ECON 251 - FINAL EXAM QUESTIONS
& ANSWERS(RATED A+)
Quiz 4: Assume the following regression: GPA= X0+ X1tablet+ u
Why might the OLS estimate of the slope on tablet be a biased estimate of the true
effect of owning a tablet? Provide an example of a variable in this context. -
ANSWERstudents who own a table and those that doe not are not identical on all other
dimensions affecting their GPA - ie those with a tablet may come from educated,
wealthier households and it is reasonable to say this would affect their GPA. The
implication of this is a correlation is that an OLS estimate of X1 will be biased
Quiz 4: Suppose one school district decided to buy tablets for its high school students.
However, the district didnot have enough money to buy atabletfor every student, so they
had a lottery to select some students to receive a free tablet(while others did not). You
obtain data on whether or not each student got a free tablet(variable lottery), and you
decide to use this variable as an instrumental variable (IV)for tablet.What conditions
must lottery satisfy to be a valid IV? - ANSWER1. cov (z,x) != 0 (relevance) ie lottery
must be correlated with owning a table
2. cov(z,u) = 0 (exogeneity) ie lottery must be uncorrelated with all factors that effect a
students GPA
Below is the relevant STATA output from the IV estimation of this regression. How do
you interpret the IV estimate of the slope on tablet? Is the effect of owning a tablet on
GPA statistically significant, and why? (Note: Stata output was 0.07) -
ANSWERStudents who own a tablet have a 0.07 higher GPA compared to those who
do not. Because the p-value is 0.421, we see that owning a table does not have a
statically significant effect on GPA
Assuming that lottery satisfies the conditions for a valid instrumental variable for tablet,
is the IV estimate of the slope unbiased? Consistent? - ANSWERIf lottery satisfies the
assumptions of a valid IV, the IV estimator is consistent but not unbiased
Between relevance and exogenity, which is testable? Which is not testable? -
ANSWERrelevance is testable, exogenity is not testable
If relevance and exogenity hold, what can we say about Z, an IV? - ANSWERit is a valid
IV for X
Given the regression: callback =X0+ BlackX1 +u what is the meaning of X1 (Note X1=1)
- ANSWERBlack applicants have a 3 percent lower probability to be called back by an
employer on average. X1 is an unbiased estimate of the causal effect of black on the
probability of being called back by the employer since exogeneity holds by construction
, Sample final: Given the regression crime= X0 + OfficersX1+ u and X1 >0, does the
positive sign of the estimated slope on officers make sense to you? Do you think this
OLS estimate in unbiased for the true effect of police size on crime? - ANSWERNo- id
expect more officers to catch criminals and lead therefore to less crimes. One reason
that the OLS estimate may be biased is due to omitted variable bias - that is officers is
correlated with some factor in the u term like the population of the city
Quiz 3: given the following regression log(salary) = X0+ X1educ+ X2white+, where
where log(salary) = weekly log-earnings in U.S. dollars, educ=years of
education,white=1 if the person is a white worker, and 0 is the person is non-white. How
do we interpret the slope of on X2white - ANSWERX2 is the difference in the mean log-
earnings between white and non-white workers with the same level of education (or you
could say "holding education fixed").
Quiz 3: given the following regression log(salary) = X0+ X1educ + X2white + X3(white x
educ) + u how do you interpret all of the parameters (NOTE: X0 = 1.02, X1 = 0.05, X2 =
0.30, X3 = 0.02 - ANSWERX0 is the predicted mean log-salary for non-white persons
with zero years of education is $1.02.
X1 is one more year of education increases salary for non-white workers by 5 percent,
on average.
X2 is white workers with no education are predicted to earn 0.30 higher log-salary than
non-whites.
X3 is means that one more year of education increases white
persons' salary by 2 percent more than for non-whites.
Quiz 3: given the following regression log(salary) = X0+ X1educ+
X2female+X3male+X3(female x educ) +X3(male x educ) +u - What Gauss-Markov does
the model above violate, if any? What are the consequences of the estimates of the
parameters and standard errors? - ANSWERFor everyone in the model male=female=1,
i.e. there is an exact linear relationship between the two variables. The violates the
Gauss-Markov assumption on no perfect collinearity. In such a situation, we cannot
estimate the model at all -neither the parameters, nor standard errors.
Quiz 2: given the following regression airfare=X1+ X2distance+ u - what is meaning of
the u term? - ANSWERThe error term u represents all factors that affect the price of an
airplane ticket,other than the explanatory variable -distance.
Quiz 2: given the following regression airfare= X1 + X2distance + u what is an example
of a factor that could be seen in the u term - ANSWERholidays, destination, high vs low
cost airline
Quiz 2: given the following regression airfare = X1 + X2distance + u - what is the
meaning of the intercept and the slope (NOTE: X1 = 103.26 and X2 = 76.32) -
ANSWERX1 is the cost of the plane ticket if no miles were traveled during the flight
& ANSWERS(RATED A+)
Quiz 4: Assume the following regression: GPA= X0+ X1tablet+ u
Why might the OLS estimate of the slope on tablet be a biased estimate of the true
effect of owning a tablet? Provide an example of a variable in this context. -
ANSWERstudents who own a table and those that doe not are not identical on all other
dimensions affecting their GPA - ie those with a tablet may come from educated,
wealthier households and it is reasonable to say this would affect their GPA. The
implication of this is a correlation is that an OLS estimate of X1 will be biased
Quiz 4: Suppose one school district decided to buy tablets for its high school students.
However, the district didnot have enough money to buy atabletfor every student, so they
had a lottery to select some students to receive a free tablet(while others did not). You
obtain data on whether or not each student got a free tablet(variable lottery), and you
decide to use this variable as an instrumental variable (IV)for tablet.What conditions
must lottery satisfy to be a valid IV? - ANSWER1. cov (z,x) != 0 (relevance) ie lottery
must be correlated with owning a table
2. cov(z,u) = 0 (exogeneity) ie lottery must be uncorrelated with all factors that effect a
students GPA
Below is the relevant STATA output from the IV estimation of this regression. How do
you interpret the IV estimate of the slope on tablet? Is the effect of owning a tablet on
GPA statistically significant, and why? (Note: Stata output was 0.07) -
ANSWERStudents who own a tablet have a 0.07 higher GPA compared to those who
do not. Because the p-value is 0.421, we see that owning a table does not have a
statically significant effect on GPA
Assuming that lottery satisfies the conditions for a valid instrumental variable for tablet,
is the IV estimate of the slope unbiased? Consistent? - ANSWERIf lottery satisfies the
assumptions of a valid IV, the IV estimator is consistent but not unbiased
Between relevance and exogenity, which is testable? Which is not testable? -
ANSWERrelevance is testable, exogenity is not testable
If relevance and exogenity hold, what can we say about Z, an IV? - ANSWERit is a valid
IV for X
Given the regression: callback =X0+ BlackX1 +u what is the meaning of X1 (Note X1=1)
- ANSWERBlack applicants have a 3 percent lower probability to be called back by an
employer on average. X1 is an unbiased estimate of the causal effect of black on the
probability of being called back by the employer since exogeneity holds by construction
, Sample final: Given the regression crime= X0 + OfficersX1+ u and X1 >0, does the
positive sign of the estimated slope on officers make sense to you? Do you think this
OLS estimate in unbiased for the true effect of police size on crime? - ANSWERNo- id
expect more officers to catch criminals and lead therefore to less crimes. One reason
that the OLS estimate may be biased is due to omitted variable bias - that is officers is
correlated with some factor in the u term like the population of the city
Quiz 3: given the following regression log(salary) = X0+ X1educ+ X2white+, where
where log(salary) = weekly log-earnings in U.S. dollars, educ=years of
education,white=1 if the person is a white worker, and 0 is the person is non-white. How
do we interpret the slope of on X2white - ANSWERX2 is the difference in the mean log-
earnings between white and non-white workers with the same level of education (or you
could say "holding education fixed").
Quiz 3: given the following regression log(salary) = X0+ X1educ + X2white + X3(white x
educ) + u how do you interpret all of the parameters (NOTE: X0 = 1.02, X1 = 0.05, X2 =
0.30, X3 = 0.02 - ANSWERX0 is the predicted mean log-salary for non-white persons
with zero years of education is $1.02.
X1 is one more year of education increases salary for non-white workers by 5 percent,
on average.
X2 is white workers with no education are predicted to earn 0.30 higher log-salary than
non-whites.
X3 is means that one more year of education increases white
persons' salary by 2 percent more than for non-whites.
Quiz 3: given the following regression log(salary) = X0+ X1educ+
X2female+X3male+X3(female x educ) +X3(male x educ) +u - What Gauss-Markov does
the model above violate, if any? What are the consequences of the estimates of the
parameters and standard errors? - ANSWERFor everyone in the model male=female=1,
i.e. there is an exact linear relationship between the two variables. The violates the
Gauss-Markov assumption on no perfect collinearity. In such a situation, we cannot
estimate the model at all -neither the parameters, nor standard errors.
Quiz 2: given the following regression airfare=X1+ X2distance+ u - what is meaning of
the u term? - ANSWERThe error term u represents all factors that affect the price of an
airplane ticket,other than the explanatory variable -distance.
Quiz 2: given the following regression airfare= X1 + X2distance + u what is an example
of a factor that could be seen in the u term - ANSWERholidays, destination, high vs low
cost airline
Quiz 2: given the following regression airfare = X1 + X2distance + u - what is the
meaning of the intercept and the slope (NOTE: X1 = 103.26 and X2 = 76.32) -
ANSWERX1 is the cost of the plane ticket if no miles were traveled during the flight
