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From |
"Scott Merryman" <smerryman@kc.rr.com> |

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

Subject |
st: Re: Interpretation of OLS coeff after Heckman selection |

Date |
Fri, 29 Aug 2003 08:54:00 -0500 |

----- Original Message ----- From: <Christer.Thrane@hil.no> To: <statalist@hsphsun2.harvard.edu> Sent: Friday, August 29, 2003 5:05 AM Subject: st: Interpretation of OLS coeff after Heckman selection > Hi everyone, > > My dependent variable, Y, is the log of expenditures and a set of dummies > (X1, X2, ...) are the explanatory variables of main concern. I also have a > bunch of controls. > > Since sample selection is a problem, I use the Heckman command. (Tobit does > not work with these data.) > > Recently someone pointed out to me the following: One cannot interpret the > OLS coefficients for X1, X2, ... in the consumption equation the usual way > (here: as semilogarithmic coefficients that need the adjustment suggested > by Halvorsen and Palmquist [1980]) WHEN X1, X2, ... also are included as > explanatory variables in the (probit) selection equation (which they are in > my case). In this case, the OLS coefficients in the consumption needs to be > adjusted according to som kind of formula.... > > Is this true? If yes, has anyone seen such a formula? Finally, has anyone > written a command or a ado/do file to perform this adjustment in Stata? > > Thanks for any help! > > Christer > Yes, it is true. The marginal effect on Y is composed of the effect on the selection equation and the outcome equation. (See Greene's Econometric Analysis) I believe the correct procedure is as follows: If the outcome coefficient is beta and the selection coefficient is alpha, then dE[y| z*>0]/dx = beta - (alpha*rho*simga*delta(alpha)) where delta(alpha) = inverse Mills' ratio *(inverse Mills' ratio * selection prediction) Example . use http://www.stata-press.com/data/r8/womenwk.dta . heckman wage educ age, select(married children educ age) mills(mills) Iteration 0: log likelihood = -5178.7009 Iteration 1: log likelihood = -5178.3049 Iteration 2: log likelihood = -5178.3045 Heckman selection model Number of obs = 2000 (regression model with sample selection) Censored obs = 657 Uncensored obs = 1343 Wald chi2(2) = 508.44 Log likelihood = -5178.304 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- wage | education | .9899537 .0532565 18.59 0.000 .8855729 1.094334 age | .2131294 .0206031 10.34 0.000 .1727481 .2535108 _cons | .4857752 1.077037 0.45 0.652 -1.625179 2.59673 -------------+---------------------------------------------------------------- select | married | .4451721 .0673954 6.61 0.000 .3130794 .5772647 children | .4387068 .0277828 15.79 0.000 .3842534 .4931601 education | .0557318 .0107349 5.19 0.000 .0346917 .0767718 age | .0365098 .0041533 8.79 0.000 .0283694 .0446502 _cons | -2.491015 .1893402 -13.16 0.000 -2.862115 -2.119915 -------------+---------------------------------------------------------------- /athrho | .8742086 .1014225 8.62 0.000 .6754241 1.072993 /lnsigma | 1.792559 .027598 64.95 0.000 1.738468 1.84665 -------------+---------------------------------------------------------------- rho | .7035061 .0512264 .5885365 .7905862 sigma | 6.004797 .1657202 5.68862 6.338548 lambda | 4.224412 .3992265 3.441942 5.006881 ------------------------------------------------------------------------------ LR test of indep. eqns. (rho = 0): chi2(1) = 61.20 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ . predict select_xb , xbs . gen delta = mills*(mills + select_xb) . gen b_age = [wage]_b[age] - ([select]_b[age]*e(rho)*e(sigma)*delta) . ci b Variable | Obs Mean Std. Err. [95% Conf. Interval] -------------+--------------------------------------------------------------- b_age | 2000 .1391227 .0006604 .1378276 .1404179 Hope this helps, Scott * * 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/

**References**:**st: Interpretation of OLS coeff after Heckman selection***From:*Christer.Thrane@hil.no

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