Econometrics problemset 5 - Århus universitet 2021 PDF

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Department of Economics and Business Economics, University of Aarhus Econometrics Spring 2021, 8/3/2021 Allan Würtz

Problem set 5

Problem 1 •

:

Describe in your own words the following concepts

(1 − )-confidence

interval

fi

• Statistical signi cance

• Economic signi

ficance

• Distribution of a test statistics under the null-hypothesis

• Consistency of an estimator

• Asymptotic distribution of an estimator

Problem 2

You may hand in this problem to your TA for feedback.

Problem C8 in

Wooldridge, page 160. Data can be downloaded from Blackboard under Stata Data Sets.

Problem 3

Problem C6 in Wooldridge, page 160. Data can be downloaded from Black-

board under Stata Data Sets.

Problem 4

Problem C9 in Wooldridge, page 161. Data can be downloaded from Black-

board under Stata Data Sets.

Problem 5

Problem C13 in Wooldridge, page 162. Data can be downloaded from Black-

board under Stata Data Sets.

Problem 6

Problem C6 in Wooldridge, page 179. Data can be downloaded from Black-

board under Stata Data Sets.

Problem 7

Consider the regression model

 =  0 +  1 1 +  2 2 +  3 3 +  4 4 +  5 5 +  (|1  2   3   4  5 ) = 0 1. Explain how to test that

1 + 2 + 3 + 4 + 5 = 1

2. Explain how to test that

1 + 2 = 3 + 4

3. Explain how to test that

1 + 2 = 1

4. Explain how to test that

 1  2 = 1

and

and

1

3 + 4 = 1

 3  4 = 1

5. Explain how to test that  1 +  2 = 1,  1 +  3 = 1 and  1 +  4 = 1

Problem 8 Consider the regression model  =  0 +  1 1 +  (|1 ) = 0

Assume the Gauss-Markov assumptions (MLR.1-MLR.5) hold and that  ∼  (0  2 ) and  independent of 1 (that is assumption MLR.6 holds). Consider the following hypotheses 0 :  1 = 0 1 :  1  0

b b

Assume a significance level of 5%. Let  0 and  1 be the OLS estimators of  0 and  1 , respectively. In an application, it was found that

b

b X

 0 = 58,  1 = 21 

 = 52,

(1 − 1 )2 = 98

=1

The -test statistics is used for testing the hypotheses. Assume that the value of  2 is known to be  2 = 12. Answer the following questions conditional on  (the sample of the explanatory variable)

b

1. What is the distribution  1 ? 2. What is the distribution of the -test statistics under 0 ? 3. Suppose the true value of  1 = 2. What is the distribution of the -test statistics? 4. What is the probability of committing a Type I error in testing the hypotheses? 5. Suppose  1 = 2 is an economically interesting effect size. What is the probability of committing a Type II error in testing the hypotheses if the effect size is  1 = 2? 6. A "Null-finding" refers to a statistical insignificant hypothesis test result. In view of your results in questions 4 and 5, discuss the reasons for Null-findings. 7. Discuss the difference between statistical and economic significance, and how they relate to the sample size.

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