Temporal single-system interpretation
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The temporal single-system interpretation (TSSI) of Karl Marx's value theory emerged in the early 1980s in response to renewed allegations that his theory was "riven with internal inconsistencies," and that it must therefore be rejected or corrected. The inconsistency allegations had been a prominent feature of Marxian economics and the debate surrounding it since the 1970s. Andrew Kliman argues that, since internally inconsistent theories cannot possibly be right, the inconsistency charges serve to legitimate the suppression of Marx's critique of political economy and current-day research based upon it, as well as the "correction" of Marx's inconsistencies.
Proponents of the temporal-single system interpretation of Marx's value theory claim that the supposed inconsistencies are actually the result of misinterpretation; they argue that when Marx's theory is understood as "temporal" and "single-system," the internal inconsistencies disappear. In a recent survey of the debate, a proponent of the TSSI concludes that "the proofs of inconsistency are no longer defended; the entire case against Marx has been reduced to the interpretive issue."
Critics of TSSI, including David Laibman (see Criticism section, below), argue that Marx intended to present what they characterize as "a structurally consistent" model of value formation in a capitalist economy with competitive profit-rate equalization. They claim that Marx's formulations fail to do this. But they claim that what they characterize as his fundamental insights can be revealed, and extended, by means of models and concepts that emerged after his time. Instead of trying to defend the consistency of Marx's original statements, non-TSSI Marxist theorists pursue what they characterize as ever-more effective versions of what they claim to be the core theory. They also claim that they believe that Marx himself would have done this.
Scope of TSSI Research
Among the main issues addressed by the TSSI are Marx's law of the tendency of the rate of profit to fall and the transformation of commodity values into prices of production––the so-called transformation problem––in Das Kapital Volume 3. TSSI authors have also challenged the "Fundamental Marxian theorem," which supposedly showed that Marx's value theory is unnecessary in order to arrive at his conclusion that exploitation of workers is the unique source of profit under capitalism.
Other research informed by the TSSI includes studies of the impact of European economic integration, theoretical and empirical analysis of economic crisis (see Crisis), critiques of the static equilibrium methodology widely employed in economics (mainstream as well as Sraffian and Marxian), and challenges to the statistical claim that industry-level values and prices are strongly correlated. Drawing on their experiences in the controversy over Marx's value theory, some proponents of the TSSI have also been active in the movement for pluralism in economics, and they have critiqued, and argued for the reform of, the interpretive methods employed in Marxian economics.
Significance of "Temporal" and "Single-system"
The words "temporal" and "single-system" in the title of the TSSI refer to the two key differences between it and the interpretation of Marx's value theory derived from Ladislaus von Bortkiewicz that at one time dominated academic Marxist economics.
According to the Bortkiewiczian interpretation, prices and values of inputs into the production process are, in Marx's theory, determined simultaneously with the prices and values of the outputs that later emerge from the production process. Thus, inputs' prices (or values) and outputs' prices (or values) are necessarily equal. In contrast, the TSSI is "temporal" or non-simultaneous, holding that prices (and values) of inputs and outputs in Marx's theory need not be (and generally are not) equal.
Second, according to the Bortkiewiczian interpretation of Marx's value theory, values and prices constitute two distinct and independent "systems." With respect to relative magnitudes, prices do not depend on values, and values do not depend on prices. Prices of outputs depend on the prices of the inputs used to produce them, while values of outputs depend on the values of the inputs used to produce them. In contrast, the TSSI is a "single-system" interpretation since it holds that, in Marx's theory, (a) prices of outputs depend in the aggregate on the so-called "value rate of profit" (the ratio of surplus-value to capital invested), while (b) businesses' investments of capital value, and thus the values of the outputs produced, depend partly on the prices of the inputs acquired by means of these investments. Value and price are therefore determined interdependently, though they remain distinct.
Proofs of Marx’s inconsistencies
"Okishio's theorem," a result produced by the Japanese Marxian economist Nobuo Okishio in 1961, was widely regarded as having disproved Marx's law of the tendency of the rate of profit to fall, but TSSI authors have shown that Marx's rate of profit (as they interpret it) can fall in circumstances in which Okishio's theorem says that "the" rate of profit cannot fall. Thus, even Duncan K. Foley, a prominent critic of the TSSI, acknowledges that
"I understand [Alan] Freeman and [Andrew] Kliman to be arguing that Okishio’s theorem as literally stated is wrong because it is possible for the money and labor rates of profit to fall under the circumstances specified in its hypotheses. I accept their examples as establishing this possibility.”
In 1906-07, Ladislaus von Bortkiewicz claimed to prove that Marx's account of "the transformation of commodity values into prices of production" (i.e., prices that allow businesses to obtain an average rate of return on their capital investments) was internally inconsistent. "Correcting" the inconsistency, Bortkiewicz produced results that seriously call into question Marx's theory that prices and profits are determined, in the aggregate, by the production of value and surplus-value: the "price rate of profit" no longer equals the "value rate of profit," and the sum of prices diverges from the sum of values. However, proponents of the TSSI claim to have disproved Bortkiewicz's position. Although no critic has successfully refuted this claim, first put forward in 1988, many Marxist economists still decline to accept it.
When Marx's theory is understood in accordance with the TSSI, rather than in accordance with Bortkiewicz's interpretation, moreover, the results of his transformation account re-emerge as internally consistent; price and value magnitudes are indeed equal in the aggregate. These equalities also re-emerge under other––atemporal––single-system interpretations. Yet under the atemporal interpretations, Marx's falling-rate-of-profit theory and other aspects of his value theory still appear to be internally inconsistent. In order for his theories to be fully acquitted of charges of inconsistency and error, he must be interpreted as having had a temporal conception of value and price determination.
Critics of the TSSI have characterized it as an orthodoxy which asserts that "Marx made no errors." For instance, David Laibman charges that its proponents are "New Orthodox Marxists" who
"assert that Marx's formulations, in both the theory of value and the analysis of capitalist accumulation and crisis, are literally and completely correct; that Marx made no errors . . . ."
Proponents of the TSSI contend that these allegations are false:
“We have never said that Marx’s contested insights are necessarily true . . . . We simply say the claims that his value theory is necessarily wrong, because it is logically invalid, are false.”
Similarly, Andrew Kliman distinguishes between internal consistency on the one hand, and truth or correctness on the other, at least nine different times. For instance, he writes that the TSSI's ability to eliminate the apparent inconsistencies in Marx's value theory does not imply
"that Marx’s theoretical conclusions are necessarily correct. It does imply, however, that empirical investigation is needed in order to determine whether they are correct or not. There is no justification for disqualifying his theories a priori, on logical grounds."
Some critics, however, claim that they find this response inadequate. They claim that they find it inadequate because they claim that the following points are relevant to the issue of whether the TSSI critics speak the truth when they charge that the TSSI is an orthodoxy which asserts that Marx made no errors:
People who claim to be followers and developers of Marx theory of value claim that the earliest formulations from the 1850s, as presented in "Capital," Vol. III, sought to model what they characterize as a "structurally consistent presentation" of value formation in a capitalist economy with competitive profit-rate equalization. They claim that it did not model this successfully. They claim that Marx's fundamental insights can be revealed, and extended, by means of models and concepts that emerged after his time. Instead of trying to defend the consistency of Marx's original statements, these non-TSSI Marxist theorists pursue what they claim are ever-more effective versions of what they characterize as the core theory. They claim that that Marx himself would have done this. Moreover, these non-TSSI theorists allege that defenders of the TSSI ignore what the critics claim are their central arguments. First, the critics allege that the "consistency" that they claim for Marx's work is achieved at the expense of any theoretical coherence. Secondly, these critics of the TSSI allege that, if input values differ from output values, each being determined by the conditions of a single "temporal" moment that the critics characterize as fortuitous, they claim that value is reduced to a mere empirical description, without structure or role in revealing what they characterize as the inner properties of capitalist social relations. Second, the critics characterize the TSSI's efforts to defend the logical coherence TSSI's of Marx's law of the falling rate of profit as a "presumed defense," resting on a distinction between a (rising) "material" or "simultaneous" rate of profit and a (falling) "value" rate of profit. The critics allege that they have shown this distinction to be invalid since analysis of the TSSI numerical examples reveals that the temporal value rate of profit either ultimately follows the course of the material rate, or diverges from it: “If the material rate rises to an asymptote, the value rate either falls to an asymptote, or first falls and then rises to an asymptote permanently below the material rate.”. The TSSI construction, the critics claim, fails to address what they characterize as "the complex determinants of the level and trend of the rate of profit in capitalist economies."
- See M. C. Howard and J. E. King, 1992, A History of Marxian Economics: Volume II, 1929–1990. Princeton, NJ: Princeton Univ. Press.
- Kliman states that "Marx’s value theory would be necessarily wrong if it were internally inconsistent. Internally inconsistent theories may be appealing, intuitively plausible and even obvious, and consistent with all available empirical evidence––but they cannot be right. It is necessary to reject them or correct them. Thus the alleged proofs of inconsistency trump all other considerations, disqualifying Marx’s theory at the starting gate. By doing so, they provide the principal justification for the suppression of this theory as well as the suppression of, and the denial of resources needed to carry out, present-day research based upon it. This greatly inhibits its further development. So does the very charge of inconsistency. What person of intellectual integrity would want to join a research program founded on (what she believes to be) a theory that is internally inconsistent and therefore false?" (Andrew Kliman, Reclaiming Marx's "Capital": A Refutation of the Myth of Inconsistency, Lanham, MD: Lexington Books, 2007, p. 3, emphasis in original). The connection between the inconsistency allegations and the lack of study of Marx’s theories was argued further by John Cassidy ("The Return of Karl Marx," The New Yorker, Oct. 20 & 27, 1997, p. 252): "His mathematical model of the economy, which depended on the idea that labor is the source of all value, was riven with internal inconsistencies and is rarely studied these days."
- Andrew Kliman, Reclaiming Marx's "Capital", Lanham, MD: Lexington Books, p. 208, emphases in original.
- Duncan K. Foley, "Response to Freeman and Kliman," Research in Political Economy, Vol. 18, 2000, p. 282.
- David Laibman, "Rhetoric and Substance in Value Theory: An appraisal of the new orthodox Marxism," in Alan Freeman, Andrew Kliman, and Julian Wells (eds.), The New Value Controversy and the Foundations of Economics (Cheltenham, UK: Edward Elgar), 2000, p. 10; Andrew Kliman, Reclaiming Marx's "Capital", pp. 148-52.
- David Laibman, "Rhetoric and Substance in Value Theory: An appraisal of the new orthodox Marxism." In Alan Freeman, Andrew Kliman, and Julian Wells, The New Value Controversy and the Foundations of Economics, (Cheltenham, UK: Edward Elgar, 2004, p. 1, emphases in original.
- Roberto Veneziani, "The Temporal Single-System Interpretation of Marx’s Economics: A critical evaluation," Metroeconomica, Vol. 55, No. 1, 2004, p. 97, emphasis in original.
- Alan Freeman and Andrew Kliman, "Two Concepts of Value, Two Rates of Profit, Two Laws of Motion," Research in Political Economy Vol. 18, 2000, p. 260, emphasis in original.
- Andrew Kliman, Reclaiming Marx's "Capital", p. xiii.
- See Gary Mongiovi, "Vulgar Economy in Marxian Garb: A Critique of Temporal Single-System Marxism," *Review of Radical Political Economics*, 34 (2002), pp. 393-416; Roberto Veneziani, "Dynamics, Disequiilibrium and Marxian Economics: A Formal Analysis of Temporal Single-System Marxism," *Review of Radical Political Economics*, 37 (2005), pp. 517-529.
- David Laibman, Research in Political Economy, 2000; page 274
- Duncan Foley, "Review of Carchedi and Freeman (eds.), Marx and Non-Equilibrium Economics" 
- Freeman, Alan and Guglielmo Carchedi (eds.). 1996. Marx and Non-Equilibrium Economics. Cheltenham, UK: Edward Elgar. 
- International Working Group on Value Theory website 
- Kliman, Andrew. 2007. Reclaiming Marx's Capital: A Refutation of the Myth of Inconsistency. Lanham, MD: Lexington Books. 
- Kliman, Andrew. writings on website 
- Laibman, David. 1999. “The Okishio Theorem and Its Critics: Historical Cost Vs. Replacement Cost,” Research in Political Economy, Vol. 17, pp. 207–227
- Laibman, David. 2000. “Rhetoric and Substance in Value Theory: An Appraisal of the New Orthodox Marxism,” Science & Society, Fall, pp. 310–332; Also in The New Value Controversy and the Foundations of Economics, ed. Alan Freeman, Andrew Kliman, and Julian Wells, Edward Elgar, 2004
- Laibman, David. 2002. “Value and the Quest for the Core of Capitalism,” Review of Radical Political Economics, 34:2 (Spring), pp. 159–178
- Mandel, Ernest and Alan Freeman (eds.), 1984. Ricardo, Marx, Sraffa: The Langston Memorial Volume. London: Verso.
- Research in Political Economy, Vol. 17, 2000. 
- Research in Political Economy, Vol. 18, 2000.