Weak Identification of Forward-Looking Models in Monetary Economics

Recently, single-equation estimation by the generalized method of moments (GMM) has become popular in the monetary economics literature, for estimating forward-looking models with rational expectations. We discuss a method for analysing the empirical identification of such models that exploits their dynamic structure and the assumption of rational expectations. This allows us to judge the reliability of the resulting GMM estimation and inference and reveals the potential sources of weak identification. With reference to the New Keynesian Phillips curve of Gali and Gertler [Journal of Monetary Economics (1999) Vol. 44, 195] and the forward-looking Taylor rules of Clarida, Gali and Gertler [Quarterly Journal of Economics (2000) Vol. 115, 147], we demonstrate that the usual 'weak instruments' problem can arise naturally, when the predictable variation in inflation is small relative to unpredictable future shocks (news). Hence, we conclude that those models are less reliably estimated over periods when inflation has been under effective policy control