The most appropriate method

[Martin Eden]

Hello to everybody,

I faced to problem with model specification.

In my paper I considering panel data. Feature of my dataset (the lot of omission (both in IDs and years)) prohibit to me using Arellano-Bond (GM). But in lot of works about my subject this approach was used.

As alternative, I used fixed effects and random effects. According to hausman test, I should to use FE. But option with RE have a better coefficients.

My question is how to correctly justify the choice of the model and explain the impossibility of application Arellano-Bond?

Thanks,
Martin

[Daniel Schaefer]

What do you mean when you say that the random effects model produces "better coefficients"? Are the coefficients larger in size? Significant at lower alpha thresholds? More stable across models? More in line with your theoretical expectations?

My understanding is that a random effects model is most useful when you have time-invariant independent variables that you think explain cross-subject time-invariant differences, and therefore account for temporal autocorrelation across subjects. In contrast, the fixed effects model generates a vector of coefficients for your set of subjects that account for all of the variance explained by temporal autocorrelation. Basically, in the random effects model you use time-invariant variables to explain temporal autocorrelation, whereas in a fixed effects model you control for all of the variance explained by temporal autocorrelation, but without any explanatory power. The Hausman test is essentially telling you that the random effects model doesn't do as well at explaining temporal autocorrelation as a fixed effects model would.

I think its reasonable to ignore the Hausman test in cases where you have time-invariant predictors and a strong substantive interest in using them to explain temporal autocorrelation across subjects. That said, you should also acknowledge in your writeup that you haven't managed to explain all of the variance accounted for by temporal autocorrelation. If your time-invariant predictors are little more than controls, you should just use the fixed effects model.

[Martin Eden]

What do you mean when you say that the random effects model produces "better coefficients"? Are the coefficients larger in size? Significant at lower alpha thresholds? More stable across models? More in line with your theoretical expectations?

My understanding is that a random effects model is most useful when you have time-invariant independent variables that you think explain cross-subject time-invariant differences, and therefore account for temporal autocorrelation across subjects. In contrast, the fixed effects model generates a vector of coefficients for your set of subjects that account for all of the variance explained by temporal autocorrelation. Basically, in the random effects model you use time-invariant variables to explain temporal autocorrelation, whereas in a fixed effects model you control for all of the variance explained by temporal autocorrelation, but without any explanatory power. The Hausman test is essentially telling you that the random effects model doesn't do as well at explaining temporal autocorrelation as a fixed effects model would.

I think its reasonable to ignore the Hausman test in cases where you have time-invariant predictors and a strong substantive interest in using them to explain temporal autocorrelation across subjects. That said, you should also acknowledge in your writeup that you haven't managed to explain all of the variance accounted for by temporal autocorrelation. If your time-invariant predictors are little more than controls, you should just use the fixed effects model.

I mean that coefficients significant at lower thresholds. Consequently, it's a little bit more consistent with my theoretical assumptions. Your comments regarding the applicability of the Hausman test are very useful. As far as I understand, I need to choose FE, since both the Hausman test for models with standard errors and the test for models with robust errors (-xtoverid-) shows p-value < 0?

Furthermore, I would like to understand how interpret the results of GMM? The fact is that I have unbalanced data and Arellano-Bond estimator drops a lot of gaps - as a result, all coefficients are insignificant. Maybe there is some way to fix it? Or is the solution just using other models like FE and RE?

I would appreciate an answer.

Thank you in advance,
Martin

[Daniel Schaefer]

Hi Martin,

I'm afraid I am not all that familiar with the Arellano-Bond estimator, and I am definitely not aware of a way to increase your N when you have unbalanced data. Maybe someone else here can help you with that.

In terms of whether or not to use the FE model or the RE model: the FE model will account for all of the temporal autocorrelation without explaining any of it. This may be why you see the model coefficients are significant at higher thresholds in the FE model: the FE model is accounting for the portion of the variance in your independent variables that explain the variation in the dependent variable that is temporally invariant across subjects. Whether or not you follow the recommendation given by the Hausman test depends on your research goals, and I go over this in detail in post #2. That said, if you don't care about modeling the temporal invariance explicitly with your independent variables, then use the FE model. The FE model will better control for temporal autocorrelation across subjects, and will keep you from underestimating the standard errors on your model coefficients.