Thus, (βbw -βbg) converges in probability to zero much faster in CASE 1.2 than in
CASE 1.1. Nonetheless, the Hausman statistic is asymptotically χ2-distributed
in both cases.
CASE 2: We now consider two simple examples in which the time-varying
regressor xit is stationary without trend. Assume:
xit = Θ2,i + Ψ2,t + eit, (21)
where Θ21,i and Ψ21,t are fixed individual-specific and time-specific effects, re-
spectively. Define
P2,1 = limN→∞ nN Pi θ2,i; p2,2 = limN→∞ N ^{ 02^;
q2,1 = limτ→∞ T Pt ψ2,t; q2,2 = limτ→∞ T Pt ψ2,t.
Notice that if the Θ2,i are allowed to vary across different i, the xit become
cross-sectionally heteroskedastic. Similarly to CASE 1, we will demonstrate
that the convergence rates of the between estimator and the Hausman statistic
depend on whether the xit is cross-sectionally heteroskedastic or homogeneous.
CASE 2.1: Assume that the Θ2,i vary across different i; that is, p2,1 -p22,2 6=
0. With this assumption, we can easily show:
|
plimN,τ →∞ NT Ant |
= |
q2,2 |
- q22,1 + σe2 ; |
|
ιl^ 1 R plvm∙N,τ →∞ NfBNT |
= |
p2,2 |
- p22,1; |
|
plimN,τ →∞ nCnt |
= |
0; | |
|
11^ 1 R plimN →∞ N Hn |
= |
2 |
-N= aNT =⇒ N(0, σV(q2,2 - ql,ι + σe));
√NbNT =⇒ n(0, σU(p2,2 - p2,1));
√1NcNT =⇒ N(0, σUσ2).
With these results, we can show
σ-,'λ σ σ σ2 ʌ , x
√nt(bw - β) =⇒ N 0, ----- v ; (22)
(q2,2 - q22,1 + σe2)
√N(βb - β)=⇒ N ∣0, ---- ]; (23)
(p2,2 - p22,1)
More intriguing information
1. The name is absent2. PEER-REVIEWED FINAL EDITED VERSION OF ARTICLE PRIOR TO PUBLICATION
3. Applications of Evolutionary Economic Geography
4. Demand Potential for Goat Meat in Southern States: Empirical Evidence from a Multi-State Goat Meat Consumer Survey
5. The name is absent
6. Business Cycle Dynamics of a New Keynesian Overlapping Generations Model with Progressive Income Taxation
7. Public infrastructure capital, scale economies and returns to variety
8. The name is absent
9. The name is absent
10. Improvement of Access to Data Sets from the Official Statistics