Notice: On April 23, 2014, Statalist moved from an email list to a forum, based at statalist.org.

# Re: st: Using a Tobit regression with the Heckman correction

 From "J. Boreham" To statalist@hsphsun2.harvard.edu Subject Re: st: Using a Tobit regression with the Heckman correction Date 17 Dec 2011 22:17:15 +0000

```Thanks for your prompt response, and for the clarification.

```
I think I need to take both types of Tobit into account. The "fee" variable is the transfer fee paid for footballers, so is only observed when "transferred" is equal to 1 - so there is a Type II Tobit. However, in addition, "fee" is always greater than or equal to 0, so there is a Type I Tobit too.
```
```
Am I right in thinking that the -heckman- command will account for the Type II Tobit, but not the Type I Tobit? I attempted to account for both by using the -tobit- command (to account for the Type I), and also including the inverse Mills ratio ("mills_ratio" below, to account for the Type II). I fear, however, that this will result in invalid standard errors, as the Heckman correction requires non-standard errors (as "the usual formulas for standard errors for least squares coefficients are not appropriate" - Heckman, Sample Selection Bias as a Specification Error, 1979)
```

John

On Dec 17 2011, Tirthankar Chakravarty wrote:

```
```I think you might be mixing up a few things here. Both -heckman- and
-tobit- fit Tobit (censored regression) models, i.e., where the
outcome of interest is not fully observed in the sample. They differ
in what they posit the censoring mechanism to be.

1) The model fitted by -tobit- is what is called the Type I tobit.
Here the observability of the outcome depends on the values of the
outcome itself - whether it crosses a non-stochastic threshold.

2) The model fitted by -heckman- is what is called the Type II tobit.
Here the observability of the outcome (your "fee" variable) depends on
the values of a binary indicator (probably what your "transferred"
variable refers to), which is modelled using a probit regression.
Conditional on the values of the binary indicator the second stage is
a simple linear regression fitted by OLS - where the conditionality is
taken into account using the Mills ratio.

There is also the possibility of fitting the whole model in one go
using partial maximum likelihood, but the important point is that the
conditional model for the outcome is a linear regression, and in the
two-step version of Heckman's estimator, the outcome is fitted using
OLS.

Lastly, note that OLS is an estimation technique and tobit is a model.

T

On Sat, Dec 17, 2011 at 1:16 PM, J. Boreham <jb648@cam.ac.uk> wrote:
```
```Dear Statalist,

```
I'm very new to Stata, so apologise if this is a silly question. I'm looking to run a Tobit regression using the Heckman correction. My Heckman code is:
```
***** heckman fee age agesq curr_app curr_goal_d curr_goal_m curr_goal_f,
/// select(transferred = age agesq curr_app curr_goal_d curr_goal_m
curr_goal_f prom) twostep *****

```
But this uses OLS rather than a Tobit model. I instead attempted to create the two stage Heckman correction by first manually producing the inverse Mills ratio, and then running a Tobit regression:
```
***** probit transferred age agesq curr_app curr_goal_d curr_goal_m
curr_goal_f prom

predict predicted_values, xb

generate denominator = normal(predicted_values)
generate numerator = normalden(predicted_values)
generate mills_ratio = numerator/denominator

```
tobit fee age agesq curr_app curr_goal_d curr_goal_m curr_goal_f mills_ratio *****
```
However, this will not account for the non-standard errors one needs when
using the Heckman correction.

So is it possible either to tell Stata to use a Tobit regression with the
"heckman" command, or instead to get the correct standard errors when
manually doing the correction by inserting the inverse Mills ratio?

John Boreham
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```
```

```
```*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```