Generalized Additive Models in Business and Economics

Abstract

The paper presents applications of a class of semi-parametric models called generalized additive models (GAMs) to several business and economic datasets. Applications include analysis of wage-education relationship, brand choice, and number of trips to a doctor’s office. The dependent variable may be continuous, categorical or count.  These semi-parametric models are flexible and robust extensions of Logit, Poisson, Negative Binomial and other generalized linear models. The GAMs are represented using penalized regression splines and are estimated by penalized regression methods. The degree of smoothness for the unknown functions in the linear predictor part of the GAM is estimated using cross validation. The GAMs allow us to build a regression surface as a sum of lower-dimensional nonparametric terms circumventing the curse of dimensionality: the slow convergence of an estimator to the true value in high dimensions. For each application studied in the paper, several GAMs are compared and the best model is selected using AIC, UBRE score, deviances, and R-sq (adjusted). The econometric techniques utilized in the paper are widely applicable to the analysis of count, binary response and duration types of data encountered in business and economics.