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simultaneous equation model with endogenous interaction terms

2 messages · Janka Vanschoenwinkel, Arne Henningsen

Original
Janka Vanschoenwinkel
# 
Dear list members,

I am building a model such as:

Y1 = Y2*X1 + X2
Y2 = Y1*X1 + X2

X2 is the exogenous variable
Z1 is the instrument of Y1
Z2 is the instrument of Y2

This is a simultaneous equation model. I know how to build a simultaneous
equation model without interaction terms:

library(systemfit)
eq1 <- Y1~Y2+X2+Z2
eq2 <- Y2~Y1+X2+Z1
inst <- ~X2+Z1+Z2
system <- list(eq1=eq1, eq2=eq2)
reg2SLS <-systemfit(system, "2SLS", inst=inst, data=mydata)
summary(reg2SLS)



I also know how to do a normal 2SLS with interaction terms:
library(systemfit)
ivreg(Y1~Y2*X1 | Z2*X1, data= Alldata)



However, I don't know how to deal with the interaction terms in the
simultaneous equation model.

I am experimenting both with R and STATA to see which formulation gives the
same result in both softwares, but until know without success.

Could somebody help me with this?

Thank you very much!

Janka
2 days later
Arne Henningsen
# 
Dear Janka

On 10 August 2015 at 11:25, Janka Vanschoenwinkel
<janka.vanschoenwinkel at uhasselt.be> wrote:
Do you mean the model:

Y1 = b10 + b11 * (Y2*X1) + b12 * X2 + e1

Y2 = b20 + b21 * (Y1*X1) + b22 * X2 + e2

where Y1 and Y2 are two (endogenous) dependent variables, X1 is a
potentially endogenous explanatory variable, X2 is an exogenous
explanatory variable, e1 and e2 are two potentially contemporaneously
correlated error terms, and b10, b11, b12, b20, b21, and b22 are
parameters to be estimated?
To estimate the above model specification, the following should work:

eq1 <- Y1 ~ I(Y2*X1) + X2
eq2 <- Y2 ~ I(Y1*X1) + X2
inst <- ~ X2 + Z1 + Z2
system <- list( eq1 = eq1, eq2 = eq2 )
reg2SLS <- systemfit( system, "2SLS", inst = inst, data = mydata )

Best regards,
Arne