Computably Inductivizing Economics

Kumaraswamy Vela Velupillai
Department of Economics, Queen's University of Belfast
K.Vela@Queens-Belfast.ac.uk

Abstract

The inductive tradition in economics could be given a new focus on the basis of recent development in a recursion theoretic approach to the principle of Occam's Razor. In this essay this claim is discussed doctrine-historically, theoretically and with selected examples of learning and other inference problems in economics.

The essay is divided into four parts. In Part I there is a general survey of the inductive approach to economics contrasted with the deductive formalism that has been dominant since Ricardo. The survey is not exhaustive but I do try to reorient the focus towards the importance of some of Petty's writings and Smith's essay on `The History of Astronomy' as the fountainhead of the inductive approach to economics. I will claim that the line from Petty and Smith via Malthus and Mill to Myrdal and Keynes and all the way to Simon and Clower is the mainstream; it is the others, the Ricardians, right up to and including the Formalists and the Bourbakian mathematical economists who were unorthodox.

In Part II of the essay I try to survey, concisely, the traditional approaches to the problem of induction: inductive logic, Bayesian inference and what I call, for want of a more suitable name, the cognitive theory of induction. I view them consistently from a recursion theoretic point of view for two reasons: one, to facilitate comparison with recursion theoretic induction (or the `Modern Theory of Induction' as I have called it in earlier writings); two, to strip these traditional theories of Formalist, Subjectivist and Logical biasses.

In Part III there is a detailed presentation of recursion theoretic induction (RTI). The modern origins of recursion theoretic induction, in my opinion, can be found in Hilary Putnam's remarkable doctoral dissertation of almost half-a-century ago. To the best of my knowledge this source has not been linked to RTI. I try, in this section, to rectify this doctrine-historical lapse - but also comment on the connection between Inductive Logic and RTI in greater detail than is usual in this literature. Putnam, of course, is a towering figure in the origins and development of both areas.

Part IV is devoted to concrete examples of learning and estimation in economics as induction problems within RTI. For example, it is demonstrated that, by utilizing computable analysis in elementary ways, it is possible to learn rational expectations equilibria (REE) that computability constrains, within RTI. The same methodology can be applied, as I demonstrate, for inference problems in dynamical economic systems and classic estimation problems.

In the concluding notes in Part V I try to outline an agenda for `Making Economics an Inductive Science'.