Generalizing Solow’s Growth Model

Providing the mainstream literature’s basic explanation for macrodynamics is Robert Solow’s (1956, 1957) neoclassical growth theory. His model is recognized as one of the most important of the 20^th century, breaking the Harrod-Domar mechanical link between saving and growth by intuitively introducing technological change into macrodynamics.

Basic model. Recall last week’s blog. The Lewis two-venue theory, comprising a large-establishment venue (LEV) denoted by _J and a small-establishment venue (SEV) denoted by ҡ, generates nonstationary growth in labor productivity via accumulating capital and the transfer of workers to more productive jobs. Solow’s adds technical change to those sources of growth. In its Harrod-neutral formulation, the enriched model is: X_J(t)=ƒ(K_J(t),A(t)H_J(t)), where X denotes real output, K is capital, H is labor hours, and  A represents technology. (In their lowercase versions, the variables represent rates of change.) Solow (2000, p.103) later expanded the definition of A to include “… worker skills and attitudes toward work, managerial and administrative habits, interpersonal attitudes, social norms and institutions, and no doubt many other hard and soft characteristics of the economic and social environment.” The variable A looks made for the GEM Project but more on that below.

Solow posits constant returns to scale, diminishing returns to factor proportions, and market-centric labor pricing and derives the economy’s macrodynamic path: x_J(t)≅a(t)–SK(t)k_J(t)–S_Ḥ(t)h_J(t) and a(t)≅x_J(t)–SK(t)k_J(t)– S_Ḥ(t)h_J(t), where a is the rate of change of the shift factor typically interpreted as technical change, SK is the share of total income paid to capital, and S_Ḥ is labor’s income share. The Solow model has been extensively used in estimation exercises, which were themselves for some time a growth industry for macroeconomists.

The neoclassical growth theory was recognized almost immediately as an important advance in macrodynamic thinking, replacing “knife-edge” growth paths with more robust steady-state paths motivated by capital accumulation and technological change. The approach showcased the longstanding “liberal” economic agenda of free markets, free trade, and sound money. Solow’s 1987 Nobel-Prize citation emphasized his provision of “a framework within which modern macroeconomic theory can be structured”, and his model continues to generate broad, understandable appeal as a guide to aggregate analysis.

The simple model, however, notably stumbles when asked to account for some notable phenomena, including the mid-19^th century growth acceleration often referred to as the Great Fact. (See Chapter 1.) Limitations of the Solow model are centrally rooted in its construction within a market-centric framework. Coherent single-venue general-equilibrium (SVGE) modeling provides no room for the increasing returns to scale or two-venue labor transfer that combined to motivate the jump in global living-standards growth that began a century and a half ago. Two-venue general-equilibrium (TVGE) modeling, by contrast, provides the heterogeneous marketplace and workplace venues of rational price-mediated exchange needed to accommodate increasing returns and Lewis inter-sectoral labor transfer.

TVGE version. A strength of the Solow framework is its remarkable versatility, enabling relevance well beyond exchange-restricted SVGE analysis. Most critically, substituting Z_J from the generalized-exchange model class featured in the GEM Project into the core equation, more explicitly motivating the “effectiveness of labor” and the role of pure profit. Solow production consistent with TVGE cyclical and trend modeling: X_J(t)=ƒ(K_J(t),A_J(t)Z_J(t)H_J(t)). A is now understood to reflect the technical efficiency of labor, once the influence of capital-labor intensity is eliminated. The product of A and Z measures general worker effectiveness and is the vehicle through which optimizing employees and employers introduce into the Solow framework microfounded meaningful wage rigidities. MWR combine with adverse nominal disturbances to induce the periodic involuntary job and income loss that shows up in the cyclicality of the Solow residual. (See Chapters 2 and 3.) The MWR channel along with capital investment, technological change, scale economies, and inter-venue labor transfer (the last three also reflected in estimation residuals) enables intuitive, policy-relevant modeling of macro cycles and trend growth. Properly generalizing labor input (H=E/Z), where E denotes cooperative labor input that is always in 1:1 correspondence with production, endows the iconic model with analytic range beyond Solow’s original aspirations (2001, p.19): “… it was clear from the very beginning what I thought [the neoclassical growth model] did not apply to, namely short-run fluctuations in aggregate output and employment, what used to be called the business cycle…. In those days I thought growth theory was about the supply side of the economy, whereas the business cycle was mostly to be analyzed in terms of changes in aggregate demand.”

The generalized-exchange version of the Solow theory is important, explaining business cycles induced by nominal demand disturbances as well as nonstationary labor-productivity dynamics. As hoped by RBC theorists, it provides a coherent analytic framework relevant to a broad range of important events, including the late-19^th century upward shift in living-standards growth associated with the Second Industrial Revolution, the 1930s depression, the 1970s stagflation, the extraordinary growth in central and east Asia beginning toward the end of the 20^th century, and the propagation of financial crises that have characterized the early 21^st century. (See Chapter 10.)

Putting the analytic strands together, Solow’s focus on technical change provides one of the most important insights in the history of macroeconomics. Beginning in the 19^th century, the broad reorganization of the global economy featuring large bureaucratic corporations generated the acceleration in multifactor productivity growth that broke the world out of millennia of living-standard stagnation, providing a central role for Lewis’s inter-venue labor transfer and Solow’s technological advance. The generalized-exchange integration of both growth models also reveals that the fundamental transformation of the production landscape created the rational MWR Channel that empowered the cyclical importance of nominal demand disturbances. Macroeconomics was henceforth tasked with making sense out of variable periods of persisting aggregate instability, producing substantial welfare loss, as well as time-varying trend growth. Market-centric theorists, mired in their inability to coherently suppress wage recontracting and derive involuntary job loss, have not been up to that challenge.

Blog Type: Wonkish Saint Joseph, Michigan