Solow Residual - Regression Analysis and The Solow Residual

Regression Analysis and The Solow Residual

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). Economists always do this by first taking the natural log of their equation (to separate out the variables on the right-hand-side of the equation); logging both sides of this production function produces a simple linear regression with an error term, :

A constant growth factor implies exponential growth in the above variables, so differentiating gives a linear relationship between the growth factors which can be deduced in a simple regression.

In regression analysis, the equation one would estimate is

where:

y is (log) output, ln(Y)

k is capital, ln(K)

ℓ is labour, ln(L)

C can be interpreted as the co-efficient on log(A) – the rate of technological change – (1 − α).

Given the form of the regression equation, we can interpret the coefficients as elasticities.