Extending the Boundaries of Automatic Selection: Non-linear Models

Econometric modelling using automatic algorithms such as PcGets (Hendry and Krolzig, 2001) and Autometrics (Doornik, 2007) has recently become popular. This paper considers automatic model selection when there is non-linearity inherent in the process. The strategy uses a new test for nonlinearity, specifies the general model using polynomials if linearity is rejected, and undertakes a general-to-specific reduction. Non-linear modelling poses a number of problems, including collinearity generated by non-linear transformations, extreme observations leading to non-normal (fat-tailed) distributions, and often more variables than observations from general expansions approximating the non-linearity, yet one must avoid excess retention of irrelevant variables. Solutions to all of these problems are proposed. A returns-to-education empirical application demonstrates the feasibility of the non-linear automatic model selection algorithm. JEL classification: C51; C22; C87