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

 From Austin Nichols To statalist@hsphsun2.harvard.edu Subject Re: st: Combine weak RD estimators through Minimum Distance / Asymptotic Least Squares Date Thu, 10 Dec 2009 14:56:22 -0500

```Jen Zhen <jenzhen99@gmail.com> :
The effect of potential benefit duration no doubt depends on the labor
market conditions which vary across time in a nonsmooth way.  Age and
experience discontinuities are presumably safer identification
strategies, but we should not expect the treatment effect to be
similar at different ages and experience levels.  You certainly should
not normalize your information in 3 dimensions; if anything, you
should adopt weights that vary appropriately and run -ivreg2- in such
a way as to produce an RD estimate.  But again, I don't think you
could safely interpret the method as consistently estimating any
single quantity of interest.

Have you read the relevant literature already?  Start here:

On Thu, Dec 10, 2009 at 1:57 PM, Jen Zhen <jenzhen99@gmail.com> wrote:
> 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
>>>
>>> Thank you very much indeed and best regards,
>>> JZ

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