Structural Representations and Identification of Marginal Policy Effects

TL;DR

This paper provides a theoretical foundation for understanding the marginal policy effect in nonseparable models, linking it to the functional derivative of outcome distributions, and proposes a new identification strategy.

Contribution

It establishes a definitional equivalence between the MPE and a weighted average structural derivative, and introduces an alternative identification approach.

Findings

MPE equals the functional derivative at a weighted average structural derivative

The equivalence is definitional, not identification-based

Proposes a new identification strategy for MPE

Abstract

This paper investigates the structural interpretation of the marginal policy effect (MPE) within nonseparable models. We demonstrate that, for a smooth functional of the outcome distribution, the MPE equals its functional derivative evaluated at the outcome-conditioned weighted average structural derivative. This equivalence is definitional rather than identification-based. Building on this theoretical result, we propose an alternative identification strategy for the MPE that complements existing methods.