在國際金融研究匯率理論可分為許多學派，購買力平價說為貨幣學派的匯率理論的重要假設之一，且為開放性總體模型的重要假設。雖然許多模型都是假設購買力平價說存在而成立的，然而購買力平價說是否成立在實證上仍是不確定的。因此檢定購買力平價說是重要的。
過去的統計分析過程都是在模型下就直接估計，因為模型假設所有變數為定態的。然而，若以非定態變數對其他非定態變數進行迴歸分析，則可能產生虛偽回歸的現象; 為避免發生虛偽回歸的問題，就發展出Unit Roots Test 和 Cointegration Test。所以在做回歸分析時，會先對變數做Unit Roots Test 和 Cointegration Test，之後才做估計。但是因為Unit Roots Test 和 Cointegration Test有檢定力不足的缺失；於是就有文章採用結合了時間數列和橫段面的Panel Data Model來研究，以提升檢定力，改善小樣本的限制，並發展出Panel-Unit Root Test 和 Panel-Cointegration Test 去避免虛偽回歸。但是這些Panel-Unit Root Test 和 Panel-Cointegration Test 都是在時間數列長和橫斷面長下推論出來的，而往往在實證上，要面臨最困難之一的問題是資料的取得，更何況是要包跨長時間和多單位的資料；而且這些Panel Data Model只能研究很長的時期，不能針對較短的時期做研究。

為了避免發生這些難題，Binder, Hsiao and Pesaran(2004)發展出在時間短和橫斷面長下的Panel Data Model，the Short Panel Vector Autoregressions (sPVAR)。本篇文章將重點放在sPVAR下的購買力平價說並檢驗開始歐元至今(1998-2004)這段期間30個國家的購買力平價說。

The studies of exchange rate theory in international finance are divided into several schools. Purchasing Power Parity (PPP) is one important hypothesis in both the Monetary Exchange Rate theory and the main theory in the Open Macroeconomics Model. Although many models are found upon the existence of PPP, but it still has not been proved empirically. That is why it’s important to examine the existence of PPP.

In the past, the statistic analyzing processes are all made directly under the models since all variables have been assumed stationary. However, regressing two non-stationary variables may result in Spurious Regression. The Unit Roots Test and Cointegration Test are developed in order to avoid the problem of spurious regression. Therefore, Unit Roots Test and Cointegration Test should be applied to the variables before estimating during regression analyses. Concerning the power deficiency of Unit Roots Test and Cointegration Test, many researches have adopted the combination time-series and cross-section Panel Data Model in order to improve the power and limitation of small samples. The Panel-Unit Root Test and Panel-Cointegration Test have therefore been developed to avoid Spurious Regression. However, Panel-Unit Root Test and Panel-Cointegration Test are applied with long time-series and large cross-section. Nevertheless, obtaining the data has always been the toughest difficulty during empirical researches, let alone the need for long period and large unit data. These Panel Data Models can only be applied to studies for long period, but not to the short periods.

In order to avoid these problems; Binder, Hsiao and Pesaran (2004) have developed the Short Panel Vector Autoregressions (sPVAR) Model, a Panel Data Model developed with short time-series and large cross-section. Therefore, this paper will focus on Purchasing Power Parity under the sPVAR Model with the examination of PPP for the 30 countries since the introduction of Euro (1998 to 2004).

1 Introduction 1
2 Theoretical Framework and Empirical Literature Reviews 5
2.1 Theoretical Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Absolute PPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.2 Relative PPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Empirical Literature Reviews . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.1 Ordinary Least Square (OLS) . . . . . . . . . . . . . . . . . . . . . . 9
2.2.2 Time-Series Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.3 Panel Data Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3 sPVAR Framework 13
3.1 Short Panel-VAR Model . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Random Effects Speci‾cation . . . . . . . . . . . . . . . . . . . . . . 16
3.2.1 Random Effects Assumptions . . . . . . . . . . . . . . . . . . . . 16
3.2.2 Random Effects Model . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3 Fixed Effects Speci‾cation . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3.1 Fixed Effects Assumptions . . . . . . . . . . . . . . . . . . . . . . .19
3.3.2 Fixed Effects Model . . . . . . . . . . . . . . . . . . . . . . . . . ….20
3.4 Unit Roots and Cointegration tests . . . . . . . . . . . . . . . . . . 22
3.4.1 Unit Roots test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.4.2 Cointegration test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4 Empirical Results 26
4.1 Data Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.2 Empirical Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.3 Unit Roots Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.4 Cointegration Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5 Conclusion and Suggestion 32
A Exchange rates and price ratios for 12 developed countries 34
References 40

[1] Abauf, N. and Jorion, P. (1990). Purchasing power parity in the long run. Journal of Finance, 45:157-174.
[2] Ahn, S. C. and Schmidt, P. (1995). E±cient estimation of models for dynamic panel data. Journal of Econometrics, 68:5-27.
[3] Bahmani-Oskooee, M. and Barry, M. (1997). The purchasing power parity and the russian ruble. Comparative Economic Studies, 39:82-94.
[4] Balassa, B. (1964). The purchasing power parity doctrine: A reappraisal. Journal of Political Economy, 72:584-596.
[5] Binder, M., Hsiao, C., and Pesaran, M. H. (2004). Estimation and inference in short panel vector autoregressions with unit roots and cointegration. Working Paper.
[6] Cassel, G. (1922). Money and Foreign Exchange after 1914. London.
[7] Cheung, Y. W. and Lai, K. S. (1993). Long-run purchasing power parity during the resent float. Journal of International Economics, 34:181-192.
[8] Chinn, M. D. (1998). Before the fall: Were east asian currencies over-valued? Na- tional Breau of Economic Research, Working Paper 6491.
[9] Coakley, J. and Fuertes, A. (1997). New panel unit root tests of ppp. Economics Letters, 57:17-22.
[10] Conejo, D. and Shield, M. P. (1993). Relative ppp and the long-run terms of trade for five latinamerican countries: A cointegration approach. Apllied Economics, 25:1511-1515.
[11] Corbae, D. and Ouliaris, S. (1988). Cointegration and tests of purchasing power parity. The Review of Economics and Statistics, 70:508-511.
[12] Culver, S. E. and Papell, D. H. (1999). Long-run purchasing power parity with short-run data: evidence with a null hypothesis of stationarity. Journal of International Money and Finance, 18:751-768.
[13] Davutyan and Pippenger (1985). Purchasing power parity did not collapse during the 1970's. American Economic Review, 75:1151-1159.
[14] Dickey, D. A. and Fuller, W. A. (1979). Distribution of the estimations for auto- gressive time series with a unit root. Journal of the American Statistics Association, 74:427-431.
[15] Dornbusch, R. (1976). Expectations and exchanges rate dynamics. Journal of Po- litical Economy, 84:1161-1176.
[16] Enders, W. (1988). Arima and cointegration tests of ppp under fixed and flexible exchange rate regimes. The Review of Economics and Statistics, 70:504-508.
[17] Engle, R. F. and Granger, C. W. J. (1987). Cointegration and error-correction: Representation, estimation and testing. Econometrica, 55:251-276.
[18] Flynn, N. A. and Boucher, J. (1993). Tests of long-run purchasing powerparity using alternative methodologies. Journal of Macroeconomics, 15:109-122.
[19] Frankel (1978). Purchasing power parity: Doctrinal perspective and evidence from the 1920's. Journal of International Economics, 8:169-191.
[20] Frankel (1981). The collapse of purchasing power parity during the 1970's. Journal of International Economics, 16:145-165.
[21] Frankel, J. A. and Mussa, M. (1980). The e±ciency of foreign exchange markets and measures of turbulence. American Economic Review, 20:374-381.
[22] Frankel, J. and Rose, A. (1996). A panel project on purchasing power parity: Mean reversion within and between countries. Journal of International Economics, 40:209-224.
[23] Granger, C. and Newbold, P. (1974). Spurious regression in econometrics. Journal of Econometrics, 2:111-120.
[24] Hakkio, C. S. (1982). Exchange rate determination and the demand for money. The Review of Economics and Statistics, 64:681-687.
[25] Im, K. S., Pesaran, M. H., and Shin, Y. (1995). Testing for unit roots in heterogeneous panels. Manuscript, University of Cambridge.
[26] Johansen, S. (1988). Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control, 12:231-254.
[27] Kao, C. (1999). Spurious regression and residual-baesed tests for cointegration in panel data. Journal of Econometrics, 90:1-44.
[28] Kao, C. and McCoskey, C. (1998). On the esatimation and inference of a cointegrated regression in panel data. Advances in Econometrics, 15:179-222.
[29] Krugman, P. R. (1978). Purchasing power parity and exchange rates-another look at the evidence. Journal of International Economics, 8.
[30] Kugler, P. and Lenz, C. (1993). Multivariate cointegration analysis and the long-run validity of ppp. The Review of Economics and Statistics, 75:180-184.
[31] Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., and Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root? Journal of Econometrics, 54:159-178.
[32] Levin, A. and Lin, C. F. (1993). Unit root tests in panel data: New results. University of California at San Diego, Economics Working Paper Series, 93-56.
[33] Levin, A., Lin, C. F., and Chu, C.-S. J. (2002). Unit root tests in panel data: Asymptotic and finite-sample properties. Journal of Econometrics, 108:1-24.
[34] MacDonald, R. (1996). Panel unit root tests and real exchange rates. Economics Letters, 50:7-11.
[35] Maddala, G. S. and Wu, S. (1995). A comparative study of unit root tests with panel data and a new simple test. Oxford Bulletin of Economics and Statistics, 61:631-652.
[36] Mark, N. (1990). Real and nominal exchange rates in the long run: An empirical investigation. Journal of International Economics, 28:115-136.
[37] McNown, R. and Wallace, M. S. (1990). Cointegration tests of purchasing power parityamong four industrial countries: Results for fixed and flexible rates. Apllied Economics, 22:1729-1737.
[38] O'Connell, P. (1998). The overvaluation of purchasing power parity. Journal of International Economics, 44:1-19.
[39] Oh, K. Y. (1996). Purchasing power parity and unit root tests using panel data. Journal of International Money and Finance, 15:405-418.
[40] Papell, D. H. (1997). Searching for stationarity: Purchasing power parity under the current float. Journal of International Economics, 43:313-332.
[41] Patel, J. (1990). Purchasing power parity as a long-run relation. Journal of Applied Econometrics, 5:367-379.
[42] Pedroni, P. (1997a). Panel cointegration: Asymptotic and finite sample properties of pooled time series tests with an application to the ppp hypothesis: New results. Indiana university Working Paper in Economics.
[43] Pedroni, P. (1997b). On the role of cross sectional dependency in dynamic panel unit root and panel cointegration exchange rate studies. Indiana university Working Paper in Economics.
[44] Pedroni, P. (2004). Panel cointegration: Asymptotic and finite sample properties of pooled time series tests with an application to the ppp hypothesis. Econometric Theory, 20:579-625.
[45] Phillips, P. C. B. (1991). Optimal inference in cointegrated systems. Econometrica, 59:283-306.
[46] Phillips, P. C. B. and Perron, P. (1988). Testing for a unit root in time series regressions. Biometrika, 75:335-346.
[47] Pippenger, M. (1993). Cointegraiton tests of purchasing power parity: the case of swiss exchange rates. Journal of International Money and Finance, 12:46-61.
[48] Quah, D. (1994). Exploiting cross-section variations for unit root inference in dynamic data. Economics Letters, 44:9-19.
[49] Shin, Y. (1994). A residual-based test of the null of cointegration against the alternative of no cointegration. Econometric Theory, 10:91-115.
[50] Taylor, M. P. (1988). An empirical examination of long run purchasing power parity using co-integration techniques. Apllied Economics, 20:1369-1382.
[51] Taylor, M. P. and McMahon, P. C. (1988). Long-run purchasing power parity in the 1920's. European Economic Review, 32:179-197.
[52] Wu, J. L. and Chen, S. L. (1999). Are real exchange rates stationary? evidence from pacific basin countries. International Journal of Finance and Economics, 4:243-252.
[53] Wu, Y. (1996). Are real exchange rates stationary? evidence from a panel data test. Journal of Money, Credit and Banking, 28:54-63.