# RE: st: logY, Tobit and the prediction of Y

 From "Alexandre, Pierre K" <[email protected]> To "'[email protected]'" <[email protected]> Subject RE: st: logY, Tobit and the prediction of Y Date Wed, 23 Apr 2003 09:27:24 -0400

```The literature on two-part model may be helpful.  Manning (1998) Journal of
Health Economics, Manning et al (1987) Journal of Econometrics, Andersen et
al. (2000) Health Economics may be useful.

Pierre K. Alexandre, Ph.D., M.S.
Assistant Professor of Health Economics
University of Miami - School of Medicine
Dept of Epidemiology and Public Health
1801 NW 9 Avenue, Suite 328
Miami, Florida 33136
Tel. 305-243-3482; Fax: 305-243-6436

-----Original Message-----
From: [email protected] [mailto:[email protected]]
Sent: Wednesday, April 23, 2003 9:17 AM
To: [email protected]
Subject: Re: st: logY, Tobit and the prediction of Y

To my question below, Mathew Stalker replied:

The prediction of Y from your model would simply be the exponential of the
predicted logY.

---

My reply: Well, according to Wooldridge, in his book Basic Econometrics
(2000:202), this does not work, since the value of Y will be systematically
underestimated by simply taking the exponential of logY.
---

However, you should note that the log of zero is minus infinity, so in your
log model no observations where Y is zero will be included.  Is this really
what you want?

---

My reply: I solved this by setting 0 expenditures to 1 befor the log
transformatiom (as I wrote in the mail).

---

Christer

[email protected]

m                                To:
[email protected]

Sent by:                         cc:

owner-statalist@hsphsun2.        Subject:  Re: st:
logY, Tobit and the prediction of Y
harvard.edu

23.04.03 15:02

statalist

[email protected] wrote on 23/04/2003 13:18:03:

> Hi,
>
> My initial model is:
>
> Y = a + b1x1 + controls + e
>
> where Y is expenditures on a commodity and x1 is income.
>
> Since there are a lot of zeroes, I use the Tobit apporach. However, since
> the log-linear model performed better than the linear, I use the former
> (Before the log transformation of Y, I follow convention and set zeroes
to
> 1.)
>
> Accordingly, the estimated Tobit model is:
>
> logY = a + b1x1 + controls + e
>
> The problem:
>
> I want to predict the value of Y (not logY) for certain values of income
> (and put it in a graph); that is, both the conditional Y (i.e. the Y
given
> that the threshold value of 0 was passed) and the unconditional (latent)
> value of Y.
>
> Does anyone know how to do this?
>
> Best regards,
>
> Christer Thrane
> Lillehammer University College
> Norway
>
>
>
>
>
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```