Macroeconomics 1st Edition Solutions Manual by Acemoglu
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- This chapter talks about means. The median is a closely related concept. The median is the numerical value separating the higher half of your data from the lower half. You can find the median by arranging all of the observations from lowest value to highest value and picking the middle value (assuming you have an odd number of observations). While the mean and median are closely related, the difference between the mean and the median is sometimes of interest.
- Suppose country A has five families. Their incomes are $10,000, $20,000, $30,000, $40,000, and $50,000. What is the median family income in A? What is the mean income?
- Country B also has five families. Their incomes are $10,000, $20,000, $30,000, $40,000, and $150,000. What is the median family income in B? What is the mean income?
- In which country is income inequality greater, A or B?
- Suppose you thought income inequality in the US had increased over time. Based on your answers to this question, would you expect that the ratio of the mean income in the US to the median income has risen or fallen? Explain.
- We can find the mean by summing the observations and dividing by the number of observations. So the mean income in Country A is ($10,000 + $20,000 + $30,000 + $40,000 + $50,000) / 5 = $30,000. The median income is the income of the family in the middle of the income distribution. The median income in Country A is $30,000. Two families have income below $30,000 and two have income above $30,000.
- A similar argument shows that the mean income in Country B is ($10,000 + $20,000 + $30,000 + $40,000 + $150,000) / 5 = $50,000. Median income in B is $30,000; as in Country A, two families have income below $30,000 and two have income above $30,000.
- Income inequality is higher in Country B. The highest income family in Country B earns $150,000, 60% of the total income in that country. The highest income family in A earns $50,000, just 33% of total income in A. We found that the median income in the two countries was the same but the mean income was very different. Means will be heavily influenced by extreme values such as the incomes of the very wealthy; median income is less sensitive to extremes. Economists sometimes use the ratio of the mean to median income in a country as a rough measure of income inequality; higher values of this ratio reflect greater inequality.
- You should expect to find that the ratio of the mean to median income has risen. As we argued above, the mean is more sensitive than the median to the incomes of the very wealthy.
- Consider the following situation: your math professor tells your class that the mean score on the final exam is 43. The exam was scored on a total of 100 points. Does this imply that you, too, scored poorly on the exam?
Answer: The mean is an average value of a set of observations. Although the mean score is representative of the values in the set of observations, a single value (for example, your exam score) could be very different from the mean. These ‘outliers’ could skew the mean toward being lower or higher than most of the other observations. So, it could be possible that you scored higher than, say 75, but your classmates’ lower scores pulled the value of the mean downward.
- This chapter stressed the importance of using appropriate samples for empirical studies. Consider the following two problems in that light.
- You are given a class assignment to find out if people’s political leanings affect the newspaper or magazine that they read. You survey two students taking a political science class and five people at a coffee shop. Almost all the people you have spoken to tell you that their political affiliations do not affect what they read. Based on the results of your study, you conclude that there is no relationship between political inclinations and the choice of a newspaper. Is this a valid conclusion? Why or why not?
- Your uncle tells you that the newspaper or magazine that people buy will depend on their age. He says that he believes this because, at home, his wife and his teenage kids read different papers. Do you think his conclusion is justified?
- The conclusion is not likely to be valid as the sample used in the study is too small. Convincing data analysis will depend on a much larger sample of people. The subjects of the study should also be randomly chosen to minimize the possibility of the results being biased.
- This is an example of argument by anecdote. Using a small sample of people to judge a statistical relationship is likely to lead to flawed conclusions. The fact that your uncle’s wife and kids do not base their reading on their political affiliations does not mean that others do not. In order to arrive at a conclusion, you need to survey more people and also make sure that they are chosen randomly.
- Some studies have found that people who owned guns were more likely to be killed with a gun. Do you think this study is strong evidence in favor of stricter gun control laws? Explain.
Answer: Not necessarily. It is quite possible that people who thought they were at risk (perhaps because they live in dangerous neighborhoods) were more likely to buy a gun for self-protection. This is an example of a case where correlation may not imply causation.
- As the text explains, it can sometimes be very difficult to sort out the direction of causality.
- Why might you think more police officers would lead to lower crime rates? Why might you think that higher crime rates would lead to more police officers?
- In 2012, the New England Journal of Medicine published research that showed a strong correlation between the consumption of chocolate in a country and the number of Nobel Prize winners in that country. Do you think countries that want to encourage their citizens to win Nobel Prizes should increase their consumption of chocolate?
- There is a great deal of evidence that increasing the number of police officers in a neighborhood can drive down crime. The police, for example, will deter criminals who realize the chances they will be caught have gone up and the police may be able to head off conflicts between gangs. Therefore more police could lead to less crime. Cities strategically assign more police to high crime areas (since by definition, those are the areas where crimes are more likely to occur). Therefore, more crime can lead to more police.
- Correlation does not necessarily imply causation. A strong positive correlation between chocolate consumption and Nobel Prize winners does not, by itself, suggest causation. It is possible that this is a chance correlation. It may also be the case that certain variables that could explain this relationship have been omitted from the study.
- The chapter shows that as a general rule people with more education earn higher salaries. Economists have offered two explanations of this relationship. The human capital argument says that high schools and colleges teach people valuable skills and employers are willing to pay higher salaries to attract people with those skills. The signaling argument says that college graduates earn more because a college degree is a signal to employers that a job applicant is diligent, intelligent, and persevering. How might you use data on people with two, three, and four years of college education to shed light on this controversy?
Answer: If the human capital explanation is correct, then we might expect to find that people who attend college but do not graduate earn salaries that are close to what college graduates earn. Consider the extreme case of people who drop out of college the week before graduation. It is very unlikely that they would have improved their job skills much in that last week. The human capital school of thought would suggest that they should therefore earn roughly the same salaries as college graduates. On the other hand, the signaling school of thought would argue that these people should earn significantly less than college graduates. Employers would interpret their failure to graduate as a signal they are not as diligent or persevering as people who see their college educations through to the end. There is substantial literature on what is often called the “sheepskin effect” (college diplomas used to be written on sheepskin; Notre Dame continued to use sheepskin until 2012). That literature suggests that human capital and signaling both contribute to the returns to education that we observe in the data.
- Maimonides, a twelfth century scholar, said, “Twenty-five children may be put in the charge of one teacher. If the number in the class exceeds twenty-five but is not more than forty, he should have an assistant to help with the instruction. If there are more than forty, two teachers must be appointed.” Israel follows Maimonides’s rule in determining the number of teachers for each class. How could you use Maimonides’s rule as a natural experiment to study the effect of teacher-student ratios on student achievement?
Answer: Maimonides’s rule generates a natural experiment to study of the effect of class size. Suppose School A has 40 third-graders and School B has 41. Following Maimonides’s rule, School A would have one 40-student class while School B would have one 20-student class and one 21-student class. Everything else equal, if smaller classes improve achievement then we should expect to see higher test scores in School B.
- Oregon expanded its Medicaid coverage in 2008. Roughly 90,000 people applied but the state had funds to cover only an additional 30,000 people (who were randomly chosen from the total applicant pool of 90,000). How could you use the Oregon experience to estimate the impact of increased access to health care on health outcomes?
Answer: The Oregon experience is a natural experiment. The state chose people randomly from the pool of applicants, and so on average the new Medicaid recipients were very similar to the people who applied but were turned down. By tracking the health outcomes of people in these two groups we can study the effect of better access to health care.
- A simple economic model predicts that a fall in the price of bus tickets means that more people will take the bus. However, you observe that some people still do not take the bus even after the price of a ticket fell.
- Is the model incorrect?
- How would you test this model?
- The model is not incorrect. Models are only approximations of real-life behavior. Even very good models make predictions that are often correct. So, on average, more people will take the bus. The model is also likely to have made some assumptions, such as no change in costs of other types of transport, or that people have no specific preferences and cost is the only determinant of the mode of transport used. In reality, some of these assumptions may be violated which could explain why a fall in the price of bus tickets does not induce everyone to take the bus. That does not imply that the model’s conclusion is incorrect. In situations where the assumptions it makes are satisfied, its prediction will often be correct.
- The hypothesis here states that as bus prices fall, the number of passengers who take the bus will increase. A natural experiment can be used to test this model. You can use data on price changes and changes in revenues earned from tickets to see whether the model is accurate.
- How would you represent the following graphically?
- Income inequality in the U.S. has increased over the past 10 years.
- All the workers in the manufacturing sector in a particular country fit into one (and only one) of the following three categories: 31.5 percent are high school dropouts, 63.5 percent have a high school diploma, and the rest have vocational training certificates.
- The median income of a household in Alabama was $43,464 in 2012, and the median income of a household in Connecticut was $64,247 in 2012.
- Since the graph needs to show how income inequality increases over a period of time, a time-series graph needs to be used here.
- A pie chart is a circular chart split into segments to show the percentages of parts to the whole. Since the given data is in percentages, a pie-chart can be used to represent each category of workers.
- A bar chart would be a good way to compare income in Alabama and Connecticut. The height of each bar would represent the income in each one of the states.
- Consider the following data that shows the quantity of coffee produced in Brazil from 2004-2012.
|Year||Production (in tons)|
- Plot the data in a time series graph.
- What is the mean quantity of coffee that Brazil produced from 2009 to 2011?
- In percentage terms, how much has the 2012 crop increased over the 2009-2011 mean?
- A time-series graph can be used to represent the quantity of coffee produced from 2004 to 2012.
- The average quantity of coffee that Brazil produced during the 2009-11 period is 2,682,587 This is the sum of the total quantity produced divided by the number of years.
- The coffee crop in 2012 is 14.6% larger than the average coffee crop in 2009-2011. The increase in production is 3,037,534 – 2,682,587 = 354,947. In percentage terms, the change is 354,947/ 2,682,587 = 13.2%.