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Re: st: Combine weak RD estimators through Minimum Distance / Asymptotic Least Squares


From   Jen Zhen <jenzhen99@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Combine weak RD estimators through Minimum Distance / Asymptotic Least Squares
Date   Thu, 10 Dec 2009 13:57:17 -0500

On Thu, Dec 10, 2009 at 12:26 PM, Austin Nichols
<austinnichols@gmail.com> wrote:
> What is the assignment variable for each?  Is it the same in each
> case, with breaks at different points, similar to
> and are you using the same data for each?

My treatment consists of different "Potential Benefit Durations" for
unemployment benefits, and people's PBDs depend on their age,
experience and in which of 3 periods (with different policy regimes)
they became unemployed. This gives me up to 3 different assignment
variables (age, experience, and time; I might have to ignore one of
these of course, if I find that it has been manipulated), with many
breaks for each.

As ideally I'd like to use information on all 3 dimensions, I also
considered normalizing all discontinuities in the same way, by
defining a common assignment variable that would reach from -1 to 1,
taking the value 1 iff the original assignment variable has the
highest value in the range I use, -1 if it has the lowest, 0 if it
takes the cutoff value, etc.
The PBD-gain from crossing the threshold, i.e. the treatment
intensity, also varies across thresholds, so I considered to also
normalize the outcome difference between treated and non-treated, by
expressing it for each of my mini-experiments as a proportion of the
respective treatment intensity; Does that sound sensible?

> Are you willing to assume that the "true" local avg treatment effect
> is the same at every point?

Yes, at least for most of discontinuities after some controls;
If I get enough power from combining the discontinuities, I might want
to split it into 2-3 combined estimators, with different LATEs for
different broad age ranges.



> On Thu, Dec 10, 2009 at 11:18 AM, Jen Zhen <jenzhen99@gmail.com> wrote:
>> Hi there,
>>
>> I have a set of Regression Discontinuity estimators none of which by
>> itself has enough power to give me statistically significant results
>> (because firstly most of the discontinuities are of limited size and
>> secondly my number of observations around each discontinuity is
>> limited). However, I suspect that if I could efficiently combine the
>> information from all (around 35-50) RD estimators, then the result
>> might actually have enough power.
>>
>> So I have been considering whether I could combine them using a
>> Minimum Distance or Asymptotic Least Squares estimator.
>>
>> However, I have not yet found out whether there is a good way to do
>> this in Stata. I am also not yet fully sure whether this method is
>> sensible in general, so any views on that would probably also be most
>> helpful.
>>
>> Thank you very much indeed and best regards,
>> JZ
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