# Re: st: RE: Econometrically sound to use Mills ratio after mprobit?

 From "R.E. De Hoyos" To Subject Re: st: RE: Econometrically sound to use Mills ratio after mprobit? Date Mon, 10 Apr 2006 17:55:33 +0100

Stephen,

You are assuming that the selection problem in a multinomial context can be accounted for by the same technique as in the binary problem (Heckman 1979). Using the multinomial logit as the first-step estimation, Bourguignon et al. (2004) have shown that this is not the right way to approach the problem.

Generally speaking, the selection problem in a multinomial context can be define as:

y1 = xb + u1
y^*_m = zl + u_m, m = 1...M (outcomes)

Where y^* is a latent function and E(u1 | x,z)=0. Define p1...pM as the conditional probabilities of observing each of the M outcomes. Then, the selectivity-adjusted y1 can be estimated as:

y1 = xb + mu(p1...pM) + e1

You would need to take into account the conditional probabilities of observing NOT ONLY outcome (1) but all other outcomes as well. The problem is how to parameterize function mu(.)?

Rafa
PS. I have a working paper version of the reference, if you are interested I can send it to you off-list.

Reference:

F. Bourguignon, M. Fournier & M. Gurgand, «Selection bias corrections based on the multinomial logit model : Monte-Carlo comparisons», Journal of Economic Surveys, forthcoming

----- Original Message ----- From: "Stephen Johnston" <sjohns21@umbc.edu>
To: <statalist@hsphsun2.harvard.edu>
Sent: Monday, April 10, 2006 5:01 PM
Subject: Re: st: RE: Econometrically sound to use Mills ratio after mprobit?

Hello Miet,

Thanks for your advice. Here is how I understand the procedure to work, I read this on an archived statalist post and I have tested it.

mprobit y x1 x2 x3

predict phat if e(sample), xb outcome (1)

capture drop phat
capture drop mills

gen mills = normden(phat)/norm(phat)

reg y2 x1 x2 mills

For the "outcome" command in the predict line, you have to specify which of the choice outcomes (in your dependent variable) you are predicting a probability for. In this case the probability predicted for the choice that is set equal to 1. You can then generate an IMR for each choice in y.

You can check that this works by generating the inverse mills ratio from a probit and then including it in an OLS equation - then use the twostep command for the heckman procedure to make sure the results match. For this you will not need to specify an outcome since it will be generated from a probit. I hope this helps. Let me know if you have any trouble.

Thanks,
Stephen

On Apr 10, 2006, at 4:35 AM, Maertens, Miet wrote:

```Dear Stephen,

Maybe the following two articles by Wooldridge and by Lechner can help
you further:
http://www.msu.edu/~ec/faculty/wooldridge/current%20research/ ape1r5.pdf

I'm also trying to perform a similar estimation with stata but I'm
struggling with calculating the Inverse Mills ratio's.  Could you  let me
know how exactly you are implementing the procedure?

Thanks,
Miet

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Stephen
Johnston
Sent: 07 April 2006 18:35
To: statalist@hsphsun2.harvard.edu
Subject: st: Econometrically sound to use Mills ratio after mprobit?

Hello,

I am estimating a multinomial probit for a selection equation with 3
choices and I am interested in using the inverse mills ratio
generated from the MNP in a second step equation.  I know how to
implement this procedure, however, I have not been able to find any
literature that proves that the Heckman two-step estimation procedure
can appropriately and directly extend from a probit selection
equation to a multinomial probit selection equation.  Does anyone
know of any papers that address this issue?

Thanks,
Stephen
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