Finite-Sample Properties of Generalized Ridge Estimators for Nonlinear Models

Abstract: Parameter estimation can result in substantial mean squared error (MSE), even when consistent estimators are used and the sample size is large. This paper addresses the longstanding statistical challenge of analyzing the bias and MSE of ridge-type estimators in nonlinear models, including duration, Poisson, and multinomial choice models, where theoretical results have been scarce. Employing a finite-sample approximation technique developed in the econometrics literature, this study derives new theoretical results showing that the generalized ridge maximum likelihood estimator (MLE) achieves lower finite-sample MSE than the conventional MLE across a broad class of nonlinear models. Importantly, the analysis extends beyond parameter estimation to model-based prediction, demonstrating that the generalized ridge estimator improves predictive accuracy relative to the generic MLE for sufficiently small penalty terms, regardless of the validity of the incorporated hypotheses. Extensive simulation studies and an empirical application involving the estimation of marginal mean and quantile treatment effects further support the superior performance and practical applicability of the proposed method.