Lag selection

[alessandro gst]

Hello, I am new to stata and statistics.
I am running a panel model (t=17, N=130) with fixed effects. Reading academic work in my subfield I have seen that many scholars tend to lag the explanatory variable to different degrees to ensure exogeneity. Normally only one lag is included, but sometimes up to 5 lags are included in the model. I was wondering whether there is a statistical test that can provide me with some information on the number of lags I should include in my model, or whether this is only a theoretical decision.
thanks a lot for your answers

[Carlo Lazzaro]

Alessandro:
when you run a panel data regression with -fe- specification, the -fe- machinery wipes out all the time invariant predictors and their potential endogeneity.
However, the potential endogeneity related to time-varying predictors remains.
Do you suspect endogeneity in your data, according, say, to the literature in your research field?
As an aside, as you have a quite relevant T dimension, you may want to consider -xtregar,fe- instead of -xtreg- (I assume that your regerssand is continuous).

[alessandro gst]

Dear Carlo,
thank you very much for your kind reply.
I have a couple of follow up questions. models in my subfields often look something like this y = xt-1 + zt-1 + λ + e. Where λ are country fixed effects and x and z are time-varying explanatory variables taken at time t-1 and e is the error. However the number of lags that is used for my explanatory variables changes from study to study. It may be a trivial question because I am new to statistics, but I was wondering whether there is a test I should consider to decide the number of lags for my explanatory variable, or whether the decision is exclusively theoretically based.

In the same vein, building on your suggestion of using xtregar, would you have any suggestion to adjudicate between xtreg and xtregar. And more in general, (since I am also planning to run a dynamic model, I was wondering how I can test for the number of lags of my dependent variable to include in the model (AR1, AR2, AR3 or more)

thank you again very much for your help

[Carlo Lazzaro]

Alessandro:
1) I'm not aware on any test about lag selection. As far as I know, it is mainly theory-driven. The same holds for choosing among AR1, AR2, ...ARn.
2) choosing between -xtreg- and -xtregar- when the T dimnension of your panel dataset looks non-negligible it's a matter of modeling the autocorrelation structure. Again, different habits can be found in different research fields.