實質匯率內生波動分析—門檻自我迴歸模型之應用

Abstract

本文引用Chen(1998)理論模型，試圖解決Rogoff(1996)所提的一個難題，即以購買力平價難題為出發點，實質匯率具長期持續性失衡與短期大幅波動共同存在之現象。Chen(1998)理論模型發現：當馬簍條件不成立時，利用Hopf分歧定理可以驗證不確定均衡存在。進一步分析，當Hopf分歧發生於某特定值時，根據Lorenz’s 定理可以發現特性根存在共軛虛根。另一方面，Chen(1998)理論模型推導出的均衡實質匯率是一條二階差分的非線性方程。 實證方面，選取日本實質有效匯率之月資料來驗證不確定均衡的存在，以解釋實質匯率短期大幅波動的原因。利用Zivot- Andrews檢定，找出結構轉變點，並藉此結構轉變點將原始序列分割成兩段，再分別配適二階自我相關模型。接著循Tsay(1989)方法將原始序列配適具有非線性特徵的門檻自我迴歸模型。最後，分析上述兩種模型，並利用樣本資料是否存在共軛虛根與落後期變數係數總和是否趨近於1的性質，以解釋實質匯率在穩定狀態下長期持續性失衡的原因。

This study aims to solve the puzzle proposed by Rogoff (1996), by adopting Chen(1998)’s theoretical model. Based on purchase power parity(PPP), the puzzle is the enormous short-run volatility and the persistent long-run inequilibrium of real exchange rate. Chen (1998) pointed out that, when the Marshall-Lerner condition is not satisfied, there exists the possibility of the indeterminacy of equilibrium. The existence of the indeterminacy of equilibrium may be established by applying the theory of Hopf bifurcation. Further, according to Lorenz’s Theorem, analysis shows that Hopf bifurcation occurs at a critical value of the key parameter, at which the eigenvalues are complex conjugates. On the other hand, it can also be derived from Chen’s model that the equilibrium of real exchange rate is a second-order nonlinear difference equation. In terms of empirical evidence, the monthly data of real effective exchange rate from Japan was chosen to prove the existence of the indeterminacy of equilibrium, and to interpret why real exchange rate fluctuates violently in the short run. The Zivot-Andrews (1992) test was used to estimate structural change point, and to divide the sample period into two subperiods which exhibit stationary second-order autoregressive model. Then, by this characteristic of nonlinearity, the threshold autoregressive model, raised by Tsay (1989), was used to interpret the movement of real exchange rate of Japan as well. Last but not least, provided that the complex conjugates exist and the sum of modulus is close to one, the reason why real exchange rate remains inequilibrium constantly under stationary condition in the long run. can be explained.