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GMM inference when the number of moment conditions in large. (English) Zbl 0941.62077
Summary: Asymptotic theory typically presumes that the dimensionality of econometric models is independent of the sample size even though this presumption is often quite unrealistic. In GMM estimation, whenever optimal instruments are not available, it can frequently be shown that adding over-identifying restrictions (moment conditions) will increase asymptotic precision. However, the conventional asymptotics which underlies this view insists that the number of moment conditions remains finite even though the number of available moment conditions may grow without bound. We consider the explicit dependence of the number of moment conditions (or instruments), \(q_n\), on the sample size, \(n\), and establish that, under conventional regularity conditions for the estimation of a linear model with general heteroskedasticity, \(q^3_n/n\to 0\) is a sufficient condition for the validity of conventional asymptotic inference about the GMM estimator.

MSC:
62J05 Linear regression; mixed models
62E20 Asymptotic distribution theory in statistics
62H12 Estimation in multivariate analysis
62P20 Applications of statistics to economics
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