# Use and Abuse of the Solow Residual

This is the last of three of weekly blogs on how the GEM Project informs growth modeling.  It looks at the famous Solow residual (SR), perhaps the most used and abused residual time-series in the history of macroeconomics. Getting ahead of the story, here’s what has always troubled me. I find it difficult to believe that the SR misuse was not a deliberate attempt to mislead in a Ptolemaic effort to prop up a model class that inherently lacks much stabilization relevance.

The SR definition is indicative of problems to come. Recall Solow’s aggregate production function, in its Cobb-Douglas simplification with a Hicks-neutral productivity term: X(t)=A(t)H(t)bK(t)1-b such that X denotes total output, H is total hours, K is capital, and A represents multifactor productivity. Once rearranged to feature output per labor hour, it became the key formula in the large literature on growth accounting: x(t)–h(t)≅((1–b)/b)(k(t)–x(t))+(1/b)a(t), where lower-case variables denote rates of change. In empirical exercises, a is typically assumed to represent technological change and to be measured by the estimation error, the Solow residual. Moses Abramovitz was probably more on target when he called the SR a “measure of our ignorance”.

Use of the residual. Fitting the highly simplified model to U.S. data since 1874 suggests that the trend improvement of multifactor productivity accounts for roughly half of the overall gain in  living-standards. Attributing a substantial part of that gain to technological change, especially in a period that includes the Second Industrial Revolution and the advent of large corporations, is plausible. (See Chapter 1.) But it is not the whole story. In an example from the generalized-exchange model, growth-accounting residuals must also be influenced by Lewis transfer, nonstationary output-per-hour gains resulting from the movement of labor from low- to high-productivity jobs. Transfer exerted an important influence on productivity advance in the early-phase of the Second Industrial Revolution.

The GEM Project expands Lewis transfer in post turning-point economies to include two-way labor flows between venues. An notable example of rational reverse flow is the significant U.S. job downsizing that characterized the 1980s and that the GEM Project associates with the sharply increased unit labor costs experienced in large establishments occurring during stagflation decade. (See Chapter 4.) Growth-accounting results are consistent with the relative contraction of high-productivity employment; from 1979 to 1990, as output-per-hour growth decelerated to 1.6% annually (well below the 2.5% average from1948 to 1998), with almost all the decrease attributable to the slowdown in multifactor-productivity (0.5% compared to its 50-year average of 1.4%). Mainstream market-centric analysis of the downsizing period has problematically concentrated on identifying some general technological regress occurring in the 1980s.

Abuse of the residual. Another SR artifact of coherent market-centric analysis, concerning macro stability and proving more consequential in the debate on the proper design of policymaking, has been exploited by RBC theorists. They used the capacity of Solow residuals to closely track stationary as well as nonstationary behavior of labor productivity to support the argument that business cycles are induced by variations in technology. If valid, that interpretation helps reestablish the classical dichotomy and fatally discredits the discretionary management of nominal demand. Fortunately for plausible policymaking, the generalized-exchange version of Solow’s growth model, outlined in last week’s blog and more fulsomely in Chapter 3, provides a much different explanation for the stationary behavior of Solow’s residuals. The GEM analysis is much more consistent with the evidence, practitioner testimony, intuition, micro-macro coherency, and Occam’s razor. Continuous-equilibrium meaningful wage rigidity (MWR) interacts with fluctuations in nominal demand, generating involuntary job loss and business cycles that are much more recognizable than those produced by periodic technological regress.

Most responsible for the abuse of the Solow residual is Finn Kydland and Edward Prescott’s 1982 article (“Time to Build and Aggregate Fluctuations”) that introduced their prototype RBC model. In it, they assert that the cyclical behavior of the Solow residual ratifies the practical use of the real business cycle approach. Technological advance and regress cause recognizable macro fluctuations, eliminating the need for money in the explanation of cycles and for discretionary action in the amelioration of recessions. Their SR use is egregious. Simply because an estimation residual was once named technological change does not mean it adequately represents technological change, especially technical regress at business-cycle frequencies.

In the generalized-exchange model class, fluctuations reflect the rational adjustments that result from the interaction of rational MWR and nominal demand disturbances, making the variance in output and employment Keynesian in nature. The Solow growth model has been easily incorporated into GEM modeling. (See last week’s blog and Chapter 3.) The enriched analysis powerfully explains cyclical movement of unemployment as continuous-equilibrium large-scale market failure. It is best understood as a macro externality that mandates active demand-management intervention by stabilization authorities. That readily recognizable world is far removed from K&P market-centric macrodynamics.

Here’s the rub. You have to be pretty unaware to believe that the cyclical behavior of the Solow residual since the advent of the Second Industrial Revolution is not influenced by the interaction of nominal demand disturbances and wage rigidities, producing a troubling dilemma. Were K&P debilitatingly naïve or did they deliberately mislead, especially as they ambitiously reached for macro-policy relevancy? Moreover, we now know that the K&P claim to optimizing microfoundations is incorrect. The RBC model is constructed on the crucial assumption of convenience that all rational price-mediated exchange occurs in the marketplace. They did not understand that the restriction on exchange has long been the most arbitrary, indefensible free parameter in common use in macro model-building. As a result, K&P have no legitimate claim to micro-macro coherence. The hard fact for modern theorists is that the Early Keynesian Neoclassical Synthesis provides a more promising starting point for the construction of coherent macroeconomics than does the approach implied by the New Neoclassical Synthesis.

Blog Type: Wonkish Saint Joseph, Michigan