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.


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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