时空数据与时空计量模型概述中文(2016年08月12日)

ᰬঠᮦᦤ࠼᷆фᰬঠ᫇⃵⁗ශᾸ἖
2015 ᒤ 07 ᴸ 22 ᰕ 2016.08.12
(Spatial Econometrics) (Spatial Effect) (Spatio-time Models)
§1 ᓅᤦ
(Spatial Econometrics) (Spatial Effect)(Anselin 1988, Anselin 1999) (Spatial Dependence) (Spatial Correlation), (Spatial Heterogeneity) Dependence) (Cross sectional data)
(Crosssectional
( Paelinck and Klaassen 1979, Cliff and Ord 1981, Upton and Fingleton 1985, (Spatial Interaction) Anselin 1988, Haining 1990, Anselin and Florax 1995) (Anselin and Bera 1998, Anselin 2001, Anselin 2002, Florax and Van DerVlist 2003, Anselin et al. 2004) (Spatio-temporal Data Analysis) (Spatial-temporal models) 2 3 4 5 6
1

§2
§2.1
yit = xit Ø + ≤it yit ≤it i y = XØ + ≤ y = (y1 , y2 , ..., yT ) X NT £ K
0
0
(1) K £1 t (2) y NT £ 1 Ø K £1
i
y
t
xit
i
t
yi , i = 1, 2, ...T ≤ NT £ 1
N £1
(Spatial Ordering)
E [≤it ≤jt ] 6= 0, 8i 6= j
(Stability) (Homogeneity)
§2.2 W j (Linkage) i j wij = 0 1
s wij
N £N
wij wij i j 0 1 wij
i (Network) wij = 1
i
j
s wij = wij /
P
j
(subjectivity) Cliff and Ord 1981( Weights)
(ad hoc) ( 17-19 ) Ng (Lag operator) L (3) Anselin 1988( ) ) (Block (Case 1991, Case 1992, Lee 2002)
1/Ng ° 1
Lyt = yt°1 2

, j wij
zi
P
j
wij zj z W NT £ NT z
i
i
W y = (IT ≠ WN )y W X = (IT ≠ WN )X W ≤ = (IT ≠ WN )≤ §2.3 (Spatio-time Lag Model) y = Ω(IT ≠ WN )y + X Ø + ≤ Ω Ω W (4)
(Endogenous) i i i X ≤ y = [IT ≠ (IN ° ΩWN )°1 ]X Ø + [IT ≠ (IN ° ΩWN )°1 ]≤ t
2 2 yt = Xt Ø + ΩWN Xt Ø + Ω2 WN Xt Ø + ... + ≤t + ΩWN ≤t + Ω2 WN ≤t ...
j
i
j
j (Spatial Multiplier)
i
j (Anselin 2003)
i y
(5)
(6)
yt
Xt
Xt ≤t
OLS (Spatial Filter) : [IT ≠ (IN ° ΩWN )]y = X Ø + ≤ (Detrend) Ω=1 §2.4 t T ¿N N £ (N ° 1)/2 N £ (N ° 1)/2 W IN ° ΩWN Ω=1 (7)
3

§2.4.1 (Direct Representation) (Geostatistics) 8i 6= j, t = 1, 2, ..., T : E [≤it ≤jt ] = æ 2 f (ø , dij ) ø dij i j ( ) f (Durbin 1988) æ (Isotropy) (8) (Cressie,1993)
(Distance Decay Function)
§2.4.2 (Spatial Error Process) (Spatial Autoregressive) (Spatial Moving Average) ≤t = µWN ≤t + ut µ ut N £1
2 E [ut ut ] = æu 2 Ωt,N = æu (BN BN )°1
0 0
SAR (9)
BN = IN ° µWN : (10)
2 ΣN T = æ u [IT ≠ (BN BN )°1 ]
0
(11) WN (BN BN )°1 WN (Global)
0
W
BN SAR 8t = 1, 2, ..., T : ≤t = ∞ WN ut + ut
(12)
2 Ωt,N = E [≤t ≤t ] = !u [IN + ∞ (WN + WN ) + ∞ 2 WN WN ]
0
0
0
(13)
2 ΣN T = æ u (IT ≠ [IN + ∞ (WN + WN ) + ∞ 2 WN WN ])
0
0
(14) SAR
W SMA §2.4.3
[IN + ∞ (WN + WN ) + ∞ 2 WN WN ] (Local)
0
0
(Spatial Error Components,SEC) son 1995, Anselin and Moreno 2003)
Kelejian
Robinson
(Kelijian and Robin-
≤t = WN √t + ªt 4
(15)