Statistical Inference in Dynamic Economic Models

absolute maximum assume assumption asymptotic bilinear restrictions characteristic values computation conditional distribution confidence region convergence corresponding covariances Cowles Commission cumulative distribution function defined definition denote derived determined diagonal distribution function disturbances economic elements endogenous equa equation system equivalent exists exogenous variables follows G₁ given Hence Hurwicz identification power identification problem independent initial value inversion iteration Koopmans least-squares estimates Lemma likelihood function linear matrix maximum-likelihood estimates Newton method nonsingular nonsingular matrix notation observations obtained parameter point parameter space predetermined variables prediction priori restrictions probability distribution properties random reduced form regard regression coefficients S₁ satisfy solution statistical stochastic strictions structural changes structural equations subset Theorem tions transformation unbiased uniquely identifying vector x₁ y₁ zero αξ Δα