Utility-Based Utility

A major virtue of von Neumann-Morgenstern utilities, for example, in the theory of general financial equilibrium (GFE), is that they ensure time consistency: consumption-portfolio plans (for the future) are in fact executed (in the future) — assuming that there is perfect foresight about relevant endogenous variables. This paper proposes an alternative to expected utility, one which also delivers consistency between plan and execution — and more. In particular, the formulation affords an extremely natural setting for introducing extrinsic uncertainty. The key idea is to divorce the concept of filtration (of the state space) from any considerations involving probability, and then concentrate attention on nested utilities of consumption looking forward from any date-event: utility today depends only on consumption today and prospective utility of consumption tomorrow, utility tomorrow depends only on consumption tomorrow and prospective utility of consumption the day after tomorrow, and so on.Utility theory, Expected utility, Time consistency, Extrinsic uncertainty, Cass-Shell Immunity Theorem

Competitive Equilibrium with Incomplete Financial Markets

This is my classic paper, written in early 1984, concerning existence and optimality in general financial equilibrium with incomplete markets for nominal assets, just now being published in a special issue of the Journal of Mathematical Economics.financial equilibrium, incomplete markets, Cass trick

Compatible Beliefs and Equilibrium

In this paper I investigate the nature of the beliefs which agents must hold (at least implicitly) in order to justify their considering various alternatives, in two distinct settings: the Walrasian model without production (with competitive equilibrium), and the sell-all version of the Shapley-Shubik market game (with Nash equilibrium). For this purpose I introduce a weak consistency requirement on behavior, one which I refer to as (having) compatible beliefs. My main conclusion is that, in this respect, these two versions of market allocation are essentially identical. For both, contemplating different choices requires varying the associated set of values of the variables defining compatible beliefs. And — though prima facie very different — it turns out that both equilibrium concepts can be recast entirely in terms of having compatible beliefs. My analysis also leads unequivocally to the interesting conclusion that, in the Walrasian model (even elaborated to encompass production, financial markets, and so on), budget constraints must hold, ab initio, with equality. This has one very important consequence: the First Basic Welfare Theorem, as usually stated, is false, as I demonstrate with two distinct counterexamples, the second of which is (in classical terms) unexceptional.general equilibrium, market game, competitive hypothesis, compatible beliefs

Utility-Based Utility

A major virtue of von Neumann-Morgenstern utilities, for example, in the theory of general financial equilibrium (GFE), is that they ensure intertemporal consistency: consumption-portfolio plans (for the future) are in fact executed (in the future) — assuming that there is perfect foresight about relevant endogenous variables. This note proposes an alternative to expected utility, one which also delivers consistency between plan and execution — and more. In particular, it turns out that one special case is in fact simply discounted (subjective) expected utility. Moreover, this alternative formulation affords an extremely natural setting for introducing extrinsic uncertainty. The key idea behind my approach is to divorce the concept of filtration (of the state space) from any considerations involving probability (on the state space), and then concentrate attention on nested utilities of consumption looking forward from any date-event: utility today depends only on consumption today and prospective utility of consumption tomorrow, utility tomorrow depends only on consumption tomorrow and prospective utility of consumption the day after tomorrow, and so on.Utility theory, Expected utility, Intertemporal consistency, Extrinsic uncertainty, Cass-Shell Immunity Theorem

Musings on the Cass Trick

This is a leisurely introduction, in the vein of a piece in the history of science, to belated publication of my well-known paper on incomplete Markets, Competitive Equilibrium with Incomplete Financial Markets.financial equilibrium, incomplete markets, Cass trick

Climate Change and Discounting the Future: A Guide for the Perplexed

Some of the most important disagreements about how aggressively to respond to the threat of climate change turn on the choice of the discount rate. A high discount rate implies relatively modest and slow reductions; a low discount rate implies immediate and dramatic action. The debate between the two sides reflects a disagreement between the positivists, who argue for a market rate, and the ethicists, who urge that the positivist approach violates the duty of the present to the future. We argue that the positivists are largely right, and that the question of discounting should be separated from the question of the ethical duties of the present. Discounting is a means of taking account of opportunity costs, and a refusal to discount may well hurt, rather than help, future generations. Nonetheless, it is also possible that cost-benefit analysis with discounting will impose excessive harms on future generations. If so, the proper response is to make investments that will help those generations, not to refuse to discount. We also explore several questions on which the ethicists' legitimate objections require qualification of the positivists' arguments, justifying a low discount rate for climate change policy.

Money in Consumption-Loan Type Models: An Addendum

In the Cass, Okuno, and Zilcha (1979), we presented several examples of consumption-loan type models exhibiting the nonexistence of any competitive equilibrium which is Pareto optimal. One sort of example—involving nonmonotonicity in tastes—seemed very special. Evidently, it depended on having just the right combination of some consumption satiation together with some boundary endowments. We conjectured that such speciality wasn't essential to the intuitive proposition being advanced, that somewhat less than total satiation might unfavorably restrict potential intertemporal market transfers—even given the institution of money, in its role as a store of value, as a common means for facilitating trade between the present and the future. Rather, we proposed as a more likely reason for such speciality the particular analytic methodology being utilized, the limitation to considering only models for which competitive equilibria could be essentially characterized as the nonnegative solutions to a first order difference equation (and thus completely represented in terms of a two-dimensional diagram). It turns out that while our intuition was correct, our reasoning wasn't. In fact, it is now apparent that the only operative constraint was simply our lack of sufficient ingenuity

Optimum Economic Growth in an Aggregative Model of Capital Accumulation: A Turnpike Theorem

Recent contributions to the theory of optimum economic growth, for example, in [1], [3], [8] or [10], like Ramsey’s seminal article [6], have been primarily concerned with the implications of maximizing the social welfare generated by the entire stream of future consumption. As an alternative formulation, in this paper it is postulated that only the social welfare associated with future consumption over some finite period is of direct concern; generations beyond the horizon are accounted for only insofar as a lower bound on the terminal capital stock is prescribed. Then, within a closed, aggregative framework, the behavior of growth paths which are optimum with respect to this social welfare is investigated

What Happened on Deliberation Day?

What are the effects of deliberation about political issues? This essay reports the results of a kind of Deliberation Day, involving sixty-three citizens in Colorado. Groups from Boulder, a predominantly liberal city, met and discussed global warming, affirmative action, and civil unions for same-sex couples; groups from Colorado Springs, a predominately conservative city, met to discuss the same issues. The major effect of deliberation was to make group members more extreme than they were when they started to talk. Liberals became more liberal on all three issues; conservatives became more conservative. As a result, the division between the citizens of Boulder and the citizens of Colorado Springs were significantly increased as a result of intragroup deliberation. Deliberation also increased consensus, and dampened diversity, within the groups. Hence Deliberation Day produced group polarization, in the distinctive form of ideological amplification. Implications are explored for the uses and structure of deliberation in general.

Ideological Voting on Federal Courts of Appeals: A Preliminary Investigation

For many decades, the United States has been conducting an extraordinary natural experiment: Randomly assigned three-judge panels on courts of appeals produce extensive evidence of the effect of judicial ideology on judges' votes. If the political party of the appointing president is treated as a rough proxy for ideology, then it becomes possible to test three hypotheses: (a) a judge's votes, in ideologically contested areas, can be predicted by the party of the appointing president; (b) a judge's ideological tendency, in such areas, will be amplified if the panel has two other judges appointed by an appointing president of the same political party; and (c) a judge's ideological tendency, in such areas, will be dampened if the panel has no other judge appointed by an appointing president of the same political party. All three hypotheses are confirmed in many areas, including affirmative action, campaign finance, sex discrimination, sexual harassment, piercing the corporate veil, disability discrimination, race discrimination, and review of environmental regulations. An important implication is that panel composition has a strong effect on likely outcomes, thus creating extremely serious problems for the rule of law. Taken as a whole, the evidence suggests that judges frequently issue collegial concurrences, that is, concurrences produced by the unanimous views of the other judges on the panel, and that judges are subject to group polarization, by which groups of like-minded people go to extremes. Notably, all three hypotheses are rejected in the areas of federalism, criminal appeals, and takings of private property, because Republican and Democratic appointees vote essentially alike. In the areas of abortion and capital punishment, the first hypothesis is confirmed, but the second and third are rejected, because judges vote their convictions, and are not affected by the composition of the panel. Disaggregating the data by circuit allows courts of appeals to be ranked along an ideological spectrum; it also shows striking differences between Republican appointees and Democratic appointees on different circuits. Normative implications are briefly explored.