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Informativeness under Model Uncertainty: Shadow Prices and Ridge Penalties

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  • Jieun Lee
  • Esfandiar Maasoumi

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 data$-$driven tolerance parameter selected via a Stein$-$type (shrinkage) risk criterion. A debiasing step is based on Karush$-$Kuhn$-$Tucker 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 method$^{\prime}$s practical usefulness.

Suggested Citation

  • Jieun Lee & Esfandiar Maasoumi, 2026. "Informativeness under Model Uncertainty: Shadow Prices and Ridge Penalties," Papers 2604.15571, arXiv.org.
    • Handle: RePEc:arx:papers:2604.15571
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