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st: tobit and marginal effects


From   "Scott Merryman" <smerryman@kc.rr.com>
To   <statalist@hsphsun2.harvard.edu>, "Marina.Balboa" <Marina.Balboa@ua.es>
Subject   st: tobit and marginal effects
Date   Fri, 1 Aug 2003 12:00:13 -0500

Marina,

I am sending this to the list as well - I'm not sure I'm correct and others have
additional insights.

Marina asked me off-list why, when you request the marginal effects of the
unconditional expected value following tobit, does Stata list in its output "y =
E[y*|y> ll]"  where ll is the lower limit; y* = y if y > ll and y* = ll if y <=
ll; i.e. does Stata really give the unconditional marginal effects.

Example:

. use "C:\Stata8\auto.dta", clear
(1978 Automobile Data)

. replace price = 4000 if price <4000
(11 real changes made)

. qui xttobit price mpg, ll(4000) i(foreign)

. mfx compute, nose predict(ys(4000,.))

Marginal effects after xttobit
      y  = E(price*|price>4000) (predict, ys(4000,.))
         =  6495.1777
-------------------------------------------------------------------------------
                        variable |          dy/dx                 X
---------------------------------+---------------------------------------------
                             mpg |       -252.7986            21.2973
-------------------------------------------------------------------------------


I believe the unconditional expectation of y is

E[y]= E[y|y>ll]*P(y>ll) + E[y|y<=ll)*P(y<ll)

    = E[y|y>ll]*P(y>ll) + 0*P(y<ll)

    = E[y|y>ll]*P(y>ll)

Hence, the unconditional expectation uses information on the censoring value.

Hope this helps,
Scott






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