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

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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?

    Can We Manage Fixed Capital Surpluses Without Money? — A Marxian Thought Experiment
    A Blog for the Curious Economist — and Everyone Else
    The Capital Question
    Marxian Political Economy Economic Policy 8 min read

    Can We Manage Fixed Capital Surpluses Without Money?

    An economist revisits a passage Marx left half-finished and asks: what if a post-capitalist society had to balance its machines, factories, and tools—without printing a single banknote?

    MG
    Based on the work of José Mauricio Gómez Julián
    Originally published • Revista Académica Contribuciones a la Economía • January 2016

    Most of us think of money as the universal lubricant of an economy—the thing that lets a shoe factory buy steel, and the steel mill pay its workers. But what happens when an economy decides it no longer needs money? Can it still keep its machines, buildings, and equipment in balance? That is the question José Mauricio Gómez Julián tackles in a compact, ambitious paper that draws directly on Karl Marx’s Capital, Volume II.

    Why Fixed Capital Matters

    Before diving in, let’s clarify what “fixed capital” means. In economics—especially in the Marxian tradition—a factory’s resources are split into two broad categories. Circulating capital is the stuff that gets used up quickly in production: raw materials, intermediate goods, energy. Fixed capital is the durable stuff—machinery, buildings, infrastructure—that transfers its value to the product gradually, over many production cycles, through wear and tear (what economists call “depreciation”).

    In any economy, these two types of capital need to exist in the right proportion. Too much fixed capital relative to circulating capital, and the machines sit idle for lack of materials. Too little, and the raw materials pile up with nothing to process them. Getting this ratio wrong creates either a surplus (overproduction of fixed capital) or a deficit (underproduction of fixed capital).

    The core insight is deceptively simple: even without money, an economy still needs a mechanism to absorb the shocks that come from uneven wear on its machines.

    The Two Scenarios: Surplus and Deficit

    Gómez Julián works through two thought experiments, both grounded in Marx’s two-sector model of reproduction (Sector I produces means of production—factories, machines; Sector II produces consumer goods). The logic is dense, but the intuition is elegant.

    1

    Scenario One

    Suppose the fixed capital used by the consumer-goods sector (Sector II) depreciates faster than expected in a given year. More machines need replacing now. Sector I sends more fixed-capital goods to Sector II, but its overall output for Sector II remains the same. The result: Sector I now produces more fixed capital than Sector II can absorb, while simultaneously Sector II needs less circulating capital (raw materials) because it is replacing machines rather than running them.

    Outcome → SURPLUS in fixed capital production
    2

    Scenario Two

    Now imagine the opposite: a smaller portion of Sector II’s fixed capital needs to be physically replaced this year (because less has worn out completely). That means less demand for new fixed-capital goods from Sector I. Meanwhile, the circulating capital flows remain unchanged. Sector I simply produces fewer fixed-capital items.

    Outcome → DEFICIT in fixed capital production

    In a capitalist economy, these imbalances ripple outward. The surplus scenario pushes more money into Sector I (as depreciation funds accumulate), but the actual exchange of goods shrinks. Money becomes a one-sided “means of purchase” rather than a smooth intermediary. In the deficit scenario, production contracts. Both situations, if left unmanaged, can trigger commercial crises—and in capitalism, those crises are cyclical, not one-off events.

    The Money Question

    Here is where the paper gets provocative. In a capitalist system, managing these imbalances requires monetary policy—central banks adjusting interest rates, governments running deficits, currencies being devalued. The entire toolkit of modern macroeconomics is, in one way or another, about using money to smooth out the frictions between production and exchange.

    But Gómez Julián asks: what if you remove money from the equation entirely? What if a post-capitalist society—one that has moved beyond the commodity form—tries to manage fixed capital imbalances without any monetary instrument at all?

    His answer is a policy of continuous relative overproduction: produce slightly more fixed capital and slightly more circulating capital than strictly necessary, and accumulate the excess as a strategic reserve.

    The logic works like this. If fixed capital wears out unevenly from year to year (sometimes more, sometimes less), a well-organized post-capitalist economy could buffer those fluctuations by maintaining reserve stocks of both fixed-capital goods and circulating-capital goods. When a year of heavy depreciation hits, the reserve steps in. When a year of light depreciation comes, the reserve grows. The goal is not maximum efficiency at every moment, but stability over time—a kind of industrial shock absorber.

    Why This Is Harder Than It Sounds

    The author is careful to note that this approach would be catastrophic in a capitalist economy. Continuous relative overproduction, without the discipline of a planned system, would generate commercial crises—overproduction in capitalism is not a “reserve strategy” but a trigger for collapse. The same policy looks entirely different depending on whether production is coordinated through market exchange or through conscious social planning.

    This is the key theoretical distinction: in a planned economy, overproduction is relative (producing more than immediate need, but deliberately) and continuous (a permanent buffer). In capitalism, overproduction is absolute (goods that cannot find buyers) and cyclical (recurring crises). Same material fact, radically different systemic consequences.

    A Critique the Author Couldn’t Ignore

    The paper ends with a sharp jab at Soviet Marxist economics. Gómez Julián points out that the standard Soviet reference text—the Dictionary of Marxist Political Economy by Borisov, Zhamin, and Makárova (1965)—never develops, or even mentions, this particular theoretical problem. The analysis is absent from the entries on “Fixed Capital,” “Simple Reproduction,” and “Extended Reproduction.” Marx himself only sketched it in embryonic form (Volume II, pp. 414–417), yet the author argues it is a “vital” issue for any theory of post-capitalist construction.

    His verdict on Soviet scholarship is unsparing: the Soviet economists, he suggests, never truly understood many of the theoretical foundations they claimed to be building on—a failure that history confirmed on November 9, 1989.

    • • •

    Why This Paper Deserves Your Attention

    You do not have to be a Marxist to find this paper interesting. At its heart, it is about a problem that any complex economy faces: how do you keep the right balance between durable infrastructure and the materials that flow through it? Modern economies answer this with monetary policy, fiscal stimulus, and market signals. Gómez Julián asks whether a fundamentally different kind of society could answer it with strategic reserves and conscious planning instead.

    Whether or not you find his vision persuasive, the thought experiment sharpens something important: our reliance on money as an economic management tool is not a law of nature—it is a feature of a particular system. And understanding why that system needs money is the first step toward imagining alternatives, or toward improving what we already have.

    This post is a summary and interpretation of the original research article. For the full theoretical development, including Marx’s formal apparatus, readers are encouraged to consult the paper directly: 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, ISSN 1696-8360.
    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.
    Read the full paper here: https://dialnet.unirioja.es/servlet/articulo?codigo=9041512

    The Capital Question — Explaining the economics that shape our world, one paper at a time.

  • THE INFLUENCE OF JAMES MILL ON MODERN ECONOMIC SCIENCE

    THE INFLUENCE OF JAMES MILL ON MODERN ECONOMIC SCIENCE

    The Forgotten Father — James Mill and the Foundations of Modern Economics
    History of Economic Thought

    The Forgotten Father

    How James Mill quietly built the foundations of modern economics — and why nobody remembers

    Based on the research of José Mauricio Gómez Julián · Read the original article

    Picture the pantheon of classical economics. Adam Smith sits at the centre, David Ricardo stands nearby, Jean-Baptiste Say holds a modest plaque. Somewhere in the back, if he appears at all, you will find James Mill (1773–1836) — Scottish philosopher, historian, journalist, and the man the economist José Mauricio Gómez Julián argues we have been unjustly forgetting for nearly two centuries. In a concise but provocative article published in Economía & Región, Gómez Julián builds a meticulous case: Mill was not merely Ricardo’s friend and editor. He was, in several crucial respects, the intellectual architect behind ideas we now attribute to others — and the quiet originator of concepts that still animate central bank boardrooms today.

    What follows is a guided walk through that argument. No equations, no jargon — just the story of a mind that anticipated, with striking clarity, debates we are still having in the twenty-first century.

    I. The Law That Was Never Say’s

    If you have taken even a single semester of macroeconomics, you have encountered Say’s Law — the proposition that “supply creates its own demand.” It is one of the most cited principles in the history of the discipline, and it is routinely attributed to the French economist Jean-Baptiste Say.

    Gómez Julián’s article asks a simple, uncomfortable question: did Say actually come up with it first?

    The evidence points elsewhere. In 1807, an English writer named William Spencer published an argument containing the essential logic: that the annual produce of a country “always creates a market to itself,” and that when commodities seem to exceed demand, the real problem is merely a misallocation of productive effort among sectors, not a general glut. James Mill seized on this reasoning in his 1808 work Commerce Defended, presenting it with considerably more force and theoretical precision.

    “How great soever annual produce may be it always creates a market to itself; and that how great soever that portion of the annual produce which is destined to administer reproduction… its effects always are to render the country richer, and its inhabitants more opulent, but never to confuse or to overload the national market.” William Spencer (1807), cited by James Mill in Commerce Defended (1808)

    Three years later, in his 1821 Elements of Political Economy — the book Gómez Julián calls Mill’s “magnus opus” — Mill refined the idea further, embedding it in a broader theory of how supply, demand, and production costs interact over time. His formulation is careful and layered: relative prices are determined in the first instance by supply and demand, but ultimately by cost of production, because competition relentlessly pushes markets toward equilibrium.

    The article’s charge is direct: Say popularised an idea that was already circulating in English-language economics, and the discipline’s later canonisation of “Say’s Law” obscured its true origin. Gómez Julián does not mince words — he uses the term “plagiarism” (or rather, the article calls it “the least known plagiarism of the Classical Economists”).

    Whether one accepts that strong characterisation or prefers a milder framing of “parallel development,” the underlying historical point stands: Mill was articulating this foundational principle at least as early as Say, and arguably with greater analytical sophistication.

    II. Money, Prices, and the Seeds of Central Banking

    Here is where Mill’s contribution moves from historical curiosity to genuine intellectual substance. Gómez Julián argues that Mill was one of the finest exponents of the Quantity Theory of Money in his era — and, crucially, that he did so without falling into the contradictions that plagued later economists.

    The Quantity Theory, in its simplest form, says that the total amount of money in circulation determines the general level of prices. Mill stated it with remarkable directness:

    “It is not difficult to perceive, that it is the total quantity of the money in any country, which determines what portion of that quantity shall exchange for a certain portion of the goods or commodities of that country.” James Mill, Elements of Political Economy (1821)

    But the real surprise, for anyone accustomed to thinking of classical economists as rigid free-market purists, is what Mill argued next. He described two distinct circumstances under which a government might create money: first, by allowing it to “float freely” in the channels of circulation (essentially, an open mint where citizens bring bullion to be coined); and second, when the government wishes to control the quantity of money at its discretion.

    This is a startlingly modern framing. Unlike his friend David Ricardo, who frequently questioned any form of government monetary intervention, Mill was willing — even eager — to theorise about deliberate monetary management. He proposed that if the government wanted less money in circulation, it should raise the metallic value of the coinage (making each coin worth more); if it wanted more, it should lower it. The mechanism differs from modern interest-rate policy, of course, but the underlying logic — that a central authority should actively calibrate the money supply to achieve macroeconomic goals — is recognisably the ancestor of what every central bank does today.

    Why this matters

    The standard history of monetary policy tends to jump from the Currency School vs. Banking School debates of the 1840s straight to the Federal Reserve’s founding in 1913. Mill’s writing suggests that the intellectual groundwork for active monetary management was already being laid two decades earlier — and by a figure typically remembered, if at all, as a mere populariser of Ricardo.

    III. Trade Without Illusions

    Ricardo’s theory of comparative advantage is one of the most celebrated ideas in all of economics. Gómez Julián notes, however, that James Mill saw international trade through a rather different and more pragmatic lens.

    For Mill, the relationship between nations was essentially the same as the relationship between individual merchants: buy in the cheapest market, sell in the most expensive. He did not need the elaborate logical apparatus of comparative advantage to explain why trade was beneficial. The article suggests that Ricardo’s theory, far from being the inevitable culmination of classical trade thinking, was in some sense a detour — and that Mill’s simpler framework was closer to how commerce actually works.

    Moreover, Mill was one of the first economists to recognise that currency devaluation could be used as a tool for international competitiveness. The idea that a nation might deliberately weaken its exchange rate to boost exports is a staple of modern policy debates; Gómez Julián traces the logic back to Mill’s Elements.

    IV. Productive Labour, Unproductive Labour, and the Nature of Capital

    Adam Smith famously distinguished between “productive” and “unproductive” labour — a tailor makes something tangible, a servant does not. But Gómez Julián argues that Mill was the first economist to define these categories with genuine clarity, going beyond Smith’s somewhat impressionistic treatment.

    Mill also drew a related distinction between productive consumption and unproductive consumption — the idea that some spending builds future capacity while other spending merely satisfies immediate desires. Karl Marx, who read Mill carefully, admired the precision with which Mill laid out these ideas. In his 1844 Comments on James Mill, Marx praised the exposition with what he called Mill’s “customary cynical acumen and clarity.” It is an extraordinary compliment from a thinker not known for flattery.

    On the question of capital, Mill made further contributions that have been overlooked. He was among the first — alongside the lesser-known Samuel Bailey — to discuss capital accumulation in depth: specifically, what happens to industrial capital’s effects when the total amount of capital remains constant. Gómez Julián notes, fairly, that Mill made an error here (treating the portion of capital invested in labour-power as fixed), but the discussion itself was pioneering.

    Mill also drew a sharp conceptual line between the circulation medium used as capital (money deployed for productive investment) and the circulation medium used as a simple medium of exchange (money used for everyday purchases). Marx would later build extensively on this distinction in his own economic writings.

    V. Population, Egoism, and the Architecture of Political Economy

    Thomas Malthus is remembered for his theory that population tends to outstrip the food supply. Mill offered a strikingly different perspective: population density is ultimately determined by the needs of capital, not by any abstract biological tendency toward over-reproduction. In a single sentence, Mill redirected the population question from biology to political economy — a reorientation with implications that echo through later Marxist and institutional economics.

    “There is a certain density of population which is convenient, both for social intercourse, and for that combination of powers by which the produce of labour is increased.” James Mill, Elements of Political Economy (1821)

    On the question of self-interest, Gómez Julián argues that Mill’s treatment of egoism, private property, and production was clearer and deeper than Adam Smith’s in The Theory of Moral Sentiments. Marx summarised Mill’s position in a single lapidary phrase: “The limit of his need constitutes the limit of his production.”

    And then there is the matter of Mill’s intellectual architecture. His Elements of Political Economy is organised into four books:

    1. Production — how wealth is created.
    2. Distribution — how wealth is divided among social classes.
    3. Exchange — how commodities trade for one another, and the role of money.
    4. Consumption — how wealth is used, and under what conditions it expands or contracts.

    This four-part structure, elegantly simple, became the template for generations of economics textbooks. John Stuart Mill’s own celebrated Principles of Political Economy (1848) follows essentially the same outline — not a coincidence, given that James was his father and tutor.

    VI. The Teacher’s Shadow

    The final dimension of Mill’s influence is indirect but enormous. John Maynard Keynes, in The General Theory of Employment, Interest and Money, wrote that “‘classical economists’ was a name invented by Marx to refer to Ricardo, James Mill, and their predecessors — that is, to the founders of the theory that culminated with Ricardo.” Notice: Keynes lists James Mill first, before Ricardo.

    Beyond his own published work, Mill shaped the discipline through personal influence. He was David Ricardo’s closest intellectual confidant, his editorial advisor, and — as Gómez Julián emphasises — one of the principal mentors who encouraged Ricardo to write his masterwork. Sraffa’s monumental edition of Ricardo’s Works and Correspondence documents the extent of this influence, and Donald Winch’s Selected Economic Writings further confirms it.

    And of course, there is John Stuart Mill, arguably the most influential economist of the mid-nineteenth century, who received his entire early education from his father. Karl Marx, commenting acidly on the younger Mill’s monetary theories, observed that John Stuart had “his customary eclectic logic to embrace his father’s soup and at the same time the opposite” — a backhanded compliment to both Mills that inadvertently testifies to how deeply James Mill’s ideas had penetrated the discipline.

    The central claim

    Gómez Julián’s article does not argue that James Mill was a greater mind than Smith or Ricardo. It argues something subtler and, in its way, more important: that Mill was the connective tissue of classical economics — the thinker who synthesised scattered insights into coherent frameworks, who mentored the people we remember, and who anticipated policy ideas (monetary management, exchange-rate competitiveness) that would not become mainstream for another century. He was, in Keynes’s telling, a founder. And yet most economics programmes today never mention his name.

    · · ·

    A Final Thought

    History is written by the remembered. In economics, as in most fields, the canon narrows with each generation: a handful of names survive, and the rest fade into footnotes. Gómez Julián’s article is a reminder that those footnotes sometimes conceal ideas of startling originality and enduring relevance.

    James Mill may never have the name recognition of Adam Smith or John Maynard Keynes. But the next time you hear a central banker discuss money supply management, or a trade minister talk about exchange-rate strategy, or an economist invoke the idea that supply and demand are two sides of the same coin — spare a thought for the Scottish philosopher who got there first, and whose influence is still hiding in plain sight.

    — End —

    Source article
    Gómez Julián, J. M. “La influencia de James Mill
    en la Ciencia Económica Moderna.”
    Economía & Región, Vol. 9, No. 2, 2015.
    ISSN 1696-8360. Read on Dialnet
    Blog post prepared for
    Economists, econometricians, mathematicians,
    political scientists, and curious readers.
    No technical prerequisites required.
  • ABSOLUTE ADVANTAGE VS COMPARATIVE ADVANTAGE: A MULTIDIMENSIONAL COMPARISON

    ABSOLUTE ADVANTAGE VS COMPARATIVE ADVANTAGE: A MULTIDIMENSIONAL COMPARISON

    Trade Theory · Econometrics · Policy

    What If David Ricardo Was Wrong?
    A New Econometric Challenge to Comparative Advantage

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

    Most people who have taken an introductory economics course have encountered a deceptively simple idea: countries should specialise in what they do relatively best, even if another country is better at producing everything. This is the doctrine of comparative advantage, largely attributed to David Ricardo’s early-nineteenth-century work on trade between England and Portugal. It has become one of the most cited justifications for free trade and for the architecture of modern trade agreements.

    A 2025 paper by Juan Manuel Gómez Julián, published in the Revista Cubana de Economía Internacional, asks a provocative question: does the actual data from trade agreements support comparative advantage — or does it point back to the older, simpler idea of absolute advantage? His answer, reached through a combination of historical analysis, mathematical reasoning, and modern econometric modelling, is likely to unsettle a good deal of conventional trade-policy thinking.

    The Two Competing Ideas, in Plain Language

    Before diving into the paper’s contribution, it helps to be absolutely clear about what is at stake. Imagine two countries:

    • Country A can produce both wheat and steel more efficiently (faster, cheaper, with fewer resources) than Country B.
    • Country B is less efficient at producing both goods.

    Absolute advantage (Adam Smith, 1776) says: Country A is simply better at both. Country B has no obvious reason to compete head-to-head, and trade between them will be shaped by the sheer gap in productive capability.

    Comparative advantage (David Ricardo, 1817) says: hold on — even though Country A is better at both, it is proportionally better at steel than at wheat. Country B, while worse at everything, is relatively less terrible at wheat. So if Country A focuses on steel and Country B focuses on wheat, and they trade, both end up better off. Absolute superiority does not matter; what matters is the ratio of efficiencies within each country.

    This idea is elegant. It is also, as Gómez Julián argues, surprisingly fragile when tested against real-world data.

    What the Paper Actually Does

    Gómez Julián approaches the question from three complementary angles, which gives the paper unusual methodological breadth.

    1. Mathematical Generalisation

    First, he examines how well each theory holds up when you push it mathematically — that is, when you ask whether the logic remains sound under more general and realistic assumptions than the original two-country, two-good textbook models. Comparative advantage, he finds, depends on a narrow set of assumptions (identical technologies in certain respects, constant costs, no transport costs, full employment) that tend to collapse when the model is made more realistic. Absolute advantage, by contrast, remains coherent under a wider range of conditions.

    2. Historical Context

    Second, the paper traces the intellectual history. Ricardo developed comparative advantage in a world where the nature of production was fundamentally different from today’s globalised, technology-intensive economy. The author argues that the theory was a product of its time — useful as a thought experiment, but not a reliable guide for modern trade policy, especially when the technological gap between trading partners is vast.

    3. Econometric Evidence

    This is where the paper makes its most distinctive contribution. Gómez Julián uses two families of statistical models to test which theory better explains the actual outcomes of trade agreements:

    • Computable General Equilibrium (CGE) models — large-scale simulation models that attempt to represent the entire economy, sector by sector, and then simulate what happens when a trade agreement changes tariffs, quotas, or market access. These are widely used by institutions like the World Bank and the WTO.
    • Objective Bayesian Generalised Linear Models (GLMs) — a modern statistical approach that uses Bayesian inference (updating beliefs with data) with minimal subjective assumptions (“objective” priors). This allows the researcher to let the data speak more freely, without imposing strong preconceptions about what the answer “should” be.

    The combined results point in the same direction: trade outcomes between countries with significant technological asymmetries are better explained by absolute advantage than by comparative advantage.

    What Does This Mean in Practice?

    The practical implications are significant, and they run against the grain of mainstream trade-policy advice for the past several decades.

    If comparative advantage is the correct lens, then free trade between any two countries — rich or poor, technologically advanced or not — is mutually beneficial almost by definition. The policy prescription is straightforward: liberalise, sign agreements, reduce barriers.

    But if absolute advantage is the better model, then the structure of the agreement matters enormously. A trade deal between a highly industrialised country and a predominantly agricultural one is not inherently win-win. It may lock the less-developed country into low-value-added exports while flooding its markets with manufactured goods that undercut local industry. The technological and wage asymmetries between the signatories become the central concern, not an afterthought.

    In other words, Gómez Julián’s findings suggest that trade agreements should be designed with deliberate attention to the power imbalances and productive capacities of the parties involved — not simply signed on the assumption that any trade is good trade.

    Why This Matters Beyond Economics

    If you are a political scientist, a policy analyst, or simply someone who follows geopolitics, this debate is far from academic. Trade agreements are among the most consequential instruments of foreign policy and domestic economic strategy. They shape industrial policy, labour markets, migration patterns, and even geopolitical alliances.

    The question of whether a trade deal is “fair” or “beneficial” depends on which economic theory you use to evaluate it. If the dominant theory is wrong — or at least incomplete — then decades of trade policy advice may have systematically underestimated the risks of liberalisation between unequal partners.

    This does not mean protectionism is the answer. But it does mean that the terms of engagement matter. A trade agreement that accounts for technological gaps, includes provisions for technology transfer, and builds in adjustment mechanisms is a very different instrument from one that simply eliminates tariffs between unequal economies and calls it a day.

    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

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

    Inflation Is (Not) Always And Everywhere A Monetary Phenomenon

    Beyond the Phillips Curve — A Marxist Reinterpretation of Inflation
    Political Economy July 2025 · 8 min read

    Beyond the Phillips Curve

    A new study argues that inflation isn’t just about too much money chasing too few goods — it’s about how the capitalist class converts technological advantage into permanent profit.

    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, IADE.

    Most of us were taught a tidy story: when unemployment falls, inflation rises, and vice versa. This trade-off — called the Phillips Curve — has anchored central bank policy for decades. But what if that story is not just incomplete, but fundamentally misleading?

    A recent paper published in Realidad Económica by José Mauricio Gómez Julián argues exactly that. Using over fifty years of U.S. data (1968–2021), the study finds no significant long-run relationship between inflation and unemployment. Instead, it identifies a surprising positive link between technological change and inflation — and uses that finding to build a Marxist reinterpretation of what inflation actually does inside a capitalist economy.

    It’s a paper that challenges both mainstream economics and the popular imagination. Let me walk you through it.

    The Phillips Curve: A Love Story with Complications

    In 1958, New Zealand economist A.W. Phillips noticed an elegant regularity in British data: wages tended to rise faster when unemployment was low. Later economists generalized this into a policy menu: want less unemployment? Accept a bit more inflation. Want to tame prices? Brace for a recession.

    This trade-off became gospel in the 1960s. Central bankers thought they could fine-tune the economy like a thermostat — dial inflation up or down by adjusting demand. But the 1970s shattered that confidence. The U.S. experienced stagflation: high inflation and high unemployment at the same time, something the Phillips Curve said shouldn’t happen.

    Since then, economists have debated whether the Phillips Curve is dead, dormant, or merely sleeping. Gómez Julián sides with a more radical verdict: the long-run Phillips Curve doesn’t just flatten — it was never there to begin with.

    What does “long run” mean here? Mainstream economists already accept that the long-run Phillips Curve is vertical (meaning no permanent trade-off). But Gómez Julián goes further: he finds that even in shorter cycles, the supposed inverse relationship is statistically fragile — easily dissolved once you account for other variables, especially technological change.

    The Data, the Tools, and What They Found

    The study uses three complementary statistical approaches — each chosen for a reason:

    Bayesian Correlations

    Unlike classical statistics, which gives you a yes-or-no answer (“significant at 5%”), Bayesian analysis lets you say something more nuanced: “Given the data, here is the probability that this relationship is positive, negative, or nonexistent.” Applied to U.S. inflation and unemployment, the Bayesian results show no consistent inverse relationship. The data simply doesn’t support the Phillips Curve story with any confidence.

    Granger Causality

    This is a standard econometric test that asks: does knowing today’s unemployment help you predict tomorrow’s inflation (or vice versa)? If the Phillips Curve were real, the answer should be yes. Gómez Julián finds that the answer is generally no. Unemployment does not Granger-cause inflation in the U.S. data. What does show predictive power? Research and development spending.

    Error Correction Models (ECM)

    These models examine whether variables that drift apart over time eventually pull back together — like two dancers who briefly separate but remain on the same floor. The ECM results confirm that inflation and unemployment do not share a stable long-run equilibrium. They are, statistically speaking, dancing to different music.

    · · ·

    The Surprising Link: Technology Drives Inflation

    Here is the paper’s most provocative finding: R&D expenditure and inflation move together positively. When firms invest more in technology, inflation tends to rise — not fall, as you might expect from a productivity-enhancement standpoint.

    Why would better technology lead to higher prices? To answer this, Gómez Julián turns to Marx — specifically, to the distinction between two types of surplus value.

    Capitalist innovates
    (new machinery, process)
    →
    Extraordinary surplus value
    (temporary advantage)
    →
    Rivals adopt technology
    →
    Inflation absorbs the gap
    →
    Relative surplus value
    (permanent for the class)
    Fig. 1 — The mechanism proposed by Gómez Julián, simplified.

    Two Kinds of Surplus Value: A Quick Primer

    If you’re not steeped in Marxist theory, don’t worry — the distinction is intuitive.

    Absolute surplus value is what a capitalist gets by making workers work longer or harder for the same pay. It’s the old-fashioned squeeze. Relative surplus value, by contrast, comes from making production cheaper — through technology, efficiency, better organization — so that the value of labor-power (i.e., the cost of maintaining a worker) falls, even if wages don’t.

    Now imagine a single firm introduces a breakthrough technology. It can produce goods faster and cheaper than its competitors. For a while, it earns extraordinary surplus value — a premium profit that exists only because it’s ahead of the pack. But here’s the catch: once competitors adopt the same technology, that advantage vanishes. The extraordinary surplus value disappears.

    Gómez Julián’s argument is that inflation is the mechanism through which this temporary advantage gets converted into a permanent one. How? As the innovating firm’s higher productivity drives down unit costs, prices don’t fall proportionally — instead, the general price level adjusts upward. The gap between the old cost structure and the new one gets absorbed by inflation. What was a one-time windfall for the innovator becomes a structural shift in profitability for the entire capitalist class.

    Inflation, in this reading, is not a policy error or a monetary accident. It is a functional mechanism of capitalist accumulation — one that converts technological advantage into lasting class-wide profit.

    What This Means for Policy

    If the paper is right, the implications are significant:

    For central bankers: If inflation isn’t primarily a monetary phenomenon — if it’s rooted in the structural dynamics of production and profit — then raising interest rates to fight inflation is treating the symptom, not the disease. You might cool the economy, but you’re not addressing the engine that generates inflation in the first place.

    For mainstream economists: The Phillips Curve may be less a stable empirical law and more a historical coincidence — a relationship that appeared to hold in a particular postwar context and has been propped up by theoretical convenience ever since. The paper adds to a growing body of evidence that the curve has become unreliable as a guide to policy.

    For non-economists: This paper reframes inflation as a political question, not just a technical one. If inflation systematically benefits capital at the expense of labor — by preserving the gains of innovation for the capitalist class while workers’ purchasing power erodes — then debates about inflation are, at their core, debates about distribution and power.

    A note of caution The paper uses R&D spending as a proxy for technological change. This is standard in the literature, but it’s not a direct measure of innovation. R&D spending can reflect many things — tax incentives, defense contracts, speculative bubbles in tech. The correlation Gómez Julián finds is suggestive and theoretically grounded, but it warrants further investigation with additional proxies and across different economies.
    · · ·

    A Challenge to Orthodoxy

    What makes this paper worth reading — whether you agree with it or not — is that it does something many economists avoid: it takes a heterodox theoretical framework seriously and tests it empirically. This isn’t armchair Marxism. It’s Bayesian statistics, Granger causality, and error correction models applied to five decades of data. The methodology is conventional; the interpretation is not.

    The mainstream view treats inflation as essentially a monetary phenomenon — too much money, not enough stuff. Milton Friedman’s famous dictum that “inflation is always and everywhere a monetary phenomenon” still echoes through central banks worldwide. Gómez Julián doesn’t deny that money supply matters. But he argues it’s not the whole story — and may not even be the most important part.

    In his framework, the relationship between technology, surplus value, and prices is structural. It doesn’t depend on whether a central bank is dovish or hawkish. It’s embedded in the logic of capitalist production itself.

    So, Is the Phillips Curve Dead?

    Probably not entirely. There are short-run contexts where demand pressures do push prices up, and the Phillips Curve captures something real about those moments. But the paper pushes us to ask harder questions: What determines the baseline around which those fluctuations occur? Why has inflation behaved the way it has over half a century, regardless of the unemployment rate?

    Gómez Julián offers a provocative answer: inflation is the economy’s way of metabolizing technological progress into profit. It’s not a bug in the system. It’s a feature.

    Whether you find that convincing depends, in part, on your theoretical priors. But the data doesn’t lie about what it doesn’t show: a reliable Phillips Curve. And that, at minimum, should give everyone — mainstream, heterodox, and curious layperson alike — something to think about.

    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. Read the full text here →

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

  • Unearthing the Truth: Genetics, Archaeology, and the Palestinian Descent from Ancient Judeans

    Unearthing the Truth: Genetics, Archaeology, and the Palestinian Descent from Ancient Judeans

    Unearthing the Truth: Genetics, Archaeology, and the Palestinian Descent from Ancient Judeans

    A deep dive into José Mauricio Gómez Julián’s recent monograph challenging the biblical exile narrative through the lens of modern science and critical historiography.
    At the intersection of history, genetics, and modern geopolitics lies a question that profoundly unsettles established narratives: Who are the true descendants of the ancient Judeans?

    In a groundbreaking recent monograph, researcher José Mauricio Gómez Julián tackles this question head-on. His paper, “The Ancient Judeans of Judea as Direct Ancestors of Contemporary Palestinians,” synthesizes three decades of converging evidence from archaeology, paleogenomics, historiography, and linguistics. The conclusion he reaches is as scientifically robust as it is politically provocative: contemporary Palestinians are the direct demographic heirs of the ancient inhabitants of the southern Levant, while modern Jewish populations represent a broader mosaic shaped heavily by religious conversions and migrations.

    The Myth of the Roman Expulsion

    The foundation of the Zionist “return” narrative rests on a specific historical claim: that the Roman Empire expelled the Jewish people en masse from Judea following the revolts of 70 CE and 135 CE, leaving the land empty for two millennia.

    However, Gómez Julián points out that modern historiography—including the work of Israeli historians like Seth Schwartz, Martin Goodman, and Shlomo Sand—has thoroughly dismantled this myth. Following the revolts, the Romans destroyed Jewish institutions (the Temple, the priesthood, and the Sanhedrin) and banned Jews from entering Jerusalem. Still, there is no historical or archaeological evidence of a mass deportation of the general population.

    The rural Judean population remained in situ (in place). Over the next millennium, these communities gradually converted to Christianity during the Byzantine period, and later to Islam following the Arab conquest. They changed their religion and their language, but they never left their soil. Astonishingly, early Zionists like David Ben-Gurion and Yitzhak Ben-Zvi explicitly acknowledged the Jewish ancestry of the Palestinian fellahin (peasants) in writings published between 1905 and 1929, before the political realities of the 1920s forced a strategic ideological shift.

    Archaeology: The Canaanite Roots of Israel

    To understand the population of ancient Judea, we must look at its origins. The traditional biblical narrative of an Exodus from Egypt and a military conquest of Canaan lacks archaeological support. Instead, the “minimalist school” of biblical archaeology—featuring scholars like Israel Finkelstein, Thomas L. Thompson, and William Dever—has established that the earliest Israelites were actually autochthonous Canaanites.

    Around 1200 BCE, approximately 250 small, unwalled villages emerged in the central highlands of Palestine. The pottery, architecture, and lack of destruction layers show continuous cultural evolution from the Late Bronze Age Canaanite substrate. The ancient Israelites did not invade from the outside; they emerged from within the local population.

    Science does not ground territorial rights, but when a fictitious genealogy is weaponized to dispossess a people with deeper roots, science has an obligation to speak.

    The Genetic Evidence: Whose DNA Matches the Land?

    Perhaps the most compelling section of Gómez Julián’s monograph relies on paleogenomics—the study of ancient DNA. If the biblical exile and return narrative were true, modern Jews would share the closest genetic profile with the ancient Levantine populations. The data, however, tells a different story.

    • Palestinians: Contemporary Palestinians possess between 81% and 87% ancestry derived from Bronze Age Levantine populations. They act as a direct genetic bridge to the ancient Canaanites and Judeans.
    • Ashkenazi Jews: Modern Ashkenazi Jews trace their ancestry to a severe genetic bottleneck of roughly 350 individuals about 600 to 800 years ago. Genetically, they are an admixed population, carrying about 40% to 55% European ancestry (primarily from Southern Europe/Italy), alongside their Middle Eastern component.
    • Y Chromosomes: Studies show that about 70% of Jewish Y chromosomes and 82% of Palestinian Y chromosomes belong to the same ancient Levantine gene pool. Both populations share a biological origin, but Palestinians retained a closer genetic continuity to the land because they remained there, while diaspora populations intermixed with Europeans.

    While the author notes with epistemic honesty that Mizrahi (Middle Eastern) Jews retain Levantine ancestry comparable to Palestinians, the overall genomic data refutes the idea that modern Ashkenazi Jews are the exclusive, pure-blooded heirs of ancient Judea.

    Language and Toponymy: The Archive of the Land

    Genetics tells only part of the story; language tells the rest. The linguistic trajectory of the southern Levant—Canaanite → Hebrew → Aramaic → Arabic—demonstrates language shifts without population replacement. Just as the Irish adopted English without being replaced by the English, the native Levantine population adopted Aramaic, and later Arabic, under successive empires.

    Furthermore, the toponymy (place names) of Palestine serves as an unbroken archive of continuity. Palestinian villages retained ancient Hebrew and Canaanite names for millennia. Beit Lahm (Bethlehem), Beisan (Beth-shean), and Bir as-Saba (Be’er Sheva) are not Arab impostures; they are the living pronunciations of the land’s ancient names by the people who never left it. Even Palestinian agricultural customs retained pre-Islamic terms, such as calling rain-dependent farmland ard ba’liyyeh (“land of Baal”), unknowingly invoking the ancient Canaanite storm deity.

    The Diaspora as a Mosaic of Conversions

    If the Romans didn’t expel millions of Jews, how did the Jewish diaspora spread across three continents? Gómez Julián argues that Judaism transformed from a geographic ethnicity into an expansive religion. In the mid-second century BCE, the Hasmonean dynasty began forcing conversions on neighboring Idumeans and Itureans.

    During the Greco-Roman period, Judaism was an active proselytizing religion. The Jewish population exploded from an estimated 150,000 in the 6th century BCE to between 4 and 8 million by the 1st century CE. This demographic explosion is mathematically impossible through natural birth alone. From the Himyarite kingdom in Yemen to the Berber tribes of North Africa, and later the Khazars and European populations, the diaspora was formed through a complex mosaic of voluntary and forced conversions.

    Conclusion: When Science Speaks to Power

    Scientific evidence cannot dictate political rights, nor should genetics determine who deserves human dignity and self-determination. However, as Gómez Julián concludes, when a fictitious genealogical narrative is weaponized to justify the dispossession, displacement, and systemic violence against a population that possesses a deeper genetic and historical continuity to the land, science has an obligation to speak.

    The convergence of archaeology, DNA, and linguistics tells a clear story: the Palestinians are not foreign Arab invaders. They are the descendants of the ancient Judeans who changed their faith and tongue over the centuries but never abandoned their homeland. Acknowledging this reality is not just an academic exercise; it is a prerequisite for any honest historical reckoning in the Middle East.

  • Marx, Adam Smith, and the Law of Large Numbers

    Marx, Adam Smith, and the Law of Large Numbers

    A new research uses probability theory — and sixty years of U.S. economic data — to test one of the most consequential (and most overlooked) assumptions in political economy.

    The Assumption Hiding in Plain Sight

    If you’ve ever read a Marxist analysis of how profits equalize across industries, you’ve probably encountered something called the average rate of profit. The idea is straightforward: competition between capitalists drives different rates of profit in different sectors toward a common, system-wide average. This is one of the pillars of Marx’s theory of value in Capital, Volume III.

    But there’s a quieter assumption underneath this one — so quiet that most discussions never mention it explicitly. To arrive at a uniform profit rate, Marx first assumes a uniform rate of surplus value across all productive sectors. In plainer terms: he assumes that the degree to which workers are exploited — the ratio of unpaid labor to paid labor — is roughly the same everywhere, whether you work in steel manufacturing, food processing, or textiles.

    Adam Smith proposed this idea before Marx. Smith argued that if one job were obviously more exploitative (in the sense of yielding far more unpaid surplus per dollar of wages paid), workers and capital would flow toward or away from it until the differences vanished. Marx adopted this observation and, as scholar Jonathan Cogliano notes, elevated it to “the status of a central economic law” within his framework.

    Yet the assumption has been challenged from multiple directions — Marxist and non-Marxist alike. Is it actually justified? Or is it a convenient simplification that distorts our understanding of how capitalism works?

    José Mauricio Gómez Julián, of the Universidad Latina de Costa Rica, decided to approach the question from an unexpected angle: probability theory. His paper, published in Ciencia Económica (2022), asks whether the mathematical law that would need to hold for this assumption to be valid actually does hold — and then checks the answer against six decades of real-world data from the United States.

    The Mathematical Backbone: The Law of Large Numbers

    If you’ve taken any statistics course, you’ve likely met the Law of Large Numbers (LLN). It tells us that as you observe more and more instances of something random — coin flips, dice rolls, stock returns — the average of those observations settles down toward the true expected value.

    There are two versions:

    • The Weak Law (WLLN): With enough observations, the sample average is probably close to the expected value.
    • The Strong Law (SLLN): With enough observations, the sample average is almost certainly equal to the expected value — a much stronger guarantee.

    Gómez Julián’s insight is this: if you think of each productive sector of the economy as a random variable representing that sector’s rate of surplus value, then the LLN tells you what happens to the average across sectors as the number of sectors grows large. In mathematical language:

    • Strong Law: The probability that the average surplus-value rate across sectors equals the global expected value, in the limit, is exactly 1.
    • Weak Law: The probability that the average deviates from the global expected value by more than any tiny amount shrinks to zero.

    If either version holds, you get the result Marx needs: across a sufficiently large number of sectors, the rates of surplus value converge to a common value — uniformity, or at least a powerful tendency toward it.

    The Catch: Independence and Identical Distributions

    Here’s where things get interesting — and where the classical LLN hits a wall.

    The textbook version of the LLN requires two conditions:

    1. Independence: The random variables (sectoral surplus-value rates) must be statistically independent of each other.
    2. Identical distribution: Each variable must follow the same probability distribution.

    Neither condition holds for the real economy. And Gómez Julián is admirably upfront about this. Sectors are deeply intertwined — the steel industry depends on mining, manufacturing depends on steel, services depend on consumer spending powered by manufacturing wages. The idea that one sector’s surplus-value rate has no relationship to another’s is economically unrealistic. Furthermore, different industries have different cost structures, different labor intensities, and different technologies. There is no reason their surplus-value rates should follow the same statistical distribution.

    So does this kill the argument? Not at all. In fact, it’s the most intellectually interesting part of the paper.

    Non-Classical Varieties: When the Rules Relax

    Over the past several decades, mathematicians and econometricians have developed non-classical versions of the LLN that weaken or entirely drop the independence and identical-distribution requirements. Gómez Julián surveys several of these:

    • Li, Rao, and Wang (1995) showed the LLN holds for random variables arranged on a lattice structure under certain conditions — a structure that, as it happens, economic data naturally exhibits.
    • Adler and Rosalsky (1987) proved the law for weighted sums of independent, identically distributed random variables belonging to a normalized sum, generalizing the classical case.
    • Chen and Sung (2016) extended those results further: the variables no longer need to be identically distributed. They only need to be “stochastically dominated” by a single random variable, with certain weighting conditions.
    • Sung (2011) showed that the strong law can hold even when variables are dependent on each other, provided their probability moments (roughly, their averages and variability) satisfy certain finiteness conditions.

    The crucial point: these results collectively tell us that the LLN’s convergence conclusion can survive even when the classical assumptions are substantially violated — which is exactly the situation with sectoral surplus-value rates.

    Gómez Julián argues that the economic dynamics described by Smith — workers and capital moving between sectors in response to unequal advantages — are precisely the kind of compensatory dependence mechanism that these non-classical versions accommodate. The variables aren’t independent, but their dependence is structured in a way that still drives convergence.

    What the Data Actually Shows

    The theoretical argument is compelling, but Gómez Julián doesn’t stop there. He turns to sixty years of U.S. data (1960–2020), sourced from the Bureau of Economic Analysis (BEA), to see what the empirical evidence says.

    He calculates sectoral surplus-value rates using macroeconomic data on gross operating surplus (representing surplus labor time) and employee compensation (representing necessary labor time), following a standard operationalization of Marx’s categories. After carefully determining which sectors qualify as “productive” in the Marxist sense — a nontrivial task, since the service sector includes activities with very different relationships to surplus-value production — he arrives at 36 productive sectors.

    Here’s what the statistical analysis found:

    Finding 1: No Identical Distributions

    A probability distribution fitting exercise (using the Bayesian Information Criterion) revealed that the 36 sectors’ surplus-value rates follow a patchwork of different distributions — Log-Normal, Cauchy, Uniform, Weibull, and Logistic — with none following a normal distribution. The identical-distribution requirement of the classical LLN is not met.

    Finding 2: No Statistical Independence

    A Pearson correlation analysis across all 630 possible sector pairs yielded a mean correlation of about 0.08 and a median of about 0.14. While these may look small, a deeper cut reveals that roughly 40% of sector pairs have correlations of 0.3 or above — a level that’s practically meaningful. The sectors are not independent. This makes intuitive sense: industries are connected through supply chains, labor markets, and shared macroeconomic conditions.

    Finding 3: Differences Tend Toward Zero

    This is the key finding. When Gómez Julián computed the differences between each sector’s surplus-value rate and the global average (both the mean and the median), he found that these differences exhibit a strong tendency toward reciprocal nullification — positive differences roughly cancel out negative ones. The sum of all differences relative to the global mean was essentially zero (on the order of 10⁻¹⁴). The mean of differences relative to the global median was 0.0012 — vanishingly small.

    Distributional fitting on these differences revealed they follow a Cauchy distribution (when measured against the global mean) or a uniform distribution (against the global median), with the medians of these distributions sitting very close to zero.

    In plain language: sectors deviate from the average in different directions, and those deviations largely cancel each other out.

    Why This Matters

    Gómez Julián’s paper makes two types of contributions that are worth distinguishing:

    For Marxist political economy: If the uniformity assumption holds — even approximately, even as a tendency rather than an iron law — then a large body of research on the long-run behavior of the average rate of profit, both within countries and across the global economy, is on sounder footing than critics have suggested. Researchers studying the tendency of the rate of profit to fall (or not) can continue to work without needing to explicitly model sector-by-sector differences in exploitation rates, at least for aggregate, long-run analyses.

    For probability theory and economics: The paper demonstrates a productive intersection between a specific question in political economy and the deep mathematics of convergence theorems. It shows that the non-classical LLN theorems aren’t just abstract curiosities — they have direct relevance to understanding real economic phenomena. The structured dependence between economic sectors isn’t a bug that invalidates the mathematical framework; it’s a feature that the right version of the framework already accounts for.

    A Few Honest Caveats — And Why They No Longer Apply

    The original 2022 paper was unusually transparent about its limitations, and that transparency is one of its strengths. Rather than forcing the data into inappropriate statistical procedures, it openly acknowledged where the available inferential tools broke down.

    At the time, three important caveats remained.

    First, formal hypothesis testing had to be abandoned.

    The reason was purely statistical rather than economic. Classical inferential procedures—Student’s t tests, Wilcoxon tests, and most conventional non-parametric alternatives—are built on assumptions that the data simply did not satisfy. Sectoral surplus-value rates are neither independent nor identically distributed. They are linked through supply chains, technological change, capital mobility, and macroeconomic shocks. Even bootstrap procedures could not fully solve the problem because ordinary resampling may weaken dependence between resamples while leaving the internal dependence structure fundamentally unchanged. Consequently, the 2022 paper relied primarily on descriptive statistics together with probability-theoretic arguments instead of formal significance testing.

    Second, the classification of productive sectors inevitably involved theoretical judgment.

    Although the paper carefully justified the inclusion and exclusion of economic activities using Marxian categories and modern national accounting, reasonable scholars could still debate where certain services belong within the circuit of capital.

    Third, the empirical evidence came exclusively from the United States.

    The descriptive regularities were remarkably strong, but demonstrating that the same convergence mechanism operates under different institutional settings naturally remained an empirical question.

    Those were genuine limitations in 2022.

    Today, however, the first—and arguably the most important—of them has largely been overcome.

    A much more comprehensive methodological paper (Gómez Julián, 2026; SSRN 5172185) develops an entirely new inferential framework specifically designed for exactly the type of data that made the original analysis difficult: dependent, heterogeneous, and unbalanced observations. Instead of trying to force classical statistical tests to work outside the assumptions under which they were derived, the newer paper constructs hypothesis testing from the ground up for this class of problems.

    The key innovation is recognizing that the convergence of sectoral surplus-value rates is fundamentally a law-of-large-numbers problem under dependence, not an independent-samples problem. The framework therefore combines three complementary asymptotic structures—triangular arrays (TAC), correlation-weighted sums (WSC), and mixingale processes (MPC)—which respectively model hierarchical dependence, contemporaneous intersectoral dependence, and temporal dependence. Rather than treating these as competing approaches, the paper proves conditions under which they become metrically equivalent and therefore support the same inferential conclusions.

    The inferential consequences are substantial.

    Instead of abandoning significance testing because dependence invalidates classical procedures, the new framework explicitly extends the Neyman-Pearson paradigm to dependent observations, derives dependence-aware confidence regions, establishes rigorous Type I error control under strong-mixing assumptions, and integrates Bayesian and frequentist inference into a single coherent architecture. Robust procedures—including fixed-b heteroskedasticity-and-autocorrelation-robust inference, block bootstrap techniques that preserve dependence, adaptive conformal inference, composite and Whittle likelihoods, and hierarchical Bayesian estimation—serve as mutually reinforcing validation mechanisms rather than isolated alternatives.

    In other words, what had been acknowledged as a methodological limitation in the 2022 paper became the central research question of the later work.

    Rather than concluding that inference was impossible under dependence, the subsequent research asks a more fundamental question: what should hypothesis testing look like when dependence is the normal state of the data rather than an exception? The result is a unified inferential framework specifically intended for datasets that violate the assumptions of classical statistics—precisely the situation encountered with sectoral surplus-value rates.

    The other caveats remain, although they are considerably less problematic than before. The classification of productive sectors continues to depend on theoretical interpretation, because that issue belongs to political economy rather than statistics. Likewise, expanding the empirical analysis to additional countries remains a desirable avenue for future research. Yet the principal statistical objection—that no valid inferential procedure existed for dependent sectoral data—has now been directly addressed through a purpose-built mathematical framework.

    Looking back, the 2022 paper can therefore be read as identifying an important statistical obstacle, while the later work attempts to remove it. Together, the two papers form a coherent research program: first demonstrating that the convergence hypothesis is theoretically plausible and descriptively supported, and then developing the inferential machinery required to test that hypothesis rigorously without relying on unrealistic assumptions of independence or identical distributions.

    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, 11(17). DOI: 10.22201/fe.24484962e.2022.11.17.2

    Gómez Julián, J.M. (2026). Hypothesis Testing for Dependent Variables with Unbalanced Data: A Unified Framework: Theory, Robustness, and Software. SSRN Electronic Journal. DOI: 10.2139/ssrn.5172185.

  • 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)

    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

    How one researcher built a theoretically rigorous rulebook for a question everyone answers differently — and what happens when you let the data decide for itself.

    Based on: Gómez Julián (2025) | ~12 min read | Originally published as a preprint on arXiv

    In 1984, two economists named Anwar Shaikh and Edgardo Ochoa opened a research tradition that would span four decades: empirically measuring Marx’s most consequential prediction — that capitalism’s average rate of profit tends to fall over time. Since then, dozens of studies have followed, each arriving at the same fundamental calculation, but each choosing differently which sectors of the economy to include. Some count everything. Others exclude finance and government. Still others carve out a narrower productive core. The results? They disagree — sometimes dramatically — about whether the profit rate actually falls.

    The problem isn’t sloppy math. It’s that nobody has ever agreed on a standard for deciding which economic activities belong in the calculation. José Mauricio Gómez Julián’s recent paper aims to change that.

    ◆

    The Question Nobody Agrees On

    Here’s the issue in plain terms. Suppose you want to calculate the “average rate of profit” for the entire U.S. economy over sixty years. You need two things: the total surplus value produced and the total capital invested. To get these, you aggregate data from individual sectors — agriculture, manufacturing, finance, retail, government, and so on.

    But should finance be in there? Finance doesn’t manufacture anything; it redistributes money. Should government? The government doesn’t compete for profits. Should retail trade? A retailer buys finished goods and sells them at a markup, but Marx argued that the act of buying and selling doesn’t create new value — it merely realizes value already embedded in the commodity.

    These aren’t arbitrary questions. If you include sectors that redistribute value rather than create it, you can artificially inflate or deflate the measured profit rate, potentially masking the very tendency Marx predicted. Different researchers have made different choices, and the field has lacked a unified standard — until this paper.

    ◆

    Three Pillars: The Theoretical Logic Behind the Criteria

    Gómez Julián’s framework is built on three interlocking concepts from Marx’s political economy. The underlying logic of the entire procedure can be stated simply: an economic sector should be included in the average-rate-of-profit calculation if, and only if, its workforce performs productive labor as Marx defined it — labor that is subordinated to capital and directly produces surplus value, or that constitutes an indispensable material condition for that production to occur. Everything else is excluded.

    Let’s walk through each pillar to see how this logic unfolds in practice.

    1. Productive vs. Unproductive Labor

    The most fundamental distinction in Marx’s economics is between labor that creates value and labor that doesn’t. Productive labor, in the Marxist sense, isn’t about whether work is “useful” in everyday language. It’s a technical category: productive labor is work performed under the subordination of capital that produces surplus value — the unpaid portion of the working day that capitalists appropriate for free.

    Unproductive labor, on the other hand, doesn’t generate new value. It may be socially necessary (think of a cashier or an accountant processing invoices), but it merely facilitates the transfer or realization of value that was already created elsewhere in the production process. It is, as Marx called it, a faux frais — a cost that must be paid out of surplus value rather than one that generates it.

    The mere functions performed by capital in the sphere of circulation — the operations necessary to serve as the vehicle for the metamorphoses of commodity-capital — do not create value or surplus value.

    — Karl Marx, Capital, Volume II

    In other words, the act of buying and selling, however essential for capitalism to function, is not productive in the value-theoretic sense. The merchant who buys goods cheaply and sells them at a markup doesn’t create value through the exchange itself; they merely appropriate a share of value created by productive workers elsewhere.

    2. Location in the Circuit of Capital

    Capital doesn’t just sit still. It moves through a circuit: it begins as commodities filled with freshly produced surplus value (C’), converts into money through sale in the market (M), and then transforms back into new commodities — raw materials, machinery, labor power — to restart production (C → C’). Activities that feed into this productive cycle — that help produce, maintain, or prepare commodities for the next round of production — sit inside the circuit. Activities that operate outside it (like government services aimed at general welfare, or purely redistributive financial operations) sit outside.

    This criterion is critical because it captures something the productive/unproductive distinction alone might miss: even an activity that doesn’t directly produce surplus value can be included if it constitutes an indispensable material precondition for the circuit to continue. Transportation is the classic example — it doesn’t transform a commodity’s physical form, but it physically moves goods to where they’re needed for consumption or further production, which Marx explicitly recognized as a productive act that adds value.

    3. Relationship with Surplus Value

    The final criterion is the most direct: does this activity produce surplus value, or is it an indispensable condition for surplus value production? If it directly creates value through productive labor, include it. If it’s a necessary supporting activity embedded in the productive circuit, include it. If it merely redistributes value already produced, or operates on entirely different logic (like government), exclude it.

    The logic here is that surplus value is the lifeblood of capitalist accumulation. Any sector that doesn’t contribute to its creation or materially enable it is, from the standpoint of the accumulation process, extraneous to the dynamic you’re trying to measure.

    The Service Sector Problem

    One of the paper’s most valuable theoretical contributions is its treatment of services. When Marx wrote, there was no statistical concept of a “service sector.” Modern macroeconomic data lumps together wildly heterogeneous activities under this label — everything from software development to hairdressing to hospital care.

    Gómez Julián, drawing on Tregenna (2009), identifies three types of service activities:

    • Those that directly produce surplus value (e.g., software development subcontracted by a manufacturing firm, transportation of goods)
    • Those that facilitate surplus value production elsewhere (e.g., warehousing that preserves commodity properties, scientific research contracted by industry)
    • Those that remain outside the circuit of capital (e.g., government administration, purely redistributive finance)

    This means you cannot simply include or exclude “services” wholesale. Each activity must be examined on its own terms, disaggregated, and asked: does this particular service perform productive labor, or doesn’t it? For “hybrid” sectors that contain both productive and unproductive components, the researcher must determine the proportions and decide based on which dominates.

    ◆

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

    Using Bureau of Economic Analysis data for the United States (1960–2020), Gómez Julián applies these theoretical criteria to 46 consolidated economic sectors. The result is a clear binary classification.

    Included — Productive

    • Farms
    • Forestry, fishing & related activities
    • Oil & gas extraction
    • Mining (except oil & gas)
    • Support activities for mining
    • Utilities
    • Construction
    • All manufacturing (wood, metals, machinery, electronics, motor vehicles, textiles, chemicals, petroleum, paper, printing, plastics, rubber, furniture, food & beverage, apparel, computers, etc.)
    • 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

    Most of these are straightforward once you accept the theoretical framework. Agriculture, mining, manufacturing — clearly productive. Finance, real estate, government — clearly outside the surplus-value production process. But several borderline cases required careful reasoning.

    The Borderline Cases

    Warehousing and storage might seem like a pure logistics function, but the paper argues that preserving the physical properties of commodities before they enter the sphere of circulation is a material precondition for their existence as commodities. Without storage, many goods would deteriorate and lose their use-value. This makes warehousing an indispensable part of the productive process, not merely a cost of circulation.

    Educational services is perhaps the most controversial inclusion. It encompasses private, public, and non-profit components. The classification system doesn’t specify their proportions. But excluding the sector entirely would mean ignoring a fundamental element for reproducing the skilled labor force in a highly industrialized economy — a cost that productive capital must bear one way or another.

    Administrative and waste management services includes activities that generate surplus value (document preparation for productive firms, personnel placement) alongside activities that don’t (security services, household cleaning). The paper argues that since most of the economy consists of productive sectors, and most of these services are contracted by those productive sectors, the productive component likely dominates.

    Information produces and distributes cultural products, software, broadcasting content, and data. In accordance with the criteria — these are material products of creative and technical labor, increasingly subcontracted by productive enterprises — it is included.

    ◆

    The Econometric Validation: Three Blind Tests

    Here is where the paper’s methodology becomes genuinely innovative. Gómez Julián doesn’t merely propose theoretical criteria and declare victory. He subjects the entire framework to empirical testing using three fundamentally different statistical methods.

    A critical point: These econometric methods operate with zero knowledge of Marxist theory. They do not distinguish between “productive” and “unproductive” labor. They have never heard of the circuit of capital. They simply analyze the raw data for all 47 economic sectors and tell you which ones structurally matter for the economy’s behavior. This makes them a powerful independent test — a way to ask the data itself which sectors form the economy’s real core.

    Test 1: Principal Component Analysis (PCA)

    PCA is a dimensionality reduction technique that identifies the directions (called “principal components”) along which the economy’s sectoral data varies most. Think of it as asking: if the entire economy were a cloud of data points, which directions through that cloud capture the most movement?

    Applied to all 47 sectors simultaneously, PCA found that economic variance is highly concentrated: a small number of sectors drive most of the variation, while many others contribute only marginal noise. Using a rigorous statistical criterion — fitting probability distributions to each sector’s contribution and selecting those in the top decile — PCA identified 26 sectors as structurally significant. A post-hoc validation confirmed that none of the 21 excluded sectors had sufficient statistical weight (eigenvalue exceeding 1) to constitute an independent driver.

    The first principal component was dominated by corporate and financial services. The second by a logistics-industrial chain. The fourth by extractive natural resources. The seventh by education and public administration.

    Test 2: Regularized Horseshoe Regression (RHR)

    This Bayesian method uses a “global-local shrinkage” prior that aggressively compresses noise toward zero while preserving strong signals — think of it as a statistical metal detector that ignores pebbles but rings loudly for gold. The name “Horseshoe” is not a metaphor; it refers to the literal U-shaped geometry of the shrinkage coefficient’s probability distribution, which piles mass at the extremes (fully suppress or fully preserve) rather than settling at mediocre intermediate values like conventional methods.

    Gómez Julián specified the model to predict total gross operating surplus from total variable capital across all sectors — deliberately grounding the specification in the labor theory of value. The severe multicollinearity inherent in input-output data (sectors move together — when steel production grows, automobile production grows) meant that no individual sector achieved traditional statistical significance. This isn’t a failure. As economists Christopher Achen and Olivier Blanchard have argued, multicollinearity in macroeconomic data is not a “problem” to be fixed with clever statistics; it’s an intrinsic, ontological property of how economies work. Blanchard memorably called it “God’s will.”

    What the model could provide was a predictive ranking based on projected predictive density (ELPD): which sectors reduce prediction error fastest. The top 15 sectors identified were:

    1. Retail Trade
    2. Textile Mills & 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 (DFM)

    The DFM extracts hidden “latent factors” from the 47 sectoral time series — unobserved forces that cause sectors to move together. The model found two such factors: one capturing short-term cyclical shocks (low persistence, autoregressive coefficient of 0.33) and one carrying the secular, long-term trend (high persistence, autoregressive coefficient of 0.91). These two factors together explain about 34% of total sectoral variation.

    Through an elaborate multi-stage validation involving stability selection, synchronized block bootstrap resampling (300 replications), and a novel “Full-Robust Thresholding” algorithm that generates counterfactual null distributions and corrects for factor indeterminacy via the Hungarian algorithm, the model identified which sectors are most structurally synchronized with these systemic factors.

    The sectors with the highest structural weight were: Real Estate, followed by State & Local General Government and Federal General Government, then Retail Trade and Food Services, with Utilities and Chemical Products providing the industrial baseline.

    ◆

    The Key Revelation: Theory and Data Diverge

    Now comes the most thought-provoking finding in the paper. The econometric methods — which are purely data-driven and completely agnostic to Marxist theory — identify a set of “core” sectors that overlaps with but also substantially differs from the theoretical classification.

    Where Theory and Data Agree

    Manufacturing sectors (textiles, metals, fabricated products, miscellaneous manufacturing) appear across multiple econometric methods and are unambiguously included by the theoretical criteria.

    Administrative & waste management services ranks 4th in the RHR and is theoretically included as productive.

    Educational services appears in the RHR ranking (7th) and is theoretically included.

    Transportation appears in the RHR ranking (15th) and is theoretically included.

    Construction appears prominently in both RHR (6th) and PCA, and is theoretically included.

    Utilities appear in the DFM results and are theoretically included.

    These convergences suggest that the theoretical criteria are tracking something real in the data: the sectors that Marx identified as productive are indeed among those that structurally drive the economy.

    Where Theory and Data Disagree — And Why It Matters

    Real Estate dominates the DFM results (ranked #1 in structural weight) but is theoretically excluded as non-productive and fictitious.

    Government sectors (federal and state/local) rank among the top DFM sectors but are theoretically excluded because they don’t pursue profit maximization.

    Retail Trade ranks #1 in the RHR and appears prominently in the DFM, yet is theoretically excluded as pure circulation.

    Finance & insurance dominate the first principal component in PCA but are theoretically excluded.

    Health care has the highest eigenvalue among all excluded sectors in PCA’s post-hoc validation table but is theoretically excluded.

    What does this divergence mean? The paper interprets it as profoundly significant. Sectors like real estate, government, and retail trade have “effectively colonized the macro-dynamics of the US rate of profit.” They statistically dominate the national accounting aggregates — they are the forces that shape the observed numbers — even though Marxist theory classifies them as unproductive or revenue-consuming.

    In Marx’s own philosophical vocabulary, the phenomenon (what the data shows on its surface) and the essence (what theory identifies as the true engine of value production) diverge. The sectors driving the observable statistical dynamics are not the same as the sectors that, according to the theory, actually generate surplus value. This is not a refutation of either the theory or the data; it’s an insight into how modern capitalism’s surface appearance differs from its underlying structure — exactly as Marx’s own method predicted it would.

    ◆

    Does the Rate of Profit Fall?

    With the theoretically selected sectors, all three trend-extraction methods — Daubechies wavelet filters (with 8 vanishing moments at decomposition depth 4), Empirical Mode Decomposition, and the Embedded Hodrick-Prescott filter (implemented within a Bayesian unobserved components model with Gibbs sampling) — produce a clear declining long-term trend in the net average rate of profit over 1960–2020. This is precisely what Marx predicted, and it serves as evidence of the internal consistency of the proposed criteria: the new proposition (the sectoral classification) fits harmoniously within the existing system of Marxist propositions.

    For the econometric criteria, the results are remarkably robust: with the single exception of the Hodrick-Prescott filter under the DFM sector selection, all combinations of econometric sector-selection criteria and filtering methods also produce a declining long-term trend. That means:

    • 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 → not clearly declining

    Regardless of which sectors you choose — based on careful Marxist reasoning or on pure data analysis — and regardless of which statistical filter you use, the long-term profit rate falls. The HP-DFM exception is attributed to the filter’s parametric specifications (its linear structure and second-order Markov assumption for the trend) potentially interacting poorly with a sectoral composition heavily weighted toward government and real estate — sectors whose dynamics may follow different logics than productive capital.

    The Empirical Mode Decomposition, being a non-parametric technique that adapts to the data’s intrinsic patterns without imposing prior assumptions about functional form, consistently produced the most accentuated declining trend across all sector selections.

    ◆

    Why This Paper Matters

    Gómez Julián’s work makes three contributions that will resonate well beyond the boundaries of Marxist economics:

    First, methodological standardization. For the first time, there is a theoretically grounded, explicit, and reproducible set of criteria for deciding which sectors belong in Marxist profit-rate calculations. This addresses a four-decade-old methodological gap and enables meaningful comparison across future studies. Researchers can now reproduce the same classification, apply it to different countries or time periods, and test whether the declining tendency holds universally.

    Second, the theory-data tension as an analytical asset. Rather than hiding the divergence between theoretical classifications and empirical results, the paper treats it as a finding in its own right. The fact that unproductive sectors statistically dominate the macro-dynamics of the profit rate tells us something important about how modern capitalism appears on its surface versus how it functions at its core. It demonstrates, empirically, that Marx’s concept of “essence” and “phenomenon” isn’t merely philosophical abstraction — it describes a real, measurable gap in economic data.

    Third, the robustness of the declining trend. Whether you select sectors based on careful Marxist reasoning or let unsupervised statistical methods decide for you, the long-term profit rate declines. This convergence across radically different methodologies strengthens the empirical case for what may be Marx’s most famous — and most contested — prediction.

    The paper does not claim to have proven Marx right beyond doubt. Internal consistency, it notes, does not guarantee overall theoretical validity. But it has demonstrated that when you take the theory seriously — when you build your measurement instrument to match the conceptual categories rather than stuffing everything into the equation and hoping for the best — the data speaks in a direction that Marx would have recognized.

    Read the full paper Gómez Julián (2025) — arXiv:2501.06270

    This post is based on the preprint “Sectorial Exclusion Criteria in the Marxist Analysis of the Average Rate of Profit: The United States Case (1960–2020)” by José Mauricio Gómez Julián, originally submitted January 2025 and revised January 2026. The author’s email is listed in the paper for correspondence. Figures, complete datasets, and full methodological documentation are available in the original PDF.