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



4 Inference

In practice, the number of cointegration relationships is often unknown. It is
therefore interesting to test hypotheses on the cointegration rank. Larsson,
Lyhagen and Lothgren (2001) suggest a “LR-bar” statistic that is based on
the standardized mean of the cross section LR statistics for the hypothesis
H0 : r = r0 against the alternative HA : r > r0 . This test statistic assumes
that the cointegration vectors are different across
i (heterogenous cointegra-
tion), whereas our framework assumes that the cointegration vectors are the
same for all cross section units (homogenous cointegration). To improve the
power of the test in the case
βi = β for all i, the homogeneity assumption
can be imposed.

Following Saikkonen (1999) a simple test procedure is constructed, where
the restriction of a homogeneous cointegration relationship can easily be
imposed. To nest the null and the alternative hypotheses we write

δyit = αiβ0yi,t-1 + γiβyi,t-1 + εit ,                   (7)

where γi is a k × (k - r) matrix with full column rank. Under the null hy-
pothesis it is assumed that
γi = 0 yielding (1), whereas under the alternative
γi is unrestricted so that the matrix

Πi = [αiβ0 , γiβ0 ]

has full rank for at least one i {1, . . . , N}. Pre-multiplying (7) with the
orthogonal complement
α0i, yields

uit = δiwi,t-1 + eit ,                                (8)

where uit = α'i,∆yü, δi = α,i,γi, wit = βyit, and ea = α,i,1εit. To test the
hypothesis
r = r0 the equation (8) is estimated by ordinary least-squares and
a LR, Wald or LM statistic can be constructed to test the hypothesis
δi = 0
for all
i.

In practice the matrices αi, and β are unknown and must be replaced
by consistent estimators. This can be done by computing orthogonal com-
plements of the estimates of
αi from the first step and the estimate of β from
the second step of the estimation procedure proposed in section 3. The fol-
lowing theorem states, that the limiting null distribution of the test statistic
is similar to the one derived by Lyhagen et al. (2001).



More intriguing information

1. The name is absent
2. AN ECONOMIC EVALUATION OF THE COLORADO RIVER BASIN SALINITY CONTROL PROGRAM
3. THE MEXICAN HOG INDUSTRY: MOVING BEYOND 2003
4. Constructing the Phylomemetic Tree Case of Study: Indonesian Tradition-Inspired Buildings
5. The name is absent
6. The role of statin drugs in combating cardiovascular diseases
7. Hemmnisse für die Vernetzungen von Wissenschaft und Wirtschaft abbauen
8. The name is absent
9. Reconsidering the value of pupil attitudes to studying post-16: a caution for Paul Croll
10. Mergers under endogenous minimum quality standard: a note
11. The name is absent
12. The bank lending channel of monetary policy: identification and estimation using Portuguese micro bank data
13. Job quality and labour market performance
14. The name is absent
15. Restructuring of industrial economies in countries in transition: Experience of Ukraine
16. Beyond Networks? A brief response to ‘Which networks matter in education governance?’
17. Foreign Direct Investment and the Single Market
18. Improvement of Access to Data Sets from the Official Statistics
19. Parallel and overlapping Human Immunodeficiency Virus, Hepatitis B and C virus Infections among pregnant women in the Federal Capital Territory, Abuja, Nigeria
20. Graphical Data Representation in Bankruptcy Analysis