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From |
"Rachel Bouvier" <rbouvier@usm.maine.edu> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: problems with Murphy-Topel |

Date |
Mon, 29 Oct 2007 12:57:00 -0400 |

Hi stata-listers: I’m working on a problem dealing with the Murphy-Topel procedure as outlined in Hardin (2002) and Hole (2006). Briefly, I have a very large stacked model in the first stage, consisting of 31 countries and up to 17 years (some countries have a shorter time series). It is stacked so that the intercepts and the coefficients can vary for each country, rather than “pooling” them all. (I posted a question about this quite a while ago, so it may seem familiar to some.) I use OLS to predict the trend of income over time for each country, and call this variable “new_predict”, and its square, “new_pred2.” I also generate another variable, called “new_flux,” which is made up of the residuals from the first stage (or how far income falls from its predicted trend). I then use those three variables from the first stage in my second stage model (also using OLS). I need to adjust the standard errors from the second stage model because those three variables were generated in the first stage. My former dissertation advisor and I modified the code used in the Hole essay to account for the fact that I use OLS in both stages. We’re running into two problems, though: if I try to display the results using the matrices b and M, I get an error code that the matrix is not positive definite. Further, the standard error for at least one of my estimated coefficients is smaller than it was before doing the adjustment, which doesn’t seem plausible. The problem likely lies somewhere in the correlation between new_predict, new_pred2, and new_flux. I think the problem might be in how we defined “zz,” but I’m not sure. I’m wondering if the fact that we used the residuals from the first stage as a variable in the second stage needs to be accounted for in a different way. If anyone out there has any suggestions, I’d be very grateful. I am out of my comfort zone with this! Thanks. I’ve copied the code below. -Rachel PS. I’m using Stata 7, but if a later version of Stata is necessary, I’ll just bite the bullet and pay for it (my department has no money for such trifles!) *first stage: xi: regress lnpppc i.code*year i.code|yearsq predict double new_predict predict double res1, res gen double res1sq=res1^2 quietly sum res1sq scalar mse=r(mean) matrix V1=(e(df_r)/e(N) )* e(V) gen double s1=res1*(1/mse) gen new_flux = res1 gen new_pred2=new_predict^2 *second stage, need to use new prefix: xi, prefix(rev):regress lnpoll new_predict new_pred2 new_flux pop_dens year i.code matrix b = e(b) matrix V2 = (e(df_r)/e(N) )* e(V) predict double res2, res gen double res2sq=res2^2 quietly sum res2sq scalar mse2=r(mean) gen double s2= res2*(1/mse2) generate zz= _b[new_predict] + 2*new_predict*_b[new_pred2] - _b[new_flux] /*this how the generated variables affect the stage-2 outcome*/ *Calculate C using scores: gen byte cons=1 matrix accum C = _Icode_* year _IcodXyear_* yearsq _IcodXyeara* cons new_predict new_pred2 new_flux pop_dens year revcode_* cons [iw=s2*s2*zz], nocons *Calculate R using scores: matrix accum R = _Icode_* year _IcodXyear_* yearsq _IcodXyeara* cons new_predict new_pred2 new_flux pop_dens year revcode_* cons [iw=s2*s1], nocons matrix C = C[94..129,1..93] matrix R = R[94..129,1..93] matrix M = V2 + (V2 * (C*V1*C' - R*V1*C' - C*V1*R') * V2) capture program drop doit matrix b=e(b) program define doit, eclass est post b M est local vcetype "Mtopel" est display end doit Rachel Bouvier, Ph.D. Assistant Professor of Economics University of Southern Maine PO Box 9300 11 Chamberlain Avenue Portland, ME 04104 (207) 228-8377 * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: problems with Murphy-Topel***From:*"Austin Nichols" <austinnichols@gmail.com>

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