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

["Michael N. Mitchell" <Michael.Norman.Mitchell@gmail.com>]

Greetings

  Solely commenting on the use of the -expression()- option, I wonder if this does what 
you want...

expression(exp(predict(xb)))

  Best regards,

Michael N. Mitchell
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On 2010-11-17 7.57 PM, Dimitriy V. Masterov wrote:
> 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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