spanel: an R package to estimate the spatial panel data

MPRA
Munich Personal RePEc Archive
spanel: an R package to estimate the
spatial panel data
Taha Zaghdoudi
Universit´e de Jendouba, Facult´e des Scieneces Juridiques
´
Economiques et de Gestion de Jendouba
June 2016
Online at https://mpra.ub.uni-muenchen.de/72673/
MPRA Paper No. 72673, posted 21 July 2016 23:21 UTC

y=λW y +Xβ +µ
µ=Zµµ+ν

NT ×1
NT ×k β
k×1µ NT ×1
W=IT⊗WNWNN×N
N T
t= 1.....T
i= 1....N
Zµ=νT⊗IN
µ
(0, σ2
µIN)νT
NT ×1 (0, σ2
νINT )µ
ν X
A=IT⊗ANAN=IN−λWN
y=A−1(Xβ +µ)
E[W0
yµ] = E[W A−1(Xβ +µ)µ0] = W A−1Ω6= 0
ω=E[µµ0]Wy
µ
Z= (X, Wy)δ= (β, λ)0
y=Zδ +µ
H= (X, W X, W 2X)
d
δ2sls = [Z0PHZ]−1Z0PHy
PH=H(H0H)−1H0H H
W3X W 4X
¯
JT=JT/T T ET=IT−¯ JT
P ZµP=¯ JT⊗IN
Q=INT −P=ET⊗INQ
˜y=λW˜y+˜ Xβ + ˜µ
QW = (ET⊗IN)(IT⊗WN)=(ET⊗WN) =
(IT⊗WN)(ET⊗IN) = W Q
Q
δ˜ H= ( ˜ X, W ˜ X, W 2˜ X) =
(QX, QW X, QW 2X) = QH
s2ˆσv
2σ2
v
P

¯y=λW¯y+¯ Xβ + ¯µ
P W = ( ¯ JT⊗IN)(IT⊗WN)=(¯ JT⊗WN)=(IT⊗
WN)( ¯ JT⊗IN) = W P
P
δ¯ H= ( ¯ X, W ¯ X, W 2¯ X) =
(P X, P W X, P W 2X) = P H
s2ˆσ1
2σ2
1=T σ2 µ+σ2 ν
µΩ = E(µ0µ) =
σ2
1P+σ2 vQΩ−1/2= (σ−1
1P+σ−1
vQ) Ω−1/2
˙y=˙ Zδ + ˙µ
˙y= Ω−1/2y˙µ= Ω−1/2µ˙ Z= Ω−1/2Z= Ω−1/2(X, WN)=(˙ X, ˙ W)
Ω−1/2WN= (σ−1
1P W +σ−1
vQW ) = (σ−1
1W P +σ−1
vW Q) = WNΩ−1/2
˙y=λW ˙y+˙ Xβ + ˙µ
Ω−1/2δ
\
δRE−2sls = [ ˙ Z0PH˙ Z]−1˙ Z0PH˙y
˙
H= ( ˙ X, W ˙ X, W 2˙ X) = (Ω−1/2X, W Ω−1/2X, W 2Ω−1/2X) = (Ω−1/2X, Ω−1/2W X, Ω−1/2W2X) =
Ω−1/2H