Orthogonal statistics and the density of the liml estimator

We show that orthogonalization is helpful for constructing densities of maximum likelihood estimators. We therefore use an orthogonal specification of the reduced form of the instrumental variables regression model to obtain an approximation of the density of the limited information maximum likelihood estimator. The approximation consists of a single infinite sum and is less involved than the expression of the true density. In comparisons with the sampling density the approximation is shown to be accurate indicating the validity of its construction