INTERTEMPORAL UTILITY SMOOTHING: THEORY AND APPLICATIONS

This paper reviews models of intertemporal choice designed to be consistent with a phenomenon called a preference for spread; that is, where a decision‐maker prefers to spread good and bad consumption evenly over time. We closely examine the notion of utility smoothing adopted in these models as a source of the preference for spread. The paper also reviews extensions of these models where a strong aversion to volatility involved in a utility sequence causes preferences to be nonmonotone. Furthermore, to gain a better understanding of the behaviour implied by these models, we apply them to the Diamond growth model.     

Testable implications of subjective expected utility theory

I show that the predictive content of the hypothesis of subjective expected utility maximization critically depends on what the analyst knows about the details of the problem a particular decision maker faces. When the analyst does not know anything about the agent's payoffs or beliefs and can only observe the sequence of actions taken by the decision maker any arbitrary sequence of actions can be implemented as the choice of an agent that solves some intertemporal utility maximization problem under uncertainty.     

Testable implications of subjective expected utility theory

I show that the predictive content of the hypothesis of subjective expected utility maximization critically depends on what the analyst knows about the details of the problem a particular decision maker faces. When the analyst does not know anything about the agent's payoffs or beliefs and can only observe the sequence of actions taken by the decision maker any arbitrary sequence of actions can be implemented as the choice of an agent that solves some intertemporal utility maximization problem under uncertainty.     

Dissertation abstract: The effect of involvement, time, and vividness on consumers’ value judgments: A test of prospect theory

The literature in psychology and behavioral economics offers abundant instances of anomalies to the rational choice paradigm. One of the most prominent works attempting to reconcile these is Kahneman and Tversky’s Prospect Theory. Its well-known S-shaped value function accounts for some of the anomalies such as reference dependence, loss aversion, and diminishing sensitivity. Although Prospect Theory describes the manner in which individuals are loss averse, it does not explain why people show loss aversion. This dissertation investigates the factors that affect the cognitive processes behind loss aversion. We find an anomaly in the S-shaped value function. Specifically, the studies demonstrate that the degree of involvement affects the slope of the value curve both for atemporal and intertemporal choices. In addition, we also test the relationship between loss aversion and involvement with varying vividness of outcomes (i.e., when outcomes are related to more versus less vivid stimuli). Testing the vividness effects further extends and confirms our proposed relationship between involvement and loss aversion. The data from several experiments show that there is a difference in the slopes of the value function for low and high involvement decisions. For low involvement conditions, the value curve has roughly the same steepness for losses as for gains close to the neutral reference point (i.e., contrary to the diminishing sensitivity characteristic). By contrast, in the high involvement conditions this is not the case: there is a distinct difference in the slopes of the loss and gain curves. This leads us to propose that different value functions exist for people in the low and high involvement conditions. This important finding suggests that in cases where people are not highly involved with a product, they display significantly less loss aversion than predicted by Prospect Theory. Three experiments investigate the relationship of loss aversion to subjects’ level of involvement in atemporal choice, intertemporal choice, and differential vividness of stimuli situations, respectively. The first study uses a 2 (involvement: low and high) by 2 (outcome: gain and loss) between subjects design. The results show that loss aversion significantly attenuates in the low involvement condition for atemporal choice. Study two replicates the results of study one in the context of intertemporal choice, where timing of outcomes (now versus three months) is introduced as another factor. Finally, the third study manipulates the vividness of outcomes and finds an interaction effect of vividness and involvement on loss aversion. Dissertation Committee: Norman Frohlich (Co- Chair), I.H. Asper School of Business, University of Manitoba Edward Bruning (Co- Chair), I.H. Asper School of Business, University of Manitoba Namita Bhatnagar, I.H. Asper School of Business, University of Manitoba Wayne Simpson, Department of Economics, University of Manitoba Michael Hu, Department of Marketing, Kent State University     

Why uncertainty matters: discounting under intertemporal risk aversion and ambiguity

Uncertainty has an almost negligible impact on project value in the standard economic model. I show that a comprehensive evaluation of uncertainty and uncertainty attitude changes this picture fundamentally. The illustration of this result relies on the discount rate, which is the crucial determinant in balancing immediate costs against future benefits, and the single most important determinant of optimal mitigation policies in the integrated assessment of climate change. First, the paper removes an implicit assumption of (intertemporal or intrinsic) risk neutrality from the standard economic model. Second, the paper introduces aversion to non-risk uncertainty (ambiguity). I show a close formal similarity between the model of intertemporal risk aversion, which is a reformulation of the widespread Epstein–Zin–Weil model, and a recent model of smooth ambiguity aversion. I merge the models, achieving a threefold disentanglement between risk aversion, ambiguity aversion, and the propensity to smooth consumption over time.     

Rational inattention,long-run consumption risk,and portfolio choice

This paper explores how the introduction of rational inattention (RI) – that agents process information subject to finite channel capacity – affects optimal consumption and investment decisions in an otherwise standard intertemporal model of portfolio choice. We first explicitly derive optimal consumption and portfolio rules under RI and then show that introducing RI reduces the optimal share of savings invested in the risky asset because inattentive investors face greater long-run consumption risk. We also show that the investment horizon matters for portfolio allocation in the presence of RI, even if investment opportunities are constant and the utility function of investors is constant relative risk aversion. Second, after aggregating across investors, we show that introducing RI can better explain the observed joint dynamics of aggregate consumption and the equity return. Finally, we show that RI increases the implied equity premium because investors under RI face greater long-run consumption risk and thus require higher compensation in equilibrium.     

Emotional Temperature,Probabilistic Choice and the Optimal Power of Incentives*

From the time of Plato it has been assumed that emotions cloud rational thinking. Fully rational individuals were supposed to be completely free of emotions. Modern psychological research challenged this paradigm. One of the insights of this research is that though emotions indeed interfere with the ability to evaluate the objective consequences of choices, they also allow the decision maker to feel the difference in utility arising from those choices. In this article, I formalise this intuition by introducing the concept of emotional temperature. I show that there exists a positive optimal emotional temperature, which leads to an irreducible probability of suboptimal choice. I apply the model to characterise the optimal contracts under moral hazard, assuming that the emotional temperature of the decision maker increases when the contract provides more powerful incentives. A more general point the article makes is that a mechanism designer needs to be aware that the mechanism will not only affect incentives but also the degree of rationality of the agents.     

Loss aversion and social security: a general equilibrium approach

Introducing an intertemporal model of loss aversion, I study the role of social security in determining intergenerational redistribution when consumers have reference-dependent preferences with loss aversion. Using a unified social security model in which different social security plans are specified via different degrees of fundedness, I examine the effect of the transition from a less funded system to a more funded one on savings, consumption, and capital accumulation for an OLG production economy. A general equilibrium analysis shows that the direction of intertemporal equilibrium is dependent on how the total savings responds to the interest rate change, but the effect of the payroll tax on capital accumulation is ambiguous. By deriving closed-form solutions, I find that an increase in fundedness intensity unambiguously increases capital accumulation in steady states, while the tax effects on consumption and savings are not conclusive. Moreover, simulation exercises show that when consumers are prone to over-consume because they care more about the contemporaneous gain utility, the fully funded system may help the individuals smooth out their lifecycle consumption.     

Intertemporal dynamic choice under myopia for reward and different risk tolerances

This paper discusses the rationality in an intertemporal dynamic choice under human psychological biases through numerical experiments. A decision maker tries to find the optimal choice in a financial problem by maximizing the subjects?? expected utility for multiple periods, which is measured by the value function in the prospect theory. The subjects are assumed to be myopic for monetary reward and show time-inconsistent preference. Additionally, they have different risk tolerances for gains and losses, causing the framing effect. Under these conditions, a comparative analysis is carried out numerically to evaluate a combined effect of the two psychological factors on the intertemporal choice. The paper also presents a simple computational method for the numerical analysis and proves its validity.     

Increases in Risk Aversion

This note gives sufficient conditions for signing the effect of an increase in risk aversion on the optimal level of the choice variable selected by a decision maker under conditions of risk. The results are illustrated with a decision model taken from the theory of insurance demand.     

Risk, ambiguity, and state-preference theory

The state-preference framework for modeling choice under uncertainty, in which objects of choice are allocations of wealth or commodities across states of the world, is a natural one for modeling ??smooth?? ambiguity-averse preferences. It does not require reference to objective probabilities, personalistic consequences, or counterfactual acts, and it allows for state dependence of utility and unobservable background risk. The decision maker??s local revealed beliefs are encoded in her risk-neutral probabilities (her relative marginal rates of substitution between states) and her local risk preferences are encoded in the matrix of derivatives of the risk-neutral probabilities. This matrix plays a central but generally unappreciated role in the modeling of risk attitudes in the state-preference framework. It can be computed by inverting a bordered Slutsky matrix and vice versa, it generalizes the Arrow?CPratt measure for approximating local risk premia, and its structure reveals whether the decision maker??s risk preferences are ambiguity averse as well as risk-averse. Two versions of the smooth ambiguity model are analyzed??the source-dependent risk aversion model and the second-order uncertainty (KMM) model??and it is shown that in both cases, the overall premium for local uncertainty can be decomposed as the sum of a risk premium and an ambiguity premium.     

Consistent planning under quasi-geometric discounting

We study properties of stationary Markov-perfect equilibria in a general model of intertemporal choice under quasi-geometric discounting. The dynamics generated by stationary Markov-perfect equilibria can be very complicated, even if the model satisfies strict convexity and smoothness properties and the decision maker is arbitrarily patient. If there exist multiple stationary Markov-perfect equilibria, then it is in general possible to construct infinitely many non-degenerate stationary sunspot equilibria as well.     

Efficient allocations under ambiguity

Important implications of the expected utility hypothesis and risk aversion are that if agents have the same probability belief, then consumption plans in every efficient allocation of resources under uncertainty are comonotone with the aggregate endowment, and if their beliefs are concordant, then the consumption plans are measurable with respect to the aggregate endowment. We study these two properties of efficient allocations for models of preferences that exhibit ambiguity aversion using the concept of conditional beliefs, which we introduce in this paper. We provide characterizations of such conditional beliefs for the standard models of preferences used in applications.     

Sustained output growth under uncertainty: A simple model with human capital

In a model where agents use their labour/education choice to adjust their consumption profile over time, I show that the impact of uncertainty on growth depends, critically, on agents’ attitudes towards risk, reflected by the coefficient of relative risk aversion. In this respect, the well known result from the literature on ‘saving under uncertainty’ can be extended into a broader context, whereby the intertemporal profile of consumption is determined via human capital accumulation rather than saving and physical capital investment.     

Regret aversion and opportunity dependence

This paper provides an axiomatic model of decision making under uncertainty in which the decision maker is driven by anticipated ex post regrets. Our model allows both regret aversion and likelihood judgement over states to coexist. Also, we characterize two special cases, minimax regret with multiple priors that generalizes Savage's minimax regret, and a smooth model of regret aversion.     

Subjective probability over a subjective decision tree

A state space has been assumed as a primitive for modeling uncertainty, which presumes that the analyst knows all the uncertainties a decision maker (DM) perceives. This is problematic because states are private information of the DM, and hence are not directly observable to the analyst. Dekel et al. [Representing preferences with a unique subjective state space, Econometrica 69 (2001) 891-934] derive, rather than assume, the subjective state space from preference over suitable choice objects.In a dynamic setting, a decision tree, that is, a pair consisting of a state space and a filtration, has been taken as a primitive. This assumption is also problematic—a decision tree should be derived rather than assumed as a primitive. We formulate a three-stage extension of the above literature in order to model a DM who anticipates subjective uncertainty to be resolved gradually over time. We identify also subjective beliefs on the subjective state space.     

Cognitive constraints, contraction consistency, and the satisficing criterion

A theory of decision making is proposed that offers an axiomatic basis for the notion of “satisficing” postulated by Herbert Simon. The theory relaxes the standard assumption that the decision maker always fully perceives his preferences among the available alternatives, requiring instead that his ability to perceive any given preference be decreasing with respect to the complexity of the choice problem at hand. When complexity is aligned with set inclusion, this exercise is shown to be equivalent to abandoning the contraction consistency axiom of classical choice theory.     

Recursive smooth ambiguity preferences

This paper axiomatizes an intertemporal version of the Smooth Ambiguity decision model developed in [P. Klibanoff, M. Marinacci, S. Mukerji, A smooth model of decision making under ambiguity, Econometrica 73 (6) (2005) 1849-1892]. A key feature of the model is that it achieves a separation between ambiguity, identified as a characteristic of the decision maker's subjective beliefs, and ambiguity attitude, a characteristic of the decision maker's tastes. In applications one may thus specify/vary these two characteristics independent of each other, thereby facilitating richer comparative statics and modeling flexibility than possible under other models which accommodate ambiguity sensitive preferences. Another key feature is that the preferences are dynamically consistent and have a recursive representation. Therefore techniques of dynamic programming can be applied when using this model.     

Prior symmetry, similarity-based reasoning, and endogenous categorization

This paper presents a rational theory of categorization and similarity-based reasoning. I study a model of sequential learning in which the decision maker infers unknown properties of an object from information about other objects. The decision maker may use the following heuristics: divide objects into categories with similar properties and predict that a member of a category has a property if some other member of this category has this property. The environment is symmetric: the decision maker has no reason to believe that the objects and properties are a priori different. In symmetric environments, categorization is an optimal solution to an inductive inference problem. Any optimal solution looks as if the decision maker categorizes. Various experimental observations about similarity-based reasoning coincide with the optimal behavior in my model.     

When expectations become aspirations: reference-dependent preferences and liquidity constraints

A large body of literature suggests that consumers derive utility from gains and losses relative to a reference point. This paper shows that such reference dependence can affect savings in opposite directions depending on whether people face liquidity constraints. Existing models for wealth and intertemporal choice predict that reference dependence reduces savings, but these models abstract from liquidity constraints. Introducing a liquidity constraint, I find that reference dependence can increase optimal savings for people without access to credit. Ex post, after reference points have been formed, liquidity constraints force consumers to take part of an income loss in early periods, inducing those who are reference dependent to concentrate the full loss in early periods and save in order to eliminate future losses. Further, anticipating a liquidity constraint raises the expected level of future consumption and thus the expectations-based reference point for future periods, creating an ex-ante savings motive. These findings underscore that it is important to account for financial market imperfections when applying or testing reference-dependent models in low-income settings, and potentially explain heterogeneity in how much the poor save when facing binding liquidity constraints.