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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