estimate probit with variable factor in parameter

[Paul Taylor]

Hi everyone,
I want to run this probit model and estimate parameters B1 and B2:
Y = ((1-pi)B1 + (pi)B2)X + e
which pi is a binary variable in data (0 or 1) and X is independent variable(s).
Can anyone help me in STATA syntax?
(I know that I can separate data in pi=1 and pi=0 but I have made some assumptions about error term that do not allow this.)
thanks

[Fei Wang]

One way is to generate interactions between X and pi, and between X and (1-pi), as below.

gen X_pi = X*pi
gen X_1_pi = X*(1-pi)
probit Y X_1_pi X_pi

But I would recommend another way, as below.

probit Y X c.X#c.pi

where the coefficient of X is B1, and B2 can be obtained by summing up the coefficients of X and c.X#c.pi. This way is convenient for further partial effects derivation with -margins-.

[Joseph Coveney]

In addition to Fei's two approaches, you can get the two coefficients directly with factor variable notation omitting the base category and a no-constant option in the regression command. See below for an example. (Begin at the "Begin here" comment; the stuff above is just to create a toy dataset for illustration. Variables out, pre and pie are Y, X and pi in your post.)


.ÿ
.ÿversionÿ17.0

.ÿ
.ÿclearÿ*

.ÿ
.ÿ//ÿseedem
.ÿsetÿseedÿ717321674

.ÿ
.ÿquietlyÿsetÿobsÿ10000

.ÿ
.ÿgenerateÿdoubleÿpreÿ=ÿruniform(-0.5,ÿ0.5)

.ÿgenerateÿbyteÿpieÿ=ÿmod(_n,ÿ2)

.ÿ
.ÿquietlyÿgenerateÿdoubleÿxbÿ=ÿ-2ÿ*ÿpreÿifÿ!pie

.ÿquietlyÿreplaceÿxbÿ=ÿ2ÿ*ÿpreÿifÿpie

.ÿ
.ÿgenerateÿbyteÿoutÿ=ÿ(xbÿ+ÿrnormal())ÿ>ÿ0ÿ//ÿrbinomial(1,ÿnormal(xb))

.ÿ
.ÿ*
.ÿ*ÿBeginÿhere
.ÿ*
.ÿprobitÿoutÿibn.pie#c.pre,ÿnoconstantÿnolog

ProbitÿregressionÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿ=ÿÿ10,000
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWaldÿchi2(2)ÿÿ=ÿ1684.13
Logÿlikelihoodÿ=ÿ-6014.8608ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿ=ÿÿ0.0000

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿoutÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
ÿÿÿpie#c.preÿ|
ÿÿÿÿÿÿÿÿÿÿ0ÿÿ|ÿÿ-1.933382ÿÿÿ.0680644ÿÿÿ-28.41ÿÿÿ0.000ÿÿÿÿ-2.066786ÿÿÿ-1.799979
ÿÿÿÿÿÿÿÿÿÿ1ÿÿ|ÿÿÿ2.048288ÿÿÿÿ.069155ÿÿÿÿ29.62ÿÿÿ0.000ÿÿÿÿÿ1.912747ÿÿÿÿ2.183829
------------------------------------------------------------------------------

.ÿ
.ÿexit

endÿofÿdo-file


.

I'm curious about your mention of assumption for the error term. Unless you're proposing a heteroscedastic probit model, then the error term is fixed at unity for identification purposes.

[Paul Taylor]

Thank you very much for your help, Fei and Joseph.
these are good ideas, especially the last one.

about error term assumption, In fact I have 2 probit regression that their error terms are correlated. and this regression is one of those. so, I could not separate data. (I want to calculate corr. of 2 error terms ,finally)