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I'm reading a paper that tries to estimate the following model: $$y = \alpha x+\beta z+\gamma xz+\epsilon$$ where x,z are dummy variables and y isn't. The estimated coefficient of $\alpha$ is positive (0.02), and the sum of $\alpha+\gamma$ is negative (-0.01,insignificant). The writer examines the marginal effect of x, conditional on z and finds a positive (0.01, with significant of 90%). My question is what is the difference in interpretation of marginal effect VS. $\alpha+\gamma$?

The paper is "Terrorism and Voting: The Effect of Rocket Threat on Voting in Israeli Elections" by Anna Getmansky and Thomas Zeitzoff (link: https://www.zeitzoff.com/uploads/2/2/4/1/22413724/zeitzoff_getmank_rockets_main.pdf). The marginal analysis is on page 11.

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  • $\begingroup$ can you include a link to the paper you are referencing? $\endgroup$
    – EconJohn ♦
    Dec 31, 2017 at 16:22
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    $\begingroup$ I added a link. $\endgroup$
    – Neta_1990
    Dec 31, 2017 at 17:02
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    $\begingroup$ Wow, I didn't know they did quantitative work on this. Seems like a little bit of a wild topic to be researching. $\endgroup$
    – EconJohn ♦
    Dec 31, 2017 at 17:20
  • $\begingroup$ @Neta_1990 I edited the title of your question. Please edit the title again if you feel my edit was inaccurate. $\endgroup$
    – Theoretical Economist
    Dec 31, 2017 at 19:22

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The paper computes the value of your coefficient $\gamma$ on its own with comparison to $\alpha +\gamma$1.

The interpretation in this context, would be that there is a limit of the returns to RightShare given the presence of observations existing contemporaneously with RightPM and InRange.

1. this of course assumes that $z=1$

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