Re: st: Polynomial Fitting and RD Design

[Austin Nichols <austinnichols@gmail.com>]

Patrick Button <pbutton@uci.edu>:
Try redefining your x so that the discontinuity is at zero.

On Wed, Aug 31, 2011 at 9:54 PM, Patrick Button <pbutton@uci.edu> wrote:
> Hello Stata users,
>
> I've been getting some unexpected Stata output when fitting polynomials
> using a pretty simple OLS regression.
>
> I am replicating a regression discontinuity design paper (Lee, Moretti and
> Butler 2004). The paper is here:
> http://emlab.berkeley.edu/~moretti/final.pdf Code and data are here:
> http://emlab.berkeley.edu/~moretti/data3.html (I am using enricoall2.dta).
>
> I need to run a regression that fits a 4th degree polynomial separately
> for points of the running variable, x, below 0.5 and above 0.5. The
> regression includes a dummy variable for if x >= 0.5 or not as well. If
> there is a discontinuity at 0.5, then this is picked up in the coefficient
> on that dummy variable.
>
> In this case the running variable is the vote share that the Democratic
> candidate got in U.S. House of Representatives elections, including just
> the Democratic and Republican votes. So x < 0.5 means a Republican won,
> and >= 0.5 means a Democrat won.
>
> I would like to pool the data instead of running a separate regression for
> each side. This is one of the recommended methods in the RD literature.
> For some reason this method does not appear in the authors' code so I need
> to do it myself.
>
> I'm running and setting up the regression as follows:
>
> ***
> gen x = demvoteshare
>
> gen D = 1 if x >=0.5
> replace D = 0 if x < 0.5
>
> *Left Side Polynomial
> gen xa = (1-D)*x
> gen x2a = (1-D)*x^2
> gen x3a = (1-D)*x^3
> gen x4a = (1-D)*x^4
>
> *Right Side Polynomial
> gen xb = D*x
> gen x2b = D*x^2
> gen x3b = D*x^3
> gen x4b = D*x^4
>
> regress realincome D xa x2a x3a x4a xb x2b x3b x4b
>
> ***
>
> Based on what the authors of the paper got, graphical analysis, and logic,
> there should be no jump in realincome at 0.5. There is no reason why
> income should be suddenly much different for districts that democrats just
> barely won or just barely lost. If it is, this invalidates the regression
> discontinuity design. So the coefficient on D should be statistically
> insignificant. However, I get the following results:
>
> ------------------------------------------------------------------------------
>  realincome |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
> Interval]
> -------------+----------------------------------------------------------------
>           D |   497414.5   94802.12     5.25   0.000       311589
> 683240.1
>          xa |   34396.25   27783.67     1.24   0.216    -20063.66
> 88856.17
>         x2a |  -22571.61   234577.9    -0.10   0.923    -482377.5
> 437234.3
>         x3a |  -429659.3   655505.3    -0.66   0.512     -1714542
> 855223.6
>         x4a |   667813.9   598416.4     1.12   0.264    -505166.7
> 1840795
>          xb |   -2805647   534665.3    -5.25   0.000     -3853667
> -1757628
>         x2b |    5828381    1112850     5.24   0.000      3647038
> 8009724
>         x3b |   -5281210    1012800    -5.21   0.000     -7266441
> -3295979
>         x4b |    1754682   339914.5     5.16   0.000      1088402
> 2420963
>       _cons |   31536.64   501.1422    62.93   0.000     30554.33
> 32518.95
> ------------------------------------------------------------------------------
>
> I have no idea why D is statistically significant, and why only the
> polynomial on the right side is statistically significant. This is not
> just a problem with this regression. I get messed up results for every
> regression I run that has a 4th degree polynomial on each side of 0.5.
>
> However, I do not get weird results like this when I use just one 4th
> degree polynomial (one for the entire thing) with the D dummy.
>
> Does anyone know what I am doing wrong? I have no idea but I have a
> feeling that i'm missing something obvious.
>
> Thank you very much for your time and consideration.
>
> --
> Patrick Button
> Ph.D. Student
> Department of Economics
> University of California, Irvine
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
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> *   http://www.ats.ucla.edu/stat/stata/
>

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