Helping a Great Idea: Michael Jensen’s Residual Rent

Residual rent, particularly when used in explaining income distribution in highly specialized economies, is a great, albeit unappreciated, idea in economic theory. Consider two facts. First, useful macroeconomics require evidence-consistent modeling of factor-income shares. Second, such modeling is inconsistent with mainstream New Keynesian (NK) market-centric general-equilibrium analysis. The enduring, elegant textbook Wicksell-Wicksteed approach has, for more than a hundred years, been badly aligned with actual economic behavior.

Old Idea

Knut Wicksell and Philip Wicksteed were among the great 19^th-century theorists who pioneered marginal analysis, transforming how economics is done. Their focus on optimizing exchange organized by general market-clearing crowded out the surplus-oriented classical analysis, accepted since Ricardo, of distributive shares. The W&W neoclassical Euler-theorem treatment of relative factor incomes constructed within the market-centric (single-venue) general-equilibrium (SVGE) framework pretty much exhausts what modern theorists have to say on the topic. Factor inputs are paid their marginal-product and opportunity cost of time, which exhausts first-degree homogeneous production. The model is part of the apogee of SVGE welfare analysis, providing ethical justification for the market distribution of income.

In the long aftermath of Walrasian and marginalist revolutions, mainstream macro models have in fits and starts been ever more carefully constructed within the coherent SVGE framework. In the modern consensus version cobbled together by New Classical, RBC and dominant NK theorists, a representative household solves an intertemporal expected-utility maximization problem in the context of competitive markets, rational expectations, and the restriction of optimizing exchange to the marketplace. It follows that the familiar Wicksell-Wicksteed first-degree homogeneous two-factor equation plays a central role in modern thinking:

X=ƒ(H,Ҡ)=H(δX/δH)+Ҡ(δX/δҠ);

XP=HP(δX/δH)+ҠP(δX/δҠ)=W^mH+P_ҠҠ,

where P_Ҡ denotes the market price of physical capital Ҡ, X is production, H is labor hours, P and W^m stand for the market price of output and labor respectively. In the textbook model, neoclassical distribution theory links the technology space and optimizing marketplace exchange, concluding that rational payments to inputs exhaust total revenue. Deep down, however, everybody must know that W&W modeling has long been unsuited to that building-block role.

Despite reservations, mainstream scholars have given in to a Ptolemaic impulse and simply ignore obvious problems rooted in large-scale production that sharply degrade the W&W capacity to describe modern economies. First, factor-market prices calibrated by labor and capital marginal productivities do not exist for large, specialized firms. Second, constant returns to scale are, in many applications, an unacceptable assumption. Third, positing large-firm labor pricing equal to market opportunity cost is broadly inconsistent with the evidence; chronic wage rents exist. Fourth, again contrary to the evidence and deeply damaging in policy-relevant application, W&W imply the non-existence of pure profit.

Only the first problem is sufficiently misunderstood to deserve attention here. Large-scale production, ubiquitous after the Second Industrial Revolution, corrupts the analytic integrity of marginal productivities for both labor hours (δX_j/δH_j) and capital stock (δX_j/δҠ_j), depriving W&W of crucial microfoundations. Generalized rational exchange imposes H_j=Έ_j/Ź_j on labor services, where Έ_j denotes labor input that is in 1:1 technical correspondence with production; δX_j/δΈ_j is not measurable in the marketplace. Meanwhile, large-establishment capital stock (Ҡ_j) is both insufficiently divisible and excessively firm-specific to support Euler-theorem distribution. Given indivisibility, portions of capital cannot be withdrawn in response to relatively small reductions in output, as illustrated by the absence of small-lot capital-stock liquidations in cyclical downturns. What is instead marginally withdrawn, with a cut in output, is some utilization of capital services (Ƙ_j) that are made available by the existing capital stock.

A Great Idea Gets a Helping Hand

Fortunately, a replacement for W&W already exists in the literature: Michael Jensen’s (2000) residual-claims distribution model. If macro theorists truly aspire to evidence-consistent analysis, Jensen must become the go-to model in mainstream textbooks.

Jensen’s revival of Ricardo’s classical residual-rent model can be powerfully restated in the context of the generalization of rational exchange from the marketplace to information-challenged workplaces. The Project’s two-venue model provides a central place for capital services, distinct from capital stock, in the highly specialized technology space. Potential production (X_j^P) is described by a capacity function (X_j^P=ƒ(Ҡ_j)), where X_j^P is increasing in physical capital Ҡ_j and provides an upper bound on output (X_j(t)≤X_j^P(t)). Capital services (Ƙ_j), the measurement of which requires no knowledge of the contemporaneous interest rate, flow from the capital stock (such that Ƙ_j^P(t)=ƒ(Ҡ_j(t), ∆Ƙ_j^P/∆Ҡ_j>0, and Ƙ_j(t)≤Ƙ_j^P(t)). Physical-capital indivisibilities in combination with optimizing workplace exchange must be accommodated in the specification of the relevant production function and factor-income distribution:

X_j(t)=ƒ(Έ_j(t),Ƙ_j(t));

P_j(t)X_j(t)=Wⁿ_jH_j(t)+ř^m(t)Ҡ^r_j(t)+P_j(t),

such that Έ_j(t)=Ź_j(t)H_j(t) and Ƙ_j(t)≤Ƙ_j^P(t)=ƒ(Ҡ_j(t)), while Wⁿ denotes the efficiency wage, ř^m is the market interest rate, P is pure profit, and Ҡ^r is the capital stock net of its sunk component (Ҡ^r=Ҡ–Ҡ^S), making the term (ř^m(t)Ҡ^r(t)) the market opportunity cost of the firm’s capital stock. Generalized-exchange modeling has established that, in highly specialized production, neither labor hours nor capital services can be efficiently priced in the marketplace, breaking down the W&W market mechanism that eliminates pure profit. The GEM Project’s technological space also accommodates increasing returns to scale, further enriching the capacity of the residual-claim distribution model to accommodate critical determinants of economic growth. Given pure profit’s role as a residual claim by owners of sunk capital on firm revenue net of production-related outlays, P_j can be greater than, less than, or equal to zero, providing signals needed for the rational management of production capacity.

The inherent nature of large-scale production disallows reliance on textbook Euler-equation modeling of factor-income distribution in modern applications. It is, therefore, good news is that the GEM Project microfounds distribution rooted in Ricardian rent, building on Jensen’s analysis. His residual-claims model class, easily and coherently introduced into generalized-exchange macroeconomics, solves the debilitating problems cited above. The Project has identified it as one of the important, overlooked theories in the economic literature.

Is the Game Worth the Candle?

Macro theory needs Jensen’s revival of classical residual rent in order to be simultaneously consistent with the evidence and the fundamental tenets of economic theory, i.e., optimization and equilibrium. Microfounding his theory aligns residual rent with the New Neoclassical Synthesis. It is therefore eligible for mainstream consideration, eligible for assuming its place as a building block of stabilization-relevant macroeconomics, and eligible for establishing Michael Jensen as a theorist of consequence. All that is surely candle worthy. Cumulative score: Worth it: 17 (Lewis, Solow, Harris-Todaro, Bernanke, Lucas, Samuelson, Kerr et al, Okun, Hicks, Sraffa, Hayek, Keynes, Burns, Robinson, Modigliani, Phelps, Stiglitz, Jensen). Not worth it: 0. As the reach of GEM theory expands, keep in mind the major objection of mainstream NK theorists to generalized-exchange macroeconomics: Adding a second (workplace) venue of rational exchange is too much work; its benefits are not worth the effort. Is it just me, or is that rationale looking more and more foolish?

Blog Type: New Keynesians Saint Joseph, Michigan