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From |
"Patrick Button" <pbutton@uci.edu> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: Re: st: Polynomial Fitting and RD Design |

Date |
Mon, 5 Sep 2011 12:40:50 -0700 |

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] -------------+---------------------------------------------------------------- D | 1616.347 605.9781 2.67 0.008 428.5441 2804.149 xa | 23487.01 15519.78 1.51 0.130 -6933.964 53907.98 x2a | 334659.2 153845.2 2.18 0.030 33100.93 636217.5 x3a | 905964.7 546408 1.66 0.097 -165072.1 1977001 x4a | 667809.6 598416.3 1.12 0.264 -505170.9 1840790 xb | -60833.88 12050.57 -5.05 0.000 -84454.71 -37213.06 x2b | 538597.3 105340.2 5.11 0.000 332115.5 745079 x3b | -1771874 334373.4 -5.30 0.000 -2427293 -1116455 x4b | 1754710 339912 5.16 0.000 1088435 2420986 _cons | 31122.81 454.4263 68.49 0.000 30232.07 32013.55 ------------------------------------------------------------------------------ Any ideas would be great and I greatly appreciate everyone's assistance. -- Patrick Button Ph.D. Student Department of Economics University of California, Irvine * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: Re: st: Polynomial Fitting and RD Design***From:*Alex Olssen <alex.olssen@gmail.com>

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