Economics

345: Applied Econometrics

Section A01
University of Victoria
Midterm Examination #1
Version 1

Spring 2011
Instructor: Martin Farnham

Name: ______________________

Student ID Number: V00___________

Signature: ___________________

Please read the following instructions for the midterm:

1) DO NOT TURN THE PAGE UNTIL AN INVIGILATOR TELLS YOU TO DO SO.

2) All bags, notes, papers, and electronic devices other than non-programmable
calculators must be put away. Please turn off any device that could make noise
during the exam.

3) Please fill out the information needed at the top of this page (name, ID, signature),
and on the NCS score card (bubble in name, student ID).

4) This exam contains 8 pages (including the cover sheet) numbered 1-8 AND 3
pages of statistical tables. The 8th numbered page is blank (for scratch work). When
you are told to begin the exam, first check to make sure all pages are there.
Immediately raise your hand if a page is missing.

5) Pace yourself. There are 75 minutes available for this exam. The exam is worth
60 points. Therefore, if you allocate 1 minute per point for each problem, on
average, you should have 15 minutes at the end to check over your answers.

6) Answer multiple choice questions on the NCS card provided. Answer other
questions in the space provided.

7) If at any time you do not understand a question, please raise your hand to ask an
invigilator for clarification.

8) POINTS WILL BE DEDUCTED FROM STUDENTS WHO DO NOT IMMEDIATELY
STOP WRITING WHEN TIME IS CALLED.

9) Have your Student ID out on your desk for invigilators to inspect.

Section 1: Multiple Choice (4 points each)

Select the most appropriate answer, and carefully bubble in the letter of the answer
on your NCS marking card.

Questions 1 and 2 refer to the following setup:

Suppose the true model of the relationship between education and the wage is given
by wage = 0 + 1educ + u . wage is the hourly wage and is measured in dollars. educ
is years of education completed.


1) Which of the following statements about the above wage equation is true?

I. The OLS estimator is unbiased if E(1 ) = 1.
II. The OLS estimator is unbiased if E(1 ) = 1.
III. The variance of the OLS estimator will be smaller, the lower is Var(u).

A) I only.
B) II only.
C) III only.
D) I and II only.
E) II and III only.


2) Suppose we estimate the above wage equation and obtain the following estimates
(I dont claim these are realistic estimates):

0 = 3

= 1.50
1

Which of the following is NOT a prediction of the fitted model?

A) A 1-year increase in education raises the wage by $1.50 on average.
B) A person with no years of education is paid a wage of $3 on average.
C) A person with 16 years of education is paid a wage of $27 on average
D) A 1.5 year increase in education raises the wage by $1 on average
E) A person with 12 years of education is paid a wage of $21 on average.

3) Suppose we set up the following hypothesis test framework about the mean of a
population that is normally distributed:

H0: =0
H1: <0

A random sample is collected and the sample mean is found to be 1.5.

Which of the following statements is TRUE?

I. We will reject the null in favour of the alternative if the standard error is
sufficiently small.
II. We will accept the null regardless of the size of the standard error.
III. We will fail to reject the null regardless of the size of the standard error.

A) I only.
B) II only.
C) III only.
D) II and III only.
E) None of the above statements is true.


4) Let X be a random variable such that X~N(3,5). Let Y=-2X-3. How is Y
distributed?

A) Y~N(-9,5)
B) Y~N(-6,5)
C) Y~N(-3, 20)
D) Y~N(-9, 20)
E) We dont have enough information to say.

Section 2: True, False, or Uncertain (5 points each).

Respond to the following italicized statements by labeling the statement true,
false, or uncertain. Then justify your claim. Answers that do not provide
justification will receive zero points. Weak justifications will receive minimal points.

1) 5 points

Suppose the true model of the relationship between education and the wage is given
by wage = 0 + 1educ + u . For unbiasedness of the OLS estimator, we need to
assume that the error term, u, and educ, are uncorrelated. It is likely true, in the real
world, that the error term and educ are uncorrelated.















2) 5 points

One way to increase the precision of the OLS estimator is to increase the sample size.














END SECTION 2

Section 3: Short Answers

You must show your work to receive credit for answers involving calculations.

1) 9 points total

If X~N(2,25), then what is the probability that X takes on a value larger than 5 or less
than 0? Draw the pdf of X and shade in the areas that correspond to P[X>5] + P[X<0].
Also, draw the pdf of the standardized version of X and shade in the corresponding
area. Label your 2 diagrams carefully.

1) (25 points total)

In Alberta, oil sands tailing ponds (disposal sites) contain toxic byproducts resulting
from the processing of petroleum products. Each year thousands of ducks die when,
unaware of the danger, they land on these ponds to rest during migration.

One way to reduce duck deaths on tailing ponds is to install deterrent systems. For
instance, these can use short-range radar to detect incoming flocks of ducks and set
off non-lethal cannons and noisemakers near the pond that scare off the ducks and
keep them from landing. These systems are costly, so oil companies may be slow to
install them.

Suppose the government of Alberta decides to mandate installation of such systems
(this is a hypothetical story). Policymakers at Alberta Environment would like to
know whether the policy is effective in reducing duck deaths. So they monitor a
random sample of 25 tailing ponds the year before mandating installation of
deterrent systems and the year after. For each tailing pond sampled they calculate
the difference in duck fatalities from the year before to the year after (D = Fatalities
after Fatalities before). A negative difference indicates a decline in duck fatalities.
Researchers calculate a value of D for each tailing pond in the sample.

Results of these surveys show that the sample mean of the difference in fatalities
from before mandating deterrent systems to after mandating deterrent systems is
-20 and that the sample standard deviation is 50. Assume that these differences, D,
are drawn from a population that has a normal distribution with mean and
variance 2.

a) 2 points
Formally write down the null hypothesis that the policy has no effect on duck
fatalities, against the alternative hypothesis that it reduces duck fatalities.





b) 4 points
Calculate the t statistic appropriate to your null hypothesis. Clearly show your
work. Wrong answers can receive partial credit if sufficient correct work is shown.

c) 3 points

Suppose you conduct the hypothesis test at the 5% significance level. What is (are)
the critical value(s) of t against which you will compare your t-statistic?




d) 3 points

Do you reject the null hypothesis at the 5% significance level? Explain briefly.




e) 4 points

Draw the t-distribution under the null (that is, assuming the null is true). In your
drawing, be sure to label with numbers the mean value of t under the null, the
edge(s) of the rejection region(s), and the t-statistic youve calculated.













f) 5 points

Now calculate a 95% confidence interval around the sample mean.

g) 4 points

Is the null contained in your confidence interval? Does the answer to this seem
inconsistent with the answer to question d? If so, can you reconcile the results?













END SECTION 3. END OF EXAM.
This Page Intentionally Left Blank (for scratch work)