adding third variable

[Yara Issa]

Hello,
I have a question regarding adding a third variable to the simple regression. I have X is not significant in the first stage on Y (Model 1). Then when I added Z to the model, now X became significant, and the magnitude became larger. This result gives an indication of the suppression effect. However, I am a bit not sure here. For the suppression effect, Z should not be correlated with Y; but in my case, the two variables are correlated. Any thoughts, please?

[Andrew Musau]

With only two right-hand side variables, you still have your work cut out to convince anyone that you do not have omitted variable bias. Correlated is ambiguous, most variables are correlated to some degree. You can look at variance inflation factors and if these are large (rule of thumb >5), then the overall fit of the model will still be fine but you cannot make anything of the individual coefficient estimates or their significance. If these variables are just controls and you have other independent variables that are not highly collinear with them, then the coefficients on these independent variables will be largely unaffected and you can just ignore the multicollinearity.

[Carlo Lazzaro]

Yara:
1) are you referring to and instrumental variabe regression (first stage) or else?
2) regradless of 1), the predictors should give a fair and true view of the data generating process you're investigating;
3) last but not least, why not sharing what you typed and what Stata gave you back, as per FAQ? Thanks.

[Yara Issa]

Dear Carlos and Andrew
Sorry if I was not clear in my question. I am looking at the subjective well-being and parenthood status (0 no kids, 1 with kids). so, I have the regression:
well-being= (0/1 parent status) (reg wellbeing i.chilldess)
the result is not significant

Then I added social network variables (support receive from ties (continue). The coefficient of parenthood status is now significant and large.
hope this is ok now

[Carlo Lazzaro]

Yara:
1) as Andrew wisely commented above, with a simple OLS it is really difficult to get reliable results.
2) you added a second predictor and your main regressor became significant. So far, so good, provided that 2 predictors (no matter their signficance) give a fair and true view of such a diffcult topic to define as subjective well-being is.
3) I'd give -linktest- a shot.
In addition: I would investigate the risk of endogeneity due to reverse causation: is it theoretically reasonable that subjective well-being explains parenthood, other things being equal?
Last but not least, why not sharing what you typed and what Stata gave you back, as per FAQ? Thanks.