ivregress liml, does not return the likelihood e(ll), and I am not able to do likelihood ratio testing. Why is that?

[Joro Kolev]

When I fit Limited Information Maximum Likelihood regression model, say

ivregress liml price (mpg =head trunk weight)
ereturn list

there is no e(ll), the maximised likelihood is missing in what ivregress liml returns.

Then likelihood ratio testing becomes impossible:

. qui ivregress liml price (mpg =head trunk weight)

. est sto full

. qui ivregress liml price

. lrtest full .
full does not contain scalar e(ll)
r(498);


This is puzzling. The estimator is called Limited Information Maximum Likelihood, and yet it does not return a value for the maximused Likelihood...

( I understand that there are at least two ways how to solve the problem. One of them is a closed form solution to an eigen value problem. But still we are finding a solution to a maximum likelihood problem and the maximised likelihood is an important quantity that should be recoverable.)

My question is how can I recover the maximised value of the likelihood? How can I do likelihood ratio testing after ivregress liml?

[Malte Hessenius]

It is definitely not very intuitive that no e(ll) is stored.

What about ivreg2 as an alternative?

ssc install ivreg2
ssc install ranktest // necessary for the following command
ivreg2 depvar X1 X2 .... (endogenousvar = Z1 Z2), liml
ereturn list // yields e(ll)

[Joro Kolev]

Thank you Max,

ivreg2 does provide e(ll), but I do not think that this likelihood is the correct system likelihood. I spent a couple of hours studying the documentation of ivreg2, I did not find anything on how they calculate e(ll). I know that the ivreg2 e(ll) is not what I need because Pagan in a paper in Economics Letters shows that Iterated Seemingly Unrelated regression is equivalent to Limited information maximum likelihood, here it is

. ivreg2 price (mpg =head trunk weight), liml noheader
------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         mpg |  -342.7629   67.19733    -5.10   0.000    -474.4673   -211.0586
       _cons |   13465.18   1464.046     9.20   0.000      10595.7    16334.66
------------------------------------------------------------------------------
. dis e(ll)
-688.45705

. sureg (price mpg)  (mpg head trunk weight), isure nolog noheader

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
price        |
         mpg |  -342.7628   52.21744    -6.56   0.000    -445.1071   -240.4185
       _cons |   13465.18   1154.152    11.67   0.000     11203.08    15727.27
-------------+----------------------------------------------------------------
mpg          |
    headroom |   .3575597   .5797288     0.62   0.537    -.7786879    1.493807
       trunk |  -.0944815   .1355905    -0.70   0.486    -.3602339     .171271
      weight |  -.0058398   .0006548    -8.92   0.000    -.0071231   -.0045565
       _cons |   39.15977   1.700472    23.03   0.000     35.82691    42.49263
------------------------------------------------------------------------------

. dis e(ll)
-877.96867

As we can see the parameter estimates in the structural equation are (almost) the same. I guess the almost comes from numerical precision, they have to be the same according to Pagan.

But the log likelihoods are different, in fact very different -688.45705 vs -877.96867 ! (This difference spills over to the Likelihood ratio test, not shown here, but the likelihood ratio test the two produce are very different, in this example LR chi2(1) = 14.51 (ivreg2) vs LR chi2(1) = 25.24 (sureg, isure) for Ho: mpg=0. )

To preempt why am I not just using sureg when I know how to get the e(ll) via sureg: Sureg is an iterative estimator and takes ages when I do simulations.

So probably I should modify my question and say: How can I get the correct likelihood from a one step closed form (not iterative estimator). So that I can speed up my simulations to manageable time.