regression is rewritten as
zbi+t = Byi(,2t)-1 + vbit , (6)
where z + = y(1l-1 - (biΣ-1 bi)-1 αiΣ-1∆yit, yit = [y(10,yi20]0 and y(1 (y(2 )
are r × 1 (k —r × 1) subvectors of yit. It is interesting to note that z + adopts an
endogeneity correction similar as the estimator of Phillips and Moon (1999).
The important difference is, however, that the latter approach employs a
nonparametric estimate of the endogeneity effect, whereas z + is based on a
parametric endogeneity correction based on a VAR(p) model.
Based on a sequential limit theory, the following theorem states that the
two-step estimator has a normal limiting distribution.
Theorem 1: Let yit be generated as in (1) and Bb2S denotes the least-squares
estimator of B in the regression (6). Furthermore εit and εjt are independent
for i 6= j . If T → ∞ is followed by N → ∞ we have
T √rNvec ( Bb2 S — B) —→ N(0, Ω2 1 ® Σv) ,
where Σv is defined in (4),
1N
ω2 = Jim Tt ∑α2(α0⊥β⊥)-1 αi⊥⊥ςiαi,⊥(β⊥αi,⊥)-1 β⊥2 ,
N→∞ N
i=1
αi,⊥ and β⊥ are orthogonal complements of αi andβ and β⊥,2 is the lower
(n — r) × r block ofβ⊥ .
From this theorem it follows that the long-run parameters are asymptotically
normally distributed and, therefore, the usual tests on the cointegration pa-
rameters involve the usual limiting distributions. In particular, the second-
step regression (6) can be treated as an ordinary regression equation, that
is, the nonstationarity of the regressors and the fact that zbi+t is estimated
can be ignored. Furthermore, it is interesting to note that for finite N and
T → ∞, the estimator are mixed normal, that is, normally distributed with
a stochastic covariance matrix. Therefore, the normal limiting distribution
is expected to yield a reliable approximation even if N is small.
More intriguing information
1. Intertemporal Risk Management Decisions of Farmers under Preference, Market, and Policy Dynamics2. DETERMINANTS OF FOOD AWAY FROM HOME AMONG AFRICAN-AMERICANS
3. A Hybrid Neural Network and Virtual Reality System for Spatial Language Processing
4. BODY LANGUAGE IS OF PARTICULAR IMPORTANCE IN LARGE GROUPS
5. Skill and work experience in the European knowledge economy
6. Government spending composition, technical change and wage inequality
7. Estimation of marginal abatement costs for undesirable outputs in India's power generation sector: An output distance function approach.
8. News Not Noise: Socially Aware Information Filtering
9. The name is absent
10. Volunteering and the Strategic Value of Ignorance