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



for some constant M2 . By Assumptions 2 and 6(i), for t = [Tr] and finite
constant
M2 , we have


sup sup E kD1Tx1,itk4
i,T 1tT

sup sup M3 (∣∣D1TIl4E ∣∣(xι,it
i,T
1tT

sup sup τ1 (r) Θ1,i 4 .

i r[0,1]


Ex1,it)k4+ kD1TEx1,itk4


Next, similarly, by Assumptions 3(ii) and (iii),

sup sup E x2,it 4 sup sup M3 Ex2,it

i,T 1tT                 i,T 1tT

< ,


Ex2,itk4+kEx2,itk4


and by Assumptions 4(ii) and (iii) and 6(iii) and (iv),


sup sup Ekx3,itk4  

i,T 1tT


sup
i,T


sup M3 E °x3,it - EFzi x3,it°4 + Ex3,it4

1tT                       i


Therefore,


sup sup
i,T 1tT

which yields (83). ¥

Part (c)

By Lemma 16(a). ¥

Part (d)

By Lemma 16(d). ¥


M2


.


E (suΡi,t °x3,it - EFzi x3,it°4)
+ supi,t E ° ° EFzi x3,it - Ex3,it°4
+ supi,t Ex3,it 4


kGx,T (xit
t


Xi)k2


2<M,


Proof of Lemma 3

By Lemma 16(c). ¥

Proof of Lemma 4

Write

., Pi Dtwii=N Pi D


Twei


(ui


Ef.Ui) + (N Pi DT⅛W,'DT) λ.   (85)


Notice that by Assumption 10,

∣Ef  ɪ P

Fw ° N


i DT wei (ui


EFwui)


2 σ2       1

) = NutrE\N Pi DtυjiWj0 DTJ


54




More intriguing information

1. Intertemporal Risk Management Decisions of Farmers under Preference, Market, and Policy Dynamics
2. Centre for Longitudinal Studies
3. The Role of Immigration in Sustaining the Social Security System: A Political Economy Approach
4. Housing Market in Malaga: An Application of the Hedonic Methodology
5. The name is absent
6. HACCP AND MEAT AND POULTRY INSPECTION
7. The name is absent
8. An Efficient Circulant MIMO Equalizer for CDMA Downlink: Algorithm and VLSI Architecture
9. Rural-Urban Economic Disparities among China’s Elderly
10. The name is absent