# st: tobit and marginal effects

 From "Scott Merryman" To , "Marina.Balboa" 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

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

. 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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```