「類別依變數模型中之內因自變數問題：方法論之探討與經濟投票研究之應用」結案報告

Abstract

In empirical political studies, researchers often intend to estimate and test the effects of independent variables on dependent variables. Among various analysis methods, the regression model is the most commonly used one. If an independent variable is an exogenous variable that fits the assumption of conditional independence, then the unbiased coefficients can be estimated with ordinary regression analysis. However, in cases where an independent variable and a dependent variable are simultaneously affected by other variables not included in the model, the independent variable will become correlated to the error terms. This would violate the assumption of conditional independence, as the estimated value of its regression coefficient would contain \"omitted variable bias.\" This type of independent variables is often called the \"endogenous explanatory variable.\" In example, the economic voting theory suggests that voters` retrospective and prospective evaluations of the economy will determine their voting decisions, whether to reward or punish the incumbent and the ruling party. In recent years, however, some scholars have challenged this theory and argued that voters` economic evaluations are often affected by their party identifications. As voters tend to favor their preferred political party, their economic evaluation should not be considered as an exogenous variable. This kind of debate involves variables` relative positions in theory, and its empirical analysis cannot be resolved by adding control variables to regression model. Although the literature contains many studies on how to handle endogenous explanatory variables, they mostly target continuous dependent variables. Among these methods, the commonly noted \"instrumental variables\" (IV) and \"two-stage least square\" (2SLS) are not applicable to the categorical dependent variables and their nonlinear regression models that are most frequently encountered in politics. In view of the above arguments, this two-year research project has two objectives: 1. In terms of methods: This project will combine the basis of generalized linear models (GLM) with mediation analysis and structural equation model (SEM) to develop an endogenous explanatory variable model that is applicable to categorical dependent variables. Not only will the model be able to consistently estimate the regression coefficient, but it can also correctly interpret the probability of occurrence for each category of dependent variables. This can avoid misinterpretations caused by coefficient-rescaling in nonlinear models. 2. In terms of applied research: This project will apply the \"categorical dependent variable`s endogenous explanatory variable model\" to economic voting research. It will be able to solve the traditional problem of applying IV and 2SLS from linear models to categorical dependent variable models, as well as verify numerous plausible debates in theory. For example: do voters` party identifications influence their retrospective and prospective evaluations of the economy before their economic evaluations affect the voting decisions, or do the economic evaluations reflect objective economic conditions independent of voters` party preferences.

政治學的經驗研究中，往往想估計並檢驗自變數對依變數的影響，而迴歸模型是最常應用的分析方法。如果該自變數為外因變數（exogenous variable），符合條件獨立（conditional independence）的假定，則一般的迴歸分析便可估計不偏之係數。不過棘手的是，若有其他未納入模型的變數同時影響到該自變數與依變數，使該自變數與誤差項產生相關，便違反了條件獨立的假定，其迴歸係數估計值有「忽略變數偏差」（omitted variable bias），這類自變數常稱為「內因解釋變數」（endogenous explanatory variable）。例如經濟投票的學理，認為選民對經濟的回顧或前瞻評估，會決定其投票的抉擇，獎勵或懲罰現任者及執政黨。不過近年也有學者挑戰此一理論，認為選民的經濟評估其實常受政黨認同的左右，偏袒自己喜歡的政黨，因此並非外因變數。這類辯論因涉及變數在學理上的相對位置，其經驗檢證無法以單一迴歸式中加入控制變數（control variables）來解決。儘管文獻中對內因解釋變數的處理方式討論甚多，但大多是針對連續（continuous）依變數，其中一般熟悉之「工具變數」（instrumental variable, IV）及「兩階段最小平方法」（two-stage least square, 2SLS），並不宜套用至政治學中最常遭遇之類別（categorical）依變數及其非線性迴歸模型。 有鑑於此，本兩年期研究計畫的目的有二： 一、 在方法方面：以廣義線性迴歸模型（generalized linear models, GLM）為基礎，結合中介分析（mediation analysis）與結構方程式模型（structural equation model, SEM），發展適用於類別依變數的內因解釋變數模型，不僅能一致估計迴歸係數，且能正確解讀依變數的各類別發生的機率，避免非線性模型中「係數受變異數尺度大小牽動」（coefficient- rescaling）引起之錯誤解讀。 二、 在應用研究方面：將「類別依變數的內因解釋變數模型」應用至經濟投票研究，既可克服傳統上將線性模型之IV 及2SLS 逕行套用至類別依變數模型的問題，又可檢證學理上數種言之成理的觀點論辯：例如選民的政黨認同是否先影響其回顧與前瞻經濟評估，然後經濟評價才影響投票抉擇；還是經濟評估反映客觀的經濟榮枯，不會受政黨偏好的左右。