Tobit model in cmp -- marginal effect on probability of positive outcome

[Peter Slade]

Hi all,

I am trying to estimate the marginal effect of the regressors on the probability of an uncensored outcome in a tobit model using the cmp module. When using the regular tobit command in Stata this can be accomplished by:

sysuse auto.dta
tobit mpg trunk weight, ll(17) 
margins, dydx(trunk weight) predict(pr(17,.)) atmeans

I had guessed that the analogous code in cmp would be:

sysuse auto.dta
cmp (mpg=trunk weight), ind("cond(mpg>17, $cmp_cont, $cmp_left)" )
margins, dydx(trunk weight) predict(pr(17 .)) atmeans

However, these give very different results for the marginal effects. I am fairly certain that in cmp the option "pr" assumes the variance of the error term is 1, as it is in a probit model (the cmp help documentation only refers to probit in its discussion of the pr option, but I had hoped it could be used for a tobit as well).

I'm wondering if there was some other way of getting these marginal effects?

Cheers,

Peter

[David Roodman]

Interesting question. Yeah, pr() is for probit and oprobit models, where the error variance is 1. But it seems like a good idea for me to generalize it.

FYI, I know that this is not a serious example, but note that to do that tobit regression correctly with cmp, you need to censor the data. cmp assumes the data are censored. So if a "censored" observation has the value 3, it will assume it was censored to 3 not 17.

The solution for now is to take over the computation, which you can do with the -expression()- option of -margins-. I get a match with this:

. sysuse auto, clear
(1978 Automobile Data)

. replace mpg=17 if mpg<17
(14 real changes made)

. cmp (mpg=trunk weight), ind("cond(mpg>17, $cmp_cont, $cmp_left)" ) qui nolr

Fitting individual models as starting point for full model fit.

Fitting full model.

Mixed-process regression                        Number of obs     =         74
                                                Wald chi2(2)      =      97.78
Log likelihood = -163.74787                     Prob > chi2       =     0.0000

------------------------------------------------------------------------------
         mpg |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
mpg          |
       trunk |  -.1487205   .1477236    -1.01   0.314    -.4382534    .1408124
      weight |  -.0063328    .000871    -7.27   0.000    -.0080399   -.0046257
       _cons |   41.90602   2.094739    20.01   0.000     37.80041    46.01163
-------------+----------------------------------------------------------------
    /lnsig_1 |   1.340901   .0951684    14.09   0.000     1.154375    1.527428
-------------+----------------------------------------------------------------
       sig_1 |   3.822487     .36378                      3.172039    4.606314
------------------------------------------------------------------------------

. margins, dydx(trunk weight) expression(normal((predict(xb)-17)/exp([/lnsig_1]))) atmeans

Conditional marginal effects                    Number of obs     =         74
Model VCE    : OIM

Expression   : normal((predict(xb)-17)/exp([/lnsig_1]))
dy/dx w.r.t. : trunk weight
at           : trunk           =    13.75676 (mean)
               weight          =    3019.459 (mean)

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       trunk |  -.0096211   .0096732    -0.99   0.320    -.0285801     .009338
      weight |  -.0004097   .0000822    -4.99   0.000    -.0005708   -.0002486
------------------------------------------------------------------------------

[David Roodman]

Alrighty! I have added that feature. The new version is available via

net install cmp, replace from(https://raw.github.com/droodman/cmp/v8.5.0)

After installing it, this should work:

sysuse auto, clear
replace mpg=17 if mpg<17
cmp (mpg=trunk weight), ind("cond(mpg>17, $cmp_cont, $cmp_left)" ) qui nolr
margins, dydx(*) predict(pr(17 .)) atmeans

I'll have this posted on SSC as well.

[David Roodman]

It is posted on SSC.