Espartaco

Marxist Philosophy of Science

“Is that to say we are against Free Trade? No, we are for Free Trade, because by Free Trade all economical laws, with their most astounding contradictions, will act upon a larger scale, upon the territory of the whole earth; and because from the uniting of all these contradictions in a single group, where they will stand face to face, will result the struggle which will itself eventuate in the emancipation of the proletariat.”

Karl Heinrich Marx · Marx-Engels Collected Works, Vol. VI, p. 290

26,476 views since December 2020

26,476 visitas desde diciembre de 2020

EnglishEspañol
SubscribeSuscribirse

Category: Political Economy

  • HOW TO CONDUCT ECONOMIC POLICY IN THE PRESENCE OF A FIXED CAPITAL SURPLUS OR DEFICIT WITHOUT RESORTING TO PAPER MONEY?

    HOW TO CONDUCT ECONOMIC POLICY IN THE PRESENCE OF A FIXED CAPITAL SURPLUS OR DEFICIT WITHOUT RESORTING TO PAPER MONEY?

    How Can Economic Policy Address Fixed-Capital Surpluses or Deficits Without Resorting to Paper Money?
    A Blog for the Curious Economist — and Everyone Else
    The Capital Question
    Marxist Political Economy Economic Policy 8 min read

    How Can Economic Policy Address Fixed-Capital Surpluses or Deficits Without Resorting to Paper Money?

    Starting from a problem outlined only embryonically by Marx in Volume II of Capital, this article examines how a post-capitalist society could address surpluses and deficits of fixed capital without resorting to paper money or, more generally, to monetary policy.

    MG
    José Mauricio Gómez Julián
    Contribuciones a la Economía • January 2016 • ISSN 1696-8360

    In contemporary economies, it is difficult to conceive of an economic policy intended to manage the surplus or deficit of a commodity without resorting, in one way or another, to monetary policy. The article begins from this observation and focuses the problem on a particularly important variable: fixed capital. Its objective is to demonstrate that, in a post-capitalist society, it would be possible to control surpluses and deficits of fixed capital without resorting to paper money or to variables associated with it.

    Introduction: The Problem and Its Scope

    The analysis constitutes a complementary theoretical development of a problem raised by Marx in Volume II of Capital. The article uses the same theoretical example as Marx, while noting that the phenomenon may originate from various causes that fall outside the scope of its analysis. Likewise, the imbalance need not occur exclusively between the major sectors of the economy: it can arise at both the intersectoral and intrasectoral levels.

    In a capitalist society, the consequences of these imbalances are not essentially different from those caused by the surplus — overproduction — or deficit — scarcity — of any other commodity. Foreign trade may provide a short-term outlet. In the case of a surplus, it can make it possible to transform into means of consumption part of the commodity of Sector I that has become immobilized in monetary form; in the case of a deficit, it can contribute to disposing of the remaining commodities associated with the amortization of fixed capital. But this solution does not eliminate the contradiction: it merely displaces it into a broader sphere, expanding its field of action and potentially the magnitude of its consequences.

    The central problem is not simply how much fixed capital exists, but how to maintain its proportionality with circulating capital when the physical replacement of the former varies from one year to another.

    The Two Theoretical Scenarios

    The reasoning is developed through the relationship between two sectors: the sector producing means of production and the sector producing means of consumption. The decisive question is how the relationship between the fixed and circulating components of constant capital changes when the proportion of fixed capital that must be physically replaced varies.

    1

    First Scenario

    If the portion of the production of means of production devoted to replacing the fixed capital of the sector producing means of consumption increases, while the total production intended to supply that sector with constant capital remains unchanged, the increase in amortization alters the proportion between the replacement of fixed capital and the circulating elements required. A larger portion of the fixed capital restored in monetary form flows toward the sector producing means of production in order to recover its natural form, so that more money circulates with the unilateral function of a means of purchase, while the mass of commodities exchanged between the two sectors changes.

    Outcome → SURPLUS IN FIXED-CAPITAL PRODUCTION
    2

    Second Scenario

    If the proportion of the fixed capital of the sector producing means of consumption that must be reproduced in kind — that is, physically replaced all at once — decreases, the portion that only needs to be replaced in money through the reserve fund increases correspondingly. The mass of circulating elements of constant capital reproduced by the sector producing means of production remains unchanged, while the production of fixed capital subject to replacement decreases.

    Outcome → DEFICIT IN FIXED-CAPITAL PRODUCTION

    The Economic Policy Proposal

    The article then takes its decisive step. Once the capitalist mode of production — and, with it, paper money in the terms of the argument being developed — has been abolished, the problem of proportionality between fixed and circulating capital is fundamentally reduced to the fact that the magnitude of fixed capital that is exhausted and must be physically replaced may vary from one year to another. These variations can offset one another successively, while, ceteris paribus, the remaining portion of constant capital required for the annual production of articles of consumption — raw materials, auxiliary materials, and intermediate materials — need not decrease.

    The answer proposed by the article is continuous relative overproduction: producing a certain quantity of fixed capital beyond immediate requirements and maintaining stocks of raw materials, auxiliary materials, and intermediate materials above annual needs.

    These surplus use-values would not be commodities produced without an outlet, but rather a reserve fund. Its function would be to provide the production process with whatever portion of constant capital is required at any given moment: fixed capital when there is a deficit in its fixed component, or circulating elements when the imbalance requires reinforcement of that component. The purpose is to prevent variations in the replacement of fixed capital from reducing or disrupting the reproduction of the system.

    In this way, the proposal does not consist in eliminating the material variations that give rise to the imbalances, but rather in consciously maintaining reserves capable of compensating for them. The year-to-year fluctuation in the physical replacement of fixed capital remains; what changes is the social mechanism through which society responds to it.

    Why the Same Policy Would Not Work Under Capitalism

    The article stresses that such a policy would have a completely different meaning within a capitalist society. There, it would constitute an element of anarchy because planning does not belong to the essence of the system. Moreover, capitalist overproduction is not “relative” in the specific sense employed by the proposal: it generates commercial crises. Nor does it take the form of continuous overproduction consciously maintained as a reserve; instead, commercial crises display a cyclical character.

    The fundamental difference therefore lies in the organization of the production process. In the post-capitalist framework proposed by the article, the surplus is deliberately produced as a reserve of use-values in order to guarantee reproduction; under capitalism, overproduction emerges within a system whose dynamics are not governed by such conscious planning and leads to commercial crises.

    • • •

    A Brief Final Assessment

    The article concludes by shifting attention from the technical problem to the history of Marxist theory. Gómez Julián points out that the Dictionary of Political Economy by Borisov, Zhamin, and Makarova — which he takes as a synthesis of Soviet economic theory of its time — neither develops nor even mentions this problem in its entries on “Fixed Capital,” “Simple Reproduction,” or “Expanded Reproduction.”

    This omission is particularly significant for the author because Marx had already posed the problem, although only in embryonic form, on pages 414–417 of Volume II of Capital. Gómez Julián regards the issue as vitally important both for Marxist theory and for the construction of a communist society or any other post-capitalist society.

    From this, he formulates a deliberately severe criticism of Soviet Marxism: he interprets the absence of this theoretical development as evidence that numerous foundations of the theory were not adequately understood either theoretically or practically, and he polemically connects that assessment with the historical outcome symbolized by November 9, 1989.

    The Article’s Thesis, in Summary

    The argument can be condensed as follows: year-to-year variations in the portion of fixed capital that must be physically replaced generate imbalances between fixed and circulating capital. Under capitalism, these imbalances manifest themselves within a commodity and monetary structure and may result in overproduction, scarcity, and crisis. In a post-capitalist society, by contrast, the article proposes dispensing with paper money in dealing with this problem through continuous relative overproduction of fixed capital and circulating elements, with the resulting surpluses accumulated as reserve funds and used according to the material requirements of reproduction.

    This post presents in accessible language the argument developed by José Mauricio Gómez Julián. The phenomenon analyzed may arise from various causes — which the article does not examine because of its chosen scope — and may occur at both the intersectoral and intrasectoral levels. For the original theoretical development and its direct connection with Marx, see: Gómez Julián, J. M. (2016), “¿Cómo realizar política económica ante superávit o déficit de capital fijo sin recurrir al papel moneda?”, Contribuciones a la Economía.
    Original Article Gómez Julián, José Mauricio. “¿Cómo realizar política económica ante superávit o déficit de capital fijo sin recurrir al papel moneda?” Contribuciones a la Economía, January 2016, ISSN 1696-8360.
    Full text: https://dialnet.unirioja.es/servlet/articulo?codigo=9041512

    Main references in the article: Karl Marx, Capital, Fondo de Cultura Económica, 2010; Borisov, Zhamin, and Makarova, Dictionary of Political Economy, 1965.

    The Capital Question — Political economy explained through its fundamental theoretical problems.

  • THE INFLUENCE OF JAMES MILL ON MODERN ECONOMIC SCIENCE

    THE INFLUENCE OF JAMES MILL ON MODERN ECONOMIC SCIENCE

    The Influence of James Mill on Modern Economic Science
    History of Economic Thought

    The Influence of James Mill

    James Mill’s contributions to modern economic science

    Based on the article by José Mauricio Gómez Julián · Read the original article

    The article begins from a precise thesis: the literature on the History of Economic Thought has paid little attention to the importance of James Mill for modern economic science. Gómez Julián argues that Mill was the first economist to propose that every supply creates its own demand, one of the finest exponents of the Quantity Theory of Money of his time, an author in whose work the germs of Modern Monetary Policy can be found, and a pioneer on issues such as productive and unproductive labour and capital accumulation. The article’s stated objective is to demonstrate how fundamental James Mill was to modern Political Economy.

    Scope of the article

    The abstract explicitly attributes to Mill the first clear definition of the notions of Productive Labour and Unproductive Labour. In the body of the article, the discussion focuses especially on Say’s Law, monetary theory, productive and unproductive consumption, capital, population, social classes, and Mill’s intellectual influences.

    I. The Least-Known Plagiarism of the Classical Economists

    Gómez Julián opens the discussion by describing as “the least-known plagiarism” of the age of the classical economists the attribution to Jean-Baptiste Say of the formulation of the so-called Say’s Law, popularly known through the statement that “every supply creates its own demand.”

    The article’s historical reconstruction begins with William Spence, author of Britain Independent of Commerce, published in 1807. The article adds that the idea had previously been developed by William Cobbett in his Political Register, under the title “Down with Commerce.” In response to Spence’s work, James Mill published Commerce Defended in 1808.

    In that work, Mill argued that a country’s annual produce is employed in making purchases and, because that same produce is what is offered for sale, one part of the produce purchases the other. From this follows the idea that annual produce creates a market for itself. Mill also clarifies that there may be an excess of a particular commodity, but not of commodities in general: a sectoral excess implies that other commodities have been produced in insufficient proportion and that the means of production must be redistributed until equilibrium is restored.

    “However great the annual produce may be, it always creates a market for itself.” James Mill, Commerce Defended (1808), as cited in the article

    The article continues with Elements of Political Economy (1821). There Mill argues that the proportion in which commodities exchange depends, in the first instance, on the relation between supply and demand. He nevertheless maintains that their relative value ultimately depends on the cost of production: changes in supply or demand may temporarily move values away from that point, while competition, when unobstructed, tends to return them to it.

    II. Monetary Theory and the Quantity Theory of Money

    On monetary matters, the article takes up an observation by Marx: James Mill sought to present Ricardo’s theory of money on the basis of simple metallic circulation, without resorting to the international complications with which, according to the article’s own formulation, Ricardo attempted to conceal the inconsistency of his conception, and without entering into controversy over the functions of the Central Bank. Gómez Julián also recalls that Ricardo questioned those functions on more than one occasion.

    Gómez Julián presents Mill as one of the finest exponents of the Quantity Theory of Money of his time. According to the article’s exposition, Mill attempts to demonstrate in a relatively solid manner that the quantity of money in circulation determines the total sum of commodity prices in an economy and likewise determines the value or price of money.

    “It is the total quantity of money in a country that determines what portion of it exchanges for a given quantity of commodities.” James Mill, Elements of Political Economy (1821), translation of the passage quoted

    Mill then explains two circumstances under which the Government creates money: 1) when it wishes to let it flow freely through the channels of circulation and 2) when it wishes to control at its discretion the quantity in circulation. In the first case, the Government leaves the Mint open to the public to convert bullion into coin, so that people coin their bullion when its monetary form is more valuable.

    It is precisely here that Gómez Julián identifies germs of Modern Monetary Policy in James Mill, in contrast with predecessors such as Ricardo, who questioned Government monetary intervention. The article adds that, for Mill, the value of money depends on its quantity: it rises with scarcity and, through the mechanism that the text itself links to the “metaphysical necessity” attributed to the later Say’s Law, the money market tends once again toward equilibrium.

    Mill also argues that, if the Government wishes the quantity of money in circulation to be smaller than it would be without intervention, it must raise the value of the metal contained in the coinage; if it wishes a larger quantity, it must reduce it. Gómez Julián presents this mechanism as another germ of Modern Monetary Policy.

    III. Trade, Comparative Advantages, and Exchange-Rate Competitiveness

    In the field of international trade, the article maintains that James Mill conceived the relationship between nations in the same way as the relationship between merchants: buy in the cheapest market and sell in the dearest. Gómez Julián explicitly contrasts this formulation with what he calls the “Ricardian illusion of Comparative Advantages,” which he describes as highly widespread at the time.

    The text adds that Mill was one of the first economists to propose using the value of the currency to gain or lose competitiveness in the world market; that is, it identifies in his work an early formulation of competitiveness through exchange rates.

    IV. Consumption, Egoism, and the Organization of Political Economy

    Gómez Julián points out that original notions of productive consumption and unproductive consumption can be found in Mill’s thought, later taken up by Marx in his theoretical system. In commenting on Mill’s exposition of these notions, Marx highlighted his “customary cynical acumen and clarity.”

    The article also gives special attention to the principles of egoism linked to private property and production. According to Gómez Julián, these issues appear in Mill with greater clarity and depth than in Adam Smith’s The Theory of Moral Sentiments. The article itself summarizes this conception through a phrase by Marx:

    “The limit of his need constitutes the limit of his production.” Karl Marx, as cited by Gómez Julián

    Mill’s clarity would also be reflected in the organization of his major work, divided into four main parts:

    1. Production
    2. Distribution
    3. Exchange
    4. Consumption

    Gómez Julián highlights the depth, simplicity, and concreteness with which Mill approaches this structure. The article does not claim that this scheme later became the general template for economics textbooks; that extrapolation is therefore excluded from this version.

    The text likewise cites Marx regarding the monetary theories of John Stuart Mill. In order to emphasize James Mill’s theoretical capacity, Marx observes that the son maintained an “eclectic logic” that allowed him to embrace his father’s positions and, at the same time, their opposites.

    V. Social Classes, Capital, and Population

    The question of social classes also receives attention in the article. Although Gómez Julián characterizes James Mill as the “bourgeois apologist par excellence” of his time, he highlights the clarity with which Mill refers to the great mass of the people as the class that can offer, in exchange for its means of subsistence, only ordinary labour.

    The article also attributes to Mill an early understanding of the distinction between the medium of circulation as capital and the medium of circulation as a simple medium of exchange. To illustrate this, it reproduces a passage from Elements of Political Economy in which Mill rejects as circular the claim that the value of commodities depends on capital, since capital itself is composed of commodities. Gómez Julián summarizes the Marxian interpretation by indicating that the medium of circulation employed for productive purposes constitutes capital.

    On population, Mill maintains that there is a certain density that is convenient both for social intercourse and for the combination of forces that increases the product of labour. From this, Gómez Julián states that Mill clearly understood that the needs of capital essentially determine population density, in contrast with the well-known arguments of Malthus.

    “There is a certain density of population which is convenient […] for that combination of powers by which the produce of labour is increased.” James Mill, Elements of Political Economy (1821), abridged translation

    VI. Capital Accumulation and Intellectual Influence

    Gómez Julián argues that James Mill was, together with S. Bailey, one of the first economists to discuss in depth the question of Capital Accumulation: in particular, the extent of the effects of industrial capital with respect to its accumulation when the magnitude of the total capital advanced remains constant.

    The article also notes the error made by both Mill and Bailey in presenting as a fixed magnitude the portion of capital invested in labour-power — variable capital — separating it from the mass of profit obtained by the capitalist.

    Finally, the text turns to John Maynard Keynes, who explains that the designation “classical economists,” invented by Marx, referred to Ricardo, James Mill, and their predecessors, that is, to the founders of the theory that culminated with Ricardo. Gómez Julián uses this passage to present Mill as one of the founders of Political Economy.

    Indirect contributions

    The article concludes by pointing to other indirect contributions: the intellectual formation of John Stuart Mill and James Mill’s role as one of David Ricardo’s principal mentors in Political Economy. In a final note, it adds that Mill was the chief motivator behind Ricardo’s decision to write his major work and observes the similarity between the title of Ricardo’s work and that of a work by James Mill published several years earlier.

    · · ·

    The Article’s Thesis

    The conclusion that emerges from the exposition as a whole coincides with the objective announced in the abstract: to show that James Mill played a fundamental role in the formation of modern economic science. The argument rests on his contributions to the relation between supply and demand, the theory of value and production costs, the Quantity Theory of Money, the antecedents of monetary policy, trade and exchange rates, consumption, egoism and private property, social classes, the distinction between money and capital, population, capital accumulation, and his direct influence on John Stuart Mill and David Ricardo.

    Bibliography Cited in the Article

    • Keynes, J. (2003). Teoría General de la Ocupación, el Interés y el Dinero. Fondo de Cultura Económica, México D. F.
    • Marx, K. (1844). Comments on James Mill, Éléments D’économie Politique.
    • Marx, K. (1989). Contribución a la Crítica de la Economía Política. Editorial Progreso, Moscú.
    • Marx, K. (2010). El Capital. Fondo de Cultura Económica, México D. F.
    • Mill, J. (1808). Commerce Defended.
    • Mill, J. (1821). Elements of Political Economy.
    • Mill, J. (1825). Colony.
    • Sraffa, P. (1795). The Works and Correspondence of David Ricardo, Vol. 10, Biographical Miscellany.
    • Winch, D. (1966). Selected Economic Writings.

    — End —

    Source article
    Gómez Julián, J. M. “La influencia de James Mill
    en la ciencia económica moderna.”
    Contribuciones a la Economía, Vol. 13, No. 1, 2015.
    E-ISSN 1696-8360. Read on Dialnet
    Popular-audience version
    Content reorganized for web reading
    without adding claims foreign to the original article.
  • ABSOLUTE ADVANTAGE VS COMPARATIVE ADVANTAGE: A MULTIDIMENSIONAL COMPARISON

    ABSOLUTE ADVANTAGE VS COMPARATIVE ADVANTAGE: A MULTIDIMENSIONAL COMPARISON

    International Trade · Economic Theory · Econometrics

    International Trade Theories Versus the Outcomes of Trade Agreements:
    Absolute or Comparative Advantage?

    Based on: Gómez Julián, J. M. (2025). “Teorías del comercio internacional versus resultados de los tratados comerciales: ¿ventaja absoluta o comparativa?” Revista Cubana de Economía Internacional, 12(1), 36–57. Read the original paper (Spanish)

    Economic theory has offered different explanations for the causes and benefits of international trade. Among them, two fundamental approaches stand out: absolute advantage and comparative advantage. The research by José Mauricio Gómez Julián examines these theories not only at the conceptual level, but also in light of the outcomes observed following the adoption of trade agreements.

    The aim of the study is to determine whether the outcomes resulting from the adoption of trade agreements between countries —especially when significant technological asymmetries exist between them— constitute evidence in favor of the theory of absolute advantage or of theories grounded in comparative advantage.

    To carry out this comparison, the paper considers three dimensions: the mathematical generalizability of the theories, the historical context in which they were developed, and the available econometric evidence.

    Absolute Advantage and Comparative Advantage

    Absolute advantage, associated with the tradition of Adam Smith, explains trade on the basis of absolute differences in countries’ productive capacities. From this perspective, differences in productivity and costs between economies are directly relevant to understanding their trade relations.

    Comparative advantage, developed from the work of David Ricardo and later extended by other theories of international trade, holds that exchange can generate benefits even when one country possesses absolute advantages over another, provided that relative differences allow for specialization.

    The paper confronts these two approaches by asking which of them has greater capacity to explain the actual outcomes associated with trade agreements, particularly when the countries participating in them exhibit substantial differences in their technological capabilities.

    Three Dimensions for Comparing the Theories

    1. Mathematical Generalizability

    The first dimension examined is the mathematical generalizability of the theories. The analysis considers the extent to which formulations corresponding to absolute advantage and comparative advantage retain a logical foundation when attempts are made to extend them beyond their particular formulations.

    This comparison forms part of the criterion used by the study to determine the relative soundness of both theoretical traditions, together with the historical and econometric evidence.

    2. Historical Context of Their Development

    The second dimension is the historical context in which the theories of international trade were formulated. The paper does not consider theoretical constructions in isolation from the historical conditions in which they emerged, but instead incorporates that context as part of the assessment of their explanatory capacity.

    In this way, the research relates the historical development of the different theories to the contemporary problem of explaining the outcomes of trade agreements between economies that may exhibit considerable technological differences.

    3. Econometric Evidence

    The third dimension concerns the econometric evidence. For this purpose, the study considers two types of models:

    • Computable General Equilibrium (CGE) models, employed in the analysis of the expected effects of trade agreements.
    • Objective Bayesian Generalized Linear Models, used to empirically examine the relationships present in the data.

    The empirical component incorporates information from the UNITED STATES-COSTA RICA TRADE AND DEVELOPMENT INDICATORS (1991–2019) database, compiled by Gómez Julián in 2024, which brings together indicators concerning trade relations and development in the relationship between the United States and Costa Rica.

    In the application of the objective Bayesian generalized linear models, relationships between one dependent variable and one independent variable are examined, with 14 dependent variables being analyzed. In this way, the contrast between the theories is not confined to abstract reasoning, but also incorporates empirical outcomes related to the observed effects of trade agreements.

    The Central Result

    The comparison of mathematical generalizability, historical context, and econometric evidence leads to a definite conclusion. According to the study, theories of international trade grounded in comparative advantage do not display a rigorous logical and empirical foundation, whereas the opposite result is found for the theory of absolute advantage.

    The outcomes observed in contexts characterized by significant technological asymmetries therefore provide evidence favorable to absolute advantage over comparative advantage as an explanation of the trade relations analyzed.

    The importance of technological differences between economies is therefore central to interpreting the outcomes of trade agreements. Treating those differences as secondary leads to conclusions different from those that emerge when the theories are confronted with the empirical results examined in the study.

    What Does This Imply for Trade Agreements?

    The paper’s conclusions extend to the way trade agreements should be analyzed. The results indicate that views regarding these agreements and the structures they adopt must take into account the technological and wage asymmetries existing between the parties.

    These asymmetries are not a secondary element. On the contrary, they are fundamental to understanding the consequences that trade integration can have between economies with different productive capacities and to properly evaluating the outcomes obtained after the adoption of such agreements.

    The study further concludes that trade agreements constitute a fundamental instrument capable of encouraging or discouraging countries’ growth and sustainable development. Their outcomes therefore cannot be assessed solely through theoretical assumptions about the general benefits of exchange, but must instead be confronted with the specific conditions and actual results of the economies involved.

    A Comparison Between Theory and Outcomes

    The paper’s central argument can be summarized as a confrontation between the predictions and foundations of international trade theories and the concrete outcomes associated with trade agreements.

    By combining the analysis of mathematical generalizability, historical context, and econometric evidence, the research concludes that the explanation based on absolute advantage possesses stronger logical and empirical support than explanations grounded in comparative advantage within the problem under study.

    Consequently, the analysis of trade agreements must pay particular attention to technological and wage differences between countries, since these differences are decisive for understanding the effects such agreements may produce on their trajectories of growth and development.

    Reference: Gómez Julián, J. M. (2025). Teorías del comercio internacional versus resultados de los tratados comerciales: ¿ventaja absoluta o comparativa? Revista Cubana de Economía Internacional, 12(1), 36–57. https://revistas.uh.cu/rcei/article/view/11142/9584

  • Inflation Is (Not) Always And Everywhere A Monetary Phenomenon

    Inflation Is (Not) Always And Everywhere A Monetary Phenomenon

    Beyond the Phillips Curve — Inflation, Technological Change, and Surplus Value
    Political Economy Oct.–Nov. 2025 · 10 min read

    Beyond the Phillips Curve

    A study using U.S. data from 1968 to 2021 finds no significant long-run inverse relationship between inflation and unemployment and argues, from a Marxist perspective, that inflation functions as a real-wage adjustment mechanism through which the benefits of technological change can be transformed into relative surplus value.

    Based on: Gómez Julián, J. M. (2025). “Más allá de la curva de Phillips: inflación, cambio tecnológico y acumulación de plusvalía en las economías capitalistas contemporáneas.” Realidad Económica, No. 375, pp. 77–108.

    For decades, the Phillips Curve has occupied a central place in mainstream macroeconomics: the idea that inflation and unemployment maintain an inverse relationship that constrains economic policy choices. This study subjects that relationship to empirical scrutiny and develops an alternative explanation of inflation from the standpoint of Marxist political economy.

    Using U.S. data for the period 1968–2021, the research finds no statistically significant long-run relationship between inflation and unemployment. Instead, it identifies relevant relationships among indicators of technological change —proxied by research and development (R&D) expenditure— prices, real wages, and the rate of surplus value.

    The central hypothesis is that inflation should not be understood solely as an imbalance between supply and demand or as a purely monetary phenomenon. Within the framework developed in the paper, it also functions as a wage-adjustment mechanism within the process of capitalist accumulation.

    What Is Really at Stake with the Phillips Curve

    The paper reconstructs the intellectual development of the Phillips Curve: William Phillips’s 1958 work on unemployment and changes in nominal wages, followed by the adaptation by Samuelson and Solow to the relationship between unemployment and inflation. This historical reconstruction describes how the theory was formulated and consolidated; it does not, by itself, amount to conceding that a universal and stable economic relationship between the two variables actually exists.

    The empirical question is precisely whether that inverse relationship withstands scrutiny against the data. For the United States over the period studied, the answer obtained is negative: when long-run relationships are examined and controls are introduced, no statistically significant inverse association emerges that could sustain the conventional trade-off.

    The Exact Scope of This Conclusion The study does not need to claim that a single historical sample has, by itself, demonstrated the universal nonexistence of every possible Phillips Curve. What it demonstrates is that the relationship does not appear significantly in the U.S. data analyzed. The research therefore functions as a first piece in a broader empirical program: if the general claim that such a curve exists is to be evaluated, the analysis must be replicated across other periods, countries, economic structures, and specifications. This study lays the first stone; completing the structure requires further evidence.

    An Empirical Strategy Broader Than a Simple Correlation

    The study combines descriptive analysis, Bayesian inference, time-series tools, and a Bayesian model of the rate of surplus value. The different techniques do not serve the same purpose: each examines a different component of the proposed structure.

    Bayesian Correlations

    Ordinary and partial Pearson and Kendall correlations are estimated among indicators of technological change, inflation, and unemployment. Partial correlations make it possible to control for variables such as nominal GDP, real GDP, and real wages. Evidence is evaluated through Bayes factors, using BF > 3 as the criterion for substantial evidence in favor of a correlation.

    The results cannot be reduced to the statement that “more R&D always means more inflation.” Ordinary correlations vary depending on the source of R&D and the price indicator: both positive and negative relationships appear. Once controls are introduced, however, particularly important positive relationships emerge between federal and capitalist R&D expenditure and the Consumer Price Index.

    The role of real wages is also central: when their effect is controlled for, several negative correlations between sources of technological change and total inflation cease to be statistically significant. This is consistent with the hypothesis that the real wage occupies a mediating position within the mechanism under study.

    Granger Causality

    The Granger tests in the paper are not used to claim that “unemployment does not cause inflation.” Their object is the temporal relationship between indicators of technological change and price indicators, using one, two, and three lags.

    With one lag, statistically significant relationships are found between all types of technological-change indicators and all types of price indicators. In addition, the average p-values are lower when technological indicators act as explanatory variables than when prices do. With two lags, price indicators explain capitalist R&D; with three, technological change again predominates as a temporal determinant of prices.

    The result, therefore, is more complex than mechanical causality in a single direction: interactions and feedback effects are present, although the temporal pattern provides important evidence supporting the role of technological change.

    Error Correction Models

    After the relevant tests of the properties of the series, the error correction models find that federal R&D expenditure statistically determines core inflation, the CPI, and the PPI; that capitalist R&D determines the CPI and the PPI; and that R&D from other sources likewise determines several price indicators.

    In the opposite direction, core inflation appears as the channel through which prices can determine indicators of technological change. Again, the result describes a dynamic structure containing feedback effects rather than a simplistic one-way causal arrow.

    · · ·

    Wages Tell a Story Too

    The study directly examines the dynamics of wages and prices. The series do not possess the same probability structure: nominal wage growth fits a Gamma distribution, total inflation growth a Cauchy distribution, and core inflation growth a logistic distribution.

    That difference matters. Directly comparing parameters from such different distributions can lead to incorrect conclusions. The paper therefore uses trend-cycle analysis with Daubechies wavelets, allowing the temporal dynamics to be compared without imposing a common distributional structure.

    The resulting trends show that price indicators lie systematically above nominal and real wages in the comparisons performed. This connects inflationary dynamics with the evolution of purchasing power and sets the stage for the Marxist mechanism at the theoretical core of the paper.

    The Marxist Mechanism: From Innovation to Real-Wage Adjustment

    When a capitalist introduces a technological innovation that raises productivity, the firm can produce commodities under better conditions than its competitors and temporarily obtain extraordinary surplus value: an advantage arising from operating ahead of the prevailing average conditions of production.

    But that advantage cannot last indefinitely. Competition drives the diffusion of the technology. Other capitalists adopt the new techniques in order not to fall behind, and as the innovation becomes generalized, the pioneer’s extraordinary advantage disappears.

    This is where the central element of the hypothesis enters. In the face of productivity increases, inflation can operate as a real-wage adjustment mechanism: prices rise without requiring nominal wages to be directly reduced, and if nominal wages do not rise proportionally, workers’ purchasing power declines.

    In this way, the benefits of technological change can continue to affect the rate of surplus value positively even after the innovation has diffused. The mechanism is not simply that “inflation absorbs a cost gap.” Its decisive distributive element is the relative reduction of the real wage in relation to productivity growth.

    Technological innovation
    federal and private R&D
    →
    Extraordinary surplus value
    temporary advantage
    →
    Technological diffusion
    capitalist competition
    →
    Pressure on the
    rate of profit
    →
    Inflation
    real-wage adjustment
    →
    Lower purchasing power
    of labor
    →
    Relative surplus value
    for the capitalist class
    →
    Accumulation and
    inequality
    Fig. 1 — A simplified version of the mechanism developed in Diagram 1 of the paper.

    The Test Connecting Technology, Prices, and Surplus Value

    One of the most important empirical components of the study is an objective Bayesian generalized linear model. The dependent variable is the natural logarithm of the gross rate of surplus value; the natural logarithm of aggregate R&D expenditure and the natural logarithm of the Consumer Price Index are used as explanatory variables.

    49–61% interval of variance in the gross rate of surplus value explained by aggregate R&D and the CPI
    0.709 median coefficient for aggregate R&D expenditure
    0.195 median coefficient for the CPI

    The model reaches an R² of 0.55. Because it is formulated in logarithms, the coefficients can be interpreted as elasticities. It also presents favorable cross-validation indicators and variance inflation factors of 1.17 for both explanatory variables.

    This result is especially important because it empirically connects three components that the theoretical interpretation presents as related: technological change, inflation, and the rate of surplus value. The finding goes beyond observing that technology and prices move together; both contain substantial information for explaining variation in the gross rate of surplus value.

    · · ·

    What the Paper Actually Argues About Inflation

    The proposed Marxist interpretation treats inflation as part of the distributive struggle between capital and labor. When rising prices reduce real wages, productivity gains can primarily benefit capital through an increase in the rate of surplus value.

    From this perspective, inflation performs a systemic function: it contributes to transforming the temporary effects of extraordinary surplus value into relative surplus value for the capitalist class as a whole, preserving the benefits of innovation even after new technologies have become generalized.

    Inflation thus appears not as a mere monetary accident, but as a mechanism connected to capitalist accumulation, real-wage adjustment, and the distribution of income between capital and labor.

    This does not imply denying that monetary variables can play a role. The more precise claim is that reducing inflation to a purely monetary phenomenon is insufficient to explain the empirical and distributive relationships examined in the study.

    What the Paper Does Not Claim to Have Finished

    The paper explicitly defines its own boundaries. The research uses only U.S. data and covers the period 1968–2021. Its results should therefore not be presented as though a single study had exhausted the historical demonstration of the nonexistence of the Phillips Curve in every economy, period, or context.

    But this limitation does not neutralize the finding. If a relationship presented for decades as a fundamental component of macroeconomic theory fails to appear in a long U.S. time series examined through a broad statistical strategy, there is substantive reason to question its generality and continue putting it to the test.

    The First Piece of the Puzzle The appropriate conclusion is neither “the curve has been universally refuted by a single sample” nor “perhaps the curve remains valid and this result is merely an anomaly.” The study provides a first empirical piece of a larger problem. Completing the puzzle requires replicating this type of research across more countries, historical periods, and economic structures. Each additional replication will make it possible to assess how far the general claim of an inverse relationship between inflation and unemployment can be sustained —or dismantled.

    The Limitations Matter — and They Also Show Where to Go Next

    R&D expenditure as a share of GDP is a proxy for technological change rather than an exhaustive measure of it. It does not fully capture technological spillovers, international technology transfers, organizational innovations, learning by doing, informal incremental improvements, or the creative adoption of already existing technologies.

    At the same time, the paper defends its use because it provides long, comparable, methodologically standardized series and because a well-documented relationship exists between R&D and subsequent measures of productivity. Precisely because it omits real forms of technological change, the indicator can be interpreted as a conservative lower bound for total technological change.

    The study also notes that the relationships it finds are complex and may be affected by variables not incorporated into the analysis. In addition, although the theoretical core is outlined and subjected to econometric examination, it must still be connected with other components of Marxist theory, such as economic cycles and the tendency of the average rate of profit to fall.

    And What Does All This Mean for Economic Policy?

    Here it is important not to attribute conclusions to the paper that it does not yet develop. The study does not present a completed theory of monetary policy and does not conclude, for example, that a particular interest-rate decision simply amounts to “treating the symptom rather than the disease.”

    Instead, it explicitly identifies these questions as an area for future research: the implications must be developed both for workers’ union organization and for economic policymakers, and the relationship between the proposed theory and contemporary monetary policies —particularly inflation-targeting regimes— remains to be examined.

    The immediate implication of the paper therefore comes before any specific policy prescription: if inflation has a structural dimension linked to technological change, real wages, surplus value, and income distribution, then a theory attempting to explain it exclusively through monetary variables leaves out an essential part of the phenomenon.

    · · ·

    Beyond the Curve

    The contribution of the study can be condensed into three results: it finds no statistically significant long-run relationship between inflation and unemployment for the United States over the period examined; it finds evidence of relevant relationships between technological change and inflation; and it obtains results consistent with the hypothesis that inflation reduces real wages and allows productivity gains to affect the rate of surplus value.

    The importance of the argument does not lie simply in replacing one correlation with another. The change in perspective is deeper: it moves from treating inflation as an isolated price problem to locating it within the reproduction and accumulation of capital and within the struggle over the distribution of the value produced.

    Within this framework, the question is no longer merely why prices rise. It also becomes: What happens to the benefits of technological improvements once they become generalized? How are productivity gains distributed between capital and labor? What role does variation in the real wage play in that process?

    These relationships —rather than a simple mechanical trade-off between inflation and unemployment— are what the paper proposes placing at the center of the analysis.

    Original paper: Gómez Julián, J. M. (2025). “Más allá de la curva de Phillips: inflación, cambio tecnológico y acumulación de plusvalía en las economías capitalistas contemporáneas.” Realidad Económica, No. 375, Year 55, pp. 77–108. Read the full paper →

    Licensed under CC BY-NC-ND 4.0 — © 2025 José Mauricio Gómez Julián

  • Discovering the Truth: Genetics, Archaeology, and the Palestinian Descendants of the Ancient Jews

    Discovering the Truth: Genetics, Archaeology, and the Palestinian Descendants of the Ancient Jews

    The Ancient Judeans of Judea as Direct Ancestors of Contemporary Palestinians

    Archaeology, paleogenomics, historiography, epigraphy, and linguistics against the exile and “return” narrative: a synthesis of José Mauricio Gómez Julián’s monograph.
    The monograph begins with a historical question carrying direct political implications: Who, strictly speaking, are the descendants of the ancient Judeans of Judea?

    Its thesis is that the convergence of critical archaeology of the southern Levant, historiography, epigraphy, paleogenomics and population genetics, and historical linguistics indicates that contemporary Palestinians constitute the most direct demographic heirs of the ancient populations of the region, including the Judeans of the Kingdom of Judah. Modern Jewish populations, by contrast, exhibit heterogeneous demographic histories, with varying proportions of Levantine ancestry alongside components acquired through migrations, conversions, and admixture with European, African, and Asian populations.

    The argument does not depend on a single discipline. Its core lies precisely in the cross-corroboration of independent lines of evidence: the Canaanite origin of the earliest Israelites, the absence of a general Roman expulsion from Palestine, archaeological continuity across the Byzantine and Islamic transitions, genomic evidence, and linguistic and toponymic continuity.
    A central methodological caveat: the monograph explicitly distinguishes between robust consensuses, well-founded conclusions, and questions that remain open. It does not claim that every detail carries the same degree of certainty. In particular, no genome from an individual unambiguously identifiable as a “Judean” of the Kingdom of Judah has yet been published in a peer-reviewed journal. The specific connection to the Judeans is therefore inferred through the convergence of archaeological and historical continuity with genetic comparisons involving ancient Levantine populations, rather than through a direct comparison between a “Judean genome” and modern Palestinians.

    From the Bible as Foundational Narrative to Critical History

    The investigation begins with the methodological problem of using the Bible as though it were a historical chronicle. It reviews the historiographical revolution associated with Thomas L. Thompson, Niels Peter Lemche, Philip R. Davies, and Keith W. Whitelam—the so-called “minimalist school”—and confronts it with maximalist objections and intermediate positions such as those of William G. Dever and Lester Grabbe.

    The fundamental point is not that all biblical content is devoid of historicity. The monograph specifically emphasizes that extreme positions have increasingly given way to a middle ground: historically useful material does exist, particularly from the first millennium BCE onward, but the patriarchal narratives, the Exodus, the military conquest of Canaan, and the United Monarchy on the scale depicted in the biblical text do not possess the archaeological support traditionally attributed to them.

    Mario Liverani provides one of the study’s key interpretive frameworks through his distinction between “normal history” and “invented history”: the ancient political entities of Israel and Judah must be reconstructed through archaeology, epigraphy, textual criticism, and comparative sources, whereas the great foundational narratives must also be analyzed as political-theological constructions developed by the post-exilic community.

    The Earliest Israelites Emerged from Canaan

    One of the most robust pillars of the argument is the autochthonous Canaanite origin of the earliest Israelites. Around 1200 BCE, approximately 250 small unwalled villages emerged in the central highlands. Their pottery displays continuity with Late Bronze Age traditions, there are no widespread destruction layers attributable to an external conquest, and the organization of the settlements is compatible with local populations undergoing sedentarization.

    Israel Finkelstein and William G. Dever, despite their profound historiographical and chronological disagreements, converge on this point: the populations later identified as Israelites emerged primarily from within Canaanite society, rather than as a foreign population that conquered Canaan from outside.

    Epigraphy: Merneptah and Tel Dan

    The monograph incorporates a line of evidence that the previous HTML version largely omitted: epigraphy. The Merneptah Stele, dating to approximately 1208 BCE, contains the earliest known extra-biblical reference to “Israel” and identifies it through an Egyptian determinative corresponding to a people or socioethnic group, rather than a territorial state.

    The Tel Dan Stele, from the ninth century BCE, contains the sequence generally interpreted as “House of David.” The reading was challenged by some minimalists but is accepted by the majority of specialists. For the monograph, these inscriptions establish a crucial distinction: criticizing the biblical narrative does not require denying the historical existence of Israel or of a Davidic dynasty. What the extra-biblical evidence does not confirm is the Exodus, the conquest of Canaan, or a Solomonic empire on the scale described in the Bible.

    From Canaanite Polytheism to Yahwistic Monotheism

    Another substantial component of the paper concerns the religious evolution of Israel. Drawing on Mark S. Smith, William G. Dever, Othmar Keel, Christoph Uehlinger, and Thomas Römer, the monograph presents Yahwistic monotheism not as the starting point of Israelite history, but as the outcome of a prolonged historical process.

    Textual, archaeological, and epigraphic evidence indicates the coexistence of Yahweh, El, Baal, and Asherah at different moments in Israelite religion. The inscriptions from Kuntillet Ajrud and Khirbet el-Qom, together with Judean pillar figurines, altars, standing stones, and other material remains, document religious practices incompatible with the retrospective image of a primordial monotheistic Israel.

    The process appears to have developed from polytheism and monolatry toward increasingly exclusive monotheism, accelerated by the crisis of the Babylonian exile and consolidated during the Persian period. The possible influence of Zoroastrianism on later elements of Judaism—dualism, eschatology, and angelology—is explicitly treated as an open debate, not as an established conclusion.

    The Philistine Case

    The monograph also uses the Philistines as an example of the historical capacity of the Levantine substrate to absorb migrant populations. Ancient DNA from Ashkelon reveals a component related to southern Europe in the early Iron Age that becomes undetectable roughly two centuries later, coinciding with increasing cultural integration into the Canaanite environment.

    This does not lead to the conclusion that Palestinians are simply “descendants of the Philistines.” The argument is broader: contemporary Palestinians represent a historical synthesis of successive populations of the southern Levant—Canaanites, Israelites, Judeans, Samaritans, Philistines, Phoenicians, and other groups—upon a local substrate characterized by strong demographic continuity.

    Assyrians, Babylonians, and the Difference Between Deporting an Elite and Emptying a Territory

    The monograph repeatedly distinguishes historically documented deportations from the idea of complete demographic emptying. Following the Assyrian conquest of the Kingdom of Israel, part of the population was deported, another part fled toward Judah, and a substantial number remained in the territory. Imperial deportation disproportionately affected political, administrative, and specialized elites; it did not automatically mean eliminating the entire peasant population.

    The same principle applies to the Babylonian conquest. Jerusalem suffered profound destruction and real deportations occurred, but other areas—particularly Benjamin—show rural continuity. The so-called “Babylonian exile” is therefore interpreted as a political, institutional, and cultural rupture of enormous importance, but not as the physical disappearance of the population of Judah.

    During the Persian period, Judaism progressively consolidated as a differentiated religious system. This transformation provides the historical context within which the monograph situates the composition and reorganization of a fundamental portion of the biblical tradition.

    From Ioudaios to “Jew”: Hasmonean Conversions and the Transformation of Identity

    The Hasmonean expansion of the second and first centuries BCE constitutes another turning point. John Hyrcanus I imposed circumcision and observance of Jewish law upon the Idumeans; Aristobulus I did likewise with Iturean populations. The Herodian dynasty itself descended from this Idumean population incorporated into Judaism.

    Following Shaye J. D. Cohen, the monograph emphasizes the semantic transformation of Ioudaios: from a primarily ethno-geographic designation—“Judean,” an inhabitant of Judea—it came to acquire religious and cultural meanings as well. From that point onward, one could become Jewish without having been born Judean. This transformation constitutes a conceptual precondition for understanding the later expansion of the diaspora.

    The Myth of a Total Roman Expulsion

    The wars against Rome were devastating. The destruction of the Second Temple in 70 CE and, especially, the Bar Kokhba revolt of 132–135 CE caused enormous human and material losses in Judea. The monograph does not minimize that destruction.

    What it rejects is a different proposition: that Rome deported the Jewish population of all Palestine en masse and emptied the land. Hadrian prohibited Jewish access to Aelia Capitolina—Jerusalem—but there is no evidence of a Roman policy of total deportation from Palestine. Settlement continuity in several regions and the relocation of the center of Jewish life toward Galilee contradict such a scenario.

    Rabbinic centers arose in Galilee at places such as Usha, Sepphoris, and Tiberias; the Mishnah was compiled there around 200 CE and the Jerusalem Talmud later followed. Roman destruction was therefore enormously significant institutionally and regionally, but it did not result in the physical disappearance of the Jewish population from the land.

    • Historiographical consensus: the absence of a mass Roman expulsion of all Jews from Palestine is not a thesis exclusive to Shlomo Sand. Historians such as Israel Bartal and Anita Shapira acknowledge that the idea of a collective exile imposed by Rome belongs much more to popular culture than to specialist historiography.
    • Necessary qualification: accepting that there was no general expulsion does not mean denying the deaths, enslavements, local displacements, and destruction produced by the Roman wars.
    • Diaspora: major Jewish communities outside Palestine predated the Roman wars and must be explained through a combination of migrations, demographic growth, and conversion rather than through a single episode of expulsion.

    From Permanence to Conversion: Continuity of the Palestinian Population

    This is one of the central links in the monograph. If the rural population was not generally expelled, the question becomes what happened to it. The proposed answer is a progressive religious transformation upon a largely continuous demographic base.

    Between the fourth and seventh centuries, an increasing share of Palestine’s population Christianized under Byzantine rule. Following the Arab conquest of 634–638, Islamization was likewise not immediate. The demographic models and archaeological evidence examined in the paper place the process across several centuries, extending into the later medieval period.

    Gideon Avni finds remarkable continuity in settlement patterns and material culture across the Byzantine-Islamic transition. Richard Bulliet and other researchers likewise show that conversion to Islam followed a gradual trajectory. The implication is fundamental to the argument: the population’s religion changed far more rapidly than its biological composition.

    Jewish Continuity Never Disappeared Either

    The monograph stresses that Jewish presence in Palestine was never completely extinguished. Jewish communities survived throughout Late Antiquity, the Middle Ages, and the Ottoman period; the so-called Musta’arabim, Arabized autochthonous Jews, shared language and many everyday practices with their Muslim and Christian neighbors.

    This does not contradict the thesis of Palestinian continuity. On the contrary, for the paper it demonstrates that remaining in the territory did not require preserving any particular religion: different branches of a historically related population could remain Jewish, convert to Christianity, or later convert to Islam.

    Ben-Gurion, Ben-Zvi, Borochov, and Belkind

    The monograph assigns particular importance to the fact that several early Zionist leaders argued, before the consolidation of the national conflict, that the Palestinian fellahin descended substantially from ancient Jewish and Canaanite populations that had remained on the land and subsequently changed religion.

    David Ben-Gurion and Yitzhak Ben-Zvi defended this continuity in works published in 1918; Ber Borochov had articulated a similar thesis in 1905, Israel Belkind rejected in 1928 the idea that Jews had ceased to inhabit the country after Rome, and Ben-Zvi returned to the local ancestry of the fellahin in 1929. The paper argues that this interpretation subsequently lost prominence as the political requirements of the Zionist movement changed.

    Paleogenomics: Continuity, Admixture, and the Limits of What DNA Can Demonstrate

    Paleogenomics supplies the quantitative dimension of the argument, but the monograph explicitly warns against treating statistical categories as though they were perfectly bounded historical populations.

    The study by Agranat-Tamir and colleagues analyzed dozens of genomes from the Bronze and Iron Age Levant. Despite the region’s cultural and political diversity, these individuals exhibit a related genetic base and provide a reference point for studying continuity with present-day populations.

    • Contemporary Palestinians: the models examined in the monograph place approximately 81% to 87% of their ancestry in Bronze Age Levantine populations, complemented by later components, including African and European contributions.
    • Ashkenazi Jews: different whole-genome studies identify a clearly admixed population. Carmi et al. model it as approximately 50% Middle Eastern and 50% European, while other analyses produce somewhat different ranges depending on methodology. A substantial share of the European component derives from southern Europe.
    • Ashkenazi bottleneck: the modern population derives from a severe genetic bottleneck estimated at approximately 350 individuals around 600–800 years ago.
    • Erfurt: DNA from 33 medieval Ashkenazi Jews from the fourteenth century reveals greater genetic heterogeneity than exists today, subsequently reduced through genetic drift and endogamy.
    • Y chromosome: approximately 70% of Jewish Y chromosomes and 82% of Muslim Palestinian Y chromosomes analyzed by Nebel et al. belonged to the same broad chromosomal pool, dominated by J1 and J2 lineages, indicating a deep shared Levantine patrilineal substrate.
    • Mizrahi Jews: they constitute a crucial qualification. The monograph cites Levantine ancestry proportions on the order of 80–90% among different Mizrahi populations, comparable to those of Palestinians.
    What the data most precisely permit us to say: contemporary Palestinians exhibit, at the whole-genome level, very high proximity to ancient Levantine populations and greater continuity than that observed among Ashkenazim, whose demographic history includes substantial European admixture. But this does not mean that modern Jews lack Levantine ancestry. The monograph explicitly rejects that symmetrical conclusion.

    Nor is there yet a published dataset of genomes unambiguously identified as Judeans of the Kingdom of Judah. The preliminary Kiriath-Jearim data mentioned in the study point toward continuity with Canaanite profiles, but formal publication remains pending. Moreover, tools such as qpAdm lose discriminatory power when historical source populations are closely related, and components generated by programs such as ADMIXTURE are statistical constructs, not historical peoples literally preserved in DNA.

    The Khazar Hypothesis

    The monograph also distinguishes between the historical existence of conversion to Judaism among the Khazar elite—which is not generally disputed—and the much stronger claim that Khazars constituted the principal origin of Ashkenazi Jews. Modern genomic analyses do not identify the massive Caucasian or Central Asian contribution that such a hypothesis would require. Accordingly, the paper regards the Khazar hypothesis as the primary explanation of Ashkenazi origins as refuted by genomics.

    Genetics cannot ground territorial rights; but it can test genealogical claims when those claims are themselves employed as political arguments.

    Language: Canaanite → Hebrew → Aramaic → Arabic

    The linguistic argument complements the genetic evidence. Hebrew belongs to the Canaanite group of languages. With the expansion of the great Mesopotamian empires, Aramaic progressively became a lingua franca and displaced Hebrew in many everyday functions, without implying replacement of the population.

    Following the Islamic conquest, a structurally similar process occurred. Arabic replaced Greek in administration under the Umayyads and progressively displaced Aramaic among the local population. The linguistic transition unfolded over centuries.

    Accordingly, the sequence Canaanite → Hebrew → Aramaic → Arabic represents for the monograph not a succession of four peoples replacing one another, but largely a succession of languages spoken over a historically continuous population base.

    Toponymy and Ethnography: Memory Preserved in the Landscape

    Place names reinforce this interpretation. Beit Lahm (Bethlehem), Beisan (Beth-shean), Bir as-Saba (Be’er Sheva), ‘Anata (Anathoth), Seilun (Shiloh), and numerous other toponyms display the preservation and phonetic transformation of ancient names within Palestinian Arabic.

    The study also recovers the ethnographic work of Tawfiq Canaan and Hilma Granqvist. Canaan documented Palestinian peasant practices with possible pre-Islamic and pre-Christian antecedents, including the term ard ba’liyyeh for rain-dependent farmland, which linguistically preserves the name of Baal, the ancient Canaanite storm deity.

    Modern Hebrew

    The paper contrasts this organic continuity with the modern revival of Hebrew. Drawing particularly on Ghil’ad Zuckermann, it characterizes Israeli Hebrew as a language revitalized in the nineteenth and twentieth centuries upon ancient Semitic foundations but with significant structural influence from European languages—especially Yiddish—spoken by many of the revivalists.

    The monograph acknowledges that more radical formulations, such as that of Paul Wexler, do not represent the linguistic consensus. Its argument does not depend upon them: it is sufficient to distinguish between a consciously revitalized language and a dialect chain that evolved historically in the same territory.

    The Jewish Diaspora as a Historical Mosaic

    If Rome did not collectively expel the population of Palestine, the enormous Jewish diaspora already present in antiquity still requires explanation. The monograph’s answer is not monocausal. The diaspora formed through migration, voluntary conversion, forced conversion, and marital absorption of local populations, with different relative weights depending on place and period.

    Hasmonean conversions demonstrate at an early stage that Jewish belonging could be acquired. During the Greco-Roman world, proselytes and “God-fearers” existed, although the precise scale of active proselytism remains debated among specialists such as Louis Feldman and Martin Goodman.

    The extraordinary demographic expansion of ancient Judaism—from a comparatively small population after the Babylonian conquest to several million people during the Roman period—constitutes for the paper strong evidence that conversion played a substantial role that natural increase alone would struggle to explain.

    The monograph then examines highly diverse cases: the Himyarite kingdom of southern Arabia, the disputed traditions concerning Berber conversions, Beta Israel in Ethiopia, Bene Israel and Cochin Jews in India, the Jews of Kaifeng in China, and Sephardic and Ashkenazi communities in Europe. The result is not a single genealogy but a mosaic of communities with different biological and cultural histories connected through Judaism.

    Two simplifications explicitly rejected by the paper:

    1. It is not sustainable to claim that all modern Jews descend biologically in a linear and homogeneous manner from the ancient Israelites.

    2. It is equally unsustainable to claim that modern Jews have no genetic connection whatsoever to the ancient Levant.

    The evidence instead indicates a history of Levantine continuity combined with very different degrees of admixture depending on the community.

    The Historiographical and Political Implications

    The monograph does not present its demographic conclusions as politically neutral. Its theoretical starting point is explicitly Gramscian: historical narratives can become mechanisms of hegemony when they begin to operate as legitimizing “common sense” within present political relations.

    From this perspective, the narrative of an ethnically continuous people expelled by Rome and “returned” two thousand years later performs, according to the paper, a specific political function: it transforms a modern colonization into the restoration of ancestral sovereignty. The investigation contrasts that narrative with the documented history of European Zionism, the Balfour Declaration of 1917, the British Mandate, organized immigration, the 1947 partition, the Nakba of 1948, and the subsequent American patronage of Israel.

    The paper therefore situates the State of Israel within the modern history of settler colonialism and Western geopolitical interests in the Middle East, arguing that the biblical-genealogical narrative operates as one of its mechanisms of cultural legitimation.

    This interpretation is not presented as a criticism of Judaism or of Jews as a population. The monograph devotes a specific section to Jewish and Israeli critics of Zionism—including Tony Judt, Judith Butler, Norman Finkelstein, and the Israeli “new historians”—precisely in order to distinguish Judaism, Jewish identity, historiography, and the political project of Zionism.

    What the Monograph Regards as Established—and What It Does Not

    • Robust consensus: the earliest Israelites emerged primarily from the local Canaanite substrate rather than through an external conquest of Canaan of the kind described in Joshua.
    • Robust consensus: Rome did not carry out a mass deportation of the entire Jewish population of Palestine following the wars of the first and second centuries CE.
    • Robust consensus according to the paper’s synthesis: a predominant share of the Palestinian population descends from ancient populations of the Levant that remained in the region while undergoing successive religious and linguistic transformations.
    • Well-founded conclusion, with qualifications: Jewish diaspora communities formed through varying combinations of Levantine ancestry, migration, conversion, and admixture with local populations.
    • Well-founded conclusion: the Canaanite–Hebrew–Aramaic–Arabic linguistic sequence is compatible with language shifts without general demographic replacement.
    • Well-founded conclusion: Jews and Palestinians share a deep Levantine genetic substrate; present differences reflect divergent later histories of permanence, migration, endogamy, admixture, and genetic drift.
    • Open debates and limitations: no DNA has yet been published from individuals unambiguously attributable to the Judeans of the Kingdom of Judah; the relative magnitude of ancient proselytism remains disputed; genetic proportions depend on statistical models and reference populations; and some religious and historiographical questions, such as the extent of Zoroastrian influence, remain open.

    Conclusion: Continuity Through Transformation

    The monograph’s final thesis is not that Palestinians constitute a biologically “pure” or immutable population. It is almost the opposite: historical continuity can coexist with migrations, admixture, religious change, cultural transformation, and profound linguistic replacement.

    Over millennia, the population of the southern Levant absorbed Canaanites, Israelites, Judeans, Samaritans, Philistines, and other groups. Assyrian, Babylonian, Persian, Hellenistic, Roman, Byzantine, and Arab conquests profoundly transformed the region’s institutions, religions, and languages without producing, in most of these episodes, the complete replacement of its population.

    Within this historical process, the paper argues that contemporary Palestinians represent the principal demographic continuity of the ancient populations that remained in the territory, including the ancient Judeans, whereas modern Jewish populations follow heterogeneous trajectories: some—particularly Mizrahi populations—retain very high levels of Levantine ancestry; others—such as Ashkenazi Jews—combine substantial Levantine ancestry with an equally substantial European contribution.

    The study therefore rejects two extremes simultaneously: both the notion of homogeneous and exclusive biological continuity between all modern Jews and the ancient inhabitants of Judea, and the inverse claim that modern Jews lack Levantine roots.

    Finally, the monograph insists upon a fundamental normative boundary: genetics does not confer territorial rights, and genetic proximity does not determine who deserves citizenship, dignity, self-determination, or political rights. Its relevance emerges when a particular historical genealogy is itself used as political justification. In such cases, the author argues, historical, archaeological, linguistic, and genomic sciences are entitled to subject that genealogy to scrutiny.

    In this way, archaeology, historiography, epigraphy, genetics, and linguistics converge upon the thesis organizing the entire investigation: the history of Palestine is far more a history of human continuity through successive transformations than a history of total expulsion followed, two thousand years later, by the return of the same population.

  • Political Economy and Probability Theory: Marx, Adam Smith, and the Law of Large Numbers

    Political Economy and Probability Theory: Marx, Adam Smith, and the Law of Large Numbers

    The Political Economy Notebook
    Exploring Economics Beyond the Textbook

    Do All Workers Get Exploited the Same?
    Testing a Marxian Assumption with Probability Theory

    How sixty years of U.S. sectoral data and non-classical laws of large numbers were used to examine a foundational assumption behind the Marxian average rate of profit

    Based on: Gómez Julián, J. M. (2022). Ciencia Económica, 11(17), UNAM

    ~ 9 min read

    A consequential assumption sits behind Marxian analyses of the average rate of profit whenever differences in the degree of labor exploitation across productive sectors are not explicitly modeled: sectoral rates of surplus value may be treated as tending toward uniformity. Adam Smith supplied the original economic argument for such a tendency, and within Marxian political economy the proposition acquired central importance. But can that tendency be defended when actual sectors are neither independent nor statistically identical? A 2022 paper by José Mauricio Gómez Julián in Ciencia Económica approaches the question from three directions at once: probability theory, the concrete labor-market mechanisms discussed by Smith and Marx, and statistical evidence from the United States between 1960 and 2020.

    The Problem, in Plain Language

    In Marxian theory, surplus value is the value produced by labor beyond the value represented by labor-power. Empirically, the paper approximates the rate of surplus value using modern national accounts: gross operating surplus is taken as a representation of surplus labor time and employee compensation as a representation of necessary labor time. Their ratio provides the sectoral rate used in the statistical analysis.

    The issue matters because the tendency toward uniform sectoral rates of surplus value is part of the foundation on which the formation of an average rate of profit and, consequently, Marxian prices of production rests. But an important nuance is easily lost here. The paper does not treat prices of production as pre-existing equilibrium prices around which market prices merely oscillate. Drawing on Carchedi and de Haan, it emphasizes a dynamic interpretation: market prices exist first, and capitalist competition — including technological competition and movements of capital — pressures them toward a systemic average. Prices of production exist through this very process of convergence rather than as a fixed center established in advance.

    The empirical question is therefore not whether every industry displays exactly the same exploitation rate at every instant. The proposition under examination is a tendency toward asymptotic uniformity: as the analysis approaches a sufficiently long period and/or a sufficiently large collection of relevant sectors, do sectoral rates behave in a way consistent with convergence toward a global expected value?

    Why the Asymptotic Perspective Matters

    The paper connects this question to Marx’s theory of knowledge. Its argument is that Marx’s method cannot be reduced to the passive acceptance of isolated empirical facts. Through a materialist appropriation of Hegelian dialectics, the analysis privileges totality: the phenomenon must be understood through its relations, its development, and the larger system of which it forms a part. In the paper, the term asymptotic regime condenses this idea statistically — a sufficiently long time horizon, a sufficiently large number of units, or both.

    This matters because a sector observed in isolation may differ substantially from another sector. Uniformity, if it exists, need not appear as point-by-point equality. It may instead be a property that becomes visible only when the system is considered on a sufficiently large scale.

    Enter the Law of Large Numbers

    The mathematical framework is the Law of Large Numbers (LLN). In broad terms, laws of large numbers describe conditions under which averages stabilize around an expected value as the amount of information grows. The strong version concerns almost-sure convergence; the weak version concerns convergence in probability.

    The difficulty is immediate. Classical formulations typically rely on strong assumptions such as independence and identical distribution. Those conditions are not realistic for capitalist sectors. Industries interact through production chains, competition, wages, technology, demand, and capital movements; and their productive structures differ. The paper’s own statistical results confirm that the sectoral variables are neither identically distributed nor, in general, linearly independent.

    That does not make the LLN irrelevant. Rather, the theoretical part of the paper asks whether more general versions of the law can accommodate the structure of the economic problem. The answer is qualified: several mathematical results relax different parts of the classical assumptions, but they do not all do so in the same way.

    What the Mathematical Literature Actually Establishes

    • Li, Rao and Wang (1995): study a strong law for weighted sums of independent random variables with multidimensional indices under specific structural and moment conditions.
    • Adler and Rosalsky (1987): establish a strong-law result for normalized weighted sums of independent and identically distributed random variables.
    • Chen and Sung (2016): generalize weighted-sum results under stochastic-dominance and weighting conditions, relaxing restrictions relevant to the distributional structure.
    • Sung (2011): is especially important for the economic application because it provides sufficient conditions under which the variables may be dependent, subject to moment and other technical requirements.
    • Andrews (1988) and Davidson (2021): provide weak-law results and a broader framework for weakly dependent processes, including mixingale-type structures relevant to econometrics.
    “Smith’s proposition concerning the law of tendency toward uniformity is consistent with the logic behind certain varieties of the Law of Large Numbers.” Translation of the paper’s conclusion — Gómez Julián, 2022

    The word certain is essential. The paper does not claim that simply invoking a non-classical LLN automatically proves the Marxian proposition. Formal consistency depends on satisfying the conditions of the particular theorem being used. In some cases this may require transformations of the dataset — for example, grouping or disaggregating sectors, arranging observations in structures such as triangular arrays, or estimating missing periods where appropriate. Whether such requirements can actually be met depends on the concrete dataset.

    What Counts as a Productive Sector?

    Before performing the statistical analysis, the paper faces a specifically Marxian classification problem: not every activity appearing in national accounts necessarily belongs in the calculation of the average rate of profit. The relevant sectors are those treated as productive in relation to the circuit of capital and the production of surplus value.

    This is particularly important for services. Drawing on the literature on productive and unproductive labor, the study distinguishes activities that directly produce surplus value, activities that facilitate its production elsewhere, and activities outside the relevant circuit of capital. After harmonizing sector classifications across the historical period and applying those theoretical criteria, the empirical analysis works with 36 productive sectors.

    What the U.S. Data Show

    The empirical component uses data from the U.S. Bureau of Economic Analysis for the period 1960–2020. Sectoral rates of surplus value are constructed from gross operating surplus and employee compensation, and the study then examines probability distributions, pairwise Pearson correlations, and the differences between sectoral location measures and their global counterparts.

    Key Empirical Findings

    • The sectors are not identically distributed: among the 36 sectors, 16 are best fitted by a Uniform distribution, 13 by Cauchy, 3 by Logistic, 2 by Log-Normal, and 2 by Weibull. None is best described by a Normal distribution.
    • The sectors are not generally linearly independent: 630 pairwise Pearson correlations are calculated. Their mean is approximately 0.081 and their median approximately 0.140.
    • Substantial pairwise dependence is not rare: 256 of the 630 correlations — about 40.63% — are at least 0.30. The paper therefore rejects the idea that the sectors can generally be treated as linearly independent.
    • Most summary measures of the differences are close to zero: relative to the global mean, the sum of sectoral differences is approximately 3.38 × 10−14 and their mean approximately 9.38 × 10−16. Relative to the global median, the corresponding values are also small.
    • There is an important exception: the median of the differences calculated relative to the global mean is not close to zero. The paper therefore describes the evidence as a tendency toward reciprocal nullification in general, not as perfect cancellation in every statistic.
    • The differences have different distributional forms: those calculated relative to the global mean are best fitted by a Cauchy distribution, with Logistic as the second-best option; those relative to the global median are best fitted by a Uniform distribution, with Normal as the second-best option.

    This pattern is important precisely because the empirical data do not reproduce the assumptions of the classical LLN. The sectors remain heterogeneous and interconnected. Yet the descriptive behavior of their deviations provides evidence, in the author’s interpretation, in favor of a tendency toward reciprocal nullification when the system is considered as a whole.

    Why Conventional Significance Tests Were Set Aside

    The paper originally considers tests for differences between sectoral means or medians and their global counterparts, including Student’s t procedures and Wilcoxon procedures, together with bootstrapping. It ultimately argues that the available inferential tests are not appropriate for drawing valid conclusions from this particular structure of data.

    The problem is not simply non-normality. Depending on the procedure, assumptions concerning distributional form, linear independence, pairing, and equal sample sizes become relevant. The economic variables are interdependent by construction, and bootstrapping does not solve the entire difficulty: although resampling can break the relation between the immediately compared groups, it does not eliminate dependence among the sectoral components that make up the global group.

    An especially important nuance is that the discarded tests did indicate statistically significant differences. The paper nevertheless refuses to treat those results as valid inferential evidence because the required conditions are not adequately satisfied. It therefore replaces that inferential route with a descriptive — or, as the paper itself suggests, perhaps more accurately semi-descriptive — analysis based on the behavior and probability distributions of the differences.

    Smith, Marx, and the Economic Mechanism

    The probability argument is only one dimension of the paper. A second dimension returns to Adam Smith’s account of labor-market adjustment. Smith argues that the total advantages and disadvantages of different employments in the same locality must either be equal or continually tend toward equality; otherwise workers and capital would move in ways that erode unusually favorable or unfavorable conditions.

    The paper organizes Smith’s discussion around seven factors affecting compensation: the simplicity or difficulty of the work; whether it is pleasant or unpleasant; danger and effects on health; regularity or temporariness of employment; the degree of trust placed in the worker; the probability of professional success; and subjective considerations such as passion for an occupation, reputation, confidence in one’s abilities, and confidence in one’s luck.

    These factors matter because they do not imply isolated sectors. Quite the opposite: sectoral rates can be linked directly through the organic interdependence of capitalist production and indirectly through common forces affecting wages and working conditions. In this sense, the economic mechanism described by Smith and Marx is more naturally compatible with generalized probabilistic frameworks that permit dependence than with a classical model requiring reciprocal independence.

    • • •

    So What Does the Paper Actually Establish?

    The conclusion is favorable to the uniformity hypothesis, but it is carefully delimited. At the theoretical level, the logic of Smith’s tendency toward uniform sectoral rates of surplus value is consistent with certain strong and weak versions of the Law of Large Numbers that allow correlated variables and/or do not require identical distributions. This formal consistency is conditional on the concrete requirements of the relevant mathematical results being satisfiable.

    At the empirical level, the U.S. data show precisely the heterogeneity and interdependence that rule out a simplistic classical-LLN argument. At the same time, the descriptive analysis of sectoral deviations produces results that point in a direction favorable to Smith and Marx’s proposition that sectoral rates tend toward uniformity.

    This is therefore not a demonstration that every capitalist economy, in every historical period, must exhibit a uniform rate of surplus value. Nor does the study claim that all sectors possess the same rate at each moment. Its narrower and more defensible conclusion is that the assumption used in long-run Marxian analyses of the average rate of profit has both a plausible probabilistic formulation and empirical evidence in its favor for the U.S. case examined.

    That distinction matters. The paper’s contribution is not to eliminate sectoral diversity, but to ask whether diversity at the level of the parts can coexist with an asymptotic regularity at the level of the whole. Its answer is cautiously affirmative — and it is precisely the combination of heterogeneity, interdependence, and systemic regularity that makes the problem mathematically and economically interesting.

    Original article: Gómez Julián, J. M. (2022). “Sobre la validez del supuesto de uniformidad en las tasas de plusvalía sectorial desde la teoría de las probabilidades.” Ciencia Económica, Año 11, No. 17, Universidad Nacional Autónoma de México, Facultad de Economía. DOI: 10.22201/fe.24484962e.2022.11.17.2. Open Access under CC BY-NC-ND 4.0.
  • bayesianOU: Exploring Market Price Gravitation via Ornstein-Uhlenbeck Process

    bayesianOU: Exploring Market Price Gravitation via Ornstein-Uhlenbeck Process

    You can also find this library at CRAN and download it directly from R and RStudio.

    LISTEN TO THIS POST AS A PODCAST:

    When Market Prices Gravitate: A Bayesian Look at an Old Question in Economics

    An old question, asked again — properly

    There is a question in economics that is older than most of the academic disciplines that border it. Do market prices — the noisy, day-to-day, here-and-now prices at which goods actually change hands — tend to settle toward some underlying center of gravity? And if they do, how fast, how violently, and through what mechanism?

    Classical political economy, from Smith and Ricardo through Marx, thought they do. The idea was that behind the churning surface of market prices there sit “prices of production”: long-run, cost-anchored prices toward which actual prices are pulled, the way a spring pulls a weight back toward its rest position. In the Marxian version, there is one more layer underneath: those prices of production themselves are supposed to gravitate around “values,” the labour embodied in commodities. Whether any of this is true is an empirical question, and for a long time the empirical tools to answer it were not really up to the job.

    A small R package called bayesianOU, written by José Mauricio Gómez Julián and hosted on GitHub, takes a serious swing at that question. It is not the first attempt to test price gravitation statistically, but it is one of the most technically careful I have seen, and it is built in a way that is instructive far beyond the Marxian debate that motivates it. What follows is a walkthrough of what the package does, why it is interesting, and — just as importantly — where it honestly admits its own limits.

    The tool that makes it possible: the Ornstein-Uhlenbeck process

    Strip the economics away for a moment and the statistical core of the package is a workhorse object from physics: the Ornstein-Uhlenbeck (OU) process. Imagine a particle moving in a fluid, attached to a spring. Brownian motion jiggles it randomly; the spring pulls it back toward a fixed point. The further it drifts away, the harder the pull. The result is a wiggly series that never settles but always tends to settle — a mean-reverting random walk.

    The OU process is exactly the mathematical object you want when you suspect a variable is noisy but anchored. It has a “speed of reversion” (how hard the spring pulls) and an “equilibrium level” (where the spring’s rest point is). Estimate those, and you can say something quantitative about gravitation: not just “yes, prices come back,” but “they come back with a half-life of about nine years.”

    That number — the half-life — is the prize. It is the difference between “market prices eventually settle” (which could mean anything) and “market prices settle on a timescale comparable to a business cycle” (which is a falsifiable, interpretable claim).

    What the package actually builds

    The package fits, by Bayesian inference, a family of models built on the OU process but considerably richer than the textbook version. There are two first-class models, sharing one inference engine.

    The single-level model

    The first model asks: do market prices revert toward an equilibrium that is a function of the prices of production, and what does that reversion look like once we let it be nonlinear, volatile, heavy-tailed, and structurally heterogeneous across sectors?

    Each of those adjectives is doing real work, and each corresponds to a feature that simpler approaches handle poorly or not at all:

    • Nonlinear drift. A plain OU process pulls back with a force proportional to the deviation. The package allows a cubic correction, so the restoring force can strengthen super-linearly when prices are far from equilibrium. This matters: real markets may behave gently near the center and violently at the extremes, and a linear model cannot represent that.
    • Stochastic volatility. Financial data, and economic data generally, go through quiet stretches and turbulent ones. The package does not assume a single noise level; it lets the volatility itself wander over time, following its own mean-reverting process on the log-variance. This is the same idea that powers modern stochastic-volatility models in finance, and it is essential for not fooling yourself about the precision of your estimates.
    • Heavy tails. Economic shocks are not Gaussian. Crashes, booms, and policy shocks produce outliers that a normal distribution would call essentially impossible. The package uses Student-t innovations and estimates the degrees of freedom from the data, so the model can discover for itself just how fat-tailed the world is.
    • Hierarchical structure across sectors. An economy has dozens of sectors, and each one presumably has its own reversion speed, its own equilibrium, its own noise. Estimating each sector in isolation throws away the information that they are all part of the same economy. Estimating them all with one set of parameters pretends they are identical. The package takes the middle path — hierarchical, or “partial pooling,” priors — where each sector’s parameters are drawn from a shared distribution whose properties the model also estimates. Sectors borrow strength from one another without being forced into lockstep.
    • A time-varying coupling. This is the most economically loaded feature. The strength with which market prices track prices of production is allowed to depend on the aggregate profit rate (what the package calls TMG). When the general rate of profit is high, the pull of production prices on market prices may be one thing; when it is low, another. Whether that modulation exists, and in which direction, is a hypothesis the model can test rather than assume.

    All of this is estimated jointly, with full Bayesian uncertainty, using Stan’s Hamiltonian Monte Carlo sampler. You do not get a point estimate of the reversion speed; you get a posterior distribution, and from it a credible interval and a probability statement like “there is a 95% chance the half-life is between six and eighteen years.”

    The nested cascade

    The second model is the more ambitious one, and it is where the package earns its “nested” branding. Instead of market prices reverting to a fixed equilibrium, they revert to a latent production price — a hidden, unobserved series that itself evolves over time according to its own OU process, driven by the general profit rate. And, if you turn on the third level, that latent production price in turn gravitates around an observed “value” index built directly from labour-content accounting.

    So the full structure is a cascade: market price → latent production price → value. Each arrow is an OU reversion, each with its own speed, and the speeds are constrained so that the outer (market) layer reverts faster than the inner (production) layer — an economically natural separation of timescales, enforced softly so the data can push back.

    The reason this matters is that it converts a slogan — “prices of production gravitate around values” — into a literal statistical hierarchy that can be fit to data and compared against alternatives. The headline empirical result, from a fit to 37 US sectors over 1960–2020, is a value-coupling coefficient essentially equal to one, with the posterior probability of it being positive effectively equal to one. In plain terms: in standardized units, prices of production track labour values almost one-for-one. That is a found result, not an assumed one — the prior on the coupling was centred at zero, deliberately neutral.

    The inference engine, and why it is not a footnote

    It would be easy to glance at the model description, nod, and move on. But how these quantities are estimated is half of what makes the package serious, and it is worth a paragraph for readers who do not think about MCMC every day.

    Bayesian inference works by exploring the space of all parameter values consistent with both the data and the prior, and characterizing that space as a probability distribution. For models this complex — with latent volatility paths, hierarchical structure, and hundreds of parameters — you cannot do that with pencil and paper. You use a Markov chain Monte Carlo sampler, specifically Hamiltonian Monte Carlo, which borrows an idea from physics: give the parameter space a “potential energy” (the log-posterior) and a “kinetic energy” (a randomly chosen momentum), and let the system glide around the posterior like a ball rolling over a landscape.

    Stan’s NUTS sampler automates this about as well as it can be automated, and the package uses it with within-chain parallelism (via Stan’s reduce_sum) to handle the fact that the likelihood must be summed over many timepoints and sectors. The diagnostics — R-hat for chain agreement, effective sample size, divergence counts — are surfaced through a validate_ou_fit function, and the package is explicit that you should look at them before believing anything.

    Model comparison is done with PSIS-LOO, a clever technique that approximates leave-one-out cross-validation without refitting the model dozens of times, by reweighting the posterior draws using importance sampling. It is the modern standard, and the package is appropriately cautious about it: because the model has a latent volatility state at every observation, plain LOO is known to be optimistic, and the documentation says so plainly.

    The honesty that makes it credible

    Here is where the package surprised me, and here is why I think it deserves a wider audience than the Marxian-economics niche it lives in.

    A naïve reading of the results would be triumphant: the value coupling is one-to-one, the reversion exists, the half-life is about nine years. But the package’s own validation section does something rare. It runs the model against legitimate rivals on genuinely held-out data — a full decade, 2011 to 2020 — and reports, without spin, that a random walk beats the OU model at forecasting, that a no-gravitation restriction ties or beats it, and that the value term adds no detectable predictive density.

    That sounds like a refutation. The package argues, carefully, that it is nothing of the sort — and the argument is the most intellectually interesting thing here.

    The key move is to distinguish two different questions. One is structural: does a reversion mechanism exist, and how fast is it? The other is predictive: can you forecast next year’s price better than a naïve benchmark? These are related but not identical, and for a slow process they come apart in a specific, predictable way.

    If gravitation is real but slow — a half-life of nine years on a dataset whose test window is a decade — then over the forecast horizon the process looks, to first order, like a random walk. The reversion is there, but it is too weak to show up in a one-step or few-step prediction. The random walk, which assumes no reversion, will forecast almost as well, because over short horizons a barely-reverting process and a non-reverting one are nearly indistinguishable. So the random walk winning the forecasting horse race is not evidence against gravitation; it is evidence consistent with gravitation being slow.

    This is not special pleading. It is a logical point about what different functionals of a model can and cannot tell you. The structural parameters — estimated from the joint likelihood over the whole panel, borrowing strength across 37 sectors and 61 years — use far more information than any single-series forecast. They can pin down a central tendency that a univariate test cannot. And the package shows, through simulation-based calibration and adversarial negative controls, that the estimation pipeline does not manufacture gravitation when none is present: feed it a true random walk and it reports a half-life of about fifty years; feed it a null value-coupling and the posterior honestly covers zero.

    The low-kappa trap, and why it matters to everyone

    The package names a difficulty it calls the low-kappa trap, and it is worth understanding because it is a trap that catches far more than Marxian price theory.

    Kappa is the reversion speed. As kappa shrinks toward zero, the OU process approaches a pure random walk. The trouble is that there is no bright line separating “slow mean reversion” from “no mean reversion.” It is a continuum, and three distinct problems stack up exactly there:

    • Algebraically, reversion speed and discrete-time persistence are two sides of the same coin; kappa going to zero is the same as the autocorrelation going to one. There is no internal frontier.
    • Statistically, the power of a unit-root test — the standard tool for asking “is this a random walk?” — collapses exactly as the truth approaches the random walk boundary. With a finite sample and a half-life comparable to the sample length, the test simply cannot tell. This is a well-known result in econometrics, and it is why decades of “is the real exchange rate stationary?” papers argued past one another.
    • Numerically, if the reversion speed is parameterized to be strictly positive (as it must be, for the sampler to behave), then “the probability that kappa is greater than zero” is trivially one — it tells you nothing. The informative quantity is the half-life, and the probability that the half-life exceeds some sensible horizon.

    The package’s response to the trap is instructive. It does not pretend the trap is not there. It states all three layers explicitly, reports the slow tail honestly (one sector has a non-trivial posterior probability of a half-life beyond forty years), and argues that the joint hierarchical posterior — which pools information across the whole panel — is a more powerful discriminator than any univariate test. That is a defensible position, and it is stated with the caveat attached rather than buried in a footnote.

    This is the broader lesson. Anyone working with time series that might be slowly mean-reverting — interest rates, real exchange rates, commodity prices, climate variables, pollutant concentrations — runs into exactly this trap. The package’s framing of it, in three layers, is one of the clearest expositions I have read, and it would travel well into any of those domains.

    What I appreciate, and what I would watch for

    A few things stand out as genuinely good practice, and they are worth naming because they are rarer than they should be.

    The separation of economic and sampler convergence. The package is scrupulous about not confusing two senses of “convergence.” Economic convergence — does the price revert? — is a statement about kappa and the half-life. Sampler convergence — did the MCMC chains agree? — is a statement about R-hat and divergences. These share a word and nothing else, and conflating them is a classic source of muddled reasoning. The documentation keeps them lexically distinct throughout.

    Neutral priors on the load-bearing hypotheses. The prior on the profit-rate modulation is centred at zero. The prior on the value coupling is centred at zero. The package does not bake the answer into the question. When the posterior then moves clearly away from zero, that means something.

    Out-of-sample integrity by construction. A subtle and common error in time-series work is “leakage”: accidentally letting future information contaminate the training procedure, so that out-of-sample results are secretly in-sample. The package offers a fit_window switch that keeps the two designs genuinely separate, and it computes the common-factor loadings from the training window only. This is the kind of plumbing detail that separates trustworthy work from work that just looks trustworthy.

    The negative results are reported. Many packages, and most blog posts about them, would quietly omit the fact that a random walk out-forecasts the model. This one leads with it and then reasons about it. That is how a field accumulates reliable knowledge rather than just encouraging headlines.

    What should a careful reader watch for? The half-life estimate of about nine years is, by the package’s own account, probably conservatively slow — a controlled study of the disaggregation step suggests the true figure may be closer to seven or eight. The cubic nonlinearity is a minor refinement on this data (its coefficient sits near its prior). The Student-t degrees of freedom and the stochastic-volatility scale are weakly identified when both are present, a known tension the documentation flags but does not resolve. And the headline value-coupling result, while striking, is measured on standardized levels that share a cost-price component by construction; the package defends this with a “wedge” argument — subtracting the shared component and testing the residual — but a sceptical reader should follow that argument itself rather than take it on trust.

    None of these caveats undermine the project. They are the project. A statistical framework that cannot articulate its own soft spots is not a framework you should believe.

    Why it is worth your time

    You do not need to be a Marxian economist, or any kind of economist, to get something out of this package. If you work with time series that exhibit slow, noisy reversion toward a moving target — and a great deal of the physical and social world does — the modelling ideas here are directly portable: the nonlinear OU drift, the stochastic volatility, the hierarchical pooling across groups, the careful separation of structural estimation from forecasting, and the three-layer diagnosis of the low-reversion trap.

    And if you are interested in the classical question of whether prices gravitate toward values, this is about as good a statistical treatment as you will find: modern machinery, honest reporting, and a willingness to let the data argue back against the theory that motivated the exercise in the first place.

    The repository, the full mathematical specification, the validation blocks, and a frank discussion of every methodological decision live at github.com/IsadoreNabi/bayesianOU, with the wiki carrying the complete technical detail. Read the methodology notes before you quote a number; that is what they are there for.

  • Revisiting the theory of long depressions BY MICHAEL ROBERTS

    Revisiting the theory of long depressions
  • Sectorial Exclusion Criteria in the Marxist Analysis of the Average Rate of Profit: The United States Case (1960-2020)

    Sectorial Exclusion Criteria in the Marxist Analysis of the Average Rate of Profit: The United States Case (1960-2020)

    LISTEN TO THIS POST AS A PODCAST

    What Counts as “The Economy”? A Marxist Framework for Measuring Capitalism’s Rate of Profit
    Marxist Economics  ·  Econometrics  ·  Political Economy

    What Counts as “The Economy”?
    A Marxist Framework for Measuring Capitalism’s Rate of Profit

    Before asking whether the rate of profit falls, we first have to decide whose profit rate we are measuring — and which economic activities actually belong in the theoretical object under study.

    Based on: Gómez Julián (2025) | United States, 1960–2020 | arXiv:2501.06270v2

    Since the empirical work of Anwar Shaikh and Edgardo Ochoa in the 1980s, researchers in Marxian economics have repeatedly tried to measure one of Marx’s most discussed propositions: the long-run tendency of the average rate of profit to fall. Yet underneath the familiar formula lies a prior problem that can materially change the result: which sectors of the economy should enter the calculation in the first place?

    Manufacturing? Almost certainly. Finance? Perhaps not. Retail trade? Transportation? Government? Education? Warehousing? Modern national accounts combine activities that occupy very different positions in Marx’s theory of value and capital.

    José Mauricio Gómez Julián’s paper argues that this cannot be treated as an arbitrary data-cleaning choice. If the quantity being estimated is specifically a Marxian average rate of profit of productive capital, then the sectoral boundary should itself follow from the theory whose proposition is being measured.

    ◆

    The Measurement Problem Comes Before the Formula

    The paper calls the conventional alternative the naive Marxist calculation (nMc): constructing a profit-rate measure from broad national-accounting aggregates without first making a theoretically explicit distinction between productive and unproductive sectors.

    The criticism is not that the arithmetic is incorrect. It is that an aggregate combining activities that create surplus value with activities that mainly circulate, redistribute, realize, or consume surplus may fail to correspond closely to the Marxian theoretical object being discussed.

    The key point: a profit-rate series is produced not only by a formula, but also by the population of sectors placed inside that formula. Change the population and the historical trajectory can change with it.

    Three Pillars: The Theoretical Logic Behind the Criteria

    The paper’s framework rests on three interlocking questions drawn from Marx’s political economy. They are meant to determine whether an activity belongs within the productive capital whose profitability is being measured.

    1. Productive vs. Unproductive Labor

    In Marxian theory, “productive” is a technical category, not a synonym for socially useful. Productive labor is labor employed within the capitalist production process that produces value and surplus value. An activity can be necessary, socially useful, and remunerated while still being classified as unproductive in this specific theoretical sense.

    Pure circulation activities are the clearest case. Buying, selling, bookkeeping, and related operations may be indispensable to capitalist commerce, but if their function is only to change the form or ownership of already-produced value, they do not thereby create new value.

    The functions of capital in circulation do not, by themselves, create value or surplus value.

    — Summary of Marx’s argument in Capital, Volume II

    2. Location in the Circuit of Capital

    Capital moves through production and circulation rather than remaining in one form. The paper therefore asks whether an activity belongs to the productive reproduction of capital or primarily to circulation, redistribution, or a different institutional logic.

    This distinction matters because not every activity carried out between production and final sale is automatically unproductive. Transportation is the classic case: changing a commodity’s location can itself constitute a necessary material transformation and can therefore add value.

    3. Relationship with Surplus Value

    The final question is whether an activity directly produces surplus value or constitutes an indispensable material condition for its production. Activities that merely redistribute or realize value are treated differently from activities whose labor participates in the productive process itself.

    The Service-Sector Problem

    One of the paper’s strongest theoretical points is that “services” cannot be treated as a single Marxian category. Modern national accounts combine radically different activities under that label.

    Drawing partly on the functional approach discussed by Tregenna, the paper distinguishes among services that:

    • directly produce surplus value;
    • facilitate or materially condition surplus-value production elsewhere;
    • remain outside the productive circuit of capital.

    Hybrid sectors therefore have to be examined internally rather than included or excluded simply because a statistical agency labels them “services.”

    ◆

    Applying the Criteria: What’s In, What’s Out

    Because BEA industry classifications change over time, the paper first consolidates the U.S. data into a common system of 47 economic activities for 1960–2020. The theoretical criteria are then applied to each activity.

    Included — Productive

    • Farms
    • Forestry, fishing & related activities
    • Oil & gas extraction
    • Mining and mining support
    • Utilities
    • Construction
    • Manufacturing industries
    • Transportation
    • Warehousing & storage
    • Information
    • Professional, scientific & technical services
    • Management of companies & enterprises
    • Administrative & waste management services
    • Educational services
    • Arts, entertainment & recreation
    • Accommodation
    • Food services & drinking places
    • Other services except government

    Excluded — Non-Productive

    • Wholesale trade
    • Retail trade
    • Finance & insurance
    • Real estate
    • Rental & leasing services
    • Health care & social assistance
    • Federal general government
    • Federal government enterprises
    • State & local general government
    • State & local government enterprises

    The Borderline Cases

    Warehousing and storage is included where preservation of a commodity’s physical properties constitutes a material continuation of the productive process. The argument is therefore stronger than the simple claim that storage is commercially useful.

    Educational services is a much more difficult case. The statistical category mixes private, public, nonprofit, productive, and potentially unproductive activities. The paper nevertheless includes it because reproduction of skilled labor power is treated as a necessary condition of production in an advanced industrial economy.

    Administrative and waste-management services is also heterogeneous. Its inclusion is explicitly conditional: the paper argues that a sufficiently large share of these activities is connected with productive enterprises and supports their production process. The same classification need not automatically hold in every country or period.

    Information is included because the modern category encompasses software, informational and cultural products, technical infrastructure, data processing, hosting, and related forms of production. An apparently “immaterial” output is therefore not treated as automatically unproductive.

    ◆

    How the Profit Rate Is Constructed

    The empirical calculation combines sectoral surplus with the capital advanced and then aggregates the selected productive sectors. In schematic form:

    \[ r_t = \sum_{i\in P} w_{it} \left( \frac{s_{it}}{c_{it}+v_{it}} \right) \]

    Here \(P\) is the set of included sectors, \(s_{it}\) is sectoral surplus, \(c_{it}\) constant capital, \(v_{it}\) variable capital, and \(w_{it}\) the corresponding sectoral weight.

    The construction is subject to an important data limitation: sufficiently disaggregated fixed-capital and intermediate-input data are not directly available for every sector throughout the full period. The paper therefore uses proportional-disaggregation assumptions inherited from earlier empirical work, including Ochoa’s methodology. These reconstructed magnitudes should not be mistaken for fully observed sectoral capital stocks.

    ◆

    Internal Consistency: Does the Theoretically Constructed Rate Fall?

    The paper distinguishes carefully between internal theoretical consistency and the much stronger claim that an entire theory has been proven true.

    Marx’s theoretical system contains a proposition concerning a long-run tendency of the average rate of profit to fall. The first empirical question is therefore whether the series generated by the proposed sectoral criteria behaves consistently with that proposition.

    Three different trend-extraction methods are used:

    • Less-asymmetric Daubechies wavelets, with eight vanishing moments and decomposition depth \(J=4\);
    • Empirical Mode Decomposition (EMD), a data-adaptive and nonparametric decomposition;
    • an embedded Hodrick–Prescott trend within a Bayesian unobserved-components model estimated through Gibbs sampling.

    Periodogram and short-time Fourier analysis are also used beforehand to examine the spectral structure and support the use of additive rather than multiplicative decomposition.

    Under the theoretically selected sector set, all three methods produce a declining long-run trend in the net average rate of profit over 1960–2020. The result is not a monotonic straight line: cyclical recoveries and large shocks remain visible around the secular movement.

    What Do the Unit-Root Tests Say?

    The evidence is more mixed than the original blog version suggested. The paper evaluates 17 specifications across four test families: Augmented Dickey–Fuller, Elliott–Rothenberg–Stock, KPSS, and Phillips–Perron.

    ADF and PP frequently fail to reject the unit-root null; some ERS specifications do reject it; and KPSS generally does not reject stationarity, particularly stationarity around a deterministic trend.

    The appropriate conclusion is therefore not that every test rejects a unit root. Read jointly with the Wavelet, EMD, and Bayesian UCM-HP evidence, the paper interprets the results as being more consistent with a deterministic, potentially nonlinear trend.

    ◆

    Three Econometric Cross-Checks

    The paper then asks whether alternative, statistically generated sectoral cores lead to a substantially different conclusion. Three methods are used: Principal Component Analysis, Regularized Horseshoe Regression, and a Dynamic Factor Model.

    A crucial clarification: these procedures do not receive the theoretical productive/unproductive labels as the answers they are supposed to reproduce. But they should not be described as completely theory-free “blind tests” either. In particular, the RHR and DFM specifications use variables chosen because of their Marxian interpretation.

    The algorithms are statistical; the research design in which they operate is not theoretically neutral.

    Test 1: Principal Component Analysis

    The PCA is implemented through Singular Value Decomposition. Seven principal components are retained according to the eigenvalue and explained-variance criteria described in the paper.

    Rather than imposing an arbitrary loading cutoff, probability distributions are fitted to sectoral contribution measures, and the upper tail is used to identify unusually large contributions. Operationally, the paper selects the top decile within each retained component.

    The union of these selections leaves 26 of the 47 activities. A post-hoc check of the 21 discarded sectors finds that none reaches an eigenvalue-equivalent contribution above one in the first five principal dimensions; the largest reported value is approximately 0.77 for health care.

    PC1 deserves a nuance. Although its loadings are visibly associated with corporate and financial activities, the later interpretation notes that contributions to PC1 are relatively uniform and therefore treats it largely as an aggregate size or inertia component rather than the most discriminating structural factor.

    Test 2: Regularized Horseshoe Regression

    The RHR exercise is deliberately specified in a way connected with the labor theory of value: Total Gross Operating Surplus is modeled using sectoral Variable Capital as predictors.

    The model uses a Regularized Horseshoe prior with an expectation of roughly 16 relevant sectors and employs QR reparameterization in Stan to improve computation under extreme multicollinearity.

    This multicollinearity is not a minor inconvenience. With 61 annual observations and 47 strongly interdependent predictors, the posterior coefficients are heavily shrunk and no credible claim of conventional individual-sector significance can be sustained.

    The robust result is therefore not a list of “significant causal sectors,” but the predictive ordering produced by projpred: which variables enter fastest as predictive performance improves.

    The top 15 sectors are:

    1. Retail Trade
    2. Textile Mills & Textile Products
    3. Fabricated Metal Products
    4. Administrative & Waste Management Services
    5. Miscellaneous Manufacturing
    6. Construction
    7. Educational Services
    8. Electrical Equipment, Appliances & Components
    9. Nonmetallic Mineral Products
    10. Support Activities for Mining
    11. Printing & Related Support Activities
    12. Primary Metals
    13. Food Services & Drinking Places
    14. State & Local General Government
    15. Transportation

    Test 3: Dynamic Factor Model

    The DFM starts from the 47 sectoral series after logarithmic differencing and standardization. The Bai–Ng IC2 criterion selects the number of latent factors, while AIC selects the VAR lag order.

    The resulting model contains two factors and one VAR lag. Its estimated transition matrix is:

    \[ A = \begin{pmatrix} 0.3329 & 0.3253 \\ 0.1680 & 0.9129 \end{pmatrix} \]

    The first diagonal coefficient corresponds to a relatively low-persistence component; the second is highly persistent and is interpreted as reflecting longer-run accumulation dynamics. Together, the two factors explain approximately 34.01% of total variation in the standardized, differenced sectoral panel.

    Validation goes well beyond ranking factor loadings. The procedure combines multi-horizon prediction, Elastic Net, stability selection, synchronized block bootstrap, Partial \(R^2\), loading–sensitivity interactions, and a Full-Robust Thresholding procedure whose null distributions correct for factor indeterminacy through Procrustes/Hungarian alignment.

    Under the paper’s strict four-part predictive screen, no individual sector survives as a stable unilateral predictor of the aggregate profit rate. This is interpreted as consistent with a systemic rather than single-sector mechanism.

    At the same time, the structural synchronization weights are highly unequal. The empirical core is led by Real Estate, State & Local General Government, Federal General Government, Retail Trade, and Food Services, with Utilities and Chemical Products among the industrial baseline.

    ◆

    The Key Revelation: Theoretical and Statistical Cores Diverge

    Where Theory and Data Overlap

    Manufacturing repeatedly appears among the statistically important sectors and is unambiguously included by the theoretical criteria.

    Construction, transportation, utilities, educational services, and administrative services also appear with substantial weight under one or more econometric approaches while belonging to the theoretically selected productive set.

    This overlap shows that the theoretical and statistical classifications are not unrelated — but it does not establish that they are measuring exactly the same concept.

    Where Theory and Data Diverge

    Real Estate carries the highest structural weight in the reported DFM ranking, despite being theoretically excluded.

    Federal and state/local government also receive high DFM weights while remaining outside the paper’s theoretical productive-capital boundary.

    Retail Trade ranks first under the RHR predictive ordering and also appears prominently in the DFM, yet is excluded theoretically as an activity of circulation.

    Finance is prominent in the PCA structure, while health care records the largest post-hoc PCA contribution among the sectors discarded by that selection.

    The statistical result is therefore a divergence between the sectoral core defined by Marxian value theory and the sectors that dominate covariance, prediction, or synchronization in the observed national accounts.

    The paper interprets this through Marx’s distinction between essence and phenomenal appearance. Activities treated as unproductive in value-theoretic terms can still exert enormous influence over the observable movement of contemporary aggregate profitability.

    This distinction is important: the econometrics establishes different statistical rankings and structures. The claim that this difference should be understood as an essence/appearance relation is the paper’s Marxian theoretical interpretation of those empirical results.

    ◆

    Does the Rate of Profit Fall?

    The paper’s strongest robustness exercise repeats the long-run trend analysis using four different sectoral selections: the theoretical criterion, PCA, Regularized Horseshoe, and DFM. Each is then passed through the three trend-extraction methods.

    • Theoretical sectors + Wavelet → declining
    • Theoretical sectors + EMD → declining
    • Theoretical sectors + HP → declining
    • PCA sectors + Wavelet → declining
    • PCA sectors + EMD → declining
    • PCA sectors + HP → declining
    • RHR sectors + Wavelet → declining
    • RHR sectors + EMD → declining
    • RHR sectors + HP → declining
    • DFM sectors + Wavelet → declining
    • DFM sectors + EMD → declining
    • DFM sectors + HP → flat/rising exception

    In other words, the qualitative declining tendency survives 11 of the 12 combinations.

    The DFM–HP exception is not discarded. The paper relates it to the interaction between the state-space HP specification and a DFM sectoral core heavily influenced by real estate and government, whose accounting dynamics may differ from those of productive capital.

    EMD yields the most pronounced declining tendency across the comparisons, which the paper associates with its adaptive, nonparametric character.

    ◆

    What the Evidence Does — and Does Not — Establish

    The first contribution is methodological standardization. The paper turns sector selection from a largely implicit convention into an explicit and reproducible theoretical procedure.

    Second, the theoretically constructed profit-rate series displays the long-run decline predicted by the surrounding Marxian theoretical system. In the terminology of the paper, this supports the internal consistency of the proposed classification.

    Third, alternative statistically generated sectoral selections also produce a declining long-run rate in almost every methodological combination. That makes it harder to attribute the qualitative result solely to one hand-picked list of industries.

    But none of this logically proves the Marxian theory of value as a whole, nor does one U.S. study establish that the tendency must hold across every country and historical period. The paper explicitly distinguishes consistency within a theoretical system from the much stronger question of the theory’s overall validity.

    What Still Needs to Be Tested

    The empirical exercise covers one country and one historical period: the United States from 1960 to 2020. The natural next step is replication across other economies, periods, and institutional structures.

    Some theoretical classifications are necessarily conditional because broad BEA sectors contain heterogeneous activities. Education and administrative services are particularly clear examples where finer disaggregation could modify the classification.

    The RHR exercise is also operating in a difficult \(N=61,\;P=47\) environment with extreme multicollinearity. Its defensible output is predictive ordering, not a set of identified causal effects for individual sectors.

    Finally, PCA and DFM answer questions about covariance, synchronization, and statistical structure that are not identical to the Marxian theoretical question of where surplus value is produced. Their value lies in comparing those distinct objects rather than pretending that they are interchangeable.

    The most defensible bottom line: the paper does substantially more than show another declining profit-rate graph. It specifies what should count as productive capital, makes that rule reproducible, checks its compatibility with the broader theoretical system, and then tests whether the qualitative result survives very different statistical constructions of the economy.

    The answer is strikingly robust: in the U.S. data examined here, the long-run decline survives almost every combination. But the paper is better read as a first systematic piece of a larger empirical program than as the final word on the law itself.

    Read the full paper Gómez Julián — arXiv:2501.06270

    This post is based on José Mauricio Gómez Julián, Sectorial Exclusion Criteria in the Marxist Analysis of the Average Rate of Profit: The United States Case (1960–2020), arXiv:2501.06270v2. The preprint was originally submitted in January 2025 and substantially revised in January 2026. Consult the original paper for the complete theoretical argument, data construction, tables, econometric specifications, robustness analysis, figures, and bibliography.