A method used to determine the contribution of each factor of production to the growth of output. Any growth unexplained by factor growth is viewed as attributable to technical progress. Consider the production function Y = F(A, K, L), where Y is output, A is the level of technical knowledge, K is the quantity of capital employed, and L is the quantity of labour employed. Each of the variables is a function of time, t, so
Y(t) = F(A(t), K(t), L(t).
Differentiation with respect to time givesWhen the markets for factors are competitive the marginal products are equal to factor rewards, so FK = r and FL = w. HenceDividing the time derivative of output by Y yieldsNow define the growth rates of output, capital, and labour by to give
gY = αKgK + αLgL + SR
where αK = rK/Y is the share of capital in national income, αL = wL/Y is the share of labour in national income, and SR is the ‘Solow residual’. The Solow residual is the part of growth that cannot be attributed to growth in the stock of capital or labour. This can be interpreted as the underlying growth in productivity due to technical progress.