Helping Great Economists: Sir Arthur Lewis

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As promised, the first installment of the Helping Great Economists game features a powerful theory from Sir Arthur Lewis, once a Professor of mine at Princeton. His celebrated two-sector growth model, widely believed to be our most useful explanation of how economies break out of subsistence, is shown to be substantially enhanced by the GEM Project’s generalization of rational exchange, which is used to microfound meaningful wage rigidity (MWR).

Original Great Idea

Lewis was awarded an early (1979) Nobel Prize for his iconic macrodynamic analysis (1954, 1958). His two-sector model is simplified by the assumption of venue-specific job and labor homogeneity. Also, workers cannot borrow or save. The distinct production functions in each of the two venues is defined for a given state of technical knowledge. Equilibrium is best understood as a rest period in the space of optimizing decision rules.

Two-sector technical heterogeneity is supported by discrete labor pricing. Behavior in each venue is governed by separate decision rules, constraints, and mechanisms of exchange. Lewis heterogeneities prevent the meaningful aggregation of his economy, producing what Gustav Ranis named “organizational dualism”.

The low-productivity sector is identified as subsistence agriculture; its high-productivity counterpart is the industrial enclave. The former is characterized by tiny production units, primitive production techniques, and the absence of input specificities, consistent with near-subsistence productivity and the absence of saving and capital accumulation. Low-productivity farming produces total real output XS: XS(t)=bSHS(t), where S stands for the subsistence sector, bS is constant labor productivity, and HS denotes venue labor supply. Product pricing (PS) is also constant.

Lewis posited, in the subsistence sector, marginal labor productivity to be zero and market institutions to be poorly developed. In place of the market, labor compensation and employment are determined by equity-based income-sharing arrangements: WS(t)=XS(t)/HS(t). HS is exogenously influenced by subsistence-sector population growth. The real wage (WS) also varies as a result of exogenous factors, such as weather and disease. The core macrodynamics here, focusing on the interaction between labor productivity and the preference to procreate, were originally provided by Malthus. By contrast, the high-productivity venue exploits input specialization and scale, generating total real output XI: XI(t)=bI(t)HI(t), such that bI>bS, where I denotes the industrial venue and bI the sector’s labor-productivity, assumed to be constant along with the product price and the labor-capital ratio.

Within his two-sector framework, Lewis constructs macrodynamics for saving, investment, and sectoral labor transfer that provide insight on how economies break out of subsistence. Industrial enclave profits are posited to be the source of all saving, which is wholly invested in capital accumulation: ΔKI(t)=ΠI(t−1)=PIXI(t-1)–WIHI(t-1), and ΔKI(t)/KI(t−1)=ΠI(t−1)/KI(t−1).There is no depreciation, and the capital price is constant. It follows that the rate of growth of the homogeneous capital stock equals the rate of return on capital.

Lewis further posited that the high-productivity enclave pays labor rents. The wage premium and (point-of-hire) labor homogeneity imply a horizontal labor supply for industrial establishments. Absorption of workers from subsistence farming is determined, given the constant capital-labor ratio, by the time path of the capital stock: ΔHI(t)/HI(t−1)=ΔKI(t)/KI(t–1)=k(t)=ПI(t−1)/KI(t−1). The final source of Lewis-model dynamics is total labor-force (HT) growth, assumed to be a positive constant, c: HT(t)=(1+c)HT(t−1).

An initial condition of Lewis’s macrodynamics is that HI(0)/HT(0) is near zero. A turning point will eventually be reached if  ПI/KI>c. In Lewis’s turning-point hypothesis, once surplus workers have exited the subsistence sector, market forces assert control of labor pricing. Homogeneous wage determination signals the economy’s consolidation into a single labor-market venue. Lewis had little interest in post-turning-point macrodynamics, believing that in such circumstances his two-sector model is no longer applicable.

GEM Helping Hand

GEM Project innovations permit a richer specification of Lewis’s large-establishment, high-productivity venue: XJ(t)=bJ(t)ŹJ(t)HJ(t), such that ŹJ=ΈJ/HJ=ŹnJ and WJ=WnJ>Wm. The variable bJ=XJ/ΈJ denotes the Jth sector’s technical efficiency of labor, as defined in last week’s post. Worker productivity rises over time as a result of physical and human capital accumulation, scale economies, and technological advance. Meanwhile, production in the low-productivity, effective-labor-supervision venue is: XK(t)=bK(t)HK(t), such that ŹK=ΈK/HK, ŹK=ŹɱK and WK=Wm. Output per worker hour is denoted by bK, moving in lockstep with technically-efficient labor productivity (XK/ΈK). The assumption of constant capital-intensity and technology in the Kth venue simplifies the analysis.

Rational workplace exchange extends the relevance of the high-productivity venue’s wage rents beyond Lewis’s turning point, implying that labor supply to that venue  to be elastic. Chronic rents also imply a persisting venue productivity differential. Most critically, generalizing the Lewis model significantly enriches the turning point. Once surplus workers have been eliminated in the subsistence sector, implying the introduction of more robust labor-transfer opportunity costs, market forces replace the underdeveloped market institutions, asserting control over labor pricing in Kth-venue establishments.

Meanwhile, nonmarket labor pricing, minimizing unit labor costs, persists in Jth-venue firms, a result derived from rational behavior in the GEM Project. Post-turning-point economies, with optimizing ZJ playing a crucial role, rationally generate (in addition to chronic labor rents) downward rigid nominal wage over stationary business cycles. Nominal-demand disturbances now play a central role in macro instability, combining with MWR to induce involuntary job-loss dynamics that are consistent with the evidence on high- and low-frequency employment fluctuations. Such instability motivates rational two-way labor transfer between the two venues, along the lines modeled by Harris and Todaro. (Their contribution will be enriched in a later installment of the game.) Meanwhile, trend aggregate labor-productivity and living-standard advance continues to depend on technical change, capital accumulation, and labor transfer to the high-productivity venue. The generalized Lewis model becomes a much more powerful platform for macrodynamic analysis that cannot be ignored in mainstream thinking.

Is the Game Worth the Candle?

Generalized-exchange macroeconomics developed in the GEM Project microfounds Arthur Lewis’s two-venue macrodynamic model. It is admitted into the rational-behavior canon and is extended from subsistence-only relevance to explaining the trend and cyclical behavior of developed market economies. Surely no one can argue that the candle was not well used in extending such a powerful helping hand to an important macroeconomist.

Cumulative score: Worth it: 1, Not worth it: 0. As the score builds, keep in mind the major objection of mainstream theorists to generalized-exchange macroeconomics: Adding a second (workplace) venue of rational exchange is too much work. Its benefits are not worth the effort.

Blog Type: New Keynesians San Miguel de Allende, Mexico


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