Panel Data Regression Models

Transcription

1 Panel Daa Regresson Models Wha s Panel Daa? () Mulple dmensoned Dmensons, e.g., cross-secon and me node-o-node (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy 3 Covered Topcs Wha s Panel Daa? Pooled Regresson Fxed Effec Models Random Effec Models her Panel Daa Models (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy Wha s Panel Daa? () ode-o-ode Example j = flow from node o node j X j = un cos beween node and node j X3 j = capacy beween node and node j (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy 4

2 Wha s Panel Daa?(3) wh cross-secon() and me() ndces X X T T X T... X T T X T X X X T X X T (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy 5 Lnear Model Panel Daa () = X + X X + bea coeffcens could be me - nvaran secon - nvaran boh k k k = k = k =, (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy 7 k Balanced Panel Daa Each cross-secons has equal number of me perods or T =T =...=T Smple Daa Srucure Less complcaed compuaon Lnear Model Panel Daa () varance of error erms could be me - nvaran secon - nvaran boh V ( ) = V ( ) = V ( ) =, (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy 6 (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy 8

3 Pooled Regresson () General Assumpon = X + X X + where ) all he coeffcens are boh me and cross-seconal nvaran (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy 9 Pooled Regresson () X X X T T X T... X X T T X T X X X X X T X X X T (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy Pooled Regresson () ) homoscedasc error erms V( ) = all, or s also me-nvaran and secon-nvaran => LS apples. (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy Fxed Effec Models () Also called LS Dummy Varable (LSDV) Model. X s consan. = + X X + ) all he coeffcens are me-nvaran and cross-seconal nvaran excep ha s secon-varan bu me-nvaran (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy

4 Fxed Effec Models () ) homoscedasc error erms V( ) = all, or s me-nvaran and secon-nvaran => LS apples f dummy varables are nroduced. (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy 3 Fxed Effec Models (4) D T T T T D (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy 5 Fxed Effec Models (3) Equvalen LSDV = D + X + D D X + where D j f =j, j=,..., = oherwse oe ha D + D D = all, (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy 4 Fxed Effec Models (5) Alernave m of FEM = + X X + oe ha s me-varan bu secon-nvaran, nsead Equvalen LSDV hs FEM s as follows (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy 6

5 Fxed Effec Models (6) Equvalen LSDV = D + X + D T D X + where D j f =j, j=,...,t = oherwse oe ha D + D D T = all, (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy 7 T Fxed Effec Models (8) Heeroscedascy -cross-secon wegh -me wegh V ( ) = V ( ) = =>WLS apples (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy 9 Fxed Effec Models (7) Common Problems many dummy varables requred mul-collneary problem lkely nerpreaon of varan coeffcens Wha f error erms are heeroscedasc? (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy 8 Fxed Effec Models (9) Heeroscedascy -cross-secon covarnce CV(, j ) = j -auo-correlaon CV( s, ) = s =>FGLS apples = = (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy j s

6 Random Effec Models () or REM shor. Also known as Error Componen Models (ECM). X s also consan. = + X X + Smlar o FEM excep ha = + ξ where ξ s cross-seconal varaon (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy Random Effec Models (3) oe ha V( ) = V( ) + V V( ) s nvaran. => LS apples. Trval. ( ξ ) + C(, ξ ) (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy 3 Random Effec Models () Case V(ξ ) s secon-nvaran and C(,ξ ) s nvaran = + X where = + ξ (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy X + Random Effec Models (4) Case V(ξ ) s secon-varan and/or C(,ξ ) s secon-varan oe ha V( ) ssecon - varan. Error erm s heeroscedasc => FGLS apples. How? (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy 4

7 (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy 5 = ) ( V (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy 6 Random Effec Models (5) Case 3 V(ξ ) s secon-varan and/or C(,ξ ) s secon-varan bu = varan. ssecon - V( ha oe ) Error erm s general => FGLS apples. How? (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy 7 = ) ( V (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy 8 FEM vs REM () They are subsue f no heorecal preference. oe ha FEM s preferred when T s large and s small. ) T s small bu s large. Degree of freedom FEM s small. REM s more effcen.

8 (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy 9 FEM vs REM () 3) For T s small and s large, FEM s preferred f cross-seconal varaon (ξ ) s non-random. herwse, REM s preferred. (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy 3 FEM vs REM (3) 4) ξ and X k are correlaed. FEM yelds unbased esmaor bu REM yelds based esmaor (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy 3 Cross-seconal Heeroscedascy () X X =... Assume me-nvaran varance-covarnace error erms. In addon o possbly of dfferen cross-secon weghs (varances), covarances beween errors of cross secons could be non-zero. (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy 3 = ) ( V Cross-secon# Cross-secon#

9 Cross-seconal Heeroscedascy () V( ) = j Cov(, j ) = jj all or hey are me-nvaran bu secon-varan => WLS wll no apples as here are non-zero covarances beween observaon. eed GLS or FGLS. (c) Pongsa Pornchawseskul, Faculy of Economcs, Chulalongkorn Unversy 33