Since SZeeZ and SZωZ coincide asymptotically, we get, using bars to denote plims,
(A.4)
V( √N β ) = [ S XZ
ZZSZX]-1[S
XZ
ZZ
ZΩZ SZZ sZX ][SXZ szz sZX ] 1,
(A.5)
V( 4N β ) = [ S XZ
- Ω Z SZX] 1 ∙
Replacing the plims Sxz, Szx, SZZ and SZωz by their sample counterparts,
Sxz, SZX, SZZ and SZêêZ and dividing by N, we get from (A.4) and (A.5) the
following estimators of the asymptotic covariance matrices of βb and βe :
(A.6) V(β) = N [SXZS-ZSZX] 1[SXZSZZSZ..Zs-ZsZX][sXZs-ZsZX] 1
= [X0PZX]-1[X0PZbb0PZX][X0PZX]-1,
(A.7) Vdd ) = N S XZ S -. . - S ZX ]—1
= [ X 0Z ( Z 0bb. 0Z )-1Z 0X ]-1 = [ X 0P Z (b b0 ) X ]-1 ∙
These are the generic expressions which we use for estimating variances and co-
variances of the GMM estimators considered.
When calculating β from (A.3) in practice, we replace PZ(Ω) by PZ(bê0) =
Z(Z0 .b.b0Z)-1Z0 [see White (1982, 1984)].
30
More intriguing information
1. A Dynamic Model of Conflict and Cooperation2. TWENTY-FIVE YEARS OF RESEARCH ON WOMEN FARMERS IN AFRICA: LESSONS AND IMPLICATIONS FOR AGRICULTURAL RESEARCH INSTITUTIONS; WITH AN ANNOTATED BIBLIOGRAPHY
3. WP 92 - An overview of women's work and employment in Azerbaijan
4. A Multimodal Framework for Computer Mediated Learning: The Reshaping of Curriculum Knowledge and Learning
5. The name is absent
6. Disturbing the fiscal theory of the price level: Can it fit the eu-15?
7. Reconsidering the value of pupil attitudes to studying post-16: a caution for Paul Croll
8. An alternative way to model merit good arguments
9. The name is absent
10. Wage mobility, Job mobility and Spatial mobility in the Portuguese economy