Chris William Sanchirico (Penn; Google Scholar), The Ramsey Rule at 100: Paring Back the Overgrowth:
In 1927 the mathematician Frank Ramsey published a paper on optimal taxation in which he put forward what has come to be known as the “Ramsey rule”. Nearly one hundred years later, Ramsey’s paper remains a go-to reference for normative tax theory in a number of fields, including legal scholarship. This paper reviews the reasoning behind the Ramsey rule and attempts to clear up various points of confusion that have grown up over decades of perfunctory citation. It explains in simple terms what the rule is and how it is derived. It then critically analyzes the rule’s most prevalent interpretations, arguing that these range from uninformative to misleading.
Conclusion
Practical tax policy is often guided by rule-of-thumb principles put forward as pragmatic adaptations of underlying, more firmly grounded mathematical analyses. Among the most
prominent of these applicative principles is the idea that taxes “distort” taxpayer behavior, and that, distortion being detrimental, the tax system should be designed to minimize it. To illuminate the harm, “deadweight loss triangles” are drawn into supply and demand diagrams, and the goal of minimizing distortion is translated into the goal of minimizing the area of such triangles.
The Ramsey rule cannot be regarded as the historical source of these practical theorems. They predate Ramsey’s analysis. Rather the Ramsey rule has been used to shore up these arguments after the fact, as if it verified them and acted as a belatedly inserted foundation.
This use of the Ramsey rule is doubly ironic. The Ramsey rule does indeed build more solidly upon broader (though still limited) mathematical foundations. But the result of that exercise is best interpreted as a refutation, rather than a verification of these more casual intuitions. Moreover, while one might have expected to see Ramsey’s analysis applied to correct and refine these casual intuitions, something like the opposite has occurred. The Ramsey formula has been misinterpreted to make it fit the intuitive preconceptions that it in fact disconfirms.
Thus, revisiting the Ramsey rule on the eve of its 100th anniversary, one finds it surrounded and obscured by a tangle of confused assertions about its meaning and significance. The order of the day is to clear out the brush and see the formula for what it is: an interesting, but not particularly useful manipulation of an arbitrage-based intuition regarding optimal tax rates.



