Trouble interpreting a discontinuity model

[Jun Park]

The picture is an excerpt from a paper I am reading. (Roads and Loans, Review of Financial Studies). I think based on the reporting of the results from the authors, beta1 is their interest. But my question is, why would the authors not include [500-h<pop<500+h] separately as they did with the 1000 threshold?

[Rich Goldstein]

first, I'm confused and since you only gave part of the cite, I can't easily check things

second, isn't the B2 term in the second line exactly what you wanted? if not, please clarify

[Jun Park]

Rich Goldstein Hi Rich, No so that is the interaction term. I thought the authors needed to include the main effects separately, which is [500-h<pop<500+h]. As you can see from beta3 and 4, beta 4 is the interaction term and beta 3 is the main effect of the discontinuity. So I'm confuse why the authors don't do that for the [500-h<pop<500+h]