How to interpret a regression with years on the LHS

Question

I would like to know how I can interpret the coefficients in a regression when the dependent variable is years.

For example, suppose I am interested in the year different cities received a new Apple store ($year$, say it goes from 1990 to 2010), and I use (a) income $inc$ and (b) indicator for having a Microsoft store $micro$ as the independent variables, and I have a dummy or fixed effect for each region. Then I estimate two equations separately:

$year_c = \beta_1 inc + region_c + \varepsilon_c$

$year_c = \beta_2 micro + region_c + \varepsilon_c$

Suppose $\beta_1 = -1$ and $beta_2 = 2$. I think it mean cities with higher income were treated 1 year earlier and cities with a Microsoft store were treated 2 years later.

But I don't know how to interpret it exactly: 1 year earlier relative to what?

Thank you.

Answer 1

If your research question is "when do cities get a new Apple store?" then I think the appropriate method is survival analysis. Because not all cities have them yet. You probably want to use some sort of multiple events model, as many cities have more than one.

Also, I'm not sure why you are doing this with two equations instead of one.

Another reason not to use OLS regression is that, per your question, the dependent variable is bounded. Survival methods (aka time to event methods) will deal with that appropriately. There are other methods for bounded dependent variables, but here, time to event seems right.