Date:         Thu, 7 May 2009 13:46:00 -0700
Reply-To:     Paul <paulvonhippel@YAHOO.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Paul <paulvonhippel@YAHOO.COM>
Organization: http://groups.google.com
Subject:      Re: Tobit predicted values using PROC QLIM
Comments: To: sas-l@uga.edu
Content-Type: text/plain; charset=ISO-8859-1

I've concluded that neither PROC QLIM nor PROC LIFEREG will supply E(Y|
X). It can be calculated as follows, using equation 16.14 in
Wooldridge, Econometric Analysis of Cross-Section and Panel Data:

proc qlim;
 model y = x;
 endogenous y ~ censored (lb=0);
 output out = fitted
              predicted expected conditional xbeta errstd;
run;
data fitted;
 set fitted;
 cdf = probnorm (xbeta_y / errstd_y);
 pdf = PDF('NORMAL',xbeta_y/errstd_y);
 y_censored_expected = cdf * xbeta_y + errstd_y * pdf; /* This is E(Y|
X) */
run;

In my data, the correlation between the conditional expectation of the
censored variable E(Y|X) and SAS's "predicted" value max(0,E(Y*|X))
is .95, with the values agreeing better and better as they get further
from zero. Where the values differ, I would say the "predicted" value
looks like a more plausible guess than the expectation of the censored
value.