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st: third variable...
My variables of interest are concerned with net votes. The dependent
variable is GENCH = change in a party's vote at the current general
election from the previous one. The key independent variable is MIDCH =
change in a party's midterm election vote from the previous general
election. I hypothesise that MIDCH has a significant effect on GENCH over
time (or, over several GEs). In the models I've fitted so far (using both
- -reg- and -xtgls-) I have found this to be the case for all parties. So
far, so good.
At a recent workshop, however, I was told both of these variables may be
influenced by a third variable (let's call it REGION) and, once controlled
for, there may be no relationship between GENCH and MIDCH. How should one
handle this in a time-series context? -ivreg- would appear to be ruled
out, since this deals with endogeneity. -xtgls- could be used regardless,
but this may be a dangerous option to take given the above. I'm not
entirely sure if simultaneous equation models would help here or not.
What I do know, however, is that the key variables in my models are all
differenced, and time trends have been fitted, which goes part of the way
to solving this problem (if, indeed, I have it). If anybody has any
comments, I'd be very grateful to you.
If region is a categorical variable, and these are xt data, then there are two possibilities: region modifies the constant term (in which some sort of fe or re model should be used) or region modifies the entire relationship (including the coeff on midch). In the latter case a set of interacted dummies would be used in a fe context, or one could use some sort of random-coefficients model (Hildreth-Houck).
I did not respond to the original enquiry since the answer seemed obvious: if there is a third variable that (one suspects) should be in the relationship, and it is measurable, the correct methodology is to include it. After having done so, one may test for its relevance. Techniques such as dealing with proxy issues would only arise if the variable in question is not quantifiable.
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