15 The Generalised Method of Moments

Least squares, instrumental variables and maximum likelihood can all be described in the same way: each chooses the parameters that make certain sample averages equal to zero. The generalised method of moments (GMM), introduced by Hansen (1982), makes that description the starting point. An economic model often implies only a set of moment conditions, such as an Euler equation that says a forecast error is unpredictable, without specifying a full probability distribution. GMM estimates the parameters from those conditions alone, gives their asymptotic distribution, uses any surplus conditions efficiently, and tests whether the surplus conditions hold. It unifies most of the estimators in this course, and it is the standard tool of empirical finance and macroeconomics.

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