Econometrics HT 18

Chapter 19 : Nonlinear regression models

By Lund University

An introduction to non-linear models.

Nonlinear regression models

It turns out that we have two types of linearity in the linear regression model. First, the dependent variable is linear in the explanatory variables. Second, the dependent variable is linear in the beta parameters. Therefore, we can consider two types of non-linearities. In this section, we will focus mainly on nonlinearity in the explanatory variables retaining linearity in the parameters. Choosing between a linear regression model and a model nonlinear in the explanatory variables can be difficult. To help us in this choice, we introduce Ramsey’s RESET test.

Linear in parameters and/or linear in data

Linear regression models which are nonlinear in data

Ramsey’s RESET test

Incorrect linear model

Linear in data / parameters

Marginal effect for a nonlinear model

Fitting a quadratic function

Marginal effects

Transforming a model into a linear model

Testing for nonlinearities