八高研一下高计2econometrics.pptx

Econometrics IProfessor William GreeneStern School of BusinessDepartment of EconomicsEconometrics IPart 21 – GeneralizedMethod of MomentsI’m trying to minimize a nonlinear program with the least square under nonlinear constraints. It’s first introduced by Ané & Geman (2000). It consisted on the minimization of the sum of squared difference between the moment generating function and the theoretical moment generating function I have a question. The question is as follows. We have a probit model. We used LM tests to test for the hetercodeaticiy in this model and found that there is heterocedasticity in this model...How do we proceed now? ?What do we do to get rid of heterescedasticiy?Testing for heteroscedasticity in a probit model and then getting rid of heteroscedasticit in this model is not a common procedure. In fact I do not remember seen an applied (or theoretical also) works which tests for heteroscedasticiy and then uses a method to get rid of it???See Econometric Analysis, 7th ed. pages 714-714FGLSFeasible GLS is based on finding an estimator which has the same properties as the true GLS. Example Var[?i] = ?2 [Exp(??zi)]2.True GLS would regress y/[? Exp(??zi)] on the same transformation of xi.With a consistent estimator of [?,?], say [s,c], we do the same computation with our estimates.So long as plim [s,c] = [?,?], FGLS is as “good” as true GLS. ? Consistent ? Same Asymptotic Variance ? Same Asymptotic Normal DistributionThe Method of MomentsEstimating a ParameterMean of Poissonp(y)=exp(-λ) λy / y!E[y]= λ. plim (1/N)Σiyi = λ. This is the estimatorMean of Exponentialp(y) = λ exp(- λy)E[y] = 1/ λ. plim (1/N)Σiyi = 1/λMean and Variance of a Normal DistributionGamma DistributionThe Linear Regression ModelInstrumental VariablesMaximum LikelihoodBehavioral ApplicationIdentificationCan the parameters be estimated?Not a sample ‘property’Assume an infinite sampleIs there sufficient information in a sample to reveal consistent estimators of the parametersCan t