Discussion Paper

No. 2015-51 | July 15, 2015
An Application of Econophysics to the History of Economic Thought: The Analysis of Texts from the Frequency of Appearance of Key Words


This article poses a new methodology applying the statistical analysis to the economic literature. This analysis has never been used in the history of economic thought, albeit it may open up new possibilities and provide us with further explanations so as to reconsider theoretical issues. With that purpose in mind, the article applies the intermittency of the turbulence in different economic texts, and specifically in three important authors: William Stanley Jevons, Adam Smith, and Karl Marx.

JEL Classification:

B16, B40, C18, Z11


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Cite As

Estrella Trincado and José María Vindel (2015). An Application of Econophysics to the History of Economic Thought: The Analysis of Texts from the Frequency of Appearance of Key Words. Economics Discussion Papers, No 2015-51, Kiel Institute for the World Economy. http://www.economics-ejournal.org/economics/discussionpapers/2015-51

Comments and Questions

Anonymous - Referee Report 1
July 21, 2015 - 09:19

This is a nice piece of work relating the statistics of the appearance of word in some classical texts to the history of economic thought. The analysis is very simple counting and comparing word occurrences in pages making a sort of time series. This is nice and probably sound but ...[more]

... quite pointless given that one can actually read the books. Such simple text analytics make sense on very large corpus of data (the entire marxism literature, not a single book by Marx) or more sophisticated parsing tools are available (many free). The multiscaling idea is very nice but - as the results clearly show - books are too short to obtain robust statistical results for this kind of analysis. Further, as the authors discuss in the text these time series are non-stationary, which can be a serious problem when scaling and mutiscaling laws have to be computed.

Estrella Trincado - Anwer of the authors to the reviewer
July 28, 2015 - 20:10

The article consists of a new way of "reading" the pieces of art which, in fact, implies trying to look at hidden -not expressed into word- intentions of the authors. It tries to open up a research line that may give new insights into neurosciences and bibliometrics. Certainly, the study ...[more]

... of a higher number of texts might provide us with other interesting results and, in this sense, the methodology stays open for future works. However, the methodology is applicable to single texts as long as their extension and number of words are enough and that the texts are comparable and homogeneous. This is the case with this article, which compares the masterpieces of three central economists, pieces of work very pondered by their authors, and in which the statistical robustness is based on the high frequency of the population due to the size of the book and the importance of the word (for the Wealth of Nations 1148 and 769 times in 664 pages, for Capital, 1284 and 3401 times in 397 pages, and for The Theory of Political Economy 457, 403 and 411 times, respectively in 206 pages). In fact, words such as “value”, used “only” 218 times, have been ruled out for these reasons. If the analogy is allowed, it is like the study of the economic situation of a certain country. The study may be carried out if we have enough data corresponding to the country, though the comparison with the situation of the rest of countries may be interesting.
The problem of the non-stationarity is very common in the temporal series analysis and we agree with the reviewer that it can introduce some distortion in the results. In any case, the variable of work (the difference of number of occurrences) offsets widely this problem. Besides, the variable has been normalized dividing it by the standard deviation in such a way that the results corresponding to the different scales are comparable.

Anonymous - Referee Report 2
August 24, 2015 - 10:09

see attached file

Estrella Trincado and José María Vindel - Authors´ Reply
September 07, 2015 - 20:04

First of all,we would like to express our gratitude for all the comments and suggestions of both referees.

The referee comments that the article deals with an interesting perspective on the use of text analysis and, precisely, that perspective is based on the using of a methodology traditionally alien ...[more]

... to the history of economic thought research: econo-physics. As he says, econo-physics is, not so much the using of a statistical analysis, but the application of models coming from physics to economics: in particular, the turbulence concept is applied in physics to the chaotic motion of a fluid. The physical explanation of this behavior is the presence of turbulent eddies transmitting energy among them. The mathematical/statistics explanation of this transfer process can be accomplished by the fractal analysis. This type of analysis deals with the behavior in the different scales of this transition process (these scales are referred to the size of the turbulent eddies). In this sense, we can speak of monofractality or uniscaling (the same behavior for all the scales) and of multifractality or multiscaling (where this behavior, although similar, is not exactly the same in all the scales). The fractal analysis, that is to say, the search of similarity in the different scales of the process (autosimilarity) has been not only applied to the velocity of fluids, but also to many others processes of apparently chaotic or turbulent nature. This is the case with economics series, in which an analogy between energy transmission from one eddy to the other, formerly mentioned, and economic information transmission can be established (econophysics).

The scaling analysis carried out in the work belongs to this type of fractal analysis usual in turbulent processes, in which the next value of the variable cannot be known. The variable used (frequency of appearance of one word in one page) is not an economic variable as such, but it contains information of an economics character, in the sense of the importance given by the author to the economic concept represented by the word. In any case, we agree with the referee that we need to clarify these aspects more, and to specify what is meant in the article by the idea of "methodology of turbulence".

With regard to the consideration of economic texts as literature, we are trying to bring our approach closer to the rhetorical analysis of economics, which makes a textual analysis examining the text in itself -, the turn of the sentences and expressions of the text - and the author performance regarding his/her audience, instead of using the more political or theoretical analysis of the texts.

Actually, Aragon and al (2006) used the concept of turbulence to characterize emotional instability because they saw that Van Gogh's works of art adhered to a pattern predicted by Kolmogorov's statistical theory. This interesting coincidence made them make an analogy with the turbulence of the artwork itself and the physical state of mind of the author, the same as our article makes an analogy between the physical state of mind of economic authors and their texts. The analogy, we think, is interesting and can make us deal with those states of mind that are out of reach now in physical terms. So, certainly, it is the physical time felt by the authors what makes them punctuate the text in one way or the other. This is what we mean with "state of mind" and "turbulent text". In this sense, the psycho-analysis dimension is used only in a neuropsychological way, meaning the measurement of a very specific result of the mind movements: an economic text. We do not mean that this perspective is the best way to capture the authors psyche; but it gives one more and innovative tool to analyse texts that we present for the consideration and discussion of the academic community.

As the referee comments, the choice of the word "utility,value, labour and capital" is unplanned, as Jevons cite those words as the most important in economics - something that makes our results not scheduled beforehand and, then, we think that more robust - but we consider that these words are very important for the three authors, as they are the basis of their theories and the clue of their critique of political economy. Those words, due to the importance of their definition in a nascent political economy, did not have so many synonyms or association of words in that period. In this sense, we think that, as the words are considered pivotal in the political economy of the time, the fact that we use a translation must not affect so much the results of the frequency of their appearance. All these points, it is true, must be mentioned in the article.

It is the concept of scale understood as the distance between pages of the appearance of words what makes the works of these three authors comparable. Indeed, the variable is expressed not in absolute, but in relative terms (difference of frequency between pages, comparing the frequency of appearance in a page with that in other page) and, if the analogy is allowed, it has more to do with the rhythm than with the music. Regarding the stability of data, figure 3, where the probability mass functions are represented, shows how the different scales share a same statistical framework, conferring a fractal structure to the process. Indeed, the process presents autosimilarity, though this autosimilarity is not perfect due to its intermittency (multifractality). It is in this sense that the sentence “a turbulent regime characterized by intermittency” has been used.

Regarding the use of the word “persistent”, it is referred to the repetition in the number of times that a word is used. In scale 1, for instance, a high persistence indicates that this word (value, for example) is frequently used the same number of times in all the pages. In this case, the author is persistent, along the text, in the use of this word. The author can give greater or lesser importance to this word, but he does it always in the same way throughout the text.

Finally, we agree with the referee that the concept of “information” should be explained in a more clear way in the article. Information is referred to the importance given by the author, in the moment of producing his work, to the concept represented by the word in question. The word “jumps” has the same meaning than “difference in the number of words”. Maybe it is not the correct word and it should be changed.