Group Shapley Value and Counterfactual Simulations in a Structural Model

TL;DR

This paper introduces the group Shapley value as a principled, additive decomposition method for interpreting counterfactual simulations in structural economic models. It shows that the group Shapley value is the unique solution satisfying the axioms of Linearity, Dummy, Symmetry, and Efficiency, and can be computed as a constrained weighted least squares problem. The authors provide robust techniques for when some input components are missing (Shapley bounds and SMNS) and illustrate the approach with a simple Roy model and two applications: capital misallocation (DV2019) and globalization (CGT2016). The results yield interpretable importance tables that rank the contributions of parameter groups to changes in outcomes, supporting more transparent and comparable “interpretable structural economics.”

Abstract

We propose a variant of the Shapley value, the group Shapley value, to interpret counterfactual simulations in structural economic models by quantifying the importance of different components. Our framework compares two sets of parameters, partitioned into multiple groups, and applying group Shapley value decomposition yields unique additive contributions to the changes between these sets. The relative contributions sum to one, enabling us to generate an importance table that is as easily interpretable as a regression table. The group Shapley value can be characterized as the solution to a constrained weighted least squares problem. Using this property, we develop robust decomposition methods to address scenarios where inputs for the group Shapley value are missing. We first apply our methodology to a simple Roy model and then illustrate its usefulness by revisiting two published papers.

Figures (1)

• Figure 1: Shapley Minimum Norm Solution with Shapley Bounds

Theorems & Definitions (3)

• Proposition 2.1
• Proposition 3.1: charnes1988extremal
• proof : Proof of Proposition \ref{['opt-result']}