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Solutions and Activities
for
CHAPTER 1
WHY STUDY PUBLIC FINANCE?
Questions and Problems
Many states have language in their constitutions that requires the state to provide for an “adequate” level of education spending. What is the economic rationale for such a requirement? There are two economic rationales for government provision of a good or service: mar- ket failure and redistribution. A market failure argument for state provision of education would be that an educated population benefits society generally because, for example, well- educated individuals have better job prospects and are therefore less likely to commit crimes. Each person who receives an education receives a private benefit (e., higher wage rate) and also confers a positive externality on the community (e., lower crime rate). In the absence of public provision of education, self-interested people would acquire less-than-optimal lev- els of education because they would not take into account its external benefit. Public educa- tion can correct this market failure. An argument can also be made that public education is redistributive because it increases the human capital of all students regardless of their indi- vidual economic status.
How has the composition of federal and state and local government spending changed over the past 40 years? What social and economic factors might have con- tributed to this change in how governments spend their funds? Since 1960, there has been a marked shift of federal spending away from defense spend- ing and toward spending on Social Security and health care. In 1960, defense spending ac- counted for approximately half of the federal budget, while Social Security and health care combined accounted for about 15% of the budget. In 2001, Social Security and health care spending each exceeded defense spending, which accounted for less than 20% of total fed- eral spending. Health spending has also increased as a fraction of state and local spending, more than doubling over the last 40 years. Otherwise, the composition of the state and local spending has been relatively stable over that time. The increases in expenditures on Social Security and health care reflect the aging of the population. As the baby boom generation has aged, it has had a greater need for these kinds of spending. Furthermore, this generation has played an increasingly important role in the political process, which has allowed them to win increases in spending directed toward their interests. The relative decrease in defense spending may have been influenced by the collapse of the Soviet Union and the end of the cold war.
1
Some goods and services are provided directly by the government, while others are funded publicly but provided privately. What is the difference between these two mechanisms of public financing? Why do you think the same government would use one approach sometimes and the other approach at other times? Direct public provision of a good or service occurs when the government itself produces the good or service. Police forces and military are examples of direct provision. Public fi- nancing of private provision of goods and services occurs when the government wishes to increase the provision of a good or service, but it does not want to directly involve itself in its provision. An example is when the government hires private companies to build or repair roads, or when the government purchases military aircraft from private companies instead of building them itself. Public funding for private provision is appealing relative to direct public provision whenever the private market can produce the goods or services more efficiently than the government. This is likely to be the case where there is an existing market or industry for the good or service, especially when that market is competitive. When there is no existing mar- ket for a good or service provided by the government, or when that market is characterized by an imperfectly competitive industry, there may be a stronger case for direct provision (although it is important to recognize that direct provision can also suffer from efficiency failures). There may be national security concerns related to private provision of certain goods and services, especially those performed by the military and police forces. The gov- ernment is more likely to provide these goods and services directly.
Why does redistribution cause efficiency losses? Why might society choose to redis- tribute resources from one group to another when doing so reduces the overall size of the economic pie? Redistribution can cause efficiency losses if there are behavioral responses to the redistribution system. The government might raise money to fund redistribution by im- posing a tax on labor income, and this might cause a reduction in the labor supply. Similarly, generous unemployment benefits might induce some who are out of work to remain unemployed. Despite these possible efficiency losses, we (collectively) choose to redistribute wealth. Some reasons for redistribution are that people have a taste or pref- erence for a certain degree of economic equity; that the existence of a large or visible underclass is somewhat discomforting or threatening; that people are risk averse and so are willing to pay for a “safety net” in case they or their families ever need assistance; and that humans are naturally empathetic. In a country with many very poor people, redistribution from the few rich to the many poor may make the majority of people better off, even if it reduces the overall size of the pie. A democratic process may therefore lead to the occurrence of this sort of redistribution.
Consider the four basic questions of public finance listed in the chapter. Which of these questions are positive—questions that can be proved or disproved—and which are normative—questions of opinion? Explain your answer. The four basic questions of public finance: 1. When should the government intervene in the economy? The word “should” suggests that this is a question about which opinion will vary, so it is normative. 2. How might the government intervene? This question is positive. It asks: How does the government actually intervene now, and how might it intervene in the future? One can check whether a government might intervene in a particular way directly by ex- amining the behavior of existing and future governments. 3. What is the effect of those interventions on economic outcomes? Economic effects can be measured and thus are not a matter of opinion, so this question is positive.
CHAPTER 1 / Why Study Public Finance? - 2 -
Whether or not the policies raise social welfare depends on the society’s taste for redis- tribution. Indeed, either of the policies makes Ted better off and makes Bill worse off than the status quo of no taxes, so if society deems it sufficiently important to redistribute to Ted, then either policy would raise social welfare. If society cares about only the “size of the pie,” however, then both policies would lower social welfare. Whenever society deems that im- proving Ted’s income by $200 improves social welfare more than reducing Bill’s income by $400 harms social welfare, the 25% tax policy raises social welfare and is the optimal policy. The 40% tax policy can never be optimal, since the 25% tax policy makes both Bill and Ted better off than the 40% tax policy.
Advanced Questions
In the United States, the federal government pays for a considerably larger share of social welfare spending (that is, spending on social insurance programs to help low- income, disabled, or elderly people) than it does for K–12 education spending. Simi- larly, state and local governments provide a larger share of education spending and a smaller share of welfare spending. Is this a coincidence, or can you think of a reason for why this might be so? Local control is often considered more important for education than for other services because there may be regional variations in curriculum preferences—whether to teach the theory of evolution, for example. There may be fewer regional variations in preferences re- lated to social programs, however, so people may be more willing to give up local control over these programs. Another possible explanation for federal control of social welfare pro- grams is jurisdiction “shopping.” If social insurance benefits varied substantially among states, people might move from one to another to avail themselves of more generous benefits.
The urban African-American community is decidedly split on the subject of school vouchers, with their leaders comprising some of the most vocal proponents and op- ponents of increased school competition. Why do you think this split exists? This community contains a disproportionate number of poor families, with many stu- dents attending substandard schools. Proponents of the voucher system may believe that it will allow them to send their children to better schools or that competition will encourage their local schools to improve in order to retain students who would have a choice of schools under the voucher system. Opponents may view it as a threat to neighborhood schools, fear- ing that if students take their vouchers and leave, inner-city schools may become even more impoverished. Philosophically, some proponents believe that market competition can solve a wide variety of problems, while some opponents are suspicious of the market system—at least as applied in the context of education—possibly viewing it as an institution that favors those with more money to spend in the marketplace.
Many states have constitutional requirements that their budgets be in balance (or in surplus) in any given year, but this is not true for the U. federal government. Why might it make sense to allow for deficits in some years and surpluses in others? Time-series graphs illustrate one striking reason to allow for deficits: during World War II the federal government spent far more than it took in. Like a family, a government some- times faces unforeseen emergencies that require it to borrow. Had the United States been constrained by a balanced budget requirement at the time of World War II, the outcome of the war might have been very different. The family metaphor is relevant for a second reason:
CHAPTER 1 / Why Study Public Finance - 4 -
borrowing allows an entity to pay over time for a durable good that is being consumed over time. It makes sense for most families to take out a mortgage to purchase a home, because that purchase delivers benefits over many years. Similarly, many government investments yield long-term benefits. Surpluses and deficits may also have beneficial macroeconomic ef- fects, such as helping to stabilize a volatile economy.
- Proper hygiene, such as regular hand-washing, can greatly limit the spread of many diseases. How might this suggest a role for public interventions? What kinds of pub- lic interventions might be possible? Suggest three distinct types of possible interven- tions. Individuals tend to ignore the external costs they impose on others by failing to wash their hands frequently enough (or by failing to employ other sorts of hygienic practices). This suggests that they tend to wash their hands less than optimally and that there may there- fore be a role for public interventions. One possible intervention would be a requirement that individuals wash their hands after using restrooms. (Such regulations are imposed for em- ployees at businesses, for example.) A second possible intervention is public provision of hand-washing facilities. This would reduce the cost of hand-washing, thereby encouraging individuals to engage in that activity more frequently. A third possibility would be an adver- tising campaign to encourage hand-washing.
In-class Projects or Demonstrations
Federal Budget Shares and Positive vs. Normative Questions
How does the federal government allocate its budget? On the first day of class (before most students have read the text), ask students individu- ally or in small teams to allocate 100 “points” among the federal budget categories, showing the proportion of the budget they think is actually spent on each category. This is a positive question; initial guesses can be verified against the data in the text.
How “should” federal government dollars be spent? After the first exercise, ask small groups of students to set an “ideal” budget (again based on 100 points so that their allocations can be easily translated into percentages), then require each team to justify its allocations. Part of this exercise forces students with differing priorities to negotiate over the 100 points. The exercise also encourages them to use eco- nomic theory to justify their allocations. Students can investigate the effects of these decisions at budgetsim/nbs/ shortbudget06.
CHAPTER 1 / Why Study Public Finance - 5 -
As Pincreases from $15 to $20, Q falls from 50 to 0. Pincreases by 33% (5/15) and Q increases by 100% (50/50). Elasticity is –1.0/0 = –3. Even though the magnitude of the change remains the same (for every $5 increase in price, the quantity purchased falls by 50), in terms of percentage change elasticity of demand increases in magnitude as price increases.
- You have $100 to spend on food and clothing. The price of food is $5 and the price of clothing is $10.
a. Graph your budget constraint. The food intercept (y in the accompanying figure) is 20 units. If you spend the entire $100 on food, at $5 per unit you can afford to purchase 100/5 = 20 units. Similarly, the clothing intercept (x) is 100/10 = 10. The slope, when food is graphed on the vertical axis, will be –2.
b. Suppose that the government subsidizes clothing such that each unit of clothing is half-price, up to the first 5 units of clothing. Graph your budget constraint in this circumstance. This budget constraint will have two different slopes. At quantities of clothing less than or equal to 5, the slope will be –1 because 1 unit of food costs the same as 1 unit of clothing ($5). At quantities of clothing greater than 5, the slope will be –2 (if graphed with food on the y-axis), parallel to the budget constraint in a. The point where the line kinks, (5,15), is now feasible. The new x-intercept (clothing intercept) is 12: if you purchase 5 units at $5 per unit, you are left with $75 to spend. If you spend it all on clothing at $10 per unit, you can purchase 7 units, for a total of 12 units. New budget constraint (bold) and original (dashed):
CHAPTER 2 / Theoretical Tools of Public Finance - 2 -
0
Food (units)
2 46810
20
15
10
5
Clothing (units)
0
Food (units)
5 10 12.
20
15
10
5
Clothing (units)
Use utility theory to explain why people ever leave all-you-can-eat buffets. The theory of diminishing marginal utility predicts that the more people eat the less util- ity they gain from each additional unit consumed. The marginal price of an additional unit of food at an all-you-can-eat buffet is zero; rational consumers will eat only until their marginal utility gain from an additional bite is exactly zero. The marginal cost of remaining at the buf- fet is the value of the time spent on the best alternative activity. When the marginal benefit of that activity is greater than the marginal benefit of remaining at the buffet, diners will leave.
Explain why a consumer’s optimal choice is the point at which her budget constraint is tangent to an indifference curve. Consumers optimize their choice when they are on the highest possible indifference curve given their budget constraint. Suppose a consumer’s choice is feasible (on the budget constraint) but not at a tangency, as at point Ain the accompanying figure. Under these cir- cumstances, the budget constraint must pass through the indifference curve where it inter- sects the chosen point. There must then be at least a segment of the budget constraint that lies above (up and to the right of) the indifference curve associated with that choice. Any choice on that segment would yield higher utility. Only when no part of the budget constraint lies above the indifference curve associated with a consumer’s choice are no feasible im- provements in utility possible. The single tangency point (C in the figure) is the only point at which this occurs.
Consider the utilitarian social welfare function and the Rawlsian social welfare func- tion, the two social welfare functions described in Chapter 2.
a. Which one is more consistent with a government that redistributes from rich to poor? Which is more consistent with a government that does not do any redistribu- tion from rich to poor? The Rawlsian social welfare function is consistent with redistribution from the rich to the poor whenever utility is increasing in wealth (or income). The utilitarian social wel- fare function can also be consistent with a government that redistributes from the rich to the poor, for example, if utility depends only on wealth and exhibits diminishing marginal utility. However, the Rawlsian social welfare function weights the least-well-off more heavily, so it will generally prescribe more redistribution than the utilitarian social welfare function.
b. Think about your answer to a. Show that government redistribution from rich to poor can still be consistent with either of the two social welfare functions. If utility depends only on wealth and exhibits diminishing marginal utility, and if effi- ciency losses from redistribution are small, then both the utilitarian and Rawlsian social welfare functions can be consistent with government redistribution. A simple example can
CHAPTER 2 / Theoretical Tools of Public Finance - 3 -
Good y
Good x
A
C
c. Which of these two income guarantee programs is more likely to discourage work? Explain. A higher income guarantee with a higher reduction rate is more likely to discourage work for two reasons. First, not working at all yields a higher income. Second, a person who works less than 1,500 hours will be allowed to keep much less of his or her earned income when the effective tax rate is 75%. With a 75% benefit reduction rate, the effec- tive hourly wage is only $2 per hour (25% of $8).
- A good is called normalif a person consumes more of it when her income rises (for example, she might see movies in theaters more often as her income rises). It is called inferiorif a person consumes less of it when her income rises (for example, she might be less inclined to buy a used car as her income rises). Sally eats out at the local burger joint quite frequently. The burger joint suddenly lowers its prices.
a. Suppose that, in response to the lower burger prices, Sally goes to the local pizza restaurant less often. Can you tell from this whether or not pizza is an inferior good for Sally? You cannot. Since Sally eats at the burger joint quite a bit, falling burger prices imply that she is richer. If this was the only effect, you could indeed conclude that pizza is an in- ferior good—Sally gets richer and buys less pizza. But there is also a substitution effect here: the relative price of pizza has gone up. This leads her to substitute away from pizza. If the substitution effect is bigger than the income effect for Sally, then she could respond in this way, even if pizza is a normal good.
b. Suppose insteadthat, in response to the lower burger prices, Sally goes to the burger joint less often. Explain how this could happen in terms of the income and substitution effects by using the concepts of normal and/or inferior goods. The substitution effect says that when the relative price of burgers falls, Sally should consume more of them. Since she actually consumes less of them, the income effect must be working in the opposite direction, leading her to consume fewer burgers (and it must be stronger than the substitution effect). Since the fall of burger prices made Sally richer, burgers must be an inferior good for Sally. (Note: A good for which falling prices leads to reduced consumption is known as a Giffen good.)
Advanced Questions
- Consider an income guarantee program with an income guarantee of $3,000 and a benefit reduction rate of 50%. A person can work up to 2,000 hours per year at $6 per hour. Alice, Bob, Calvin, and Deborah work for 100, 333¹/ 3 , 400, and 600 hours, respec- tively, under this program. The government is considering altering the program to improve work incentives. Its proposal has two pieces. First, it will lower the guarantee to $2,000. Second, it will not reduce benefits for the first $3,000 earned by the workers. After this, it will reduce benefits at a reduction rate of 50%.
a. Draw the budget constraint facing any worker under the original program. The budget constraint for the original program is depicted in the graph that follows. With zero hours worked (2,000 hours leisure), a worker gets to consume $3,000—the guaranteed income level. After 1,000 hours of work, the benefits have been reduced to zero (50% of $6,000 in income).
CHAPTER 2 / Theoretical Tools of Public Finance - 5 -
b. Draw the budget constraint facing any worker under the proposed new program. The budget constraint for the proposed program is depicted in the following graph. At zero hours of work (2,000 hours of leisure), the worker now only gets to consume the lower $2,000 guarantee. She can work for up to 500 hours without any benefit reductions, so if she works for 500 hours, she gets to consume $5,000 (= $2,000 + $6/hr ×500 hrs) and has 1,500 hours of leisure. After working an additional 2,000/3 ≈666 hours, for a total of about 1,133 hours of work or 833 hours of leisure, she will be receiving no benefits. (Her benefits have been reduced by 50% ×$6/hr ×2,000/3 hrs = 50% ×$4, = $2,000.) The dashed line also depicts the original budget constraint.
c. Which of the four workers do you expect to work more under the new program? Who do you expect work less? Are there any workers for whom you cannot tell if they will work more or less? Workers working fewer than 500 hours see their hourly wage effectively doubled under the plan. The substitution effect therefore tends to make Alice, Bob, and Calvin all work more. One can calculate that the two budget constraints cross at 333¹/ 3 hours of
CHAPTER 2 / Theoretical Tools of Public Finance - 6 -
0
$3,
$6,
$12,
1,000 2,000 Leisure (hours)
Consumption (dollars)
0
$2,
$7,
$12,
833 1,500 2,000 Leisure (hours)
Consumption (dollars)
$5,
1,666.
b. Now the government imposes a $10 per unit subsidy on the production of the good. What is the consumer surplus now? The producer surplus? Why is there a deadweight loss associated with the subsidy, and what is the size of this loss?
A subsidy in effect lowers the cost of producing a good, yielding the bold supply line. The new supply function is Q = 20(P+ 10) because the producer receives the price plus $ when it produces. Solving for a new equilibrium,
20 P+ 200 = 1,200 – 10P. 30P = 1,000. P= $100/3 ≈$33; Q = 20 (100/3 + 10) = 2,600/3 ≈866. Consumer surplus = ½ (2600/3)(120-100/3) ≈37,555. Producer surplus = ½ (100/3 + 10)(2,600/3) ≈18,777. Cost of subsidy = 10(2600/3) ≈8,666. Total surplus = consumer surplus + producer surplus – cost of subsidy ≈47,666, less than the original 48,000.
There is efficiency loss because trades are induced for which the actual resource cost (without the subsidy) is greater than consumer willingness to pay. The deadweight loss is the area of the triangle that encompasses these new trades (the shaded area in the graph, pointing to the original equilibrium): ½ (2,600/3 – 800)(10) ≈333.
- Governments offer both cash assistance and in-kind benefits, such as payments that must be spent on food or housing. Will recipients be indifferent between receiving cash versus in-kind benefits with the same monetary values? Use indifference curve analysis to show the circumstances in which individuals would be indifferent and sit- uations in which the form of the benefits would make a difference to them. Generally recipients can attain a higher level of utility (they can choose a consumption bundle on a higher indifference curve) when they are given cash rather than a specific good. People who would purchase the same amount of food or housing as the in-kind grant pro- vides would be indifferent between in-kind and cash benefits because they would use the cash to purchase the same items. However, people whose preferences would lead them to purchase less food or housing than the in-kind grant provides would prefer to receive cash. That way they could spend some of the cash on food or housing and the rest on the other goods they prefer. Suppose the government provides the first ten units of food at no cost. The person represented in panel (a) of the following graph would prefer cash. The indiffer- ence curve tangent to the extension of the new budget constraint identifies a consumption bundle that includes less than ten units of food. The person represented in panel (b) would choose the same point given cash or food. The optimal consumption bundle includes more than ten units of food.
CHAPTER 2 / Theoretical Tools of Public Finance - 8 -
0
Price
800 867
$120.
$40.
$43.
$33.
Supply
Demand
- Consider Bill and Ted, the two citizens in the country of Adventureland described in Problem 9 from Chapter 1. Suppose that Bill and Ted have the same utility function U(Y) = Y1/2,where Yis consumption (which is equal to net income).
a. Rank the three tax policies discussed in Problem 9 from Chapter 1 for a utilitarian social welfare function. Rank the three for a Rawlsian social welfare function. The utility function is increasing in income. Rawlsian social welfare is therefore equal to the utility of the individual with lower income. For 0% and 25% tax rates, Ted has the lower incomes ($120 and $320, respectively). For a 40% tax rate, Bill has the lower in- come ($240). Since $320 > $240 > $120, Rawlsian social welfare is highest under the 25% tax rate and lowest under the 40% tax rate. To compute utilitarian social welfare, we compare: Utilitarian social welfare with a 0% tax = 1,0001/2 + 1201/2≈42. Utilitarian social welfare with a 25% tax = 6001/2 + 3201/2 ≈42. Utilitarian social welfare with a 40% tax = 2401/2 + 2801/2≈32. We see that the 0% tax rate is best.
b. How would your answer change if the utility function was instead U(Y) = Y1/5? This change does not affect the order of tax rates according to the Rawlsian social welfare function. To compute social welfare for the utilitarian social welfare function we compare: utilitarian social welfare with 0% tax = (1000)1/5 + 1201/5≈6. utilitarian social welfare with 25% tax = 6001/5 + 3201/5 ≈6. utilitarian social welfare with 40% tax = 2401/5 + 2801/5≈6. We see that the 25% tax rate is best and the 40% tax rate is the worst.
c. Suppose that Bill and Ted instead have different utility functions: Bill’s utility is given by UB(Y) = ¼Y1/2, and Ted’s is given by UT(Y) = Y1/2. (This might happen, for example, because Bill has significant disabilities and therefore needs more income to get the same level of utility.) How would a Rawlsian rank the three tax policies now? Since the two have different utility functions, it is no longer easy to see who is better off under each situation. Under the 0% tax policy, we see that Ted has utility 1201/2≈ 10 and Bill has utility ¼ 1,0001/2≈7. We see that Bill is worse off under this policy.
CHAPTER 2 / Theoretical Tools of Public Finance - 9 -
Other goods
10 Food
Other goods
10 Food
(a) (b)
(150 – 2) = 5T, or T= 150/7 = 20. Plugging back into the budget constraint gives:
M= 150 – 2(20) = 100. You now take 20 trips and go on 100 movie-and-a-pizza outings.
CHAPTER 2 / Theoretical Tools of Public Finance - 11 -
1
Solutions and Activities
for
CHAPTER 3
EMPIRICAL TOOLS OF PUBLIC FINANCE
Questions and Problems
Suppose you are running a randomized experiment and you randomly assign study participants into control and treatment groups. After making the assignments, you study the characteristics of the two groups and find that the treatment group has a lower average age than the control group. How could this arise? Random draws do not guarantee that the average of all demographic and other variables will be exactly the same for groups, although if the size of the groups is large, they should converge to the same value. One reason the average ages might differ in this experiment is that the samples are too small. Imagine tossing a coin 10 times. You would expect to get ap- proximately 5 heads and 5 tails, but you would not assume that your coin was biased if you instead got 6 or 7 heads. However, if you tossed the coin a very large number of times and got heads in 60% or 70% of the tosses, you would tend to conclude that the coin was biased. The law of large numbers says that the more times a fair coin is tossed, the closer the per- centage of heads will tend to be toward 50%. Similarly with the groups from the randomized experiment: it is possible for the average age of the treatment and control groups to be quite different if the sample size is small, but as the sample size gets larger, these differences should disappear.
Why is a randomized trial the “gold standard” for solving the identification problem? If participant assignment to the treatment group and the control group is truly random and the groups are large enough, it is statistically unlikely that membership in one group or the other will be biased in a way that is related to the question being studied. On average, the two groups will have the same characteristics. This would not be true if subjects were al- lowed to choose their own groups, because people with certain traits in common may be more or less likely to select a given group.
What do we mean when we say that correlation does not imply causality? What are some of the ways in which an empirical analyst attempts to disentangle the two? Correlation merely means that two events tend to occur together; causality means that one event causes the other. Correlation can occur when a third event causes both of the other events. For example, ice cream consumption and air-conditioning use tend to happen to- gether. They are correlated, but their relationship is not causal. A third event, hot weather, causes the other two events. The point of much empirical work is to control for possible variables that might cause other events (that are not causally related) to occur together. Ran- domized trials, regression analysis of data that include control variables, and quasi-ex-peri- ments are all ways to investigate causal relationships by controlling for other possible mechanisms that might influence the variables of interest.
members of the affected group averaged $18,200 in earnings while members of the unaffected group averaged $17,700 in earnings.
a. How can you estimate the impact of the policy change? What is the name for this type of estimation? The question here is one of differences in changes: both groups experienced a change in earnings, but it is not immediately obvious whether either group experienced a bigger change. The appropriate approach to estimate the impact on each group is called a differ- ence-in-differences approach. Treatment group difference: $18,200 – $17,000 = $1, Control group difference: $17,700 – $16,400 = $1, Thus, we estimate that the impact of the policy change was to lower earnings by $100.
b. What are the assumptions you have to make for this to be a valid estimate of the impact of the policy change? The essential assumption you have to make is that trends in earnings would have been the same for the two groups had there been no policy change. If, for some reason, one group would have experienced larger income growth than the other in the absence of the policy change, then the difference in difference estimate will be biased.
Consider the example presented in the appendix to this chapter. Which coefficient es- timates would be considered “statistically significant” or distinct from zero? There are two ways to determine at a glance whether a coefficient is statistically distinct from zero. The first way is to consider whether zero falls in the range bounded by two standard errors less than the estimate and two standard errors greater than the estimate. The second way is to divide the coefficient estimate by the standard error. If the quotient is approximately two or greater, the estimate can be considered statistically significant. By these standards, the estimated coefficient for the indicator, or dummy, variable “Black” is not distinct from zero; neither are the estimated coefficients for living in a central city, another urban area, or a rural area. All of the other variables pass this test of statistical significance: White, High School Dropout, High School Graduate, Some College, Age, TANF, and the constant term.
A researcher wants to investigate the effects of education spending on housing prices, but she only has cross-sectional data. When she performs her regression analysis, she controls for average January and July temperatures. Why is she doing this? What other variables would you control for, and why? This researcher has access to very limited data and would like to control for the charac- teristics of the location of the housing stock. Housing prices reflect, among other things, the desirability of house location, and the researcher thinks that climate must affect desirability. She is unable to use historical prices to look at changes in price for a single location over time because she has only cross-sectional data, so she must use the data she has to control for systematic differences. Examples of other variables she could include are: local unem- ployment rates, average population age, number of school-age children, etc.
It is commonly taught in introductory microeconomics courses that minimum wages cause unemployment. The federally mandated minimum wage is $5, but approxi- mately 1/3 of states have higher state-mandated minimum wages. Why can’t you test the “minimum wages cause unemployment” theory by simply comparing unemploy- ment rates across states with different minimum wages? Can you think of a better way to test it? The problem with this test is that all states are not the same. Different states have popu- lations with different characteristics and different preferences. Some of these characteristics
CHAPTER 3 / Empirical Tools of Public Finance - 3 -
may be related to both the choice of the state-level minimum wage and the unemployment level. For example, consider states with a large number of people who have taken an eco- nomics course. People in these states may be inclined to favor low minimum wages (based on what they were taught in their introductory micro class) and also may find it very easy to get a job (they have studied economics, after all!). This would lead us to observe a relation- ship between unemployment rates and minimum wages across states even without any of the direct causation suggested by economic theory. A better way to test this would be to look at how unemployment rates changedafter a new minimum wage law was passed in one state compared with the change in unemploy- ment rates in a nearby state that did not change its law. This is the approach taken, for exam- ple, in Card and Krueger (1994).
Advanced Questions
Suppose that your friend Oscar has collected data and determined that towns with newly constructed high schools tend to have higher SAT scores than other towns. He tells you that he has proved that new high schools cause higher SAT scores. When you object that “correlation does not imply causation,” he is ready with more data. He shows you convincing evidence that SAT scores tend to increase shortly after towns build new high schools, but that there is no tendency for new high schools to be built in towns that have recently seen large increases in SAT scores. Is this enough evi- dence to prove that new high schools cause higher SAT scores, or can you think of an alternative explanation for Oscar’s data? The timing evidence is certainly more convincing than simple correlations—and it strongly suggests that SAT scores do not cause new schools to be built. However, there are alternative explanations to the conclusion that new schools cause higher SAT scores. For ex- ample, consider a town that has recently experienced a wave of “yuppification”—a number of young, well-educated couples have recently moved to what was traditionally a more blue- collar town. As these new couples have children who begin to approach high school age, they may vote to raise taxes to build a new school for their children. Their children—the children of well educated parents—are likely to do well on their SATs. This story would thus lead to the pattern Oscar found in these towns: a new high school gets built shortly before the children of better-educated parents begin to take their SATs. But in this story, the new school does notcause better SAT scores.
Researchers often use panel data (multiple observations over time of the same peo- ple) to conduct regression analysis. With these data, researchers are able to compare the same person over time in order to assess the impacts of policies on individual be- havior. How could this provide an improvement over cross-sectional regression analysis of the type described in the text? Panel data sets allow researchers to control for attributes of a person that do not change over time. For example, it is particularly hard to obtain data about attitudes, preferences for leisure, familial or cultural values, and the like, but these traits are likely to be fairly stable in adults. Therefore a researcher can control for these unobservable, or unmeasurable, influ- ences on behavior by using panel data. In effect, the researcher can hold the person’s under- lying preferences and attitudes constant while observing their responses to policy over time.
Suppose that your state announced that it would provide free tuition to high- achieving students graduating from high school starting in 2007. You decide to see whether this new program induces families with high-achieving children graduating in 2007 or later to purchase new cars. To test your findings, you use a “falsification
CHAPTER 3 / Empirical Tools of Public Finance - 4 -
Solution for Jonathan Gruber text book
コース: Economic of public sector (EPS2200)
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