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.
In the 1950s, many economists[citation needed] undertook comparative studies of economic growth following World War II reconstruction.
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.
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[citation needed] 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 primarily an observation to explain, rather than predict the outcome of a theoretical analysis.
An example economic model of this form is given below:[1] where: 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: Observe: Similarly: Therefore: The growth factor in the economy is a proportion of the output last year, which is given (assuming small changes year-on-year) by dividing both sides of this equation by the output, Y: The first two terms on the right hand side of this equation are the proportional changes in capital and labour year-on-year, and the left hand side is the proportional output change.
The remaining term on the right, giving the effect of productivity improvements on GDP is defined as the Solow residual: The residual, SR(t) is that part of growth not explicable by measurable changes in the amount of capital, K, and the number of workers, L. If output, capital, and labour all double every twenty years the residual will be zero, but in general it is higher than this: output goes up faster than growth in the input factors.
The above relation gives a very simplified picture of the economy in a single year; what growth theory econometrics does is to look at a sequence of years to find a statistically significant pattern in the changes of the variables, and perhaps identify the existence and value of the "Solow residual".
The most basic technique for doing this is to assume constant rates of change in all the variables (obscured by noise), and regress on the data to find the best estimate of these rates in the historical data available (using an ordinary least squares regression).
as: Mankiw, Romer, and Weil augmented the Solow-Swan model with a human capital term.
[3] However, Thomas Piketty's famous study of inequality in 2014, using a version of the Solow model, argued that a stable, relatively low profit share of national income was largely a twentieth century phenomenon.
It has been suggested that this will tend to make it harder to gain experience with the available technologies and that a zero Solow residual in these cases actually indicates rising labour productivity.