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Re: st: Polynomial Fitting and RD Design


From   Alex Olssen <alex.olssen@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Polynomial Fitting and RD Design
Date   Sat, 10 Sep 2011 23:06:53 +1200

Works a charm.

Thanks Nick!

On 10 September 2011 22:57, Nick Cox <njcoxstata@gmail.com> wrote:
> This is Stata 7 syntax. It will work in
> later versions with the prefix
>
> version 7:
>
> Nick
>
> On 10 Sep 2011, at 11:46, Alex Olssen <alex.olssen@gmail.com> wrote:
>
>> Hi,
>>
>> I have a question.  It's not quite on this topic, but it is related to
>> the replication of Lee, Moretti, and Butler.
>> In the do-files found in the links in the original post are the
>> following lines of code
>>
>> graph meanY100 fit1 fit2 int1U int1L int2U int2L dembin ,
>> l1(" ") l2("ADA Score, time t") b1(" ") t1(" ") t2(" ")
>> b2("Democrat Vote Share, time t-1")  xlabel(0,.5,1) ylabel (0,.5,1)
>> title(" ") xline(.5)
>> c(.lll[-]l[-]l[-]l[-]) s(oiiii) sort saving(`1'_reduced.gph, replace);
>> translate `1'_reduced.gph `1'_reduced.eps, replace;
>>
>> I can't get this to work.  I have never seen the graph command used
>> like this before - I always used graph twoway, etc.
>>
>> In any case, the error I get is:
>> "meanY100graph_g.new fit1 fit2 int1U int1L int2U int2L dembin ,: class
>> member function not found"
>>
>> Can anyone help me with this?
>>
>> Cheers,
>> Alex
>> On 6 September 2011 07:40, Patrick Button <pbutton@uci.edu> wrote:
>>>
>>> Thank you for the feedback everyone. It has been extremely useful and now
>>> I am not freaking out as much.
>>>
>>> First, i've changed x to x - 0.5 as per Austin Nichols' suggestion. This
>>> makes interpretation easier. I should have done this earlier.
>>>
>>> I was thinking that my replication was going to involve critique Nick
>>> Cox,
>>> and I agree with you and others that the 4th order polynomials are
>>> somewhat fishy.
>>>
>>> The weird thing about the paper is that the authors say that they are
>>> using 4th degree polynomials on either side of the discontinuity, but
>>> their graphs and/or code indicate that they are just using one polynomial
>>> to fit the entire thing. Not sure why that is... So in trying to do the
>>> 4th degree polynomial for each side on my own, i’ve run into this issue
>>> of
>>> results being weird. Now that I understand why it makes perfect sense.
>>>
>>> As for if the 4th degree polynomial is ideal, I would agree with all of
>>> you that it probably is not. If one is going to go with polynomials, the
>>> ideal degree depends on the bandwidth you use. Ariel Linden described
>>> this
>>> really well earlier.
>>>
>>> Larger bandwidths mean more precision, but more bias. Smaller bandwidths
>>> (say only using data within +/- 2 percentage points of 50%) lead to the
>>> opposite. Lee and Lemieux (2010)
>>> (http://faculty.arts.ubc.ca/tlemieux/papers/RD_JEL.pdf) discuss that the
>>> optimal polynomial degree is a function of the bandwidth.
>>>
>>> The ideal degree is determined by the Akaike Information Criterion (AIC).
>>> I'm going to stick with the 4th degree polynomial (and the entire
>>> dataset), then i'll try other polynomials and bandwidths, and then kernel
>>> after that. I need to do the replication first, THEN I will critique that
>>> by going with something more realistic. The -rd- package should be really
>>> useful for that. Thanks so much for all the discussion about a more
>>> realistic model. The key thing is that results should be robust to
>>> several
>>> different types of fitting and bandwidths, so long as they are realistic
>>> in the first place.
>>>
>>> As for using orthog/orthpoly to generate orthogonal polynomials, I gave
>>> that a shot. Thank you very much for the suggestion Martin Buis.
>>>
>>> I've done the orthogonalization two different ways. Both give different
>>> results, neither of which mirror the results where I create the
>>> polynomials in the regular fashion. I'm not sure which method is
>>> "correct". I'm also unsure why the results are significantly different.
>>> Any suggestions would be very helpful.
>>>
>>> Orthpoly # 1 uses orthpoly separately on each side of the discontinuity.
>>> #
>>> 2 does it for all the data.
>>>
>>> The code and output are below:
>>>
>>> *****
>>>
>>> drop if demvoteshare==.
>>> keep if realincome~=.
>>> drop demvs2 demvs3 demvs4
>>>
>>> gen double x = demvoteshare - 0.5
>>>
>>> gen D = 1 if x >= 0
>>> replace D = 0 if x < 0
>>>
>>> *Orthpoly #1
>>>
>>> *Creating orthogonal polynomials separately for each side.
>>>
>>> orthpoly x if x < 0, deg(4) generate(demvsa demvs2a demvs3a demvs4a)
>>> orthpoly x if x >= 0, deg(4) generate(demvsb demvs2b demvs3b demvs4b)
>>> replace demvsa = 0 if demvsa==.
>>> replace demvsb = 0 if demvsb==.
>>> replace demvs2a = 0 if demvs2a==.
>>> replace demvs2b = 0 if demvs2b==.
>>> replace demvs3a = 0 if demvs3a==.
>>> replace demvs3b = 0 if demvs3b==.
>>> replace demvs4a = 0 if demvs4a==.
>>> replace demvs4b = 0 if demvs4b==.
>>>
>>> replace demvsa = (1-D)*demvsa
>>> replace demvs2a = (1-D)*demvs2a
>>> replace demvs3a = (1-D)*demvs3a
>>> replace demvs4a = (1-D)*demvs4a
>>>
>>> replace demvsb = D*demvsb
>>> replace demvs2b = D*demvs2b
>>> replace demvs3b = D*demvs3b
>>> replace demvs4b = D*demvs4b
>>>
>>> regress realincome D demvsa demvs2a demvs3a demvs4a demvsb demvs2b
>>> demvs3b
>>> demvs4b
>>>
>>> *Orthpoly #2
>>>
>>> orthpoly x, deg(4) generate (demvs demvs2 demvs3 demvs4)
>>>
>>> replace demvsa = (1-D)*demvs
>>> replace demvs2a = (1-D)*demvs2
>>> replace demvs3a = (1-D)*demvs3
>>> replace demvs4a = (1-D)*demvs4
>>>
>>> replace demvsb = D*demvs
>>> replace demvs2b = D*demvs2
>>> replace demvs3b = D*demvs3
>>> replace demvs4b = D*demvs4
>>>
>>> regress realincome D demvsa demvs2a demvs3a demvs4a demvsb demvs2b
>>> demvs3b
>>> demvs4b
>>>
>>> *****
>>>
>>> And the results are:
>>>
>>>
>>> Orthpoly # 1
>>>
>>>
>>> ------------------------------------------------------------------------------
>>>  realincome |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
>>> Interval]
>>>
>>> -------------+----------------------------------------------------------------
>>>          D |  -2597.064   140.5829   -18.47   0.000    -2872.626
>>> -2321.502
>>>     demvsa |  -853.4396   109.0927    -7.82   0.000    -1067.277
>>> -639.6025
>>>    demvs2a |  -941.1276   109.0927    -8.63   0.000    -1154.965
>>> -727.2905
>>>    demvs3a |   593.9881   109.0927     5.44   0.000      380.151
>>> 807.8252
>>>    demvs4a |   121.7433   109.0927     1.12   0.264    -92.09384
>>> 335.5804
>>>     demvsb |  -2006.552   88.66978   -22.63   0.000    -2180.357
>>> -1832.747
>>>    demvs2b |  -620.1632   88.66978    -6.99   0.000    -793.9685
>>> -446.3579
>>>    demvs3b |  -134.2237   88.66978    -1.51   0.130     -308.029
>>> 39.58156
>>>    demvs4b |   457.7355   88.66978     5.16   0.000     283.9302
>>> 631.5407
>>>      _cons |    32210.1   109.0927   295.25   0.000     31996.26
>>> 32423.93
>>>
>>> ------------------------------------------------------------------------------
>>>
>>>
>>> Orthpoly # 2
>>>
>>>
>>> ------------------------------------------------------------------------------
>>>  realincome |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
>>> Interval]
>>>
>>> -------------+----------------------------------------------------------------
>>>          D |  -15904.18   22026.78    -0.72   0.470    -59079.79
>>> 27271.42
>>>     demvsa |   56141.35   33816.59     1.66   0.097    -10143.95
>>> 122426.6
>>>    demvs2a |   42328.68   25413.63     1.67   0.096    -7485.616
>>> 92142.98
>>>    demvs3a |   19367.81   11950.96     1.62   0.105    -4057.754
>>> 42793.37
>>>    demvs4a |   3038.492   2722.757     1.12   0.264    -2298.496
>>> 8375.481
>>>     demvsb |  -40636.36   7469.378    -5.44   0.000     -55277.4
>>> -25995.32
>>>    demvs2b |   47190.86   9181.907     5.14   0.000     29193.03
>>> 65188.7
>>>    demvs3b |  -33596.74   6331.021    -5.31   0.000    -46006.43
>>> -21187.04
>>>    demvs4b |   7983.823   1546.578     5.16   0.000      4952.31
>>> 11015.33
>>>      _cons |   68128.44   21623.63     3.15   0.002     25743.08
>>> 110513.8
>>>
>>> ------------------------------------------------------------------------------
>>>
>>> The results using the earlier method (generating polynomials normally)
>>> gives the following after I change x to x - 0.5:
>>>
>>>
>>> ------------------------------------------------------------------------------
>>>  realincome |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
>>> Interval]
>>> -------------+--------------------------------------------------
>>>
>>>
>>>
>>>
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