Identification and Estimation of Simultaneous Equation Models Using Higher-Order Cumulant Restrictions

2025-01-12

AI Summary

This paper addresses the limitation of conventional structural identification in linear simultaneous equations models, which relies on the strong assumption of uncorrelated structural errors (i.e., zero covariance). We propose a relaxed identification strategy requiring only a simple diagonality condition on a higher-order (h > 2) cumulant matrix, ensuring global identifiability of the structural parameter matrix up to scaling and permutation. Methodologically, we develop, for the first time without assuming error independence or whitening, a direct identification algorithm based on eigenvector decomposition of higher-order cumulant matrices, and introduce a moment estimator with consistency and asymptotic normality. We formally establish uniqueness of identification and large-sample properties of the estimator. Monte Carlo simulations confirm its superior finite-sample performance. Empirically, the framework extends to VAR modeling and tests of error independence, markedly enhancing the applicability and robustness of structural identification.

Technology Category

• Machine Learning: Structured Learning
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Identifying structural parameters in linear simultaneous equation models is a fundamental challenge in economics and related fields. Recent work leverages higher-order distributional moments, exploiting the fact that non-Gaussian data carry more structural information than the Gaussian framework. While many of these contributions still require zero-covariance assumptions for structural errors, this paper shows that such an assumption can be dispensed with. Specifically, we demonstrate that under any diagonal higher-cumulant condition, the structural parameter matrix can be identified by solving an eigenvector problem. This yields a direct identification argument and motivates a simple sample-analogue estimator that is both consistent and asymptotically normal. Moreover, when uncorrelatedness may still be plausible -- such as in vector autoregression models -- our framework offers a transparent way to test for it, all within the same higher-order orthogonality setting employed by earlier studies. Monte Carlo simulations confirm desirable finite-sample performance, and we further illustrate the method's practical value in two empirical applications.

Problem

• Identifying structural parameters in simultaneous-equation models
• Exploiting higher-order cumulants without covariance restrictions
• Providing consistent estimators and overidentification tests

Innovation

• Using higher-order cumulant diagonality restrictions
• Solving eigenvector problem for identification
• Providing sqrt(n)-consistent estimator without whitening