📝 SummarXiv

Abstract

This paper addresses the longstanding challenge of analyzing the mean squared error (MSE) of ridge-type estimators in nonlinear models, including duration, Poisson, and multinomial choice models, where theoretical results have been scarce. Using a finite-sample approximation technique from the econometrics literature, we derive new results showing that the generalized ridge maximum likelihood estimator (MLE) with a sufficiently small penalty achieves lower finite-sample MSE for both estimation and prediction than the conventional MLE, regardless of whether the hypotheses incorporated in the penalty are valid. A key theoretical contribution is to demonstrate that generalized ridge estimators generate a variance-bias trade-off in the first-order MSE of nonlinear likelihood-based models -- a feature absent for the conventional MLE -- which enables ridge-type estimators to attain smaller MSE when the penalty is properly selected. Extensive simulations and an empirical application to the estimation of marginal mean and quantile treatment effects further confirm the superior performance and practical relevance of the proposed method.