Midterm Exam for Econometrics (1): Fall 2013
Prof. TaeHwan Kim
1. [42 points] We consider using the variable ¡°Airline Travel¡± (i.e. how much we consume on airline travel) as our dependent variable ( ) and ¡°Income¡± (i.e. how much we earn) as the explanatory variable ( ). Suppose that the OLS regression is given by
(0.5) (0.11)
where = 100 and the numbers in parentheses are standard errors. Denoting the true slope parameter by , supp...
Midterm Exam for Econometrics (1): Fall 2013
Prof. TaeHwan Kim
1. [42 points] We consider using the variable ¡°Airline Travel¡± (i.e. how much we consume on airline travel) as our dependent variable ( ) and ¡°Income¡± (i.e. how much we earn) as the explanatory variable ( ). Suppose that the OLS regression is given by
(0.5) (0.11)
where = 100 and the numbers in parentheses are standard errors. Denoting the true slope parameter by , suppose that we wish to test against at the 5% significance level. [Note that there is nothing to be proved here. What is important is to state or explain clearly!]
Propose your test statistic and compute its value.
Find the null distribution of your test statistic and explain how you like to obtain the correct critical values that can achieve the 5% significance level.
Explain the meaning of 5% significance level.
State your decision rule.
Explain what is Pvalue and how to compute Pvalue¡¦(»ý·«)
for this test
Discuss whether the computed slope estimate can be interpreted as measuring the causal effect of income on airline travel.
2. [28] Consider the following multiple regression in matrix form:
DGP:
OLS: ,
where all the notations are the same as used in class; for example is the matrix of explanatory variables, is the OLS estimator and so on. Prove that and are independent. You need to state clearly what assumptions are needed in your proof.
3. [30 points] In old days, it was believed that the Korean society was a prominently maledominated society. Such an undesirable social characteristic has been constantly improved over time, but some people think that such a problem of gender inequality is still present in many areas of the society, especially in terms of income. To test such a conjecture, we have collected income data ( ) for a group of 100 people including randomly selected men and women ( i.e. den
