Jorda (2005) 提出一新的估算衝擊反應函數方法為局部投射(Local Projection), 此法能避免模
型錯置的問題, 使得其結果更為穩健。Wu, Lee, and Wang (2008) 一文將局部投射由定態過程的時
間序列變數I(0), 延伸為可套用在非定態時間序列變數I(1) 的情況, 使得局部投射在總體計量上的應
用更為廣泛, 其文中利用差分後定態的方法, 並在資訊集合中加入共整合向量, 使得資訊集合更為完
整, 對預測的精確度也有所提升。本文延伸Wu, Lee, and Wang (2008) 及Lee (2010), 放寬原文共
整合向量為已知的假設, 由Johansen (1995) 推論的結果得知共整合向量具有超一致性的性質, 利用
此條件本文進行OLS 估算衝擊反應函數係數, 其結果得知在漸進理論中, 無論共整合向量為假定已
知或利用Johansen MLE 估算所得出, 皆具有一致性的衝擊反應函數係數。

Jorda (2005) proposed the new method to estimate impulse response functions by local
projection. The new method, local projection, can avoid the misspecification problem. That
is, local projections are robust to misspecification of the data generating process (DGP). Wu,
Lee, and Wang (2008) extended the Jorda’s local projection from stationary time series I(0) to
non-stationary time series I(1). It makes the local projection be a more generally applicative
method for the Macroeconomic. In the article, I relax the cointegration vector which assumed
to be known in the Wu, Lee, and Wang (2008) and Lee(2010). From the inference of Johansen
(1995) I can get the property of super-consistent between β and ˆ β in the cointegration vector. I
use the above condition and OLS to estimate impulse response functions, and in the asymptotic
theorem, the cointegration vectors which assumed to be known or estimated by Johansen MLE
are both get the consistent coefficients of impulse responses.

1 研究動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 文獻回顧. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3 模型設定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.1 衝擊反應函數在定態過程的討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.2 利用局部投射估算之衝擊反應函數在非定態過程的討論. . . . . . . . . . . . . . . . 7
4 衝擊反應函數在局部投射下共整合向量一般化推論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.1 共整合向量在Johansen MLE 下的漸進分配推論. . . . . . . . . . . . . . . . . . . 10
4.2 局部投射之投影係數一致性推論. . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.2.1 命題. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.2.2 輔助定理. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.2.3 定理. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
5 資料產生過程為共整合VAR 下的討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
6 模擬分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
7 結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

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