A General Theory of Hypothesis Testing in the Simultaneous Equations Model

Classical exponential-family statistical theory is employed to characterize the class of exactly similar tests for a structural coefficient in a simultaneous equations model with normal errors and known reduced-form covariance matrix. We also find a necessary condition for tests to be unbiased and derive their power envelope. When the model is just-identified, we show that the Anderson-Rubin, score, and conditional likelihood ratio tests are optimal. When the model is over-identified, there exists no optimal test. Nevertheless, Monte Carlo simulations indicate that the power curve of the conditional likelihood ratio test is reasonably close to the power envelope