ECON 251 - FINAL EXAM QUESTIONS AND ANSWERS
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. - Answers -
students 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? - Answers -1. 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) - Answers -
Students 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? - Answers -If 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? - Answers
-relevance is testable, exogenity is not testable
If relevance and exogenity hold, what can we say about Z, an IV? - Answers -it is a
valid IV for X
Given the regression: callback =X0+ BlackX1 +u what is the meaning of X1 (Note X1=1)
- Answers -Black 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? - Answers -No- 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
What are the two reasons OLS might be biased? - Answers -exogeneity (omitted
variable bias) or reverse causality (the y term effects x and x effects y - in the
crimes/officers example - a city might hire more officers in response to an increase in
the number of crimes)
How do you design a random experiment? Use the crime/ officer example from practice
exam - Answers -We have a large group of participants (cities in this case) and we
randomly assign them to two groups - group will hire a large police force, and another
will hire a small police force (draw diagram that you did in class to asses knowledge)
Sample final: if you conducted a random experiment Would you get an unbiased
estimate of the effect of police size on crime from this experiment? - Answers -Yes you
would get an unbiased estimate because cov (officer,u) = 0 holds by construction (Ie
OLS is unbiased and consistent)
Sample exam: Some researchers have noticed that during a local elections year the city
governments tend to hire more police officers (and, therefore, reduce crime) in order to
increase their chances to be reelected. Suppose that you have a dummy variable for
whether there are local elections in a given year (election). Assuming that elections are
unrelated to any factors in the error term and have no direct effect on crime, how would
you use this variable in order to produce a consistent estimate of the slope on officers? -
Answers -We would use this as a IV for the following reasons: One we are told that
election has no effect on crime. Two it has the principle of relevance - cov (officers,
election)!=0. Finally we have the property of exogenity - cov (officers, u)=0
Sample exam: The IV estimation results are presented below. Interpret the IV estimate
on the slope of officers. Does police size have a statistically significant effect on crime?
(note X1 = -0.02 and p-value is 0.000) - Answers -one more police officer hired in a
given city reduces the number of crimes committed in that city by 0.02, on average.
Because 0.000 < 0.01, police size does have a statistically significant effect on crime
Sample exam: How would rewrite the model if you want the slope β2 to be interpreted
as the effect of an increase in police size on the % change in crime? - Answers -
log(crime) = X1+ X2officers+u
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 - Answers -X2 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 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. - Answers -
students 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? - Answers -1. 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) - Answers -
Students 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? - Answers -If 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? - Answers
-relevance is testable, exogenity is not testable
If relevance and exogenity hold, what can we say about Z, an IV? - Answers -it is a
valid IV for X
Given the regression: callback =X0+ BlackX1 +u what is the meaning of X1 (Note X1=1)
- Answers -Black 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? - Answers -No- 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
What are the two reasons OLS might be biased? - Answers -exogeneity (omitted
variable bias) or reverse causality (the y term effects x and x effects y - in the
crimes/officers example - a city might hire more officers in response to an increase in
the number of crimes)
How do you design a random experiment? Use the crime/ officer example from practice
exam - Answers -We have a large group of participants (cities in this case) and we
randomly assign them to two groups - group will hire a large police force, and another
will hire a small police force (draw diagram that you did in class to asses knowledge)
Sample final: if you conducted a random experiment Would you get an unbiased
estimate of the effect of police size on crime from this experiment? - Answers -Yes you
would get an unbiased estimate because cov (officer,u) = 0 holds by construction (Ie
OLS is unbiased and consistent)
Sample exam: Some researchers have noticed that during a local elections year the city
governments tend to hire more police officers (and, therefore, reduce crime) in order to
increase their chances to be reelected. Suppose that you have a dummy variable for
whether there are local elections in a given year (election). Assuming that elections are
unrelated to any factors in the error term and have no direct effect on crime, how would
you use this variable in order to produce a consistent estimate of the slope on officers? -
Answers -We would use this as a IV for the following reasons: One we are told that
election has no effect on crime. Two it has the principle of relevance - cov (officers,
election)!=0. Finally we have the property of exogenity - cov (officers, u)=0
Sample exam: The IV estimation results are presented below. Interpret the IV estimate
on the slope of officers. Does police size have a statistically significant effect on crime?
(note X1 = -0.02 and p-value is 0.000) - Answers -one more police officer hired in a
given city reduces the number of crimes committed in that city by 0.02, on average.
Because 0.000 < 0.01, police size does have a statistically significant effect on crime
Sample exam: How would rewrite the model if you want the slope β2 to be interpreted
as the effect of an increase in police size on the % change in crime? - Answers -
log(crime) = X1+ X2officers+u
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 - Answers -X2 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").
