纽约联储-关于夏普利-欧文-肖罗克斯（Shapley-Owen-Shorrocks）分解法的实践者笔记（英）-2025.8_14页_656kb

Overview: This note introduces the Shapley-Owen-Shorrocks decomposition, a method for decomposing contributions of inputs in non-linear economic models. It provides an additive decomposition that sums to one and is symmetric, making it suitable for analyzing aggregate outcomes like inequality, R-squared, or counterfactual scenarios.

Method: The decomposition uses the Shapley value extended for inequality decompositions. It calculates the contribution of each input by averaging the difference in outcomes over all possible orderings of input exclusion, ensuring exact additivity and interpretation of contributions.

Key Features:

• Satisfies four properties: exact additivity, symmetry, irrelevance of null factors, and linearity in the outcome function.
• Handles non-linear aggregations by accounting for interactions through a weighting scheme based all possible sub-models.

Applications: Useful in regression decomposition, structural economic models, welfare analysis, and group contributions. Examples include decomposing R-squared in linear models, quantifying effects of policy changes in lifecycle models, and separating drivers in inequality studies.

Advantages: Offers an intuitive and symmetric alternative to order-dependent decompositions, widely applicable but underutilized. Computational implementation is feasible, though complexity grows with input size.

Implementation: Provided an algorithm for MATLAB, emphasizing the need for careful handling of input groups and sub-models.