Phys C 7:595-601
64. Leyvraz F (2003) Scaling theory and exactly solved models in the kinetics of irreversible aggregation. Phys Rep 383:95-212
65. Lotti F, Santarelli E (2004) Industry dynamics and the distribution of firm sizes: a non-parametric approach. South Econ J 70(3):443-466
66. Lotti F, Santarelli E, Vivarelli M (2003) Does Gibrat's law hold among young, small firms? J Evol Econ 13(3):213-235
67. Lotti F, Santarelli E, Vivarelli M (2007) Defending Gibrat's Law as a long-run regularity. IZA Discussion Papers 2744. Institute for the Study of Labor (IZA)
68. Lucas RE Jr (1978) On the size distribution of business firms. Bell J Econ 9(2):508-523
69. Luttmer EGJ (2007) Selection, growth, and the size distribution of firms. Q J Econ 122(3): 1103-1144
70. Maillart T, Sornette D, Spaeth S, Von Krogh G (2008) Empirical tests of Zipf's law mechanism in open source Linux distribution. Phys Rev Lett 101:218701
71. Malcai O, Biham O, Solomon S (1999) Power-law distributions and Ĺevy-stable intermittent fluctuations in stochastic systems of many autocatalytic elements. Phys Rev E 60(2):1299-1303
72. Malevergne Y, Sornette D (2006) Extreme financial risks (from dependence to risk management). Springer, Heidelberg
73. Malevergne Y, Sornette D (2007) A two-factor asset pricing model and the fat tail distribution of firm sizes. Working paper. http://papers.ssrn.com/sol3/papers.cfm?abstractid=960002
74. Malevergne Y, Pisarenko VF, Sornette D (2005) Empirical distributions of log-returns: between the stretched exponential and the power law? Quantitative Finance 5(4):379-401
75. Malevergne Y, Pisarenko VF, Sornette D (2009) Gibrat's law for cities: uniformly most powerful unbiased test of the Pareto against the lognormal (http://papers.ssrn.com/sol3/papers.cfm?abstractid=1479481)
76. Morse PM, Feshbach H (1953) Methods of theoretical physics. McGraw-Hill, New York
77. Nielsen J (1997) Do websites have increasing returns? http://www.useit.com/alertbox/9704b.html
78. Nowak A, Kus M, Urbaniak J, Zarycki T (2000) Simulating the coordination of individual economic decisions. Physica A 287:613-630
79. Nowak A, Vallacher RR, Kus M, Urbaniak J (2005) The dynamics of societal transition: modeling nonlinear change in the Polish nonlinear system. Int J Sociol 35(1):65-88
80. Okuyama K, Takayasu M, Takayasu H (1999) Zipf's law in income distribution of companies. Physica A 269:125-131
81. Pammolli F, Fu D, Buldyrev SV, Riccaboni M, Matia K, Yamasaki K, Stanley HE (2007) Generalized preferential attachment model for business firms growth rates: I. Empirical evidence. Eur Phys J B 57:127-130
82. Podobnik B, Horvatic D, Pammolli F, Wang F, Stanley HE, Grosse I (2008) Size-dependent standard deviation for growth rates: empirical results and theoretical modeling. Phys Rev E 77:056102
83. Podobnik B, Horvatic D, Petersen AM, Stanley HE (2009) Quantitative relations between risk, return and firm size. Europhys Lett 85:50003. doi:10.1209/0295-5075/85/50003
84. Reid GC (1992) Early life cycle behaviour of micro-firms in Scotland. Small Bus Econ 7:89-95
85. Reynolds PD, Storey DJ, Weshead P (1994) Cross-national comparisons of the variation in new firm formation rates. Reg Stud 28:443-456
86. Riccabonia M, Pammolli F, Buldyrev SV, Pontac L, Stanley HE (2008) The size variance relationship of business firm growth rates. Proc Natl Acad Sci USA 105(50):19595-19600
87. Rossi-Hansberg E, Wright MLJ (2007a) Urban structure and growth. Rev Econ Stud 74(2):597-624
88. Rossi-Hansberg E, Wright MLJ (2007b) Establishment size dynamics in the aggregate economy. Am Econ Rev 97(5):1639-1666
89. Rozenfeld H, Rybski D, Andrade JS, Batty M, Stanley HE, Makse HA (2008) Laws of population growth. Proc Natl Acad Sci USA 105(48):18702-18707
90. Rozenfeld H, Rybski D, Gabaix X, Makse H (2009) Zipf's Law for all cities (preprint). Abstract at http://www.thic-apfa7.com/share/data/48rozenfeld.pdf
91. Sakai K, Watanabe T (2009) The firms as a bundle of barcodes. Working Paper Series No. 38. JSPS Grants-in-Aid for Creative Scientific Research (Understanding Inflation Dynamics of the Japanese Economy). http://www.ier.hit-u.ac.jp/_ifd/doc/IFDWP38.pdf
92. Schwarzkopf Y, Farmer JD (2008) Time evolution of the mutual fund size distribution. arXiv:0807.3800 (preprint)
93. Shefrin H (2000) Beyond greed and fear: understanding behavioral finance and the psychology of investing. Harvard Business School Press, Boston
94. Shiller RJ (2000) Irrational exuberance. Princeton University Press, Princeton, NJ
95. Shleifer A (2000) Inefficient markets: an introduction to behavioral finance. Oxford University Press, Oxford
96. Simon HA (1955) On a class of skew distribution functions. Biometrika 52:425-440
97. Simon HA (1960) Some further notes on a class of skew distribution functions. Information Control 3:80-88
98. Simon H, Bonini C (1958) The size distribution of business firms. Am Econ Rev 48(4):607-617
99. Sinha S, Pan RK (2006) How a "hit" is born: the emergence of popularity from the dynamics of collective choice. In: Chakrabarti BK, Chakraborti A, Chatterjee A (eds) Econophysics and sociophysics: trends and perspectives. Wiley-VCH, Berlin, ISBN-10: 3-527-40670-0
100. Sornette D (2003) Why stock markets crash: critical events in complex financial systems. Princeton University Press, Princeton, NJ
101. Sornette D (2006) Critical phenomena in natural sciences, chaos, fractals, self-organization and disorder: concepts and tools, 2nd edn. Springer Series in Synergetics. Springer, Heidelberg
102. Stanley MHR, Buldyrev SV, Havlin S, Mantegna RN, Salinger A, Stanley HE (1995) Zipf plots and the size distribution of firms. Econ Lett 49:453-457
103. Stanley MHR, Amaral LAN, Buldyrev SV, Haylin S, Leschhorn H, Maass P, Salinger MA, Stanley HE (1996) Scaling behavior in the growth of companies. Nature 379:804-806
104. Steindl J (1965) Random processes and the growth of firms. A study of the Pareto Law. Griffin, London
105. Sutton J (1997) Gibrat's legacy. J Econ Lit 35:40-59
106. Sutton J (2002) The variance of firm growth rates: the "scaling" puzzle. Physica A 312:577-590
107. Takayasu M, Sameshima S, Ohnishi T, Ikeda Y, Takayasu H, Watanable K (2008) Massive economics data analysis by econophysics methods - the case of companies' network structure. Epoth-making simulation. In: Annual Report of the Earth Simulator Center, April 2007 -March 2008. Earth Simulator Center, Yokohama, Chap. 3, pp. 263-268
108. Weiss CR (1998) Size, growth, and survival in the upper austrian farm sector. Small Bus Econ 10:305-312
109. White EN (ed) (1996) Stock market crashes and speculative manias. The International Library of Macroeconomic and Financial History, 13. Elgar, Cheltenham
110. Yamasaki K, Matia K, Buldyrev SV, Fu D, Pammolli F, Riccaboni M, Stanley HE (2006) Preferential attachment and growth dynamics in complex systems. Phys Rev E 74:035103(R)
111. Yanagita T, Onozaki T (2008) Dynamics of a market with heterogeneous learning agents. J Econ Interact Coord 3:107-118
112. Zipf GK (1949) Human behavior and the principle of least effort. Addison-Wesley, Cambridge, MA