Econometric Applications of Adaptive and Semi-Parametric Regression in Social Sciences
The paper presents econometric applications of adaptive and semi-parametric regression in economics and other social sciences focusing on generalized additive models (GAMs). The dependent variable may be continuous, categorical or count. Our semi-parametric models are flexible and robust extensions of Gaussian, Logit, Poisson, Negative Binomial and other generalized linear models. Applications include analysis of wage-education relationship, brand choice, number of trips to a doctor’s office, analysis of anti-social behavior, decision to use a professional tax-preparer, analysis of multiple bids as a consequence of target management resistance, and analysis of patent data on manufacturing firms and data on tort filings. Backfitting and penalized regression spline approaches are employed for implementing GAM. These semi-parametric regression models 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. Alternative techniques, including Multivariate Adaptive Regression Splines (MARS) and regression trees are also employed in these applications and compared with GAMs. For each application studied in the paper, several adaptive and non-adaptive models 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 social sciences.
Keywords - Generalized Linear Models; Semi-parametric Regression; Generalized Additive Models; Regression Trees