Viewing the relative efficiency of IV estimators in models with lagged and instantaneous feedbacks

The asymptotic efficiency of OLS and IV estimators is examined in a simple dynamic structural model with a constant and two explanatory variables: the lagged dependent variable and another autoregressive variable, which may also include lagged or instantaneous feedbacks from the dependent variable. The parameter values are such that all variables are stationary. The asymptotic efficiency of OLS and various IV estimators is expressed via the moments of the data series in the model parameters. Various computational and graphical aids are employed to examine and illustrate the relationships between parameter values, instrument weakness, and estimator efficiency. Symbolic computer algebra and image sequences are used in animations to identify regions in the parameter space where consistent IV estimators may be less efficient than inconsistent OLS estimators, upon comparing the asymptotic approximation to their mean squared errors.