ASYMPTOTIC ROBUSTNESS OF TESTS OF OVERIDENTIFICATION AND PREDETERMINEDNESS

Many statistical test procedures have been proposed for identification restrictions on one or several equations and the econometric predeter minedness of one or several variables in a system of structural equati ons. This study is devoted to unifying many test procedures in a syste matic way and to deriving the asymptotic distributions of the test sta tistics under a set of local alternative hypotheses and very general c onditions on the disturbances. By making use of a new martingale centr al limit theorem and a martingale convergence theorem, we show that th e limiting distributions of test statistics are noncentral chi2-distri butions under the local alternative hypotheses and central chi2-distri butions under the null hypotheses. These limiting distributions are ro bust in the sense that they hold for a variety of disturbance distribu tions and models. Our results show that many tests already known among econometricians can be carried out without making the usual relativel y restrictive assumptions.