🤖 AI Summary
This paper addresses the challenge of welfare analysis for dynamic models in high-dimensional state spaces. Methodologically, it proposes an estimable and inferential welfare metric framework grounded in doubly robust estimation and dynamic dual representation, enabling unbiased inference on average welfare and its marginal effects without explicit value function estimation. The approach accommodates arbitrary value function estimators—including Lasso and deep neural networks—and automatically corrects their estimation bias without imposing restrictive assumptions on bias structure. Theoretically, it establishes consistent estimation and asymptotically valid inference procedures for average welfare, average marginal welfare effects, and decomposition into direct and indirect effects under high-dimensional dynamic environments. Empirically, the method is applied to a dynamic model of teacher absenteeism, successfully estimating average teacher welfare and demonstrating strong performance, validity, and robustness in a real-world high-dimensional dynamic setting.
📝 Abstract
This paper introduces metrics for welfare analysis in dynamic models. We develop estimation and inference for these parameters even in the presence of a high-dimensional state space. Examples of welfare metrics include average welfare, average marginal welfare effects, and welfare decompositions into direct and indirect effects similar to Oaxaca (1973) and Blinder (1973). We derive dual and doubly robust representations of welfare metrics that facilitate debiased inference. For average welfare, the value function does not have to be estimated. In general, debiasing can be applied to any estimator of the value function, including neural nets, random forests, Lasso, boosting, and other high-dimensional methods. In particular, we derive Lasso and Neural Network estimators of the value function and associated dynamic dual representation and establish associated mean square convergence rates for these functions. Debiasing is automatic in the sense that it only requires knowledge of the welfare metric of interest, not the form of bias correction. The proposed methods are applied to estimate a dynamic behavioral model of teacher absenteeism in cite{DHR} and associated average teacher welfare.