Estimating Non-Linear Functions with OLS Regression
Posted by Dann on October 10, 2007
In empirical research, you’ll often come across variables that are not related in a linear way. There are methods to estimate non-linear functions, but many involve things far more complicated than OLS regression. Luckily we have a method of estimating non-linear functions using OLS!
A prime example of a non-linear function in economics is the Cobb-Douglas production function (CDPF). Below you’ll see the CDPF and subsequently the resulting form once when take the log of both sides.
Notice how the log-log form now highly resembles our OLS regression equation? Below is another image showing how these results can be interpreted in our OLS regression.
Sometimes this way of estimating non-linear functions will not work very well. There are other methods to estimate non-linear functions, but this OLS-based method should be sufficient to describe most non-linear relationships.
(More information on the Cobb-Douglas Production Function can be found here and some good working examples not related to regression can be found here)
