自Nelson和Plosser (1982)後，研究經濟資料是否具有單位根現象，已成為近二十年來熱門且重要的課題。因

為資料性質的不同(恆定或非恆定)，對實證計量模型的設定、統計推論以及原理論的發展有深遠的影響。與傳

統探討單一時間數列之單位根的論文不同的是，本篇論文將橫斷面的資料擴大，探討混合型資料的單位根現象

( Panel Unit Root )。就此課題，文獻上已有兩個不同的檢定方法: Levin、Lin和Chu (1997)的LLC檢定法以及Im、

Pesaran和Shin (1995)的IPS檢定法。

我們的研究，有別於以上兩者，是從「概似比」的角度(likelihood ratio) 和應用檢定共積關係的Johansen

(1988)「Trace檢定」，建構新的單位根檢定統計量。首先於文中推導出，「Trace檢定」可用於檢測單一時間數

列的單位根現象。進而，再將橫斷面資料擴大，採用mean group方法，加總平均每個橫斷面時間數列的「Trace

檢定」統計量，形成混合型資料之單位根檢定統計量 。根據中央極限定理，標準化後的 檢定統計量，極限上

收斂至標準常態分配。此外，我們也推導得出 檢定統計量與傳統ADF、LLC以及IPS檢定統計量極限上的關係。

最後，我們以「蒙地卡羅」模擬方法，分析小樣本下「型一誤差」與「檢定力」的表現。發現新的混合型資

料之單位根檢定統計量表現優良，近似於標準常態分配。故在做混合型資料的單位根分析時，採用 檢定統計

量，可得到較精確的推論。

Bernard, A. B. and Jones, C. I. (1996) " Productivity Across Industries and Countries: Time Series Theory and Evidence." Review of Economics and Statistics, 78(1), 135-146.
Coakley, J. and Fuertes, A. M. (1997) " New Panel Unit Root Tests of PPP." Economics Letters, 57(1), 17-22.
Dickey, D. A. and Fuller, W. A. (1979) " Distribution of the Estimators for Autoregressive Time Series with a Unit Root." Journal of the American Statistical Association, 74, 427-431.
Dickey, D. A. and Fuller, W. A. (1981) " Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root." Econometrica, 49, 1057-1072.
Engle, R. F. and Granger, C. W. (1987) "Co-Integration Variables and Error Correction: Representation, Estimation, and Testing." Econometrica, 55, 251-276.
Evans, R. and Karras, G. (1996) " Convergence Revisited." Journal of Monetary Economics, 37, 249-265.
Fleissig, A. R. and Strauss, J. (1997) " Unit Root Tests on Real Wage Panel Data for the G7." Economics Letters, 56(2), 149-155.
Fuller, W. A. (1976) Introduction to Statistical Time Series. New York: Wiley.
Granger, C. W. J. (1983) " Co-Integration Variables and Error-Correction Models." Unpublished University of California, San Diego, Discussion Paper 83-13.

Hamilton, J. D. (1994) Time Series Analysis. Princeton University Press.
Im, K. S., Pesaran, M. H. and Shin, Y. (1995) " Testing for Unit Roots in Heterogeneous Panels." WP 9526, DAE, University of Cambridge.
Johansen, S. (1988) " Statistical Analysis of Cointegration Vectors." Journal of Economic Dynamics and Control, 12, 231-254.
Johansen, S. (1991) " Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models." Econometrica, 59, 1551-1580.
Koopmans, T. C. and Hood, W. C. (1953) Studies in Econometric Method. New York: Wiley.
Levin, A. and Lin, C. F. (1992) " Unit Root Test in Panel Data: Asymptotic and Finite Sample Properties." University of California, San Diego, Discussion Paper, 92-23.
Levin, A. and Lin, C. F. (1993) " Unit Root Test in Panel Data: New results." University of California, San Diego, Discussion Paper, 93-56.
MacDonald, R. (1996) " Panel Unit Root Tests and Real Exchange Rates." Economic Letters, 50, 7-11.
Nelson, C. and Plosser, C. (1982) " Trends and Random Walks in Macro-economic Time Series: Some
Evidence and Implications." Journal of Monetary Economics, 10, 130-162.

O'Connell, P. (1998) " The Overvaluation of Purchasing Power Parity." Journal of International Money and Finance, 17, 41-50.
Oh, K. Y. (1996) " Purchasing Power Parity and Unit Root Test Using Panel Data." Journal of International Money and Finance, 15(3), 405-418.
Papell, D. H. (1997) " Searching for Stationary: Purchasing Power Parity Under the Current Float." Journal of International Economics, 43, 313-332.
Quah, D. (1994) " Exploiting Cross-section Variation for Unit Root Inference in Dynamic Data." Economics Letters, 44, 9-19.
Said, S. E. and Dickey, D. A. (1984) " Testing for Unit Roots in Autoregressive-Moving Average Models of Unknown Order." Biometrika, 71, 599-607.
Song, F. M. and Wu, Y. (1997) " Hysteresis in Unemployment: Evidence from 48 U.S. States." Economic Inquiry, 35(2), 235-243.
Strazicich, M. C. " Are state and Provincial Governments Tax Smoothing? Evidence from Panel Data." Southern Economic Journal, 62(4), 979-988.
Wu, Y. (1996) " Are Real Exchange Rates Nonstationary? Evidence from a Panel-Data test." Journal of Money, Credit and Banking, 28(1), 54-63.