3SLS equation

[Biswanath Behera]

Suppose I have two equations
Y1= Y2+X1+X2+Z+eit
Y2= X1+X2+X3+M+uit

Suppose equation 1 have 6 variables and equation 2 have 5 variables. I want to use 3SLS to solve the above two equations simultaneously. Since, Y2 appears in both the equations it leads to a simultaneity. Can I use the 3SLS here?

[George Ford]

help reg3. in the 3rd set of examples, the first one is IV.

I think it goes something like this.

clear all
sysuse auto, clear
reg3 (eq1: price = mpg foreign displacement) (eq2: mpg = weight foreign length) , endog(mpg) exog(foreign displacement weight length) ireg3
reg3 (eq1: price = mpg foreign displacement) (eq2: mpg = weight foreign length) , inst(foreign displacement weight length) ireg3

[Biswanath Behera]

Yes sir, thank you for your clarification and for the reference.

[Biswanath Behera]

George Ford Sir, how do we check for the identification and the reliability of instruments used in 3SLS? Is there any post estimation techniques? For example in system GMM there is Sargan and Hansen test for instrumental validity. So, what are the post estimation techniques (codes) to be used after 3SLS in STATA for the same?

[George Ford]

I don't think so. Use ivreg2 for the main equation and use those results.

ivreg2 price (mpg = length weight) foreign displacement, r endo(mpg)

or you could try to code them yourself from the reg3 results.

eregress will give you the same results as ivreg2. ivreg2 also incoporates the residual correlation (LIML). Yet, the results between reg3 and ivreg2/eregress are not identical. But, if you are using reg3 to address residual correlation, then I'd use ivreg2 or eregress (the former giving you more diagnostics). Since both equations do not include an endogenous variable, I think these alternatives are sensible.

[Biswanath Behera]

Okay Sir George Ford ,
Thank you for the insights. I will look into it.

[sabrina queen]

Hi Sir George Ford


I would like to get insight from you

Now, I am building a simultaneous equation, and it will be run with the reg3 syntax

along with the simultaneous equation :
Y1 = X1 + X2 + X3 + X4
Y2 = Y1 + X1 + + X4 + X5 + X6

the variables Y1 and X1 are bound to the instrument variables X7 + X8 so the syntax I created is like this

reg3 (eq1: Y1 = X1 + X2 + X3 + X4) (eq2: Y2 = Y1 + X1 + + X4 + X5 + X6), endog(Y1 X1) exog (X7 X8) first

I want to ask
1. Can the independent variable in EQ 1 also be used as an independent variable in EQ 2? such as X1 and X4. For the notes, X1 is an endogenous variable that is influenced by the instrument variable, while X4 is not.
2. I see that the instrument variables X7 and X8 affect not only X1 but also Y1, so I also make Y1 an endogenous variable that is also bound to the instrument variable, is this possible to estimate?


thank you

[George Ford]

Should be good to go. 2 endo, 2 exclusions (assuming the exclusions are legit).

[sabrina queen]

Hai George Ford
Thank You for your suggestion before

I need your suggestion again.

I try ivreg3 syntax with 3 endogenous variables and 3 instruments, but Stock Yogo Weak id critical values do not appear.


Underidentification test (Kleibergen-Paap rk LM statistic): 29.168
Chi-sq(1) P-val = 0.0000

Weak identification test (Kleibergen-Paap rk Wald F statistic): 10.514
Stock-Yogo weak ID test critical values: <not available>

Hansen J statistic (overidentification test of all instruments): 0.000
(equation exactly identified)


Is it possible to use the ivreg2 syntax with three endogenous variables and three instruments?

If not, can you suggest a possible syntax?

[George Ford]

With ivreg2, you'll estimate each equation independently. So you don't get the correlated error adjustment.

[sabrina queen]

Hi George Ford
Thank you for your suggestion again

if I have syntax like this
reg3 (ln_gdpril vdigital inklusi ln_loan ir ln_er inflasi), 2sls endog(vdigital inklusi ln_loan) exog(ln_mobile mma digpay) first noconstant vce(robust)

I want to know, If I have reg3 how do I check the validity of instruments, such as the Hansen Test, Underidentification Test, and Weak Identification Test?

Can this syntax " ivreg2 ln_gdpril ir ln_er inflasi (vdigital inklusi ln_loan = ln_mobile mma digpay), robust small noconstant " be used to check the validity of the instrument ?

[George Ford]

You can use ivreg2 to do the tests by equation.