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The Nature of the Problem
Linear Restrictions on the Coefficients of a Single Equation
Restrictions on the VarianceCovariance Matrix
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admissible structure admissible transformation Assumption block triangularity chapter clearly coefficient restrictions column vector consider consistent estimates Corollary corresponding covariance matrix covariance restrictions Define denote discussion disturbance terms disturbance variance elements of q(x elements of zi endogenous variables equa equation in question equation is identified equation of Eq equation under Eqs example exclusion restrictions exists exogenous fcth equation follows function homogeneous Hth block identified with respect implies independent restrictions indirect least squares inequalities involved irregular points Jacobian known least squares Lemma likelihood function linear combination linear restrictions linearly independent measure zero nonlinear nonsingular nonstochastic nonzero normalization rule observational information order condition overidentified parameters plim predetermined variables prior information prior restrictions probability limit proof reduced form result row kernel satisfying Eq scalar multiple second equation set of measure solution structural equation submatrix subset sufficient condition Suppose Theorem tion true first equation turbance uncorrelated unit hypersphere values variance-covariance matrix