[Carlo Lazzaro]

Jaspal:
1) I do share Jeff Wooldridge 's advice about including -sq_age- in my previous example (that was intended as a drill and, as such, surely poorly thought-through);
2) as Jeff stated, -linktest- and friends are tests for the functional form of the dependent variable (actually, I've read oftentimes that it is a misspecification test or a mispecification test of the functional form/specification of the regressand);
3) there are different ways the -linktest- can be carried out (which one is best, I do not know):
a) the augmented regression reported by Jeff in his last reply;
b) the auxiliary regression with the regressand regressed onto fitted, sq_fitted. cu_fitted, (and sometimes) qu_fitted (see https://www.stata.com/bookstore/heal...s-using-stata/ pages 60-63.
Sometimes clustered-robust standard errors are invoked, sometimes not (if the original regression used non-default standard errors).

Sticking with Jaspal's last question, if heteroskedasticity was detected, -robust- or -cluster()- standard errors (both options do the same job under -xtreg-) are mandatory (regardless their impact on coefficients satistical significance, which is anyway biased if default standard errors are used despite evidence of heteroskedasticity and/or autocorrelation).

[Jeff Wooldridge]

Jaspal: What test did you perform to see if you have serial correlation? It's true your N is quite small, but maybe at the borderline of where clustering can be trusted.

What I meant by my comment about RESET is that it cannot generally detect omitted variables unless they are functions of x. I discuss this a bit in my introductory econometrics book and in a "Companion to Econometric Theory" chapter. The point is simple. If we only observe x, we can only test hypotheses about E(y|x), not E(y|x,v) where v is unobserved. If all variables were jointly normal, both E(y|x,v) and E(y|x) are linear functions. RESET detects nonlinearity in E(y|x), and so it will fail to reject even if v is very important and omitting it is badly biasing your estimates on x. On the other hand, if RESET rejects, all you know for sure is you missed some functional forms in x. It can't tell you whether that's due to omitted v.

[Jaspal Channa]

Carlo:
Thank you for your help! I'll include this uncertainty in my analysis and will adjust the SE to make them robust.

[Jaspal Channa]

Jeff:
Thanks very much! I performed the test below:

xtserial lnyrslost lnalc lngdpnethe lnhe lnhrs lnlru lnobese lnoop lnpol

Wooldridge test for autocorrelation in panel data
H0: no first order autocorrelation
    F(  1,      34) =      1.141
           Prob > F =      0.2931

The Wooldridge test. Perhaps you've heard of it.

Is there a simple WLS transformation I could use to remove the issue of heteroskedasticity?
Ahh I see what you mean about the RESET test. Makes sense.

[Carlo Lazzaro]

Jaspal:
your data do not support evidence of autocorrelation.
That said, if you detected heteroskedasticity, why not going -robust- or -cluster()-?

[Jaspal Channa]

Carlo:
I am reluctant to use them because they lead to insignificant results. I am wondering if there is an alternative way to produce unbiased results that could still allow statistically significant findings to be inferred.

[Carlo Lazzaro]

Jaspal:
have you tried logging the regressand?

[Jaspal Channa]

Carlo:
Yes, the regressand is logged.

[Carlo Lazzaro]

Jaspal:
I'm afraid you have to move to non-default standard errors, then.
Your seeming statistical significance with default standard errors is actually biased because of heteroskedasticity.

[Jaspal Channa]

Carlo:

Could I not use WLS to estimate my panel data model?

[Carlo Lazzaro]

Jaspal:
most -weights- option imposes -robust- standard errors.

[Federico Tedeschi]

I'd be careful constructing the "link" test by hand. I assume that when you used the built-in command, Stata is properly compute the standard error that accounts for the first-step estimation of beta. The procedure proposed by Carlo is sound but I don't think the standard error is correct.

I prefer a modification of RESET in which I can compute a valid standard or or joint F test. I will also not that it's almost always a good idea to cluster your standard errors to account for serial correlation and heteroskedasticity.

xtreg y x1 x2 ... xK, fe vce(cluster id)
predict xbhat, xb
gen xbhatsq = xbhat^2
gen xbhatcu = xbhat^2
xtreg y x1 x2 ... xK xbhatsq xbhatcu, fe vce(cluster id)
test xbhatsq xbhatcu

I should also point out that RESET is not a general misspecification test no matter how many times this is said. It is a pure test of functional form. Therefore, you might want to expand your model to include squares and interactions to see if the are important -- if the test rejects. For example, in Carlo's example, I'm pretty sure the square of age would be important, and it is omitted from the equation.

I think it should not be:

gen xbhatcu = xbhat^2

but

gen xbhatcu = xbhat^3