Introduction to Econometrics
Chapter 7 : Nonlinear and logarithmic regression model
By Lund University
So far, the dependent variable has been modeled as a linear function of the explanatory variables plus an additive error term. In this section, we will look at nonlinear models. First, we look at general non-linear models. Then, we focus on the most important class of non-linear models, logarithmic 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-linearity. 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
Logarithmic regression models
This section is about logarithmic models, specifically the log-log model, the loglinear model and a model where we only log (some of) the x variables. We show that in the log-log model, the beta parameters will be elasticities.