1. The question beneath the statistics

A recession ends. Factories reopen, employment begins to rise and gross domestic product starts growing again. But has the economy actually returned to the path it was following before the crisis? Or has the crisis changed the path itself?

That deceptively simple question sits at the heart of Gómez Julián’s essay On the Law of the Tendential Fall in the Average Rate of Profit: Unit Roots and Non-Stationarity of Time Series. The paper brings together a technical problem in time-series econometrics and a much older problem in political economy: Karl Marx’s claim that the average rate of profit is subject to a long-run tendency to fall.

The connection may initially seem strange. A unit root belongs to the vocabulary of stochastic processes, forecasting and econometrics. Marx’s falling rate of profit belongs to theories of accumulation, technological change, crisis and class relations. Gómez Julián’s argument is that they meet at one fundamental idea: economic history may leave permanent traces.

If shocks alter the future path of an economy rather than merely disturbing it temporarily, history is not noise around the model. History becomes part of the model.

The paper therefore treats non-stationarity as more than an annoying statistical property that must be removed before running a regression. It interprets it as evidence against a picture of capitalism in which every disturbance is followed by an automatic return to an unchanged long-run equilibrium.

The route from that proposition to Marx, however, has several stages. Understanding them separately is the easiest way to see both what is powerful about the argument and where econometric caution is required.

2. Stationarity: does the economy forget?

In everyday language, something stationary remains roughly where it is. In time-series analysis the meaning is more precise. A weakly stationary process has a constant mean and variance through time, and the covariance between two observations depends on how far apart they are—not on the historical date at which they occur.

The intuitive issue is memory. Imagine an economic variable fluctuating around a stable center. A recession pushes it downward, but forces inside the system progressively pull it back. Given enough time, the effect of the original shock fades. The process “forgets.”

Now imagine another process. A negative shock pushes the variable downward and the next period begins from that lower level. Later shocks are added to everything that happened before. The effects accumulate. There is no built-in statistical mechanism guaranteeing a return to the old path. This second world is the natural habitat of the unit root.

This distinction matters enormously for economics. If output is trend-stationary, a recession is essentially a temporary displacement from a pre-existing trajectory. If output contains a unit root, the recession can change the trajectory from which the future proceeds. Growth may resume without the lost output ever being recovered.

3. What a unit root actually means

The paper introduces the idea through the simplest autoregressive model. Let the current value of a variable depend on its previous value plus a new disturbance:

When the absolute value of ρ is below one, the influence of an old shock becomes progressively smaller. The process is mean-reverting under the usual conditions. But when ρ = 1, we obtain:

This is the canonical random walk. Today’s level contains yesterday’s level in full. Every shock is therefore incorporated into the future path. The variance of the level grows with the horizon, and conventional statistical inference applied mechanically to such levels can become misleading.

This is why unit roots are associated with the famous problem of spurious regression. Two unrelated trending series can produce an impressive coefficient, a high R-squared and apparently significant test statistics simply because both contain persistent stochastic trends.

The econometric response is not to declare all relationships between non-stationary variables meaningless. Rather, researchers ask whether the variables are cointegrated—whether some stable long-run combination of them exists—or otherwise transform and model the series in a way consistent with their integration properties.

4. The Mankiw–Krugman dispute: will lost output come back?

Gómez Julián devotes a substantial part of the paper to a remarkably public argument that unfolded after the 2008 financial crisis. The Obama administration’s Council of Economic Advisers expected a strong rebound. The underlying intuition was familiar: unusually weak growth during a recession should eventually be followed by unusually strong growth as the economy returns toward normal.

Gregory Mankiw objected. Drawing on earlier work with John Campbell, he argued that aggregate output behaves much more persistently than the conventional picture of temporary deviations from a stable trend would suggest. If a fall in output can have a permanent component, then one cannot simply assume that everything lost during a recession will be recovered through subsequent above-normal growth.

Conditional recovery versus unconditional forecasting

Mankiw’s point was subtler than “recoveries never happen.” If one knew with certainty that a recession had ended, then strong post-recession growth might indeed be likely. But a forecast made in real time does not possess that information. There remains some probability that the recession will continue, that another contraction will follow, or that part of the loss reflects a permanent change rather than temporary under-utilization.

Arnold Kling supplied an especially intuitive version of the contrast. Suppose output is low because frightened households temporarily postpone purchases. Once fear disappears, spending can rebound: that resembles a trend-stationary story. But suppose resources have been committed to the wrong houses, technologies or forms of human capital. Those resources cannot simply be unspent. The economy may grow again, but some of the loss remains in history.

Krugman and DeLong: look at unemployment

Paul Krugman and Brad DeLong approached the problem from another angle. High unemployment and low capacity utilization indicate unused resources. If unemployment is far above normal, they argued, one should expect it to fall; combined with Okun’s law, that creates a case for unusually rapid output growth during recovery.

DeLong supported the argument with a relationship between unemployment and subsequent GDP growth. Mankiw’s response was econometric rather than rhetorical: he suspected that the apparent relationship was being driven disproportionately by observations surrounding the exceptionally strong recovery after the 1981–82 recession.

The subsequent calculations discussed in Gómez Julián’s paper were revealing. For the full sample, the regression produced an adjusted R-squared of about 11 percent and a t-statistic of 3.5. Removing eight quarters associated with the Reagan-era rebound reduced the adjusted R-squared to about 5 percent and the t-statistic to 2.1. The relation did not literally vanish, but its apparent strength became substantially more dependent on a particular historical episode.

A later study by David Cushman, also reviewed in the paper, went further. Cushman asked what a conventional econometric forecaster working in 2009 might have concluded. His results supported Mankiw’s skepticism about the stronger rebound projections and judged DeLong’s dynamic Okun-law specification to perform poorly relative to alternative forecasts.

5. From persistent shocks to profitability

At this point the paper changes scale. The argument is no longer merely about forecasting GDP after a recession. Gómez Julián asks what kind of economic mechanism could make history matter so persistently.

Olivier Blanchard provides an important bridge. Writing about financial crises, Blanchard observed that, across countries, output often does not return to its old trend path after a crisis. Instead, the economy can remain permanently below it. That is a profound distinction: the rate of growth can normalize while the level of productive activity remains permanently reduced.

Gómez Julián then connects this phenomenon to Marxian political economy. Marx’s law of the tendential fall in the rate of profit is not a claim that profitability must decline mechanically every year. It is a claim about a long-run force generated by capitalist accumulation, operating through a system that also contains counteracting influences and recurrent cyclical recoveries.

In broad Marxian terms, profit must be evaluated relative to the capital advanced to obtain it. Technical development raises productivity, but capitalist competition also encourages firms to substitute machinery, infrastructure and other forms of accumulated capital for living labor. The paper emphasizes the resulting relationship between the organic composition of capital, profitability and the development of productive forces.

The crucial insight is that a cyclical rebound and a secular tendency are perfectly compatible. A profit rate can fall, recover sharply, experience another boom and still exhibit a lower long-run trajectory across successive historical cycles.

This is the point at which non-stationarity acquires its political- economic meaning in the paper. If crises leave lasting scars, and if the variable organizing accumulation itself evolves historically, then “returning to normal” cannot simply mean returning to an eternal statistical center. What counts as normal after one historical cycle may already differ from what counted as normal before it.

6. Do profits lead investment?

The argument still requires another link. Even if profitability follows an important long-run trajectory, why should it organize the broader movement of output and employment? Gómez Julián’s answer is investment.

Investment expands productive capacity, creates demand for machinery and construction, reorganizes labor and shapes future production. If changes in profitability systematically precede changes in investment, then profitability becomes a plausible transmission mechanism between Marx’s theory of accumulation and the macroeconomic path observed in time-series data.

Tapia’s result is particularly important for Gómez Julián because it reverses a familiar Keynesian or Minskyan narrative in which autonomous investment “calls the tune.” In the interpretation favored by the paper, expected profitability is what gives capitalists the incentive to accumulate. Investment therefore reacts to profit conditions, and movements in profitability propagate into the wider economy.

The paper’s final causal picture can therefore be reconstructed as a sequence:

If profitability is historically conditioned, and investment depends strongly on profitability, then successive periods of accumulation do not begin from a clean slate. Each begins with a capital stock, a profit environment and a productive structure inherited from the preceding period.

7. What the evidence can—and cannot—establish

This is also where precision becomes especially important. The paper brings together several empirical facts that can be mutually reinforcing, but they are not logically interchangeable. A careful reading should keep four distinctions in view.

These qualifications do not destroy Gómez Julián’s central argument. They make its strongest defensible form clearer.

Non-stationarity contributes evidence for persistence and historical dependence. Blanchard contributes evidence that major crises can leave output permanently below its old trajectory. The profitability literature cited by Gómez Julián contributes a separate claim: the average rate of profit displays a long-run declining tendency. Kothari, Lewellen and Warner and Tapia contribute another link: profitability contains important information about subsequent investment.

The Marxian conclusion emerges from the combination of these propositions, not from the unit root alone.

Non-stationarity supplies the memory. Profitability supplies the direction proposed by the theory. Investment supplies the transmission mechanism.

This distinction is essential because it transforms a potentially overextended statistical claim into a much richer research program. Instead of asking whether one test can “prove Marx,” the relevant questions become: How persistent are shocks to output and profitability? Are breaks temporary or permanent? How should the profit rate itself be measured? Does profitability lead accumulation across countries and historical regimes? And does the long-run trajectory survive alternative specifications?

Those are empirical questions—and therefore questions on which Marxian, Keynesian and mainstream econometric approaches can genuinely confront one another using evidence.

8. Why this matters beyond econometrics

It would be easy to treat the unit-root controversy as a specialist dispute about the properties of an autoregressive coefficient. Gómez Julián’s paper insists that much more is at stake.

Consider the expression the economy will return to normal. It sounds descriptive, almost innocent. Statistically, however, it embeds a hypothesis. It assumes that there exists some stable reference path toward which the economy tends to return after a disturbance.

If the process is strongly path-dependent, that assumption may fail. A banking crisis can destroy firms, interrupt careers, cancel investment projects and alter the capital stock. A prolonged recession can change the composition of production. Investment not undertaken today means productive capacity that does not exist tomorrow. The future therefore reflects not only current conditions but also the sequence by which those conditions were reached.

For political scientists, this has an immediate implication. Economic crises cannot always be understood as temporary deviations after which politics resumes on an unchanged material foundation. If output, employment, investment and profitability carry historical scars, then crises can alter the terrain on which subsequent distributional conflicts and policy decisions occur.

For economists, the message is equally important. Choosing between a stationary and non-stationary representation is never merely a cosmetic preprocessing decision. It changes what the model says an economic shock is. In one representation, the shock is a temporary displacement. In another, it becomes part of the state from which all subsequent development proceeds.

And for readers of Marx, the paper offers an unusual bridge between nineteenth-century political economy and modern time-series reasoning. Marx’s theory is historical in structure: accumulation changes the conditions under which the next round of accumulation occurs. Gómez Julián’s use of non-stationarity gives that historical intuition a statistical analogue. The economy need not circle eternally around an unchanged center because the process itself can transform the point from which the next movement begins.

9. The argument in one view

Stripped of its polemical edges, the paper can be summarized as a five-part argument.

That final proposition is the most intellectually interesting part of Gómez Julián’s essay. The significance of non-stationarity is not that a statistical test can settle a two-century debate in political economy. It is that the statistical language of permanent shocks, stochastic trends and path dependence is difficult to reconcile with a simplistic image of economic history as temporary noise around an eternally self-restoring equilibrium.

Marx’s falling rate of profit and the unit-root literature are not the same theory, and one does not mechanically prove the other. But they meet around a common challenge: what if the economic system carries its own history forward?

Once that possibility is admitted, a crisis is not merely something that happens to an otherwise unchanged economy. It becomes one of the events through which the economy itself is historically made.

Conclusion: taking history seriously

The paper begins with an econometric distinction but ends with a claim about the nature of political economy. Stationarity describes a world capable, under appropriate conditions, of forgetting. Unit-root behavior describes a world in which disturbances can survive inside the future.

Gómez Julián argues that the second image is more compatible with the historical character of capitalist development and with Marx’s analysis of accumulation. The evidence on permanent output losses challenges easy assumptions of automatic restoration; the evidence on profits and investment gives profitability a mechanism through which it can shape the real economy; and the cited long-run profit-rate estimates provide the directional component required for the Marxian argument.

The technically careful conclusion is therefore stronger when stated modestly. Unit roots do not demonstrate the falling rate of profit. What they undermine is the presumption that economic disturbances must disappear without changing the long-run path. Once persistence is combined with evidence about the historical movement of profitability and its relationship to accumulation, the paper’s central thesis comes into view.

The deepest question is not whether an economy eventually grows again. It is whether, after history has happened, the old path still exists to be returned to.