Levin Lin(1992) Oh(1996),Wu(1996) Papell(1997) Im, Pesaran Shin(1996) Canzoneri, Cumby Diba(1999) Lee, Pesaran Smith(1997) FGLS SUR

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1 EVA M, SWEEEY R 3,. ;. McDonough ; 3., 3006 ; ; F4.0 A Levin Lin(99) Im, Pesaran Shin(996) Levin Lin(99) Oh(996),Wu(996) Paell(997) Im, Pesaran Shin(996) Canzoner Cumby Diba(999) Levin Lin(99) Coe Helman(995) R&D Sillovers Im, Pesaran Shin(996) Lee, Pesaran Smih(997) O Connell(998) O Connell FGLS Sweeney(000) SUR O Connell(998) Sweeney(000)

2 Levin Lin(99) Im, Pesaran Shin(996) Coe Helman(995) Sweeney Li(999) --- Levin Lin(99) Im, Pesaran Shin(996) Levin Lin(99) Im, Pesaran Shin(996) Levin Lin(99) Im, Pesaran Shin(996). Levin Lin(99) z i z zˆ i, = zi, zi ~ z = zˆ zˆ z i = z z ˆ = zˆ = i= - Dickey-Fuller ~ z i, ~ = ~ + ε 3 z z

3 ε = i =,,, ~ z ~ z i= = ˆ = 4 ~ z i= = ~ ˆ = z 5 i= = ˆ σ ˆ σ ( ~ z ~ z ) = i= = = Levin Lin(99) µ --- ( ˆ ) (0,0. ) µ.5 µ µ (0,), µ = + o( ) µ = + o( ) Levin Lin(99) 0, 6 ( ˆ ) + 3 (0,0.) (0,) - Augmened Dickey-Fuller - ~ k z = ~ z + φ j ~ z ζ j + j= 6 ζ k = ~ z I() Levin Lin(99) (6) (6) ~ z i, = ---. Im, Pesaran Shin(996) z i Im, Pesaran Shin(996) -

4 ki = i ~ z ~ + φ j z j + 7 j= ~ z ζ ζ k i (6) (7) Levin Lin(99) Im, Pesaran Shin(996) - Levin Lin(99) Im,Pesaran Shin(996) Levin Lin(99) [] Im, Pesaran Shin(996) Im,Pesaran Shin(996) (7) i = i =,..., Im, Pesaran Shin(996) --- Γ Γ = E( ) 8 Var( ) / / ( ~ ) ˆ ( ˆ ~ ) = i= z = ( ) ( ~ z z ), E ) i = ( Var( ) --- Γ Im, Pesaran Shin(996) Im, Pesaran Shin(996) (7) --- Γ 3 Levin Lin(99) Im, Pesaran Shin(996), 3., - Ω - 3

5 Ω z i = z + (0,), i =,,, =,,,, z 0 = 0 () () Levin Lin(99) - (6) ~ z i, Im, Pesaran Shin(996) - (7) ~ z i, 0,000, ε ε 3. O Connell,998 Sweeney,000 - Ω - Ω - Ω, - Ω - Ω Ω = C Λ C = P P C Ω Λ Ω P C / Λ { ε } E = i, (0,) i=,,, =,,, cov( ) I E = / U = P E = C Λ E ε 4

6 z i = z +, z 0 = 0 i =,,, =,,, cov( U ) = E[ U U ] = E[ P = P cov( E ) P = C Λ, µ / E I E Λ / P C = P = C E( E Λ E C ) P = Ω - - () () z Levin Lin(99) - (6) ~ z i, Im, Pesaran Shin(996) - (7) ~ z i, 0, Engle Granger(987) Engle Granger --- Y Y Y Y α + π = 8 Engle Granger(987) Y Y --- Levin Lin(99) Im, Pesaran 5

7 Shin(996) Y Y (9) Y Y (9) Y Y Y Y Y (9) Levin Lin(99) Im, Pesaran Shin(996) π ˆ --- (9) αˆ - Ω i, - Ω, - Ω i -, - i π ˆ π ˆ 6

8 = ˆ α + π Y ˆ Y, αˆ π i Y i, Y, Y i, i Y i, (9) Y = b + τ ˆ τ Y () () ˆ - (6) (7) ~τ 0,000 0,000 (9) Y 5 τ 7

9 [] CAZOERI M, CUMBY R, BEHZAD D. Relaive Labor Produciviy and he Real Exchange Rae in he Long Run: Evidence for a Panel of OECD Counries [J]. Journal of Inernaional Economics, Aril 999, 47: [] COE D, HELPMA E. Inernaional R&D Sillovers [J]. Euroean Economic Review, May 995, 39: [3] EGLE R, GRAGER C. Coinegraion and Error Correcion: Reresenaion, Esimaion and esing [J]. Economerica, March 987, 55: [4] IM K, PESARA H, SHI Y. esing for Uni Roos in Heerogeneous Panels [R]. Working Paer, Dearmen of Alied Economics, Universiy of Cambridge, Augus 996. [5] LEE K, PESARA H, SMIH R. Growh and Convergence in a Muli-Counry Emirical Sochasic Solow Model [J]. Journal of Alied Economerics, July/Augus 997, : [6] LEVI A, LI CF. Uni Roo ess in Panel Daa: ew Resuls [R]. Discussion Paer 93-56, Universiy of California, San Diego, December 993. [7] LEVI A, LI CF. Uni Roo ess in Panel Daa: Asymoic and Finie-Samle Proeries [R]. Discussion Paer 9-3, Universiy of California, San Diego, May 99. [8] O COELL P. he Overvaluaion of Purchasing Power Pariy [J]. Journal of Inernaional Economics, February 998, 44: -9. [9] OH K. Purchasing Power Pariy and Uni Roo ess Using Panel Daa [J]. Journal of Inernaional Money and Finance, June 996, 5: [0] PAPELL D. Searching for Saionary: Purchasing Power Pariy under he Curren Floa [J]. Journal of Inernaional Economics, ovember 997, 43: [] SWEEEY R. Mean Reversion in G-0 ominal Exchange Raes [R]. Working Paer, Georgeown Universiy, July 000. [] SWEEEY R, LI ZH. An Emirical Inquiry on he Presence of Uniform Cross-Counry Producion Funcions [R]. Working Paer, Georgeown Universiy, Seember 999. [3] WU YR. Are Real Exchange Raes onsaionary? Evidence from a Panel-Daa es [J]. Journal of Money, Cred and Banking, February 996, 8:

10 Some Mone Carlo Exerimens on Panel Uni-Roo ess & Panel Coinegraion ess EVAS M, SWEEEY R, LI Zhi-hong 3 (. Dearmen of Economics, Georgeown Universiy, Washingon DC 0057, USA;. McDonough School of Business, Georgeown Universiy, Washingon DC 0057, USA; 3. Human Sudies Insiue, he Science and echnique Universiy, Changsha 3006, China) Absrac: In his aer, we firsly develo some Mone Carlo rocedures o generae he finie-samle densiy disribuions for anel uni-roo es saisics accouning for cross-secional roeries. A simle Mone Carlo framework is hen develoed o generae he finie-samle densiy disribuions for single-equaion anel coinegraion es saisics accouning for he underlying hyoheical coinegraing relaionshi. Keywords: anel daa; uni-roo es; coinegraion es Levin Lin(993) Im, Pesaran Shin(996) Y π ˆ 9

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