Causality or correlation in panel data regression using random effect model

[amalie thomsen]

Hi all,

I have a question regarding a panel data regression using a Random Effect Model (REM). I am using STATA version 15.1.

After preparing the dataset for panel data regression using **xtset**, I ran the following regression code: **xtreg Y X1 X2 Xn, re**

I am getting significant results to a 95% significance level, which is great.

My question is: Can I interpret these results as a causality or a correlation, now that it is a panel data REM regression?

If it is a correlation, how would I then test for causality, this being a possibility when working with panel data.

I hope someone can help.

All the best,
Amalie

[Carlo Lazzaro]

Amalie:
1) I assume that you have already excluded via -hausman- that -fe- specification fits your data better;
2) I also assume that you have already checked that your regression model is not misspecified (ie, you did not detect endogeneity, non-linear relationships between predictors and regressand, autocorrelation and heteroskedasticity affetcting the distribution of the idiosyncratic error) or you have fixed it according to post estimation test outcomes;
3) causality is often a (too) strong statement. I would say that, when adjusted for the other predictors, the independent variable, say, X1, contributes to explain the variation in the regessand and its effect reaches ststidtical significance;
4) I'm not sure I have got you right about

...now that it is a panel data REM regression...

; -re- specification has surely some relevant advantage vs .fe. specification (eg, estimation coefficients of time-invariant predictor) but it comes under a pretty tight assumption (that may well be hard to prove in empirical researches) of no correlation between both the error terms and the vector of regressors. Hence, I simply see it as a statictical tool with its own advantages and downsides.

[amalie thomsen]

Hi Carlo,

Thanks for your answer.

Yes, I have applied a Hausman test. Regarding your 2nd assumption, how would you check that your regression model is not misspecified?

I understand that causality can be (too) strong a statement. Do you have any academic references on this statement?

At the same time, I know that causal inferences are possible when using panel data. Would you use lag effects to test for this?

/Amalie

[Carlo Lazzaro]

Amalie:
1) in https://www.wiley.com/en-us/Introduc...-9780470032701, page 19, Gary Koop gives some advice about how to interpret correlation as synonim for causality.
2) I've never used that approach; hence, I cannot advise about.