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I am trying to estimate the enrollment premium at high-fees schools i.e., impact of high-fee school enrollment on learning outcomes. I am instrumenting high-fee school enrollment by using a continuous treatment instrument. The treatment is a voucher of varying size randomly assigned to all applicants. So, the instrument takes a value of zero for all control applicants, and takes a continuous value for all treated applicants. Does this sound like a valid instrument? Or, would it be better if I made the instrument categorical, by say, dividing the continuous value to 3 or 4 categories?

In the first case, what would be the interpretation of the LATE?

Any thoughts would be greatly appreciated.

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The voucher sounds valid, because it has clearly nothing to do with your second-stage equation (learning outcome) as it is distributed randomly, but probably makes it more like for parents to be able to afford high-fee schooling.

The general advise for categorical vs continuous variables; take the second option if you can because you lose information if you transform a continuous into categories variable.

I am not quite sure about the details of LATE, but I think it always work as long as each group has at least one person who goes and who does not go to a high fee school in each voucher category (though don't know about the technical details; thus can't vouch for this).

In addition, perhaps consider using 2SLS with first and second-stage equations, rather than LATE. The advantage of that would be, that you could differentiate between different levels of high-fee schools. Of course, only if your data allows this.

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  • $\begingroup$ Thanks Tom! How about using both a dummy treatment variable and a continuous voucher size variable (zero for controls and continuous for treatments) as instruments. That give me a much stronger first stage. $\endgroup$ – Vijay Sep 2 '17 at 8:04
  • $\begingroup$ I think you can do this. It is the same like having x and x^2 in a regression model. Test it out and see whether both instruments are actually significant in the first stage. $\endgroup$ – Tom Pape Sep 2 '17 at 10:58

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