When and why should we use Tobit Regression model?

[Prateek Bedi]

I am trying to find out determinants of corporate cash holdings for a panel dataset of 1696 firms over a period of 21 years. The dependent variable is the ratio of 'Cash and Cash Equivalents' to 'Total Assets' and hence its value, by definition, ranges from 0 to 1. The independent variables include firm-specific characteristics (mainly accounting variables from financial statements) and macroeconomic variables. I used FEM for estimation (after confirmation using Hausman Test) and obtained results in line with the theory. I have the following questions:

1. Since my dependent variable ranges from 0 to 1 (by definition), should I use Tobit regression model?
2. Since my model has endogeneity issues (due to Omitted Variable Bias and Simultaneity), I planned to address them through dynamic panel regression model. But if Tobit model is the correct estimation technique in my case , how can I combine it with Fixed Effects or dynamic panel regression?
3. If a model demands Tobit regression technique and it is not applied, what are the effects on quality of estimates?

Thanks

[Clyde Schechter]

1. Since my dependent variable ranges from 0 to 1 (by definition), should I use Tobit regression model?

No, that is not a situation that calls for tobit. Your dependent variable is one that, in principle, only takes on values between 0 and 1. It is not censored at 0 and 1. A censored variable is one where the real value of the variable is not known because the measurement process itself is capable only of reporting values within a certain range. For example, an ordinary bathroom scale cannot report a weight greater than 300 lbs. If we have a study where the outcomes are bathroom scale measurements, and one of our participants actually weighs 310 lbs, the scale will report it as 300--but that is a censored value. This is the kind of situation that calls for -tobit- (or other techniques for dealing with censored data). Your situation is nothing like that--there are no negative or > 1 values that are being (mis-)recorded as 0 or 1 in your data.

Now, linear regression models can be problematic for variables that are restricted in range (even when that restriction is natural and does not arise from censorship) because linear models will typically predict values outside that range for sufficiently extreme values of the predictors. For outcomes restricted to the 0 to 1 range (like proportions) it is often better to use approaches like -fracreg- or -betareg-. But I do not think those can be applied to longitudinal (panel) data, and I am not aware of anyway to handle endogeneity in those models. There are other Forum members who are more familiar with those issues than I am and I hope that one of them will respond.

But, in any case, -tobit- is not a consideration here.

[John Mullahy]

Prateek: Given your data's structure I strongly endorse Clyde's recommendation to avoid Tobit.

An excellent reference for fractional regression in the panel data context is this Journal of Econometrics paper by Leslie Papke and Jeff Wooldridge https://www.sciencedirect.com/scienc...0440760800050X

[Prateek Bedi]

Clyde Schechter and John Mullahy: Thanks a lot for your very helpful clarifications and insights. I shall now explore fractional regression technique. Have a great day!

[Prateek Bedi]

Hello Clyde Schechter and John Mullahy. Thanks to your inputs, I read about fractional data and I tried to search relevant commands/functions for the same in Stata. I did find relevant commands like glm, fracreg, betareg and fracglm which consider the possibility of a fractional dependent variable. However, I could not find an appropriate command for running fractional regressions in case of panel dataset (balanced or unbalanced).

I request you to guide me further with regard to application of fractional regression in a panel data setting.

Thank you!

[Prateek Bedi]

Eagerly waiting for a response Clyde Schechter and John Mullahy. It would be really helpful if you may provide further guidance.

[John Mullahy]

Beyond what Papke & Wooldridge discuss on p. 124 of their paper, I am not aware of any Stata commands that handle this situation.

[Prateek Bedi]

Alright. Thanks a lot, Prof. John Mullahy. Really appreciate your guidance.

[Corine Habr]

Hello, I have panel data where the dependent variable takes the value 0 for a number of the observations. The variable is not artificially censored, it is just that either the comany issues debt in which case we have a positive number, or it doesn't, so variable =0 in this case. Does this mean i have a corner solution at 0, and does it justify the usage of a tobit model?