Researchers often estimate income inequality by using data that give only the number of cases (e.g., families or households) whose incomes fall in “bins” such as $ 0 to $9,999, $10,000 to $14,999, . . . , ≥$200,000. We find that popular methods for estimating inequality from binned incomes are not robust in small samples, where popular methods can produce infinite, undefined, or arbitrarily large estimates. To solve these and other problems, we develop two improved estimators: a robust Pareto midpoint estimator (RPME) and a multimodel generalized beta estimator (MGBE). In a broad evaluation using U.S. national, state, and county data from 1970 to 2009, we find that both estimators produce very good estimates of the mean and Gini coefficient but less accurate estimates of the Theil index and mean log deviation. Neither estimator is uniformly more accurate, but the RPME is much faster, which may be a consideration when many estimates must be obtained from many data sets. We have made the methods available as the rpme and mgbe command for Stata and the binequality package for R.

Are middle schools ill-suited for early adolescents, or can school characteristics account for any differences in student functioning? Achievement, school engagement, and perceived competence of children starting middle schools in 5th and 6th grades were compared to those of their same-grade peers in elementary schools in a national, longitudinal sample (NICHD Study of Early Child Care and Youth Development, n = 855; 52% Female, 82% White). Classroom quality (observed and teacher-reported) and school characteristics (composition and size) were considered as explanations for any relationships between school-level and student functioning. Fifth grade middle school students did not differ from those in elementary school, but students entering middle school in 6th grade, compared to those in elementary school, experienced lower classroom quality, which in turn predicted slightly lower achievement. They also had lower school engagement, explained by larger school size. Classroom quality and school characteristics predicted youth functioning regardless of school type. We suggest reshaping the research and policy debate with renewed focus on classroom quality and school size instead of grade organization.

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