Valid Inference for a Class of Models Where Standard Inference Performs Poorly; Including Nonlinear Regression, ARMA, GARCH, and Unobserved Components

Standard inference works poorly in models of the form y=gamma*g(beta,x) epsum, because the standard error for beta_hat depends on gamma_hat. In this paper we show that this problem is usefully studied by working with the linearization of g(.) and the resulting reduced form regression. Bias and dispersion in beta_hat depend on correlation between the 'regressors' and on gamma, as does the size of the t-test. A reduced form test however is exact when g(.) is linear and has nearly correct size in examples from non-linear regression, ARMA, GARCH, and Unobserved Components models. Further, its distribution does not depend on the identifying restriction gamma is not equal to 0