Likelihood Ratio Test / 3SLS System

[Loukas]

Hello All

I want to test a restriction with the likelihood ratio test. The two models are:

The Restricted (REST)
R1 = C(11)*(C(1)+XCR) + C(12)*(C(2)+XDCR) + C(13)*(C(3)+XDTR) + C(14)*(C(4)+XEI) .....
R2 = C(21)*(C(1)+XCR) + C(22)*(C(2)+XDCR) + C(23)*(C(3)+XDTR) + C(24)*(C(4)+XEI) .....
.
.
.
R60 = C(601)*(C(1)+XCR) + C(602)*(C(2)+XDCR) + C(603)*(C(3)+XDTR) + C(604)*(C(4)+XEI) .....

The Unrestricted (UNREST)
R1 = C(605) + C(606)*XCR + C(607)*XDCR + C(608)*XDTR + C(609)*XEI .....
R2 = C(616) + C(617)*XCR + C(618)*XDCR + C(619)*XDTR + C(620)*XEI .....
.
.
.
R60 = C(716) + C(717)*XCR + C(718)*XDCR + C(719)*XDTR + C(720)*XEI .....

The Restrictions
C(605) = c(11)*c(1) + c(12)*c(2) + c(13)*c(3) + c(14)*c(4) .....
C(616) = c(21)*c(1) + c(22)*c(2) + c(23)*c(3) + c(24)*c(4) .....
.
.
.
C(605) = c(601)*c(1) + c(602)*c(2) + c(603)*c(3) + c(604)*c(4) .....

The two systems are estimated with 3SLS , treating one explanatory variable as endogenous and using a few instruments.

I would like to ask 2 questions:

Q.1. Is it possible to run a likelihood ratio test when the models are systems?
This is the command I am typing for the test statistic:

scalar LR = -2*( REST.@logl - UNREST.@logl )

when I double click the new object I get “ NA “.

Even this yields the same:

Scalar LR = sys1.@logl where sys1 is a simple OLS system.


Q.2. For the estimation of the restricted model with 3SLS is it appropriate to use stacked instruments or equation-by-equation instruments?
I am not sure what the difference between the two is. However, with @STACKINST I get “Near Singular Matrix” where with @INST I get a successful estimation.


Thank you in advance

[EViews Gareth]

EViews won't compute the log-likelihood value for 3SLS (or 2SLS) in systems. You could theoretically compute it yourself using the determinant of the residual covariance matrix (@detresid) and a little knowledge of the form of the likelihood function for 3SLS.

In general if you don't know/want stacked instruments, you probably just need to use @inst

[EViews Glenn]

One issue to keep in mind is that for 2SLS and 3SLS, the likelihood is not maximized in the usual fashion so that LR tests are problematic, at best.

[Loukas]

Thank you both for your immediate response.

Since I have successfully estimated both models I think I could run a Wald test.
Using Excel I could calculate the right hand side of the restriction and then impose the restriction on the coefficients of the unrestricted model.
The restriction in EViews, for some arithmetic values A, B, C would look like this:

C(605) = A
C(616) = B
.
.
C(716) = c

In total there are going to be 66 restrictions tested.

Do you think that this test is equivalent to the likelihood ratio test??

The literature suggests the LR test. However, the LR might only be embraced because it includes a lot less calculations.

Thank you for your time

[startz]

The Wald test is asymptotically equivalent to a likelihood ratio test, but it won't be exactly the same.

I wonder if there is a way to look at the change in the J-statistic to do what you want?

[EViews Gareth]

(If EViews reported the J-statistic...)

[startz]

Oh yeah. Well, the J-statistic now shows up for single equation TSLS and for system GMM. Since system 2SLS and 3SLS are special cases of GMM, maybe the J-stat should be added to the to-be-added-someday list.