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From |
"Pascal Stock" <pascalstock@freenet.de> |

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

Subject |
st: Correction for heteroscedasticity in a probit model with selection |

Date |
Wed, 12 May 2010 19:33:59 +0200 |

Hello STATA users, I am trying to figure out how to solve for heteroscedasticity when the variance of the residuals has the form Var(e_i)=sigma_e^2 * (1-(p^2)*d_i). This is the heteroscedastic error term in a two-step selection model. In the equation e_i is the residual of observation i in the structual equation after estimation the equation with the inverse mills ratio from the selection equation. P is the correlation coefficient of the residuals of the selection and structual equation. D_i is the delta of observation i and defined according to Greene(2003, p. 784 ? 785)). I know that I can correct for heteroscedasticity by weighting the observations with 1/((1-(p^2)*d_i)^0.5) as the expectation of the residual then gives the homoscedastic sigma_e^2. Unfortunately I cannot use in the ?probit? command the weighting ?iweight=1/((1-(p^2)*d_i)^0.5)? together with the cluster option ?vce(cluster master_deal_no)? as I have 50 copies of each observation that differ only with respect to the values of one independent variable and have identical values in the other independent variables. How do I use the ?hetprob? and have to define the variable modeling heteroscedasticity when the variance of the residuals is biased by (1-(p^2)*d_i) ? Trying it myself and given the description of the "hetprob" model by James Hardin and W Gould I defined the variance variable as variance_variable=ln((1-(p^2)*d_i)^0.5), because the heteroscedasticity correction is (ß_0 + X * ß_i)/exp(ln((1-(p^2)*d_i)^0.5))=(ß_0 + X*ß_i)/(1-(p^2)*d_i)^0.5 such that the expectation of the variance is E[Var[e_i/(1-(p^2)*d_i)^0.5)]] = 1/(1-(p^2)*d_i)* E[Var(e_i)] = 1/(1-(p^2)*d_i) * sigma_e^2 * (1-(p^2)*d_i) = sigma_e^2 and thus homoscedastic. Do you think this manual correction for heteroscedasticity in the Heckman selection model is correct? Thanks for your help and kind regards Pascal * * 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/

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