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38 CHAPTER 2. SOME USEFUL TIME-SERIES METHODShypotheses, use the fact that√T (ˆβ − β) D → N(0, V), (2.40)(19)(eq. 2.41)⇒µwhere V =(D 0 W −1 D) −1 ∂w, and D =E t. To estimate D, youcanµP Tt=1 ∂ŵ t.∂β 0Let R be a k×q restriction matrix and r is a q dimensional vector ofuse ˆD = 1 T∂β 0 constants. Consider the q linear restrictions Rβ = r on the coefficientvector. The Wald statistic has an asymptotic chi-square distributionunder the null hypothesis that the restrictions are trueW T = T (Rˆβ − r) 0 [RVR 0 ] −1 (Rˆβ − r) D → χ 2 q. (2.41)It follows that the linear restrictions can be tested by comparing theWald statistic against the chi-square distribution with q degrees of freedom.GMM also allows you to conduct a generic test of a set of overidentifyingrestrictions. The theory predicts that there are as manyorthogonality conditions, n, as is the dimensionality of w t . The parametervector β is of dimension k