Informativeness under Model Uncertainty: Shadow Prices and Ridge Penalties
Abstract
We develop inference under model uncertainty due to weak, noisy, multiple candidate restrictions and theories, and nuisance control covariates. A unified framework is given with degrees of misspecification and corresponding shadow prices, based on a Lagrangian constrained optimization approach, and a datadriven tolerance parameter selected via a Steintype (shrinkage) risk criterion. A debiasing step is based on KarushKuhnTucker conditions. We introduce individual shadow prices (ISP) for different restrictions to measure empirical relevance and propose a plateau rule to separate signal from noise. We establish consistency and asymptotic normality of the estimators and characterize the ISP. Simulations and an application to a Solow growth model illustrate the methods practical usefulness.
Cite
@article{arxiv.2604.15571,
title = {Informativeness under Model Uncertainty: Shadow Prices and Ridge Penalties},
author = {Jieun Lee and Esfandiar Maasoumi},
journal= {arXiv preprint arXiv:2604.15571},
year = {2026}
}