Testing Panel Data Regression Models with Spatial Error Correlation

and

a_σ2 Ih=
∂ d
a_σ2 ∣H₀=
∂ _tt I
∂λ I н§

Jt In,

I_t (B^,B)-∖

∂²_vI_τ (B'B}-∖W'B + b'w)(b'b)-∖

where B = Iχ — ATU and A is the MLE of A under Hq. Using (A.2), we get

¾=H L = -⅛^γU-b)+⅛^,ι⅛ (≡)²]≡∙

°^σμ ^l¾ ^^cr_z√

This uses the fact that

(A.25)

(A.26)

(A.27)

(A.28)

"¹⅛∣H= = ⅛^iτ B^tB)(^j_τ i_n) = ⅛j_t b'b,
dσ_μ IHg σ_v σ_v

d⅛ d∣_ff. = (⅛⅛ -B'B)(⅛⅛ B∙B) = ±j_τ (B^,B)²,

JO и I ∕ι∩ (7 (7 (7

μ и ^u is -id '^j is

^tr[ "⅛L∙ = ⅛^trljτ ≡] = ⅛r[B'B].
^m∕< IH_{0 σ},_j σ_i7

Similarly

<9L I TN 1 ʌ,r .^, ʌ,,ʌ

(A.29)

~w =—zτ S—τ~∖^u [It (B B)]u = 0,

5σ2∣H₀= 2⅛ 2⅛

which yields

_λ2 _ u'[I_τ B'B]u

^σv ~ TN ’

This uses the fact that

d⅛. = ⅛⅛ bNj_t (S'SN) = ^_τ ⅛

U O °^, у ^u is

^∖_ll, = Ji¹τ ι_κ)(Iττ B'B) = τ_lτ b'b.

(J(J ,, I ∕ι∩ (7 (7 (7

Z√ 0'-⁷i√ ^l7 у ^u is

Γ -lljfl∣ ₌ ^tn

^{l u} ∂σl ^jIh₀= Bl ∙

Also,