This working paper extends the methodology of non-smooth affective portfolio theory (APT) for eliciting (IR)rational preferences of investors endowed with continuous quasilinear utility functions, where assets are portfolios of risky and ambiguous state-contingent claims. The elicitation is a solution of the affective Afriat inequalities;see technical appendix 1. Solving the smooth affective Afriat inequalities is Np-hard; see technical appendices 2, 3, and 4. The proposed extension is a methodology for the elicitation of (IR)rational preferences of individuals endowed with random continuous quasilinear utility functions defined over finite subsets of discrete social goods as a refutable model of social exclusion in the incomplete markets for social goods; see technical appendices 5 and 6. The methods of elicitation are generalized estimating equations (GEE) and alternating logistic regression (ALR); see technical appendices; 7 and 8.
The equilibrium prices in asset markets, as stated by Keynes (1930): “…will be fixed at the point at which the sales of the bears and the purchases of the bulls are balanced.” We propose a descriptive theory of finance explicating Keynes’ claim that the prices of assets today equilibrate the optimism and pessimism of bulls and bears regarding the payoffs of assets tomorrow.
This equilibration of optimistic and pessimistic beliefs of investors is a consequence of investors maximizing affective utilities subject to budget constraints defined by market prices and investor’s income. The set of affective utilities is a new class of non-expected utility functions representing the attitudes of investors for optimism or pessimism, defined as the composition of the investor’s attitudes for risk and her attitudes for ambiguity. Bulls and bears are defined respectively as optimistic and pessimistic investors.
The equilibrium prices in asset markets, as stated by Keynes (1930): “…will be fixed at the point at which the sales of the bears and the purchases of the bulls are balanced.” We propose a descriptive theory of finance explicating Keynes’ claim that the prices of assets today equilibrate the optimism and pessimism of bulls and bears regarding the payoffs of assets tomorrow.
This equilibration of optimistic and pessimistic beliefs of investors is a consequence of investors maximizing Keynesian utilities subject to budget constraints defined by market prices and investor’s income. The set of Keynesian utilities is a new class of non-expected utility functions representing the preferences of investors for optimism or pessimism, defined as the composition of the investor’s preferences for risk and her preferences for ambiguity. Bulls and bears are defined respectively as optimistic and pessimistic investors. (Ir)rational exuberance is an intrinsic property of asset markets where bulls and bears are endowed with Keynesian utilities.
We propose Keynesian utilities as a new class of non-expected utility functions representing the preferences of investors for optimism, defined as the composition of the investor’s preferences for risk and her preferences for ambiguity. The optimism or pessimism of Keynesian utilities is determined by empirical proxies for risk and ambiguity. Bulls and bears are defined respectively as optimistic and pessimistic investors. The resulting family of Afriat inequalities are necessary and sufficient for rationalizing the asset demands of bulls and bears with Keynesian utilities.
We conduct two experiments where subjects make a sequence of binary choices between risky and ambiguous binary lotteries. Risky lotteries are defined as lotteries where the relative frequencies of outcomes are known. Ambiguous lotteries are lotteries where the relative frequencies of outcomes are not known or may not exist. The trials in each experiment are divided into three phases: pre-treatment, treatment and post-treatment.
The trials in the pre-treatment and post-treatment phases are the same. As such, the trials before and after the treatment phase are dependent, clustered matched-pairs, that we analyze with the alternating logistic regression (ALR) package in SAS. In both experiments, we reveal to each subject the outcomes of her actual and counterfactual choices in the treatment phase. The treatments differ in the complexity of the random process used to generate the relative frequencies of the payoffs of the ambiguous lotteries. In the first experiment, the probabilities can be inferred from the converging sample averages of the observed actual and counterfactual outcomes of the ambiguous lotteries. In the second experiment the sample averages do not converge.
If we define fictive learning in an experiment as statistically significant changes in the responses of subjects before and after the treatment phase of an experiment, then we expect fictive learning in the first experiment, but no fictive learning in the second experiment. The surprising finding in this paper is the presence of fictive learning in the second experiment. We attribute this counterintuitive result to apophenia: “seeing meaningful patterns in meaningless or random data.” A refinement of this result is the inference from a subsequent Chi-squared test, that the effects of fictive learning in the first experiment are significantly different from the effects of fictive learning in the second experiment.
Optimism-bias is inconsistent with the independence of decision weights and payoffs found in models of choice under risk, such as expected utility theory and prospect theory. Hence, to explain the evidence suggesting that agents are optimistically biased, we propose an alternative model of risky choice, affective decision-making, where decision weights — which we label affective or perceived risk — are endogenized.
Affective decision making (ADM) is a strategic model of choice under risk, where we posit two cognitive processes: the “rational” and the “emotional” processes. The two processes interact in a simultaneous-move intrapersonal potential game, and observed choice is the result of a pure strategy Nash equilibrium in this potential game.
We show that regular ADM potential games have an odd number of locally unique pure strategy Nash equilibria, and demonstrate this finding for affective decision making in insurance markets. We prove that ADM potential games are refutable, by axiomatizing the ADM potential maximizers.
Affective decision-making is a strategic model of choice under risk and uncertainty where we posit two cognitive processes — the “rational” and the “emotional” process. Observed choice is the result of equilibrium in this intrapersonal game.
As an example, we present applications of affective decision-making in insurance markets, where the risk perceptions of consumers are endogenous. We derive the axiomatic foundation of affective decision making, and show that affective decision making is a model of ambiguity-seeking behavior consistent with the Ellsberg paradox.
Affective decision-making is a strategic model of choice under risk and uncertainty where we posit two cognitive processes — the “rational” and the “emotional” process. Observed choice is the result of equilibirum in this intrapersonal game. As an example, we present applications of affective decision-making in insurance markets, where the risk perceptions of consumers are endogenous. We then derive the axiomatic foundation of affective decision making, and show that, although beliefs are endogenous, not every pattern of behavior is possible under affective decision making.
Conventional deadweight loss measures of the social cost of monopoly ignore, among other things, the social cost of inducing competition and thus cannot accurately capture the loss in social welfare. In this Article, we suggest an alternative method of measuring the social cost of monopoly. Using elements of general equilibrium theory, we propose a social cost metric where the benchmark is the Pareto optimal state of the economy that uses the least amount of resources, consistent with consumers’ utility levels in the monopolized state. If the primary goal of antitrust policy is the enhancement of consumer welfare, then the proper benchmark is Pareto optimality, not simply competitive markets. We discuss the implications of our approach for antitrust law as well as how our methodology can be used in practice for allegations of monopoly power given a history of price-demand observations.
Keywords: Monopoly power, Antitrust economics, Applied general equilibrium
The present paper introduces new sign tests for testing for conditionally symmetric martingale-difference assumptions as well as for testing that conditional distributions of two (arbitrary) martingale-difference sequences are the same. Our analysis is based on the results that demonstrate that randomization over zero values of three-valued random variables in a conditionally symmetric martingale-difference sequence produces a stream of i.i.d. symmetric Bernoulli random variables and thus reduces the problem of estimating the critical values of the tests to computing the quantiles or moments of Binomial or normal distributions. The same is the case for randomization over ties in sign tests for equality of conditional distributions of two martingale-difference sequences.
The paper also provides sharp bounds on the expected payoffs and fair prices of European call options and a wide range of path-dependent contingent claims in the trinomial financial market model in which, as is well-known, calculation of derivative prices on the base of no-arbitrage arguments is impossible. These applications show, in particular, that the expected payoff of a European call option in the trinomial model with log-returns forming a martingale-difference sequence is bounded from above by the expected payoff of a call option written on a stock with i.i.d. symmetric two-valued log-returns and, thus, reduce the problem of derivative pricing in the trinomial model with dependence to the i.i.d. binomial case. Furthermore, we show that the expected payoff of a European call option in the multiperiod trinomial option pricing model is dominated by the expected payoff of a call option in the two-period model with a log-normal asset price. These results thus allow one to reduce the problem of pricing options in the trinomial model to the case of two periods and the standard assumption of normal log-returns. We also obtain bounds on the possible fair prices of call options in the (incomplete) trinomial model in terms of the parameters of the asset’s distribution.
Sharp bounds completely similar to those for European call options also hold for many other contingent claims in the trinomial option pricing model, including those with an arbitrary convex increasing function as well as path-dependent ones, in particular, Asian options written on averages of the underlying asset’s prices.
This paper proposes nonparametric statistical procedures for analyzing discrete choice models of affective decision making. We make two contributions to the literature on behavioral economics. Namely, we propose a procedure for eliciting the existence of a Nash equilibrium in an intrapersonal, potential game as well as randomized sign tests for dependent observations on game-theoretic models of affective decision making. This methodology is illustrated in the context of a hypothetical experiment — the Casino Game.
We present necessary and sufficient conditions on the asset span of incomplete derivative markets for insuring marketed portfolios. If the asset span is finite dimensional there exists a polynomial-time algorithm for deciding if every marketed portfolio is insurable, moreover this algorithm computes the minimum cost insurance portfolio.
In addition, we extend the Cox-Leland characterization of optimal portfolio insurance in complete derivative markets to asset spans of incomplete derivative markets where every marketed portfolio is insurable.
We present versions of the two fundamental welfare theorems of economics for exchange economies with a countable number of agents and an infinite dimensional commodity space. These results are then specialized to the overlapping generations model.
An Edgeworth equilibrium is an allocation that belongs to the core of every n-fold replica of the economy. In [2] we studied in the setting of Riesz spaces the properties of Edgeworth equilibria for pure exchange economies with infinite dimensional commodity spaces. In this work, we study the same problem for economies with production. Under some relatively mild conditions we establish (among other things) that: 1. Edgeworth equilibria exist; 2. Every Edgeworth equilibrium is a quasiequilibrium; and 3. An allocation is an Edgeworth equilibrium if and only if it can be “decentralized” by a price system.
JEL Classification: 021
Keywords: Edgeworth equilibrium, Riesz spaces, production economies
This study is an effort to give a simple measure of the local size of the equilibrium set of OLG economies in which there may be more than one good and more than one consumer per period, and in which the generations may differ across time.