Discussion Paper

No. 2012-1 | January 03, 2012
A Note on the Estimation of Long-Run Relationships in Panel Equations with Cross-Section Linkages


The authors address the issue of estimation and inference in dependent non-stationary panels of small cross-section dimensions. The main conclusion is that the best results are obtained applying bootstrap inference to single-equation estimators, such as FM-OLS and DOLS. SUR estimators perform badly, or are even unfeasible, when the time dimension is not very large compared to the cross-section dimension.

JEL Classification:

C15, C23, C33



Cite As

Francesca Di Iorio and Stefano Fachin (2012). A Note on the Estimation of Long-Run Relationships in Panel Equations with Cross-Section Linkages. Economics Discussion Papers, No 2012-1, Kiel Institute for the World Economy. http://www.economics-ejournal.org/economics/discussionpapers/2012-1

Comments and Questions

Christoph Hanck - SUR
January 09, 2012 - 10:30

I think this is a rather useful piece that convincingly illustrates that not all of the Monte Carlo evidence on statistical procedures need be representative; here, that SUR estimators may work much less well for moderately wide than for narrow panels in a cointegration regression.

Of course, the fact ...[more]

... that SUR works poorly for small T/N ratios is not entirely surprising in view of the need to estimate a NxN variance-covariance matrix with T observations. Maybe this point could have been made more clearly. Ideally, a theoretical analysis sending T and N to oo with, say, T/N -> c>1, could have supplemented the MC evidence, although it is not clear if that is analytically feasible.

Relatedly, would it be promising to develop some kind of fixed-b asymptotics-approach if estimation of the long-run variance is the key problem (as your simulations show)?

The bootstrap of course clearly is a useful alternative, and is shown to offer improvements here. I was a bit surprised to see the block length selection issue handled so quickly here. At least to my knowledge block length selection is still a rather thorny and unsolved issue? I was also puzzled to see that the bootstrap c.i.s undercover even though the associated bootstrap tests are also undersized? Usually, an oversized test should be associated with an undercovering c.i., no?

Some small comments:

- I was a bit surprised to see such a narrow range for phi_ij and rho_ij in the MC design, any particular reason for this?
- on page 5 the use of boldface below the displayed eqs. of the estimators comes a little surprising.
- row, not raw ;-)

Stefano FACHIN - reply to Hanck
January 19, 2012 - 11:08

First of all, we would to thank Hanck for his very helpful comment. In fact, he helped us to spot an embarassing mistake in our paper - obviously, undercovering confidence intervals must be associated to oversized tests. Our results, which go in the opposite direction, are due to a bug ...[more]

... in the section of our program which computed the summary results, and of course to superficial cut-and-paste from the output to the text.
Sorry for this! The correct results are reported in the attached table. Essentially, coverage is similar to the table in the text, while type I errors are around 8%.
On the simulation design ("why are phi and rho chosen in a very narrow range?"), the answer is very simple: our aim is to show that using exactly the design used by Moon and Perron (2004) with different combinations of T and N leads to totally different results (namely, SUR is not the best, or it is even unfeasible).
Finally, we agree that block length is a thorny issue. Since the bootstrap procedure proposed is not the key contribution, we felt that tackling it was outside the scope of the paper and adopted a rule already used in the literature.

Anonymous - Referee Report
May 10, 2012 - 09:50

See attached file