VIF test of multi-collinearity

[Peter Meier]

Dear list members,

after running some -ivregress2 2sls- and -ivprobit- regressions, I am unsure which specifications have excessive multi-collinearity. I understand that running the -vif- command after the regressions should tell me but I am still unsure about the following:

(1) Am I right in assuming that any regressor that gets a VIF>10 should be dropped, including if it gets a value of just say 10.50?

(2) Other than after -reg-, after both -ivregress2 2sls- and after -ivprobit- I get the error that I cannot use -vif- but only -vif, uncentered-, which compared to the simple -vif- after -reg- seems to always yield higher estimates. Am I right in assuming that then indeed the uncentered version is appropriate and I need to drop any regressor yielding a VIF>10 there?

(3) I tried to export the VIF results into -outreg2- with the option -addstat(VIF,e(vif))- but got a syntax error and did not find a more suitable syntax for this in the help file examples. How do I instead get the VIF results to be displayed directly in my Excel regression table?

Thank you so much!
PM

[Jeff Wooldridge]

Your question is unanswerable without seeing estimates and standard errors. What kind of results are you getting? Why are you computing VIFs in the first place? No fixed rule of thumb can work for dropping variables due to collinearity. A large sample size can easily offset of VIF > 10. It's all in the standard errors.

Plus, are the collinear variables being used as controls only? Or are they your key variables?

[Peter Meier]

Thanks for the feedback! I'm copying in an example below: a common first stage, second stages for 2 different outcome variables y1 and y2, and VIF values for all coefficients where -vif, uncentered- produced values greater than 10.

Here I get a high VIF value also on my instrumented regressor xx, which is of core interest. x1 is an additional regressor of interest, but I could also drop it if including it produced questionable results. The rest are controls I could also drop context-wise, but I figured readers would ask for all of them if I just drop them without providing a good data-based argument for doing so.

Best regards, PM

	1st stage	2nd stage 1	2nd stage 2	VIF>10
	(1)	(2)	(3)
	xx	y1	y2
z1	0.06***
	(0.01)
z2	-0.09***
	(0.00)
xx		-0.38**	2,698.03***	34.17
		(0.18)	(245.59)
x1	-0.08***	-0.03	1,529.21***	86.45
	(0.01)	(0.09)	(125.61)
x2	0.01***	0.02***	-64.66***	20.57
	(0.00)	(0.00)	(6.05)
x3	-0.00**	-0.05**	566.35***
	(0.00)	(0.02)	(29.95)
x4	0.01***	-0.84***	216.94***
	(0.00)	(0.03)	(65.21)
x5	0.00	-0.18***	-30.14
	(0.00)	(0.03)	(39.46)
x6	-0.00	-0.86***	289.12***
	(0.00)	(0.04)	(72.17)
x7	-0.01***	-0.10***	-204.16***
	(0.00)	(0.02)	(29.79)
x8	-0.05***	0.04**	-339.42***	97.67
	(0.00)	(0.02)	(24.32)
x9	-0.01***	0.01***	-16.67***	51.72
	(0.00)	(0.00)	(2.33)
x10	0.01***	-0.01***	-13.44***	22.11
	(0.00)	(0.00)	(2.68)
x11	0.05***	0.06***	-50.47**	79.67
	(0.00)	(0.02)	(22.97)
Constant	1.13***	-0.08	11,237.61***
	(0.03)	(0.31)	(415.82)
Obs	25,000	25,000	20,000

[Jeff Wooldridge]

After seeing that, I'm still puzzled why you'd even compute the VIFs. For y2, you have t statistics on the key variables of over 10. Why do you care about collinearity in such a case? Since I don't know what y1 and y2 are -- in fact, the round number of observations makes me think this is generated data -- I can't say more. xx and x1 aren't significant for explaining y1. It could be they're highly correlated with one another, but that isn't a problem for y2. Those standard errors properly capture all of the sampling uncertainty; there's nothing more to say, really.

I'll also note that the other explanatory variables with VIF > 10 are statistically significant. Again, why are you checking the VIFs?