Large-N and Large-T Properties of Panel Data Estimators and the Hausman Test



Notice that since ∣∣Z⅞τ (E⅛^χ3jitEx3jit) ∣∣4 ≤ τ (r)4 G (¾)4 by Assumption
6(iv), we have sup,
∣∣Z⅞feT (A¾y.⅛fe,i - Ex3kti) ∣∣4 ≤ (ʃθɪ τ (r)4 dr) supiG(¾)4
for
к = 1,2, and 3. Therefore, by Lemma 10, we have

E KD3kτ (Ej^ix3k,i — Ex3k1i} K


(uniformly in i)



< ∞, for к = 1, 2, 3,


where τ3ι (r) = 0. So,

supE ∖∖D (Eτz.x3,i - Ex3ji) ∣∣4 < ∞.               (67)

Similarly, it follows that

sup sup E ∣∣Z⅛τ (E∏sx3 - E⅛)∣∣4 < ∞∙            (68)

N,T l<i<N


In addition, notice that

sup sup ∣∣Z⅛τ (Ex31i - Ex3)Il
N,Tl<i<N

sup sup


N,T l<i<N


(D33τ {Ex33tι — Ex33)
D3∙2τ (Ex321i — Ex32) — H32μg32i
D33τ {Ex33yι — Ex33) — H33μg33.


(69)


+ sup sup

N 3<i<N


0

-^32 At332

-^33 At333


By Assumption 6(v), as T → ∞,


sup sup


N 3<i<N


(D33τ (Ex33g. — Ex33)
D3,2τ
(¾2,i — Ex32) — H3g32 .

D33τ (Ex33ji — Ex33) — H33μg33 .


sup sup


D33τ {Ex33,i — Ex33j)            ''

D32τ (Ex32,i — Ex32j) — H32g32 i At3323J

D33τ (Ex33ιi — Ex33j) — H33 μg33 i — μ933 j) J


sup
i,j


f           D33τ (Ex33ji — Ex33j)

D32τ (Ex32,i — Ex32j) — H32 μg32 i At332i3

D33τ (Ex33,i — Ex33j) — H33g33 i — μ933 j


46




More intriguing information

1. Apprenticeships in the UK: from the industrial-relation via market-led and social inclusion models
2. The name is absent
3. Ex post analysis of the regional impacts of major infrastructure: the Channel Tunnel 10 years on.
4. Public Debt Management in Brazil
5. Regional science policy and the growth of knowledge megacentres in bioscience clusters
6. Factores de alteração da composição da Despesa Pública: o caso norte-americano
7. The name is absent
8. An Attempt to 2
9. The Impact of Hosting a Major Sport Event on the South African Economy
10. Effects of red light and loud noise on the rate at which monkeys sample the sensory environment