The Wald approach to testing direct explicit restrictions on a parameter vector is generalized to the case of nonlinear implicit constraints. When applied to subsystems of simultaneous equations models, the generalization enables the symmetric joint testing of nonlinear overidentifying structural restrictions under very wide conditions. By varying the choices of certain matrices used to construct the generalized Wald statistic, one produces a whole class of tests which have equal asymptotic power yet whose associated structural coefficient estimators have different asymptotic efficiencies for any given reduced-form estimator from which they are derived.

A class of parametric for heteroscedasticity in linear models is discussed. For models with nonstochastic regressors, new exact within this class are suggested which utilize existing tables of the distribution of the von Neumann ratio and of the Durbin-Watson bounding ratios. Bound tests for heteroscedasticity in least squares regression are proposed. A rigorous treatment of within this class for heteroscedasticity in the errors of structural relations in dynamic simultaneous equations models is provided.