Desegregation and Black Dropout Rates Jonathan Guryan University of Chicago First Version: November 1999 This Version: May 2000 ABSTRACT In 1954 the Supreme Court of the United States ruled that separate schools for black and white children were “inherently unequal.” This paper studies whether the desegregation plans of the next 30 years in fact benefited the black students for whom the plans were designed. Analysis of data from the 1970 and 1980 censuses suggests that desegregation plans of the 1970’s reduced the high school dropout rates of blacks by one to three percentage points during this decade. Desegregation plans can account for about half of the decline in dropout rates of blacks between 1970 and 1980. A similar analysis suggests that desegregation plans had no effect on the dropout rates of whites. The results are robust to controls for time-varying region and family income effects, as well as to tests for selective migration, though mean reversion may account for some portion of the larger estimated effects. Further investigation of conditions in segregated schools in 1970 suggests that peer effects explain at least some of the decline in the dropout rates of blacks due to desegregation plans. The author thanks Joshua Angrist, Daron Acemoglu, Jim Poterba, Adam Ashcraft, David Autor, David Card, Ken Chay, Aimee Chin, Sue Dynarski, Campe Goodman, Sean May, John Johnson, Steve Pischke, Melissa Schettini, Jon Zinman, and participants at the MIT Public Finance/ Labor Seminar and the MIT Labor Lunch for their suggestions and guidance. Financial support was provided by the National Science Foundation through a Graduate Research Fellowship. 1. Introduction From Plessy v. Ferguson1 in 1896 until Brown v. Board of Education2 in 1954, Southern and Border States legally segregated their school systems by race. Black schools received fewer resources and black children were taught almost exclusively by black teachers. Outside the South, migration, housing patterns, and actions by state and local leaders contributed to similar racial isolation in the schools. With the Brown decision, the Supreme Court deemed segregated schools “inherently unequal” and therefore unconstitutional. Over the next 30 years, federal courts ordered the implementation of desegregation plans for many of the largest school districts in the United States. It was the intent of these court orders to provide equal educational resources to blacks by eradicating segregation on the basis of race. Indeed, the desegregation of the public schools was the most significant innovation in the educational system of the post-World War II U.S. Nevertheless, few economists have studied the effect of desegregation on integration’s intended beneficiaries, black students.3 The fact that black high school dropout rates fell from the late 1960’s through the early 1980’s is documented in Figure I. The contribution of court-ordered integration to this decline is an important open question. In this paper I use variation in the timing of desegregation plans in large school districts, the result of judicial enforcement of the Brown decision, to estimate integration’s effect on black high school dropout rates. Using the 1970 and 1980 1 163 U.S. 537 (1896). 2 347 U.S. 483 (1954). 3 Boozer, Krueger, and Wolkon (1992) and Card and Krueger (1992) are notable exceptions. St. John (1975) and Armor (1995) survey the education literature on the effect of desegregation on black achievement. They conclude that the results of studies, as well as the methods employed therein, vary significantly. 2 censuses, I compare high-school-aged blacks in districts that desegregated between 1970 and 1980 to those in districts that desegregated both before and after. I find that dropout rates among blacks declined between 1970 and 1980 by two to three percentage points in districts that desegregated in the interim relative to districts that desegregated both earlier and later. The results are robust to controls for district and time-varying region effects, controls for family income, and controls for potential confounds from the selective migration of blacks. Models that condition on lagged dropout rates produce estimates of a one percentage point decline in dropout rates as a result of desegregation. The smaller magnitude of these estimates suggests that mean reversion may account for some of the decline in dropout rates attributed to the effect of desegregation plans. As I describe in an appendix, however, under reasonable assumptions, estimates from the difference-in- differences and lagged dependent variable specifications provide upper and lower bounds on the effect of desegregation plans on dropout rates.4 Therefore, on balance, the results reported here are consistent with a one to three percentage point decline in dropout rates due to desegregation. The effects I estimate are quite substantial. A one to three percentage point decline in dropout rates can account for about half of the decline in black dropout rates from 1970 to 1980. These estimates are also relevant to current policy issues. In September of this year, a federal district judge in North Carolina ended the nearly thirty- year-old busing order in Charlotte.5 Earlier this year, on the twenty-fifth anniversary of the busing order in Boston, white families filed suit claiming that racially based assignment plans in the Boston school system were unconstitutional.6 The Boston School Committee then voted to end the use of race as a criterion for the assignment of students to schools. These and other decisions are made without the benefit of a comprehensive definitive study of the effect the original desegregation efforts had on black achievement. The effects of desegregation are not only of interest to economists because of policy concerns. The forced integration of the public schools also provides an opportunity to evaluate how peers and school inputs affect students’ educational outcomes. As a result of desegregation plans, large numbers of students lost control over 4 Imbens, Liebman, and Eissa (1997) make a similar point. 5 57 F. Supp. 2d. 228 (1999). 6 379 F. Supp. 410 (1974), 1999 U.S. Dist. Lexis 12941 (1999). 3 the choice of both peers in school and the quality of the schools they attended. While the net effect of desegregation on student educational outcomes is interesting because of the inherent historical importance of integration, this reduced-form estimate is also of interest because it provides a well-identified empirical estimate of two economically important structural parameters. There are large and growing literatures on both peer and school quality effects on economic outcomes. Theoretical work by Benabou (1993) on residential segregation, by Epple and Romano (1998) on private school tuition vouchers, and by Becker and Murphy (1992) on learning on the job, assumes that economic agents affect each other’s productivity. Empirical evidence on peer effects is mixed, however. Case and Katz (1991) present evidence that a teenager’s neighborhood peers affect various outcomes. The authors note, however, that this association need not be causal. Unobserved factors that determine a child’s residential location also determine economic outcomes. Evans, Oates, and Schwab (1992) show that estimates of neighborhood peer effects that account for endogenous neighborhood choice are close to zero, while similar estimates that presume exogenous residential location yield large peer effect estimates. Cutler and Glaeser (1997) use an instrumental variables strategy and find evidence of significant neighborhood peer effects. Empirical evidence on the effect of school quality on scholastic achievement and economic success is also mixed. Hanushek (1986) argues that there is little evidence that increased spending or improvements in crude measures of school quality have any effect on student performance. Krueger (1999) and Angrist and Lavy (1999) show direct evidence that class size impacts student test scores. Card and Krueger (1992) present direct evidence of a positive relationship between school quality and earnings, although Heckman, Layne-Farrar and Todd (1996) argue that the estimated relationship is driven by false assumptions. These studies notwithstanding, endogenous choice of residential location and educational expenditures generally makes the task of identifying the causal effect of school quality on economic outcomes difficult. Desegregation provides a source of plausibly exogenous variation in both the peers and the resources at the schools students attend. Data limitations make it difficult to identify each effect separately, though a number of authors have noted that much of the 4 gap between black and white school inputs was closed before 1970.7 Moreover, my examination of the characteristics of predominantly black and white schools in 1970 suggests that peer effects explain some portion of the overall decline in dropout rates attributed to desegregation. Together these findings imply that the benefits of integration could not be obtained simply by increasing observed school quality. The paper is organized as follows. In the next section, I present a brief history of school desegregation and discuss the literature on the effectiveness of desegregation plans. Section 3 lays out my identification strategy. Section 4 describes the data. In Section 5, I present the results and examine potential threats to validity. In Section 6, I examine peer and school quality effects separately. Section 7 concludes. 2. Background There was no nationally organized campaign that desegregated the public schools in the U.S. Rather, a series of court cases brought chiefly by private civil rights groups led to the court orders that were the most effective stimulus to desegregation. Political forces dictated that the enforcement of the Brown decision occurred mainly in the courts. What is germane here is that the courts’ role in the process necessitated law enforcement on a case-by-case basis. As a result, the timing of integration varied at the school district level. Although desegregation began first in the South, tabulations of the timing of major desegregation plans in the largest school districts in the country reveal significant inter- and intra-regional variation. Table I lists the sample of large school districts considered in this study.8 School districts are listed chronologically by the year in which they instituted a major desegregation plan. Of the 22 districts that implemented desegregation plans in the 1960’s, seven are located outside of the South. Similarly, of the 77 districts that implemented plans in the 1970’s, 35 are located outside of the South. 7 See, for example, Card and Krueger (1992) or Margo (1990). 8 I discuss the sampling procedure and data more specifically in Section IV. The sample of districts used is the same as in Welch and Light (1987). 5 2.1. Legal History A 1955 Supreme Court ruling, often called Brown II9, gave the federal district courts responsibility for determining whether districts were segregated and for evaluating plans to remedy segregation. Litigation followed, mostly with the intent of allowing individual black students access to white schools, but very little integration occurred before the mid-1960’s. The Civil Rights Act of 1964 gave the Department of Health, Education and Welfare (HEW) power to cut federal funding to school districts that discriminated on the basis of race. The law also authorized the Department of Justice to join school integration suits it deemed in the national interest. Many rural Southern school districts desegregated soon after the passage of the law.10 Some larger districts, where desegregation was more complex, allowed students the option of transferring schools within the district. In 1968, with its Green v. New Kent County, Virginia11 decision, the Supreme Court outlawed plans that did not effectively integrate the schools, ordering the end to the use of so-called “freedom of choice” plans. The decision stimulated new litigation throughout the South. After Green, desegregation plans were more likely to include the pairing of nearby schools, or the redrawing of attendance zone boundaries. It was not until 1971, with the Swann v. Charlotte- Mecklenburg County12 decision, that the Supreme Court approved busing of students outside of their neighborhood for the purpose of racial integration. The use of busing made desegregation feasible in many of the larger school districts of the North and West, where residential segregation was more severe. Proving that school or state officials intentionally segregated the schools was necessary to win a legal battle, but was significantly more difficult outside of the South. In the absence of laws requiring separate school systems by race, plaintiffs had to sift through transcripts of school board meetings and interview school officials to produce evidence of intent. In 1973, the Court made it easier to warrant a desegregation order outside of the South when it ruled in Keyes v. School District No. 1, Denver, Colorado13 9 349 U.S. 294 (1955). 10 Orfield (1978) p. 279. 11 391 U.S. 430 (1968). 12 402 U.S. 1 (1971). 13 413 U.S. 189 (1973). 6 that the plaintiff only needed to show segregative action in one school or neighborhood in the school district. In 1974, the Court restricted remedies to include only school districts where plaintiffs could prove intentional segregation. The Milliken v. Bradley14 ruling outlawed the inclusion of suburbs of Detroit in the city’s busing plan. By 1986, some school districts had been under court order for twenty years. In that year, a Fourth Circuit Court of Appeals declared the schools of Norfolk, Virginia integrated, ending the court order issued in 1971.15 Decisions by the Supreme Court in 1991 and 1992 clarified what school districts could do once court orders were lifted, allowing districts to return to neighborhood schools.16 2.2. The Effectiveness of Desegregation Plans Much research has focused on the effect of desegregation plans on the racial composition of school districts. Coleman (1975) suggested that court-ordered desegregation plans increased the speed of white migration out of cities. Subsequent research confirmed Coleman’s claim, but also found that induced white migration was not extensive enough to offset fully the effect of desegregation plans on the integration of schools. In particular, Welch and Light (1987) show that desegregation plans of the 1960’s, 1970’s and 1980’s decreased the index of dissimilarity in school districts by about 20 percentage points.17 Rossell and Armor (1996) show that, net of effects on white enrollment, desegregation plans led to a 10 to 20 percentage point increase in the fraction of white students at the typical black student’s school. There is reasonably strong evidence that desegregation plans led to a decrease in the segregation of public school districts. Through the reassignment of students to different schools, desegregation plans may have also improved the quality of educational resources available to black students. 14 418 U.S. 717 (1974). 15 784 F. 2d. 521 (4th Circuit 1986). 16 498 U.S. 237 (1991), 503 U.S. 467 (1992). 7 3. Identification Desegregation plans affect black dropout rates through three main channels. First, the reassignment of students within the school district affects the set of peers with which students attend school. New student assignment plans may cause parents to withdraw their children from the public schools, or to move out of the district altogether. Net of effects on the total enrollment and the racial composition of the district, desegregation plans alter the set of peers with which black children attend school. Second, desegregation plans may move black students to better schools. If whites attended better schools than blacks did before integration, then on average desegregation should improve the quality of schools that blacks attend. Though total support for schools may decline as a result of desegregation-induced migration, integration may still lead to a change in the average quality of schools to which black students are assigned. Third, there may be other effects of desegregation plans on black educational outcomes. Parents may become more involved in their children’s education as a result of increased information, or in order to reap the benefits of the fight they have recently won. The legal victory that usually accompanies a desegregation plan may also make black children feel enfranchised. Any analysis of the effect of desegregation plans will estimate the net effect of these three changes. The estimation of the net effect of desegregation plans on black educational outcomes is not completely straightforward, however. A comparison of integrated and segregated school systems at any point in time confounds the effect of the desegregation plans with the effect of factors that led to the imposition of the plan in the first place. I focus on a sample of large school districts, 86 percent of which implemented desegregation plans between 1961 and 1982. I use variation in the timing of the imposition of these plans to identify the effect of desegregation plans on black educational outcomes. In its simplest form the identification strategy is to use a difference-in-differences estimator. An example should help to clarify. Consider two school districts: 17 The index of dissimilarity can be thought of as the number of students that would have to move from their present school to fully integrate the district, relative to the number of students that would have to change schools to go from a fully segregated district to a fully integrated district. 8 Birmingham, Alabama, which desegregated in 1970, and St. Louis, Missouri, which desegregated in 1980. I compare high-school-aged blacks in the 1970 and 1980 censuses. In 1970, 17-year-olds in both cities had attended segregated schools all their lives. In 1980, 17-year olds in Birmingham had attended integrated schools since 2nd grade, while those in St. Louis had attended segregated schools throughout their education. The experiences in St. Louis are used to represent what would have happened in Birmingham in the absence of desegregation. A comparison of the change in the dropout rate in Birmingham relative to the change in the dropout rate in St. Louis is an estimate of the effect of desegregation. In the full analysis, the treatment group comprises districts that implemented desegregation plans between 1970 and 1979. In these districts, high school students in April of 1980 attended at least one year of school after the implementation of a desegregation plan, while high school students in April of 1970 attended segregated schools throughout their education.18 Districts that desegregated before 1970 and after 1979 are assigned to the control group. In the control districts, no desegregation plan was implemented between the time the 1970 and 1980 censuses were conducted. The analysis focuses on districts where there was ever a desegregation plan because I feel these districts should be more comparable, but expanding the control group to encompass all districts that did not desegregate in the 1970’s produces similar results. I observe the change in dropout rates in treatment districts, but it is unclear whether this change is due to desegregation or due to other factors that vary over time. Assuming that these other potential determinants of dropout status affect the treatment and control groups similarly, the change in dropout rates in the control group is an estimate of what would have happened in the treatment group in the absence of desegregation. Suppose that the dropout rates of high-school-aged blacks can be written19 (1) E[Di|t,g] = βt + γg + δTi 18 Census data refer to April 1st of the census year. 19 The notation that follows borrows heavily from Angrist and Krueger (1998). 9 where Di is an indicator of dropout status of individual i, βt is an effect for year t common to all school districts, γg is a time-constant effect specific to the treatment or control group, indexed by g, Ti is an indicator for living in 1980 in a district that desegregated between 1970 and 1980, and δ is the effect of desegregation on dropout rates. The dropout status of high-school-aged blacks can now be written (2) Di = βt + γg + δTi + εi where εi is an error term such that E[εi|t,g] = 0. The simplest difference-in-differences comparison is (3) {E[Di| g=treatment, t=1980] - E[Di| g=treatment, t=1970]} - {E[Di| g=control, t=1980] - E[Di| g=control, t=1970]} = δ. Since Ti is equal to the product of a dummy that equals 1 for observations in 1980 and an indicator for treatment observations, δ can be estimated with a simple regression of the model in (2). Suppose, however, that assignment to the treatment group is correlated with time-varying determinants of dropout status. The regression framework allows convenient control for a vector of individual characteristics, Xi, by estimation of the equation, (4) Di = Xi´β0 + β t + γg + δTi + εi where β0 is a vector of coefficients that includes a constant. Validity of the estimate of δ now only requires that, conditional on Xi, inclusion in the treatment group is uncorrelated with unobserved time-varying determinants of dropout status. Notice also that because there are many observations per school district, district effects can be included instead of the treatment main effect, γg. Since the treatment group is defined in terms of districts, the district indicators completely characterize the time- 10 constant effect specific to treatment districts and are thus more general. The model can now be written as, S −1 (5) Di = Xi´β0 + β t + ås =1 disαs + δTi + εi where dis indicates that i resides in school district s and S denotes the total number of school districts in the sample. The difference-in-differences estimator eliminates bias from any association between treatment and time-invariant characteristics of districts. But if desegregation is correlated with low past completion rates, i.e. a lagged dependent variable, then difference-in-differences estimates will exaggerate the effect of treatment.20 A more general model would allow for fixed district effects and control for lagged district-level dropout rates. The model can be written as follows: S −1 (6) Dit = Xit´β0 + β t + å s =1 dis αs + δTit + γE[Dit-1|s] + εit . Equation (6) is unidentified as written. Taking first differences and aggregating to the school district level yields (7) yst – yst-1 = (Xst – Xst-1)´β0 + β t + δTst + γ(yst-1 - yst-2) + εst - εst-1 where yst is the school district level dropout rate in year t. The model in equation (7) can be estimated using yst-2 as an instrument for (yst-1 - yst-2). In practice I cannot identify districts in 1960, and thus cannot estimate the model with fixed effects that controls for lagged dropout rates.21 I therefore report estimates that control for lagged dependent outcomes directly, without differencing or district effects. The model estimated in this case becomes, (8) Dit = Xit´β0 + δLDgi + γE[Dit-1|s] + εit 20 See, for example, Ashenfelter and Card (1985), and Appendix I. 21 The public use 1960 census does not identify geographic areas smaller than states. 11 where gi is an indicator for treatment districts. The estimate of δLD measures the conditional mean difference in dropout rates between treatment and control districts in 1980, controlling for dropout rates in 1970. If the timing of desegregation plans is a function of either time-invariant district characteristics or lagged district-level dropout rates, then under reasonably plausible assumptions the differencing and lagged dependent variables estimates will provide an upper and lower bound of the true effect of desegregation on black dropout rates. Specifically, suppose selection into treatment is an increasing function of fixed determinants of dropout rates such that, ì1 if α s > y Tst = í î0 otherwise where y is a constant. Call δˆLD the estimator that controls for lagged dependent variables and estimates the treatment effect. ˆ = δ + Cov(α s , Tst ) æ1 − σ α ö ≥ δ 2 plim δ LD ç ÷ Var(Tst ) ç σ α + σ ε2 ÷ ~ 2 è ø ~ where Tst is the residual from a regression of Tst on lagged dropout rates. The relationship is derived in Appendix I. Alternatively, suppose treatment is positively selected on lagged dropout rates, y st −1 , such that, ì1 if y st −1 > y Tst = í î 0 otherwise Call δˆDD the difference-in-difference estimator of the treatment effect. plim δ DD ˆ = δ − Ε[ε st −1 y st −1 > y ] ≤ δ 12 If treatment is positively selected either on lagged outcomes or on fixed determinants of lagged outcomes then, plim δˆDD ≤ δ ≤ plim δˆLD . Thus, the two estimators should bracket the causal effect of interest.22 4. Data In a report commissioned by the U.S. Commission on Civil Rights, Welch and Light (1987) evaluated the effect of desegregation plans on integration. They sampled 125 school districts for this purpose. This sample represents less than one percent of U.S. school districts, but about 20 percent of total enrollment and about half of minority enrollment in 1968.23 The analysis to follow focuses on this sample of very large school districts. Table I lists the districts included in the study and when they implemented a desegregation plan. Column 3 shows whether the district is assigned to the treatment or control group. I match 15-, 16- and 17-year-olds from the 1970 and 1980 censuses to the 125 districts based on individuals’ county group or SMSA of residence. County group is the smallest geographic identifier available on public use census data files in 1970 and 1980.24 Assigning individuals to districts is not straightforward, however, because the physical area described by county groups changed from 1970 to 1980. I use maps provided by the census bureau to determine the smallest geographic area identifiable in both years. To cover the 125 geographic areas I use three different census samples: the 1970 one-percent Metro sample, the 1980 one-percent Metro sample and the 1980 five-percent State sample. All three samples identify county groups, although the county groups in the State sample are slightly different because they do not cross state lines. The 1970 five-percent State sample does not identify any geographic area smaller than a state. The 1980 five-percent State sample identifies county groups and only SMSA’s that do not 22 The claim is derived more rigorously in Appendix I. 23 Welch and Light (1987), p. 34. 13 cross state lines. Where possible, I use the 1980 State sample because of the larger sample size, but in many cases it is impossible to match the area identified in 1970 with the county groups or SMSA’s identified in the 1980 State sample. Since the Metro samples are one-fifth the size of the State sample, observations are weighted to reflect the portion of the population they represent. 5. Results As can be seen in the means presented in Table II, the high school dropout rate of blacks in districts that did not desegregate in the 1970’s remained unchanged over that time period. In contrast, districts that desegregated between 1970 and 1980 experienced a decline in black dropout rates of 3.6 percentage points. The simplest difference-in- differences estimate as specified in equation (3) compares the change in dropout rates in treatment districts (-3.6 percent) to the change in dropout rates in control districts (0.2 percent). The relative change (-3.8 percent) is an estimate of the effect of desegregation plans on black dropout rates. An alternative method of obtaining the simple difference-in-differences estimate is by estimation of equation (2). This method is useful because it allows convenient control for characteristics that could potentially explain differential trends in dropout rates by treatment-control status. Estimates in Table III show that neither changes in demographic characteristics nor changes in the effect of these characteristics on dropout rates can explain the decline in black dropout rates between 1970 and 1980 among districts that implemented a desegregation plan in the interim. A nice feature of the ‘experiment’ is that there did not seem to be an appreciable shift in black dropout rates between 1970 and 1980 among districts that did not desegregate in the interim. As measured by the coefficient on the indicator for being an observation from 1980, the change in dropout rates among control districts is never significantly different from zero. The results of a natural experiment are always more 24 These groupings are very similar to PUMA’s in the 1990 census. 14 convincing when they are not measured amidst unexplained trends in the dependent variable. The specification of the simple difference-in-differences model allows controls for fixed characteristics only at the treatment group level. There is significant variation in dropout rates across districts. Because the data include many observations per district, I estimate the model controlling for district-level fixed differences in dropout rates. These fixed effects fully characterize the pre-treatment difference in dropout rates between treatment and control districts. Estimates that include fixed district effects instead of a treatment main effect, shown in Columns 4–6 of Table III, produce nearly identical point estimates of the effect of desegregation plans on black dropout rates (a 3 – 3.4 percentage point decline), but are significantly more precise. 5.1. Regional Variation in Dropout Rates and in the Timing of Desegregation The legal process that led to court-ordered desegregation plans proceeded differently in and out of the South. Additionally, there is significant regional variation in dropout rates. If not properly controlled for, region-specific trends in dropout rates may be attributed to the effect of desegregation plans. Such worries turn out to be unfounded as shown by the results from various specifications. Controls for permanent and time- varying region effects leave the results virtually unaffected (3.0 – 3.5 percentage point declines). Estimates that allow state-specific trends in dropout rates suggest a smaller decline (2 – 2.8 percentage points) in black dropout rates associated with desegregation. Alternatively, regressions run separately for each region, presented in Table IV, reveal that the estimated effect of desegregation plans on black dropout rates is remarkably consistent across regions. Estimates range from two to three percentage points in the Northeast to four to five percentage points in the West. The estimated effects in and out of the South are virtually the same, a three percentage point decline. 15 5.2. Two Control Groups Another useful feature of the experimental design is that there are two obvious control groups that can be used to check the robustness of the estimates. If there are secular trends in the timing of desegregation plans that are correlated with determinants of dropout rates, then the estimates presented in Tables III and IV are biased. For instance, schools that desegregated later may have been less in need of compensatory intervention for black students. Natural convergence would then be spuriously attributed to the treatment effect. However, if such determinants of the timing of desegregation plans operated monotonically, then regressions that compare districts that desegregated in the 1970’s to districts that desegregated in the 1960’s and 1980’s separately should yield more convincing estimates. Another concern is that desegregation plans may not take effect immediately. Districts that desegregated in the late 1960’s may not have felt the full effect of desegregation by 1970. These districts would have experienced some effect of desegregation between 1970 and 1980, leading to an underestimate of the effect of desegregation plans on the districts that desegregated in the 1970’s. Estimates that compare the districts that desegregated in the 1970’s separately to districts that desegregated earlier and later, presented in Table V, suggest that the estimates from the standard specifications are reasonable. Estimated effects of desegregation plans on black dropout rates are slightly larger when comparing to districts that desegregated in the 1980’s (3.2 – 3.9 percent declines compared to 2.3 – 3.0 percent declines), which lends weak support to each of the above concerns. However, the estimates do not differ significantly either from each other or from the estimates of the standard specifications in Table III. 5.3. Changing Demographics Demographic characteristics may have changed differently in the districts that desegregated in the 1970’s. For instance, if family income among high-school-aged blacks increased more in these districts, then one would expect to see larger declines in 16 dropout rates even if desegregation had no effect. Changing gender and age compositions could similarly explain the relative decline in dropout rates in the districts that desegregated in the 1970’s. Additionally, the economic characteristics of black families may have remained relatively constant in the treatment and control districts, but the effect of family income on dropout rates may have changed over time. If, for instance, family income among blacks is permanently higher in treatment districts and the relationship between family income and dropout rates became stronger over time, imperfect controls for this shift would lead to spuriously negative estimates of desegregation on dropout rates. The regression results presented in Columns 5 and 6 of Table III address these worries by controlling for the age, gender and family income of high-school-aged blacks and by allowing the effects of these characteristics on dropout rates to vary over time. Again, the estimated decline in black high school dropout rates due to desegregation plans remains consistently near three percentage points. 5.4. Selective Migration Large-scale integration may have induced migration of blacks and whites. Assignment of observations to districts in the analysis thus far has been based on residence on April 1st of the current year. Validity of the estimates presumes that migration into and out of districts is not affected by desegregation plans. At the very least the analysis assumes that desegregation-induced migrants do not have different dropout propensities from the rest of the population in the absence of desegregation. While much has been written on desegregation-induced white migration—often termed “white flight”—little has been discussed about the parallel phenomenon for black families. One might still worry that families of potential dropouts avoided desegregating areas when they moved, or that families of good students sought desegregating districts. 17 The former concern is likely to be more relevant as movers tended to be from lower- income families and had higher dropout rates.25 The data allow three empirical checks of whether selective migration did in fact bias the previous estimates. In both 1970 and 1980 there are questions on the public use census files asking whether individuals have moved during the previous five years. In Table VI, I present estimates from models similar to those in Table III but with a discrete dependent variable that indicates whether the individual has moved from the county group where he lived five years ago. These results do not suggest that desegregation had any effect on migration. Columns 1–3 in Table VII present estimates from models that again use dropout status as the dependent variable, but control for whether you have moved from your county group of five years ago. Estimates of the treatment effect are unchanged from those in Table III. While it is not available in the 1970 census, there is a question asked of half of the 1980 sample that indicates individuals’ county group of residence in 1975. Columns 4–6 of Table VII report estimates of models from Table III using county group in 1975 to assign districts to the 1980 data. Estimates of the effect of desegregation on black high school dropout rates are larger but more imprecise due to smaller sample sizes. Differential migration into desegregating districts in the period from 1975 to 1980 do not seem to explain the estimated treatment effects from the standard specifications in Table III. The questions available on the public use census files address migration into districts, as opposed to migration out of districts. Welch and Light (1987) and Rossell and Armor(1996) show that the implementation of desegregation plans led to an increase in the speed of migration of whites out of urban school districts. If there is a similar phenomenon among blacks, the previous estimates are compromised. In fact, the problem is not as serious as it may seem because the districts referred to in this analysis are larger in physical area than actual school districts. In practice, districts as measured by county groups include many of the suburban areas to which migrants may have fled. Moreover, the data show no indication that desegregation plans led to a decrease in the 25 The dropout rate in the sample among those who had moved from their county group of residence from five years ago is 18.3 percent, while that of non-movers is 11.7 percent. The average family income of movers is $11,608, while that of non-movers is $13,298. 18 population of high-school-aged blacks in districts. Estimates in Table VIII, together with those presented in Tables VI and VII, suggest that desegregation had little effect on migration in or out of districts. 5.5. Mean Reversion Perhaps the most important concern with estimates in Table III is that mean reversion may explain the decline in dropout rates attributed to desegregation. The difference-in-differences strategy presumes that treatment is selected on fixed characteristics of districts. If that is the case, differencing over time eliminates the resulting fixed differences between treatment and control group dropout rates. On the other hand, the fact that dropout rates in 1970 were higher in treatment districts than in control districts may lead to biased estimates. If treatment was not selected on the fixed characteristics that led to permanently higher dropout rates, but on unusually high dropout rates in 1970, then mean reversion may explain the decline in dropout rates in the treatment districts during the 1970’s. If treatment is determined largely by lagged outcomes and not by permanent differences in dropout rates then models that control for 1970 dropout rates and compare treatment and control dropout rates in 1980 are more appropriate. Estimates that control for lagged district-level dropout rates are presented in Table IX. The basic specification that controls for lagged outcomes associates a 2.2 percent decline in dropout rates with desegregation. Models that also control for age, region, gender and family income yield estimates of a smaller decline (0.9 – 1.4 percent). Treatment effects are negative, but smaller in magnitude than estimated by difference-in-differences models. The smaller magnitudes suggest that mean reversion may account for a large portion of the treatment effect estimated by the difference-in-differences estimator. Controlling for lagged dependent variables assumes a linear relationship between dropout rates in 1970 and 1980 in the absence of treatment. Alternatively, I can match districts non-parametrically based on 1970 dropout rates. For instance, the estimates in Columns 5–7 of Table IX are from a model in which I break up the sample based on deciles of the 1970 district-level dropout rate distribution computed separately by age. I 19 then compare treatment and control group dropout rates in 1980 within each of these thirty strata, conditional on various characteristics. To get estimates of full-sample coefficients I take averages of the thirty coefficients weighted by the number of treatment observations in the stratum.26 Matching estimates yield slightly smaller negative estimates of desegregation plans on black dropout rates. Given that specifications that control for lagged dropout rates produce less negative estimates and that pre-treatment dropout rates are higher in treatment districts it is possible that mean reversion can account for some of the difference-in-differences treatment effects. However, it is not clear that the estimators that control for 1970 dropout rates are more appropriate than the difference-in-differences estimator. If treatment is selected on fixed characteristics, estimates that control for lagged outcomes will be biased in the direction of the permanent difference in dropout rates. Since treatment dropout rates are higher in 1970, estimates that control for dropout rates in 1970 will be biased positively. The claim is explained more rigorously in Appendix I, but the implication is that under certain assumptions the lagged outcome and difference- in-differences estimators provide an upper and lower bound of the causal effect of desegregation plans on dropout rates. In particular, I show that if treatment is selected either on fixed (permanent) characteristics or on lagged outcomes then these two estimates will bracket the true value of the coefficient of interest. 5.6. The Effect of Desegregation Plans’ Characteristics While the ultimate goal of every desegregation plan was at some level the same, the methods each employed varied. Some plans redrew attendance zone boundaries in the district. Others assigned all children to the school closest to their home. Still others created schools, called magnets, that specialized in certain disciplines to attract students. More can be learned about the way desegregation plans affected black educational outcomes by examining differential effects of different plans. An important distinguishing characteristic of a desegregation plan is whether it allows students any choice about which school to attend. Table X presents difference-in- 26 See Angrist and Lavy (1998) or Acemoglu and Angrist (1998) for an explanation of this estimator. 20 differences estimates from models that allow the effect of a desegregation plan to vary by whether the plan allowed choice. The results suggest that plans that assigned students to schools were associated with a larger decline in the dropout rates of blacks than plans that allowed choice. 5.7. Estimated Effects for Whites There is reasonably consistent evidence that desegregation plans led to significant declines in high school dropout rates of blacks. The analysis thus far presumes that changes in unobservable characteristics of districts were not different in the districts that desegregated in the 1970’s. One way to check this assumption is to perform the same analysis on whites. Additionally, the effect of desegregation plans on white dropout rates is interesting in its own right. Just as black students are placed in schools with white students, white students are placed in schools with black students. Just as black students are assigned to better schools, white students are assigned to worse schools. Estimates of the standard specifications for high-school-aged whites are reported in Table XI. Whereas blacks experienced a decline in dropout rates as a result of desegregation plans, there did not seem to be any similar effect on whites. Estimated effects of desegregation plans on white dropout rates are all positive but insignificantly different from zero. Standard errors of the estimated effects are fairly small, but point estimates are too small to distinguish from zero. As mentioned earlier, one might worry that desegregation-induced migration out of districts would bias the estimates. In fact, if desegregation caused white families with good students to leave the district then dropout rates among the remaining high-school- aged whites would be higher. Remember, however, that districts as defined in the analysis are larger in physical area than school districts. They include the suburban areas to which whites likely moved to avoid desegregation. So, white migration is not necessarily a large problem for the analysis. Indeed, examination of the effect of desegregation plans on the population of high-school-aged whites in the district shows no evidence of desegregation-induced migration from districts as defined in this analysis. 21 The results for whites have two important implications. First, they lend credence to the results for blacks. If the results for whites had suggested that desegregation plans led to a decline in dropout rates of whites, one might think that district-specific trends in unobservables were driving the decline in black dropout rates. Second, it seems that desegregation plans did not have large effects on white dropout rates. Since black students are in the minority even in large school districts, whites should have, on average, experienced smaller changes in their set of peers and in the quality of schools they attended. Thus, it is not surprising that the effects of desegregation were smaller in magnitude on whites than on blacks. However, using the median point estimates from the standard specifications for blacks and whites, the analysis suggests that overall dropout rates declined as a result of desegregation plans. 6. School Quality or Peer Effects? Given the apparent negative impact of desegregation on black dropout rates, a natural question is whether the improvement in black educational outcomes was a result of improved school quality or of interactions between blacks and whites. As mentioned in the introduction, the net effect of desegregation plans is interesting on its own, but desegregation also provides an opportunity to study the existence of human capital spillovers in schools and the effectiveness of school quality. In light of data limitations, however, it is not a simple task to identify each effect separately. If school-level data on peers and resources were available, finer measures of the timing of desegregation plans could be used to identify peer and school quality effects on educational outcomes. Information that is available provides evidence that at least some of the effect of desegregation plans worked through their effect on the composition of students’ peers in school. Data collected by the U.S. Department of Health, Education, and Welfare (HEW) in 1970 provide school-level full-time teacher and student enrollment counts by race for the largest school districts in the nation. With this data I can compute the pupil-teacher ratio and the proportion of black students and teachers in each school. 22 One might suspect that in segregated school districts black students attended schools with higher pupil-teacher ratios. Coleman (1966) shows that, perhaps surprisingly, there were few large observable differences between the schools that black and white children attended in the mid-1960’s. His findings are consistent with those of Card and Krueger (1992) who show that the convergence in observable school quality began well before the Brown decision in 1954, and that by the mid-1960’s the schools that black and white students attended were observationally almost indistinguishable. Indeed, the HEW data from 1970 suggest that, in districts that would desegregate in the ensuing decade, blacks did not attend schools with higher pupil-teacher ratios. If anything, schools that had proportionally more black students had lower pupil-teacher ratios. As seen in Table XII, the average pupil-teacher ratio in schools with more than 75 percent black students was 26.7 while the average pupil-teacher ratio in schools with less than 25 percent black students was 27.9. The data do not seem to be consistent with the view that predominantly black schools had larger pupil-teacher ratios. One observable dimension along which predominantly black and white schools did differ in 1970 was the characteristics of teachers. In school districts that were to desegregate in the next decade, predominantly black schools were much more likely to have black teachers. In schools with a more than 75-percent-black student body 56.5 percent of teachers were black. In schools with a less than 25-percent-black student body 7.9 percent of teachers were black. This relationship is striking. A regression of the fraction of black teachers in a school on the fraction of black students in a school yields a coefficient of 0.53 with a standard error of less than 0.01. This slope indicates that a 10 percentage point increase in the fraction of black students in a school was associated with a 5.3 percentage point increase in the fraction of black teachers in the school. What is also striking is that the relationship holds within school districts. Estimation of the same model including fixed school district effects shows that a 10 percentage point increase in the fraction of black students in a school was associated with a 4.5 percentage point increase in the fraction of black teachers in the school. That black students in segregated school districts were more likely to be taught by black teachers is of interest for two reasons. First, black teachers may have had more or less education and experience than white teachers. Second, conditional on the skill level 23 of the teacher his race may have an effect on his students. What evidence exists suggests that the latter effect is likely to be that a black teacher has a positive effect on black students.27 Since desegregation likely caused black students to be less likely to be taught by black teachers, this effect cannot explain the decline in black dropout rates I attribute 28 to desegregation plans. As for the former point, a comparison of black and white teachers in the March 1970 Current Population Survey (CPS), presented in Table XIII, shows that black teachers on average had 2.5 years less of potential experience and 1.5 years less of education.29 What does this imply about the effect of desegregation on the average experience and education level of the typical black student’s teacher? Some simple notation will make the relevant calculation more clear. Let EB and EW be the population average level of education or experience of black and white teachers, respectively. Also, let NBs denote the enrollment of black students at school s and let τBs denote the fraction of black teachers at school s. The fraction of black teachers at the typical black student’s school is åN τ Bs Bs s ≡τB. åN s Bs In segregated school districts the average education (or experience) level of the typical black student’s teacher is QS = τ B E B + (1 − τ B ) EW assuming all teachers are either black or white. If school districts are fully integrated then the typical black student’s teacher would have QI = τ P E B + (1 − τ P ) EW 27 See Ehrenberg and Brewer (1994). Coleman (1966) finds little effect of the proportion of white teachers on the test scores of students. 28 Freeman (1977) claims that desegregation led to a decline in demand for black teachers, but that a coincidental increase in black voting power offset this decline such that the relative employment of blacks in teaching remained stable. 29 The same relationship is true amongst teachers who lived in the SMSA’s in which the school districts that desegregated in the 1970’s are located. 24 years of education (or experience), where τP denotes the fraction of teachers in the population who are black. Using data from the 1970 census and from the 1970 HEW enrollment survey, I can calculate QI – QS as an estimate of the effect of desegregation on the education (or experience) level of the typical black student’s teacher. As measured in the census, the average education levels of white and black teachers in 1970 were 15.9 and 15.6 years respectively. Similarly, white and black teachers in 1970 respectively had 16.4 and 15.5 years of potential experience. In school districts that would desegregate in the 1970’s, the typical black student went to a school with 80 percent black teachers, while 29 percent of teachers in the population were black. These estimates imply that in these segregated school districts the typical black student was taught by teachers with 15.7 years of education and 15.7 years of experience. The estimates also imply that if these school districts were fully integrated the typical black student would be taught by teachers with 15.8 years of education and 16.1 years of experience. Desegregation could have at most increased the educational attainment by 0.1 years and the experience level by 0.4 years of the typical black student’s teacher. If these changes in the quality of schools that black students attended were to explain the decline in black dropout rates due to desegregation the combined elasticity of dropout rates with respect to teachers’ education and experience levels would have to be near –9. It seems reasonable to assume that changes in the characteristics of black students’ teachers cannot explain the decline in black dropout rates in school districts that desegregated in the 1970’s. The evidence suggests that pupil-teacher ratios were not larger in predominantly black schools. Similarly, previous work has shown that there were no marked differences in the term length and teacher salaries at schools that blacks and whites attended by the mid-1960’s. Desegregation may have led to an improvement along other dimensions of the quality of schools that blacks attended. One might consider a student’s peers one of those dimensions. Did the effect of desegregation plans on black dropout rates work through the plans’ effect on the peer composition or the quality of the schools blacks attended? It seems that peer effects played at least some role. It may seem surprising that sitting in class next to a white student would induce a black student to finish high school. Race is a 25 powerful proxy for socioeconomic status, however. It seems less surprising that a child whose parents are high school dropouts is more likely to stay in school because he attends school with children whose parents are high school graduates. This argument suggests that socioeconomic integration regardless of race may be at least as important as racial integration. 7. Conclusions Despite desegregation’s prominent role in post-World War II education policy, few economists have studied its impact on the educational outcomes of the affected students. Comparisons of the educational attainment of black students from segregated and integrated school systems confound the effect of desegregation with the determinants of desegregation itself. I exploit variation in the timing of desegregation plans to identify the effect of these plans on the high school dropout rates of blacks. Specifically, I compare the change in black dropout rates from 1970 to 1980 in districts that desegregated in the interim to the change in districts that desegregated in the 1960’s and the early 1980’s. Using data from the 1970 and 1980 censuses, I control for time-varying region effects and for changes in family income across districts. The results suggest that desegregation plans led to a one to three percentage point decline in the dropout rates of blacks, and that desegregation had little or no effect on the dropout rates of whites. Estimates from models that control for lagged dropout rates indicate that mean reversion may account for some of the apparent decline in dropout rates attributed to desegregation. I show, however, that under certain reasonable assumptions, the difference-in-differences and lagged dropout rate specifications should provide estimates that bracket the causal effect of desegregation on dropout rates. Desegregation also provides an opportunity to study the effect of peers and school quality on the educational outcomes of students. The production function of a school has long been of interest to economists. Under most circumstances, the peers and quality of resources at a child’s school are subject to his or his parents’ choice. Subsequently, the estimation of peer and school quality effects is difficult in practice. Desegregation plans 26 took away the ability to choose a child’s peers and school resources. Accordingly, desegregation allows for estimation of the net effect of these two characteristics of schools. Data limitations make separate estimation of peer and school quality effects difficult, although examination of the conditions in segregated schools in 1970 suggests that peer effects had some role in the decline in dropout rates attributed to desegregation plans. Further investigation of the mechanisms by which desegregation plans affected the educational outcomes of black students is clearly warranted. Other natural avenues for future work include an examination of the effect of desegregation plans on wages later in life, and an analysis of the termination of desegregation plans. 27 References Acemoglu, Daron and Joshua Angrist, “Consequences of Employment Protection? The Case of the Americans with Disabilities Act,” NBER Working Paper No. 6670 (July 1998). Angrist, Joshua D. and Victor Lavy, “Does Teacher Training Affect Pupil Learning? Evidence from Matched Comparisons in Jerusalem Public Schools,” NBER Working Paper No. 6781 (November 1998). Angrist, Joshua D. and Victor Lavy, “Using Maimonides’ Rule to Estimate the Effect of Class Size on Scholastic Achievement,” Quarterly Journal of Economics (May 1999) pp. 533- 575. Angrist, Joshua D. and Alan B. Krueger, “Empirical Strategies in Labor Economics,” MIT Department of Economics Working Paper (October 1998). Armor, David J., Forced Justice: School Desegregation and the Law, Oxford University Press (New York: 1995). Ashenfelter, Orley and David Card, “Using the Longitudinal Structure of Earnings to Estimate the Effect of Training Programs,” Review of Economics and Statistics (November 1985) pp. 648-660. Becker, Gary S. and Kevin M. Murphy, “The Division of Labor, Coordination Costs, and Knowledge,” Quarterly Journal of Economics (November 1992) pp. 1137-1160. Benabou, Roland, “Workings of a City: Location, Education, and Production,” Quarterly Journal of Economics (August 1993) pp. 619-652. Boozer, Michael A., Alan B. Krueger, and Shari Wolkon, “Race and School Quality Since Brown v. Board of Education,” Brookings Papers on Economic Activity: Microeconomics, Martin N. Bailey and Clifford Winston, Eds. (1992) pp. 269-326. Card, David and Alan B. Krueger, “School Quality and Black-White Relative Earnings: A Direct Assessment,” Quarterly Journal of Economics (February 1992) pp. 151-200. Card, David and Alan B. Krueger, “School Resources and Student Outcomes: An Overview of the Literature and New Evidence from North and South Carolina,” Journal of Economic Perspectives (Fall 1996) pp. 31-50. Case, Anne C. and Lawrence F. Katz, “The Company You Keep: The Effects of Family and Neighborhood on Disadvantaged Youths,” NBER Working Paper No. 3705 (May 1991). Coleman, James S., Equality of Educational Opportunity, U. S. Department of Health, Education, and Welfare (Washington D. C.: 1966). Coleman, James S., “Trends in School Segregation, 1968-1973,” The Urban Institute (Washington, D.C.: August 1975). 28 Crain, Robert and Rita Mahard, “The Effect of Research Methodology of Desegregation- Achievement Studies: A Meta-Analysis,” American Journal of Sociology (Vol. 88 No. 5, 1983) pp. 839-854. Cutler, David M. and Edward L. Glaeser, “Are Ghettos Good or Bad?,” Quarterly Journal of Economics (August 1997) pp. 827-872. Ehrenberg, Ronald G. and Dominic J. Brewer, “Do School and Teacher Characteristics Matter? Evidence from High School and Beyond,” Economics of Education Review (Vol. 13 No. 1, 1994) pp. 1-17. Epple, Dennis and Richard E. Romano, “Competition Between Private and Public Schools, Vouchers, and Peer-Group Effects,” American Economic Review (March 1998) pp. 33- 62. Evans, William N., Wallace E. Oates and Robert M. Schwab, “Measuring Peer Group Effects: A Study of Teenage Behavior,” Journal of Political Economy (October 1992) pp. 966-991. Fancher, Betsy, “Voices From the South: Black Students Talk About Their Experiences in Desegregated Schools,” Southern Regional Council (August 1970). Finch, Minnie, The NAACP: Its Fight for Justice, The Scarecrow Press, Inc. (Metuchen, N.J.: 1981). Hanushek, Eric A., “The Economics of Schooling: Production and Efficiency in Public Schools,” Journal of Economic Literature (September 1986) pp. 1141-1177. Heckman, James J., Robert J. LaLonde, and Jeffrey A. Smith, “The Economics and Econometrics of Active Labor Market Programs,” Handbook of Labor Economics, Vol. III, Orley Ashenfelter and David Card Eds. (Amsterdam: 1999). Heckman James, Anne Layne-Farrar and Petra Todd, “Does Measured School Quality Really Matter? An Examination of the Earnings-Quality Relationship,” Does Money Matter? The Effect of School Resources on Student Achievement and Adult Success, Gary Burtless, Ed., Brookings Institution Press (Washington, D.C.: 1996) pp. 192-289. Hill, Roscoe and Malcom Feeley, Eds., Affirmative School Integration, Sage Publications (Beverly Hills, CA: 1968). Hoxby, Caroline, “The Effects of Class Size and Composition on Student Achievement: New Evidence from Natural Population Variation,” mimeo (July 1996). Imbens, Guido, Jeffrey B. Liebman, and Nada Eissa, “The Econometrics of Difference in Differences,” mimeo (January 1997). Jones, Leon, From Brown to Boston: Desegregation in Education, 1954-1974: Vols. I & II, The Scarecrow Press (Metuchen, N. J.: 1979). Keynes, Edward and Randall K. Miller, The Court vs. Congress: Prayer, Busing, and Abortion, Duke University Press (Durham, NC: 1989). 29 Krueger, Alan B., “Experimental Estimates of Education Production Functions,” Quarterly Journal of Economics (May 1999) pp. 497-532. Manski, Charles F. “Academic Ability, Earnings, and the Decision to Become a Teacher: Evidence from the National Longitudinal Study of the High School Class of 1972,” Public Sector Payrolls, David A. Wise Ed. (1987). Margo, Robert A., Race and Schooling in the South, 1880-1950, University of Chicago Press (Chicago: 1990). Miller, LaMar P. Ed., Brown Plus Thirty: Perspectives on Desegregation, Metropolitan Center for Educational Research, Development and Training, (New York: 1986). Orfield, Gary, Must We Bus? Segregated Schools and National Policy, The Brookings Institution (Washington, D. C.: 1978). Orfield, Gary, Public School Desegregation in the United States, 1968-1980, Joint Center for Political Studies (Washington, D. C.: 1983). Orfield, Gary and Susan Eaton, Dismantling Desegregation: The Quiet Reversal of Brown v. Board of Education, The New Press (New York: 1996). Peltzman, Sam, “The Political Economy of the Decline of American Public Education,” Journal of Law and Economics (April 1993) pp. 331-370. Peltzman, Sam, “Political Economy of Public Education: Non-College-Bound Students,” Journal of Law and Economics (April 1996) pp. 73-120. Rodgers, Harrell R., Jr. and Charles S. Bullock, III, Law and Social Change: Civil Rights Laws and Their Consequences, McGraw-Hill Book Company (New York: 1972). Rossell, Christine and David Armor, “The Effectiveness of School Desegregation Plans, 1968- 1991,” American Politics Quarterly (July 1996) pp. 267-302. U. S. Bureau of the Census, Public Use Samples of Basic Records From the 1970 Census: Description and Technical Documentation (Washington, D. C.: 1972). U. S. Bureau of the Census, Census of Population and Housing, 1980 (United States): Public Use Microdata Samples Technical Documentation (Washington, D. C.: 1983). U. S. Commission on Civil Rights, “Racial Isolation in the Public Schools,” (1967). U. S. Commission on Civil Rights, “Southern School Desegregation, 1966-67,” (July 1967). U. S. Commission on Civil Rights, “School Desegregation: The Courts and Suburban Migration,” (December 1975). U. S. Commission on Civil Rights, “Fulfilling the Letter and Spirit of the Law: Desegregation of the Nation’s Public Schools,” (August 1976). 30 U. S. Commission on Civil Rights, “Desegregation of the Nation’s Public Schools: A Status Report,” (February 1979). U. S. Department of Health, Education and Welfare, Office for Civil Rights, Directory of Public Elementary and Secondary Schools in Selected Districts; Enrollment and Staff by Racial/Ethnic Group (Fall 1970). Welch, Finis and Audrey Light, “New Evidence on School Desegregation,” U. S. Commission on Civil Rights Clearinghouse Publication 92 (June 1987). Wilder, Margaret G., “Black Assimilation in the Urban Environment; The Impact of Migration and Mobility,” R & E Research Associates, Inc. (Palo Alto, CA: 1979). 31 FIGURE I: FRACTION OF 15-18-YEAR OLDS NOT ENROLLED IN SCHOOL, BY RACE 0.16 0.14 0.12 0.1 0.08 0.06 White Black 0.04 0.02 0 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 Note: Figure shows the fraction of 15-17 year olds not enrolled in school and 18-year-olds not enrolled in school and not high school graduates. Data are from the October Current Population Survey. Each data point represents the midpoint of a three-year moving average. TABLE I: LIST OF SCHOOL DISTRICTS IN THE SAMPLE Grade of Desegregation Year of Treatment or School District Desegregation 1970 1980 Control NEW ORLEANS PARISH LA 1961 Elem Before Control NEWARK NJ 1961 Elem Before Control HARFORD COUNTY MD 1965 JHS Before Control OAKLAND CA 1966 HS Before Control HARTFORD CT 1966 HS Before Control GRAND RAPIDS MI 1968 HS Elem Control TACOMA WA 1968 HS Elem Control RICHMOND CA 1969 HS Elem Control BREVARD COUNTY FL 1969 HS Elem Control LEE COUNTY FL 1969 HS Elem Control PINELLAS COUNTY FL 1969 HS Elem Control POLK COUNTY FL 1969 HS Elem Control VOLUSIA COUNTY FL 1969 HS Elem Control CADDO PARISH LA 1969 HS Elem Control CALCASIEU PARISH LA 1969 HS Elem Control RAPIDES PARISH LA 1969 HS Elem Control TERREBONNE PARISH LA 1969 HS Elem Control CUMBERLAND COUNTY NC 1969 HS Elem Control NEW HANOVER COUNTY NC 1969 HS Elem Control SAN ANTONIO TX 1969 HS Elem Control PITTSYLVANIA COUNTY VA 1969 HS Elem Control BIRMINGHAM AL 1970 After Elem Treatment PASADENA CA 1970 After Elem Treatment STAMFORD CT 1970 After Elem Treatment BROWARD COUNTY FL 1970 After Elem Treatment DADE COUNTY FL 1970 After Elem Treatment PALM BEACH COUNTY FL 1970 After Elem Treatment EAST BATON ROUGE PARISH LA 1970 After Elem Treatment ROCHESTER NY 1970 After Elem Treatment GASTON COUNTY NC 1970 After Elem Treatment MECKLENBURG COUNTY NC 1970 After Elem Treatment CHARLESTON COUNTY SC 1970 After Elem Treatment GREENVILLE COUNTY SC 1970 After Elem Treatment RICHLAND COUNTY SC 1970 After Elem Treatment HOUSTON TX 1970 After Elem Treatment NORFOLK VA 1970 After Elem Treatment ROANOKE VA 1970 After Elem Treatment JEFFERSON COUNTY AL 1971 After Elem Treatment MOBILE AL 1971 After Elem Treatment LITTLE ROCK AK 1971 After Elem Treatment SAN FRANCISCO CA 1971 After Elem Treatment Note: Table lists school districts in the Welch and Light (1987) study, which are also the districts used in this study. Districts are chosen based on the following criteria, as described in Welch and Light (1987). Every district with 50,000 or more students in 1968 and 20 to 90 percent minority representation are included. Districts with 15,000 or more students in 1968 and ten to 90 percent minority representation were chosen with sampling probabilities proportional to their size and regional representation. The remaining districts—those with fewer than 15,000 students in 1968, less than ten percent minority representation—were excluded from the sample. Grade of Desegregation columns identify the grade a 17-year-old in 1970 (1980) was in when the school district desegregated. Year of Desegregation column reports the year the district’s major desegregation plan was implemented according to Welch and Light (1987). TABLE I (CONT.) Grade of Desegregation Year of Treatment or School District Desegregation 1970 1980 Control DUVAL COUNTY FL 1971 After Elem Treatment HILLSBOROUGH COUNTY FL 1971 After Elem Treatment MUSCOGEE COUNTY GA 1971 After Elem Treatment FORT WAYNE IN 1971 After Elem Treatment WICHITA KS 1971 After Elem Treatment JEFFERSON PARISH LA 1971 After Elem Treatment TULSA OK 1971 After Elem Treatment NASHVILLE TN 1971 After Elem Treatment DALLAS TX 1971 After Elem Treatment ARLINGTON COUNTY VA 1971 After Elem Treatment ORANGE COUNTY FL 1972 After Elem Treatment FAYETTE COUNTY KY 1972 After Elem Treatment LANSING MI 1972 After Elem Treatment CLARK COUNTY NV 1972 After Elem Treatment OKLAHOMA CITY OK 1972 After Elem Treatment AMARILLO TX 1972 After Elem Treatment ATLANTA GA 1973 After JHS Treatment ROCKFORD IL 1973 After JHS Treatment INDIANAPOLIS IN 1973 After JHS Treatment PRINCE GEORGE'S COUNTY MD 1973 After JHS Treatment CINCINNATI OH 1973 After JHS Treatment LAWTON OK 1973 After JHS Treatment MEMPHIS TN 1973 After JHS Treatment FORT WORTH TX 1973 After JHS Treatment WACO TX 1973 After JHS Treatment RALEIGH COUNTY WV 1973 After JHS Treatment DENVER CO 1974 After JHS Treatment BALTIMORE MD 1974 After JHS Treatment BOSTON MA 1974 After JHS Treatment SPRINGFIELD MA 1974 After JHS Treatment MINNEAPOLIS MN 1974 After JHS Treatment PORTLAND OR 1974 After JHS Treatment JEFFERSON COUNTY KY 1975 After JHS Treatment DETROIT MI 1975 After JHS Treatment SACRAMENTO CA 1976 After HS Treatment NEW BEDFORD MA 1976 After HS Treatment OMAHA NB 1976 After HS Treatment JERSEY CITY NJ 1976 After HS Treatment DAYTON OH 1976 After HS Treatment DALLAS TX 1976 After HS Treatment MILWAUKEE WI 1976 After HS Treatment Note: Table lists school districts in the Welch and Light (1987) study, which are also the districts used in this study. Districts are chosen based on the following criteria, as described in Welch and Light (1987). Every district with 50,000 or more students in 1968 and 20 to 90 percent minority representation are included. Districts with 15,000 or more students in 1968 and ten to 90 percent minority representation were chosen with sampling probabilities proportional to their size and regional representation. The remaining districts—those with fewer than 15,000 students in 1968, less than ten percent minority representation—were excluded from the sample. Grade of Desegregation columns identify the grade a 17-year-old in 1970 (1980) was in when the school district desegregated. Year of Desegregation column reports the year the district’s major desegregation plan was implemented according to Welch and Light (1987). 34 TABLE I (CONT.) Grade of Desegregation Year of Treatment or School District Desegregation 1970 1980 Control SAN DIEGO CA 1977 After HS Treatment KANSAS CITY KS 1977 After HS Treatment KANSAS CITY MO 1977 After HS Treatment AKRON OH 1977 After HS Treatment FRESNO CA 1978 After HS Treatment LOS ANGELES CA 1978 After HS Treatment SAN BERNARDINO CA 1978 After HS Treatment NEW CASTLE COUNTY DE 1978 After HS Treatment PHILADELPHIA PA 1978 After HS Treatment EL PASO TX 1978 After HS Treatment LUBBOCK TX 1978 After HS Treatment SEATTLE WA 1978 After HS Treatment TUCSON AZ 1979 After HS Treatment CLEVELAND OH 1979 After HS Treatment COLUMBUS OH 1979 After HS Treatment LONG BEACH CA 1980 After After Control DOUGHERTY COUNTY GA 1980 After After Control ST. LOUIS MO 1980 After After Control BUFFALO NY 1980 After After Control TOLEDO OH 1980 After After Control PITTSBURGH PA 1980 After After Control AUSTIN TX 1980 After After Control SAN JOSE CA 1981 After After Control SOUTH BEND IN 1981 After After Control CHICAGO IL 1982 After After Control ECTOR COUNTY TX 1982 After After Control MESA AZ None MODESTO CA None VALLEJO CA None PUEBLO CO None GARY IN None SAGINAW MI None ALBUQUERQUE NM None LAS CRUCES NM None NEW YORK NY None LORAIN OH None Note: Table lists school districts in the Welch and Light (1987) study, which are also the districts used in this study. Districts are chosen based on the following criteria, as described in Welch and Light (1987). Every district with 50,000 or more students in 1968 and 20 to 90 percent minority representation are included. Districts with 15,000 or more students in 1968 and ten to 90 percent minority representation were chosen with sampling probabilities proportional to their size and regional representation. The remaining districts—those with fewer than 15,000 students in 1968, less than ten percent minority representation—were excluded from the sample. Grade of Desegregation columns identify the grade a 17-year-old in 1970 (1980) was in when the school district desegregated. Year of Desegregation column reports the year the district’s major desegregation plan was implemented according to Welch and Light (1987). 35 TABLE II: MEANS OF SELECTED VARIABLES BY TREATMENT-CONTROL STATUS 1970 1980 Variables Full Sample Full Desegregated Control Full Desegregated Control 1970-1979 1970-1979 Dropout .120 .135 .143 .116 .110 .107 .118 (.325) (.342) (.351) (.321) (.313) (.309) (.323) Female .50 .50 .50 .50 .50 .50 .51 (.50) (.50) (.50) (.50) (.50) (.50) (.50) Age 16 .33 .32 .33 .31 .33 .33 .33 (.47) (.47) (.47) (.46) (.47) (.47) (.47) Age 17 .32 .32 .32 .24 .33 .33 .34 (.47) (.46) (.47) (.43) (.47) (.47) (.47) Northeast .11 .12 .10 .17 .11 .09 .16 (.32) (.33) (.30) (.37) (.31) (.28) (.36) Midwest .29 .31 .25 .44 .28 .22 .42 (.45) (.46) (.43) (.50) (.45) (.41) (.49) South .48 .44 .50 .32 .50 .55 .36 (.50) (.50) (.50) (.47) (.50) (.50) (.48) West .11 .11 .12 .08 .11 .13 .07 (.31) (.31) (.33) (.26) (.32) (.34) (.26) Family Income 13,218 7,815 7,870 7,695 16,924 17,117 16,439 (11,598) (5,621) (5,703) (5,435) (13,090) (13,087) (13,087) Poverty 171 157 157 158 181 184 175 (128) (115) (115) (115) (135) (135) (134) Year of Desegregation 1973.8 1973.8 1973.8 1973.8 1973.7 1973.6 1974.0 (5.1) (5.2) (3.1) (8.2) (5.0) (3.1) (8.0) No. Obs. 53,331 7,256 5,019 2,237 46,075 31,827 14,248 (unwieghted count) Note: Data are weighted using population weights. Desegregated 1970-1979 group is 15-, 16-, and 17-year-old blacks who live in districts that desegregated between 1970 and 1979. Control group is all other 15-, 16, and 17-year-old blacks in districts that desegregated between 1961 and 1982. Dropout is an indicator for not being enrolled in school. Poverty measures what percentage of the poverty line the individual’s family income is. 36 TABLE III: DIFFERENCE-IN-DIFFERENCES ESTIMATES OF THE EFFECT OF DESEGREGATION ON DROPOUT RATES OF BLACKS (1) (2) (3) (4) (5) (6) (7) (8) Desegregated -.038 -.035 -.035 -.034 -.030 -.030 -.028 -.021 1970-1979 (.011) (.011) (.009) (.005) (.005) (.005) (.010) (.007) *1980 Desegregated .027 .026 .023 .044 1970-1979 (.008) (.008) (.007) (.008) 1980 .001 -.003 -.004 -.004 .014 .023 .008 .001 (.008) (.008) (.007) (.003) (.039) (.038) (.015) (.010) Age 16 .048 .048 .048 .048 .048 .048 .048 (.004) (.004) (.004) (.004) (.004) (.004) (.004) Age 17 .166 .166 .166 .162 .162 .162 .162 (.006) (.006) (.006) (.006) (.006) (.006) (.006) Female .011 .022 .011 .011 (.004) (.008) (.004) (.004) Female -.018 *1980 (.009) Poverty/103 -.198 -.025 -.196 -.194 (.031) (.048) (.030) (.030) Poverty/103 -.239 *1980 (.058) Family -.028 -.038 -.031 -.033 Income/106 (.028) (.013) (.028) (.028) Family .042 Income/106 (.013) *1980 Northeast -.060 (.030) Northeast -.019 -.017 *1980 (.039) (.039) Midwest -.059 (.030) Midwest -.014 -.014 *1980 (.039) (.039) South -.046 (.030) South -.008 -.008 *1980 (.038) (.038) West -.084 (.030) West -.007 -.004 *1980 (.040) (.039) District No No No Yes Yes Yes No Yes Effects State No No No No No No Yes Yes Effects State *1980 No No No No No No Yes Yes Effects R2 .002 .048 .049 .056 .061 .062 .060 .064 No. Obs. 53,331 53,331 53,331 53,331 52,416 52,416 52,416 52,416 Note: Data are weighted using population weights. Desegregated 1970-1979 group is 15-, 16-, and 17-year-old blacks who live in districts that desegregated between 1970 and 1979. Control group is all other 15-, 16, and 17-year-old blacks in districts that desegregated between 1961 and 1982. Standard error estimates are corrected for district*year correlation in the error term. 37 TABLE IV: MODELS RUN SEPARATELY BY REGION: DIFFERENCE-IN-DIFFERENCES ESTIMATES OF THE EFFECT OF DESEGREGATION ON DROPOUT RATES OF BLACKS Northeast Midwest West South Exclude South (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Desegregated -.031 -.021 -.025 -.027 -.048 -.042 -.028 -.029 -.033 -.029 1970-1979 (.026) (.007) (.012) (.009) (.024) (.010) (.015) (.010) (.015) (.005) *1980 Desegregated .020 .014 .052 .024 .019 1970-1979 (.018) (.008) (.015) (.011) (.011) 1980 -.013 .008 -.002 .019 .020 .003 .004 .012 -.001 .009 (.026) (.020) (.006) (.013) (.015) (.013) (.011) (.011) (.011) (.010) Age 16 .063 .064 .050 .050 .025 .026 .045 .045 .049 .050 (.010) (.010) (.007) (.007) (.006) (.006) (.006) (.006) (.005) (.005) Age 17 .182 .183 .172 .172 .122 .123 .158 .159 .164 .165 (.016) (.016) (.009) (.010) (.012) (.012) (.008) (.008) (.008) (.008) Female .007 .022 .019 .028 .010 .004 .009 .027 .013 .017 (.007) (.012) (.009) (.017) (.009) (.020) (.006) (.012) (.006) (.012) Female -.026 -.015 .011 -.030 -.007 *1980 (.015) (.019) (.020) (.013) (.012) Poverty/103 -.227 -.248 -.148 .015 -.130 -.083 -.268 .024 -.170 -.056 (.063) (.117) (.006) (.046) (.037) (.097) (.049) (.116) (.031) (.047) Poverty/103 -.038 -.290 -.046 -.323 -.179 *1980 (.136) (.059) (.100) (.133) (.058) Family .047 .193 -.035 -.284 -.031 -.218 -.010 -.743 -.018 -.190 Income/105 (.060) (.318) (.046) (.159) (.035) (.253) (.047) (.255) (.031) (.138) Family -.104 .353 .190 .777 .232 Income/106 (.326) (.161) (.256) (.261) (.140) *1980 District Effects No Yes No Yes No Yes No Yes No Yes R2 .063 .069 .059 .063 .046 .058 .052 .061 .057 .064 No. Obs. 6,100 6,100 15,691 15,691 6,567 6,567 23, 885 23,885 28,531 28,531 Note: Data are weighted using population weights. Desegregated 1970-1979 group is 15-, 16-, and 17-year-old blacks who live in districts that desegregated between 1970 and 1979. Control group is all other 15-, 16, and 17-year-old blacks in districts that desegregated between 1961 and 1982. Standard error estimates are corrected for district*year correlation in the error term. 38 TABLE V: SPECIFICATIONS WITH ALTERNATIVE CONTROL GROUPS: DIFFERENCE-IN-DIFFERENCES ESTIMATES OF THE EFFECT OF DESEGREGATION ON DROPOUT RATES OF BLACKS Control Desegregated Control Desegregated After 1980 Before 1970 (1) (2) (3) (4) Desegregated -.039 -.032 -.030 -.023 1970-1979 (.007) (.007) (.005) (.005) *1980 1980 .001 .006 -.008 -.003 (.006) (.006) (.002) (.004) Age 16 .046 .045 .048 .047 (.005) (.004) (.005) (.004) Age 17 .165 .160 .168 .165 (.007) (.007) (.006) (.006) Female .008 .013 (.004) (.004) Poverty/103 -.198 -.200 (.034) (.033) Family -.026 -.028 Income/106 (.031) (.030) District Effects Yes Yes Yes Yes R2 .057 .065 .057 .063 No. Obs. 44,694 43,888 45,843 44,684 Note: Data are weighted using population weights. Desegregated 1970-1979 group is 15-, 16-, and 17-year-old blacks who live in districts that desegregated between 1970 and 1979. Control group is all other 15-, 16, and 17-year- old blacks in districts that desegregated between 1961 and 1982. In Columns 1 and 2, the Control group is 15-, 16, and 17-year-old blacks in districts that desegregated after the Treatment districts (after 1979). In Columns 3 and 4, the Control group is 15-, 16, and 17-year-old blacks in districts that desegregated before the Treatment districts (before 1970). Standard error estimates are corrected for district*year correlation in the error term. 39 TABLE VI: DIFFERENCE-IN-DIFFERENCES ESTIMATES OF THE EFFECT OF DESEGREGATION ON MIGRATION (1) (2) (3) (4) Desegregated -.003 -.004 -.005 -.005 1970-1979 (.016) (.012) (.006) (.005) *1980 Desegregated .012 .006 1970-1979 (.013) (.010) 1980 -.029 -.030 -.022 -.017 (.014) (.010) (.005) (.070) Age 16 .008 .007 .007 (.003) (.003) (.003) Age 17 .004 -.001 -.001 (.003) (.003) (.003) Female .003 .003 (.003) (.003) Poverty/103 .020 .017 (.029) (.029) Family -.055 -.051 Income/106 (.030) (.030) Northeast -.000 (.020) Northeast -.007 *1980 (.070) Midwest -.004 (.019) Midwest -.005 *1980 (.069) South .014 (.019) South .002 *1980 (.069) West .045 (.022) West -.030 *1980 (.070) District No No Yes Yes Effects R2 .005 .010 .028 .028 No. Obs. 53,331 53,331 52,416 52,416 Note: Data are weighted using population weights. Desegregated 1970-1979 group is 15-, 16-, and 17-year-old blacks who live in districts that desegregated between 1970 and 1979. Control group is all other 15-, 16, and 17-year-old blacks in districts that desegregated between 1961 and 1982. Standard error estimates are corrected for district*year correlation in the error term. 40 TABLE VII: DIFFERENCE –IN-DIFFERENCES ESTIMATES OF THE EFFECT OF DESEGREGATION ON DROPOUT RATES CONTROLLING FOR MIGRATION Control For Moving Use Residence in 1975 for 1980 (1) (2) (3) (4) (5) (6) Desegregated -.035 -.034 -.027 -.045 -.048 -.039 1970-1979 (.011) (.005) (.005) (.015) (.010) (.009) *1980 Desegregated .025 .025 1970-1979 (.008) (.008) 1980 -.001 -.002 -.002 .018 .032 .039 (.008) (.003) (.004) (.012) (.008) (.007) Age 16 .048 .048 .048 .050 .052 .051 (.004) (.004) (.004) (.006) (.006) (.006) Age 17 .165 .165 .162 .174 .175 .170 (.006) (.006) (.006) (.008) (.008) (.008) Moved .061 .061 .038 (.012) (.012) (.011) Female .011 .016 (.004) (.006) Poverty/103 -.197 -.140 (.031) (.040) Family -.269 -.129 Income/106 (.280) (.044) District Effects No Yes Yes No Yes Yes R2 .050 .058 .062 .049 .060 .064 No. Obs. 53,331 53,331 52,416 21,669 21,669 21,222 Note: Data are weighted using population weights. Desegregated 1970-1979 group is 15-, 16-, and 17-year-old blacks who live in districts that desegregated between 1970 and 1979. Control group is all other 15-, 16, and 17-year-old blacks in districts that desegregated between 1961 and 1982. Columns 4-6 present regressions where the district of residence for 1980 observations is defined as the district of residence in 1975. Standard error estimates are corrected for district*year correlation in the error term. 41 TABLE VIII: ESTIMATED EFFECTS OF DESEGREGATION PLANS ON DISTRICT ENROLLMENT BY RACE 1970 1980 1980-1970 Difference-in-Differences Black Enrollment Desegregated in 70’s 20,484 18,789 -1,695 410 Desegregated in 60’s, 80’s 21,369 19,264 -2,105 (8,872) White Enrollment Desegregated in 70’s 78,083 71,741 -6,342 2,935 Desegregated in 60’s, 80’s 78,920 69,643 -9,277 (25,534) Note: Estimated enrollment counts are based on weighted counts of 15-, 16-, and 17-year-olds from the 1970 and 1980 censuses. Standard errors of the difference-in-differences estimated effect of desegregation plan on enrollment are reported in parentheses. 42 TABLE IX: SPECIFICATIONS THAT CONTROL FOR LAGGED DROPOUT RATES: ESTIMATES OF THE EFFECT OF DESEGREGATION ON DROPOUT RATES Lagged Dropout Rate Matching (1) (2) (3) (4) (5) (6) (7) Desegregated -.022 -.012 -.014 -.009 -.009 -.011 -.007 1970-1979 (.006) (.007) (.007) (.006) (.004) (.007) (.007) Lagged Dropout Rate .548 .108 .086 .055 (.058) (.048) (.048) (.045) Age 16 .043 .045 .045 (.005) (.005) (.005) Age 17 .148 .152 .154 (.012) (.011) (.010) Northeast .045 .066 -.004 -.000 (.026) (.016) (.008) (.008) Midwest .045 .069 .003 .013 (.025) (.016) (.009) (.009) South .058 .074 .020 .021 (.026) (.014) (.009) (.009) West .021 .044 .002 .007 (.027) (.015) (.005) (.006) Female .004 .003 (.003) (.003) Poverty/103 -.276 -.268 (.035) (.027) Family Income/106 .054 .047 (.031) (.028) R2 .029 .050 .051 .061 No. Obs. 44,590 44,590 44,590 43,912 44,590 44,590 43,912 Note: Regressions are weighted using population weights. Note: Data are weighted to reflect the census population. Desegregated 1970-1979 group is 15-, 16-, and 17-year-old blacks who live in districts that desegregated between 1970 and 1979. Control group is all other 15-, 16, and 17-year- old blacks in districts that desegregated between 1961 and 1982. Columns 1 and 2 present estimates comparing the conditional mean difference in dropout rates between Treatment and Control districts in 1980, controlling for 1970 district-level dropout rates. Columns 3 and 4 present estimates of a matching model described in the paper. Standard error estimates are corrected for district*year correlation in the error term. 43 TABLE X: DIFFERENTIAL EFFECTS OF VOLUNTARY DESEGREGATION PLANS ON DROPOUT RATES OF BLACKS (1) (2) (3) (4) (5) (6) (7) Desegregated -.041 -.043 -.040 -.039 -.032 -.034 -.035 1970-1979 (.011) (.011) (.011) (.010) (.010) (.009) (.009) *1980 Desegregated .018 .028 .029 .024 .016 .020 .021 1970-1979 (.008) (.011) (.011) (.010) (.010) (.009) (.009) *1980 *Voluntary Plan Desegregated .027 .021 .020 .023 .024 .023 .024 1970-1979 (.008) (.008) (.009) (.009) (.008) (.007) (.007) Voluntary Plan -.011 -.010 .002 .006 .005 .004 (.007) (.007) (.008) (.007) (.007) (.007) Post .002 .001 -.004 -.004 .001 -.046 -.034 (.008) (.007) (.008) (.007) (.007) (.047) (.047) Age 16 .048 .048 .047 .047 .047 (.004) (.004) (.004) (.004) (.004) Age 17 .166 .166 .161 .161 .161 (.006) (.006) (.006) (.006) (.006) Female .011 .011 .022 (.004) (.004) (.008) Female -.018 *1980 (.009) Poverty/103 -.198 -.200 -.027 (.031) (.031) (.048) Poverty/103 -.243 *1980 (.058) Family -.025 -.024 -.372 Income/106 (.029) (.029) (.125) Family .417 Income/106 (.128) *1980 Northeast -.067 -.049 -.057 -.057 (.030) (.030) (.043) (.043) Northeast .032 .033 *1980 (.048) (.048) Midwest -.061 -.042 -.058 -.057 (.030) (.030) (.043) (.043) Midwest .046 .046 *1980 (.047) (.047) South -.047 -.036 -.056 -.055 (.030) (.030) (.043) (.043) South .053 .052 *1980 (.047) (.047) West -.086 -.069 -.090 -.090 (.030) (.030) (.043) (.044) West .054 .056 *1980 (.048) (.048) R2 .002 .003 .048 .050 .056 .056 .056 No. Obs. 53,331 53,331 53,331 53,331 52,416 52,416 52,416 Note: Regressions are weighted using population weights. Desegregated 1970-1979 group is 17-year-old blacks who live in districts that desegregated between 1970 and 1979, 16-year-old blacks who live in districts that desegregated between 1971 and 1980, and 15-year-old blacks who live in districts that desegregated between 1972 and 1981. Control group is all other 15-, 16, and 17-year-old blacks in districts that desegregated between 1961 and 1982. Standard error estimates are corrected for district*year correlation in the error term. 44 TABLE XI: DIFFERENCE-IN-DIFFERENCES ESTIMATES OF THE EFFECT OF DESEGREGATION ON DROPOUT RATES OF WHITES (1) (2) (3) (4) (5) (6) (7) Desegregated .005 .006 .006 .007 .007 .002 .002 1970-1979 (.011) (.011) (.009) (.004) (.004) (.003) (.003) *1980 Desegregated .013 .012 .004 1970-1979 (.007) (.007) (.006) 1980 .024 .021 .019 .017 .039 .026 .059 (.009) (.009) (.007) (.003) (.004) (.018) (.019) Age 16 .049 .049 .049 .050 .050 .050 (.003) (.003) (.003) (.003) (.003) (.003) Age 17 .138 .138 .137 .136 .135 .136 (.005) (.005) (.005) (.005) (.005) (.005) Female .010 .010 .014 (.002) (.002) (.003) Female -.009 *1980 (.004) Poverty/103 -.302 -.302 -.250 (.019) (.018) (.022) Poverty/103 -.135 *1980 (.029) Family -.118 -.118 -.122 Income/106 (.013) (.013) (.028) Family .049 Income/106 (.029) *1980 Northeast -.045 (.022) Northeast -.005 -.006 *1980 (.018) (.018) Midwest -.042 (.021) Midwest .014 .016 *1980 (.018) (.018) South -.002 (.021) South .014 .013 *1980 (.018) (.018) West -.026 (.022) West .035 .035 *1980 (.018) (.018) District No No No Yes Yes Yes Yes Effects R2 .003 .040 .043 .049 .083 .083 .084 No. Obs. 203,063 203,063 203,063 203,063 200,379 200,379 200,379 Note: Data are weighted using population weights. Desegregated 1970-1979 group is 15-, 16-, and 17-year-old whites who live in districts that desegregated between 1970 and 1979. Control group is all other 15-, 16, and 17-year-old whites in districts that desegregated between 1961 and 1982. Standard error estimates are corrected for district*year correlation in the error term. 45 TABLE XII: CHARACTERISTICS OF BLACK AND WHITE SCHOOLS IN 1970 < 25 Percent 25-75 Percent > 75 Percent Black Enrolment Black Enrollment Black Enrollment Pupil-Teacher Ratio 27.9 23.9 26.7 (12.9) (10.6) (6.5) Fraction Black Teachers .079 .241 .565 (.113) (.172) (.243) Number of Schools 3381 667 1079 Note: The unit of observation is a school. Data are from the U.S. Department of Health, Education and Welfare’s Directory of Public Elementary and Secondary Schools in Selected Districts. Sample statistics only include districts that desegregated between 1970 and 1979. Standard deviations are reported in parentheses. TABLE XIII: CHARACTERISTICS OF BLACK AND WHITE TEACHERS IN 1970 Black Teachers White Teachers Years of Completed Education 15.6 15.9 (2.1) (1.8) Potential Experience 15.5 16.4 (11.7) (14.5) No. Obs. 1,404 13,558 Note: Data are from the 1970 Census. Standard deviations are reported in parentheses. 46 APPENDIX TABLE I: PROBIT ESTIMATES OF THE EFFECT OF DESEGREGATION ON DROPOUT RATES OF BLACKS (1) (2) (3) (4) (5) (6) Desegregated -.028 -.026 -.026 -.021 -.025 -.025 1970-1979 (.010) (.009) (.008) (.008) (.008) (.007) *1980 Desegregated .024 .023 .019 .017 .019 .020 1970-1979 (.007) (.007) (.006) (.006) (.005) (.005) 1980 -.006 -.011 -.011 -.005 -.043 -.026 (.007) (.007) (.007) (.006) (.036) (.035) Age 16 .069 .068 .067 .067 .067 (.006) (.006) (.006) (.006) (.005) Age 17 .185 .185 .181 .181 .180 (.007) (.007) (.007) (.007) (.007) Female .011 .011 .022 (.004) (.004) (.007) Female -.019 *1980 (.007) Poverty/103 -.176 -.179 -.033 (.033) (.032) (.042) Poverty/103 -.241 *1980 (.054) Family -.055 -.053 -.031 Income/106 (.032) (.032) (.011) Family .034 Income/106 (.012) *1980 Northeast -.042 -.030 -.034 -.035 (.018) (.019) (.023) (.023) Northeast .032 .034 *1980 (.040) (.040) Midwest -.044 -.029 -.039 -.039 (.018) (.019) (.024) (.024) Midwest .044 .045 *1980 (.041) (.041) South -.032 -.025 -.039 -.037 (.020) (.021) (.026) (.026) South .048 .047 *1980 (.039) (.039) West -.057 -.047 -.055 -.056 (.015) (.016) (.019) (.019) West .049 .051 *1980 (.046) (.047) Note: Marginal effects at the mean of explanatory variables are reported. Data are weighted using population weights. Desegregated 1970-1979 group is 15-, 16-, and 17-year-old blacks who live in districts that desegregated between 1970 and 1979. Control group is all other 15-, 16-, and 17-year-old blacks in districts that desegregated between 1961 and 1982. Standard error estimates are corrected for district*year correlation in the error term. 47 Appendix 1: Differences v. Lagged Dependent Variables Models This section shows that if selection into treatment is based either on lagged outcomes or on fixed characteristics, the difference-in-differences estimator and an estimator that controls for a lagged dependent variable provide estimates that bracket the causal effect of interest. Assume there is no secular trend in dropout rates so that we can write the dropout rate in school district s at time t as, y st = α s + δ Tst + ε st where Tst is an indicator for being treated (living in 1980 in a district that desegregated in the 1970’s). Treatment is selected either on fixed characteristics such that, ì1 if α s > y Tst = í î0 otherwise or on lagged values of y such that, ì 1 if y st −1 > y Tst = í î0 otherwise where y is a constant. Define δˆLD as the estimator that controls linearly for a lagged dependent variable. Define δˆDD as the difference-in-differences estimator. 48 A1.1. The Lagged Dependent Variable Estimator, δˆLD : ~ ˆ = Cov( y st , Tst ) plim δ LD ~ Var (Tst ) ~ ~ Cov(α s + δ Tst + δ Tst + ε st , Tst ) ˆ = ~ Var(Tst ) ~ ˆ where Tst is the residual from a regression of Tst on y st −1 , and Tst is the predicted value from a regression of Tst on y st −1 . Therefore, ~ ˆ = δ + Cov(α s + ε st , Tst ) . plim δ LD ~ Var(Tst ) If treatment is selected on fixed characteristics, Cov(α s + ε st , Tst − k − φ (α s + ε st −1 )) plim δ LD ˆ =δ + ~ Var(Tst ) Cov(Tst , y st −1 ) where k is a constant and φ = . Expanding the equation, Var( y st −1 ) Cov(α s , Tst ) Cov(Tst , y st −1 ) æ σ α ö 2 plim δ LD ˆ =δ + − ç ~ ÷ Var( y st −1 ) ç Var(Tst ) ÷ ~ Var(Tst ) è ø assuming no serial correlation in ε. In the analysis in this paper, t and t-1 are ten years apart. Thus, the assumption of no serial correlation in ε seems reasonable. Simplifying, 49 Cov(α s , Tst ) æ σ2 ö plim δ LD ˆ =δ + ç1 − 2 α 2 ÷ ~ ç σ +σ ÷ Var(Tst ) è α ε ø which implies that if treatment is positively selected on fixed characteristics, plim δ LD ˆ ≥ δ . In other words, if treatment is positively (negatively) selected on fixed characteristics, the estimator that controls for lagged outcomes produces positively (negatively) biased estimates of the treatment effect. A1.2. The Difference-in-Differences Estimator, δˆDD : Cov( y st − y st −1 , Tst ) plim δ DD ˆ = Var(Tst ) Cov(δ Tst + ε st − ε st −1 , Tst ) = Var(Tst ) Cov(ε st − ε st −1 , Tst ) =δ + Var(Tst ) Cov(ε st −1 , Tst ) =δ − Var(Tst ) assuming no serial correlation in ε. If treatment is positively selected on lagged outcomes, plim δˆDD ≤ δ . In other words, if treatment is positively (negatively) selected on lagged outcomes, the difference- in-differences estimator produces negatively (positively) biased estimates of the treatment effect. Therefore, if treatment is selected positively either on fixed characteristics or on a lagged dependent variable, plim δ DD ≤ δ ≤ plim δ LD . ˆ ˆ 50 If treatment is selected negatively either on fixed characteristics or on a lagged dependent variable, plim δ LD ≤ δ ≤ plim δ DD . ˆ ˆ 51