Normality of Residuals in Random Effects Model

[Fabian Knusel]

Dear Statalist,

I am currently writing a seminar paper and need some help. I am calculating the following random effects model:

xtreg mean_reg c.x1##c.x2 x3 x4, re r

My panel data has 163 observations if that is important.

With the commands -hist mean_reg- and -qnorm mean_reg- I found out that my dependent variable and the residuals are not normally distributed.
Running -gladder mean_reg- and -ladder mean_reg- suggested that I transform my variable into 1/mean_reg. With this transformation the distribution is better, but still not optimal. I attached both -qnorm- outputs.
Unfortunately, transforming the variable leads to all around insignificant coefficients. Also, as I have never seen or done a transformation like that, I would not know how to interpret the coefficients.

So my question is this: Is transforming my variable as mentioned above the only way to deal with my distribution issues? Or can I make an argument to leave my variable as it is?

Thanks in advance for your help!
Fabian

[Jeff Wooldridge]

Normality is not needed for anything. All statistical properties of RE estimation are asymptotic even when the error is normally distributed. Provided you have enough data for the asymptotics to work well, both components of the error term can have any well-behaved distribution. The real key is: How big are N and T in your panel data? Hopefully, N is somewhat large and T is somewhat small. Otherwise you probably shouldn't use RE.

JW

[Fabian Knusel]

Thank you for your answer.

N is 21 and T is 9, with 163 total observations (panel is unbalanced). Would you say this is enough data for "the asymptotics to work well"? And, would you choose a different model based on my N and T?

[Jeff Wooldridge]

That's not much. What are your cross sectional units? You have T = 9 years?

I would be much more inclined to use two-way fixed effects -- regardless what a nonrobust Hausman test might say. At least we know FE can be unbiased under certain assumptions. With N = 21, you can just get away with clustering your standard errors at the unit level.

Do your key variables change across i and t, I hope?

[Fabian Knusel]

Thank you for your help.

N is 21 countries and T is 9 years. And yes, my key variables do change across i and t.

In this case, I will definitely look at the two-way fixed effects model as well. Also, I used year dummies in my random effects model too which I did not state in my opening question - sorry for that.
Coming back to the skewed distribution of my dependent variable, your position is that I can disregard that fact and leave my variable as it is?

[Jeff Wooldridge]

What is the variable? Is it always positive?

[Fabian Knusel]

My dependent variable is a measurement for the restrictiveness of a country's immigration policy. It is always positive with values between 0 and 1 and right-skewed.
I put the output of the gladder command in the attachment. The distribution of the variable as it is now is on the top right under "identity".

[Jeff Wooldridge]

Then you can take two other approaches, at least. First, try the log-odds transformation. Second, use a fractional logit model with correlated random effects.

[Fabian Knusel]

I will look into that. Thank you very much for your help!