Estimation of ill-conditioned models using penalized sums of squares of the residuals

TL;DR

This paper introduces a penalized estimation method for ill-conditioned econometric models that improves numerical stability and inference by shrinking estimates towards simple regressions rather than zero.

Contribution

It demonstrates that the proposed penalized estimator generalizes the ridge estimator and offers superior properties for inference and stability in econometric modeling.

Findings

The penalized estimator encompasses the ridge estimator as a special case.

It provides better bootstrap inference for coefficients.

It enhances numerical stability of estimates.

Abstract

This paper analyzes the estimation of econometric models by penalizing the sum of squares of the residuals with a factor that makes the model estimates approximate those that would be obtained when considering the possible simple regressions between the dependent variable of the econometric model and each of its independent variables. It is shown that the ridge estimator is a particular case of the penalized estimator obtained, which, upon analysis of its main characteristics, presents better properties than the ridge especially in reference to the individual boostrap inference of the coefficients of the model and the numerical stability of the estimates obtained. This improvement is due to the fact that instead of shrinking the estimator towards zero, the estimator shrinks towards the estimates of the coefficients of the simple regressions discussed above.