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Extension of Classical Methods II
Foundations of Probability
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2SLS and 3SLS 3SLS estimator assumptions asymptotically Chapter characteristic roots conclude Consequently consistent estimator context converges Corollary covariance matrix defined derived Dhrymes econometric elements entity equation is identified error process example exogenous variables FIML estimator follows forecast given GLSEM Hence implies imposed instrumental variables instruments ith equation ith structural equation Kullback information lag operator Lagrange multipliers least squares Lemma likelihood function limiting distribution LIML linear maximizing maximum likelihood mean mean value theorem ML estimator Moreover NL2SLS NL3SLS nonlinear nonsingular matrix notation null space obeys obtain order conditions orthogonal parameter vector plim preceding discussion predetermined variables prior restrictions probability space procedure Proof Proposition q.e.d. Remark random variables random vectors rank reduced form representation respect sample sequence solution stationary process structural errors structural parameters suppose T—oo test statistic Theorem tion validity verify zero
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