在VAR模型中Granger-causes的概念,是將變數群拆成兩組,藉由預測能力界定兩組變數的因果關係,此種因果結構可視爲雙群。但某些實例應用當中,須以多群的因果結構且帶入領先落後之概念,才足以解說系統的複雜程度,本文考慮在VAR模型中將變數群拆作三組,再以三組變數分別作爲(1)外衍變數、(2)中介變數和(3)內衍變數,如此將形成單向的三群因果路徑,本文中將探討三群因果結構之涵義與應用。 在三群因果路徑的定義中,爲判別三群路徑結構是否存在,必須先行界定規劃y1t,y2t,y3t分屬鈴外衍、中介和內布示的狀況,但實際上我們很難預先規劃變數群歸屬鈴外衍、中介和內衍的狀況,因此直接使用定義來判定路徑結構是相當不便的。本文將提供一較實用的判定程序,在未知y1t,y2t,y3t的分屬狀況時,仍能判別三組變數群間之領先落後關係。 本文以國內生產毛額支出面法中之三項要素:民間消費、政府消費和淨出口作爲實例探討對象,我們嘗試發掘三項要素間的路徑結構,以表達GDP要素間之領先落後關係,我們發現三群路徑結構存在,且民間消費為外衍變數,淨出口爲中介變數,政府消費則爲內衍變數。
The concept of Granger cause is to explain the causality between two groups of variables in a VAR model. But, for capturing the complexity of the system in some empirical studies, a more refined unidirectional causality using more than two groups of variables should he considered. In this research, we construct a Three-Group causal path with three groups: (i) independent group, (ii) intermediate group and (iii) dependent group. Since it isn’t easy to pre-assign the order of the three groups in the causal path, we propose a practical procedure to confirm the position of each group in the path order. Through the practical procedure, we investigate the three-group causal path among personal consumption, government expenditures and net exports from Taiwan GDP. Finally, the result shows that there exists a three-group causal path and personal consumption, net exports and government expenditure are the independent variable, the intermediate variable and the dependent variable, respectively.