Question about Heterogeneous (and possible cross correlated) Dynamic Narrow Panel

[Daniel Perez]

Dear Statalist colleagues,

I am working with a narrow panel dataset (N <10, T = 30), where I find that the series of interest are cointegrated. I intend to obtain consistent estimators of the short-term and, particularly, long-term parameters.
Looking around, I found the Stata commands by JanDitzen that are really useful, particularly for implement the CCE estimator (either by MG or Pooled) and for my particular interest in long-term specifications: error correction, ARDL, or DL.

I did not yet test for unobserved cross-correlation, but I have some confusion from my lack of experience in panel time-series data.

I have read in some texts (for example, Baltagi and Pesaran) that when panel variables have unit roots and/or are cointegrated, what should be used are FM-OLS (Fully Modified OLS), DOLS (Dynamic OLS), or DSUR (Dynamic SUR). So I have the following two questions:

1) The number of observations allows me to consider the CCE test and estimators? In such a case, if I use CCE, would the estimators also be consistent for cointegrated variables (like FM-OLS, DOLS, or DSUR)?

2) If the better option is to apply any of these estimators: FM-OLS, DOLS, do you know any Stata command (in the release or community ADO) that estimates them?

I really appreciate any help and/or opinion on this topic.

Thanks.

[JanDitzen]

Daniel asked me this question via private messages and I believe the question is of broader interest.

From my point of view there are two questions:

1. Do you have heterogeneous slope coefficients? If you find heterogeneous slopes, use the MG estimator. If slopes are homogeneous use a pooled estimator. For the former you need a large N, for the latter small N is sufficient.
2. Do you have cross-sectional dependence? If you have strong cross-sectional dependence in your variables, use the CCE estimator, otherwise do not use it! To identify the unobserved common effects, you require a large number of cross-section units (N) and time periods (T).

The answer to the two questions imply the assumptions on the behaviour of N and T.

Given your dataset I would strongly advise against the use of the literature on cross-sectional dependence and common correlated effects (i.e. the concept of weak and strong cross-section dependence, CCE estimator, CD test) and the MG literature. Both literatures assumes a large number of observations across space (N) and the CCE on time (T). Especially N<10 is not large.
However, we are in an applied setting here and "large" can mean a lot. Usually I differentiate between "large" in a theory context and here the relative speed of the increase of N/T is important for any asymptotics to be valid. N<10 is very small, for the estimation of the MG estimator and removing strong cross-sectional dependence using cross-section averages. Secondly what is computationally feasible. While T=30 is doable, it will give you a low degree of freedom for the individual regressions. The same argument holds for N<10, you can do a CCE-MG regression, but the cross-sectional averages will do a bad job identifying the common factors.

In a nutshell, I would strongly advice against the use the CCE estimator. I am a bit more lenient to say you can use the MG estimator, but then closely look at the distribution of individual coefficients and how outliers drive the results. In both cases (MG or pooled) you can use xtdcce2 without cross-section averages. The pooling options will allow you to estimate the model with pooled coeffiicents. You can also estimate an ARDL or ECM model. I would say you can use FM-OLS, DOLS or DSUR (I am not sure about the assumptions here on N, but it should be fine), but maybe some other members on this board are more experienced with such estimators.

Hopefully this helps!

[Daniel Perez]

Thank you again Jan.