Hi Jihad,

By running a pooled OLS on panel data you fail to take into account individual and/or time effects. Even if the omitted variable bias is always present in all econometric models, a panel data model with individual and/or time effects has the useful particularity to reduce it. I recommend running a fixed effects model instead, as it is likely to be more efficient than pooled OLS and consistent compared to a random effects model.

I further recommend you to take a look at specific chapter of the classic Wooldridge book: https://mitpress.mit.edu/books/econometric-analysis-cross-section-and-panel-data-second-edition

Best,

Ricardo

A p-value alone is not really meaningful to decision making. 

Perhaps you want to concentrate on comparing performances of competing models by holding out some of the known data, and seeing how well you would have predicted for it with each. 

I run fixed effects and random effects models, the most appropriate one is the Pooled OLS model.

Maybe I should add another variable or run nonlinear model ..

Thank you for your replies ..

My experience is mostly in sampling and inference for establishment surveys at given points in time, for official statistics, so, cross-sectional surveys.  There, heteroscedasticity is the rule, and it is very important. (See https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity, based on an argument by Ken Brewer.)  So, I'm curious as to why heteroscedasticity is ignored here.   -  By the way, one of the other causes of heteroscedasticity is omitted variables, but I counted that as "nonessential," not because it is unimportant, but because that describes a situation about which you may be able to do something, whereas heteroscedasticity caused by the relative 'size' of a member of a population, when dealing with a random variable, is not a "problem," but a natural part of the error structure.  OLS is a special case of WLS (weighted least squares), but OLS appears to implicitly assume all members of a population are of equal size. 

You might want to look through some of the work by Kelvyn Jones.  See https://www.researchgate.net/profile/Kelvyn_Jones, with regard to multilevel models. 

Dear Jihad,

As I said, the omitted variable biais is inevitable and it is present in all econometric models, you cannot avoid it! In your particular quest, it may cause at least two problems: i) technical and ii) theorical. Even if you manage to go about the technical problems by using WLS or fixed effects or whatever suits the data at hand, there will still be omitted variables! Then, you must always rely on the theoretical underpinnings of your model to posit a correct and credible INTERPRETATION of your results. Be cautious about causal claims as some coefficients may be capturing some of the effects caused of the ommited variables. So you must have an idea of what they are and interpret the coefficients accordingly and based upon solid theoretical grounds.

Two questions

1) How are you testing for omitted variable bias. If you have instrumental variables you can estimate your system by instrumental variables and test the the values of the coefficients are different which implies endogeneity. But then the instrumental variables have solved your problem! If you have other variables had you any good reason for leaving them out? If adding them to a model changes the coefficients of other variables then they are omitted variables. In general I do not know of any way of testing for omitted variable bias as you describe.

2) Please explain how you arrived at the conclusion " I run fixed effects and random effects models, the most appropriate one is the Pooled OLS model". While it is an advanced text the book by Wooldridge as recommended by Ricardo Nogales Carvajal is a good guide to this kind of analysis.

The ovtest in stata is the Ramsey Regression Equation Specification Error Test (RESET) and is more a general test of model miss-specification rather than a test of omitted variables. Look up RESET in your econometrics test book for more details. The pooled model does, in any case suffer from miss-specification and you should try to improve it.

Panel models can include unobserved effects in your model. If the unobserved effects are correlated with the explanatory variables then use fixed effects as random effects are biassed in such circumstances. If they are uncorrelated with the explanatory variables use random effects. The Hausman test can be used to choose between fixed and random effects. You should also be guided by theory and common sense as to which is appropriate.

I presume that your panel dimension is large. Have you tried a two-way model?

Without a knowledge of your project and data it is difficult to make proposals in the abstract. To summarize, your pooled model appears to have problems. Panel models can account for some endogeneity.