Preference aggregation under uncertainty: Savage vs. Pareto

Following Mongin [J. Econ. Theory 66 (1995) 313; J. Math. Econ. 29 (1998) 331], we study social aggregation of subjective expected utility preferences in a Savage framework. We argue that each of Savage's P3 and P4 are incompatible with the strong Pareto property. A representation theorem for social preferences satisfying Pareto indifference and conforming to the state-dependent expected utility model is provided.     

Pollution standards vs charges under uncertainty

Conventional analysis of pollution control policy under uncertainty does not properly account for the potential cost effectiveness difference between standards and charges, thus drawing misleading conclusions for the case of inefficient standards. Correcting for this anomaly, the following conclusions can be drawn. When uncertainty involves the position of the marginal damage cost schedule, rather than policy indifference, a charge is always superior to an inefficient standard. When uncertainty is about the position of the marginal control cost schedule, policy indifference may occur, but if it does it must be the case that the slope of marginal damage cost exceeds that of marginal control cost.     

Weighted and quadratic models of choice under uncertainty

This paper extends the weighted and quadratic utility models of choice under risk to the context of choice under uncertainty. An important characteristic of the models is that they admit ‘dynamically consistent’ updating rules.     

Full versus quasi MLE for ARMA-GARCH models with infinitely divisible innovations

We compare the backtesting performance of ARMA-GARCH models with the most common types of infinitely divisible innovations, fit with both full maximum likelihood estimation (MLE) and quasi maximum likelihood estimation (QMLE). The innovation types considered are the Gaussian, Student’s t, α-stable, classical tempered stable (CTS), normal tempered stable (NTS) and generalized hyperbolic (GH) distributions. In calm periods of decreasing volatility, MLE and QMLE produce near identical performance in forecasting value-at-risk (VaR) and conditional value-at-risk (CVaR). In more volatile periods, QMLE can actually produce superior performance for CTS, NTS and α-stable innovations. While the t-ARMA-GARCH model has the fewest number of VaR violations, rejections by the Kupeic and Berkowitz tests suggest excessively large forecasted losses. The α-stable, CTS and NTS innovations compare favourably, with the latter two also allowing for option pricing under a single market model.     

Choice under complete uncertainty: axiomatic characterizations of some decision rules

Summary. We provide characterizations of four new rules for individual decision-making under complete uncertainty. They are what we call the min-max rule, the max-min rule, the lexicographic min-max rule and the lexicographic max-min rule. These rules provide orderings of the sets of possible outcomes associated with uncertain prospects. They provide significant alternatives to commonly-used rules that focus on worst outcomes or best outcomes only, and lexicographic versions of those rules. Received: August 20, 1998; revised version: November 3, 1999     

Models for which the MLE and the conditional MLE coincide

The MLE, CMLE and MMLE coincide in a linear regression model with fixed individual effects. In this case, there is no incidental parameters problem and the MLE is consistent. The equivalence of these estimators is important because CMLE=MLE implies both the consistency of the MLE and the efficiency of the CMLE. In general, we cannot expect to find a CMLE or MMLE, since there may be no fixed-dimension sufficient statistic for the effects, nor an appropriate transformation of the data whose distribution does not depend on the effects. However, we show that the MLE, CMLE and MMLE do coincide in systems of seemingly unrelated regressions and in systems of simultaneous equations. We establish this result for systems in which (exogenous) variables in addition to (or other than) the intercept may have coefficients which vary over individuals, provided that the set of such variables is the same in every equation.The financial support of the National Science Foundation is gratefully acknowledged.     

Proper scoring rules for general decision models

If a decision maker whose behavior conforms to the max-min expected utility model is faced with a scoring rule for a subjective expected utility decision maker, she will always announce a probability belonging to her set of priors; moreover, for any prior in the set, there is a scoring rule inducing the agent to announce that prior. We also show that on the domain of Choquet expected utility preferences with risk neutral lottery evaluation and totally monotone capacities, proper scoring rules do not exist. This implies the non-existence of proper scoring rules for any larger class of preferences (CEU with convex capacities, multiple priors).     

Preferences for environmental quality under uncertainty

Although the expected effects of environmental policies and interventions are rarely known with certainty, stated preference surveys rarely elicit preferences over uncertain environmental outcomes. This article presents empirical results challenging the view that ignoring such uncertainty during preference elicitation is of no consequence so long as people only care about final environmental states. We show that measured preferences for final environmental states, water quality in this case, depend on whether people choose between final states or between lotteries over final states. In contrast to the typical finding for monetary lotteries, we find significant under-weighting of low probability events related to water quality.     

The nature of the steady state in models of optimal growth under uncertainty

Summary. We study a one-sector stochastic optimal growth model with a representative agent. Utility is logarithmic and the production function is of the Cobb-Douglas form with capital exponent . Production is affected by a multiplicative shock taking one of two values with positive probabilities p and 1-p. It is well known that for this economy, optimal paths converge to a unique steady state, which is an invariant distribution. We are concerned with properties of this distribution. By using the theory of Iterated Function Systems, we are able to characterize such a distribution in terms of singularity versus absolute continuity as parameters and p change. We establish mutual singularity of the invariant distributions as p varies between 0 and 1 whenever . More delicate is the case . Singularity with respect to Lebesgue measure also appears for values such that . For and Peres and Solomyak (1998) have shown that the distribution is a.e. absolutely continuous. Characterization of the invariant distribution in the remaining cases is still an open question. The entire analysis is summarized through a bifurcation diagram, drawn in terms of pairs .Received: 9 April 2002, Revised: 29 October 2002, JEL Classification Numbers: C61, O41.Correspondence to: Tapan MitraThis research was partially supported by CNR (Italy) under the "Short-term mobility" program and by M.U.R.S.T. (Italy) National Group on "Nonlinear Dynamics and Stochastic Models in Economics and Finance" . We are indebted to Rabi Bhattacharya for providing us with the reference to Solomyak's (1995) paper. The present version has benefitted from comments by Mukul Majumdar and two anonymous referees.     

Bertrand vs. Cournot equilibrium with risk averse firms and cost uncertainty

Summary. In an oligopoly game with cost uncertainty and risk averse firms, we show that Bertrand and Cournot equilibrium have different convergence properties when the market is replicated. The Cournot equilibrium price converges to the competitive price. Under very typical and somewhat general conditions, the highest Bertrand equilibrium price converges to one higher than the competitive equilibrium. We also give examples to show how to compute the limit of the highest Bertrand equilibrium prices and illustrate the ideas of the proof. We explore conditions under which the supply curve is upward sloping, a useful condition for our results. Received: April 20, 2000; revised version: May 10, 2001     

A new model for decisions under uncertainty

A representation for preferences between uncertain acts that is not unduly more complex than the Ramsey-Savage model can simultaneously accomodate Allais's paradox, Ellsberg's paradox, preference reversals and cyclic preferences.     

Necessary conditions for comparative statics under uncertainty

We investigate the comparative static properties of three classes of CDF changes: first and second degree stochastic dominant shifts, and mean preserving contractions. For each class, we provide conditions that are necessary and sufficient for a dominating shift to cause an unambiguous change in the choice variable. This allows us to see the trade-offs one must make between restrictions on preferences and CDF changes to obtain interesting comparative statics results. We then investigate the implications of our results for the two-period consumption-savings models and for distinguishing agents that do and do not obey the expected utility hypothesis.     

Influence of decision styles on use of decision models

This article discusses how the “decision style” of an administrator influences the adoption and use of particular decision models. Several “interactive” and “analytical” decision models often used to guide decision making are described and critiqued to point out their virtues and deficiencies. Propositions are suggested that contend that “systematic,” “judicial”, “speculative”, and “intuitive” styles have clear-cut preferences for a particular decision model. This model seems to be used, even when another would be more suitable. Effective decision makers are postulated to adapt their styles, or at least to see the benefits of different styles. Mixed-mode models are proposed that seem to simulate the behavior of successful decision makers.     

Neutral taxation under uncertainty

The analogs under uncertainty of two well-known certainty results are derived: first, if there are timing differences between tax payments and accruals, neutrality is preserved if the resulting tax credits or liabilities are carried forward at the risk-free interest rate, provided that tax credits and liabilities are sure to be redeemed eventually. Second, the invariance of asset valuations with respect to the rate of income tax, at a given pre-tax interest rate, proved by Johansson and Samuelson under certainty, can be extended to cover the case of uncertainty, given analogous ceteris paribus conditions.     

Lobbying under political uncertainty

This paper considers a model of lobbying described as a common agency game; it departs from the current literature by assuming that the special interest groups are not a priori organized or unorganized and that the type of the politician is not common knowledge. We characterize equilibria when the choice set of the politician consists of two policies; we discuss the conditions leading to efficiency and the characteristics of the groups explaining their relative success in the process of influence. We also offer some results for the general case, including disjoint necessary and sufficient conditions for the equilibria to be efficient.