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Youth Joblessness and Race: Evidence from the 1980 Census George Cave In 1983 the Census Bureau released microdata based on the "long- form" questionnaire completed by about one-fifth of the respondents in the 1980 Census. "Public-Use ~ ~ ~ ~ ~ ~~~ Microdata Sample C" identities the retype of area"--central city, urban fringe, rural, and so on--for a full 1 percent of the U.S. population (Bureau of the Census, 1983~. The large size of this data set enables researchers to study the impact of area type and many other factors on a multitude of individual variables measured by the questionnaire. In addition to the 1 percent population sample, a 0.1 percent subsample provides data on 226,947 individuals surveyed in the 1980 Census. This paper compares the data on unemployment and other labor force behavior reported for black youths with that reported for white youths. The key question addressed is, Do black youths face special problems in the labor market due to their race? A related question is whether correcting black and white youth labor force statistics for location, education, family income, and other factors tends to eliminate the racial differences. This paper, like most others in the empirical literature on youth unemployment, uses simple single-equation methods to correct for these factors. However, the results must be interpreted very carefully for several reasons. First, most coefficients estimated on data for individuals are subject to "ecological correlation bias" if the labor market characteristics of the respondents' local areas are missing from the data set. Second, the most common single-equation or system methods may not estimate structural coefficients for individuals' and employers' behavior. Third, single-equation methods introduce simultaneity bias if, for example, the probability of unemployment influences the probability of labor force participation. Finally, even system methods may ignore some simultaneity and overcorrect for factors other than race. To some extent, residential location within the local labor market, quantity and quality of education, family income, and so on are, like unemployment, partly the consequences of race in the labor market. To ignore the effect of race on these determinants of labor George Cave is on the staff of the Manpower Demonstration Research Corporation. 367

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368 force status is to ignore the indirect labor market effects of race on unemployment. This paper is organized as follows. First, the data sets and the statistical methods used most extensively in this study are described. Next, a brief overview is given of the seasonal, cyclical, frictional, and structural components that complicate empirical analysis of the youth unemployment problem. This section also includes a survey of several earlier empirical analyses. The empirical analysis of the labor force status of out-of-school black and white teenagers included in the Census microdata follows. Then the very different behavior of those teenagers who were enrolled in school at any time during the two months before Census day is explored. The paper ends with a summary of the major findings. THE DATA The 0.1 percent subsample of "Public-Use Microdata Sample C" has 226,947 self-weighting observations on individuals. Of these, 8,653 are young men aged 16-19. Because only 1,190 of these young men are black, stratifying the sample by region, education, and other factors produces some data cells with no nonwhites. The problem becomes even more severe when students are excluded from this group; there remain 2,061 white males, but only 372 black males. Fortunately, it is easy to increase the number of nonwhites by a factor of 10 by using the full 1 percent sample of nonwhites. However, calculations based on stratified samples containing nonwhites from the full C sample but only those whites in the 0.1 percent subsample require special techniques. Heteroscedasticity could arise from the 10-fold greater chance a nonwhite respondent had to get into such stratified samples. Still, the huge Census microdata samples enable appropriately cautious researchers to home in on interesting subgroups in ways that smaller samples do not permit. The main dependent variables used here reflect labor force status during the week of the Census survey.) Unfortunately, questions that would have identified "discouraged" workers during the survey week were not asked. However, analyzing nonstudents separately picks up some part of the often-neglected behavior of those who are not in school yet are neither employed nor unemployed. . . This measure of labor force behavior is the most common. Alter- natives are available: the number of weeks spent in unemployment and in employment in 1979 are recorded for everyone 16 years and older in "Public Use Microdata Sample C." Survey-week labor force behavior is related systematically to weeks and spells of unemployment over the course of a year; see Betsey (1978) and Hanoch (1976~. Using survey- week behavior does not distinguish between the short-term and long-term unemployed.

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369 Other variables available for all respondents include census region, type of area, householder status, age, race, marital status, disabil- ities, years of school completed, whether the respondent has ever worked, and income status. For those with at least some employment in 1979, earnings, usual weekly hours, and industry in which employed are also available. Unfortunately, crucial variables that are not available include actual hourly wages, the number of spells of unemployment in 1979, the number of job offers refused during job search, and eligibil- ity for unemployment compensation. METHODOLOGY Two basic methods are used in this analysis to compare black and white labor force behavior. Both attempt to explain dummy variables for employment, unemployment, and nonparticipation. When black and white samples are combined, and when race is one of the independent variables, the coefficient of race shows the increase in the probability of the behavior, conditional on the other independent variables, that can be attributed to being black. As in Freeman (1982), linear probability models (LPMs) are estimated because they explain quite simply some important relationships among the three dependent variables. However, because of well-known econometric difficulties with linear probabilities, logistic methods are used as well .2 Using both methods, linear and logistic, equations are estimated for two types of dependent variables, unconditional and conditional. Unemployment and employment equations are estimated both for the entire population and for labor force participants only. In these models, the coefficients for conditional employment and unemployment have the same magnitude, but different signs. The next section points out structural interpretations for the conditional equations; these reflect employer behavior and make the unconditional equations reduced forms confounding employer and individual structural coefficients. OVERVIEW OF THE YOUTH UNEMPLOYMENT PROBLEM The Many Faces of Unemployment Even though economists have produced a large literature on unemployment and take many separate approaches to the subject ,3 not 2See Nerlove and Press (1973:Ch. 2). The LPM predicts probabilities outside the unit interval, is subject to heteroscedasticity, and in general does not fit the statistical assumptions underlying least squares regression. 3 Two important strands of this literature are largely theoretical: macroeconomic general equilibrium and wage-search distributions. Hey

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370 much fundamental progress has been made in explaining unemployment. An adequate economic explanation of unemployment would separate relevant factors reflecting the preferences of individuals for consumption of goods and uses of time from factors constraining individuals' choices about consumption and work. Moreover, such an explanation would systematize many of the stylized facts about unemployment. Further, such an explanation would yield empirically testable hypotheses for existing data about unemployment. One problem is that the same word, unemployment, is used to denote many very different phenomena. For a long time, empirical work on unemployment among individuals has tried to classify such unemployment as "seasonal," "cyclical," "frictional," or "structural," although it has been recognized that a given spell of unemployment for a given individual might be very difficult to categorize. Seasonal and Cyclical Unemployment One sort of seasonal unemployment is a characteristic of certain occupations, such as construction work. Workers committed to such occupations generally do not take other kinds of jobs during the off-season, perhaps because their wages reflect compensating differ- entials for the known risk of unemployment at certain times of the year. This sort of demand-side unemployment is unlikely to affect young people, who generally have not yet committed themselves to occupations. The failure of schools and colleges to stagger their vacation periods produces another kind of seasonal unemployment, 4 which can be attributed to the supply side of the youth labor market. A deluge of young people compete for relatively few jobs each summer. If the kinds of jobs young people take during their summer vacations paid lower wages, some have argued, 5 the problem would be smaller. Cyclical unemployment occurs less predictably and is tied to the business cycle and to cycles of product demand within industries. There has been a great deal of recent work on the nature of long-term contracts between firms and workers who are periodically laid off temporarily and then rehired. Feldstein {1976) estimated that 75 (1981) provides a survey. Some important articles in the empirical literature are cited in the next section. however, Clark and Summers (1982:209) cite gross flow evidence that demand for young workers, on the whole, adjusted remarkably well to increased supply during the summer over the years 1968-1976. They surmise from preliminary statistical work that federal Neighborhood Youth Corps and CETA programs may explain their surprising findings on this point. 5See Brown (1981) for a survey of many of the issues surrounding minimum wage differentials for youth.

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371 percent of laid-off workers in manufacturing subsequently are rehired by the same employer. He cited 1975 evidence that 41 percent of unemployed men aged 25-64 who had been laid off had made no attempt to find jobs during the previous month. However, since young people tend not to have made solid commitments to particular firms or even to particular industries, temporary-layoff theories are less-convincing explanations for their unemployment than for the unemployment of older workers. The next subsection provides rough evidence that even cyclical unemployment tied to the business cycle is less important for younger people than for more-established workers. This lack of cyclical sensitivity is reassuring, since elsewhere in the paper I focus on cross-sectional data pertaining only to March 1980 and calendar 1979. Cyclical Sensitivity of Youth Unemployment Because I talk about a single cross-section of individuals in the remainder of the paper, I do not have much to say about cyclical influences on youth unemployment. How important are they? Persistent unemployment of at least 3.5 percent (measured as annual averages of monthly Current Population Survey estimates) has afflicted the U.S. civilian labor force since the mid-1950s. The aggregate rate fell from 5.5 percent in 1954 to 4.1 percent in 1956. Then it jumped to 6.8 percent with the 1958 recession. It fell again to 5.5 percent in 1959 and 1960 and then rose abruptly to 6.7 percent for 1961. With the exception of a slight faltering in 1963, it fell steadily from its 1961 level until it reached the post-1953 trough of 3.5 percent in 1969, a war year e Since then, as Table 1 shows, it rose in 1970 and 1971, fell in 1972 and 1973, rose through 1975 to a three-decade peak, and fell to the 1979 low preceding the most recent recession. Although the aggregate time series is sensitive enough to reveal broad trends, it masks a great deal of the labor market behavior that disaggregation reveals. In addition to aggregate unemployment rates, Table 1 shows unemployment rates for certain sex, age, and race groups, including groups of teenagers 16-19 years old. With the exception that teenage unemployment was below 12 percent for the three years preceding 1958, 1969 was the post-1953 trough for each of the disaggregated series as well as for the aggregate unemployment rate. But many of the disaggregated series have kept the same rank relative to each other ever since 1950. Moreover, some of the series are much more stable over time than others. Table 1 shows coefficients of variation (ratios of standard deviations to means) for the aggregate series and for 20 disaggregated groups for the period between 1972 and 1982. It also shows the rank of each coefficient of variation (c.v.) among the 21 coefficients reported. The aggregate series ranks 14th at 21.09 percent. All 7 groups of teenagers rank above the aggregate series; in fact, the teenage groups account for 4 of the top 4 groups and 7 of the top 11 groups. The coefficient for the top group, black women aged 16-19, is barely a third of the aggregate coefficient. At the other end of the

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372 a, o C9 a, C~ o o Q . _ C: 4- a) o Q a, S: - o o a' ~5 m Y C c' 0 ~) ~ a) 1 ~; E ~ ~ ~7 1 - O C:5- 1 =3 0 O ~ ~ 1 4~ a' ~ cs a) 1 - E~ ~= O (O- 1 33 0 I ~ (, a) ~D-CS a) 1 E ~ ~ 7: O ~- I 3 0 Y ~ 1 C) ~ ~o ~ a) 1~ O ~ ~ 0~ c~ 1 -~ (~ 1ON 0:) ~N 0 1 O ~ 1 ~D~ ~ 1 - a) ~ ~ ~ 1 - 1 3 0 1 1 ~ <) ~ a) 1 a) ~ c: ~ 1 - 1 0 1 Y ~ON 1 (: a) ~ 1 ~ E - 04 1 =3 Y C: ~ 1 c) a) 0 ~ a) 1 ~ EC~ ~= - O tT5- 1 tn 3 0 a) ~ aN 1 a) ~ 1 - E I I _ 0< 1 33 a) ~ ~ 1 ~ 0 0 ~ a' 1 - Em == I "C O ~S- 1 33 0 1 Y ~ 1 C) ~ ~ 1 t~ a) 1 1 - ~ ~ 1 ~ ~ 1 Y ~ 1 C) ~ o~ a) 1 ~ a) (\J ~ ~ 1 _= ~- 1 0 1 0 0N 1 ~ ~ ~ 1 - O 1 1 =~0 1 3 a) ~ 1 ~ co~ a) 1 ._ ~ ~ ~ ~ 1 - 1 3 0 1 ~ I a) ~ 1 E O vC) 1 3- 1 0 0 T:) a) 1 E~l ~= I O tT5- 1 3 0 1 a~ 1 ~ ~ 1 a,) 1 1 '~ ~) 1 1 ~ , c o~ a) I a) ~ ~ =, ~ ~5- 1 O I 0N 1 1 1 1 <) 1 1 ~ 1 o~ a) 1 ~i c: 7D 1 ~5- 1 0 1 1 1 a' 1 ~ a) 4~ 1 1 1 1 1 ~J O \0 0~ ~ 1 ... . - 1 LS~ h~ ~h~ I- 1 1 ~N ~- ... . - 1 ~S:) J ~ O 0 1 ~) ~ J J I l l ~) ~ J h~ 0 1 . . . - 1 ~N - ) - I ~ ~ 1 1 =N (:~ - I ... . - 1 ~ c~ \0 1-~ 1 ~N I 1 1 \0 ~ \0 0 1 ... . - 1 ~) IS ~h~ ~ I 1 1 JN O~ I . .. . . , C5$ ~ I '- ~N I l l 01~-= 0 - 1 . . . . I \0 L]> ~ \0 0 1 l l 0~ - ~J . . .. . , h~ ~ 0O J I NN I 1 l ~J 0N ~ 0 1 .. ~ J J ~ ~ 0 l l ~N I 1 0N ~ 1 N I 1 l 03 ~ h~ \0 1 . . . - 1 h~ J ~<) 0 1 1 0 0 ~\0 ~- 1 ... . - 1 1- ~ Ct~ 1 1 0a~c ~m - ~= 00 0N G~ 0N . N h~ <)h~J 00N0 ... J ~0 00a~ ... <)'~h~ h~cr ... 1- ~J 0 . ~0 N .. ~h~ N N .. N N . N a: o o J L~ r~ o 0 h~ N 0 ~0 ~0 o o 0 ~0 r~ J o c~ r~ c~ 0 N h~ ~0 0 0 h~ 0 . ~0 N J . 0N . N ~0 o N o L~ J o 0 r~ N ~0 0 ~0 0\ N N ~0 1 1 ~ -- O > ._ a) 4~ ~ ~ 4~ o 0 o o 0 o J ~0 0 N o: LS) o 0 o o 0\ L`> ~0 o 0 ~0 N 0N o N > C) `' O Q J O 4 E 4 Q a' C] o 4- ~n - LS) N . _ 4- - m .O o o o o :8 to :t en . - ~n Q J O a' m =` o g J w0 4 Q a) cn O 4_ .. ~ LL 00 C: ~ O ~

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373 scale, groups containing older men account for all of the bottom six ranks. Older women tend to rank just below the groups of teenagers. Thus, from a disaggregation of time series using coefficients of variation to index instability, it can be seen that older men's unemployment is most susceptible to macroeconomic forces exerted on all demographic groups over time, while teenage unemployment is influenced least by such forces. Frictional Wage-Search Unemployment Frictional wage-search unemployment results from the dynamics of labor markets. People move in and out of the labor market as they age, as their skills change, as wage levels rise and fall, and as family needs and financial fortunes vary. 6 Jobs are created as firms are established, as plants are opened in new areas, and as older workers are forced to retire.7 But it may take a few weeks for would-be workers and firms with vacancies to search out and find each other. A job applicant might not take the first offer of wages and working conditions, and a firm might not be willing to meet the first appli- cant's wage bid. Such "search" unemployment might affect young people disproportionately more than adults, B because they are making gradual transitions from full-time schooling to full-time labor force partici- pation. Young people experiment with industries and occupations before making lifetime commitments. Sometimes they have parents to support extended periods away from both school and the labor force, and some- times they might misreport such nonparticipation as unemployment. According to "search theories" of frictional unemployment, 9 heterogeneity among individuals and among firms leads firms to search for workers and individuals to search for vacancies. The latter type of search has virtually been identified with unemployment by many labor economists, usually under the restrictive assumption that the utility function governing individual behavior is defined over discounted future wages, net of search costs but ignoring foregone leisure. 6When movement into the labor force exceeds steady state levels, structural unemployment may arise in addition to frictional unemployment. It may take some time for employers to adjust their hiring and wage policies to the increased supply of potential employees. 7Destruction of jobs by the same kinds of processes may lead to structural unemployment for established workers at the same time that it creates frictional unemployment for new entrants into the same or another job market. but see note 15 below. See Hey (1981:Ch. 5) for an accessible survey of this literature.

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374 According to these theories, every worker is unemployed because he turns down all proffered vacancies until he has been offered his acceptance wage. The acceptance wage is the wage such that there is no marginal gain in expected utility from continuing to search. Though firms search for workers, if only in the sense that they do not necessarily hire the first applicant for a given vacancy, most search theories tend to ignore this phenomenon and attribute unemployment solely to workers' searching for firms. The testable assertion here-- that the unemployed have refused actual job offers--has not been pitted against empirical evidence very often. But when it has been tested, the idea that most of the unemployed have refused wage offers has not fared well.~ Structural Unemployment In contrast to voluntary, frictional unemployment is the notion of involuntary, structural unemployment, which is defined by Killingsworth (1978:22) as "joblessness--usually long-term--which results from basic changes in the economic structure: new technology, the decline of some industries and the growth of new ones, geographic relocation of industries, permanent changes in consumer tastes, changes in labor force characteristics, and so on." For unskilled workers, among whom are most young people, legal minimum wages or high union wage scales may be an important barrier to Thor example, Rosenfeld (1977) has reported empirical work on the 3,238 out of 4,668 unemployed in the May 1976 CPS who answered supplementary questions on their job-search behavior. The high nonresponse rate and low potential for disaggregation indicate a need for more special surveys of this kind. Yet the implications of the respondents' answers for the validity of search unemployment theories seem clear. Since only 32 percent were on layoff, and more than 81 percent of laid-off workers reported some effort to find an interim job, only 6 percent of the unemployment could have been seasonal or cyclical in the sense used in this paper. Search unemployment due to high acceptance wages seemed less than universal: 22 percent stated willingness to accept jobs paying less than the federal minimum wage, then $2.30 per hour; another 33 percent were willing to take a wage between the minimum and S2.99; and only 22 percent reported an acceptance wage of $4.00 or more. Finally, only 10 percent of those who were unemployed four weeks or more and who had contacted at least one employer reported having refused any job offers. i~Killingsworth (1978) recently retold the postwar history of this old idea.

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375 employment. 12 In an important theoretical paper, Weiss (1980) shows that even in the absence of legal minimum wages or union pay scales, firms may find it optimal to set wages fairly high and to refuse to employ members of certain demographic groups, even though they are willing to work for lower wages. At the risk of excluding some dislocated workers from the definition, 3 the structurally unemployed may be thought of as those who have searched for jobs but found no employers willing to hire them. This simple definition maximizes the contrast between frictional unemployment and structural unemployment, while remaining consistent with neoclassical labor economics. The frictionally unemployed will join the ranks of the employed as soon as they lower their acceptance wages. But lowering their acceptance wages will not help the struc- turally unemployed find worker 4 they have not refused any wage offers. There is some empirical evidence that the notion that the unemployed are refusing wage offers is especially inappropriate for young men.~5 If this is true, then empirical models of search t2See Demsetz (1961~. But a legal minimum wage or union wage scale need not be binding constraints on employer behavior if there are other, higher, wage rigidities. i3Lucas (1978) seems to. We might conceivably argue that the laid-off skilled steelworker in Pittsburgh who won't sell his house and take a minimum-wage job is voluntarily unemployed, but we cannot argue as easily that an unskilled teenager who cannot get that same job is unemployed voluntarily. ~ 4 Indeed, in Weiss's (1980) model it is precisely the positive relationship between the acceptance wage and expected productivity that causes the unemployment of workers with low acceptance wages. Compare Lucas (1978:354~: "The unemployed worker at any time can always find some job at once. . . e However miserable one's current work options, one can always choose to accept them." Stephenson (1976) analyzed 281 respondents of the 300 unemployed males aged 18-21 with 8-12 years of education who sought full-time jobs in November 1971 at the Indianapolis state employment service office. He states (on p. 110~: "Nearly 90 percent of both white and black youths, when describing the search before their last job, said they took their first offer. In contrast to the search literature which usually implies a choice among several offers, the central search problem of young men may be to find a single offer." Cave (1983) exploits this insight in modeling unemployment among unskilled workers. Of course, because of its self-selection, Stephenson's sample may not be representative of all unemployed youth in Indianapolis at the time.

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376 unemployment 6 may not be appropriate for individual data on youth unemployment. Alternative models directly analogous to those used on aggregate date t 7 are proposed at the end of the next subsection. Implications for Empirical Work on Youth Unemployment Young people's behavior in labor markets is even more complex than the behavior of their elders. Unlike prime-age males, young people have nonparticipation as a real option, and they exercise it often. Whether they are in or out of the labor market, they must make another constrained choice their elders rarely face--whether to stay enrolled in school. Moreover, they work part-time rather than full-time more often than older people do. Empirical studies of youth labor markets must deal in some fashion with the joint determination of school enrollment, military status, labor force participation, hours worked per week, and wages. There is important simultaneity between par- ticipation and the chance of unemployment-if participation is chosen. There is also simultaneity between the number of years of education a person has and the chance he or she will find a place in the labor force. In addition to the simultaneity problems, there are problems of definition for the labor force variables. Several very different kinds of behavior are reported as the same empirical phenomenon, "youth unemployment." For someone who has quit school permanently and who cannot rely on family financial support, reported unemployment may reflect a chronic inability to find any hours of employment at any wage level. This kind of involuntary, structural unemployment may constitute what Conant (1961) called "social dynamite," and it has grave implications for adult poverty and crime. At the other end of the spectrum of interpretations of these statistics, reported unemployment in a particular week may reflect brief job search or normal experimentation with possible careers. For someone who has i6Since the search literature is mainly theoretical, there are few empirical search models to criticize. Kiefer and Neumann (1979, 1981) are careful to use data on permanently laid-off men for whom their sophisticated search model seems especially appropriate. i7For example, Fleisher and Rhodes (1976~. i8Recent empirical work, though not conclusive because of poor data, tends to make Conant's fears seem ill-founded. Freeman and Wise (1982) briefly survey work that, based on longitudinal data, finds no significant effect of employment history per se on later labor force behavior, once persistent individual skill and motivation differences have been controlled for. But Cave (1981) and Levy (1982) criticize these results as possibly reflecting unavoidable selection bias against the relatively small demographic group Conant worried about.

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377 completed his or her education fairly recently, reported unemployment may reflect a single episode of leisurely job search or unrealistic wage expectations. Summer unemployment by those who have never left school ought to be treated as possibly the common experience of many young people. Someone who has worked long enough in the past to be eligible for state unemployment compensation may misreport actual nonparticipation as unemployment. A further problem of definition arises because many chronically jobless youths may not show up in unemployment statistics at all. Discouraged workers are counted among those who are not even part of the labor force in a particular week. They may have been unemployed for a long period in the recent past, they may be permanent school- leavers, and they may have low reservation wages, but unless they engage in specific search activities they are not counted as part of the unemployed labor force. In addition to being too inclusive an indicator of chronic joblessness, youth unemployment may be too exclusive. Another important statistical problem plaguing empirical work on youth labor force behavior has sometimes been called "ecological correlation bias" (see Freeman, 1982:115~.~9 Much of the empirical work on unemployment has used the Standard Metropolitan Statistical Area (SMSA), not the individual, as the unit of observation.20 The proportion of variation in labor force behavior across areas that is generally explained by SMSA regressions is much higher than the pro- portion of variation across individuals that is explained by regressions using individuals. Individual regressions may attribute to individual characteristics (such as education, race, and family income) explanatory power that really belongs to area variables (such as the density of employment opportunities) that are correlated with the individual characteristics. It is surprising that few studies of individual labor force behavior have made use of area information that may be available (albeit at great cost) even in microdata. 2 ~ i9Rosen (1984), reporting on data from a BLS cooperative federal-state statistical program, indicates that there is a great deal of variation in unemployment among local areas. In 1979, local unemployment rates ranged from 40 percent in Menominee County, Wisconsin, to less than 1 percent in Sioux County, Nebraska. 20Examples are Gilman (1965), Kalachek (1969), Fleisher and Rhodes (1976), and part of Freeman (1982~. These SMSA regressions generally explain a much higher proportion of variation in SMSA unemployment than is explained (typically well under 10 percent) in individual regressions. 2 ~Abowd and Killingsworth (1984) are an exception, although one might quibble with their choice of geographic area variables to match with individual data.

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401 out of the labor force, as one might expect for students at the middle of the spring term in 1980--56.2 percent of all white male students and 74.2 percent of the black male students did not participate in the labor force. The black-white ratio is only 1.32, just half the ratio of participation rates for black and white nonstudents reported in the last section. Employment-to-population ratios, however, are worse for black students relative to white students than they were for black nonstudents relative to white nonstudents. The fraction of all white male students who had jobs was 38.6 percent; this was 1.97 times the fraction of all black male students who had jobs. The ratio for male nonstudents was only 1.67. The employment-population ratio for white female students was 38.2 percent, 2.06 times the ratio for black female students. However, 2.06 is almost as high as 1.94, the analogous ratio for female nonstudents. Labor Force Participants Of the 4,856 white male students, 2,125 were labor force partici- pants; 2,123 of the 8,239 black students were participants. Even though the original sample contained 2.2 million people, only 505 unemployed black male teen students made it into this final group. Of the 2,125 white student participants, 205 were unemployed. This means that the black unemployment rate among teenage students was 23.8 percent, while the white unemployment rate was 11.8 percent. Note that the ratio of the black rate to the white rate is worse for male students than it was for male nonstudents: 2.02, compared with 1.65 as computed from Table 4, or compared with 1.68, as computed from the LPM regressions on the 0.1 percent sample reported in Table 5(a). Table 8(h) shows that 2,013 of the 4,811 white female students were labor force participants; part (g) of the same table shows that 2,065 of the 8,505 black female students participated in the labor force. Some 176 of the whites and 489 of the blacks were unemployed, which yields female student rates of 8.7 percent and 23.7 percent, respec- tively. The black-white ratio of female student unemployment rates computed from this table is 2.71. Since parts (g) and (h) of Table 4 imply a nonstudent ratio of 2.38, the racial ratio of unemployment rates is worse for female students as well as for male students. Gross Effect of Race on Unemployment In Tables 9(a)-9(d) are linear probability models exactly like those in Table 5, but this time they are estimated for students. "MODEL01" of Table eta) shows that the gross racial differential in male unemployment-population ratios was 1.55 percent and of marginal statistical significance. 3 Part (c) of the table shows a slightly 3 Like the LPM coefficient, the logistic coefficient is small and barely significant at the 7 percent level. In the sample restricted to labor force participants, the logistic coefficient on race is large and has an asymptotic t-statistic of 5.8. J

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402 TABLE 9(a) Linear Probability Models: Civilian, Student Male Teenagers - MO[)Fl: MOF)~-l()1 SSF:,?87.511459 F ilATIO3.28 DFE5660 PROR>F0.(17()~4 DEP VAR: U MSE0.050797 R-SQUARE().()()()G VARIAL31EDEF8TIMA1EERROR -r RAr loPRot~>l T I 1 N l ~ i\Ct- i' 11() . 051483(-).0()3234298 15.9177().()()()1 COLOR1().()15515(-).()()85723()1 1.8()'39().()-7()14 MODEI: MODEL() ~SSE1,?72.lt8 ~ RATIO124.' [)FE5660 PROB>F().()()()1 DEP VAR: M MSF0.224820 R-SQUAREt-).()215 VARIABLEE)rESTIMATEERROR T RAI-IOPROB>ITI INIE-~(,FPl1().38612()C).0(-)68()lt213 5t, . 74 72() . ()(:)() 1 COl()I\1-().2()1257().018(134 -11.1598().(:)(-)()1 MO[~LI: M()~tI()3 SSE1346.9G6 ~ RAl-Io1()().,21 DFE5G6() I'F?~.E().()()(11 DEP VAl<: N t4SE0.23798() R-SQUARE().(-)17lJ VARIAl3IF[)tES1IMA1EE[lfIIl lN[Ll\(~Ll,!1().562391().~(:)7()(-)()527 8(-).33Gl~(:).(~()~)1 COIOFl1().185-lit2(-).(-)1855Il 1().()1()6().()()()1 SOURCE: Bureau of the Census, "Public-Use Microdata Sample C" (Washington, D.C.: U.S. Department of Commerce, 1983): blacks, noninmate 1 percent sample; whites, noninmate 0.1 percent subsample. TABLE 9(b) Linear Probability Models: Civilian, Student Labor Force Participants, Male Teenagers MODEL: MODEL2 1 SSE 260. 2237()3 F RAT I O 36. 46 DF E 2326 PROB>F t).00()1 DEl' VAR: U MSE 0.111876 R-SQUARE 0. ()154 PAKAM E r E R S TAN DAR D VAR I ABl ~DE EST I MATE ERROR T RAT I O PROB> I T I I Nr~Rcr ~r 1 (1. 1176li7 0.007255864 16.2141 ().00()1 OOLOR 1 (:).148363 0.(:)24572 6.()38() (-).(:)0(-)1 __ __ __ _ ___ _____ ___ _ _____ _ __________________ _ __ _________ ________ _ ___ _ ___ h10[)E 1: MOr)t L,?? SSE 260.223703 F RAT IO 3G.4G DFE 2326 PROB>F ().()(:)01 r)EP VAll: M MSE ().111876 R-SQUARE 0. ()154 PARAMETER STANDARD VAR I AE3I ~[)F FST I MAIE ERROR T RAT I O PROB> I T I INIERCEPI 1 ().882353 0.007255864 121.G055 0.00(-)1 COI ()~< 1 -().148363 ().()24572 -6.038() 0.0()()1 MO[)E l: MOL)[ L 3 1 SSE 259.708068 ~ RAT I 0 1 3. 7() D r E 2324 P RO B> F () . C) 001 DEP VAR: U MSE 0.11175() R-SQUARE (). (:)174 PARAME T E ~STANDARD VAfl I Al3LE- ~DE ~sr I MAI E ERROR T RAT I C PROB> I l- I 1 N r ~ R(,~ i' ~1 () .12713(1 O .00855751 14.8559 O . ()0() 1 SC) 1 -(). (!33641 0.016118 -2.0871 (). ()37() C()l 0~< 1 0.153358 (~.()3789'' 4.()469 (-).()()()1 IN1-RACT 1 0.()()9351145 0.050459 (:).1853 ().853() MOL)El: MO[)LI 32 SSE 259. 708()68 F RAT I O 1 3. -1() DFE 2324 PROB>F 0.0001 DEP VAR: M MSE 0.111750 R-SQUARE 0.0174 PARAME r ER STANDARD VAR IABl E DF ESt I MATE ERROR T RAT I O PROB> I T I 1 N r F KCE ~-r 1 0 . 872870 0.00855751 102.0005 O .00(-) 1 SO 1 0.033G41 0.016118 2.0871 0.0370 COLOR 1 -().153358 ().037895 -4. (:)469 0.00() 1 1 N T RAC T 1 - (-) .00935114 0.050459 - 0.1853 0.8530 SOURCE: Bureau of the Census, "Public-Use Microdata Sample C" (Washington, D.C.: U.S. Department of Commerce, 1983): blacks, noninmate 1 percent sample; whites, noninmate 0.1 percent subsample.

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403 TABLE 9(c) Linear Probability Models: Civilian, Student Female T. t1ODEL: MODEL01 SSE211.346319 F RATIO3.77 DFE5683 PROB>F0.0524 F)EP VAR: U MSE0.037189 R-SQUARE0.0007 VARIABLEDFESTIMATEERROR T RATIOPROB>ITI INTERCEPT10.0365830.002780295 13.15790.0001 COLOR10.0137600.007090884 1.94060.0524 tA()DEL: MODEL02 SSE1256.516 F RATIO155.97 DFE5683 PROB>F0.0001 ()tP VAR: M MSE0.221101 R-SQUARE0.0267 VARIABLEDFESTIMATEERROR T RATIOPROB>ITI INTERCEPT10.3818330.006779186 56.32440.0001 O()LOR1-0.2159290.017290 -12.48890.0001 MODEL: MODEL03 SSE1318.858 F RATIO130.26 DFE5683 PROB>F0.0001 DEP VAR: ~MSE0.232071 R-SQUARE0.0224 VARIABLEDFESTIMATEERROR T RATIOPROB>ITI INTERCEPT10.5815840.006945323 83.73750.0001 (,OLOR10.2021690.017713 11.41330.0001 SOURCE: Bureau of the Census, "Public-Use Microdata Sample C" (Washington, D.C.: U.S. Department of Commerce, 1983): blacks, noninmate 1 percent sample; whites, noninmate 0.1 percent subsample. TABLE 9(d) Linear Probability Models: Civilian, Student Labor Force Participants, Female Teenagers FlODEL: MODEL21 SSE194.368636 F RAT1041.33 DFE2200 PROB>F0.0001 DfP VAR: U MSE0.088349 R-SQUARE0.0184 PARAMETERSTANDARD VARIABLEDFESTIMATEERROR T RATIOPROB>ITI INTERCEPT10.0874320.006624908 13.19740.0001 COLOR10.1453730.022613 6.42870.0001 MODEL: MODEL22 SSE194.368636 F RATIO41.33 DFE2200 PROB>F0.0001 [)~-P VAR: M MSE0.088349 R-SQUARE0.0184 PARAMETER V,~RIABLEDFESTIMATE T RATIO PROB>ITI INTERCEPT 1 0.912568 0.006624908 137.7481 0.0001 C()LOR 1 -0.145373 0.022613 -6.4287 0.0001 _______________________________________________________________________ F1()DEL: MODEL31 SSE194.338377 F RATIO13.88 DFE2198 PROB>F0.0001 OFP VAR: U MSE0.088416 R-SQUARE0.0186 PARAMETERSTANDARD VARIABLE DFESTIMATEERROR T RATIOPROB>ITI INTERCEPT 10.0898330.007846721 11.44850.0001 SO 1-0.008377060.014656 -0.57160.5677 C()LOR 10.1400520.032831 4.26590.0001 1~TRACT 10.0137860.045803 0.30100.7635 MODEL: MODEL32 SSE 194.338377 F RAT10 13.88 DFE 2198 PROB>F 0.0001 DEP VAR: M MSE 0.088416 R-SQUARE 0.0186 PARAMETER STANDARD VARIABLE DF ESTIMATE ERROR T RATIO PROB>ITI INTERCEPT 1 0.910167 0.007846721 115.9933 0.0001 SO 1 0.008377063 0.014656 0.5716 0.5677 (-OLOR 1 -0.140052 0.032831 -4.2659 0.0001 1NTRACT 1 -0.013786 0.045803 -0.3010 0.7635 SOURCE: Bureau of the Census, ''Public-Use Microdata Sample C" (Washington, D.C.: U.S. Department of Commerce, 1983): blacks, noninmate 1 percent sample; whites, noninmate 0.1 percent subsample.

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404 more significant racial differential of 1.38 percent for females. However, as was the case for nonstudents, a regression for a sample restricted to labor force participants tells a very different story. Table 9(b) gives as the gross differential between black and white male student unemployment rates a highly significant 14.8 percent. This difference is greater than the white unemployment rate, 11.8 percent. When computed from this regression, the ratio of black to white student unemployment rates is 2.26. When computed from Table 8 the ratio is 2.02. Once again, the difference between the two computa- tions stems from the reduced sampling error in the tenfold larger sample summarized in the earlier table. "MODEL31" shows that, once again, the racial differential is larger outside the South than in the South. Part (d) of Table 9 shows a gross female student racial unemployment differential that is very close to the male differential; it is 14.5 percent and highly significant. "MODEL31" shows something different for women, however. The implied ratios of black to white student unemployment rates are 2.89 in the South and 2.56 outside the South. For men, the ratio was larger outside the South. Effect of Additional Explanatory Variables Tables 10(a)-10 (d) show the same equations for students that were estimated for nonstudents in Table 6. There are two dramatic changes. First, for male students but not for female students, race loses its significant effect entirely, regardless of whether age is included. Second, for male students but not for female students, household income, net of the teenager's earnings, emerges from insignificance as a strong explainer of variation in unemployment. When age is included in the equation, household income is the greatest reducer of chi-square for young men, stronger even than education. SUMMARY This paper presented a very brief review of the economic literature on unemployment, in particular the implications for empirical work on youth unemployment and labor force participation. New structural models for use with microdata were developed. These models may reduce two important sources of bias in estimates of the impact of race on unemployment: simultaneity and ecological correlation. Original empirical work based on 1980 Census microdata shows, using simple, single-equation methods, that the labor force participation decision cannot be ignored in estimating the impact of race on unemployment. For students and nonstudents, male and female, there is no gross racial differential to be explained if unemployment is measured as the ratio of the number of unemployed to the size of the population. However, when samples are restricted to labor force participants, large and significant racial differentials emerge. These racial differentials vary by sex, region, and school enrollment status. A racial difference

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405 TABLE 10(a) Conditional Employment Probabilities Using Age as a Regressor, Civilian, Student Labor Force Participants, Male Teenagers LOGISTIC REGRESSION PROCEDURE DEPENDENT VARIABLE: U 2328 OBSERVATIONS 304 POSITIVES 2024 NEGATIVES 7 O OBSERVATIONS DELETED DUE TO MISSING VALUES -2 LOG LIKELIHOOD FOR MODEL CONTAINING INTERCEPT ONLY= 1804.1$ CONVERGENCE OBTAINED IN 6 ITERATIONS. MAX ABSOLUTE DERIVATIVE=0.4640D-05. MODEL CHI-SQUARE= 73.14 WITH 10 D.F. D=0.031. -2 LOG L= 1731.04. P=0.0 VARIABLEBETA STD. ERROR CHI-SQUARE P D INTERCEPT 1.76G78657 1.173324442.27 0.1321 EDUCATN -0.12846921 0.062821744.18 0.0409 0.002 AGE -0.10924862 0.084958741.65 0.1985 0.001 HH1NCOME -0.01426909 0.0042830611.10 0.0009 0.005 FAM -0.11351487 0.777431070.02 0.8839 0.000 D1SAB1L 0.94116955 0.366565856.59 0.0102 0.003 SO -0.38920228 0.161541405.80 0.0160 0.002 CC -0.20908409 0.172255551.47 0.2248 0.001 SOXCOL 0.46637668 0.388383681.44 0.2298 0.001 CCXCOL 0.92305443 0.395068085.46 0.0195 0.002 COLOR 0.24863929 0.392565500.40 0.5265 0.000 SOURCE: Bureau of the Census, "Public-Use Microdata Sample C" (Washington, D.C.: U.S. Department of Commerce, 1983): blacks, noninmate 1 percent sample; whites, noninmate 0.1 percent subsample. TABLE 10(b) Conditional Employment Probabilities, Civilian, Student Labor Force Participants, Male Teenagers LOGISTIC REGRESSION PROCEDURE DEPENDENT VARIABLE: U 2328 OBSERVATIONS 304 POSITIVES 2024 NEGATIVES , O OBSERVATIONS DELETED DUE TO MISSING VALUES -2 LOG LIKEllHOOD FOR MODEL CONVERGENCE OBTAINED IN 6 ITERATIONS. MAX ABSOLUTE DERIVATIVE=0.2649D-05. MODEL CHl-SQUARE= 71.46 ~lTH 9 D. F. CONTAINING INTERCEPT ONLY= 1804.18 D=0.030. -2 LOG L= 1-732.72. P=0.0 VARIABLEBETA STD. ERROR CHI-SQUARE P D INTERCEPT 0.40037328 0.50537597 0.63 0.4282 EDUCATE -0.1829C)315 O.C)45268()(3 16.33 O.C)()()1 0.()()7 HHINCOME -O.C)1358426 0.00422821 10.32 0.0013 0.004 FAM -0.19656901 0.77373926 0.()6 0.7995 ().()()() D1SAB1L 0.92588989 0.36581134 6.41 0.0114 0.()()3 SO -0.388~)3809 ().16150578 5.77 ().0163 0.0(-)2 CC -0.21812()70 C).172C)960() 1.61 ().2(95~) 0.()()1 SOXCOL 0.44365482 0.38765566 1.31 ().252l' 0.()()1 CCXCOL 0.91135256 0.39467425 5.33 C).()2()9 ().C)~)2 COLOR 0.25223778 0.39166524 0.41 0.5196 O.O()C) SOURCE: Bureau of the Census, "Public-Use Microdata Sample C" (Washington, D.C.: U.S. Department of Commerce, 1983): blacks, noninmate 1 percent sample; whites, noninmate 0.1 percent subsample.

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406 TABLE 10(c) Conditional Employment Probabilities Using Age as a Regressor, Civilian, Student Labor Force Participants, Female Teenagers LOCI s r IC REGRESSION PROCEDURE DEPENDENT VARIABLE: U 2202 OBSERVATIONS 1982 U = 0 220 U = 1 O OBSERVATIONS DELETED DUE TO MISSING VALUES -2 LOG LIKELIHOOD FOR MODEL CONTAINING INTERCEPT ONLY= 1430.79 MODEL CHI-SQUARE= 61.55 WITH 10 D.F. (SCORE STAT.) P=0.0 . CONVERGENCE OBlAINED IN 6 ITERATIONS.R= 0.147. MAX ABSOLUTE DERIVATIVE=0.1323D-11.-2 LOG L= 1379.95. MODEL CHI-SQUARE= 50.84 WITH 10 D.F.(-2 LOG L.R.) P=0.0000. VARIABLEBETA STD. ERROR CHI-SQUARE P R INTERCEPT 1.75277707 1.39271281 1.58 0.2082 EDUCATN -0.07694844 0.09504671 0.66 0.4182 0.000 AGE -0.18154598 0.11397084 2.54 0.1112 -0.019 HH1NCOME -0.00251025 0.00444995 0.32 0.5727 0.000 FAM 0.20474210 0.45725416 0.20 0.6543 0.000 D1SAB1L 1.04000882 0.47274892 4.84 0.0278 0.045 SO -0.10730316 0.17961398 0.36 0.5502 0.000 CC 0.05299589 0.18402893 0.08 0.7734 0.000 SOXCOL 0.15040473 0.40052623 0.14 0.7073 0.000 CCXCOL -0.44346755 0.40144515 1.22 0.2693 0.000 COLOR 1.40902455 0.36442253 14.95 0.0001 0.095 _ SOURCE: Bureau of the Census, "Public-Use Microdata Sample C" (Washington, D.C.: U.S. Department of Commerce, 1983): blacks, noninmate 1 percent sample; whites, noninmate 0.1 percent subsample. TABLE 10(d) Conditional Employment Probabilities, Civilian, Student Labor Force Partici pa nts, Female Teenagers LOGISTIC REGRESSION PROCEDURE DEPENDENT VARIABLE: U 2202 OBSERVATIONS 1982 U = 0 220 U = 1 O OBSERVATIONS DELETED DUE TO MISSING VALUES -2 LOG LIKELIHOOD FOR MODEL CONTAINING INTERCEPT ONLY= 1430.79 MODEL CHI-SQUARE= 59.45 WITH 9 D.F. CONVERGENCE OBTAINED lN 6 ITERATIONS. MAX ABSOLUTE DERIVATIVE=0.0 . MODEL CHI-SQUARE= 48.14 WITH 9 D.F. (SCORE STAT.) P=0.0 . R= 0.145. -2 LOG L= 1382.65. (-2 LOG L.R.) P=0.0000. VARIABLEBETA STD. ERROR CHI-SQUARE P INTERCEPT -0.25593762 0.641359740.16 0.6899 EDUCATN -0.18882782 0.0573203710.85 0.0010 -0.079 RH1NCOME -0.00182823 0.004408510.17 0.6784 0.000 FAM 0.17669396 0.455456500.15 0.6981 0.000 D1SAB1L 0.99716482 0.470698124.49 0.0341 0.042 SO -0.12178188 0.179837480.46 0.4983 0.000 CC 0.03780462 0.183842860.04 0.8371 0.000 SOXCOL 0.11184032 0.399101050.08 0.7793 0.000 CCXCOL -0.45539480 0.400617711.29 0.2557 0.000 COLOR 1.41227175 0.3629883715.14 0.0001 0.096 SOURCE: Bureau of the Census, "Public-Use Microdata Sample C" (Washington, D.C.: U.S. Department of Commerce, 1983): blacks, noninmate 1 percent sample; whites, noninmate 0.1 percent subsample.

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