0
$\begingroup$

I have a dataset that covers loan applications from the year 2012 to 2017. It also includes information on the borrower (e.g., age, income, employment status) and information on the loan (loan duration, loan amount, interest rate).

I have a regression where the main independent variable of interest is a gender dummy (1 = female) and the dependent variable is a loan interest rate. I run two specifications of this model. In the first I include, besides the gender dummy, a set of borrower- and loan-level control variables. The second model is identical to the first one, but here I add year and country fixed effects.

In the first model, the coefficient of the gender dummy is negative and statistically insignificant. In the second model, the coefficient of the gender dummy now becomes positive and statistically significant. Can someone help my grasp why the sign of the coefficient flips when adding the year and country fixed effects to the model and why it becomes significant? Or what kind of further testing or analysis I can do to figure this out myself?

$\endgroup$
3
  • $\begingroup$ Welcome to Cross Validated! If you are testing a null hypothesis of no effect (this is typical, so I feel confident in assuming you are), getting an insignificant effect means that your positive point estimate lacks the precision to call it a significantly positive value. In other words, it might be positive, zero, or negative. Thus, it should not really be so shocking that a “significant” result has a different sign. $\endgroup$
    – Dave
    Aug 19, 2023 at 11:39
  • $\begingroup$ Thanks! I am indeed testing a null hypothesis of no effect. One thing I don't yet quite understand is how in what way the inclusion of the fixed effects contribute to the sign becoming positive instead of negative? $\endgroup$
    – Juliuslah
    Aug 19, 2023 at 11:49
  • $\begingroup$ Cross-posted at statalist.org/forums/forum/general-stata-discussion/general/… $\endgroup$
    – Nick Cox
    Aug 19, 2023 at 14:14

1 Answer 1

2
$\begingroup$

As an aside, you don't have a gender variable, you have a sex variable. "Female" is a sex. "Feminine" is a gender.

When you add variables to models, the parameter estimates for the other variables change (unless the variables are all orthogonal to each other, which rarely happens in observational studies). Sometimes they change sign, but that's not really key. They change.

Significance or not is also not the key issue. See Andrew Gelman's paper The Difference between Significant and not Significant is not, Itself, Statistically Significant.

Why does the parameter estimate for sex change when you add year and country? Because one of those two (I'm guessing it's "country") mediates the relationship between sex and interest rate. (Note: Some people use "mediate" only when the new variable reduces an effect, but I think it useful to use it more broadly).

There are lots of posts on mediation here, and also lots of material on the web and in books. That should help. (You can try searching the 'mediation' tag to get started).

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.