Solution Manual For Modern Labor Economics: Theory and Public Policy, 13th Edition

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Answers to Chapter 1•Review Questions1.Answer d.In product markets, firms sell and individuals buy. Also, human beings are not asintimately involved in the transactions, so nonpecuniary factors are less important.2.Answer d.If people strive to make themselves as happy as they can (i.e., maximize their utility),and a human being is “attached” when labor market transactions take place, it seemslikely that feelings, emotions, personalities, and working conditions will play a role indetermining the nature of these transactions. All these factors seem to play an importantrole in determining a human being’s happiness.3.Answer b.This is the only statement that refers to “what is” true about the labor market. All theothers, either explicitly or implicitly, make reference to “what should be” true aboutlabor market outcomes.4.Answer a.This statement makes reference to “what should be,” while all the others refer to howlabor market variables are actually linked.5.Answer a.A model is useful precisely because it is abstract. If it accurately captured all of thecomplexity of the real world or people’s actual thought processes, it would be so intricatethat no patterns or principles could be discerned. Models can be used not only to predictbehavior but also to illustrate the kind of behavior that should take place to reach certaingoals.6.Answer d.Individuals or households are assumed to maximize utility, while firms are assumed tomaximize profits.7.Answer d.The two most fundamental assumptions of positive economics are scarcity (peoplecannot get everything they want) and rationality (people consistently weigh costs andbenefits).8.Answer c.Utility maximization means people strive to be as happy as possible, and that happinessmay depend in part on how other people are doing, not solely on an individual’s owncircumstances. The concept of mutually beneficial transactions is a normative one,unrelated to what actually happens in some instances. Positive models refer to actuallinks between economic variables, and these links can only be exposed by holding otherfactors constant.9.Answer b.The test of a positive economic model is how well it predicts average tendencies. It doesnot have to capture everyone’s idiosyncrasies all the time. Normative models, on theother hand, relate to standards that someone feels should be attained.

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236Ehrenberg/Smith•ModernLabor Economics:TheoryandPublic Policy,ThirteenthEdition10.Answer b.Normative statements are frequently connected to mandated transactions, not justvoluntary transactions. These mandates can be driven by the quest for mutuallybeneficial gain, but they need not be. Other ethical principles or goals like fairness maybe the driving force behind normative statements.11.Answer d.If one person gains and no one else loses, that is a transaction that seemingly could besupported by unanimous consent. Therefore, if such a transaction can still be made, aPareto efficient outcome has not been achieved.12.Answer b.In most situations there are many different Pareto efficient outcomes, but many of theseoutcomes would probably be considered unfair. The outcome that is finally achievedmay be arrived at voluntarily or by government mandate.13.Answer d.Moving from one Pareto efficient outcome, even if it is to another Pareto efficientoutcome, will make one person worse off at the same time it makes someone else betteroff. Deciding among Pareto efficient outcomes, therefore, involves some assessment ofthe fairness or equity of the outcomes. These judgments have traditionally been made inthe political arena and are often influenced by each party’s initial income or wealthposition. Most political systems have been willing to support at least some redistributionof wealth from the rich to the poor.14.Answer d.Other reasons include price distortions caused by government taxes or the lack of amarket where the transaction can be worked out.15.Answer d.Also, in some instances, government action is the impediment to the Pareto efficientoutcome. In these instances the government must get out of the way before thetransaction can be completed.16.Answer c.Least squares regression makes no assumptions with respect to the relationship betweenindependent variables (those on the right side of the equation) or the size of thecoefficients attached to these variables. For the estimated parameters to be unbiasedestimates of the true values, however, the error term must be random.17.Answer b.One can reject the hypothesis that the true value of a particular coefficient is zero only ifthe estimated parameter is more than twice the size of its standard error (thet-statisticwill then be greater than 2). A small standard error is no guarantee of a non-zeroparameter if the estimated parameter is also very small. A random error term helps toensure that the estimates are as precise as possible, but the existence of a random errorterm does not have any bearing on the existence of a relationship between theindependent and dependent variables.18.Answer b.A coefficient in a multiple regression indicates the effect on the dependent variable, onaverage, of a one-unit change in the independent variable, assuming the other variablesare held constant. A non-zero estimate for the coefficient does not ensure that the truevalue of the parameter is different from zero. In this case, however, a parameter estimatefour times as large as its standard error allows us to reject the hypothesis of a “true”value of zero.

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AnswerstoChapter123719.Answer d.The relatively small value of the standard error means the coefficient on theWvariablehas been measured with a relatively small margin of error. Also, since the coefficient is2.5 times its standard error, the hypothesis that the true value of the coefficient is zerocan be rejected. However, a relationship that is significant in a statistical sense is notnecessarily significant in an economic sense. Holding all else constant, in this equation,every $1 increase in the wage is accompanied by just a one-half hour reduction in totalannual hours, a very insignificant amount.20.Answer a.SinceWandVare positively correlated, the coefficient onWwould pick up some of thenegative effectVexerts onH, making the coefficient onWsmaller.•Problems21a.The drawing is a model because it is a deliberate abstraction designed to illustrate certain keycharacteristics of human beings.21b.The model highlights that human beings walk upright on two legs. It also highlights the relativesize of the head and limbs. It pushes all the details of our appearance, particularly things like theshape of our hands and feet, into the background. It also says nothing about the mental capacitiesthat distinguish us from other animals. There are, of course, other characteristics that it doesn’tcapture either.21c.A simple drawing was easy to make. Anything more involved would require some artistic skill.Also, such a simple drawing highlights the idea that models are abstract. A more realistic drawingwould not have gotten across the idea that “humans walk upright on two legs” any better than thissimple drawing. In fact, a more realistic drawing might have obscured this point by focusingattention on other features.21d.This is a positive model since it attempts to show “what is” true about human beings. It does notattempt to assess our bodily design or illustrate “what should be.”22a.The person is being inconsistent. If it is worth taking 30 minutes to save $5 in the first situation, itshould also be worth it in the second situation. However, he may be acting like this because thepercentage savings is much smaller in the second case. Studies of perception have revealed thatthe larger or more intense the stimulus (in this case the original expenditure on insurance), thelarger any change (in this case the cost savings) has to be before it will be recognized.22b.No, a model with poor predictive power may still be useful in a normative sense, in this case as aguide to more rational decision making. In this example, if confronted with his inconsistency, theworker may realize that his choice in the second instance was obscured by the large dollaramounts. As a result he may be able to avoid similar mistakes in the future.23a.The outcome is Pareto efficient because there is no way any of the remaining firms or workers canreach an agreement that is mutually beneficial. For example, firm 9 will only benefit from a wagebelow $360, but worker 9 will not benefit from anything below $400. Since all the mutuallybeneficial deals have already been made, the outcome is Pareto efficient.

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238Ehrenberg/Smith•ModernLabor Economics:TheoryandPublic Policy,ThirteenthEdition23b.With deals below $480 prohibited, only firms 1, 2, and 3 will be interested in hiring. On the otherhand, all 10 workers would be willing to work. Suppose for simplicity that workers 1, 2, and 3 arehired. Worker 4, who has been shut out of the market, could easily strike a mutually beneficialdeal with firm 4 by offering to work for, say, $400, but the law prohibits this. Since mutuallybeneficial deals can still be made, the outcome under the legislated wage is not Pareto efficient.23c.The three workers who continue to be hired each gain $100 (the difference between the legislatedwage of $480 and the wage of $380 that would have emerged if all mutually beneficial trades wereallowed). The three firms that hire them each lose $100 relative to what they would have gainedunder the lower wage. The five workers who would have been hired under the lower wage alsolose. Assuming workers 4 through 8 have been shut out, the total loss to these workers is $200($80+$60+$40+$20). Combining the worker and firm losses yields a total loss of $500.23d.The winners do not gain enough ($300) to compensate the losers (−$500) and still come out ahead.Such a law can only be justified using principles developed outside of economics. For example,those who gain might have been very poor to begin with, while those who lost might have beenwell off. In such a situation, the redistribution might be justified by appealing to notions of equityor fairness.23e.Eight workers would be hired, the same outcome as in23a.23f.This is a Pareto efficient outcome since no mutually beneficial deals still exist. Even if person 9were paid his minimum acceptable wage of $400, the firm would not gain by hiring him. Whilethe outcome is Pareto efficient, it is not necessarily equitable since the firm has reaped all thebenefits.24a.See the scatter of points in Figure 1-2.24b.See the straight line in Figure 1-2.Figure 1-2

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AnswerstoChapter1239*24c.See Table 1-5 and the points plotted as squares in Figure 1-3.Table 1-5URActual%∆WPredicted%∆WResidual5.43.43.30.16.53.02.10.95.43.43.30.15.52.83.2−0.45.02.83.7−0.94.43.64.4−0.83.74.35.2−0.93.75.05.2−0.23.56.15.40.73.46.75.51.2*24d.The residuals do not seem random. They tend to be positive when the unemployment rate isrelatively high or relatively low, and negative otherwise. From the scatter of points inFigure 1-2, it appears a convex curve would fit the data better.*24e.See the solid curve in Figure 1-2.Figure 1-3

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240Ehrenberg/Smith•ModernLabor Economics:TheoryandPublic Policy,ThirteenthEdition*24f.See Table 1-6 and the points plotted as triangles in Figure 1-3. For six of the ten years the fitimproved. There were two years where it worsened slightly and two years where it was essentiallyunchanged. The fit improved most at the lowest and highest values of the unemployment rate. Forboth values, the residual was 0.3 units less when the nonlinear function was used.Table 1-6.URActual%∆WPredicted%∆WResidual5.43.43.10.36.53.02.40.65.43.43.10.35.52.83.0−0.25.02.83.5−0.74.43.64.2−0.63.74.35.2−0.93.75.05.2−0.23.56.15.60.53.46.75.80.924g.See the scatter of points in Figure 1-4.Figure 1-424h.See the lines labeled “1960s” and “1970s” in Figure 1-4. The 1970s line lies 3.7 units above the1960s line at every value of the unemployment rate.24i.See the line labeled “Combined” in Figure 1-4. The omission of theD70 variable severely biasesthe coefficient on the unemployment variable in an upward direction. TheD70 variable normallywould exert a positive effect on the dependent variable. However, sinceD70 and the unemploymentrate are positively correlated (notice that both unemployment and inflation were higher in the1970s), when theD70 variable is omitted, most of its positive effect on the dependent variable willbe attributed to the unemployment rate variable. Notice that omitting a variable is a problem herebecause the omitted variable and the remaining variable are correlated. Omitting a variable that isnot correlated with the independent variable would not create bias in the estimated coefficient.

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AnswerstoChapter1241001*24j.To allow both the position and slope of the curve to be different, estimate the equation%∆Wt=a0+a1URt+a2D70t+a3D70URt+ei.For the 1960s, the vertical intercept would be given by the estimate ofa, while for the 1970s itwould be given bya+a2. Similarly, for the 1960s, the slope would be given by the estimate ofa, while for the 1970s it would be given bya+a3.•Applications25a.The notion of exercising a preferential option for the poor is very different from promoting thenorm of Pareto efficiency. Under Pareto efficiency, only mutually beneficial changes should beundertaken. But when exercising a preferential option for the poor, some parties may be calledupon to sacrifice so that the poor can advance.25b.When the goal is to promote Pareto efficient outcomes, the government mainly plays a facilitatingrole. Its task is to promote voluntary exchange based on accurate and complete information. Whenbarriers to such transactions exist, however, the government sometimes can act in a way toovercome these barriers. Some examples of these actions include providing for the production ofpublic goods, eliminating capital market imperfections, or establishing substitutes for the market.Pope Leo XIII sees the task of government as promoting and protecting the interests of the poorand disadvantaged. Government need not act on behalf of all members of a society. Rather,government actions must be judged by their impact on the poor, even when these actions requiresacrifice by others.26a.The survey suggests people care about where their income stands relative to others in thepopulation.26b.The norm of Pareto efficiency says that all mutually beneficial changes should be undertaken.In this case, many people disagree that the program should be enacted, even though everyonegains. Therefore the responses are inconsistent with the norm of Pareto efficiency.26c.It appears that the premise of the question would have to have everyone gaining by roughly thesame amount for the reform to be supported unanimously.27a.Estimating the parametersα0andα1would require cross-sectional data on earnings and employee-generated revenues for a number of workers at one or more firms. Estimates of the parameterswould be derived by choosing values forα0andα1such that the squared differences between theactual and predicted values of employee earnings were minimized. Most statistical and spreadsheetprograms have commands that will use this criterion to find the parameter estimates.27b.The precision of an estimate is indicated by its standard error. If the estimated parameter isapproximately twice the value of its standard error, it is possible to reject with reasonableconfidence the hypothesis that the true value of the parameter equals zero.*27c.If the hypothesis is that parameterα1equals one, rather than zero, then the value of the estimatedparameter, minus one, must be approximately twice the standard error of estimated parameter.1

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242Ehrenberg/Smith•ModernLabor Economics:TheoryandPublic Policy,ThirteenthEdition*27d.Frank’s hypothesis implies that the relationship between earnings and productivity is much flatterthan the standard theory predicts. For a graphical depiction of this effect, see Figure 1-5. Lineabrepresents the relationship betweenEandRimplicit in the standard model, while linecdwould beconsistent with Frank’s hypothesis. Consequently, the prediction would be thatα0would be muchgreater than it is in the standard model, while the value ofα1would be much less (and definitelyless than one).Figure 1-5*27e.The equation to be estimated isEi=α0+α1Ri+α2Di+α3DiRi+ei.This equation allows both the intercept and slope to change as the degree of employee interactionincreases. Since the hypothesis is that relationship between earnings and productivity flattens outas the degree of interaction increases, the expectation would be that the estimate of the parameterα2would be greater than zero and the estimate of the parameterα3would be less than zero. Theeffect of increased interaction is also shown in Figure 1-5. Linecdrepresents a possiblerelationship betweenEandRwhen there is modest worker interaction, while lineefrepresentsa situation of more extensive interaction.*27f.It seems unlikely thatDis correlated with the level of employee productivity (R) since high-productivity people can be found in all types of work environments. Therefore, eliminatingDshould not bias the estimates of the remaining parametersα0andα1.

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6Ehrenberg/Smith•ModernLaborEconomics: TheoryandPublicPolicy,ThirteenthEdition•Review QuestionsChoose the letter that represents theBESTresponse.Labor Economics: Some Basic Concepts1.A unique feature of the labor market relative to standard product markets isa.individuals are the sellers, firms are the buyers.b.nonpecuniary characteristics play a larger role in labor market transactions.c.intense competition exists among the sellers.d.bothaandb.2.Feelings, emotions, personalities, and working conditions play an important role in labor markettransactions becausea.labor services cannot be separated from workers.b.people strive to make themselves as happy as they can.c.people are sometimes irrational.d.bothaandb.3.Which of the following is a statement associated with positive economic reasoning?a.Workers are entitled to a just wage.b.An increase in the payroll tax paid by firms will reduce wages and employment opportunities.c.Employers should be required to pay for health insurance for their employees.d.Professional athletes are overpaid.4.Which of the following is a statement associated with normative economic reasoning?a.It is important that everyone who wants to attend college be able to do so.b.Holding all else constant, workers in more dangerous occupations earn more than thoseemployed under safer conditions.c.Welfare programs can lead to reductions in work incentives.d.Subsidies given to firms that purchase new capital equipment will lead to an increase inemployment.5.Which of the following is a true statement about economic models?a.A model is deliberately abstract.b.A model accurately captures the all of the complexity of the real world.c.A model shows the thought process people go through when making decisions.d.A model must accurately predict behavior to be useful.The Models and Predictions of Positive Economics6.The goal often pursued in positive economic models of the labor market isa.utility maximization.b.profit maximization.c.income maximization.d.eitheraorb.

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Chapter1Introduction77.Positive economic models typically assumea.people cannot get everything they want and so must make choices.b.people undertake a particular course of action if the marginal benefits of that action outweighthe marginal costs.c.people are often inconsistent and inflexible when making their choices.d.bothaandb.8.Predictions of positive economic models are usually conditional ona.individuals caring only about themselves.b.the transactions being mutually beneficial.c.everything else being held constant.d.bothaandb.9.For a positive economic model to be useful, it musta.explain how people should behave.b.tend to predict how people behave on average.c.explain how people actually behave.d.apply to everyone.Normative Economics10.Normative economic statementsa.must be based on the principle of mutually beneficial gain.b.are based on ethical principles or goals.c.relate to voluntary transactions only.d.bothbandc.11.A Pareto efficient outcome has been achieved whena.all mutually beneficial transactions have been made.b.it is impossible to make someone better off without making someone else worse off.c.at least one person can gain and no one else will lose.d.bothaandb.12.Which of the following is true about a Pareto efficient outcome?a.the outcome must have been purely voluntary.b.the outcome may not satisfy society’s sense of fairness.c.the outcome is unique.d.Bothaandb.13.Policies that move two parties from one Pareto efficient outcome to anothera.will make one of the parties worse off.b.are often influenced by the parties’ initial endowment of resources.c.can be designed scientifically outside of the political system.d.bothaandb.

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8Ehrenberg/Smith•ModernLaborEconomics: TheoryandPublicPolicy,ThirteenthEdition14.Pareto efficient transactions may not occur becausea.parties may not have all the relevant information.b.they may be against the law.c.the cost associated with completing the transaction may deter one or more of the parties.d.all of the above.15.Government may help to bring about Pareto efficient outcomes bya.producing public goods.b.eliminating capital market imperfections.c.providing a way to substitute for market transactions.d.all of the above.Statistical Testing of Labor Market Hypotheses (Appendix 1A)16.Least squares regression assumes thata.the relationship between the independent variables is linear.b.the coefficients associated with the independent variables are greater than zero.c.a random error term accounts for any differences between the actual and predicted values of thedependent variable.d.all of the above.17.One can be reasonably confident a relationship between an independent and a dependent variablehas been found ifa.the standard error of the estimated parameter is small.b.the standard error of the estimated parameter is less than half the value of the estimatedparameter.c.the error term of the least squares regression is random.d.thet-statistic for the estimated parameter is about 0.5.In answering Questions18through20, please refer to the following information.Suppose that for a sample of 10,000 individuals, the relationship between annual hours supplied (H),the hourly wage rate in dollars (W), and the level of nonlabor income in dollars (V) (e.g., interestincome, gifts, public assistance) was estimated by multiple regression to beHi=1200+0.5Wi−0.04Vi.(225)(0.2)(0.01)The subscriptirefers to theith household wherei=1 to 10,000. Standard errors of the estimatedparameters are in parentheses.18.The coefficient of−0.04 associated with the independent variableVmeans thata.on average, when a person’s wage and nonlabor income both increase by $1, he wishes to work0.04 hours less.b.on average, when a person’s nonlabor income increases by $1, he wishes to work 0.04 hoursless, holding all else constant.c.the true value of the parameter associated with theVvariable is equal to zero.d.bothbandc.

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Chapter1Introduction919.Comparing the size of the coefficient on theWvariable and its standard error, one can conclude thata.the relationship betweenHandWhas been estimated with reasonable precision.b.statistically, one can be confident that the true relationship betweenHandWis not zero.c.from an economic standpoint, the relationship betweenHandWis insensitive to changes inW.d.all of the above.20.SupposeWandVare positively correlated (e.g., people with high wages save more and thus earnmore interest income). What would happen ifVwere omitted from the multiple regression?a.The coefficient onWwould become smaller.b.The coefficient onWwould become larger.c.The standard error associated with the coefficient onWwould become smaller.d.Bothbandc.•ProblemsLabor Economics: Some Basic Concepts21.The concept of a model is one of the most important concepts in economics. Helping the reader tounderstand and apply labor market models is the primary purpose of this book. Figure 1-1 is anexample of a model, but in this case, it is a model of a human being.Figure 1-121a. What does it mean to call this drawing a model?21b. What essential characteristics of a human being does it capture? What characteristics does it pushinto the background?21c. Why do you think such a simple drawing was used to illustrate the concept of a model? Would amore realistic drawing make for a better model?21d. Is this model a positive or normative model? Explain your reasoning.22.Models of positive economics typically assert that people weigh costs and benefits in a consistentmanner. That is, if the benefits of following a particular course of action exceed the costs, thenthat action will be taken, otherwise it will not.

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10Ehrenberg/Smith•ModernLaborEconomics: TheoryandPublicPolicy,ThirteenthEditionConsider a worker who is told he can save $5 on his dental insurance premium of $50 if he goes tothe company’s personnel office and fills out a form. The whole process will take 30 minutes.Suppose the worker fills out the form.A month later, the same worker is told that he can reduce his health insurance premium from $1,000to $995 by taking 30 minutes to fill out a form in the personnel office. The worker declines the offer.22a. Does the model of rational choice based on costs and benefits serve as a positive economic modelfor this person? If not, can you explain why the person might have acted as he did?22b. When an economic model fails to predict behavior accurately, does that mean it is useless? Whatother purpose could the model serve?Pareto Efficiency23.Consider a labor market in which there are 10 firms and 10 workers. Each firm can hire only one ofthese workers. Each firm has a maximum it would be willing to pay the worker. It would like to hireits worker for as far below this maximum as possible, but if no other options exist, it will hire aworker at a wage equal to its maximum willingness to pay value. The maximum wage each firm iswilling to pay is shown in Table 1-2.Suppose that each worker in this market can work for only one firm. Each worker has a minimumwage that will just be acceptable. Any offer below this minimum will be rejected and the workerwill not participate in the market. Each worker would like to be hired at a wage as much above theminimum acceptable wage as possible, but if no other options exist, will work at a wage just equalto this minimum. The minimum wage acceptable to each worker is also shown in Table 1-2.Table 1-2MaximumAcceptableMinimumAcceptableFirm#Wage($)Person#Wage($)152012402500226034803280446043005440532064206340740073608380838093609400103401042023a. Suppose that the first 8 workers are hired by the first 8 firms and each worker is paid a wage of$380. Show why this is a Pareto efficient outcome.23b. Concerned that workers will be exploited by firms, suppose that the government passes a law thatprohibits deals below $480; that is, individuals and firms must contract for work at $480 or above.What will be the consequences of this law?23c. Assuming the Pareto efficient outcome from23awould have emerged without governmentinterference, which workers gain because of the law in23b? How much do they gain? Who losesbecause of the law? How much do they lose?

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Chapter1Introduction1123d. Is it possible for the winners in23cto fully compensate the losers and still come out ahead? If not,how could such a law be justified?23e. Now suppose that the maximum willingness to pay values in Table 1-2 represent values for a singlefirm that is the only buyer of labor. Also suppose that this firm is aware of each worker’s minimumacceptable wage. In this situation, the firm could offer the first worker a wage of $240, and since theonly other option would be not to work at all, the worker would accept. Similarly, the second workercould be offered a wage of $260 (the first would still earn $240) and he would accept. How manyworkers would be hired under this pay scheme?23f. Is the answer to23ea Pareto efficient outcome? Is it an equitable outcome?Statistical Testing of Labor Market Hypotheses (Appendix 1A)24.Up until the 1970s economists believed there was a stable tradeoff between the unemployment rateand the rate of wage inflation. This relationship is known as the Phillips curve. To summarizebriefly, the logic of the Phillips curve rests on two assertions. The first is that the general rate ofchange in wages is proportional to the amount by which the number of jobs exceeds the number ofpeople looking for work on a percentage basis. For example, when the number of jobs exceeds thenumber of people willing to work by 10 percent, the wage is presumed to rise at a faster pace thanwhen the number of jobs exceeds the number of people willing to work by only 5 percent.The second assertion is that the unemployment rate is inversely related (probably in a nonlinearway) to the percentage difference between the number of jobs and the number of people willing towork. As Chapter 15 will point out, even when the number of jobs and the number of people willingto work are equal, there will still be a small positive rate of unemployment. This rate should diminish(probably at a decreasing rate) as jobs become more plentiful relative to the supply of workers. Onthe other hand, as the number of jobs falls below the number of workers, the unemployment ratewill rise.The result of these two assertions is that the rate of wage inflation will be inversely related (probablyin a nonlinear way) to the unemployment rate. By the 1970s economists began to realize that therewere also a number of other factors that could change over time and cause the terms of the entiretradeoff to either worsen or improve. In other words, a stable tradeoff exists only at a particularpoint in time. The difficulties a shifting tradeoff can cause for economists wishing to empiricallymeasure the Phillips curve are explored in the problems below.24a. Plot the 1960−69 data in Table 1-3 with the unemployment rate on the horizontal axis and wageinflation on the vertical axis.24b. Fitting a linear equation to the data for 1960–69 using the least squares regression technique yields%∆Wt=9.2−1.1URt,(1.21) (0.25)where%∆Wtrefers to the wage inflation for any yeart, andURtrefers to the unemploymentrate for any yeart. The standard errors of the estimated parameters (the vertical intercept and theslope) are in parentheses. Add this line to the graph produced in Question24a.

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12Ehrenberg/Smith•ModernLaborEconomics: TheoryandPublicPolicy,ThirteenthEditiontTable 1-3 contains the annual unemployment rate and rate of wage inflation experienced by the U.S.economy each year over the period 1960–79.Table 1-3YearUnemployment Rate (%)Rate of Wage Inflation (%)19605. 43. 419616. 53. 019625. 43. 419635. 52. 819645. 02. 819654. 43. 619663. 74. 319673. 75. 019683. 56. 119693. 46. 719704. 86. 619715. 87. 219725. 56. 219734. 86. 219745. 58. 019758. 38. 419767. 67. 219776. 97. 619786. 08. 119795. 88. 0Source:Economic Report of the President: 1989, Table B-39 (p. 352) and Table B-44 (p. 358).*24c. Assess how well this line fits the data. For each of the years 1960–69, find the difference betweenthe actual level of wage inflation and the level predicted by the regression line (these differencesare called residuals). Make a plot where the unemployment rate is on the horizontal axis and thecorresponding residual value is on the vertical axis.*24d. Do the residuals plotted in24cseem to be the result of just random errors? Is there a curve otherthan a straight line that could fit this data a little better?*24e. To capture the nonlinearities suggested by the plot of the data and the residuals from the linearregression line, the rate of wage inflation was regressed on the reciprocal of the unemployment rate(since the reciprocal function decreases at a decreasing rate). The least squares technique yieldedthe following relationship.%∆W= −1.43+24.61.URt(0.98) (4.25)Add a plot of this line to the graph created in24aand24b.*24f. Compute the residual errors using the nonlinear relationship estimated above. Plot the newresiduals (using different symbols) on your previous residual plot. Where has the fit of the lineimproved most?

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