Econometricians Have Their Moments: GMM at 32

The 2013 Nobel Prize for Economics was awarded to Eugene Fama, Lars Hansen and Robert Shiller for their work on empirical asset pricing. Hansen's primary contribution to the cited work was the development of the generalised method of moments (GMM), a statistical method that has proved such a valuable tool for testing the validity of empirical asset pricing models. The public announcement of the award also acknowledges the wider impact of GMM on empirical analysis in economics and beyond, referring to the 1982 Econometrica paper in which Hansen introduced the method as ‘one of the most influential in econometrics’. In this paper, we reflect on how the GMM‐based inference framework has evolved since 1982, reviewing developments on four main issues: model diagnostic testing, moment selection, identification and inference in misspecified models. We also illustrate the broader influence of GMM on econometrics by briefly exploring the connections between GMM and three other estimation methods: indirect inference, moment inequality based techniques, and a group of techniques that can be presented equivalently within either the generalised empirical likelihood or info‐metric frameworks.