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I am looking for an empirical paper that perform a difference-in-difference regression where the whole did regression (treated+post+post*treated) is interacted with a continuous variable (or a categorical one)... Do you have an idea of such a paper ?

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My own not-yet-published paper!

Sorry, I can't immediately think of a more authoritative paper, though mine does fit the bill (assuming that it is non-wrong).

(I formulate the DID slightly differently -- rather than including a dummy for treated (implicitly assuming that any difference between T and C is a level effect) I weight the control group by propensity scores for being in the treatment group.)

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Price and Wolfers (2010) measured NBA referees on how many fouls they called based on their race and the race of the players they called fouls on. See Table 3:

Joseph Price & Justin Wolfers, 2010. "Racial Discrimination Among NBA Referees," The Quarterly Journal of Economics, MIT Press, vol. 125(4), pages 1859-1887, November. http://www.nber.org/papers/w13206

The continuous variable is the foul rate, and the "treatment" is the change in fouls called over the change in % white referees.

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  • $\begingroup$ Thanks for sharing, really interesting topic. I read it in a different way though. In table 3, I think the treatment is 'percentage of white referees in a game', in an extreme case, players in a game with nonwhite referees are the treatment group and all white referee are the control group. This is the first difference. player's race in different group constructs the second difference. $\endgroup$ – Jason Goal Apr 20 '19 at 16:48

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