CH-7-8 Unemployment – Macroeconomics : Chapter Notes

This Document Contains Chapters 7 to 8 CHAPTER 7 Unemployment Notes to the Instructor Chapter Summary This is a relatively easy chapter that examines the determination of the natural rate of unemployment. It discusses why all free-market economies have some unemployment and what determines the unemployment rate in the long run. In keeping with the long-run focus of Part II of the book, this chapter abstracts from cyclical unemployment completely. The chapter has four primary goals: 1. To show that unemployment is the natural consequence of labor force dynamics and that the rate of unemployment is determined by the rates of job separation and job finding. 2. To discuss how the process of job search leads to frictional unemployment and how government policies such as unemployment insurance influence the amount of frictional unemployment. 3. To discuss the various causes of wage rigidity (minimum wages, unions, and efficiency wages) and also how wage rigidity leads to structural unemployment. 4. To teach some of the important facts about patterns of unemployment in the United States and in Europe. Comments It should be possible to present the material in this chapter in one lecture. When presenting this material, I stress the reasons why we care about unemployment; the lecture notes reflect this. I also like to discuss efficiency-wage theories in more detail; there are a number of supplements on this topic. Use of the Dismal Scientist Web Site Use the Dismal Scientist Web site to download annual data for the unemployment rate in the United States, Germany, Japan, Canada, and the United Kingdom over the past 40 years. Assess whether these rates have generally moved together or not. Chapter Supplements This chapter includes the following supplements: 7-1 Social Costs of Unemployment 7-2 Job Finding and Job Separation 7-3 A More General Theory of the Natural Rate of Unemployment 7-4 Dutch Male Unemployment and Unemployment Benefits (Case Study) 7-5 Robert Lucas and $500 Bills 7-6 More on the Minimum Wage 7-7 Minimum Wages and Efficiency Wages (Case Study) 7-8 Implicit Contracts 7-9 The Two Views of Unions 7-10 Efficiency Wages I: The Solow Condition 7-11 Efficiency Wages II: The Shapiro–Stiglitz Model 145 7-12 Efficiency Wages and Wage Differentials 7-13 More on Henry Ford (Case Study) 7-14 More on the Duration of Unemployment (Case Study) 7-15 Trends in Unemployment 7-16 The Secrets to Happiness 7-17 Additional Readings Lecture Notes Introduction The long-run model of the economy has thus far assumed full employment. Our discussion of the labor market in Chapter 3 ignored the reality that not everyone in the labor force has a job. We now turn to one of the most closely watched macroeconomic variables—unemployment. We retain our long-run focus: Our concern is not fluctuations in unemployment, but the long-run level of unemployment. Fluctuations in unemployment, like fluctuations in income, are a problem that we defer until we analyze the short-run behavior of the economy. The long-run or average level of unemployment is sometimes known as the natural rate of unemployment. In our analysis of the classical model, we took the supplies of capital and labor as given and assumed that each was fully utilized. Here, we continue to assume a constant supply of fully utilized capital but allow for the supply of labor to differ from the amount employed in the production of goods and services. We also discuss how labor supply and population are related. Why do economists care about unemployment? Perhaps the main reason that an economist would give is not the one that would immediately spring to the mind of a noneconomist. Since labor is an input into the production of goods and services that people want to consume, unemployment may signal a waste of a scarce resource. Other reasons include the significant human and social costs of unemployment and the fact that the prospect of unemployment Supplement 7-1, confronts individuals with undesirable uncertainty about future income. Finally, the burden of “Social Costs of the cost of unemployment is borne largely by those who are unemployed; it is not distributed Unemployment” evenly across society. Why do we expect any unemployment at all in the long run? It might seem that a wellfunctioning economy would be one without any unemployment. But this is almost certainly not the case. Most basically, in a well-functioning economy, people will be moving into and out of the labor force and will be switching between jobs. Often, this process means that people will Figure 7-1 spend some time unemployed before or between jobs. Thus, we always observe some unemployment in a market economy. 7-1 Job Loss, Job Finding, and the Natural Rate of Unemployment To obtain insight into the workings of the labor market, consider a simple model of flows into and out of employment. We assume that the labor force is fixed (= L); that is, we take as given the population and the labor force participation rate. Recall from Chapter 2 that the labor force equals the sum of employed and unemployed workers: U + E = L. Suppose that a constant fraction of unemployed workers find new jobs every month. We will Supplement 7-2, “Job Finding and denote this fraction by f, the job-finding rate. Then, fU workers move from unemployed to Job Separation” employed status every month. Similarly, suppose that a constant fraction s of employed workers move into unemployment, either because they quit or because they are fired; we call s the separation rate. (Note that this doesn’t preclude the possibility of people switching jobs without ever being unemployed; such changes are simply not counted.) Hence, sE workers move from employed status to unemployed status. We look for a situation where the levels of employment Figure 7-2 and unemployment (and hence also the employment and unemployment rates) are constant. For this to be true, flows into employment must exactly match flows out of employment: fU = sE. We can use this equation and the definition of the labor force to solve for the employment and unemployment rates. Since L = E + U, it follows that 1 = E/L + U/L. Also, E/L = (f/s)(U/L). So 1=1+ f / s (U / L) 1= s+s f  (U / L)  s  ⇒(U / L)= s+ f  . Similarly, we have  f  (E / L)= s+ f  . From this simple model, we can draw an equally simple but important conclusion: Policies to Supplement 7-3, affect the natural rate of unemployment must change either the job-finding rate or the separation “A More General Theory of the rate. In particular, if policymakers wish to reduce the unemployment rate, they must increase the Natural Rate of job-finding rate and/or decrease the job-separation rate. Unemployment” The deeper questions of unemployment, however, are not addressed directly by this model. First, we want to know why we observe unemployment in society—or, in terms of this model, why the separation rate is not very small or the job-finding rate is not very large. Second, we might wonder whether or not policymakers would want to change the natural rate of unemployment (and, related to this, we would like to know what sorts of policies will affect the natural rate). There are two main reasons why the unemployment rate is not zero. We have alluded to the first already: Workers may spend some time unemployed in the process of moving between jobs. The second is that, for a variety of reasons, the labor market might not be in equilibrium at the point where supply equals demand. We consider these in turn. 7-2 Job Search and Frictional Unemployment Workers and firms spend time searching for each other. Our models so far have assumed that all workers and all firms are identical but, obviously, there are many different types of jobs and many different types of workers. An economy that is functioning well is one that matches up jobs and skills; in a complex economy, we cannot expect such matches to occur instantaneously. Moreover, firms and workers sometimes need time to learn about one another; it may be necessary, for example, for a worker to try a few jobs before finding the one most suitable. Thus, we should expect, and indeed we should regard as desirable, that unemployed workers do not take the first job that becomes available and that firms do not hire the first applicant for a position. Instead, time and effort are spent in the process of searching, in the attempt to find a good match between workers and firms. The resulting unemployment is termed frictional unemployment. Frictional unemployment means that the job-finding rate is less than one, and it also helps to explain why the separation rate is positive. Note that private institutions—employment agencies and headhunters—have developed in an attempt to improve the matching of workers and firms. Causes of Frictional Unemployment The types of goods that households and firms purchase change over time. When spending shifts from certain types of goods to others, the demand for labor that produces those goods also shifts. This change in composition of demand among industries or regions is known as a sectoral shift. In a dynamic economy, sectoral shifts are always occurring, and because it takes time for workers to move from contracting sectors to expanding ones, the economy will experience frictional unemployment. Other causes of job separation and frictional unemployment include changes in the demand for certain types of labor skills, firm failures, job loss due to poor performance, and quitting a job to start a new career or move to a new region. Public Policy and Frictional Unemployment Recognizing that some frictional unemployment is desirable in a market economy is the easy part. It is much harder to know whether the U.S. economy exhibits too much, too little, or the right amount of frictional unemployment. To put this another way, it is unclear whether firms and workers spend too much or too little effort in the business of searching for each other. The main reason why this is unclear is that firms’ and workers’ search decisions generate externalities. When a firm and a worker are successfully matched, they both derive some benefit. A worker who chooses to search harder is more likely to get a good match. But a good match benefits the firm as well; there is an external benefit to the firm. Since the worker does not get all the benefit from his effort, he is likely to work too little from a social perspective. Exactly the same argument applies to the firm. Thus, we might actually find people searching too little, accepting jobs too readily, and finding jobs at a rate too high from a social point of view. This would mean, perhaps surprisingly, that we would have too little unemployment. We cannot draw such a conclusion with confidence, however, because there are many different sorts of externalities associated with workers’ and firms’ searching decisions. It is, thus, not possible to conclude unequivocally that we have too much or too little search unemployment. This is an important area of current research in labor economics. Many government policies influence the amount of frictional unemployment that we see in the economy. Perhaps most importantly, unemployment insurance influences individuals’ incentives to search. Unemployment insurance allows unemployed workers to collect some payments from the government while they are unemployed. This reduces the immediate necessity for workers to accept the first job that comes along and so may increase the natural rate of unemployment. The presence of unemployment insurance may also make firms more willing to lay off workers. Of course, the main purpose of unemployment insurance is not to affect the natural rate of unemployment; this is perhaps better thought of as a side effect. Unemployment insurance is designed to mitigate some of the hardship associated with being unemployed; it thus has distributional goals. It also reduces uncertainty about workers’ incomes. Supplement 7-4, Case Study: Unemployment Insurance and the Rate of Job “Dutch Male Finding Unemployment and Unemployment Another piece of evidence suggesting a link between unemployment insurance and the level of Benefits” unemployment is the fact that the probability of finding a job increases markedly when the worker ceases to be eligible for unemployment insurance. 7-3 Real-Wage Rigidity and Structural Unemployment Another reason why we may observe some unemployment even in the long run is real-wage rigidity. The classical model assumed that the real wage adjusts to bring about equilibrium in the labor market. This is in keeping with the standard economists’ approach to markets: Prices adjust to bring about equality between supply and demand. Nevertheless, there are reasons why the labor market may be rather different from, say, the market for soybeans; there may be reasons why the real wage might get permanently stuck at a level above that consistent with Figure 7-3 equilibrium. We consider three reasons: minimum-wage laws, unions, and efficiency wages. All Supplement 7-5, provide explanations of why the real wage may be “too high,” implying that some workers may “Robert Lucas and $500 Bills” be unemployed. The resulting unemployment is often referred to as structural unemployment. Workers are unemployed not because they are searching for a good match, but because the supply of labor exceeds the demand for labor. Workers are waiting for jobs to become available at the current wage. Minimum-Wage Laws Minimum-wage laws are an obvious reason why the real wage might not clear the market. If the equilibrium wage is below the government-mandated wage, then we immediately have wage rigidity. In practice, of course, minimum-wage laws are irrelevant for many workers since they are paid much more than the minimum wage. But for some workers—primarily young and/or unskilled workers—this constraint may be relevant. Economists are often opposed to minimum-wage laws, not necessarily because they are opposed to improving the lot of the poor, but because they don’t think that the minimum wage is a very efficient or fair means of doing so. If our analysis is right, the minimum wage will make those who have jobs better off (because they will earn more than the equilibrium wage), but it will also mean that some people who would have had jobs are now unemployed, and hence, worse off than without minimum-wage laws. Moreover, it is not clear that the minimum wage Supplement 7-6, really helps the working poor: Heads of households represent less than one-quarter of those “More on the earning the minimum wage, while teenagers make up more than one-third. A better policy Minimum Wage” option might be the earned income tax credit, which gives poor families an income tax break. Case Study: The Characteristics of Minimum-Wage Workers The Current Population Survey, which is used to compute the unemployment rate and other labor-force data, can also be used to study the characteristics of workers who earn the minimum wage. In a report issued in 2014, the Bureau of Labor Statistics provided detailed information about these workers. Roughly 1.5 million workers reported that they were paid the minimum wage of $7.25 per hour during 2013, and an additional 1.8 million workers reported that they were paid less than the legal minimum because their jobs are exempt from the minimum-wage Supplement 7-7, law, enforcement of the law is not perfect, or the workers themselves may have incorrectly “Minimum Wages reported their actual wage. Minimum-wage workers are more likely to be women, young, less and Efficiency educated, and working part time. The leisure and hospitality industry had the highest proportion Wages” (19 percent) of their workforce with reported wages at or below the minimum. Roughly half of all workers paid at or below the minimum wage were employed in this industry. Table 7-1 Unions and Collective Bargaining Unions provide another explanation of real-wage rigidity of differing importance in different countries. Wage agreements between unions and firms usually set wages and let the firm choose the level of employment. The bargaining process between the firm and its workers might well lead to a wage above that consistent with supply equal to demand. In essence, this is because the labor market loses the features of a competitive market; instead, workers have some monopoly power, which allows them to set a wage above the market-clearing level. Just as with minimum-wage laws, the result is that those who are employed are better off, Supplement 7-8, and those who are unemployed are worse off. Economists sometimes characterize this situation “Implicit Contracts” as an insider/outsider problem. The unionized workers are insiders; the unemployed are Supplement 7-9, outsiders. If the insiders have enough power, the outsiders may not be able to persuade the firm “The Two Views to employ them, even at a lower wage. of Unions” It does not necessarily follow that unions are bad for the economy. Unions have had many different effects on the pay and working conditions of workers, and labor economists continue to analyze these effects. The long-term relationship between a union and a firm may have many Supplement 7-10, desirable consequences. “Efficiency Wages I: The Solow Efficiency Wages Condition” Supplement 7-11, Another class of theories that has recently been developed to explain real-wage rigidity is “Efficiency Wages efficiency-wage models. The starting point of these models is the idea that workers’ productivity II: The Shapiro- Stiglitz Model” might be positively related to the wages they are paid. In this case, it is no longer obvious that Supplement 7-12, firms always prefer the wage to be lower. Thus, in such a setting, a firm might not want to “Efficiency Wages employ a worker willing to work for less than the going wage because the firm might also think and Wage that worker’s productivity would be lower. Differentials” These theories had their origin in development economics, where the idea was that, at very low levels of income, higher wages would mean better nutrition and, hence, higher productivity. More recent theories have drawn out links between wages and productivity that are more plausible for developed economies. One such link is that firms paying high wages may be able to attract better workers and reduce turnover. Another is that high wages may improve workers’ effort and discourage shirking. Case Study: Henry Ford’s $5 Workday One famous experiment, dating from 1914, seems to support the idea of efficiency-wage theory. Supplement 7-13, “More on Henry Ford introduced a daily wage of $5, which was approximately twice the prevailing wage at the Ford” time. The evidence suggests that this policy did indeed pay off in terms of greater effort, lower absenteeism, and other benefits. 7-4 Labor Market Experience: The United States The Duration of Unemployment Supplement 7-14, Evidence on the duration of unemployment can help us ascertain the relative importance of “More on the frictional and structural unemployment. While short unemployment spells may well be due to Duration of frictional unemployment, long-term unemployment is more likely to indicate structural Unemployment” unemployment. It turns out that, while most spells of unemployment are short, total unemployment is principally accounted for by the fewer spells of long-term unemployment. Policies designed to reduce the natural rate of unemployment, therefore, need to be targeted at the relatively few long-term unemployed. Case Study: The Increase in U.S. Long-term Unemployment and the Debate over Unemployment Insurance During the severe recession of 2008–2009, the duration of unemployment rose significantly Figure 7-4 Table 7-2 more than in previous recessions. Some economists believe the sharp increase in duration resulted from expanded unemployment insurance benefits that Congress passed in early 2009. Other economists argue that the effect of extending the time people could collect benefits (from the usual 26 weeks to 99 weeks) reduced the incentive to seek work only slightly. These economists point to the absence of jobs during the deep recession, not a lack of desire to find work, as the reason for the prolonged duration of unemployment. Variation in the Unemployment Rate Across Demographic Groups The unemployment rate varies across demographic groups. Younger workers have notably higher unemployment rates than older workers, and blacks have notably higher unemployment Supplement 7-15, rates than whites. Differences in unemployment rates tend to be due more to differences in job“Trends in separation rates than to differences in job-finding rates. Higher youth unemployment may, Unemployment” therefore, reflect the process of young workers seeking a good job match. The higher unemployment rates for blacks are less easily explicable in economic terms. Transitions Into and Out of the Labor Force The simple model presented at the start of this chapter considered only flows into employment and unemployment and held the labor force fixed. Many of the unemployed at any time are new Table 7-3 or recent entrants into the labor force and perhaps are not searching actively for a job. By contrast, unemployed workers often withdraw from the labor force, perhaps because they cannot obtain a job. Such discouraged workers do not show up as unemployed in the official unemployment data. In addition, some workers may only be able to find part-time jobs, even though they would prefer to work full time. These workers are officially counted as employed, but a more appropriate description might be “underemployed.” The Bureau of Labor Statistics provides several alternative measures of labor underutilization—some broader and some narrower than the official unemployment rate—to help gauge the relative importance of these issues (see Supplement 2-11, “Alternative Measures of Unemployment”). Case Study: The Decline in Labor Force Participation: 2007– 2014 The labor-force participation rate fell from 66.1 percent in 2007 to 63.0 percent in 2014. This decline followed a nearly two-decade period during which the rate had fluctuated narrowly Table 7-4 between about 66 percent and 67 percent. A recent study at the Federal Reserve Bank of Philadelphia looks at individuals not in the labor force to assess why they are not working or looking for work. About half of the increase in nonparticipation is accounted for by an increase in retirement, primarily reflecting the aging of the baby-boom generation. Another reason is that the deep recession of 2007–2009 and the subsequent slow recovery pushed unemployment, particularly long-term unemployment, upward. The reduction in good job opportunities certainly increased the number of discouraged workers. It also likely led some older workers to retire earlier than planned, caused workers with physical limitations to more quickly apply for disability benefits, and kept some students in school longer. The drop in labor-force participation is not necessarily an adverse development: retirement may represent a beneficial change after a lifetime of work, and staying in school longer means more investment in productivity-enhancing education. But a smaller labor force than would otherwise be the case also implies a smaller output of goods and services and, thus, lower GDP. 7-5 Labor Market Experience: Europe Europe’s experience of unemployment has been rather different from that of the United States. Figure 7-6 In most European countries, unemployment rose substantially in the early 1980s and has since remained stubbornly high. The two main reasons that have been advanced to explain this unemployment are generous unemployment benefits and a decrease in demand for unskilled labor. Unemployment benefits are higher in Europe than in the United States, and workers are generally eligible for such benefits for a longer period of time. As the discussion earlier in the chapter showed, this will tend to increase the equilibrium unemployment rate. The demand for unskilled labor has fallen in Europe and in the United States, but the consequences have been different: In the United States, real wages of unskilled workers have fallen; in Europe, employment of unskilled workers has gone down. Unemployment Variation in Europe Labor market conditions vary significantly across European countries. The unemployment rate, which for Europe as a whole has averaged well above the unemployment rate in the United States, has actually been below the U.S. rate in nations representing roughly one-third of the population of Europe. Much of the variation in the unemployment rate across Europe can be attributed to variation in the extent of long-term unemployment. Finally, variations in national unemployment rates in Europe are correlated with variations in labor-market policies and the role of labor unions in ways that are consistent with how economists would expect policies and unions to affect unemployment. The Rise of European Leisure Supplement 7-16, In the early 1970s, Americans and Europeans worked roughly the same number of hours. Since “The Secrets to then, hours worked have declined for Europeans, while hours worked have remained about the Happiness” same for Americans. Today, Americans work on average about 30 percent more hours than do residents of western Europe. The greater number of hours reflects both more hours worked on average by Americans who are employed and a higher level of overall employment in the United States relative to the population. One hypothesis for this difference is that higher tax rates in Figure 7-7 Europe compared to the United States reduce the incentive to work. Another hypothesis emphasizes the greater importance of labor unions in Europe, which bargain for a shorter workweek and more holidays. A final hypothesis focuses on differences in preferences between Europeans, who prefer more consumption of leisure, and Americans, who prefer more consumption of goods and services. 7-6 Conclusion While our models give us some insight into the causes of unemployment, they do not tell us unequivocally whether the natural rate of unemployment is too high or too low, nor do they indicate easy remedies for unemployment. They do indicate, however, that a number of government policies, such as unemployment insurance, job-training programs, and minimumwage laws, have effects on the unemployment rate. ADDITIONAL CASE STUDY 7-1 Social Costs of Unemployment Analysts have identified a number of costs of unemployment not discussed in the textbook. First, there is some evidence that unemployment adversely affects productivity. A survey of unemployed professional workers indicated that feelings of loyalty and commitment to the job that existed prior to unemployment were replaced by cynicism and low commitment during unemployment; moreover, these feelings persisted after the workers were reemployed. If such responses to unemployment are widespread, then even shortterm unemployment might have long-term consequences. Other studies focused on the impact of unemployment on psychological health and suicide. A 1980s study of British youth by Michael Banks and Phillip Ullah concludes that employment positively affects the mental health of young workers. Banks and Ullah surveyed initially unemployed youth and found that a move to employment improved their measures of depression, anxiety, and general well-being. A survey by Stephen Platt indicates that there is strong evidence, from many studies of U.S. data, of a correlation between the state of the economy and the suicide rate. The evidence for other countries is less clear, although still broadly supportive of this association. As one example, Daniel Hamermesh and Neal Soss looked for economic causes of suicide among U.S. males between 1947 and 1967. On the basis of their estimates, these authors concluded that increases in the unemployment rate do have a significant effect on suicides: A 1-percentage-point increase in the unemployment rate increases the suicide rate by between 0.06 and 1.42 suicides per 100,000, depending on age. (These correspond to increases in the suicide rate of roughly 1 percent to 4 percent.) ADDITIONAL CASE STUDY 7-2 Job Finding and Job Separation News sources frequently report information on changes in employment and unemployment. But as is evident from the model presented in Chapter 7, these are the net result of flows from employment to unemployment, from unemployment to employment, and in and out of the labor force. A month in which no one changes employment status and a month in which 1 million people are hired and 1 million people are fired look identical from the point of view of employment statistics. Our understanding of employment and unemployment is, therefore, enhanced by a study of the underlying gross flows. Figure 1 reveals that the gross flows are sizable in the U.S. economy. In May 1993, 5 million people were hired. Of those, 2 million were previously unemployed, and 3 million were not in the labor force. But 5 million left employment: 3.2 million left the labor force and 1.8 became unemployed. So the net change in employment was approximately zero. Source: Figures 1, 2, and 3 from J. Ritter, “Measuring Labor Market Dynamics: Gross Flows of Workers and Jobs,” Federal Reserve Bank of St. Louis Review (November/December 1993): 39–57. Figures 2 and 3 reveal that substantial labor market activity is normal in the U.S. labor market. Figure 2 shows job-finding and -separation rates based on Bureau of Labor Statistics data. Figure 3 shows the creation and destruction of manufacturing jobs as documented by Steve Davis and John Haltiwanger. 2 Both indicate that there is always substantial movement of workers in and out of jobs in the U.S. economy. Figures 2 and 3 also reveal a puzzle. According to Figure 2, there has been a pronounced downward trend—most noticeably in the 1980s—in both finding rates and separation rates. Yet there is no comparable trend in the job-creation and -destruction rates shown in Figure 3. Some downward trend makes sense because young people tend to change jobs more frequently than older people. As the babyboom generation has aged, therefore, we would expect less turnover in the labor force. Figure 2 Figure 3 LECTURE SUPPLEMENT 7-3 A More General Theory of the Natural Rate of Unemployment The textbook considers flows between employment and unemployment and shows that the unemployment rate can be written as U/L = s/(s + f ), where s is the separation rate and f is the job-finding rate. This analysis is evidently incomplete, since it ignores movements in and out of the labor force. We present here a more general model. Since the unemployment rate equals U/L, it follows that the unemployment rate will be constant when ∆U/U = ∆L/L. The labor force changes because of new entrants and retirements. We assume that the current labor force gives birth to new workers and, hence, that the flow of new entrants into the labor force equals bL, where b is the birth rate. Similarly, we suppose that a constant fraction, r, of the labor force retires each period. Thus, we have ∆L = bL – rL ⇒ ∆L/L = b – r. Changes in the number of unemployed workers arise, as before, because of job findings and job separations. Thus, we have a flow into unemployment equal to sE and a flow out of unemployment equal to fU. We assume that new entrants to the labor force are unemployed at first, and we suppose that a fraction of unemployed workers retires each period. If we assume retirement is independent of whether or not a worker is employed, then the retirement rate for the unemployed equals r. We then have ∆U = sE – fU + bL – rU ⇒ ∆U/U = s(E/U) – f + b(L/U) – r. The unemployment rate is thus unchanging when b – r = s(E/U) – f + b(L/U) – r ⇒ b = s(E/U) – f + b(L/U). Multiply through by U/L to get b(U/L) = s(E/L) – f(U/L) + b. Since E + U = L, we have (E/L) = 1 – (U/L), so This differs from the result in the textbook only in that the birthrate is added to the numerator and to the denominator: Both unemployment and the labor force increase as a result of new entrants into the labor force. An increase in the birthrate, like an increase in the separation rate, increases the unemployment rate. Notice that (because of the assumption that the retirement rate is the same for the employed and the unemployed) the retirement rate does not affect the equilibrium unemployment rate. CASE STUDY EXTENSION 7-4 Dutch Male Unemployment and Unemployment Benefits A study by Gerard van den Berg on Dutch male unemployment in the mid-1980s does not find strong evidence of a link between unemployment benefits and unemployment duration. He found that a 10 percent decrease in unemployment benefits reduced average duration of unemployment by about 3 percent. The less educated the worker, moreover, the weaker was the effect: A 10 percent decrease in benefits decreased duration by 10 percent for university-educated workers, by only 5 percent for those with high school education, and had no effect on duration for workers with only an elementary school education. These results suggest that attempts to decrease unemployment by decreasing benefits (and thus encouraging job search) are unlikely to be successful. As explained in Section 7-4 of the textbook, policies that are aimed at reducing unemployment must be targeted at the long-term unemployed, who are very often those with the least human capital. If van den Berg’s results are general, then changes in unemployment benefits are likely to have little effect on overall unemployment. LECTURE SUPPLEMENT 7-5 Robert Lucas and $500 Bills Economists are often not very specific about how markets get into equilibrium. They do generally believe, however, in the existence of economic forces that make prices adjust to the point where supply equals demand. Consider, for example, the labor market discussed in Chapter 7 of the textbook, and suppose that the real wage is above the level consistent with equilibrium. Then, there are more workers available than jobs, so jobs will be rationed in some way (since, presumably, firms cannot be forced to employ more workers than they want). As a consequence, some workers will be unemployed, but they would like to work at the going wage. The story we might then tell is the following. An unemployed worker would go to a factory and offer to work for a little bit less than the going wage. The firm would have every incentive to hire that worker and fire one of its existing workers because that would increase its profits. If all unemployed workers did this, then the wage would quickly be bid down to the level where supply equaled demand. Because of this sort of story, economists are often suspicious of models in which the relevant price fails to clear the market. The economist Robert Lucas describes such a situation as one where there are “$500 bills lying on the sidewalk.” In more prosaic terms, there are unexploited profit opportunities. An unemployed worker and a firm could apparently get together and easily come to an arrangement that would benefit them both. A basic idea of economics is that people will take advantage of profit opportunities when they exist—they won’t leave $500 bills lying on the sidewalk. (The U.S. Federal Reserve and U.S. Treasury no longer issue a $500 bill, having discontinued its use in 1969. Although these bills may still circulate, most are now held by numismatic dealers and collectors and so may well be valued at far more than $500—making Lucas’ point even stronger!) Any economic theory that suggests that a market may be in equilibrium even when supply does not equal demand must confront the $500 bill test. A notable feature of efficiency-wage models or the insider/outsider models of unions is that they provide an explanation of how the real wage may be too high and yet will not be bid down to the point where supply equals demand. LECTURE SUPPLEMENT 7-6 More on the Minimum Wage The overall impact of the minimum wage depends both on the level of the minimum relative to wages elsewhere and the number of workers who are potentially covered by the legislation. The percentage of workers covered by minimum wages rose during the 1960s and 1970s from less than 40 percent at the end of the 1950s to more than 80 percent by the beginning of the 1980s. Minimum-wage legislation thus has the potential to affect a large number of workers. The minimum wage has declined relative to average earnings, however, lessening its impact on employment. Figure 1 shows the minimum wage and average hourly earnings for private production and nonsupervisory workers; this clearly shows the marked decline in the minimum wage relative to hourly earnings during the 1980s, 1990s, and 2000s. Note: All figures are in dollars. Average hourly earnings is for production and nonsupervisory workers on private nonfarm payrolls. Source: Department of Labor, Bureau of Labor Statistics. Charles Brown, in a review of the evidence on minimum wages, concludes that both their harmful and beneficial effects tend to be exaggerated. For example, summarizing research on the effects of the minimum wage on teenage unemployment, Brown notes that a 10 percent increase in the minimum wage probably raises the teenage unemployment rate somewhere between 0 and 3 percentage points, with the lower end more likely. He concludes, “my reading of the time series estimates is that they are not negligible … but one should look elsewhere (and I am not sure where) for the primary causes of high unemployment rates in the youth market, particularly for black youth.” But if the effects on employment are exaggerated, so too are the effects on income distribution because of “the surprisingly weak relationship between being a worker whose hourly wage is low and being a member of a family whose annual income is low.” A stronger argument for the minimum wage is made by Linda Martin and Demetrios Giannaros, who argue that changes in the minimum wage significantly influence the poverty rate in households headed by women. Increases in the minimum wage may then help to counteract the feminization of poverty. Brown also exposes a common fallacy in discussions of the minimum wage: that minimum wages do not have a big effect on employment because we do not observe large-scale discharges of workers following an increase in the minimum wage. This is a fallacy because turnover in minimum-wage jobs is very high (over 10 percent per month), so employers do not need to fire workers to reduce employment; attrition will serve. Brown concludes that it “is hard for me to see evidence that minimum-wage increases have benefits which would overcome an economist’s aversion to interfering with reasonably competitive markets. But the case against the minimum wage seems to me to rest more upon that aversion than on the demonstrated severity of any harm done to those directly affected.” CASE STUDY EXTENSION 7-7 Minimum Wages and Efficiency Wages One of the biggest controversies in macroeconomics during the last decade concerns the effects of an increase in the minimum wage on unemployment. Standard analysis suggests that an increase in the minimum wage will increase unemployment. But studies by David Card, Lawrence Katz, and Alan Krueger of fast-food restaurants in New Jersey and Pennsylvania found—surprisingly—that an increase in the state minimum wage in New Jersey was accompanied by an increase in employment at fast-food restaurants in that state. Restaurants across the state line in Pennsylvania, where there was no change in the minimum wage, did not increase employment. Many economists are skeptical about the Card–Katz–Krueger results because they do not see any good explanation of why an increase in the minimum wage would increase employment. One explanation is that firms might have monopsony power in labor markets. As a monopsonist hires more workers, it drives up the wage it must pay and so has an incentive to hire fewer workers and thus pay a lower wage than would prevail under perfect competition. In the presence of a minimum wage, the monopsonist firm must pay a higher wage anyway and so will find it optimal to increase employment above the level it would choose in the absence of a minimum wage. It seems doubtful, however, that fast-food restaurants have much of an influence on market wages. Another possible explanation is efficiency wages. The idea of efficiency wages is that higher wages might be beneficial to the firm because they increase workers’ effort or reduce turnover costs. This means that if the firm is forced to pay a higher wage, it will also find that the marginal product of labor will increase. One way to think of this is that it shifts the labor demand curve to the right. This is illustrated in Figure 1. At the wage w1, the marginal product of labor is low, and the firm hires the quantity of labor L1. If the firm is forced to pay a higher wage w2, the higher marginal product of labor means that the firm wants to employ more labor, L2. Notice that the argument is not that firms are better off paying the higher wage. (After all, they could have paid that wage before, had they wanted to.) The argument is that if firms are forced to pay a higher wage, they are also better off employing more workers. ADVANCED TOPIC 7-8 Implicit Contracts In the mid-1970s, a number of authors provided another explanation of wage rigidity: Firms and workers might find it in their mutual best interest to write wage contracts that specified a fixed wage. The basic intuition is that in an uncertain world, contracts may serve more than one function. As well as being the means whereby workers are remunerated for their services, they may also be a means for the firm to insure workers against income risk. That is, if workers are risk-averse (i.e., they prefer a certain gain to a gamble that yields the same amount on average), and firms are risk-neutral (or at least less risk-averse than workers), the firm and its workers might agree to stabilize the wage. Workers would prefer this and would be willing to concede a little in terms of their average wage for this security. In other words, workers would effectively pay an insurance premium in the form of a slightly lower average wage. This seemed a very promising line of inquiry because it was based on a clear empirical observation that firms and workers are in general engaged in a long-term relationship, which might not be well modeled by the second-by-second price adjustment of “auction” models. Many workers and firms do enter into explicit contracts of 12-, 24-, or 36-month duration—sometimes longer. Even if there is no explicit contract, there may well be an implicit understanding between the firm and its workers. When this research first appeared, many economists thought that it would provide a good microeconomic theory of unemployment that was immune from the Lucas $500 bill criticism. Let us consider the environment in which such contracts make sense. The first idea is that the world is uncertain so that, in the absence of contracts, workers’ wages fluctuate: In good “states of the world,” workers’ productivity, and hence their wage, is high; in bad states of the world, their wage is low. Workers would prefer more stable wages because they dislike risk. Firms may be able to provide some insurance because they have better access to capital markets and so may be risk-neutral. The striking contribution of the contracting literature is the following: Under certain conditions, an efficient contract will have the property that the firm will pay the same in both good and bad states of the world. Wage rigidity emerges as optimal. The role of the wage is thus very different in a contracting story from our usual view of the labor market. Normally, we think of the wage as adjusting to clear the labor market. Here, the role of the wage is to allocate risk. Also, under certain conditions, this theory could explain layoffs and involuntary unemployment. So contract theory does provide an explanation of rigid wages at the microeconomic level. But, because the wage is playing a more complicated role in these stories, it does not immediately follow that this implies unemployment—in an optimal contract, the wage and employment decisions are separated. It turns out that, overall, contract theory does not really explain unemployment very easily: Optimal contracts often imply higher employment than would occur in an auction market. Early models also included some important unexplained restrictions on the form of contracts, such as no work-sharing or severance pay. When these assumptions were relaxed, the models no longer generated layoffs and involuntary unemployment. The principal extensions to this literature focused on different informational assumptions: There may be information that is available to firms, but not to workers, and vice versa. Circumstances where firms and workers differ in their knowledge are known as cases of asymmetric information. They may then have an incentive to conceal their knowledge (say, about the state of the world, or how hard they are working). This led analysts to focus on contracts that gave workers and firms an incentive to tell the truth. There is now a large body of literature on contracting that has greatly advanced our understanding of long-term contractual arrangements and of the importance of information imperfections. But its initial promise to provide a microeconomic basis for theories of long-run unemployment and short-run employment fluctuations has not really been fulfilled. The attention of macroeconomists is now in large part focused elsewhere—on theories of efficiency wages (discussed in Chapter 7) and on theories that emphasize the goods market (see Chapter 14). ADDITIONAL CASE STUDY 7-9 The Two Views of Unions The discussion of unions in the textbook focuses on the fact that they may use their bargaining power to raise wages above the competitive level, giving rise to unemployment. Union members—insiders—benefit from the higher wages, but those not protected by unions—outsiders—suffer because of the consequent unemployment. This view of unions stresses that unions, through their monopoly power, distort the price system and lead to misallocation of resources. Such a view of unions is incomplete because it ignores the fact that unions may make positive contributions to the workplace and to society. Labor economists Richard Freeman and James Medoff suggest that unions’ ability to improve employer–employee communications and hence productivity and efficiency counterbalances their adverse monopoly effects. Unions provide a collective voice that allows workers to communicate and discuss working conditions or other problems with management. As such, they can help reduce quit rates, improve morale, and encourage more efficient production. Economic analysis, Freeman and Medoff note, emphasizes market responses to problems. If you get poor service from a store, you go elsewhere; if you don’t like your job, you quit. An alternative approach is to discuss and attempt to correct problems, by complaining to the store manager or communicating with management. Individuals’ incentives to address problems in the workplace are limited by free-rider problems (it may not be worth an individual’s time to seek improved safety, even though all workers would benefit from it) and fear of job loss. Unions, by providing collective bargaining, facilitate communication between workers and management. The overall effects of unions on the economy are hard to evaluate. Freeman and Medoff make a strong case, however, that it is misleading to focus solely on the undesirable monopoly effects of unions and indeed conclude, “If our research findings are correct, the ongoing decline in private sector unionism … deserves serious public attention as being socially undesirable.” ADVANCED TOPIC 7-10 Efficiency Wages I: The Solow Condition Suppose that a firm has a production function Y = F(K, E × L), where E represents the efficiency (perhaps effort) of labor. Efficiency-wage theories suggest that E may depend on the real wage. To keep things simple, suppose that the price level (P) equals 1, so the real wage simply equals the nominal wage (W). Thus, we have E = E(W). Suppose also that the capital stock is fixed (K = K ). The firm wishes to maximize profit: Profit = F( K , E(W)L) – WL. (Note that F( ) equals the firm’s revenue since P = 1.) Whereas we previously thought about the firm as simply choosing the quantity of labor, we now think about the firm choosing both W and L. The firm recognizes that a higher wage makes its workers more productive. Think first about the wage the firm would want to set. If it raises the wage a little bit, each worker will work a little bit harder. Call the amount of extra effort brought forth by a $1 increase in the wage the marginal effort (ME = ∆E/∆W). Since each worker will work harder, the total change in labor, measured in effective workers, is equal to ME × L. To get the extra output that this implies, we must multiply by the marginal product of labor. Thus, the extra revenue brought forth by a $1 increase in the wage equals MPL × ME × L. Increasing the wage, though, also increases the firm’s costs. If the wage is increased by $1, the firm’s costs will rise by $L. By now we are familiar with the idea that the firm will want to increase the wage until the extra benefit just matches the extra cost: MPL × ME × L = L ⇒ MPL × ME = 1. Now, think about the firm’s choice of labor. An extra worker will increase revenue by an amount equal to average effort times the marginal product of labor. An extra worker will increase costs by an amount equal to the wage. Thus, the optimal amount of labor is given by: MPL × E = W. Dividing by E, we find that MPL = W/E. Substituting into the earlier result, we obtain: (W/E)ME = (W/E)(∆E/∆W) = (∆E/E)/(∆W/W) = 1. The firm thus will want to choose the wage such that the elasticity of effort with respect to the wage equals 1. This is known as the Solow condition. The resulting wage is the efficiency wage W*. Once the firm has found this wage, it then chooses employment such that the marginal product of labor equals the wage. The key point about this is that wages and employment are no longer determined in the labor market by demand and supply conditions. The firm, given an effort function and a production function, chooses W and L optimally. If we add up the employment by all firms in the economy and find that total employment is less than labor supply—that is, if L* E. It is possible that the efficiency wage, although higher than E, would still be below the marketclearing wage, in which case there would be no implications for unemployment. But it is also possible that, to prevent its workers from shirking, the firm will have to pay a wage above the market-clearing level. Figure 2 shows how this generates the possibility of unemployment: L′ < L . Note that increases in b or decreases in q increase the efficiency wage and so increase unemployment. For example, a decrease in q means that firms become less capable of monitoring their workers, and so shirking becomes a more attractive option. An increase in b means the worker is more likely to lose his job whether or not he shirks and, therefore, is less worried about being caught shirking. This is actually a drastically simplified version of the Shapiro–Stiglitz model. Without going into details, the more general model also has the possibility that people will be reemployed if they are fired. Firms will bid up the wage in an attempt to make it costly to shirk—if they are paying a higher wage than other firms, workers won’t want to lose their jobs. Of course, every firm cannot pay a wage above the average. But as the wage gets bid up, this generates unemployment, which generates another cost to shirking—if you are caught, you will have to spend some time unemployed. Unemployment serves as a worker-discipline device. The main change this makes to the model is that the NSC schedule is now upward sloping, as shown in Figure 3. Shapiro and Stiglitz show that the equilibrium level of employment in this model is below the social optimum. In extensions of this model, it can be above or below the socially efficient level, but it won’t be optimal in general. One point worth remembering is that, in this model, we wouldn’t actually observe any shirking. Firms are aware of the threat that workers may shirk, but the actions that they take ensure that workers in fact choose not to shirk. Accordingly, the fact that we don’t see many layoffs as a result of shirking in the real world is not evidence against the theory. One objection to the theory does deserve some notice. With sufficient imagination, it may be possible to devise other ways around the shirking problem. The most popular suggestion is known as bonding. The idea is that workers could be made to post a bond with the firm when they are hired. If they were then caught shirking, they would forfeit the bond. The threat of losing the bond would serve as a replacement for the threat of being unemployed, so workers would choose not to shirk even at full employment. An initial reaction to this idea is that we don’t see such agreements. But, in fact, there may be institutions in place that work in such a manner. An example is that workers may initially be paid less than their marginal product, with an implicit promise that they will be rewarded with higher wages when they are more senior. The bonding idea is not without its own problems. Firms would have an incentive to cheat—to claim that workers were shirking, fire them, and take the money. More ingenious contracts still might find a way around this problem. The extent to which bonding lowers the incentive to shirk is an open question. ADDITIONAL CASE STUDY 7-12 Efficiency Wages and Wage Differentials One piece of evidence that supports efficiency-wage theory is that wages vary across industries. Numerous researchers have documented the presence of such wage differentials. For example, Alan Krueger and Lawrence Summers look at data on individuals working in different industries. They attempt to explain workers’ wages on the basis of workers’ characteristics in the manner suggested by human capital theory. That is, they use variables such as education, age, occupation, and union membership; a number of demographic variables such as race, gender, marital status, and region of the country; and a number of other interaction variables. They then look to see whether, after they control for all these effects, systematic differences in wages in different industries still exist. They do. Table 1 reports the Krueger–Summers results for one-digit industries based on the 1984 census. The numbers indicate the differential attributable to a particular industry as a percentage of the average differential. For example, a worker in the construction industry earned 10.8 percent more than the average worker of similar ability and background. Table 1 Industry Differential (1984) Construction 0.108 Manufacturing 0.091 Transportation and public utilities 0.145 Wholesale and retail trade –0.111 Finance, insurance, and real estate 0.055 Services –0.078 Mining 0.222 Source: Based on Table 1 in A. Krueger and L. Summers, “Efficiency Wages and the Interindustry Wage Structure,” Econometrica 56 (March 1988): 259–293. These findings tell us that there are industry-specific differences in wages that cannot be explained by standard variables. Such results are at best indirect evidence in support of efficiency wages; they certainly do not “prove” that efficiency-wage models are a good description of the labor market. Krueger and Summers discuss the possibility that these wage differentials might be the result of differences in labor quality not captured by their human capital variables or differences in job attributes (some jobs may be less pleasant and so require the payment of compensating differentials). They do not, however, believe that such effects explain the data. Their conclusion is that a competitive view of the labor market cannot explain interindustry wage patterns, and so we need theories that explain why firms might pay wages that differ from their competitive level. Efficiency wages provide such a theory. There is still relatively little evidence that bears directly on efficiency-wage theories. A recent study by Alan Krueger is an exception. One explanation of efficiency wages suggests that firms will want to pay higher wages when they have difficulty monitoring workers’ performance. Krueger compared the wages paid by company-owned fast-food restaurants and those operated by franchisees. Presumably, a manager of a franchise has stronger incentives to monitor workers’ performance since his own return depends directly on the performance of the enterprise. Monitoring is likely to be more difficult at company-owned outlets; survey evidence confirms this. As efficiency-wage models would predict, wages are indeed higher at company-owned restaurants. Finally, William Dickens, Lawrence Katz, Kevin Lang, and Lawrence Summers have provided evidence that firms do spend considerable resources on the monitoring of employees. They note that employee crime is a problem: “Employee theft is believed to transfer between $15 and $56 billion per year from businesses to their workers and to account for between 5 percent and 30 percent of business failures each year.” They also cite survey evidence revealing that “U.S. businesses spend approximately $12 billion a year on security products, personnel, and services, and that a major concern in budgeting these expenditures is the control of employee crime” and also that “a group of 168 large retailers spent an average of 0.42 percent of sales on security and loss prevention in 1985 and that employee theft was the largest component of inventory losses these expenditures attempted to control.”7 It is apparent, in other words, that employee crime is important and that firms’ efforts to monitor workers are significant. These observations provide strong support for the underlying motivation of many efficiency-wage models. CASE STUDY EXTENSION 7-13 More on Henry Ford Daniel Raff and Lawrence Summers place Henry Ford’s decision to institute a $5 day in the context of Ford’s adoption of assembly-line manufacture. The resultant specialization made workers’ tasks more and more routine and menial. Perhaps as a consequence, employee turnover at the Ford Motor Company in 1913 reached 370 percent per annum: Ford hired over 50,000 workers that year, although the average work force was under 14,000. Over 7,000 workers left Ford in March of that year alone. Another interesting detail is that Percival Perry, an associate of Ford’s who opened Ford’s original British plant, instituted a similar doubling of pay prior to Ford’s decision, based on an effort to cover subsistence for a worker’s family. He recounted the productivity benefits to Henry Ford in 1912. The new wage package instituted in January 1914 raised wages from $2.34 to $5 and cut the working day by an hour to eight hours. Only men over age 22 who had worked for Ford for over six months were eligible. Ford also restricted eligibility to those that they were satisfied would “not debauch the additional money” received.2 A substantial majority of workers did indeed receive the $5 a day pay. The evidence clearly suggests that Ford was paying a wage above the market-clearing level, since long lines for jobs developed. Literally thousands of applicants sought positions at Ford. Quit rates fell dramatically, and the turnover rate fell to about 50 percent in 1914 and under 20 percent in 1915. Ford’s profits improved, despite the cost of the program. CASE STUDY EXTENSION 7-14 More on the Duration of Unemployment The median duration of unemployment measures one facet of the severity of unemployment. The median is the point that splits the distribution of unemployment duration in half. For example, in December 1998, half of all unemployed individuals had been without a job for 6.8 weeks or less, and half had been without a job for 6.8 weeks or more. Figure 1 shows the unemployment rate and the median duration of unemployment over the past five decades. The unemployment rate exhibits a cyclical pattern—rising during economic contractions and falling (with a slight lag) during expansions. The median duration of unemployment has closely followed the path of the unemployment rate throughout most of this period. During the expansion of the 1990s, however, the duration of unemployment exhibited a clear break from this pattern. While the unemployment rate declined steadily after peaking at 7.8 percent in June 1992, the median duration of unemployment remained stuck at about eight weeks for nearly five years before declining to about six weeks by the turn of the century. Why didn’t the duration of unemployment fall in conjunction with the decline in the unemployment rate from mid-1992 through the end of 1997? What accounts for the drop in duration after September 1997? The answers to these questions can be found by examining more detailed statistics on the duration of unemployment. The Bureau of Labor Statistics provides data on the number of individuals who have been unemployed for less than 5 weeks, 5 to 14 weeks, 15 to 26 weeks, and 27 or more weeks. When the economy is expanding, it becomes easier to find a job, and when the economy is contracting, it takes longer to find a job. Thus, the percentage of the unemployed who have been without jobs for less than 5 weeks generally falls during a recession and rises during an expansion while the percentage of the unemployed who have been out of work for 15 weeks or more follows the opposite pattern. Source: Department of Labor, Bureau of Labor Statistics. During most of the expansion of the 1990s, the long-term unemployed as a percentage of total unemployment showed only a slight downward trend, causing the stickiness in the duration of unemployment. Not until late 1997 did the number of long-term unemployed begin a significant decline, leading to the drop in the median duration of unemployment. The decline in the duration of unemployment does not necessarily imply that the long-term unemployed found jobs. It is possible that an increasing number of these job seekers became discouraged and dropped out of the labor force. However, the number of individuals who were not in the labor force because of discouragement over their job prospects actually fell during the late 1990s. Thus, the data provide some support for the notion that the longer-term unemployed were finding jobs. Although median duration did decline in the late 1990s, it remained above levels reached during earlier economic expansions. And when the economy headed into recession in 2001, median duration once again rose in line with increasing unemployment. By 2005, with economic recovery well underway, the unemployment rate continued to head downward, accompanied by declining duration. As in the recovery of the late 1990s, however, duration remained above the level typically seen several years into an economic expansion. With the economy heading back into recession during 2008, unemployment began to climb sharply once more, and the duration of unemployment moved up as well. As discussed in the text, the rise in duration during the recession of 2008–2009 was unprecedented and was viewed by some economists as resulting from the generous expansion of unemployment insurance benefits by Congress in early 2009. But other economists disputed this view, pointing out that the number of unemployed far exceeded available jobs. The reason why duration increased so sharply remains unclear. With unemployment falling as the economic recovery gradually gained speed, median duration fell sharply from 2012 to 2014. But at over 12 weeks, it still remained at a level previously seen only in recessions. LECTURE SUPPLEMENT 7-15 Trends in Unemployment The average unemployment rate in the United States has fluctuated over the past few decades, from less than 5 percent in the 1950s and 1960s to more than 6 percent in the 1970s and 1980s, and back to less than 5 percent in the 1990s and 2000s. Three possible explanations for these fluctuations are demographic changes, sectoral shifts, and changes in productivity growth. The entrance of the baby-boom generation into the workforce in the 1970s and 1980s lowered the average age of the workforce, which would tend to increase the unemployment rate. As the baby-boom workers aged, the average age of the workforce declined, reversing the rise in the unemployment rate. Sectoral shifts focus on the volatility in oil prices during the 1970s and 1980s. This volatility required the reallocation of workers between more-energy-intensive and less-energy-intensive industries, leading to increased unemployment. As oil prices became more stable in the 1990s, the unemployment rate fell. Finally, the slowdown in productivity growth during the 1970s and the pickup in productivity growth during the 1990s and 2000s could have affected the natural rate of unemployment. Although long-run trends in real wages reflect long-run trends in productivity, workers may be slow to adjust the real wage that they ask from their employers. As a result, a slowdown in productivity during the 1970s reduced labor demand (employers respond without delay!) and led to a rise in unemployment because real wages were slow to adjust. Likewise, the step-up in productivity during the 1990s led employers to demand more labor, and with real wages slow to adjust, unemployment would have fallen. See related discussion in Supplement 14-8, “Did the NAIRU Decline in the 1990s?” ADDITIONAL CASE STUDY 7-16 The Secrets to Happiness Why are some people more satisfied with their lives than others? This is a deep and difficult question, most often left to philosophers, psychologists, and self-help gurus. But part of the answer is macroeconomic in nature. Recent research has shown that people are happier when they live in a country with low inflation and low unemployment. From 1975 to 1991, a survey called the Euro-Barometer Survey Series asked 264,710 people living in 12 European countries about their happiness and overall satisfaction with life. One question asked, "On the whole, are you very satisfied, fairly satisfied, not very satisfied, or not at all satisfied with the life you lead?" To see what determines happiness, the answers to this question were correlated with individual and macroeconomic variables. Other things being equal, people are more satisfied with their lives if they are rich, educated, married, in school, self-employed, retired, female, or either young or old (as opposed to middle-aged). They are less satisfied if they are unemployed, divorced, or living with adolescent children. (Some of these correlations may reflect the effects, rather than causes, of happiness; for example, a happy person may find it easier than an unhappy one to keep a job and a spouse.) Beyond these individual characteristics, the economy's overall rates of unemployment and inflation also play a significant role in explaining reported happiness. An increase in the unemployment rate of 4 percentage points is large enough to move 11 percent of the population down from one life-satisfaction category to another. The overall unemployment rate reduces satisfaction even after controlling for an individual's employment status. That is, individuals employed in a high-unemployment nation are less happy than their counterparts in a low-unemployment nation, perhaps because they are more worried about job loss or perhaps out of sympathy with their fellow citizens. High inflation is also associated with lower life satisfaction, although the effect is not as large. A 1.7percentage-point increase in inflation reduces happiness by about as much as a 1-percentage-point increase in unemployment. The commonly cited “misery index,” which is the sum of the inflation and unemployment rates, apparently gives too much weight to inflation relative to unemployment. LECTURE SUPPLEMENT 7-17 Additional Readings The study of the labor market is an important subdiscipline of economics, and as a result there are a number of good textbooks available on the topic. See, for example, Daniel Hamermesh and Albert Rees, The Economics of Work and Pay (New York: HarperCollins, 1988). A recent survey of theories of unemployment, including an extensive discussion of search theory, is C. Davidson, Recent Developments in the Theory of Involuntary Unemployment (Kalamazoo, Mich.: Upjohn Institute, 1990). The minimum wage is discussed in C. Brown, “Minimum Wage Laws: Are They Overrated?” Journal of Economic Perspectives 2, no. 3 (Summer 1988): 133–45. A recent survey of the economic effects of a minimum wage is John Kennan, “The Elusive Effects of Minimum Wages,” Journal of Economic Literature (December 1995): 1950–65. The Spring 1988 issue of the Journal of Economic Perspectives contains a symposium on “Public and Private Unionization,” with papers by Edward Lazear, Richard Freeman, and Melvin Reder that address the decline in private sector unionism since the 1950s. A sympathetic portrayal of the role of unions can be found in R. Freeman and J. Medoff, What Do Unions Do? (New York: Basic Books, 1984). Many of the important papers on efficiency wages are collected in G. Akerlof and J. Yellen, eds., Efficiency Wage Models of the Labor Market (Cambridge, Mass.: Cambridge University Press, 1990). The introduction to this volume clearly sets out the main issues in the literature and makes a case for the importance of efficiency wage theories. Three symposia in the Journal of Economic Perspectives address the position in the labor market, and more generally the economic status, of women (Winter 1989, Fall 2000) and African-Americans (Fall 1990). Another symposium in the same journal discusses European unemployment (Summer 1997). CHAPTER 8 Economic Growth I: Capital Accumulations and Population Growth Notes to the Instructor Chapter Summary These next two chapters present the Solow growth model. Although they are two of the more difficult chapters in the book, they cover material that students usually find interesting. Chapter 8 proceeds by first holding population and technology constant and showing how the rate of saving determines the steady-state capital–labor ratio. The chapter then discusses the positive and normative implications of the Golden Rule level of accumulation. Following this, the model is expanded to consider population growth. The purpose of the chapter is to teach students about some of the determinants of economic well-being and to offer some explanations of international differences in living standards. The three sections of the chapter teach the following lessons: 1. The rate of saving determines the size of a country’s capital stock. Increases in the saving rate lead to temporarily higher growth and a permanently higher level of capital and output. 2. Because the U.S. economy has less capital than at the Golden Rule, raising consumption of future generations entails a sacrifice of consumption by current generations. 3. High population growth reduces steady-state income per worker because it is hard to maintain high capital per worker when the number of workers is growing quickly. Comments Teaching all the material in Chapters 8 and 9 will probably require three to four lectures. An abridged version of these chapters (presenting the basic model of the determination of the capital stock and discussing population growth and technological progress informally) could be presented in one to two lectures. Supplements 8-9 and 9-7 present notes to aid such a presentation. The lecture notes emphasize the connections between the Solow growth model and the classical model of Chapter 3 wherever possible, reminding students that the economic forces discussed in the classical model are still operative (for example, the real interest rate is still the equilibrating mechanism in the loans market). The lecture notes distinguish carefully between the steady-state capital stock and the Golden Rule, emphasizing that the latter concerns only the technological possibilities of the economy, whereas the former depends on people’s behavior (their saving decisions). Since economic growth is intrinsically one of the more difficult topics covered in the textbook, it can be a challenge even to very able students. The following are some common difficulties students encounter with the material in this chapter and ways to overcome them. 1. Interpreting a Dynamic Model The Solow growth model is likely to be the first dynamic model that many economics students encounter. It is worth explaining the idea of a dynamic model and making sure that students are comfortable with time-series graphs. Students need to grasp the difference between levels and 179 growth rates; they should also understand the meaning of a steady state and the basic concept of a differential equation. 2. Confusion Between the Population and the Labor Force Students are sometimes troubled by the fact that the Solow model uses the terms population and labor force more or less interchangeably. It may be useful to refer back to Chapter 2 of the text and to make the explicit assumption that the labor-force participation rate is constant. An alternative—if somewhat outdated—approach is to discuss the model in terms of households with one worker per household. 3. The Transition from F(K, L) to f (k) Students sometimes have difficulty understanding the analysis of the Solow model in terms of the intensive form production function. I assure students that this is just a useful simplification that makes graphical analysis easier and that there is no trickery involved! Supplement 8-9 presents notes framed solely in terms of the familiar production function and so could be used to avoid the problem entirely. 4. The Meaning of the Long Run My students have told me that the material in the Instructor’s Resources on the subject of the long run (Supplements 3-1 and 8-1) is helpful; I suggest handing these out to students. In addition, discussing the decomposition of output into trend and cycle helps illustrate these ideas; the MacroBytes material on the Web site is useful for this purpose. 5. The Connection Between the Solow Model and the Classical Model Related to point 3, students may have difficulty seeing the connections between the models in Chapter 3 and those in Chapters 8 and 9. I pay attention to the fact that we use the conclusions from Chapter 3 when setting up the model in Chapter 8. It is also worth reiterating that saving includes both private and government saving; Supplements 3-6 and 8-4 may be helpful (see also Supplement 17-1). Remember also that the chapters on the Solow model are somewhat self-contained and can certainly be taught later in the course. 6. The Algebra of Growth Rates Students may find the Solow model confusing if they do not understand the simple algebra of growth rates. I suggest reviewing this material and referring students to the FYI section in Chapter 2 of the textbook on products and percentage changes. Supplement 8-5 may help as well. 7. Why Population Growth Reduces the Capital–Labor Ratio by nk The presence of the nk term in the equation governing the evolution of the capital–labor ratio can trouble students. The simplest formal derivation of this term is probably as follows: Since k = K/L, we can use standard results on growth rates to write ∆k/k = ∆K/K – ∆L/L. Since ∆L/L = n, we write ∆k/k = ∆K/K – n; multiplying by k yields ∆k = (∆K/K)k – nk. (Note that we have now obtained the term that tends most to confuse students.) Using k = K/L, we have ∆k = ∆K/L – nk, and we obtain the equation in the text by noting that ∆K = sF(K, L ) – δK ⇒ ∆K/L = sf (k ) – δk. 8. Confusion Between the Steady State and the Golden Rule This is one of the biggest problems that students encounter. I suggest the following remedies: (a) Downplay the discussion of the Golden Rule, perhaps presenting it less formally after the analysis of population growth and technological progress, as in Supplement 9-7. (b) Stress the technological nature of the Golden Rule—it can be defined independently of any behavioral assumptions. (c) Make sure that students understand the difference between f (k) and sf (k) in the graphical analysis. Use of the Web Site The chapter exercises on the Solow growth model can seem a little intimidating to the students at first, so it may be a good idea to focus some attention just on steady states. For example, students could graph combinations of population growth rates and saving rates that keep output per worker constant. Since the Solow growth model can seem abstract to students, another idea is to calibrate the model roughly to the U.S. economy and then ask questions about the long-run effects of changes in saving rates such as those observed in the 1980s. The Web-based software can be used to look at the Golden Rule and to show that the Golden Rule is achieved as a steady state when the saving rate equals capital’s share. For a very difficult question, one can use the fact that k is the only steady-state variable in the model, so it is possible to consider a change in exogenous parameters in the middle of a transition path by finding the value of k and then resetting the initial parameters to give that value. For example, one could ask the following question: Consider a country in steady state with n = 0.01 and s = 0.1. Policymakers want to double output per worker over the next 20 years and then keep it constant at the new level. What changes in the saving rate now and in 20 years’ time are needed? Use of the Dismal Scientist Web Site Use the Dismal Scientist Web site to download annual data for the U.S. population 16 years and older since 1950. Also, download annual data for real disposable personal income over the same time period. Compute the growth rate of per-capita income on average over each decade (1950s, 1960s, etc.). Discuss changes in the growth rate of per-capita income over these decades. Chapter Supplements This chapter contains the following supplements: 8-1 How Long Is the Long Run? Part Two 8-2 Growth Facts 8-3 Does the Solow Model Really Explain Japanese Growth? (Case Study) 8-4 The Decline in the U.S. Saving Rate 8-5 Growth Rates, Logarithms, and Elasticities 8-6 Labor-Force Participation 8-7 Bridge Jobs and the Transition to Retirement 8-8 How Much Variation in Per-Capita Output Is Explained by s and n? (Case Studies) 8-9 The Solow Growth Model: An Intuitive Approach—Part One 8-10 Additional Readings Lecture Notes Introduction Having analyzed the overall production, distribution, and allocation of national income, we now Supplement 8-1, consider the determinants of long-run growth. One stylized fact of macroeconomics is that, in “How Long Is the developed economies, output grows over time. This growth is irregular and is sometimes Long Run? Part interrupted by periods of falling output (recessions), but the overall trend is indisputably upward. Two” Real GDP in the United States has tripled over the last 50 years, and per-capita real GDP has Supplement 8-2, “Growth Facts” more than doubled. Looking at the economic performance of different countries, it is also evident that different countries enjoy very different standards of living. Traditionally, macroeconomics analyzes the behavior of output in terms of both its overall Table 8-1 upward trend and the fluctuations around that trend. The fluctuations around the trend are known as the business cycle. Much of macroeconomics is devoted to understanding these short-run changes; we turn to them later on. But macroeconomists are also keen to understand the growth of the natural rate of output in the long run. Our model of economic growth is known as the Solow growth model and is an explicitly dynamic analysis that shows how the growth of output is affected by saving, population growth, and technological progress. This chapter analyzes the role of saving and population growth while Chapter 9 examines the role of technological progress. 8-1 The Accumulation of Capital Our starting point is the production function: Y = F(K, L). From this equation, we see three possible sources of long-run output growth. First, the capital stock may increase over time. Second, labor employed may change over time, perhaps as population changes. Third, as discussed in the next chapter, the production function itself may change over time (technological progress). Our analysis of economic growth considers all of these factors but focuses primarily on the determination of the capital stock. While our previous analysis of national income fixed K at K, we now examine the long-run determination of K. For the present, we suppose no technological progress and no population growth. The Supply and Demand for Goods Suppose that the production function has constant returns to scale. [Recall that this means that, for any positive z, zF(K, L) = F(zK, zL).] If z = (1/L), Y/L = F(K/L, 1). That is, we can write the production function in per-capita terms and obtain a function of only Figure 8-1 one variable—the capital–labor ratio—rather than two. Let y = Y/L and k = K/L, and write this as y = f (k). As an example, the Cobb–Douglas function Y = (KL)1/2 becomes y = k1/2, and the more general Cobb–Douglas function Y = KαL1–α becomes y = kα. This way of writing the production function is mathematically simple and has the advantage of focusing our attention on output per person, which is a better measure of living standards than total output. Keep in mind, though, that it is just a useful trick; we could also carry out all the following analysis with the original production function and get the same answers. Just as in the analysis of Chapter 3, the marginal product of capital is important in this model; in this case, it tells us how much extra output per worker will be produced if capital per worker is increased: MPK = f (k + 1) – f (k). As in Chapter 3, we expect the marginal product of capital to decrease as the capital–labor ratio increases. The Solow model is a long-run version of our previous analysis of national income and, like that model, is based on equilibrium in the markets for goods and factors of production. For simplicity, we suppose that there is no government (G = T = 0). We write everything in percapita terms: c = C/Y; i = I/Y. We have equilibrium in the market for goods: y = c + i. We also have a simple consumption function: c = (1 – s)y. This model writes the consumption function in terms of the saving rate s. We immediately have the familiar result that investment equals saving (i.e., there is equilibrium in the market for loanable funds): i = sy = sf (k). Output is divided between consumption and investment. Although it is not explicit here, the real interest rate is adjusting to ensure that saving equals investment, and the wage rate and rental rate are adjusting to bring about equilibrium in the markets for factors of production, just as in the classical model of Chapter 3. Investment means that the economy is acquiring new factories, machines, houses, and so forth, Figure 8-2 Figure 8-3 which tends to increase the economy’s capital stock and allow for more production. But, at the same time, some of these machines and factories wear out and have to be replaced. This depreciation decreases the capital stock. If there were no investment at all, the capital stock would decline over time. We suppose that δ percent of the capital stock wears out each period, so if the capital stock at the start of the period is k, the depreciation during the period is δk. The rate of depreciation can be interpreted in terms of the lifetime of the typical piece of capital. If, say, the typical machine lasts for five years, then the depreciation rate is 20 percent (since a factory with 100 machines would have to replace an average of 20 every year). In general, the average lifetime of a piece of capital equals 1/ δ. For some types of capital, such as buildings, the depreciation rate might be very low (perhaps 1 percent to 2 percent), while for, say, personal computers, it would be much higher (perhaps 10 percent to 20 percent). We look at a situation where the economy is in a steady state, which entails finding a balance between the investment that is carried out in each period and the depreciation of the capital stock that occurs over time. The overall change in the capital stock is the net effect of new investment and depreciation: Growth in the Capital Stock in the Steady State ∆k = sf (k) – δk. The economy will be in steady state if the capital stock is constant: ∆k = 0. In this case, the only investment being undertaken is replacement investment. The equilibrium condition is just sf (k) = δk. This equation defines the steady-state value of k, which we call k*. We can work out an explicit example for the Cobb–Douglas case: y = k1/2. This means that in the steady state sk1/2 = δk ⇒ s = δk1/2 ⇒ s/δ = k1/2 For example, if people save 30 percent of their income and the depreciation rate is 10 percent, then the steady-state capital–labor ratio is (0.3/0.1)2 = 9. This illustrates two important and Figure 8-4 Table 8-2 intuitive results: Increases in the saving rate increase the steady-state capital–labor ratio, while increases in the depreciation rate decrease it. If k is at its steady-state value, it will not change. What happens if k is at some other value? The answer is that the steady-state equilibrium is stable, meaning that, if you start the economy from another point, it will tend to approach the steady state. Suppose that k δ, then increases in the capital–labor ratio will increase output by more than the required increase in depreciation, so consumption also increases. If MPK < δ, increases in the capital–labor ratio actually reduce sustainable consumption. The Golden Rule level of capital accumulation (k*gold) is where the marginal product of capital, net of depreciation, equals zero: MPK – δ = 0. Graphically, it is the point where the f (k) line is at the maximum distance above the δk line. Finding the Golden Rule Steady State: A Numerical Example Policymakers who wish to influence the marginal product of capital can enact policies aimed at influencing the saving rate. Suppose that, by means of appropriate tax policies, the government can effectively choose the saving rate. By an appropriate choice of s, it could place the economy at the Golden Rule. That is, it could choose s such that the steady state of the economy (k*) corresponded to the Golden Rule (k*gold). For example, if y = k1/2, then the Golden Rule occurs when s = 1/2. If the depreciation rate is 10 percent, then, at this equilibrium, k* = k*gold = 25; y = 5; and c = 2.5. The Transition to the Golden Rule Steady State Suppose that policymakers decide that they would like to move the economy to the Golden Rule. There are two possibilities: We start off either with more capital than at the Golden Rule or with less capital than at the Golden Rule. First, consider the less realistic case, where we have more capital than at the Golden Rule, so the saving rate is too high. Suppose that at time t0 the saving rate is suddenly reduced. To start, we have the same amount of output and we are saving less, so we are able to consume more immediately. Gradually, depreciation will start to eat into the capital stock, since it is now wearing out faster than we are replacing it. As this happens, output, and thus consumption, will fall. But, by the definition of the Golden Rule, consumption will be higher at the Golden Rule than it was before the change in the saving rate. Thus, consumption is higher at every point in time. If the economy is below the Golden Rule and policymakers want to move to the Golden Rule, they must increase the saving rate. Initially, this means that we have less output for consumption purposes. But initially, we do not get any benefit from the higher saving rate. The benefit comes about only gradually, as the capital–labor ratio increases. Thus, in the short run, consumption falls. Given that the U.S. economy is below the Golden Rule (as shown later), should policymakers be trying to encourage saving? If we increase the saving rate, the short-run consequence is a decline in living standards, since consumption must fall immediately, but output will grow only slowly over time. So we trade off lower consumption in the present for higher consumption in the future. It is not self-evident that this is desirable. Over time, people die and new generations are born. Current generations make the sacrifice, while future generations reap the benefit. The Golden Rule does not tell us the optimal level of capital accumulation but simply picks out one point of interest. Whether or not policymakers should encourage saving thus depends on how we weigh the relative interests of current and future generations. Since an infinite number of future generations would be made better off, it might seem worth the short-run sacrifice. But, conversely, history teaches that technological progress adds to economic growth, so continuing improvements in technological progress are likely to make future generations better off anyway. The debate about economic growth is thus more subtle than casual reading of the newspapers would indicate. It is not self-evident that we want to encourage economic growth; our decisions on desirable levels of growth must be motivated in part by considerations of intergenerational distribution. 8-3 Population Growth The Solow model teaches us that we cannot explain sustained economic growth in terms of growth in capital per worker since the economy will tend toward a steady state where capital per worker is constant. We now consider population change as a possible explanation of sustained economic growth. We will assume a population growth rate equal to n. For example, if n = 0.02, then the population increases by 2 percent every year. If it is 100 million one year, it will be 102 million the next year. If it is 250 million this year, it will be 255 million next year. The Steady State With Population Growth The difference this makes to the model is that the change in the capital stock becomes ∆k = i – δk – nk, since population growth decreases the amount of capital per worker, other things being equal. To keep the capital–labor ratio constant, we not only need investment to replace depreciated capital, we also need investment with which to equip new workers; we need to supply the n new workers with k units of capital each. So the steady-state capital stock is now defined by i = sf (k) = (n + δ)k. With this one change, our analysis proceeds much as before. Graphically, we simply look for the Figure 8-11 intersection of sf (k) with (n + δ)k. The Effects of Population Growth Supplement 8-5, We now have an explanation for steady-state growth absent from the first version of the Solow “Growth Rates, Logarithms, and model. If population is growing, then in the steady state we will observe output and the capital Elasticities” stock also growing at the rate n. (Recall that the production function is constant returns to scale, which means that if K is growing at the rate n and L is growing at the rate n, then Y must also be growing at the rate n.) Population Growth = 0 Population Growth = n L is constant L grows at rate n K is constant K grows at rate n k is constant k is constant y is constant y is constant Y is constant Y grows at rate n Population growth is another possible cause of income differences across countries. The Figure 8-12 Solow growth model predicts that, other things equal, countries with higher rates of population Supplement 8-6, “Labor Force growth will have lower steady-state capital–labor ratios. Participation” The introduction of population growth also alters the Golden Rule. Where previously our condition for the Golden Rule was MPK – δ = 0, it now becomes MPK – δ = n. Supplement 8-7, “Bridge Jobs and Case Study: Population Growth Around the World the Transition to Retirement” International comparisons provide some evidence to support the prediction of the Solow model that output and population growth are negatively related. But as in the earlier case study, the data do not determine causality. While low population growth is associated with high income, we cannot rule out that it is high income that reduces fertility rather than the reverse. Figure 8-13 Alternative Perspective on Population Growth Supplement 8-8, “How Much Population growth may have additional effects beyond its interaction with capital accumulation. Variation in Per- Capita Output Is Malthus, who lived in the late 1700s and early 1800s, argued that population grows at a Explained by s geometric rate while food production grows at an arithmetic rate, implying that humankind is and n? destined to live in poverty. He failed to recognize that technological advance would more than Supplement 8-9, offset population growth. Indeed, today only 2 percent of Americans work on farms but still “The Solow manage to produce more than enough food to feed the nation. Recent work by Michael Kremer Model: An Intuitive Approach—Part has suggested that population size itself affects positively the speed of technological advance. He One cites historical evidence showing that large populations generate more ideas and thus more rapid technological change. 8-4 Conclusion The Solow model, as developed in Chapter 8, shows how saving and population growth determine an economy’s long-run capital stock and level of income per person. The next chapter introduces technological progress to the Solow model to explain the steady-state growth in income per person. LECTURE SUPPLEMENT 8-1 How Long Is the Long Run? Part Two In the Solow growth model of Chapters 8 and 9, the time horizon of the model is very different from the classical model of Chapter 3. The classical model considers a snapshot of the economy at a point in time (under the assumption that prices have adjusted to clear markets). The Solow growth model, by contrast, attempts to explain the behavior of economies over many decades. Of particular note in that model is the behavior of the capital stock through time. The capital stock is a slow-moving variable—changes in the capital stock entail the building of new factories, new machines, new houses, and the like. A period of just a few years might well then be called the short run in the context of the Solow model, for it may take many, many years for the economy to adjust to its steady-state equilibrium. In fact, in discussions of the Solow growth model, the term “long run” is usually reserved for the case when the economy has reached steady state. The long run might then be measured in decades, not years, and referred to more accurately as the “very long run.” ADDITIONAL CASE STUDY 8-2 Growth Facts Ideally, we would like a model of economic growth that can explain why economies grow and why growth experiences differ so much from country to country and from time period to time period. Stephen Parente and Edward Prescott have cataloged four basic stylized facts of growth that we wish to explain. Growth Fact Number 1 There is great income disparity among nations. This is illustrated in Figure 1, which shows that the five poorest countries in the world possess per-capita GDP that is consistently equal to about 3 percent of U.S. GDP per capita. This is roughly comparable to the difference in income between the most productive and least productive workers in the United States. Source: Figures 1–5 from S. Parente and E. Prescott, “Changes in the Wealth of Nations,” Federal Reserve Bank of Minneapolis Quarterly Review 17 (Spring 1993): 3–16. Growth Fact Number 2 The evidence is mixed on whether this disparity in income is increasing or decreasing over time. If we look at the range for the last few decades, as illustrated in Figure 1, there seems to be little change over time. If we look at the standard deviation of the log of per-capita output, which provides another measure of income dispersion, there is some slight evidence of increased disparity since 1960 (Figure 2). The picture is different for different regions of the world: While income disparity has hardly changed in western Europe over the last 120 years, there has been a dramatic increase in income disparity in Southeastern Asia (Figure 3). Growth Fact Number 3 Almost all countries are getting richer. Figure 4 shows the change in per-capita GDP of the five richest countries, the five middle countries, and the five poorest countries, between 1960 and 1985. Each group experienced significant growth over this period, although there has been some slowdown recently. Note that the five poorest countries were not the same over this period. In 1960, Tanzania, Ethiopia, Uganda, Burma, and Lesotho were the poorest countries in the world. In 1985, Burma and Lesotho had been replaced in this group by Mali and Zaire. Growth Fact Number 4 While most countries grew between 1960 and 1985, some grew at very rapid rates, while others grew much more slowly. A few countries experienced declines. Figure 5 shows the distribution of annual growth rates of income per capita for this period, expressed relative to the United States. The United States grew at about 2.0 percent per annum over this period. All countries that grew at a relative rate of –2.0 or greater thus experienced absolute increases in income. Of the 102 countries in Parente and Prescott’s data set, all but 15 grew. Most of these were in sub-Saharan Africa. At the other end of the distribution, countries like Taiwan and Lesotho experienced annual growth rates of real per-capita GDP of about 6 percent or more. (Recall that Lesotho was one of the five poorest countries in 1960.) Countries, therefore, move around in the distribution of income over time. Typically, however, richer countries have outperformed poorer countries somewhat. If we divide the set of countries into two equal groups based on their income in 1960, we find that about two-thirds of those below the median grew more slowly than the United States, while about two-thirds of those above the median grew more quickly than the United States. While the Solow model is a great aid to our thinking about economic growth, it cannot explain all of these growth facts. Building models that are consistent with all of these observations is one of the most challenging problems in macroeconomics. CASE STUDY EXTENSION 8-3 Does the Solow Model Really Explain Japanese Growth? Lawrence Christiano has questioned whether postwar Japanese growth and saving behavior is well explained by a simple growth model. He looks at the behavior of a growth model that is similar to the Solow model, except that consumption and saving decisions are derived explicitly from optimizing decisions of households (in contrast to the Solow model, which makes the simpler assumption that the saving rate is constant). This extra complication is necessary because Christiano wants to try to explain changes in saving behavior through time. He assumes that the economy suffers a major one-time reduction in its capital stock and looks to see whether or not the predicted behavior of such a model matches the Japanese experience. Christiano’s main conclusion is that it does not; in particular, the Japanese saving rate is hump-shaped and peaked in 1970, whereas the growth model predicts that it should peak immediately after the shock and fall thereafter. A modified version of the model, which recognizes that very high saving might be unlikely if people are near subsistence consumption, matches the data better, however. Figures 1, 2, and 3 show the predictions of the standard model and the modified (slow convergence) model, as well as actual Japanese data. Source: Figures 1, 2, and 3 are from L. Christiano, “Understanding Japan’s Saving Rate: The Reconstruction Hypothesis,” Federal Reserve Bank of Minneapolis Quarterly Review 13 (Spring 1989): 15. ADDITIONAL CASE STUDY 8-4 The Decline in the U.S. Saving Rate Figure 1 shows personal saving as a percentage of disposable personal income since 1960. From the early 1960s through the mid-1970s, the personal saving rate fluctuated between about 10 percent and 13 percent, and it showed an upward trend. In the late 1970s, however, the saving rate began a decline that accelerated in the late 1990s and early 2000s, bringing the rate to 2.5 percent by 2005. Many commentators have pointed to the plummeting saving rate in recent years as a possible cause of concern. The Solow growth model explains why this is a source of such concern. A lower saving rate translates, in the long run, into a lower capital–labor ratio and hence lower output per capita. Decreased saving permits increased consumption today, but at a cost of lower consumption in the future. More recently, the personal saving rate has increased somewhat, probably in response to the sharp drop in household net worth, which in turn resulted from declining home prices and a plunging stock market. Whether this might also represent a turnaround in the trend for the saving rate, however, remains to be seen. Note: Data are personal saving as a percentage of disposable personal income. Source: U.S. Department of Commerce, Bureau of Economic Analysis. Personal saving is only part of the story. Government saving fell in the 1980s (i.e., the government deficit increased). Thus, both the government’s fiscal policies and individuals’ consumption/saving decisions contributed to a fall in national saving, from over 23 percent of national income in the late 1970s to under 18 percent of national income in the early 1990s. As the government deficit shrank and turned to surplus, national saving rose to over 20 percent of national income by 2000. Recently, as the budget deficit has reemerged, public saving has fallen, accompanying the decline in personal saving. The relationship between personal and government saving is also noteworthy because of an idea called Ricardian equivalence, which is discussed in Chapter 19 of the textbook. Briefly, this theory suggests that increased dissaving by the government might be offset by increases in private saving. In this case, the government’s fiscal policy actions would have a much smaller impact on the economy. The data from the 1980s and 2000s do not seem consistent with this theory, but the data from the 1990s are more supportive. ADVANCED TOPIC 8-5 Growth Rates, Logarithms, and Elasticities Whenever we wish to understand the behavior of variables through time, such as when we are interested in economic growth or inflation, we need to make use of growth rates. The following is a brief summary of the mathematics of growth rates and the two related ideas of logarithms and elasticities. Why We Use Growth Rates When an economic variable increases through time, it is often misleading simply to consider its absolute change. For example, an increase in GDP from $5 trillion to $5.1 trillion is surely very different from an increase in GDP from, say, $1 trillion to $1.1 trillion, even though the increase in each case is $100 billion. In the first case, the $100 billion increase represents a 2 percent increase; in the second case the same increase in dollar terms represents a 10 percent increase. As another example, when we analyze inflation, we are really interested in both the determination of the price level at a point in time and in the determination of the change in the price level through time—in other words, the inflation rate. Suppose, for example, that the time series for the GDP deflator looked like this: Time Price Level (P) Inflation Rate (π) 1 2 3 4 5 6 . . . 41 42 100 110 120 130 140 150 . . . 500 510 0.1 0.09 0.083 0.077 0.071 . . . 0.02 and so on. Then the change in prices every year would be 10. A bundle of goods that cost $100 in the initial year would cost $150 five years later. The trouble with simply looking at the year-to-year difference in the level is that it treats an increase in the price of a good from $10 to $20 in exactly the same way as an increase in the price of a good from $100 to $110. Yet in the first case, the good has doubled in price; in the second case, it has gone up by 10 percent. In the preceding example, we can see that an increase in P by 10 every time means that the percentage growth rate is declining. It is often, therefore, more meaningful to look at changes in variables through time in terms of the percentage growth rate of that variable. For example, if the price deflator were growing at 10 percent per year, the series for P would look like this: Time P π 1 100 2 110 0.1 3 121 0.1 4 133.1 0.1 5 146.4 0.1 6 161.1 0.1 . . . . . . . . . The Mathematics of Growth Rates Suppose that some variable, x, is growing at the rate gx. Then this means that xt = (1 + gx)xt–1. Equivalently, we can rewrite this to show that the growth rate gx is gx = (xt – xt–1)/xt–1 = ∆xt /xt–1, where ∆ indicates the change between one period and the previous period. In other words, it is the proportionate change, or percentage change, in the variable. The growth rate of a product of two variables is approximately equal to the sum of the growth rates of the variables. Suppose that zt = xtyt. Then, zt = xtyt = (1 + gx)xt–1(1 + gy)yt–1 = (1 + gx)(1 + gy)xt–1yt–1 = (1 + gx)(1 + gy)zt–1. Also, zt = (1 + gz)zt–1. Hence, (1 + gz) = (1 + gx)(1 + gy) = 1 + gx + gy + gx gy ⇒ gz = gx + gy + gx gy. But since gx and gy are usually small numbers, their product will be a very small number, so we can write gz ≅ gx + gy. For example, if x is growing at 4 percent and y is growing at 2 percent, then gx = 0.04, gy = 0.02, and gx gy = 0.0008. Thus, gz = 0.04 + 0.02 + 0.0008 = 0.0608 ≅ 0.06. So the growth rate of z is approximately 6 percent. Similarly, the growth rate of the ratio of two variables is given by the difference between the growth rates. That is, if wt = xt /yt, then gw = gx – gy. Logarithms In the Data Plotter available on the textbook Web site, various transformations of the data are possible. One of these is to take the logarithm of a series. This is included because economists often find it more convenient to use natural logarithms to discuss growth rates. Logarithms, written either as log or ln, are transformations of variables. The definition of the natural logarithm of a variable ln(x) is the log to the base e = 2.71828...: in other words, ln(x) = b implies that eb = x. There is nothing very mysterious about logarithms; they are simply a convenient way of rescaling data series. A logarithm is just a function, like others we use in economics, but with some very useful properties. In particular, suppose we take the logarithm of our earlier price series. Time P π ln(P) 1 100 2 110 3 121 4 133.1 5 146.4 6 161.1 . . . . . . 4.6 0.1 0.1 0.1 0.1 0.1 . . . 4.7 4.8 4.9 5.0 5.1 . . . We find, therefore, that a constant percentage growth rate corresponds to a constant difference in terms of the logarithm. In general, gx = ∆x/x ≅ ∆ln(x). This is convenient because it allows us to perform many calculations using just addition and subtraction rather than multiplication and division. Logarithms have the property that ln(xy) = ln(x) + ln(y). We can use this to show, as we did before, that the growth rate of a product equals the sum of the growth rate of the individual variables. As before, let zt = xt yt. Then gz = ∆ln(zt) = ln(zt) – ln(zt–1) = ln(xt yt) – ln(xt–1 yt–1) = ln(xt) + ln(yt) – ln(xt–1) – ln(yt–1) = ∆ln(xt) + ∆ln(yt) = gx + gy. Natural logarithms turn out to be very convenient in many uses, partly because they do simplify discussion of growth rates. If a variable is growing at a constant rate through time, this means that its percentage change from year to year is the same. In log terms, ∆ln(xt) = n. So ln(xt) – ln(xt–1) = n ⇒ ln(xt) = ln(xt–1) + n. With every time period that goes by, ln(x) gets bigger by n. So this means that ln(xt) is a linear function of time, such as ln(xt) = a + nt. The slope of the line is the growth rate of xt. If a variable is growing at a constant rate through time, then the graph of that variable through time looks like Figure 1A. The graph of the log of the variable, however, looks like Figure 1B. Elasticities Many of the parameters in economics are expressed in terms of elasticities. For example, this is true of many of the parameters in the exercises in the textbook Web site. The idea behind the use of elasticities is similar to that behind the use of logarithms—they permit us to consider how much one variable changes, in percentage terms, when another variable changes, also in percentage terms. As an example, we know that investment depends on the real interest rate. We could simply think about the change in investment for a given change in the real interest rate as ∆I/∆r. Thus, if ∆I/∆r = –0.1, then a one-unit increase in the real interest rate would decrease investment by 0.1 units. The trouble with this is that this relationship between ∆I and ∆r would be different if we simply changed the units (for example, if we were measuring investment in billions, and we instead divided by 1000 and measured in trillions). We can get around this problem by defining the elasticity of y with respect to x as That is, it tells us the percentage change in y for a given percentage change in x. The elasticity of investment with respect to the interest rate (or, more concisely, the interest elasticity of investment) is thus Note that ADDITIONAL CASE STUDY 8-6 Labor-Force Participation The Solow growth model does not distinguish between growth in the population and growth in the labor force. Instead, it makes the implicit assumption that the labor-force participation rate—the share of the population in the labor force—is constant through time so that the growth rate of the labor force will be the same as the growth rate of the population. This assumption is a reasonable one for the purpose of modeling the process of economic growth. But, for the United States over the period 1950–2000, laborforce participation increased and contributed importantly to the overall growth of the labor force. From 1950–2000, the U.S. noninstitutional civilian population, age 16 and over, grew 1.4 percent per year on average, while the civilian labor force, age 16 and over, grew 1.7 percent per year on average. The faster growth of the labor force was due to a rise in labor-force participation, from nearly 60 percent in 1950 to over 67 percent in 2000. As Figure 1 shows, this rise in overall labor-force participation occurred because of a dramatic increase in women entering the workforce. Participation among men actually declined over this period, partly due to a trend toward earlier retirement among older men. Note: Data are labor force as a percentage of noninstitutional civilian population, age 16 and over. Source: U.S. Department of Labor, Bureau of Labor Statistics. Over the past decade, however, labor force participation plateaued and then declined during and after the recession of 2008–2009, falling to 63 percent by 2014. Whether the participation rate will increase once the economy has fully recovered remains an unanswered question. Figure 2 illustrates the fall in labor-force participation among men, age 65 and over, reflecting the trend toward earlier retirement. After declining from just over 45 percent in 1950, the participation rate of older men bottomed out at about 16 percent and has risen several percentage points in the past twenty years to about 23 percent. The participation rate of older women, by contrast, changed little through the mid-1990s, averaging below 10 percent, but has increased markedly in the past fifteen years, reaching 15 percent in 2015. Note: Data are labor force as a percentage of noninstitutional civilian population, age 65 and over. Source: U.S. Department of Labor, Bureau of Labor Statistics. ADDITIONAL CASE STUDY 8-7 Bridge Jobs and the Transition to Retirement As noted in Supplement 8-6, labor-force participation among American men age 65 and over has increased in the past two decades after declining steadily for much of the post–World War II period, while for older women, participation has ticked up a bit in recent years after remaining roughly constant through the end of the twentieth century. An even more dramatic shift in participation rates has occurred for Americans age 60 to 64. As shown in Figure 1, labor-force participation for men in this age group fell steadily until the mid-1980s and has since risen, while participation for women in the same age group, which was flat prior to the mid-1980s, has trended up significantly since then. But although Americans are remaining in the workforce longer than in the recent past, it is not the case that they all are remaining in the same jobs or even the same careers as they reach their golden years. A recent paper by Cahill, Giandrea, and Quinn documents the importance of so-called “bridge jobs” as a step on the path to eventual retirement. Note: Data are labor force as a percentage of noninstitutional civilian population, age 60–64. Source: U.S. Department of Labor, Bureau of Labor Statistics. The authors use data from the Health and Retirement Study (HRS) to assess the importance of bridge jobs among older Americans. These data cover a nationally representative sample of men and women who were aged 51 to 61 in 1992. The HRS collects information on this sample every two years. In their paper, Cahill, Giandrea, and Quinn estimate that between half and two-thirds of the survey respondents who had left full-time career jobs had moved into bridge jobs rather than directly out of the labor force. For these workers, retirement is a process, not a single event. Younger, healthier, and highly skilled workers who do not have defined benefit pensions are more likely to use bridge jobs, as are men at both ends of the socioeconomic scale. The authors conclude that traditional one-step retirement, in which a person works in a career job and then exits the labor force, is becoming the exception, not the rule. CASE STUDY EXTENSION 8-8 How Much Variation in Per-Capita Output Is Explained by s and n? The case study “Saving and Investment Around the World” showed that cross-country evidence provides some support for the prediction of the Solow model that countries with higher saving rates have higher levels of output per capita. The case study “Population Growth Around the World,” in turn, provides supporting evidence for the prediction that countries with higher population growth rates have lower levels of output per capita. A natural question to ask is: How much of the international variation in living standards is explicable in terms of these two factors? Greg Mankiw, David Romer, and David Weil have shown that these two variables alone are capable of accounting for about 60 percent of the variation in per-capita output. When they add a simple measure to account for human capital (the percentage of the working-age population in secondary school), they explain close to 80 percent of the cross-country differences. LECTURE SUPPLEMENT 8-9 The Solow Growth Model: An Intuitive Approach—Part One This supplement presents a more intuitive and less mathematical explanation of the Solow growth model than appears in the textbook. We carry out all our analysis using the production function found in the classical model of Chapter 3: Y = F(K, L). This equation indicates three reasons why output may change: (1) because the capital stock changes; (2) because the labor force changes; or (3) because the economy’s ability to produce goods with given resources [as summarized by F( )] changes. We consider each in turn, first analyzing changes in K, then in L, then technological progress. The Accumulation of Capital Suppose that the labor force and the production function are unchanging. What determines the capital stock? First, it is important to observe that the capital stock increases as a consequence of investment: Firms’ spending on new factories and machines increases the stock of capital available in the economy. Recall from the classical model of Chapter 3 that equilibrium in the loanable-funds market (brought about by the adjustment of the real interest rate) implies that investment equals national saving. It follows immediately that the capital stock will increase as a consequence of saving. In the classical model, the level of saving is fixed and exogenous because the level of output is fixed. But since long-run growth entails changes in output, it is no longer appropriate to assume that saving is fixed. Rather, it seems plausible that, as output (or, equivalently, income) increases, so also does saving. We make the simple assumption that total national saving is proportional to output, so Total Investment = Total Saving = sY, where s is the saving rate. If this were the only factor affecting the capital stock, then continuing new investment would mean that the capital stock would increase without limit. Output would increase until there was so much capital in the economy that additional machines and factories produced almost no extra output (recall the discussion of diminishing marginal product in Chapter 3). Capital, however, also wears out over time and needs to be replaced. We refer to this wear and tear of capital as depreciation and make the simple assumption that a constant fraction of the capital stock wears out every year. Letting this depreciation rate equal δ, we obtain Total Depreciation = δK. (The rate of depreciation can be interpreted in terms of the lifetime of a typical piece of capital: If δ is the depreciation rate per year, then the average piece of capital lasts 1/δ years.) Since investment increases the capital stock and depreciation decreases the capital stock, it follows from the previous discussion that the capital stock grows if total saving exceeds total depreciation. Likewise, the capital stock declines if total saving is less than total depreciation. It turns out that, given time, the capital stock will adjust to a point where total saving exactly equals total depreciation: sY = δK. Once at this point, the capital stock will remain there, with new investment each year being just enough to replace worn-out capital. Such a situation is known as a steady state. This result is perhaps consoling—if it were not true, then either the capital stock would keep declining through time, and eventually workers would have no machines to operate, or else it would keep increasing until there were hundreds of machines and factories for every worker. If the capital stock is below its steady-state level, total saving exceeds total depreciation and the capital stock increases; the opposite occurs if the capital stock exceeds its steady-state level. Features of Steady State We are assuming that the labor force, L, is constant. We have just concluded that, in steady state, K is constant. It follows immediately that total output, Y, is also constant. (The amount of output available for consumption by individuals and the government must also be fixed: Since Y = C + I + G, and Y and I are fixed, it follows that C + G is fixed.) Thus, we have not yet explained long-run growth. Output may grow in the short run while the capital stock is adjusting to its steady-state level, but output is not growing in steady state. An increase in the rate of saving increases the steady-state level of output. To see this, suppose that the economy is originally in steady state, and then suppose that the saving rate goes up. Since total saving originally equals total depreciation, an increase in the saving rate must make total saving larger than total depreciation and so causes the capital stock to increase. The economy will eventually reach a new steady state at a higher level of capital and output. An increase in the depreciation rate has the opposite effect: It decreases the steady-state capital stock. Population Growth Now, let us suppose that the population grows at the rate n (for example, 2 percent per year). Once again, it turns out that the economy will reach a steady state—in this case, one where the capital stock is growing at the same rate as the population. Otherwise, the amount of capital relative to the number of workers would either become arbitrarily large (if the capital stock grew faster than the rate n) or arbitrarily small (if the capital stock grew more slowly than the rate n). In the steady state, both the population and the capital stock are growing, but the capital–labor ratio (the number of machines per worker) is constant: K/L = Constant. Recall from Chapter 3 that the production function possesses constant returns to scale. By definition, this means that if K and L are both growing at the rate n, then output is also growing at the rate n. In the steady state with population growth, output grows at the rate of growth of the population. It follows immediately that output per person is constant. There is another important and perhaps less obvious consequence of population growth: Higher population growth means lower living standards. To see this, suppose that we start with an economy in steady state with no population growth (so the growth rate of K equals the growth rate of L equals zero). Now, suppose that the population starts growing. We can no longer be in steady state because L is now growing faster than K. It follows that the amount of capital per worker will start to fall. In the original steady state, saving equals depreciation. But as the extra labor causes output to start growing, so saving will increase, exceeding depreciation and in turn causing the capital stock to increase. To start off with, however, the growth in the capital stock will still be less than the growth in the labor force, so the capital–labor ratio will continue to decline. Eventually, the increases in saving will allow the capital stock to grow at the same rate as the labor force, and the economy will be in the new steady state— but with a lower amount of capital per person than in the original steady state. Since there is less capital per person, output per person and, hence, living standards will also be lower. The model with population growth can explain output growth, but since output grows at the same rate as the population in steady state, it follows that output per person is unchanging. Even this model cannot explain rising living standards. To do so, we must introduce technological progress. LECTURE SUPPLEMENT 8-10 Additional Readings Robert Solow’s book on growth theory is a useful introduction to the topic: R. Solow, Growth Theory (New York: Oxford University Press, 1970). The Golden Rule was introduced by Edmund Phelps in a paper that, uncharacteristically for economics, displays a sense of humor: E. Phelps, “The Golden Rule of Accumulation: A Fable for Growthmen,” American Economic Review 51 (September 1961): 638–43. Instructor Manual for Macroeconomics Gregory N. Mankiw 9781464182891, 9781319106058