A parametric approach to the estimation of cointegration vectors in panel data



of free parameters is k - r for all cointegration vectors. As demonstrated by
Johansen (1995, p. 75), any linear hypothesis of the form
Rjβj = rj can be
rewritten as in (10). Inserting the hypothesis in (5) yields a set of
r equations

zj,it = θj (φjyi,t-1) + vjit ,                           (11)

where zj,it is the j ’th element of zit. Accordingly, under the alternative
the parameter vector
θj can be estimated by a least squares regressions of
zbj,it on (Φ0jyi,t-1). Since the system equations for j = 1, . . . , r do no longer
involve the same set of regressors, the SUR system should be estimated by
GLS in order to achieve asymptotic efficiency. It is interesting to note that
no “switching-algorithm” needs to be applied as in Johansen and Juselius
(1994).

Let ett and e*t = [e↑itt,... ,v*it]0 denote the residual vectors of the unre-
stricted regression (5) and the restricted regression (11), respectively. A test
statistic that is asymptotically equivalent to the ML statistic is

ξLR = NT


NT

log∑∑

i =1 t =1


0
vvitvvi0t


- log


NT

V λ V λ ~* ~* 0
eLv^v^
i=1 t=1


(12)


The asymptotic properties of such a test are considered in the following
theorem.

Theorem 3: Let yit be generated as in (1). Furthermore εit and εjt are
independent for
i 6= j. Under the null hypothesis (10) the test statistic ξLR
defined in (10) is asymptotically χ2 distributed with r(k-r) - jr=1 qj degrees
of freedom.

Alternatively, a Wald test procedure can be applied that is based on the
results of Theorem 1.

5 Extensions

So far we have considered the cointegrated VAR(1) model with E(εit) = 0
for all
i and t. Although such a limitation is convenient for expositional
purposes, it is of course too restrictive for practical applications. A more
realistic model is the cointegrated VAR(
p) model with individual specific



More intriguing information

1. The name is absent
2. The name is absent
3. The name is absent
4. CAPACITAÇÃO GERENCIAL DE AGRICULTORES FAMILIARES: UMA PROPOSTA METODOLÓGICA DE EXTENSÃO RURAL
5. Evolutionary Clustering in Indonesian Ethnic Textile Motifs
6. The name is absent
7. CONSIDERATIONS CONCERNING THE ROLE OF ACCOUNTING AS INFORMATIONAL SYSTEM AND ASSISTANCE OF DECISION
8. Exchange Rate Uncertainty and Trade Growth - A Comparison of Linear and Nonlinear (Forecasting) Models
9. Placenta ingestion by rats enhances y- and n-opioid antinociception, but suppresses A-opioid antinociception
10. The name is absent