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Correlated Walks Down the Babylonian Markets (Pdf) OFFPRINT Correlated walks down the Babylonian markets N. E. Romero, Q. D. Y. Ma, L. S. Liebovitch, C. T. Brown and P. Ch. Ivanov EPL, 90 (2010) 18004 Please visit the new website www.epljournal.org TARGET YOUR RESEARCH WITH EPL Sign up to receive the free EPL table of contents alert. www.epljournal.org/alerts April 2010 EPL, 90 (2010) 18004 www.epljournal.org doi: 10.1209/0295-5075/90/18004 Correlated walks down the Babylonian markets N. E. Romero1(a),Q.D.Y.Ma2,3(a),L.S.Liebovitch4,C.T.Brown5 and P. Ch. Ivanov2,6,7(b) 1 Physics Department, Florida Atlantic University - Boca Raton, FL 33431, USA 2 Harvard Medical School and Division of Sleep Medicine, Brigham and Women’s Hospital - Boston, MA 02115, USA 3 College of Geography and Biological Information, Nanjing University of Posts and Telecommunications Nanjing 210003, China 4 Center for Complex Systems and Brain Sciences, Florida Atlantic University - Boca Raton, FL 33431, USA 5 Anthropology Department, Florida Atlantic University - Boca Raton, FL 33431, USA 6 Center for Polymer Studies and Department of Physics, Boston University - Boston, MA 02215, USA 7 Departamento de F´ısica Aplicada II, Universidad de M´alaga - 29071 M´alaga, Spain, EU received 27 January 2010; accepted in final form 29 March 2010 published online 5 May 2010 PACS 89.65.Gh – Economics; econophysics, financial markets, business and management PACS 02.50.-r – Probability theory, stochastic processes, and statistics PACS 89.65.Ef – Social organizations; anthropology Abstract – To investigate the evolution of market dynamics in different stages of historical development, we analyze commodity prices from two distinct periods —ancient Babylon, and medieval and early modern England. We find that the first-digit distributions of both Babylon and England commodity prices follow Benford’s law, indicating that the data represent empirical observations typically arising from a free market. Further, we find that the normalized prices of both Babylon and England agricultural commodities are characterized by stretched exponential distributions, and exhibit persistent correlations of a power law type over long periods of up to several centuries, in contrast to contemporary markets. Our findings suggest that similar market interactions may underlie the dynamics of ancient agricultural commodity prices, and that these interactions may remain stable across centuries in two distinct historical periods. Copyright c EPLA, 2010 The emergence of markets and market economics is described by scaling laws [11–13]. To understand how an active area of research in archeology and economic these scaling laws relate to the underlying market regula- anthropology, where a main focus is to understand how tory mechanisms and interactions among market entities, markets developed in early civilizations and what their most studies have focused on high-frequency recordings characteristics were [1–4]. A plausible hypothesis is that of modern market activity as represented by commodi- markets emerge in certain societies as a result of the ties, company stocks or currency foreign exchange over exchange of goods, services or information, allowing a relatively short time periods ranging from months and particular distribution of resources. Buyers and sellers, as years up to several decades [14–16]. However, every market primary market participants, exert demand and supply is embedded in its historical, cultural and technological forces responsible, among others, for driving the price context, and market dynamics may evolve with changes of any asset. The complex interactions between numer- in economic conditions, government politics and market ous market agents acting through feedback at different regulations —e.g., correlations in stock price fluctuations time scales within various economic conditions and market change significantly when a company is transferred from regulation lead to highly irregular and complex dynam- one stock market to another [17], while networks of inter- ics of market activity [5–10]. Recent empirical investiga- action of company stocks across the entire economy exhibit tions have demonstrated that key market observables such stable behavior over a limited time horizon [18,19]. The as price, trading volume and frequency of trading do not evolution of market dynamics across different histori- change in a random manner but rather exhibit surprisingly cal periods has not been systematically studied. Here robust dynamical patterns over a wide range of time scales we investigate several key aspects of the dynamics of commodity prices in two distinct historical periods corre- sponding to different economic conditions and develop- (a)These authors contributed equally to this paper. ment of society —ancient Mesopotamia and medieval and (b)E-mail: [email protected] early modern England. 18004-p1 N. E. Romero et al. We study the probability distribution and correlation market prices [25], census statistics [26], income tax properties of commodity prices from Babylon in the payments, and accounting data [27]. However, numerical period of 463–72 B.C. and from England in the period of processes influenced by human factors such as advertised 1209–1914 A.D. These data sets represent an exceptionally prices for consumers, assigned telephone or license plate long time window into the market dynamics at two impor- numbers, amount of cash withdrawals, or randomly pick- tant and different periods of civilization. By comparing, ing numbers do not follow Benford’s law [26–28]. Benford’s in an statistical framework, key measures of the market test has been utilized in identifying fraudulent reports dynamics during these two periods, we can identify impor- in taxes [27], transactions of federal campaigns [29], tant similarities or dissimilarities of their respective econ- toxic release reported by industrial plants [30], account- omy in relation to empirical observations of contemporary ing audits [31] and fabricated survey answers [32]. There- markets. fore, a distribution of the first-digits which does not Situated in the south region of Iraq, on the Euphrates follow Benford’s law could indicate the presence of system- River, Babylon was the political and cultural capital of atic omissions, estimations, rounding, falsification or even ancient Mesopotamia. Archaeological excavations started fabrication in the recorded data. The first-digit distri- in 1899 by Robert Koldewey have uncovered astronom- bution of Babylon commodity prices could thus expose ical diaries, written in cuneiform on clay tablets, from certain abnormalities, which could lead one to suspect that the period 652 B.C. to 69 A.D. Since the tablets contain these prices are not a record of real empirical observa- celestial observations, all information inscribed on them is tions typically arising from a free market where supply dated, including records of the weather, the level of the and demand forces are present. Euphrates River, socio-political events and market quota- Our analysis of the first significant digits of the Babylon tions of six commodities: barley, dates, mustard (cascuta), commodity price records indicates a good agreement with cress (cardamom), sesame and wool. The commodity Benford’s law (fig. 1a) with the coefficient of determination prices are expressed in weight quantities that could be R2 =0.93. These results are comparable with our analysis purchased per shekel of silver, recorded three times a of six similar agricultural commodities from medieval and month. Babylon had an agriculturally based economy and early modern England, which also conform to Benford’s its diet was primarily based on barley and dates. Mustard distribution (fig. 1b) (with R2 =0.94). Extending our and cress were used as spices and sesame primarily for its analysis to 80 different English commodities of mixed (not oil. All six commodities were also used in official rituals only agricultural) nature to significantly increase the data of Babylonian cultic life [20]. Many clay tablets are still samples, we obtain an almost perfect fit to Benford’s law missing or broken. Since they were stored vertically and (fig. 1c) (with R2 =0.95). These findings indicate that the prices were listed last in the monthly reports, i.e.,at Babylonian market quotations exhibit properties shared the lower edge of each clay tablet, there is a considerable by empirical observations of natural process, suggesting amount of data lost. they represent reliable recordings of commodity prices. The English commodity annual price records consti- Further, since multiplicative process have been associated tute a point of reference in many historical analyses, with emergence of Benford’s distribution [33] and since because they represent a data set over a significantly long contemporary stock market prices also follow Benford’s period. In our study, we use records from 80 agricultural law [25], our results in fig. 1 may indicate that processes and other commodities traded in England in the period of multiplicative nature underlie the market dynamics in 1209–1914 [21]. Prices are expressed in grams of silver per distinct historical periods and economic conditions. metric physical unit. To compare with Babylon data, we Next, we study the probability distributions of differ- select six similar agricultural commodities: barley, beans, ent agricultural commodity prices in Babylon and we oats, peas, pepper and wheat, for which there are prac- compare them with the prices of similar commodities from tically continuous annual records throughout the entire medieval and early modern England. We find that the period (with relatively few missing data points mainly in price distribution of each Babylonian commodity i is char- thefirsthalfoftheperiod). acterized by different average Si(t) and standard devia- Most archaeologists, epigraphers, and economic histori- tion σi. However, after normalization of the prices Si(t) ans have inferred that the Babylonian data represent real to S˜i(t)=(Si(t) −Si(t)/σi,whereSi(t) is the aver- and accurate price quotations [2,4,22]. However, there is age recorded price of that commodity, the distributions of no conclusive evidence and it is possible that the Babylon all Babylonian commodities fall onto a single curve.
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