Endogeneity problem for small panel sample

[islam abdelbary]

How to deal with endogeneity problem for a small panel sample which T>N, Is in this case the GMM methods will not appropriate?

some papers mention to least squares dummy variable corrected model (xtlsdvc) can handle this problem, But what the solution of the Hausman test was insignificant and the random effect model is most appropriate.

Can anyone help me????

[Philip Gigliotti]

You can only address endogeneity with causal inference methods. And my baseline assumption is that every variable is endogenous. If you don't have a credible causal identification strategy you're sunk. This could be difference in differences, instrumental variables or regression discontinuity design. If all else fails propensity score matching can be used.

If no natural experiment is available, your best best is a two way fixed effects model, but the consistency of your estimates still has to be justified by theory, and you can't prove it or defend it with identifying assumptions.

This view may sound extreme but it is aligned with the mainstream currents of research in economics and causal inference, and the standard for publication in economics journals and other journals that adhere to standards of causal inference.

[islam abdelbary]

Thanks, Philip Gigliotti for your reply, but what do you mean by causal inference methods. Do you mean panel VAR or panel Granger causality?

In fact, the endogeneity problem comes from include institutions variable in the economic growth model, mainly all papers used IV or GMM to overcome this problem, but in my case, I couldn’t use any. Instruments variables used before none of them are adequately applicable to the MENA region, also GMM estimator will be inconsistent especially for MENA sub sample 5 countries during 20 years

[Philip Gigliotti]

Causal inference methods are econometric procedures that can replicate the assumptions of a randomized experiment, which is the gold standard of causality. For an excellent treatment see the text causal inference for statistics, social and biomedical sciences by imbens and Rubin.

The assumption of this framework, which is the standard approach in economics, finance and many other social scientific areas, is that there is "no causation without randomization." There is no way for a variable to be exogenous unless it was assigned in a randomized experimental framework. Under this assumption every variable is endogenous, it's just a matter of degree. Further more there is no way to derive a consistent estimate given the assumptions of ols regression.

The solution to this problem.is to find natural experiments, or conditions existing in the observational data that can replicate the assumptions of a randomized experiment. The main ones are difference in difference, instrumental variables or regression discontinuity design. If that is not available, propensity score matching is an artificial data structuring technique that can approximate randomization.

Often a natural experiment is not available, and propensity score matching is not always seen as a suitable replacement. In this case, in my opinion the best choice is to use a two way fixed effect model. In the absence of simultaneity these results will be plausibly consistent. A strong result in a two way fixed effects model is publishable in many cases in a good but probably not top venue.

[Phil Bromiley]

@Philip is more doctrinaire than many of us. For example, he explicitly assumes everything is endogenous with absolutely no information about the data or context.

While natural experiments are very nice when you can find them, there are a great many papers published in most social science areas using less robust techniques.

As for Islam's problem, he does have a very difficult issue. Almost none of the techniques related to endogeneity have small sample properties. Both ols and most corrections for endogeneity produce biased parameters in small samples - it is not obvious that 2SLS or GMM give you lower bias than ols in small samples. Naturally, it would depend on a bunch of sample-specific issues like how good the instruments are, how serious the endogeneity is, etc. So, in my opinion, Islam is probably better off with something simple (maybe both OLS and 2SLS).

[islam abdelbary]

Phil Bromiley and @Phillip Gigliotti, many thanks for your reply, I was working for my model during the last period. 2sls through Instruments variables used before none of them are adequately applicable to the MENA region such as Settler Mortality, Enrollment in Christian Missionary Schools, Characteristics of Geography, % of Western European Languages as a mother tongue, Ethnolinguistic Fractionalization.
what about adding specification effects such as i.year or i.country ? is that could help to reduce endogeneity?

Do you have any suggestions books or papers dealing with this issue?

thanks,
Islam

[Philip Gigliotti]

If you have multiple years in your sample you need year fixed effects (i.year) regardless of model specification. There is too much that goes on year to year to not include them in panel data analysis.

My suggestion is also to add country fixed effects. This model is now a two way fixed effects model which should be plausibly consistent in the absence of simultaneity. Do not use i.country. specify a panel data fixed effects model

xtset country year

xtreg depvar indepvar i.year, fe vce(cluster country)

[Philip Gigliotti]

If you have multiple years in your sample you need year fixed effects (i.year) regardless of model specification. There is too much that goes on year to year to not include them in panel data analysis.

My suggestion is also to add country fixed effects. This model is now a two way fixed effects model which should be plausibly consistent in the absence of simultaneity. Do not use i.country. specify a panel data fixed effects model

xtset country year

xtreg depvar indepvar i.year, fe vce(cluster country)

There's a number of robustness checks you can use to test for consistency in your two way fe model.

Wooldridges has a test using a one year lead of your explanatory variable to test for strict exogeneity, the identifying assumption of a 2 way fixed effects model. Specify your original model with an additional one year lead of your explanatory variable. If the coefficient on the lead is null you have an argument for exogeneity. Test according to the following specification.

xtreg depvar indepvar F.indepvar i.year, fe vce( cluster country)

You can also try a test for conditional independence. Regression your explanatory variable on your control variables individually in separate binary two way fe models. If all the coefficients are null you have an argument for conditional independence of your explanatory variable, that it is not correct with endogenous factors in the model. You can also specify this model backwards regressing your controls on your explanatory variable. These results should also be null.

A third test is to specify your two way fixed effects model of your depvar on explanatory variable with and without controls. If the magnitude and significance of your explanatory doesn't chnage when controls are added, you have a plausible argument for consistency.

If your model passes these tests then I think you've got a decent result.

[islam abdelbary]

@Philip Gigliotti, thanks for your advice it seems very helpful, could you please suggest a book or paper as reference for that methods