Towards Understanding the Instrumental Variables Methods in Biometrics and Econometrics

• Published in: Journal of the Japan Statistical Society, Japanese Issue Vol. 54; no. 2; pp. 109 - 143
• Main Author: Kunitomo, Naoto
• Format: Journal Article
• Language: Japanese
• Published: Japan Statistical Society 04.03.2025; 一般社団法人 日本統計学会
• Subjects: 2標本問題; ATE; LATE; LIML; Noncompliance; TSLS; 多操作変数下での最適推定; 操作変数法; 政策評価; 構造方程式; 統計的因果推論; 臨床試験
• ISSN: 0389-5602; 2189-1478
• DOI: 10.11329/jjssj.54.109

Causality is a fundamental and crucial subject of analysis in many research fields, including statistical science. In the fields of biometrics and econometrics, statistical causal inference has been widely applied. In this paper we first introduce the counterfactual model, initiated by Rubin (1974), and the instrumental variables method proposed by Angrist, Imbens, and Rubin (1996, referred to as AIR) in biometrics and statistics. Next, we explain simultaneous equations and structural equations in econometrics using a simple demand function as an example. We interpret statistical causality using general structural equations and discusses statistical estimation methods for structural equations, including the instrumental variables approach. Since the Ordinary Least Squares (OLS) method is inconsistent in estimating structural equations, alternative methods such as the Wald method, Limited Information Maximum Likelihood (LIML), Two-Stage Least Squares (TSLS), and Generalized Method of Moments (GMM) are discussed with their advantages and disadvantages. Furthermore, we review the historical development of structural equations and presents new findings regarding the instrumental variables estimation method in two-sample. Finally, we explore future challenges in statistical causal analysis in biometrics and econometrics.