ECN 140: Econometrics
Spring 2006
Professor: Oscar Jorda
MIDTERM EXAM
Name_____________________________________________________________Student ID_____________________
1
6
2
7
3
8
4
9
5
10
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Be
sure to write your answers in the table provided above
1) The expected value of a discrete random variable
A) is the outcome that is most likely to occur.
B) is computed as a weighted average of the possible outcome of that random variable, where the
weights are the probabilities of that outcome.
C) equals the population median.
D) can be found by determining the 50% value in the c.d.f.
2) The OLS estimator is derived by
A) connecting the Yi corresponding to the lowest Xi observation with the Yi corresponding to the highest
Xi observation.
B) minimizing the sum of squared residuals.
C) minimizing the sum of absolute residuals.
D) making sure that the standard error of the regression equals the standard error of the slope estimator.
3) A large p-value implies
A) a large
.
B) rejection of the null hypothesis.
C) that the observed value
D) a large t-statistic.
is consistent with the null hypothesis.
4) Two random variables X and Y are independently distributed if all of the following conditions hold, with
the exception of
A)
.
B) knowing the value of one of the variables provides no information about the other.
C) if the conditional distribution of Y given X equals the marginal distribution of Y.
D)
.
of the population value
5) An estimator
A)
C)
is consistent if
.
B) Y is normally distributed.
.
D) its mean square error is the smallest possible.
1
6) An estimator
of the population value
is unbiased if
A)
.
B)
C)
.
D)
has the smallest variance of all estimators.
.
7) The reason why estimators have a sampling distribution is that
A) individuals respond differently to incentives.
B) in real life you typically get to sample many times.
C) economics is not a precise science.
D) the values of the explanatory variable and the error term differ across samples.
8) The conditional distribution of Y given X = x,
A)
C)
, is
.
B)
.
D)
.
.
, is calculated as follows:
9) The conditional expectation of Y given X,
A)
B)
C)
D)
10) An example of a randomized controlled experiment is when
A) one U.S. state increases minimum wages and an adjacent state does not, and employment differences
are observed.
B) random variables are controlled for by holding constant other factors.
C) some 5th graders in a specific elementary school are allowed to use computers at school while others
are not, and their end-of-year performance is compared holding constant other factors.
D) households receive a tax rebate in one year but not the other.
ANALYTICAL QUESTIONS. Write your answer in the space provided.
11) A few years ago the news magazine The Economist listed some of the stranger explanations used in the past
to predict presidential election outcomes. These included whether or not the hemlines of women's skirts
went up or down, stock market performances, baseball World Series wins by an American League team,
etc. Thinking about this problem more seriously, you decide to analyze whether or not the presidential
candidate for a certain party did better if his party controlled the house. Accordingly you collect data for
the last 34 presidential elections. You think of this data as comprising a population which you want to
describe, rather than a sample from which you want to infer behavior of a larger population. You generate
the accompanying table:
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Joint Distribution of Presidential Party Affiliation and Party Control of
House of Representatives, 1860-1996
Democratic Control Republican Control
of House (Y = 0)
of House (Y = 1)
Democratic President
0.412
0.030
(X = 0)
Republican President
0.176
0.382
(X = 1)
Total
0.588
0.412
Total
0.441
0.559
1.00
(a) Interpret one of the joint probabilities and one of the marginal probabilities.
(b) Compute
. How does this differ from
? Explain.
(c) If you picked one of the Republican presidents at random, what is the probability that during his term
the Democrats had control of the House?
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(d) What would the joint distribution look like under independence? Check your results by calculating the
two conditional distributions and compare these to the marginal distribution.
12) Your textbook defined the covariance between X and Y as follows:
Prove that this is identical to the following alternative specification:
4
Answer Key
Testname: MID12006.TST
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Be
sure to write your answers in the table provided above
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
B
B
C
A
C
D
D
B
D
C
1
Answer Key
Testname: MID12006.TST
ANALYTICAL QUESTIONS. Write your answer in the space provided.
11) (a) 38.2 percent of the presidents were Republicans and were in the White House while Republicans controlled
the House of Representatives. 44.1 percent of all presidents were Democrats.
(b)
.
= 0*Pr(X=0|Y=0) + 1*Pr(X=1|Y=0)
= 0 + 1*Pr(X=1, Y=0) / Pr(Y=0)
= .176/.588 = 0.299.
gives you the unconditional expected value, while
is the conditional expected value.
(c)
Pr(Y=0|X=1) = Pr(Y=0, X=1) / Pr(X=1)
=.176 / .559 = 0.315
(d)
Joint Distribution of Presidential Party Affiliation and Party Control of
House of Representatives, 1860-1996,
under the Assumption of Independence
Democratic Control Republican Control
of House (Y = 0)
of House (Y = 1)
Democratic President
0.259
0.182
(X = 0)
Republican President
0.329
0.230
(X = 1)
Total
0.588
0.412
Total
0.441
0.559
1.00
(there is a small rounding error).
(there is a small rounding error).
12)
=
.
2
E-views Question
1. Interpret the results. The estimated coefficients suggest that wage is $8.85 per hour
regardless of geographic location or experience (other factors might determine this
level). Workers in the south earn $1.59 less on average relative to other workers. An
additional year of experience increases hourly wage by $0.036. The overall fit of the
model is quite poor, with an R2 of only 2.7%.
2.
W (south, 5 years) = 8.85 − 1.59 × 1 + 5 × 0.036 = $7.44
3. Can simply test
H0 : β1 ≥ 0
vs.
H1 : β1 < 0,
where β1 is the regression coefficient on the variable South. The t statistic, from the
e-views output is -3.28, less than the critical value of -1.645 for this one sided test at
the 95% level. Therefore we reject the null hypothesis that workers in the South are
paid at least as much as in the rest of the country.