Test-type Questions
计量经济代考 NOTE: You can find answers to some questions almost completely and directly in the lecture notes. Some intermediate steps may not be explain
NOTE: You can find answers to some questions almost completely and directly in the lecture notes. Some intermediate steps may not be explain fully in details in the notes. (for example, something may be normally distributed thanks to the Central Limit Theorem, but this may not be explicitly written; or some details on how to go from one line to the next may not be written either)
You have to provide the missing details/steps.
(a) Under which conditions is this the GMM estimator?
(b) Show that this simplifies to the OLS estimator if W = I (idenity matrix).
(c) Under which condition(s) is this the GLS estimator?
(d) Show that this simplifies to the 2SLS estimator if W = Z (Z′Z)−1 Z′ , where Z correspond to some valid instruments. Would this estimator still be unbiased if V ar(u) ≠ σ2I?
2. 计量经济代考
What essential assumptions must Z satisfy for the IV esimator to be consistent for β? Explain.
3.
Show that given just identification the 2SLS estimator reduces to the IV estimator.
4. 计量经济代考
Give a real-world example of a situation where IV estimation is needed because of inconsticency of OLS and specify suitable instruments.
Show how to construct a GMM estimator based on these results. (let say a 2-step, with I as the weighting matrix in the first step) Assuming there is no endogeneity issue, what would be the moment condition for a nonlinear least squares estimation of this model?
Explain in a few words what the GMM Hansen test of overidentification is about and write H0.
8. 计量经济代考
Explain in details how GLS procedure can be seen as a special case of GMM. Is it efficient in the case of a linear model? What about in the case of a nonlinear model?
9.
Show how to construct the three different type of tests associated to GMM.
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