计算机网络 财大试卷,上海财大研究生高级计量经济学期末试卷

上海财经大学研究生试题命题纸

(20 --20 学年 第 学期)

课程名称：计量经济学(I )( 经济学院各专业)(B ) 命题教师：周亚虹

1. Given a random variables y, and random vectors x, z. The linear projection of y on x is defined as ：.

1(|)(')(')L y x xE x x E x y ?=(a) Let , show that (|)u y L y x =?(')0E x u = (b) show that ((|,)|)(|)L L y x z x L y x =(c) show that ((|,)|)(|)L E y x z x L y x =

2．Let y and z be random scalars, and x be a 1K ×random vector, where one element of x can be unity to allow for a nonzero intercept. Consider the population model

(|,)E y x z x z βγ=+, 2(|,)Var y x z σ=.

where interest lies in the vector

1K ×β. To rule out trivialities, assume that 0γ≠. In addition,

assume that x and z are orthogonal in the population: (')0E x z =.Consider two estimators of β

based on N independent and identically distributed observations: (1) ?β

(obtained along with ?γ) is from the regression of y on x and z; (2) β

% is from the regression of y on x. Both estimators are consistent for β. (along with the standard rank conditions)

(a) Show that , without and additional assumptions(except those needed to apply the law of large

numbers and central limit theorem), ?))β

βββ??%?)is always positive semidefinite (and usually positive definite). Therefore-from the standpoint of asymptotic analysis-it is always better to include variables in a regression model that are uncorrelated with the variables of interest.

(b) Consider the special case where 2

(K K z x μ=?,where

()K K E x μ≡, and K x is

symmetrically distributed: . Then 3

()K K E x μ?0=K β is the partial effect of K x on (|)E y x

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