IV regression -- No Endogeneity Detected. Should I stick to OLS?

[Ash Sharma]

Dear Statalisters:

My question is regarding whether I should stick to OLS when no endogeneity is detected in my model.

I'm estimating the effect of some individual personality traits on individual performance. My N is above 300 and the OLS structure is as follows:

reg y x1 x2 x3 x4 x1x2 x1x3 x2x3 x1x2x3

where:
y -- dependent var (performance)
x1, x2, x3 -- explanatory vars (personality traits)
x4 -- vector of control vars
x1x2, x1x3, x2x3 -- 2way interaction terms
x1x2x3 -- 3way interaction term

Now, I'm told that x1 and x2 may be endogenous (there's not enough theoretical reason for that). I found 2 instrumental vars -- z1 and z2 (1 each for x1 and x2) -- and conducted IV regression by using Stata's own module and the extended version proposed by Baum, Schaffer, & Stillman.


1. Stata module:

ivregress 2sls y x4 (x1 x2 x1x2 x1x3 x2x3 x1x2x3 = z1 z2 z1z2 z1x3 z2x3 z1z2x3)
estat endog

The tests of endogeneity suggest that x1 and x2 are not endogenous.
----------------------------------------------------------------------------------------------------------
Durbin (score) chi2(6) = 1.40071 (p = 0.9658)
Wu-Hausman F(6,339) = .222554 (p = 0.9694)
----------------------------------------------------------------------------------------------------------

2. Baum et al. module:

ivreg2 y x4 (x1 x2 x1x2 x1x3 x2x3 x1x2x3 = z1 z2 z1z2 z1x3 z2x3 z1z2x3), endog (x1 x2)

Again, the tests suggest no endogeneity.

----------------------------------------------------------------------------------------------------------
Wu-Hausman F test: 0.22255 F(6,339) P-value = 0.96938
Durbin-Wu-Hausman chi-sq test: 1.40071 Chi-sq(6) P-value = 0.96582
----------------------------------------------------------------------------------------------------------

While the results of IV regressions are somewhat similar to those of OLS estimation, the 3-way interaction term is no more significant.

1. In this case, is it safe to say that the original OLS results are best estimates?
2. Should I inspect further for other issues? What other tests should I run?
3. Am I correct in instrumenting the interactions of exogenous and endogenous vars by using interactions of instruments and exogenous vars?

Since the equation is exactly identified (1 instrument per endogenous var), I do not get the Sargan stats.

Any help is appreciated.

Thanks in advance!

[Carlo Lazzaro]

Grad:
welcome to this forum.
You do not mention whether you performed OLS post-estimation tests, such as -estat ovtest- and -estat hettest-.

If the the test suggest no endogeneity, you should probably stick with OLS, provided that the right-hand side of your regression equation gives a fair and trye view of the data generating process concerning your data.

[Ash Sharma]

Thanks, Carlo!
Appreciate your response.

I'm using robust SE in OLS. Should that not control for heteroscedasticity?

My concern is since the coefficient of the 3way interaction estimated by 2SLS model is not distinguishable from 0, the OLS model is probably biased. Would an extended regression be of any help in this case?

Aside - is there a way in Stata to calculate ITCV for interaction terms (or something else) to get a sense of the probability of any omitted variable with the requisite correlations to bias the results?

Thanks again.

Best

[Carlo Lazzaro]

Grad:
- yes, the -robust- option in OLS takes heteroskeadsticity (but not autocorrelation) of the residual distributioninto account . The meaning of my previous reply was that applying non-default standard errors without investigating whether they are necessary or not, can give back more biased standard errors vs the default ones (that's why I mentioned -estat hettest-);
- if by extended regression you mean that you should give a fair and true view of the data generating process concerning your data, I sponsor your approach;.
- admittedly, I do not know if Stata built-in commandd and/or user-written programme include the option you're interested in. Usually, you would compare different OLS model via adjusted R-sq.

[Ash Sharma]

Thanks again, Carlo.

I tried a different set of instruments this time. While all tests still report no endogeneity, I also got the 3-way interaction significant at p<.05.

Aside, I also tried an extended regression. The instruments are significant in the auxiliary model and the errors are not correlated.

corr(e.x1, e.x2) | p = .20
corr(e.x1, y) | p = .53
corr(e.x2, y) | p = .52

Can I take it as another proof of no endogeneity?

Best

[Nick Cox]

Grad Researcher (may I call you Grad):

Please check out https://www.statalist.org/forums/help#realnames and at greater length #3 in https://www.statalist.org/forums/help#adviceextras where we underline our strong and explicit preference for using full real names -- and what to do about registering your real name.

This is all intended positively: active people here like Carlo all use real names and we believe that such openness and transparency are positive.

Not following the policy suggests that you didn't read the FAQ Advice or decided that you wanted to ignore it, which isn't in the spirit of the site. Easy enough to catch up there!

[Carlo Lazzaro]

Grad:
I'm still not clear with the meaning of extended regression.
Usually, instruments are suggested by previous researches on the same topic.
Hence, your choice should take advantage from what other already did wnen presented with your same research topic.
Ideally (and here comes the trickiest part of the stuff), you should not be totally driven by previous researches but should also avoid re-inventing the wheel: all in all, it's a matter ob (dinamic) balance!

[Carlo Lazzaro]

I totally agree with NIck's kind reminder about using real name.

[Ash Sharma]

Nick:

Thanks for your reply and my apologies for the inconvenience. The original motivation behind the anonymity was only to ensure a blind and fair review process. However, I understand and agree with your point, and will do my bit to continue the tradition.

I could not find a way to change it in the settings, so I have already written to admin asking this favor.

Best,
Ash

[Carlo Lazzaro]

Ash:
thanks for re-registering according to the FAQ.
Your concern about (double) blindness is absolutely correct when it comes to techical journal submission.
I have been contributing to this forum quite frequently in the last four years but my overall experience with Statalist (the old name for Stata forum) sums up to 11 years: during these years, I can say that no thread was skipped and no reply was driven by the original poster's identity.