平滑轉換的費雪方程式：以七大工業國之四項資產為例

Smooth Regime-Switching Fisher Equations: Empirical Evidence from Four Kinds of Assets in G7

張喬翔(Chiao-Hsiang Chang)

指導教授 ： 吳博欽

中原大學/商學院/國際貿易研究所/碩士(2011年)

https://doi.org/10.6840/cycu201100443

摘要

中文摘要
不論是經濟成長造成物價持續的上漲，抑或是天災、人禍的衝擊而侵蝕貨幣的購買力，依據理論上著名的費雪假說，一般皆認為可以藉由投資行為來對抗通貨膨脹。Irving Fisher (1930) 提出名目利率為預期實質利率與預期通貨膨脹率的總合，換言之為名目利率應隨著通貨膨脹率的變化而調整。將費雪假說擴及到一般金融資產，若其名目報酬具有避險能力，則實質報酬應不受通貨膨脹影響。在實證上費雪假說有相當多的研究與討論，如名目利率是否會與通貨膨脹率同幅度的調整，或是股票、房地產等資產是否能對抗通貨膨脹，但多數都局限於線性模型。
諸如西元1997年的亞洲金融風暴、西元2000年的網路泡沫化及西元2006年的次貸危機等衝擊，都使得總體經濟變數產生結構轉變。另外，資本市場的不完全、投資人的異質性與風險趨避的態度，也都會使得總體經濟變數呈現非線性的走勢。因此本文在以通貨膨脹率的落後期為解釋變數下，建立平滑轉換的費雪方程式，接著在不同轉換變數與不同轉換變數落後期下，衡量兩區間的實質資產報酬率與通貨膨脹率之落後期對資產報酬率的邊際效果，而經濟個體與政策制定者可以輕易的衡量景氣狀態與政策效果。
本文的樣本國家為七大工業國，樣本期間為西元2000年1月至西元2010年9月，資料頻率為月資料。而所選用的標的資產為股票、債券、房地產與黃金，其中股票、房地產與黃金皆為指數型式，並以報酬率的方式呈現，而債券為殖利率。另外，通貨膨脹率以消費者物價指數的變動率為計算方式；轉換變數則有匯率及貨幣供給。
根據本文實證結果指出，在匯率為轉換變數下，加拿大、法國、義大利、英國與美國的股價報酬率存在區間轉換；債券殖利率存在非線性走勢的國家則有加拿大、法國、義大利與美國；而德國、義大利、日本、英國、與美國的房地產報酬率存在平滑轉換的過程。在貨幣供給為轉換變數下，加拿大、法國、義大利、英國與美國的股價報酬率存在區間轉換；債券殖利率存在非線性走勢的國家則有法國與義大利；而德國、義大利與美國的房地產報酬率存在平滑轉換的過程。其次，雖有部分國家的資產報酬率不存在區間轉換，但其通貨膨脹率落後期對資產報酬率的模型之配適度仍優於傳統的線性模型。

關鍵字

外生的平滑轉換自我迴歸模型 ； 非線性 ； 費雪效果 ； 結構轉變

並列摘要

Abstract
In 1930, Irving Fisher proposed that nominal interest rates comprise expected real interest rates and expected inflation rates. This proposition is the famous Fisher hypothesis. In other words, nominal interest rates will keep pace with expected inflation rates. Transposing the notion of Fisher hypothesis to other financial assets imply that the nominal returns of assets adjust on a one-to-one basis to inflation rates in a competitive market. While the Fisher hypothesis has been investigated in both theoretical and empirical economics, the models employed in most previous studies are linear forms.
Actually, fatal economic events such as the Asian Financial Crisis in 1997, the Dot-com bubble crash in 2000, the Subprime Mortgage Crisis in 2006, may make financial assets returns have structural changes. In addition, incomplete capital markets, and heterogeneous and risk-averse investors are also the sources of nonlinear adjustment in macroeconomic time series variables. Therefore, this study constructs smooth regime switching Fisher equation with lagged inflation rates to investigate different marginal effects of lagged inflation rates on financial asset returns as lagged exchange rate and lagged money supply in different transition regions.
In performing empirical estimation we choose the G7 countries as sample objects, and the data used are monthly returns of stock, bond, real estate and gold from January 2000 to September 2010. The empirical study shows the following results:
First, choosing lagged exchange rate as the transition variable there exist dynamic smooth switching process of stock returns in Canada, France, Italy, UK and US, and of real estate returns in Germany, Italy, Japan, UK and US. In addition, there are different real asset returns locate in distinct regions in Canada, France, Italy and US.
Second, while lagged money supply is regarded as the transition variable, the results suggest that the stock returns in Canada, France, Italy, UK and US, and the real estate returns in Germany, Italy and US display dynamic smooth switching process. In addition, the real interest rates in France and Italy also have similar process. Overall, the empirical evidences support that the nonlinearity of real returns and nominal returns in most assets in G7 countries.

並列關鍵字

STARX model ； Nonlinearity ； Structural changes ； Fisher effect

參考文獻

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