本文中，我們延續 Mark (2007)的實質匯率模型，在未拋補利率平價說成立 下，透過實質匯率與名目利率之間的關係，結合利率平價與考慮股票價格波動的 泰勒法則，建立一個實質匯率模型。我們發現匯率的決定因素除了須視德國相對 於美國的通貨膨脹率與產出水準外，仍須考慮股票價格。此外，我們嘗試由模型 求出的理性預期與學習機制下的實質匯率路徑，解釋德國馬克兌美元的實質匯率 波動。首先，比較美國和德國 1979 年前後貨幣政策的實証結果，我們發現美國 於 1979 年以後由於股票價格波動幅度劇增，使得美國央行開始關心美國股票價 格的波動對本國經濟體系造成的影響，促使美國央行透過泰勒法則來穩定產出缺 口與股票市場的波動。另外，根據資料顯示，德國央行於 1979 年以前採取穩定 通貨膨脹率與實質匯率波動的貨幣政策，然而由於 1999 年歐元的崛起，使得德 國逐漸喪失貨幣政策的自主權無法有效干預匯率的波動，以及股票價格波動幅度 劇增，故促使德國央行 1979 年以後採取穩定產出波動以及股票價格波動的貨幣 政策。此外，我們藉由本文所建立的實質匯率模型，分別求出的理性預期與學習 機制下的實質匯率路徑。在理性預期的假設下，我們發現多考慮股票價格的匯率 決定因素，對實質匯率路徑解釋能力幫助不大；然而在學習機制的假設下，多了 股票價格的決定因素，不但可以讓實質匯率模型更能解釋短期實際實質匯率波動 外，同時也符合 Mark (2007)提出六個主要匯率大幅度波動中的四個實質匯率大 幅度波動，並且可以描述長期實質匯率的趨勢。據此，在本文中，我們發現在探 討實質匯率模型時，相較於理性預期的假設，學習機制下考慮股票價格變動率的 實質匯率模型更貼近實質匯率短期與長期的波動，因此當我們在探討學習機制假 設下的匯率模型，不可忽略股票價格對匯率的影響。此外，由本文實質匯率模型 可看出，股票價格與實質匯率之間具有反向的關係，即當股票價格波動過大時，
央行會採取貨幣政策來抑制股票價格上揚，並且透過利率與匯率之間的關係，從 而促使本國貨幣升值。
附錄一、表
表 2、一般動差法估計考慮股票市場波動的利率反應函數(落後一期的實質匯率)。
表 3、模型求出路徑與實際路徑之間的相關係數與相對標準差。
相關係數 相對標準差 形式
理性預期 學習機制 理性預期 學習機制 考慮股價波動的
實質匯率模型
0.235 0.527 0.358 0.817 Level
Mark(2007) 0.308 0.346 0.965 1.054
考慮股價波動的 實質匯率模型
0.078 -0.026 0.597 1.622 1-qtr return
Mark(2007) 0.030 -0.039 2.085 1.254
考慮股價波動的 實質匯率模型
0.040 0.378 0.455 1.331 4-qtr return
Mark(2007) 0.235 0.044 1.525 1.164
考慮股價波動的 實質匯率模型
-0.095 0.441 0.364 1.204 8-qtr return
Mark(2007) 0.308 0.157 1.264 1.014
考慮股價波動的 實質匯率模型
-0.094 0.396 0.362 1.205 16-qtr return
Mark(2007) 0.424 0.335 1.055 1.086
附錄二、圖
30 40 50 60 70 80 90 100 110
1970 1975 1980 1985 1990 1995 2000 2005
German GDP deflator modified German GDP deflator
圖 1、修正後與實際德國國內生產毛額平減指數。
-3 -2 -1 0 1 2 3 4
1970 1975 1980 1985 1990 1995 2000 2005 G-US inflation real exchange rate
圖 2、德國馬克兌美元實質匯率與德國相對於美國通貨膨脹率。
-4 -3 -2 -1 0 1 2 3 4
1970 1975 1980 1985 1990 1995 2000 2005 inflation(G-US, US-G) real exchange rate
圖 3、德國馬克兌美元實質匯率與相對通貨膨脹率，其中 1970.1-1979.2 為德國相 對美國的通貨膨脹率，而 1979.3-2007.3 為美國相對德國的通貨膨脹率。
-2 -1 0 1 2 3
1970 1975 1980 1985 1990 1995 2000 2005 G-US interest rate real exchange rate
圖 4、實質匯率與相對名目利率。
0 1 2 3 4 5
1970 1975 1980 1985 1990 1995 2000 2005 US inflation US interest rate
圖 5、美國名目利率與通貨膨脹率。
-1 0 1 2 3 4 5
1970 1975 1980 1985 1990 1995 2000 2005 German inflation German interest rate
圖 6、德國名目利率與通貨膨脹率。
-3 -2 -1 0 1 2 3
1970 1975 1980 1985 1990 1995 2000 2005 G-US inflation G-US interest rate
圖 7、德國相對於美國名目利率與通貨膨脹率。
-4 -2 0 2 4 6 8
1970 1975 1980 1985 1990 1995 2000 2005 G-US output gap G-US interest rate
圖 8、德國相對於美國名目利率與產出缺口。
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
1970 1975 1980 1985 1990 1995 2000 2005 real exchange rate G-US interest rate
圖 9、德國相對於美國名目利率與實質匯率。
-30 -20 -10 0 10 20
1970 1975 1980 1985 1990 1995 2000 2005 US stock price return US interest rate
圖 10、美國的名目利率與股票價格變動率。
-40 -30 -20 -10 0 10 20 30
1970 1975 1980 1985 1990 1995 2000 2005 GM stock price return GM interest rate
圖 11、德國名目利率與德國股票價格變動率。
-6 -4 -2 0 2 4 6
1970 1975 1980 1985 1990 1995 2000 2005 G-US stock price return G-US interest rate
圖 12、德國相對於美國的名目利率與股票價格變動率。
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
1970 1975 1980 1985 1990 1995 2000 2005 actual interest differential fitted interest differential
圖 13、模型求出的相對利率路徑與實際的相對利率路徑。
-3 -2 -1 0 1 2 3 4
1975 1980 1985 1990 1995 2000 2005 real exchange rate rational expectation path
圖 14、實際實質匯率與理性預期下實質匯率路徑。
（1973 年第一季開始）
-3 -2 -1 0 1 2 3 4
80 82 84 86 88 90 92 94 96 98 00 02 04 06 real exchange rate rational expectation path
圖 15、實際實質匯率與理性預期下實質匯率路徑。
（1979 年第三季開始）
-3 -2 -1 0 1 2 3
80 82 84 86 88 90 92 94 96 98 00 02 04 06 real exchange rate learning path
圖 16、實際實質匯率與學習機制下實質匯率路徑。
附錄三
即所謂的正交條件(orthogonality condition)，可表示為：
[ t t] 0 出具有一致性(consistency)且漸進常態分配(asymptotic normal distribution)的參數 數估計式
β
1及β
2，即j
=1, 2式中
x 同樣為解釋變數向量，
tjη
tj+1為相對利率反應函數中下一期的誤差項。 (Bayesian information criterion, BIC )選取 VAR 模型的最適階數，也就是極小化min 2 ln p ln
附錄四
因此，預期平穩條件將決定於下述微分方程，可以表示為： 入式(4.6)中必須為漸進局部穩定均衡(locally asymptotically stable)。另外我們將式 (4.5)代入式(4.6)，則微分方程式(4.6)可以分別表示為：
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