Growth accounting

Growth Accounting

Growth accounting is a technique used to identify the contribution of various factors to economic growth and indirectly estimate technological progress. By analyzing the growth rate of total output, it separates the portion due to increases in factor inputs (capital and labor) from the unexplained portion, known as the Solow residual.

Technical Derivation

The production function, which models the relationship between inputs and output, is represented by:

Y = F(A, K, L)

where Y is output, K is capital, L is labor, and A represents technology and other factors affecting productivity.

Differentiating the production function and dividing by Y, we get:

g_Y = (FA/Y)g_A + (rK/Y)g_K + (wL/Y)g_L

where g represents growth rates, F_A is the marginal product of technology, r is the interest rate, and w is the wage rate.

Solow Residual

The Solow residual, which measures technological progress, is calculated as:

SolowResidual = g_Y - α * g_K - (1 - α) * g_L

where α is the share of income attributed to capital.

Interpretation

Growth accounting reveals that technological progress, as represented by the Solow residual, plays a crucial role in economic growth beyond what can be explained by increases in capital and labor. This technique has been widely applied to analyze the growth performance of economies, indicating that technological advancement is essential for sustained economic expansion.