Tobit with difference-in-differences specification Is it possible to estimate a tobit model (e.g. a nonlinear model) with a DiD (difference-in-differences) specification?  If so, how does such specification look like? 
If it is possible is this implemented in R or Stata?
Comment: @Dimitriy V. Masterov: Thanks for your answer! Would this still work if I used lognormal data? I mean a log transformation of the dependent variable y causes a missing if y=0. Cameron & Trivedi suggest to "trick" Stata for lognormal data in tobit models by setting the censoring point "slightly smaller than the minimum noncensored value of ln(y)". Does this also work with a DID specification?
 A: I can see no reason why DID  estimation should not be possible with a Tobit model. However, I believe there is a caveat, please correct me if I'm wrong. I assume that you are interested in the marginal effects as the Tobit-coefficients are not really informative. 
Say, you include a dummy "After" for the period after the policy intervention or whatever you want to analyze and a dummy "TG" for the treatment group as well as an interaction of the two. In a linear model the coefficient of the interaction gives the effect of the policy reform.
The marginal effect of a dummy variable is the change from 0 to 1 and in nonlinear models the marginal effect of a variable depends on were you evaluate it (e.g., the atmeans option in Stata), so it is important to specify the fact that you work with dummy variables and where you want to evaluate the marginal effect, especially at what values of the dummies included for DID you want to evaluate the marginal effects of the other ones. Just including an interaction gives you wrong results. The DID is taking the differences between the following means, where the first number is 1 if the individual belongs to the treatment group and the second is 1 for observations in the period after the policy reform:
(1,1)-(1,0) - [(0,1)-(0,0)]. So my take in Stata 12 is the following:


*

*Run Tobit with the two dummies indicating affiliation to treatment group (TG) and the period after the reform (A, or possibly more periods), 

*margins, predict(ystar(0,.))  over (TG A)

*lincom 1.TG#1.A-1.TG#0.A-(0.TG#1.A-0.TG#0.A)


I am not sure whether it is even necessary to include the interaction, as it indicates the marginal effect of a variable on the marginal effect of another one and the same is achieved by step 3 in the above. 
Take a look at http://www.maartenbuis.nl/publications/interactions.pdf on dummy variables in non-linear models in Stata including the syntax I use in step 2. The reasoning of the paper surely applies to other software as well. He refers to the logit and Poisson model, but the points should apply to the Tobit model too.
