Regressions with Truncated Dependent Variable

[Neelakanda Krishna]

Dear Stata Members
My dependent variable is a truncated or bounded dependent variable which has 0 as the lower limit and 1 as the upper limit. I am dealing with a panel and in that case is it alright to use usual panel regression by employing xtreg dep_var indep_var? In Economics and Finance such bounded variables are very common and usually research articles employ panel regression techniques. Is that methodologically correct?

tabstat dep_var,stat(n mean sd p25 p50 p75 min max) col(stat)

    Variable |         N      Mean        SD       p25       p50       p75       Min       Max
-------------+--------------------------------------------------------------------------------
     dep_var |    202448  .2285361  .2546204         0  .1742105  .3449566         0         1
----------------------------------------------------------------------------------------------

.I have 55528 observations of dep_var with 0.
If not panel, what should be the regression one should use for truncated dep var

[Nick Cox]

"methodologically correct"? No.

Empirically convenient or adequate? Possibly, but sounds a stretch, especially with so many exact zeros.

But backing up, I would not describe this as truncated unless you tell me that values outside [0, 1] are possible but not reported as such for some reason or reasons. I support your description that the outcome variable is bounded, and it's hard for many of us to defend any analysis that does not respect the bounds. Being able to find contrary examples in any literature is not an argument to the contrary.

What you could do is compare results from xtreg with those from a better analysis and at best you might be able to make a case that substantive conclusions are similar. If they aren't, you would have a different answer.

[Neelakanda Krishna]

Dear Nick Cox
Thanks for the remarks.

I would not describe this as truncated unless you tell me that values outside [0, 1] are possible but not reported as such for some reason or reasons. I

. Sorry for using the wrong terminology. Values out side 0 and 1 are possible but they are replaced by zeroes and 1. The logic is to Set dep_var to 0 if dep_var <0; set dep_var to 1 if dep_var>1.

those from better analysis and at best you might be able to make a case that substantive conclusions are similar.

. In fact, I am searching for such analysis in say other domain that deals with bounded dependent variables like mine. Are there any regressions that suits say "Censored regression model". I haven't used them but first I would like to know whether that is good in my context or not.

[Nick Cox]

You do have truncation as I would use the term, so zero need to apologise. I think you need advice from panel experts now.

[Daniel Feenberg]

There is no panel tobit in stata, but it would be worth trying https://www.stata.com/manuals/rtobit.pdf with a factor variable for the fixed effect (firm id) instead of having xtreg take out means. Panel procedures are much faster and use less memory than their non-panel counterparts, but don't have any advantage in bias or consistency. You don't say how many observations per respondent, so I don't know if this is really practical. Stata regression procedures can handle thousands of variables if you have at least a little patience.

[Neelakanda Krishna]

Dear [email protected]

Thanks for the support as I was in search for help related to the panel. My IDs are firms and there about 25921 firms in my sample. My sample is unbalanced one having 20 years and I have 327624 observations in total.

[Andrew Musau]

With such sample sizes, Bill Greene's analysis suggests that you should be fine with estimating an unconditional fixed effects Tobit model (Tobit with dummies). You can just estimate this and use Greene's paper as a justification.

Reference
Greene, W. “Fixed Effects and Bias Due to the Incidental Parameters Problem in the Tobit Model.” Econometric Reviews, 23 (2004), 125-147.

[Daniel Feenberg]

Stata can't handle more than 10,998 independent variables and each firm would be a separate independent variable. See https://www.stata.com/statalist/arch.../msg00654.html so my suggestion won't work directly. Can you aggregate in some way? Divide the sample by major industry group? Drop short panels? People have developed panel tobit procedures, but I don't that any have been made available to other researchers.

[Andrew Musau]

Stata can't handle more than 10,998 independent variables and each firm would be a separate independent variable.

Have you tried Stata MP? It may very well be that tobit limits you to that many variables, but that is not a global limit for Stata. See https://www.stata.com/products/detailed-size-limits/.

[Neelakanda Krishna]

Thanks [email protected] and Andrew Musau. for your time and support. Dear Feenberg, I have industries which boils down to <50 which can nest the firms. So I can implement yours. Dear Andrew, thanks for the reference and I have just did what you instructed and I think the results look okay