Alternatives to simple regression in Stata
In this post we looked at dependence of EARNINGS on S (years of schooling). In the end I suggested to think about possible variations of the model. Specifically, could the dependence be nonlinear? We consider two answers to this question.
This name is used for the quadratic dependence of the dependent variable on the independent variable. For our variables the dependence is
Note that the dependence on S is quadratic but the right-hand side is linear in the parameters, so we still are in the realm of linear regression. Video 1 shows how to run this regression.
The general way to write this model is
The beauty and power of nonparametric regression consists in the fact that we don't need to specify the functional form of dependence of on . Therefore there are no parameters to interpret, there is only the fitted curve. There is also the estimated equation of the nonlinear dependence, which is too complex to consider here. I already illustrated the difference between parametric and nonparametric regression. See in Video 2 how to run nonparametric regression in Stata.