Solow residual
Source: econterms

A measure of the change in total factor productivity in a Solow growth model. This is a way of doing growth accounting empirically either for an industry or more commonly for a macroeconomy. Formally, roughly following Hornstein and Krusell (1996):

Suppose that in year t an economy produces output quantity yt with exactly two inputs: capital quantity kt and labor quantity lt. Assume perfectly competitive markets and that production has constant returns to scale. Let capital's share of income be fixed over time and denoted a. Then the change in total factor productivity between period t and period t+1, which is the Solow residual, is defined by:

Solow residual = (log TFPt+1) - (log TFPt)

= (log yt+1) - (log yt)
- a(log kt+1) - a(log kt)
- (1-a)(log lt+1) - (1-a)(log lt)
 Analogous definitions exist for more complicated models (with other factors besides capital and labor) or on an industry-by-industry basis, or with capital's share varying by time or by industry.

The equation may look daunting but the derivations are not difficult and students are sometimes asked to practice them until they are routine. Hulten (2000) says about the residual that:
-- it measures shifts in the implicit aggregate production function.
-- it is a nonparametric index number which measures that shift in a computation that uses prices to measure marginal products.
-- the factors causing the measured shift include technical innovation, organizational and institutional changes, fluctuations in demand, changes in factor shares (where factors are capital, labor, and sometimes measures of energy use, materials use, and purchased services use), and measurement errors.

From an informal discussion by this editor, it looks like the residual contains these empirical factors, among others: public goods like highways; externalities from networks like the Internet; some externalities and losses of capital services from disasters like September 11; theft; shirking; and technical / technological change.