Whether to add an interaction term

[Stella Chen]

Hi all,

I am doing some regression like y=b0+b1*money, where money is the amount donated to a party. I want to investigate if donations to winners would have a greater effect, thus I add y=b0+b1*money+b2*winner, where winner is a binary dummy conditional on money>0. In this case, should I add an interaction term of money*winner? Since winner is conditional on money, will the interaction bring a spurious result?

[George Ford]

what is y?

[Stella Chen]

what is y?

Hi George,

y is some economic benefit from government, like contracts or grants.

[Maarten Buis]

This is a common problem when studying anything to do with donations, volunteering, filantropy, etc.: What do you do with the people who did not donate money, time, or whatever else someone could donate? This problem is biggest when the donation is the dependent/explained/left-hand-side/y variable. Fortunately, that is not the case for you. As an independent/explanatory/right-hand-side/x-variable you need to worry about non-linearity: The step from donating nothing to donating 1 dollar/euro/pound/... is qualitatively very different than the step from 1 dollar/euro/pound/... to 2 dollars/euros/pounds/... If you add such a variable linearly, you are saying that going from 0 to 1, or 1 to 2, or 100 to 101 has the same effect, thus ignoring that non-donors are usually very different from donors. If you want to take that distinction into account then you would at least expect a (postive or negative) "jump" in the line at 0. The way to allow for that is to just add a indicator (dummy) variable for non-donor in addition to the donation amount. Here is a Stata tip that discusses that:

https://journals.sagepub.com/doi/ful...36867X20909707

Now I suspect that you have another indicator that is 1 if the donation went to a winner and 0 when not (this obviously includes the people who did not donate). Yes, you can add an interaction of that variable and the money amount. Don't forget the main effects. But otherwise go for it. It is probably a helpful to use margins and marginsplot to interpret your model.

[George Ford]

Lowess would be useful too with only one key variable of interest.

[Maarten Buis]

Lowess has its uses, but it would not be my choice for this application. A lowess makes a smooth curve, but a qualitative change between donor and non-donor just is not smooth.

[George Ford]

I was thinking about non-linearities in the relationship at low values of money (near zero)

[Stella Chen]

This is a common problem when studying anything to do with donations, volunteering, filantropy, etc.: What do you do with the people who did not donate money, time, or whatever else someone could donate? This problem is biggest when the donation is the dependent/explained/left-hand-side/y variable. Fortunately, that is not the case for you. As an independent/explanatory/right-hand-side/x-variable you need to worry about non-linearity: The step from donating nothing to donating 1 dollar/euro/pound/... is qualitatively very different than the step from 1 dollar/euro/pound/... to 2 dollars/euros/pounds/... If you add such a variable linearly, you are saying that going from 0 to 1, or 1 to 2, or 100 to 101 has the same effect, thus ignoring that non-donors are usually very different from donors. If you want to take that distinction into account then you would at least expect a (postive or negative) "jump" in the line at 0. The way to allow for that is to just add a indicator (dummy) variable for non-donor in addition to the donation amount. Here is a Stata tip that discusses that:

https://journals.sagepub.com/doi/ful...36867X20909707

Now I suspect that you have another indicator that is 1 if the donation went to a winner and 0 when not (this obviously includes the people who did not donate). Yes, you can add an interaction of that variable and the money amount. Don't forget the main effects. But otherwise go for it. It is probably a helpful to use margins and marginsplot to interpret your model.

Thanks Maarten, that really helps.
Also thanks George for the clarification.

I'm also wondering if any of you are experts in duration models and Granger causality in unbalanced panel data.
I have the unbalanced data as I described.
I wanna check how long the firms take to get their first contract, and if political donations will accelerate this process.
I also wanna check reverse causality that contract leads to donations. Thus I need to do a duration model, and a Granger test in unbalanced panel data.
I'm not sure if I need to transfer the panel data into crosssectional one for the duration model, with only one observation for each firm. If I need to do that, how should I deal with annual control variables.
Also I couldn't find any packages in Stata for unbalanced panel data Granger test.

[Maarten Buis]

I was thinking about non-linearities in the relationship at low values of money (near zero)

With donations there is no smoothness near zero: Those who do not donate are completely different from those who donate a very small amount. Especially, because those who donate small amounts tend to be rather poor and that small amount is actually larger share of their available income. Lowess just is not made for such abrupt changes.

[Maarten Buis]

I wanna check how long the firms take to get their first contract, and if political donations will accelerate this process.

Assuming you have data on firms since their founding you can do a duration model on the time since being "born" till first contract. In Stata this type of model is called a survival model. See help st for all that is possible in Stata with that kind of data. Don't forget the pdf manuals: they are mode detailed than the help-files. On top of that you can look at Stephen Jenkins' material here: https://www.iser.essex.ac.uk/resourc...sis-with-stata or mine here: http://www.maartenbuis.nl/wp/survival.html and this book: https://www.stata.com/bookstore/surv...-introduction/

[Stella Chen]

Assuming you have data on firms since their founding you can do a duration model on the time since being "born" till first contract. In Stata this type of model is called a survival model. See help st for all that is possible in Stata with that kind of data. Don't forget the pdf manuals: they are mode detailed than the help-files. On top of that you can look at Stephen Jenkins' material here: https://www.iser.essex.ac.uk/resourc...sis-with-stata or mine here: http://www.maartenbuis.nl/wp/survival.html and this book: https://www.stata.com/bookstore/surv...-introduction/

Thanks Maarten for all the materials of the duration model. Is it reasonable that I add fixed effects in Cox model?
And by any chance do you have materials about how to do unbalanced panel Granger test?