Establishing preference functions for macroeconomic decision models: Some observations on Ragnar Frisch's contributions

The article reviews Ragnar Frisch's contributions to solving the problem of establishing preference functions for macroeconomic decision models, and compares Frisch's approach with other possible approaches to the problem. The article mainly considers linear and quadratic preference functions. In discussing the methodology attention is drawn to the analogy with problems in the analysis of consumer demand.     

Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions

Consider a committee which must select one alternative from a set of three or more alternatives. Committee members each cast a ballot which the voting procedure counts. The voting procedure is strategy-proof if it always induces every committee member to cast a ballot revealing his preference. I prove three theorems. First, every strategy-proof voting procedure is dictatorial. Second, this paper's strategy-proofness condition for voting procedures corresponds to Arrow's rationality, independence of irrelevant alternatives, non-negative response, and citizens' sovereignty conditions for social welfare functions. Third, Arrow's general possibility theorem is proven in a new manner.     

Equicorrelated substitutes and Nasse's extension of the linear expenditure system

Nasse's (1970) model can be used to provide an easily implementable approximation of the equicorrelated-substitutes model. The preference independence transformation based on this approximation is also considered.     

Frisch and Tinbergen on economic planning

The Frisch-Tinbergen model of central economic planning represents the first important non-Soviet planning model. This constrained optimization model makes the central planner a staff adviser to the Premier. The central planner explores the Premier's preference ordering and recommends instruments that maximize the Premier's utility, given the constraints within an econometric model. This model assumes Premiers have no preference over instruments or models and that planning agencies have neither internal structure nor operating responsibilities. The paper explores the consequences of removing such limiting assumptions, utilizing the results of more recent contributions to the theory of.-economic systems.     

Keynes's errors in the liquidity preference versus loanable funds controversy

How Keynes could have been so persistently wrong in the liquidity preference versus loanable funds controversy remains a puzzling enigma. This paper attempts to shed some light on this puzzle by tracing the evolution of Keynes's thinking and by looking at some of the policy issues with which he was concerned. In particular, it argues that two errors were inherent in Keynes's reasoning process. As a result, he regarded the two theories as “radically opposed” and thought that the loanable funds theory was a “wrong” theory with misleading policy implications.     

The independence transformation under almost additivity

When the consumer's tastes are close to preference independence, each transformed good is uniquely associated with one observed good. The off-diagonal elements of the composition matrix of the transformation are equal apart from sign and are inversely proportional to the difference between the income elasticities of the corresponding observed goods.     

Chernoff's dual axiom,revealed preference and weak rational choice functions

A new and a weaker concept of rationalizability is introduced and its implications on the properties of individual choice are investigated. Especially, (i) it is shown that a property of choice functions, called Chernoff's dual axiom in this paper, plays a crucial role for the rationality of choice, and (ii) weakening the concept of rationalizability facilitates characterization of revealed preference relations.     

Zero-sum condition: A necessary and sufficient condition for a transitive voting system

A simple and quick way to ascertain whether or not any given majority voting system can always produce a transitive social preference orderings without imposing any restriction on the distribution of diverse individual preference orderings is to examine whether all individual voting (preference) vectors satisfy the Addition Rule or not. This conclusion was obtained by first reformulating the voting mechanism into that of a linear mapping from T^m defined by q = Σp_i. It was found that the subset P of T that can accommodate all possible individual preference ordering profiles and such that every sum vector q = Σ p_i of its member vectors p_i is contained in T can be expressed as P = {p: p∈ T, s(p) = 0}. It was also pointed out that this is equivalent to the requirement that all individual preference (voting) functions must satisfy the Addition Rule. Finally, Borda's Rule and Saposnik's Contributive Rule were shown to be examples of transitive voting rules which satisfy these necessary and sufficient conditions.     

Multi-valued decision rules and coalitional non-manipulability: Two possibility theorems

In this paper we show that under the restriction that the individual's sincere preference orderings are linear (strict), there exists a fairly wide class of coalitionally non-manipulable democratic decision rules. These positive results are established without any restriction on the pairwise choice. It is also shown that the possibility of manipulation even by a single individual arises once he adopts a pessimistic approach in comparing two different sets of outcomes which reflect his attitude to risk.     

The Marglin-McFadden-Mishan debate on public investment criteria: Some Clarifications

This paper reviews the post 1963 debate on public investment criteria stemming largely from Marglin's work. At issue here, are the two main propositions of Marglin, namely, that the social marginal rate of time preference is the appropriate social rate of discount (SRD) for public projects, and that the social opportunity cost (SOC) of capital raised to facilitate public investment is, in general, in excess of the money cost of such investment. Both supported and challenged by different writers, this debate does not provide any clear consensus as to the current status of these propositions. The central purpose of this paper is to put the series of apparent claims and counterclaims found in the literature to an analytical test, and draw the appropriate conclusions. This we do by explicitly considering the technology, fiscal policy and savings reinvestment behavior in a simple model of maximizing the present discounted value of the marginal net consumption stream generated by the public project. We argue that given Marglin's assumptions, the criterion that the marginal social rate of time preference be the SRD is valid as has already been demonstrated by Diamond (1968) and McFadden (1972). His other conclusion that the SOC should generally exceed unit v is seen to be correct only in special cases.     

Remarks on the first welfare theorem with nonordered preferences

A strong convexity assumption is used to establish the first fundamental theorem of welfare economics using the strong definition of Pareto optimality without assuming that the weak preference relations are complete or transitive. An example demonstrates that Debreu's (Proc. Nat. Acad. Sci., 40 (1954), 588–592) nonsatiation and convexity assumptions are insufficient to establish the result in the absence of transitivity.     

Essential aggregation procedures on restricted domains of preferences

The restricted domains of individuals' preferences that permit the construction of Arrow social welfare functions and nonmanipulable voting procedures in which each of n voters has some power are characterized. In this context a domain is the Cartesian product of n sets of strict preference orderings. Variants of this result are obtained under the additional requirement of neutrality and in the case when alternatives are vectors whose ith components affect only the ith voter. Kalai and Muller's analogous result (J. Econ. Theory16 (1977), 457–469) concerning nondictatorial procedures is discussed and proved as a corollary to the main theorem.     

An econometric model of tenure choice and demand for housing as a joint decision

This paper models a household's choice of tenure and demand for housing services as a joint decision imposing the restriction that both discrete and continuous decisions are derived from a single preference ordering. The utility index for households is the translog form of the reciprocal indirect utility function allowing for random preferences. Each household chooses between the two main tenures, the owner-occupied and subsidised rental sectors, but households may be rationed in either or both of these sectors and refused admission, in which case they are assumed to enter the third sector, uncontrolled rental. The model is estimated on UK data for 5895 households.     

The theory of public goods: Misplaced emphasis?

The note takes up for critical examination the tendency in the modern theory of public goods to emphasize the problem of correct revelation or concealment of preferences. It is argued that a strategy which consists in playing down one's preferences for a public good in order to get a lower share in the costs of providing the good is not likely to succed in an open political decision-making process involving elected representatives. This conclusion is supported by the fact that there seems to be little empirical evidence which shows the importance of the preference revelation issue.     

Growth dynamics in a model of endogenous time preference

We incorporate endogenous time preference in a simple Diamond-type economy with production and analyze the resulting dynamics both for the competitive and command equilibrium. We assume an individual's rate of time preference is decreasing in consumption (decreasing marginal impatience) and show that this intuitively more appealing assumption is consistent with a stable, non-trivial competitive equilibrium. Analysis of the competitive equilibrium indicates that the observed ‘non-convergence’ of cross-country per capita income could partially be explained by cross-country differences in ‘innate patience’. Examination of the local dynamics around the ‘optimal’ solution suggests that this particular preference structure exhibiting diminishing marginal impatience may generate endogenous business cycle phenomenon.     

Optimal taxation and discount rate for public investment in a growth setting

This paper studies the optimal policy of a government which maximizes intertemporal social welfare using such instruments as taxes on interest income and wages, and debt in conjunction with public investment. In doing so, it has to face a decentralized economy where in each generation individuals and firms are free to maximize their own objectives subject to their own private constraints. The welfare function is a sum of discounted generational utilities and its maximization is handled by using dynamic programming. From the first order conditions so derived, it appears that an optimal policy of taxation and public capital accumulation is that which sets the tax rates according to Ramsey's optimal taxation structure and which equates the rate of return on public investment to the rate of social time preference.     

Risk aversion,impatience, and optimal timing decisions

In this paper, a theory measuring a decision maker's aversion to temporal risks is developed in the context of a simple choice framework that admits the interpretation “time varying utility of wealth.” A relation “more temporally risk averse” is defined and characterized in terms of instantaneous risk aversion (the usual single variable case) and impatience. A further characterization of this relation is obtained in the context of a class of action timing problems known as optimal stopping problems and is applied to preference based investigations of information production, incentives to innovate, and job search.     

Social choice and telling the truth

This paper presents a straightforward proof of Gibbard's theorem that any non-manipulable choice rule with at least three outcomes is dictatorial. The proof is similar to proofs of Arrow's impossibility theorem, but does not rely on that theorem. The last part of the paper discusses the relation between Gibbard's and Arrow's theorems. The paper contains no new result, and is intended to make this important area of social choice theory accessible to a wider audience.     

Maximal elements of non-binary choice functions on compact sets

We give sufficient conditions for the existence of maximal elements on compact sets for ‘contraction consistent’ (but possibly non-binary) choice functions. Our result generalizes the Bergstrom-Walker theorem on the existence of maximal elements with acyclic preference relations.     

Axiomatic reference-dependence in behavior toward others and toward risk

Summary. This paper considers the applicability of the standard separability axiom for both risk and other-regarding preferences, and advances arguments why separability might fail. An alternative axiom, which is immune to these arguments, leads to a preference representation that is additively separable in a reference variable and the differences between the other variables and the reference variable. For other-regarding preferences the reference variable is the decision-maker’s own payoff, and the resulting representation coincides with the Fehr-Schmidt model. For risk preferences the reference variable is initial wealth, and the resulting representation is a generalization of prospect theory.Received: 28 April 2004, Revised: 27 April 2005, JEL Classification Numbers: D81, D64.An earlier version of this paper was titled “An Axiomatic Characterization of the Fehr-Schmidt Model of Inequity Aversion.” I am grateful to Rachel Croson, Jill Stowe, and Karl Vind for helpful comments. Financial support was provided by the Private Enterprise Research Center, the Program in the Economics of Public Policy, and the Program to Enhance Scholarly and Creative Activities.