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

First we consider the case of uncorrelated errors, that is, Q = I . It turns
out that for small T all tests have a tendency to reject the null hypothesis
b = 1 too often.⁴ The size bias is most severe for the DOLS procedure. If
the errors are generated with a contemporaneous correlation using Q 6= I ,
then the usual t-statistics based on the assumption of i.i.d. errors (2S-OLS)
rejects the null hypothesis much too often. The use of robust standard errors
as in (15) reduces the size bias of the test drastically although a moderate
tendency to over-reject the null hypothesis remains if T is small. In contrast,
the standard errors of the DOLS procedure are seriously over-estimated if
the errors are contemporaneously correlated. Consequently, the test based
on the DOLS procedure has a severe (negative) size bias.

7 Conclusions

In this paper, a parametric approach for estimation and inference in coin-
tegrated panel data models is suggested. Following Ahn and Reinsel (1990)
and Engle and Yoo (1991), an asymptotically efficient estimator is proposed,
where all individual specific short-run parameters are estimated in the first
step and the long-run parameters are estimated from a pooled regression in
a second step. A test procedure is suggested that allows to test the number
of cointegrating relationships and a likelihood ratio statistic is proposed that
allows to test hypotheses on the long-run parameters. Monte Carlo simu-
lations demonstrate that the parametric approach is much more effective in
reducing the small sample bias than the FM-OLS of Pedroni (1995, 2000)
and Phillips and Moon (1999) or the DOLS estimator suggested by Kao and
Chiang (2000). Furthermore, the estimated standard errors of the two-step
estimator can easily be adjusted to account for heteroskedasticity and con-
temporaneous correlation of the errors, a feature that is often encountered
in cross-country studies.

⁴The standard errors of the FM-OLS estimators computed by the NPT 1.1 program
produces implausibly small values yielding an empirical size close to one.

14

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