Censoring point for Exponential Tobit where censoring is from below at 0

[Alfonso Sánchez-Peñalver]

Hi everyone,

I have a question about where to set the censoring point when we want to estimate an exponential model and the dependent variable is censored from below at 0. The problem is that when transforming the dependent variable into its natural logarithm, the censoring point is indeterminate since ln(0) is indeterminate.

If we follow Cameron and Trivedi (2010, Ch. 16) letting y be the dependent variable, and `x' be a local macro with the list of independent variables

gen lny = ln(y)
summarize lny, mean
replace lny = r(min) - 1e-7 if missing(lny)
tobit lny `x', ll

In other words they suggest setting the censoring point at the minimum value above zero in the original variable, which is the minimum value of the log-transformed variable. My concern with this practice is that value would depend on the actual sample and we don't know exactly how close the first positive value of the original variable is to zero. I was wondering if it wouldn't be more appropriate to set the censoring point at a value that is very close to zero, but not zero, i.e. ln(1e-7), so we would change the replace line with

replace lny = ln(1e-7) if missing(lny)

I believe that this would be more appropriate in the scaling of the coefficients on the independent variables, but I was hoping that if you guys had more experience with exponential Tobit you could comment.

Thanks,

Alfonso

Reference:
Cameron A.C. and P.K. Trivedi (2010) Microeconometrics Using Stata, Revised ed., College Station, TX: Stata Press