Endogenous Regressors in Nonlinear Probability Models:A Generalized Structural Equation Modeling Approach

Abstract

社會科學研究中，解釋變數常發生棘手的內因（endogeneity）問題。線性模型之內因自變數處理方式，如工具變數及其延伸，討論頗多。但若依變數為類別變數，其非線性的機率模型面對內因自變數，問題遠比線性模型複雜得多，絕不宜盲目以線性模型的處理方式比照適用。本文的目的，在釐清內因問題的起源，並區分實證研究較常遇到的兩大內因來源：未觀測到的潛在因素及內因中介變數，回顧線性模型文獻中對兩者的因應方式，並分析這些方法在非線性機率模型中面臨的困難與挑戰。接著本文提出廣義結構式模型的解決方案，既可同時因應兩種內因問題，亦能兼顧非線性模型的統計特性。為了說明廣義結構式模型的應用，本文舉經濟投票文獻中對「整體經濟回顧與前瞻型評價」的內因性辯論為例，建立能兼容相競學理的廣義結構式模型，並以實證資料TEDS2012進行檢驗，發現回顧型評價對投票抉擇有顯著的影響。

Endogeneity of explanatory variables is a common problem in many areas of social sciences. Ironically, there seems to be a gap between being aware of the problem and knowing how best to handle it. The problem is exacerbated when the outcome variable of interest is categorical and thus non-linear probability models are involved. The study fills the gap by first distinguishing two main sources of endogeneity, including unmeasured confounders (＂latent factors＂) and measured but omitted causes (＂endogenous mediators＂), and then proposing an integrated approach to confront the two problems simultaneously. This strategy generalizes structural equation models to categorical outcome by including a shared latent factor between correlated error terms to tackle unobserved confounders, on the one hand, and extending mediation analysis to deal with potentially endogenous discrete mediators, on the other hand. For illustrative purpose, this proposed modeling strategy is presented with an example of heated debates in economic voting literature concerning the possible endogeneity of voters` economic perceptions.