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Stem-and-leaf displays have been widely taught since John W. Tukey publicized them energetically in the 1970s. They remain useful for many distributions of small or modest size, especially for showing fine structure such as digit preference. Stata's implementation stem produces typed text displays and has some inevitable limitations, especially for comparison of two or more displays. One can re-create stem-and-leaf displays with a few basic Stata commands as scatterplots of stem variable versus position on line with leaves shown as marker labels. Comparison of displays then becomes easy and natural using scatter, by(). Back-to-back presentation of paired displays is also possible. I discuss variants on standard stem-and-leaf displays in which each distinct value is a stem, each distinct value is its own leaf, or axes are swapped. The problem shows how one can, with a few lines of Stata, often produce standard graph forms from first principles, allowing in turn new variants. I also present a new program, stemplot, as a convenience tool.

In a recent article in this journal, Stutzer (1984) investigated the relative in-efficiencies of fixed versus variable rate subsidies as they pertain to analyzing different forms of revenue sharing. His analysis butlds on the theoretical presumption that a variable rate subsidy is generally less inefficient than a fixed rate subsidy of equal size. In this article it is shown that if the good being subsidized is a public good, it is possible that a fixed rate subsidy will be more efficient than a variable rate subsidy from a benefit-cost analysis perspective, once collective decision-making aspects are incorporated into the analysis. This indicates the importance of incorporating the presence of public goods, when appropriate, into an efficiency analysis to see whether traditional results are still valid.