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st: predictions and policy simulation based on tobit estimates

From   marco stampini <>
Subject   st: predictions and policy simulation based on tobit estimates
Date   Tue, 28 Nov 2006 08:03:34 -0800 (PST)

I would need to use tobit estimates to study how the dependent variable (y) changes in a counterfactual scenario (something like: what if a policy got rid of the variability in some of the independent variables X?)

I estimate the tobit and get the unconditional expected value (unconditional meaning without restricting to cases in which y is positive) yuncond. (The following step would be to predict again, after setting some of the X to zero, but before I have a problem).

I would like yuncond to have same average and same variance as y. Using the code below, I obtain similar average but much smaller variance. 

This always happens, because the predicted value does not contain the error term. When using OLS, a way out of the problem is to estimate the disturbance and add it to Xb. 

But here, in a tobit, I do not know how to proceed.
Can anybody help?
Thank you
Marco Stampini

* estimate the tobit
xi:tobit y $X, ll(0)

* get Xb and the estimated variance
predict yhatstar, xb
scalar sigma=_b[/sigma]

* get unconditional expected value
gen yuncond= normal(yhatstar/sigma)*yhatstar + sigma*normalden(yhatstar/sigma)

* compare with observed variable
sum y yuncond_with

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