Sunday, 31 May 2015

In Praise of Frank Ramsey's Contribution to the Theory of Taxation

Frank Ramsey's brilliant 1927 paper, modestly entitled, ‘A contribution to the theory of taxation’, is a landmark in the economics of public finance. Nearly a half century later, through the work of Diamond and Mirrlees (1971) and Mirrlees (1971), his paper can be thought of as launching the field of optimal taxation and revolutionising public finance.1
Ramsey, in his short life, made pathbreaking contributions to two other fields, the theory of optimal growth (Ramsey, 1928) and the theory of subjective probability (Ramsey, 1926).2 Here, he addresses a question which he says was posed to him by A. C. Pigou: given that commodity taxes are distortionary, what is the best way of raising revenues, i.e. what is the set of taxes to raise a given revenue which maximises utility. The answer is now commonly referred to as Ramsey taxes. The basic insight was that taxes should be set so as to reduce the consumption of each good (along its compensated demand curve) equi-proportionately. He establishes this result in two contexts:
  1. if the government needs to raise only a small amount of tax revenue; and
  2. if utility functions are quadratic.
The analysis is beautiful, mathematically sophisticated, making use of all the artillery in the theory of consumer behaviour, including the symmetry of the Slutsky relations. The conclusion overturned simplistic analyses that somehow continue to prevail in some quarters for decades after Ramsey's paper and, in some subfields of economics, continue to this day. Some economists argued against differential taxation on the grounds that it is best just to have a single tax (typically on wages). A wage tax introduces a single distortion – between the marginal rate of substitution between labour and consumption and the marginal rate of transformation. Interest income taxes and commodity taxes introduce additional distortions. (Interestingly, Ramsey's analysis has, wrongly, continued to be used by some economists to argue against the taxation of capital.)3
As another example of such simplistic economics, some macroeconomists continue to argue that monetary authorities should only interfere with the market in setting short-term interest rates.
Ramsey showed that efficient taxation required imposing a complete array of taxes – not just a single tax. A large number of small distortions, carefully constructed, is better than a single large distortion. And he showed precisely what these market interventions would look like. (He even explains that the optimal intervention might require subsidies – what he calls bounties – for some commodities. ‘A tax on sugar might reduce the consumption of damsons more than in proportion to the reduction in the total consumption of sugar and so require to be offset by a bounty on damsons’, Ramsey, 1927, p. 54). Similar reasoning would suggest that if there are a variety of tools for managing the macroeconomy, in general, they should all be employed.
In this short celebratory article, I briefly describe Ramsey's basic insights (Section 'Major Insights'), and the early history of the development of the ideas based on Ramsey's paper (Section 'Earlier Dissemination'). While several of these crucial developments showed that Ramsey's conclusions held under more general conditions than he had assumed, later analyses showed crucial qualifications, so that the policy relevance of Ramsey's analysis may be limited.