Econometric issues in forward-looking monetary models
Recently, single equation approaches for estimating structural models have become popular in the monetary economics literature. In particular, single-equation Generalized Method Moments estimators have been used for estimating forward-looking models with rational expectations. Two important examples are found in Clarida, Gali, and Gertler (1998) for the estimation of forward- looking Taylor rules and in Gali and Gertler (1999) for the estimation of a forward-looking model for inflation dynamics. In this thesis, we address the issues of identification which have been overlooked due to the incompleteness of the single-equation formulations. We provide extensions to existing results on the properties of GMM estimators and inference under weak identification, pertaining to situations in which only functions of the parameters of interest are identified, and structural residuals exhibit negative autocorrelation. We also characterize the power of the Hansen test to detect mis specification, and address the issues arising from using too many irrelevant instruments as well as from general corrections for residual autocorrelation, beyond what is implied by the maintained model. In general, we show that the non-modelled variables cannot be weakly exogenous for the parameters of interest, and that they are informative about the identification and mis-specification of the model. Modelling the reduced form helps identify pathological situations in which the structural parameters are weakly identified and the GMM estimators are inconsistent and biased in the direction of OLS.We also ¯nd the OLS bias to be increasing in the number of over-identifying instruments, even when the latter are irrelevant, thus demonstrating the dangers of using too many potentially irrelevant instruments. Finally, with regards to the "New Phillips curve", we conclude that, for the US economy, this model is either un-identified or mis-specified, casting doubts on its utility as a model of in°ation dynamics.