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Least Squares Under Ideal Conditions
Violations of the Ideal Conditions
4 other sections not shown
2SLS estimator 3SLS asymptotic covariance matrix asymptotic distribution asymptotically efficient coefficient consider consistent estimator constant term converges in distribution COROLLARY defined DEFINITION degrees of freedom dimension disturbances Econometrics efficient relative elements exactly identified exists FIML estimator finite and nonsingular full ideal conditions Hence idempotent identical implies independent indirect least squares instrumental variables k-class estimator least squares estimator Lemma likelihood function linear combination LVR estimator maximize maximum likelihood estimator model Yr nonsingular matrix nonstochastic normal distribution normal equations notation Note null hypothesis observations OLS estimator overidentified partition plim positive semidefinite priori restrictions probability limit Proof PROPOSITION random variables regressors satisfies the full scalar Section 1.5 seemingly unrelated regressions sequence set of equations solution squared errors submatrix sufficient condition sum of squared test statistic Theorem trace unbiased estimator variance vector zero mean