A COMPANION TO Theoretical Econometrics

Large sample properties of full information estimators

Theorem 8. For a linear simultaneous equations model satisfying the assump­tions in Theorem 2 and with a nonsingular error covariance matrix, the following asymptotic properties of the 3SLS estimator hold:

Подпись:'ft(X 3SLS - §) ^ N(0, V3sls)

^3SLS - V2SLS
where

V3SLS = plim (Z'(X-1 ® PX)Z/T)-1

V2SLS = plim {1/T(Z'(I ® PX)Z)-1(Z'(X-1 ® PX)Z)(Z'(I ® Px)Z)-1}.

Theorem 9. Under regularity conditions which are satisfied by the classical simultaneous equations model

Vt(5fiml - 5) Л N {0, plim [(1/T)(d[7] [8] log L/3535')]-1}.

Furthermore, if there are no restrictions on X, then the asymptotic covariances of the 3SLS and FIML estimators coincide and thus, 3SLS and FIML are asymptot­ically equivalent. Finally, FIML and 3SLS are asymptotically efficient within the class of all consistent, uniformly asymptotically Gaussian estimators of 5.

Theorem 10. FIML and linearized FIML are asymptotically equivalent.

For the instrumental variable method, suppose the instrument matrix for Z in y = Z5 + u is Z, of the form

( Z Z11

Z12

" Z1G

N>

II

Z21

Z22

" Z2G

VZG1

ZG2

" ZGG

Recall that the data matrix Z is diagonal (Z1, Z2,..., ZG).

Following the partitioning of Z, into (Y,, X) we can further decompose each submatrix

Z as Zij = (Zj1, Zj2)

where Zij1 and Zij2 are parts of the instrument matrices for the right-hand side endogenous and exogenous variables, respectively, appearing in the jth equation with respective dimensions T x (G, - 1) and T x Kj.

Theorem 11. eous system y = Z5 + u, let XIV = (Z'Z) 1Z'y,

where Z is defined in the preceding paragraph. Suppose

1. Pr(|Z'ZM0) = 1

2. plim (Z'u/T) = 0

3. plim (Z'Z/T) is nonsingular and finite

4. plim (Z'Z/Т) = plim (Z'(X <8> I)Z/T).

Then XIV and X3SLS are asymptotically equivalent if and only if the following two conditions hold:

Добавить комментарий

A COMPANION TO Theoretical Econometrics

Normality tests

Let us now consider the fundamental problem of testing disturbance normality in the context of the linear regression model: Y = Xp + u, (23.12) where Y = (y1, ..., …

Univariate Forecasts

Univariate forecasts are made solely using past observations on the series being forecast. Even if economic theory suggests additional variables that should be useful in forecasting a particular variable, univariate …

Further Research on Cointegration

Although the discussion in the previous sections has been confined to the pos­sibility of cointegration arising from linear combinations of I(1) variables, the literature is currently proceeding in several interesting …

Как с нами связаться:

Украина:
г.Александрия
тел./факс +38 05235  77193 Бухгалтерия
+38 050 512 11 94 — гл. инженер-менеджер (продажи всего оборудования)

+38 050 457 13 30 — Рашид - продажи новинок
e-mail: msd@msd.com.ua
Схема проезда к производственному офису:
Схема проезда к МСД

Партнеры МСД

Контакты для заказов шлакоблочного оборудования:

+38 096 992 9559 Инна (вайбер, вацап, телеграм)
Эл. почта: inna@msd.com.ua