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Welfare Analysis in Dynamic Models

Victor Chernozhukov, Whitney Newey, Vira Semenova

TL;DR

This paper develops identification, estimation, and inference for welfare metrics in dynamic models with high-dimensional state spaces. It introduces dynamic dual and doubly robust representations, along with Lasso and neural-network based estimators for the value function, enabling automatic debiasing and valid inference when nuisance components are high-dimensional or imperfectly specified. It also provides a Oaxaca-Blinder–like decomposition of welfare into direct and indirect effects, and demonstrates substantial welfare misestimation if state heterogeneity is ignored in the DHR teacher-absenteeism application. The framework generalizes to average welfare, group welfare, policy effects, and marginal welfare, employing Neyman orthogonality and cross-fitting to deliver robust, scalable inference for complex dynamic discrete choice and related models.

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.

Welfare Analysis in Dynamic Models

TL;DR

This paper develops identification, estimation, and inference for welfare metrics in dynamic models with high-dimensional state spaces. It introduces dynamic dual and doubly robust representations, along with Lasso and neural-network based estimators for the value function, enabling automatic debiasing and valid inference when nuisance components are high-dimensional or imperfectly specified. It also provides a Oaxaca-Blinder–like decomposition of welfare into direct and indirect effects, and demonstrates substantial welfare misestimation if state heterogeneity is ignored in the DHR teacher-absenteeism application. The framework generalizes to average welfare, group welfare, policy effects, and marginal welfare, employing Neyman orthogonality and cross-fitting to deliver robust, scalable inference for complex dynamic discrete choice and related models.

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.

Paper Structure

This paper contains 31 sections, 19 theorems, 285 equations, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Setup
  4. Decomposition of Differences in Average Welfare
  5. DHR revisited
  6. Dynamic Dual and Doubly Robust Representations of Welfare Metrics
  7. Dynamic Dual Representation
  8. Doubly Robust Representation
  9. Overview of Estimation and Inference
  10. Average Welfare and Related Averages
  11. General case.
  12. Estimation of Value Function and Dynamic Dual Representation
  13. Least Squares Criterion for Value Function
  14. Mean Square Convergence for Lasso Estimator
  15. Least Squares Criterion for Dynamic Dual Representation
  16. ...and 16 more sections

Key Result

Proposition 3.1

Suppose both density functions $\pi^0(s)$ and $\pi^1(s)$ have the same support of the state variable $S$. Then the counterfactual welfare $\delta_{\langle 1 \mid 0 \rangle}$ is a special case of equation eq:linfunc with whose Riesz representation eq:rieszweight holds with

Theorems & Definitions (63)

  • Example 2.1: Average Welfare
  • Example 2.2: Group Average Welfare
  • Example 2.3: Average Policy Effect
  • Example 2.4: Average Marginal Effect
  • Example 2.5
  • Example 3.1: School attendance
  • Example 3.2: Breast cancer screening
  • Proposition 3.1: Decomposition of Differences in Average Welfare
  • Remark 3.1: Overview of Related Literature
  • Proposition 5.1: Dynamic Dual Representation
  • ...and 53 more