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Large Sample Properties of Generalized Method of Moments Estimators

Why this mattered

Hansen’s 1982 paper mattered because it turned moment restrictions from a collection of special-purpose estimating tricks into a general econometric framework. Instead of requiring a fully specified likelihood, GMM allowed researchers to estimate structural parameters from the orthogonality conditions implied by a model, with large-sample results for consistency, asymptotic normality, efficiency, and specification testing. This made rigorous inference possible in settings where economic theory gave testable implications but not a complete probability model, especially in dynamic, nonlinear, and time-series environments.

The paradigm shift was methodological and practical: after GMM, economists could take Euler equations, instrumental-variable restrictions, and rational-expectations implications directly to data without solving or estimating every part of the surrounding equilibrium model. This helped move empirical macroeconomics and finance toward testing structural restrictions under weaker distributional assumptions, a point later highlighted in Hansen’s 2013 Nobel recognition for empirical analysis of asset prices.

Its influence is visible in later breakthroughs such as Hansen and Singleton’s estimation of nonlinear rational-expectations models from stochastic Euler equations, the broad use of overidentification tests in empirical economics, and the later growth of semiparametric and moment-based inference. GMM became a shared language for connecting theory to data when the model was informative but incomplete.

Abstract

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