Hi,
I am having the same problem as Christer, with the only difference that I am
running -heckprob- since my Y is a dichotomous variable.
I m not sure if I can use Scott suggested since in heckprob only the rho is
reported, but not the sigma or mills. Can somebody help me with this. I also
thought of using -mfx- command after -heckprob- to get the marginal effects,
but do they they adjust for the fact that some variables are also in the
selection equation.
Any help will be greately appreciated.
Thanks,
Irena Dushi
-----Original Message-----
From: Scott Merryman [mailto:[email protected]]
Sent: Friday, August 29, 2003 9:54 AM
To: [email protected]
Subject: st: Re: Interpretation of OLS coeff after Heckman selection
----- Original Message -----
From: <[email protected]>
To: <[email protected]>
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
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