Question

a) You collect data on a random sample of individuals’ years of schooling and health. You regress health on schooling
and find a positive coefficient. Can you conclude from this estimate that getting more education causes an increase
in health (Yes or no)? Justify your answer.
b) You have a cross-sectional dataset that includes individuals’ education and wages. Explain what it means to have a
“ceteris paribus” estimate of the effect of education on wages.
c) You are interested in predicting the outcome of an election (share of votes for Democrats). You send out a poll to a
random sample of individuals subscribed to “The Economist” asking who they will vote for in the upcoming
election.
i. Is this sample affected by selection bias? Yes or no. If yes, in which direction is this likely to bias your
estimates? Justify your answer.
ii. Is this sample affected by response bias? Yes or no. If yes, in which direction is this likely to bias your
estimates? Justify your answer.
d) You have a random sample of 10,000 households’ net worth (i.e. value of assets owned by household members
minus the liabilities (debts) they owe) in the US. You find that mean net worth is 5 times higher than median net
worth. What does this tell you about the shape of the wealth distribution in the US? Are there more observations to
the left or to the right of the mean? Do you think the left or the right tail is longer?
e) Using the random sample of question 1d. above, you calculate a sample mean net worth of $600,000. What does the
Central Limit Theorem tell us about this value relative to the true mean net worth in the US population?

Answer 1

a. Yes. It can be stated that the positive association between education and health states that getting more education leads to better health outcomes in the society. Thus, as the level of education increases, health outcome in the society also improves.

b.The “ceteris paribus” estimate of the effect of education on wages states that keeping all the other variables constant, the impact of education on wage rate of people has been computed.

c. 1. Yes, this sample is impacted by selection bias as it considers only the sample of people who read Economist.It might lead to negative bias as it includes only the readers of Economist.

ii. Yes, the study might be impacted by the response bias which will be in the positive direction.

d. Since the mean wealth is 5 times higher than the median wealth, thus, the distribution is positively skewed, and there are more observations to the right of the mean. In case of a positively skewed distribution, the right tail is longer.