Interaction terms and testing for significance in Stata

[Kian Williams]

Hi all! I have a mix of a Stata and statistics question that I've been struggling with. Basically, I'm running an OLS regression generally as follows:

reg Δconfidence group1 Δquotagroup1 group1xΔquotagroup1 group2 Δquotagroup2 group2xΔquotagroup2 group3 group4 controls

Where group1, group2, group3, and group4 are binaries that take a value of 1 if an individual respondent is part of that group.

Where Δquotagroup1 and Δquotagroup2 are the changes in admissions quotas that affect members of group 1 and 2 respectively, between two periods.

And Δconfidence in the change in reported confidence in an institution reported by individuals in the sample (that belong to group 1, 2, 3, or 4).

I'm trying to determine the effect of changes in the quota for group 1 on the change in reported confidence of individuals in group 1, and the same for group 2.

Further, I would like to determine whether the effect of the quota change for group 1 on the confidence reported by individuals in group 1 is higher than the individuals that are not affected by the group 1 quota (so everyone else in the sample not part of group 1).

Here is where I am struggling. I'm understanding that the coefficient of Δquotagroup1 + the coefficient of group1xΔquotagroup1 would give the effect of the change in quota for group 1 on individuals in group 1, as that would be taking the derivative of the function for group 1 (where group2 and all other group variables are set to 0) with respect to the Δquotagroup1.
But I am not sure how to test for the statistical significance of this sum in Stata. Does this setup make sense, and is there a way to do this? Thanks so much, and please let me know if anything is unclear or doesn't make sense!

[Clyde Schechter]

-help lincom- will show how you can get inferential statistics about linear combinations of coefficients following a regression.

There is a better way, however. Write your regression command with factor variable notation (see -help fvvarlist- if you are not familiar with it) and then you can use the -margins- command afterwards. So something like -margins group, dydx(Δquotagroup1)- will give you the average marginal effect of Δquotagroup1 on each of the groups. It's less typing than using -lincom- and you don't have to worry about whether you've selected the right coefficients and added them correctly, as -margins- handles all that for you.

That said, can you clarify some things about your context, because your design looks questionable to me. You state "I would like to determine whether the effect of the quota change for group 1 on the confidence reported by individuals in group 1 is higher than the individuals that are not affected by the group 1 quota (so everyone else in the sample not part of group 1)." But in most contexts, if the quota for group 1 changes, the quotas for all other groups must also change so that the total remains constant, given what I assume is a fixed capacity to accommodate admissions. Which would imply that the other individuals are affected by the group 1 quota.

[Kian Williams]

Hi Clyde. Okay, thanks so much for the help. Factor variables and the margin command seem like the best way to do this.

And that's a good point. In this case there aren't quotas for groups 3 and 4, they just fall into general admissions and the rest of the admissions pool is filled out by members of those groups. But I would expect there to be an indirect effect of the quota increases on the confidence reported by groups 3 and 4. So it may make sense to interact the quota variables for 1 and 2 with the other groups as well, then.