Why school integration works

Ed, the times op-ed on busing (attached) cited the following to support this claim

"....An economist and professor of public policy, Rucker C. Johnson at the University of California, Berkeley, studied the life outcomes of black children who got access to the trifecta of quality Head Start, increased school funding and desegregation. He saw the entire trajectory of their lives change. Compared with kids stuck in segregated schools, even their own siblings, they were more likely to graduate from high school and more likely to get out of poverty. As adults, they earned more, were less likely to go to jail and even lived longer. The earlier and longer these children got access to integrated schools, Dr. Rucker found, the stronger the results....."
the op-ed cites his new book, which I can get a copy of to actually see his metrics, but here is an interview with Johnson characterizing his books findings:

"....Using nationally representative longitudinal data spanning more than four decades, I analyze the life outcomes of cohorts tracked from birth to adulthood across several generations, from the children of Brown to Brown’s grandchildren. The slow and uneven pace of desegregation, school funding reforms, and Head Start programs across the country created a natural “policy lab,” that allowed for rigorous, empirical evaluation of integration, school funding and Head Start. The research findings are clear: African Americans experienced dramatic improvements in educational attainment, earnings and health status — and this improvement that did not come at the expense of whites. Moreover, the longer students were exposed to integration and strong school funding, the better their outcomes in adulthood. This was true for children of all races. The beneficial effects were found not just for the children who attended desegregated schools, but for their children as well. School integration didn’t fail.The only failure is that we stopped pursuing it and allowed the reign of segregation to return......"

".... We use children’s differential exposure to Head Start spending (at age 4) andcourt-ordered school finance reforms (SFRs) (between the ages 5 through 17), depending on place and year of birth, to examine whether the marginal effect of Head Start spending on children’s adult outcomes are larger among individuals who were subsequently exposed to SFR-induced K12 spending increases.We present extensive tests to document that the policy-induced variation in Head Start spending and K12 public school spending we exploit is unrelated to other childhood family, community, or policy changes. For non-poor children, SFR-induced K12 spending increases led to significant improvements in educational and economic outcomes, while increases in Head Start spending had no effect.However, for poor children, both Head Start spending increases and SFR-induced K12 spending increases led to significant improvements in educational outcomes, economic outcomes, and reductions in the likelihood of incarceration. Importantly, the long-run effects of increases in Head Start spending are amplified when followed by attending schools that experienced SFRinduced increases in K12 per-pupil spending. Across all the outcomes, the marginal effect of the same increase in Head Start spending was more than twice as large for students from K12 school districts that spent at the 75th percentile of the distribution than those from K12 school districts that spent at the 25th percentile. Similarly, the benefits of K12 school-spending increases on adult outcomes were larger among poor children who were exposed to higher levels of Head Start spending during their pre-school years. For poor children, the combined benefits of growing up in districts/counties with both greater Head Start spending and K12 per-pupil spending are significantly greater than the sum of the independent effects of the two investments in isolation. There are two important caveats to our work. First, because the counterfactual childcare and pediatric care may be better today than in the late 1960s and 70s, the marginal effect of Head Start may be smaller today than in the earlier period that we study. Second, public school spending levels during the period we study were lower than current levels. If school spending exhibits diminishing marginal product, the effects presented here may be larger than one would observe with similar spending increases today. These caveats do not minimize the importance of the findings or their profound implications for policy. However, they do suggest that the contemporary magnitude of the effects may be smaller than those we present here. At the same time, the returns to education have increased, so the consequences of access to high-quality human capital investments from preK-12 are large...."
Rucker Johnson and C. Kirabo Jackson, "Reducing Inequality Through Dynamic Complementary Evidence From Head Start and Public School Spending," National Bureau of Economic Research June 2017, https://gsppi.berkeley.edu/~ruckerj/RJabstract_LRHeadStartSchoolQuality.pdf

Valerie Strauss, "Why school integration works,"Washington Post, May 16, 2019, https://www.washingtonpost.com/education/2019/05/16/why-school-integration-works/

going through his CV seem like the support for that claim of the books is likely drawn from a 2017 NEBR paper of his that found