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Suppose I want to measure the effect of tornadoes on voter turnout at the county level. I suspect that counties that experience tornadoes will have lower voter turnout in the subsequent election than counties that do not, but I also expect the effect will decay the further away from Election Day the tornadoes occur (though I do not have priors regarding the nature of that decay).

Is there a modeling strategy or strategies I should use to assess whether such a decay exists and, if it does, measure it?

Edited for clarification: If I have some counties that experienced tornadoes in June, some in August, and some in October, I wouldn't expect all of those tornadoes to be equally effective at suppressing voter turnout. I would expect the October tornadoes to be most effective, because they occur right before Election Day, and June tornadoes to be least effective, because there are several months between them and Election Day. What I'm looking for is a model that doesn't assume all tornadoes should be equally effective at supressing voter turnout (e.g., a simple turnout~tornadoes regression) but rather accounts for the variation in treatment timing - sort of like a tornadoes*time interaction, but the time variable is undefined for "control" counties that did not experience tornadoes.

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  • $\begingroup$ I honestly don't understand the question. Please clarify. $\endgroup$ Commented Jul 25, 2017 at 4:15
  • $\begingroup$ I've edited the question in the hope of clarifying my request. $\endgroup$ Commented Jul 26, 2017 at 13:45

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Do you have many counties? Let $T_i$ be indicator of tornado hitting, $\text{days}_i$ be number of days before election tornado hit, $Y_i$ be turnout in percent and $x_i$ some other county covariates I presume you must have, chosen because they are predictive of turnout.

As tornadoes are quite localized, maybe matching is an idea: you must have neighboring, similar counties which were not hit. Choose some regression model which are apt for percentages, maybe beta regression or fractional response model. Then, in the linear predictor part of the model, a decaying influence of days since the tornado can be represented as exponential decay, that is, $ C\cdot e^{-\alpha \text{days}_i}$. That would make it into a nonlinear regression model. Since the variable $\text{days}_i$ will not be defined when $T_i=0$, you will need the ideas from How do you deal with "nested" variables in a regression model?

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