st: tobit, margins, and prediction with outcome in logs

["Dimitriy V. Masterov" <dvmaster@gmail.com>]

I am trying to estimate a censored regression model of expenditures,
where about a third of my observations have a zero value. I
transformed the expenditure variable by taking the log and it passed
the LM test for normality. I also can't reject the null of
homoskedasticity with an auxiliary regression, so I think the
statistical assumptions for a tobit are satisfied.

I am interested in seeing how the average latent variable prediction
of exp depends on the value of the variable x1 and a dummy variable
di. I would like to use margins to do something like this:

margins, predict(ystar(`e(llopt)',.)) at(x1==(0(10)100)) over(di),

but I cannot figure out how to get margins to perform the
transformation back to y from ln(y) with the expression() option.

Instead, I tried to do the following:

/* Trick Stata to handle the log transformation */
gen lny=ln(exp);
qui sum lny;
scalar gamma=r(min);
replace lny = gamma - 0.0000001 if lny==.;

/* Estimate the model */
tobit lny x1 x2 x3 di, ll;

matrix btobit=e(b);
scalar sigma=btobit[1,e(df_m)+2];

/* Transform back to E[y|x] */
forvalues v=0(10)100 {;
	replace x1=`v';
	predict xb if e(sample), xb;
	generate yhat`v'=exp(xb+0.5*sigma^2)*(1-normal((gamma-xb-sigma^2)/sigma));
	drop xb;
};

collapse (mean) yhat*, by(di);

Does this accomplish what I think it does? Is there a better way of
doing this or estimating that does not require the re-transformation
business? I don't really have any sensible exclusion restrictions to
try a two-part model.

Dimitriy
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