1 Teaching notes on GMM 1

Generalized Method of Moment (GMM) estimation is one of two developments in econometrics in the 80ies that revolutionized empirical work in macroeconomics. (The other being the understanding of unit roots and cointegration.) The path breaking articles on GMM were those of Hansen (1982) and Hansen and Singleton (1982). For introductions to GMM, Davidson and MacKinnon (1993) have comprehensive chapter on GMM and I recommend that you read the chapter on GMM in the Hamilton (1994) textbook. This is a good supplement to the teaching notes. For more comprehensive coverage see the recent textbook by Alastair Hall (Oxford University Press 2005). I think that one can claim that there wasn’t that much material in Hansen (1982) that was not already known to specialists, although the article definitely was not redundant, as it unified a large literature (almost every estimator you know can be shown to be a special case of GMM). The demonstration in Hansen and Singleton (1982), that the GMM method allowed for the estimation of non-linear rational expectations models, that could not be estimated by other methods, really catapulted Hansen and Singleton to major fame. We will start by reviewing linear instrumental variables estimation, since that will contain most of the ideas and intuition for the general GMM estimation.