The Asymptotic Distribution of Tests for Over-identification in Partially Identified Linear Structural Equations

We study the asymptotic distribution of the statistics suggested by Sargan/Byron/Wegge and Basmann for testing for over-identification in partially identified linear structural equations and derive closed form expressions for their asymptotic densities. These allow us to understand the asymptotic behaviour of these statistics in cases where identification of the structural parameters fails. We also consider variants of these statistics using estimators of the structural variance based on the LIML estimator and show that they have unexpected properties. 1 Address for correspondence: Giovanni Forchini, Department of Econometrics and Business Statistics, Monash University, Clayton, Victoria 3800, Australia. E-mail: [email protected] 2 I thank Les Godfrey, Grant Hillier, Peter Phillips, Chris Skeels and Katharina Hauck for helpful comments and discussions. This research was partially supported by Australian Research Council grant DP0771445.