中央财经大学2014-2015第一学期计量经济学期中考试卷A答案

中央财经大学2014-2015学年第一学期 《计量经济学》期中考试卷(A 卷)答案

1. a ） (5分)

01

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=0 (1)

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===------=+∑∑∑，，采用最小二乘法推导目标方程对和分别计算一阶导数：从等式（）可以推导得：（）将等式（）代入1

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i i x y y x x x y y x x x x y y x x y y x x x x x ββββ=======-

----∑∑∑∑∑∑∑等式（）得：

（）（）化简等式（）得：即

b) (5分)

A1: the conditional distribution of error term given X has a mean of zero A2: all samples are independently and identically distributed A3: outliers are unlikely c ）(5分)

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n n i i i i i i i n n i i i i n i i i i i n i i y y x x x x x x y y x x x x x x x x x x x x x x E x x ββεβββεβεββεβ======-++-+=-+????

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i X x x x x E X x x εβεβ====?? ? ? ? ?

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=∑∑∑∑ d) (5分)

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2.

a) (5分)

Because there is not any independent variable on ability, and corr(ability, ACCA)>0. If I can add some independent variables to the regression to control for important omitted variables, I will put IQ as a good proxy variable for ability b) (10分)

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Suppose true model is: log()but the estimated model is: log()??log()()log()()(?=()

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i wage ACCA IQ wage ACCA wage ACCA ACCA ACCA wage ACCA ACCA ACCA IQ ACCA ACCA βββεββεβ

ββ

ββεβ===+++=++=---+++=

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i i ACCA ACCA ACCA ACCA ACCA ACCA ACCA

ACCA ACCA IQ

ACCA ACCA ACCA ACCA ACCA ACCA ACCA ACCA ACCA ACCA IQ βββ

εββδδ==========----=++----+

=+-=+∑∑∑∑∑∑∑∑∑∑2i i

ACCA δμ+c) (5分)

Because corr(ACCA, IQ)>0 and corr(IQ, wage)>0 then

220βδ>, the regression will likely

over-estimate the effect of ACCA score on wage rate. 3.

Omitted from the analysis are reasons why the survey respondents slept more or less than average. People with certain chronic illnesses might sleep more than 8 hours per night. People with other illnesses might sleep less than 5 hours. This study says nothing about the causal effect of sleep on mortality.

4. You can show the correlation among all independent variables, if there is any one which is larger than 0.5, then there is not any multicollinearity （多重共线性） problem in your model.

5.

a) (10分)

β1 = the difference of the average wage rate between female and male β3 = the ACCA return for male

β2 = the difference of the ACCA return between female and male b) (10分)

6.

a) (5分) Random sampling

b) (5分) Surveying on the GPA, public service, CET6, Internship, Gender, age, family background, outlook

c) (5分) regression success on GPA, public service, CET6, Internship, Gender, age, family background, outlook

d) (5分) if finding some significant factors, then trying your best to do it.

ACCA

β0+β1

Log(wage)

β0