Informativeness under Model Uncertainty: Shadow Prices and Ridge Penalties

TL;DR

This paper introduces a unified inference framework under model uncertainty, utilizing shadow prices and ridge penalties to handle weak or noisy restrictions, with practical validation through simulations and an economic growth application.

Contribution

It develops a novel approach combining shadow prices, ridge penalties, and a data-driven tolerance for inference under model uncertainty, including a plateau rule for signal detection.

Findings

Establishes consistency and asymptotic normality of estimators.

Introduces individual shadow prices (ISP) for restriction relevance.

Demonstrates practical usefulness via simulations and an economic application.

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.