연세대 계량경제학 족보 연세대 계량경제학 중간 족보.docx 업로드
연세대 계량경제학 족보 연세대 계량경제학 중간 족보.docx
연세대 계량경제학 족보 연세대 계량경제학 중간 족보.docx
Midterm Exam for Econometrics (1): Fall 2014
Prof. Tae-Hwan Kim
1. [50 points] For a randomly selected 5 families, the following observations have been collected in the table and summary statistics are provided below the table. Note that the total number ( ) of observations is 5.
Family
( )
Airline Travel ($100)
( )
Income ($1000)
( ) 1 3 20 2 15 45 3 15 49 4 20 60 5 40 95
, , ,
, , ,
Use ‘Airline Travel’ as the dependent variable and ‘Income’ as the only explanatory variable (i.e. there is no constant in this regression). Compute the OLS estimate for the slope.
Discuss the consequences of not including the constant term in the regression.
Predict the Airline Travel consumption of a family whose annual Income is $65,000.
Discuss whether you can measure the causal effect of ‘Income’ on ‘Airline Travel.’
Suppose that the true variance of the error term is known as . Test the following null and alternative at the 5% significance level. The null is that the true slope parameter is 0.4 and the alternative is that the true slope parameter is not 0.4. [Hint: approximately]
2. [25 points] Consider the following DGP:
where is a vector.
Define the projection matrices: and .
Prove that and
Prove that if is the column of then,
3. [25 points] Consider the following DGP:
where is a vector.
Let be the OLS estimator for . We will consider another estimator for which is given by where be a number between 0 and 1.
Show that this new estimator has a smaller variance than the OLS estimator; that is, show that is p.s.d (positive semi definite).
Does the result in (1) contradict the Gauss Markov Theorem Say ‘Yes’ or ‘No’ and then explain your reasoning.
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자료제목 : 연세대 계량경제학 족보 연세대 계량경제학 중간 족보.docx
파일이름 : 연세대 계량경제학 족보 연세대 계량경제학 중간 족보.docx.doc
키워드 : 연세대,계량경제학,족보,중간,docx
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