The Solow residual is a number describing empirical productivity growth in an economy from year to year and decade to decade. Robert Solow, the Nobel Memorial Prize in Economic Sciences-winning economist, defined rising productivity as rising output with constant capital and labor input. It is a "residual" because it is the part of growth that is not accounted for by measures of capital accumulation or increased labor input. Increased physical throughput – i.e. environmental resources – is specifically excluded from the calculation; thus some portion of the residual can be ascribed to increased physical throughput. The example used is for the intracapital substitution of aluminium fixtures for steel during which the inputs do not alter. This differs in almost every other economic circumstance in which there are many other variables. The Solow residual is procyclical and measures of it are now called the rate of growth of multifactor productivity or total factor productivity, though Solow (1957) did not use these terms.
History In the 1950s, many economists undertook comparative studies of economic growth following World War II reconstruction. Some said that the path to long-term growth was achieved through investment in industry and infrastructure and in moving further and further into capital intensive automated production. Although there was always a concern about diminishing returns to this approach because of equipment depreciation, it was a widespread view of the correct industrial policy to adopt. Many economists pointed to the Soviet command economy as a model of high-growth through tireless re-investment of output in further industrial construction. However, some economists took a different view: they said that greater capital concentrations would yield diminishing returns once the marginal return to capital had equalized with that of labour – and that the apparently rapid growth of economies with high savings rates would be a short-term phenomenon. This analysis suggested that improved labour productivity or total factor technology was the long-run determinant of national growth, and that only under-capitalized countries could grow per-capita income substantially by investing in infrastructure – some of these undercapitalized countries were still recovering from the war and were expected to rapidly develop in this way on a path of convergence with developed nations. The Solow residual is defined as per-capita economic growth above the rate of per-capita capital stock growth, so its detection indicates that there must be some contribution to output other than advances in industrializing the economy. The fact that the measured growth in the standard of living, also known as the ratio of output to labour input, could not be explained entirely by the growth in the capital/labour ratio was a significant finding, and pointed to innovation rather than capital accumulation as a potential path to growth. The 'Solow growth model' is not intended to explain or derive the empirical residual, but rather to demonstrate how it will affect the economy in the long run when imposed on an aggregate model of the macroeconomy exogenously. This model was really a tool for demonstrating the impact of "technology" growth as against "industrial" growth rather than an attempt to understand where either type of growth was coming from. The Solow residual is primarily an observation to explain, rather than predict the outcome of a theoretical analysis. It is a question rather than an answer, and the following equations should not obscure that fact.
As a residual term in the Solow model Solow assumed a very basic model of annual aggregate output over a year (t). He said that the output quantity would be governed by the amount of capital (the infrastructure), the amount of labour (the number of people in the workforce), and the productivity of that labour. He thought that the productivity of labour was the factor driving long-run GDP increases. An example economic model of this form is given below:
Y ( t ) = [ K ( t ) ] α [ A ( t ) L ( t ) ] 1 − α {\displaystyle Y(t)=[K(t)]^{\alpha }[A(t)L(t)]^{1-\alpha }\,}
where:
Y(t) represents the total production in an economy (the GDP) in some year, t. K(t) is capital in the productive economy – which might be measured through the combined value of all companies in a capitalist economy. A(t) represents multifactor productivity (often generalized as "technology"). The change in this figure from A(1960) to A(1980) is the key to estimating the growth in labour 'efficiency' and the Solow residual between 1960 and 1980, for instance. L(t) is labour; this is simply the number of people working, and since growth models are long run models they tend to ignore cyclical unemployment effects, assuming instead that the labour force is a constant fraction of an expanding population. To measure or predict the change in output within this model, the equation above is differentiated in time (t), giving a formula in partial derivatives of the relationships: labour-to-output, capital-to-output, and productivity-to-output, as shown:
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