When estimating causal effects, you want to compare individuals as similar as possible. It is from this need that stems the exchangeability (/ignorability) or conditional exchangeability (/ conditional ignorability) assumption, stating that the probability of treatment must be "as good as random".

Another assumption need is $0<P(t_i = t| x)<1$, $x$ being a vector of independent variable.

My question is, when doing policy evaluation, the assignment-to-treatment mechanism is deterministic rather than stochastic. Living in a certain state in a certain year determines you being treated or not, with probability 1. How are those assumptions compatible with this?

My only current precaution is to make the residents of treated and control states comparable by conditioning on a number of relevant variables, but the doubt about what just asked remains.

Many thanks

  • $\begingroup$ How is the treatment state chosen? $\endgroup$ – Dimitriy V. Masterov Jan 25 at 17:45
  • $\begingroup$ If you are dealing, say, with a US state-level reform dating 1999 onward and are working with individual-level data, using other surronding states as controls, then individual $i$ is treated with probability 1 given that she is resident in that state during and after 1999. $\endgroup$ – Fabio I. Jan 25 at 23:36
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    $\begingroup$ This is not really a problem (as long as you adjust your standard errors for the clustered treatment assignment) as long as states are exchangeable, rather than individuals, and every state has the potential to be chosen. Reforms, however, may not always satisfy this condition. $\endgroup$ – Dimitriy V. Masterov Jan 26 at 0:46
  • $\begingroup$ You are right, the point about the exchangeability of $states$ is what I was missing. $\endgroup$ – Fabio I. Jan 26 at 0:55

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