## Wednesday, August 10, 2011

### Flip a Coin - FIML or 3SLS ?

When it comes to choosing an estimator or a test in our econometric modelling, sometimes there are pros and cons that have to weighted against each other. Occasionally we're left with the impression that the final decision may as well be based on computational convenience, or even the flip of a coin.

In fact, there's usually some sound basis for selecting one potential estimator or test over an alternative one. Let's take the case where we're estimating a structural simultaneous equations model (SEM). In this case there's a wide range of consistent estimators available to us.

There are the various "single equation" estimators, such as 2SLS or Limited Information Maximum Likelihood (LIML). These have the disadvantage of being asymptotically inefficient, in general, relative the "full system" estimators. However, they have the advantage of usually being more robust to model mis-specification. Mis-specifying one equation in the model may result in inconsistent estimation of that equation's coefficients, but this generally won't affect the estimation of the other equations.

The two commonly used "full system" estimators are 3SLS and Full Information Maximum Likelihood (FIML). Under standard conditions, these two estimators are asymptotically equivalent when it comes to estimating the structural form of an SEM with normal errors. More specifically, they each have the same asymptotic distribution, so they are both asymptotically efficient.