MLE for two correlated regressions

[Paul Taylor]

Hi everyone,
I want to estimate parameters b1,b2,b3 in these two regressions in MLE (maximum likelihood estimation), which their error terms are correlated:
Y1 = b1 *X + eps1
Y2 = (p)*b2 * X + (1-p)*b3*X + eps2
X is independent variables and p is a binary [0,1] variable, which in second regression can distinguish observations with p=0 from p=1 in b3 and b2.
I assume that r = CORR(eps1,eps2) is NOT zero and error terms have Multivariate Normal distribution.

I wanted to run this model in MLE but I could not. :|
Can anyone help me?

[Joseph Coveney]

Same as before, mutatis mutandis.

.ÿ
.ÿversionÿ17.0

.ÿ
.ÿclearÿ*

.ÿ
.ÿ//ÿseedem
.ÿsetÿseedÿ717321674

.ÿ
.ÿquietlyÿdrawnormÿe1ÿe2,ÿdoubleÿcorr(1ÿ0.5ÿ\ÿ0.5ÿ1)ÿn(50)

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

.ÿgenerateÿbyteÿpieÿ=ÿmod(_n,ÿ2)

.ÿ
.ÿquietlyÿgenerateÿdoubleÿxb1ÿ=ÿ-2ÿ*ÿpreÿifÿ!pie

.ÿquietlyÿreplaceÿxb1ÿ=ÿ2ÿ*ÿpreÿifÿpie

.ÿ
.ÿgenerateÿdoubleÿxb2ÿ=ÿ(pieÿ-ÿ0.5)ÿ*ÿpre

.ÿ
.ÿforvaluesÿyÿ=ÿ1/2ÿ{
ÿÿ2.ÿÿÿÿÿÿÿÿÿgenerateÿdoubleÿout`y'ÿ=ÿxb`y'ÿ+ÿe`y'
ÿÿ3.ÿ}

.ÿ
.ÿ*
.ÿ*ÿBeginÿhere
.ÿ*
.ÿmvregÿout1ÿout2ÿ=ÿibn.pie#c.pre,ÿnoconstant

EquationÿÿÿÿÿÿÿÿÿÿÿÿÿObsÿÿÿParmsÿÿÿÿÿÿÿÿRMSEÿÿÿÿ"R-sq"ÿÿÿÿÿÿÿÿÿÿFÿÿÿÿÿÿP>F
--------------------------------------------------------------------------
out1ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ50ÿÿÿÿÿÿÿ2ÿÿÿÿ.8921528ÿÿÿÿ0.2579ÿÿÿ8.339325ÿÿÿ0.0008
out2ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ50ÿÿÿÿÿÿÿ2ÿÿÿÿ.8582197ÿÿÿÿ0.1148ÿÿÿ3.111797ÿÿÿ0.0536

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿtÿÿÿÿP>|t|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
out1ÿÿÿÿÿÿÿÿÿ|
ÿÿÿpie#c.preÿ|
ÿÿÿÿÿÿÿÿÿÿ0ÿÿ|ÿÿ-1.776693ÿÿÿ.5722428ÿÿÿÿ-3.10ÿÿÿ0.003ÿÿÿÿ-2.927264ÿÿÿ-.6261215
ÿÿÿÿÿÿÿÿÿÿ1ÿÿ|ÿÿÿ1.464861ÿÿÿ.5521319ÿÿÿÿÿ2.65ÿÿÿ0.011ÿÿÿÿÿ.3547254ÿÿÿÿ2.574996
-------------+----------------------------------------------------------------
out2ÿÿÿÿÿÿÿÿÿ|
ÿÿÿpie#c.preÿ|
ÿÿÿÿÿÿÿÿÿÿ0ÿÿ|ÿÿÿ-.974048ÿÿÿ.5504775ÿÿÿÿ-1.77ÿÿÿ0.083ÿÿÿÿ-2.080857ÿÿÿÿ.1327613
ÿÿÿÿÿÿÿÿÿÿ1ÿÿ|ÿÿ-.9340375ÿÿÿ.5311315ÿÿÿÿ-1.76ÿÿÿ0.085ÿÿÿÿ-2.001949ÿÿÿÿ.1338739
------------------------------------------------------------------------------

.ÿ
.ÿexit

endÿofÿdo-file


.

[Joseph Coveney]

Sorry, misread that the equations are different (precoffee).

Try something like the following in lieu of -mvreg-.

*
* Begin here
*
sureg (out1 = ibn.pie#c.pre, noconstant) (out2 = c.pre)

[Joseph Coveney]

And if you're interested in the full illustration, then here:

.ÿ
.ÿversionÿ17.0

.ÿ
.ÿclearÿ*

.ÿ
.ÿ//ÿseedem
.ÿsetÿseedÿ717321674

.ÿ
.ÿquietlyÿdrawnormÿe1ÿe2,ÿdoubleÿcorr(1ÿ0.5ÿ\ÿ0.5ÿ1)ÿn(300)

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

.ÿgenerateÿbyteÿpieÿ=ÿmod(_n,ÿ2)

.ÿ
.ÿquietlyÿgenerateÿdoubleÿxb1ÿ=ÿ-2ÿ*ÿpreÿifÿ!pie

.ÿquietlyÿreplaceÿxb1ÿ=ÿ2ÿ*ÿpreÿifÿpie

.ÿ
.ÿgenerateÿdoubleÿxb2ÿ=ÿpre

.ÿ
.ÿforvaluesÿyÿ=ÿ1/2ÿ{
ÿÿ2.ÿÿÿÿÿÿÿÿÿgenerateÿdoubleÿout`y'ÿ=ÿxb`y'ÿ+ÿe`y'
ÿÿ3.ÿ}

.ÿ
.ÿ*
.ÿ*ÿBeginÿhere
.ÿ*
.ÿsuregÿ(out1ÿ=ÿibn.pie#c.pre,ÿnoconstant)ÿ(out2ÿ=ÿc.pre),ÿ///
>ÿÿÿÿÿÿÿÿÿisureÿnoheaderÿnolog

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------+----------------------------------------------------------------
out1ÿÿÿÿÿÿÿÿÿ|
ÿÿÿpie#c.preÿ|
ÿÿÿÿÿÿÿÿÿÿ0ÿÿ|ÿÿ-1.873873ÿÿÿ.2719157ÿÿÿÿ-6.89ÿÿÿ0.000ÿÿÿÿ-2.406818ÿÿÿ-1.340928
ÿÿÿÿÿÿÿÿÿÿ1ÿÿ|ÿÿÿ2.199701ÿÿÿÿ.268748ÿÿÿÿÿ8.18ÿÿÿ0.000ÿÿÿÿÿ1.672964ÿÿÿÿ2.726437
-------------+----------------------------------------------------------------
out2ÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿpreÿ|ÿÿÿ1.061183ÿÿÿ.2018302ÿÿÿÿÿ5.26ÿÿÿ0.000ÿÿÿÿÿ.6656034ÿÿÿÿ1.456763
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.0213064ÿÿÿ.0472371ÿÿÿÿ-0.45ÿÿÿ0.652ÿÿÿÿ-.1138895ÿÿÿÿ.0712766
------------------------------------------------------------------------------

.ÿ
.ÿgsemÿ///
>ÿÿÿÿÿÿÿÿÿ(out1ÿ<-ÿibn.pie#c.pre,ÿnoconstant)ÿ///
>ÿÿÿÿÿÿÿÿÿ(out2ÿ<-ÿc.pre),ÿ///
>ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿcovariance(e.out1*e.out2)ÿ///
>ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿnocnsreportÿnodvheaderÿnolog

GeneralizedÿstructuralÿequationÿmodelÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿ=ÿ300
Logÿlikelihoodÿ=ÿ-783.65728

------------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------------+----------------------------------------------------------------
out1ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿpie#c.preÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ0ÿÿ|ÿÿ-1.873873ÿÿÿ.2719392ÿÿÿÿ-6.89ÿÿÿ0.000ÿÿÿÿ-2.406864ÿÿÿ-1.340882
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ1ÿÿ|ÿÿÿ2.199701ÿÿÿ.2687705ÿÿÿÿÿ8.18ÿÿÿ0.000ÿÿÿÿÿÿ1.67292ÿÿÿÿ2.726481
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿÿÿÿÿÿÿÿÿ0ÿÿ(omitted)
-------------------+----------------------------------------------------------------
out2ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿpreÿ|ÿÿÿ1.061183ÿÿÿ.2018302ÿÿÿÿÿ5.26ÿÿÿ0.000ÿÿÿÿÿ.6656034ÿÿÿÿ1.456763
ÿÿÿÿÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿ-.0213064ÿÿÿ.0472455ÿÿÿÿ-0.45ÿÿÿ0.652ÿÿÿÿÿ-.113906ÿÿÿÿ.0712931
-------------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿvar(e.out1)|ÿÿÿ.9529528ÿÿÿ.0778147ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.8120175ÿÿÿÿ1.118349
ÿÿÿÿÿÿÿÿvar(e.out2)|ÿÿÿ.9177812ÿÿÿ.0749419ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.7820488ÿÿÿÿ1.077071
-------------------+----------------------------------------------------------------
ÿcov(e.out1,e.out2)|ÿÿÿ.4876971ÿÿÿ.0609079ÿÿÿÿÿ8.01ÿÿÿ0.000ÿÿÿÿÿ.3683198ÿÿÿÿ.6070744
------------------------------------------------------------------------------------

.ÿ
.ÿexit

endÿofÿdo-file


.