I'm trying to understand the encouragement design but I have some doubts. For example, if I want to introduce a voucher for teachers that can be used for professional development(the treatment) and I want to estimate its impact on student performance(dependent variable) obviously I have some problems, since not all the individuals in the treatment group will actually use the voucher. How can I introduce the encouragement design in this case? for example is it right if I send (randomly in the treatment group) some invitations to some professional developments program and I use their participation to these invitations as instrumental variable? And what's the difference with intention to treat?
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$\begingroup$ a dummy variable with a value of 1 if the teacher used the voucher would be an excellent start. $\endgroup$– JamzyApr 13, 2015 at 23:06
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The fact that you can only encourage but not force the teachers to participate puts you squarely in the world of Local Average Treatment Effect (LATE) and Intention to Treat analysis.
Essentially if you use the voucher as a instrumental variable, you will get an estimate of the effect of the voucher on "the sort of person who you can encourage to take a class by giving them a voucher".
Read the Instrumental Variables section in Mostly Harmless Economics, to get a good easy to understand explanation of exactly the situation you are interested in.
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$\begingroup$ The voucher here is actually the treatment. If I understood correctly if I use the dummy variable suggested by jamzy as the instrument I would be doing an intention to treat analysis. What I don't understand is what happens if I want to also use an encouragement design by giving some invitations to a randomly selected teacher in the treatment group. In this case can I still use the the instrument suggested by jamzy? Actually can I just give the encouragement to all the treatment group? $\endgroup$– LexApr 14, 2015 at 7:40
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1$\begingroup$ If you want to measure the effect of giving the voucher on student performance, then run a regression with a dummy for GotVoucher. Do not include a dummy for whether they used the voucher. $\endgroup$ Apr 14, 2015 at 21:06
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$\begingroup$ If you want to measure the effect of taking a class on student performance, then run an instrumental variables regression using the dummy for Got Voucher as the instrument for whether they took the class. $\endgroup$ Apr 14, 2015 at 21:07
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1$\begingroup$ Running a regression directly using the dummy for whether they took a class will give you incorrect estimates of the casual effect of taking a class on student performance. $\endgroup$ Apr 14, 2015 at 21:08