Inter-temporal choices with temporal reference dependence

I develop an intertemporal choice model for rational deviators whose preferences depend not only on their actual consumption but also on comparison to their beliefs about the optimal consumption. The standard decision maker is loss averse with respect to this belief-dependent reference point. When psychologically weighted loss aversion is low, a decision maker deviates from the standard intertemporal choice behavior and over-consumption, as well as the alternative possibility of under-consumption can be rationalized. When the decision maker has time-varying degrees of loss aversion, he re-optimizes the consumption plan through adjusted beliefs as subsequent selves realize that past decision for the present period is no longer optimal. In the dynamic model, I solve for consistent intertemporal optimization rules by which a dynamic deviator should meet rational intertemporal consistency at each point in time. Finally, I demonstrate that the dynamic reference dependent model can solve a puzzling feature in lifecycle consumption data.     

Prices or Quantities Can Dominate Banking and Borrowing*

The possibility of intertemporal banking and borrowing of tradable permits is often viewed as tilting the various policy debates about optimal pollution control instruments towards favoring such time-flexible quantities. This paper shows that this view can be misleading, at least for the simplest dynamic extension of the original “prices versus quantities” information structure. The model of this paper allows firms to know and act upon the realization of uncertain future costs two full periods ahead of the regulators. For any given circumstance, the paper shows that either a fixed price or a fixed quantity is superior in expected welfare to time-flexible banking and borrowing. Furthermore, the standard original formula for the comparative advantage of prices over quantities contains sufficient information to completely characterize the regulatory role of intertemporal banking and borrowing. The logic and implications of these results are analyzed and discussed.     

Robust portfolio rules and detection-error probabilities for a mean-reverting risk premium

I analyze the optimal intertemporal portfolio problem of an investor who worries about model misspecification and insists on robust decision rules when facing a mean-reverting risk premium. The desire for robustness lowers the total equity share, but increases the proportion of the intertemporal hedging demand. I present a methodology for calculation of detection-error probabilities, which is based on Fourier inversion of the conditional characteristic functions of the Radon-Nikodym derivatives. The quantitative effect of robustness is more modest than in i.i.d. settings, because model discrimination between the benchmark and the worst-case alternative model is easier, as indicated by the detection-error probabilities.     

Thinking Ahead: The Decision Problem

We propose a model of costly decision making based on time-costs of deliberating current and future decisions. We model an individual decision-maker's thinking process as a thought-experiment that takes time, and lets the decision maker 'think ahead' about future decision problems in yet unrealized states of nature. By formulating an intertemporal, state-contingent, planning problem which may involve costly deliberation in every state of nature, and by letting the decision maker deliberate ahead of the realization of a state, we attempt to capture the basic observation that individuals generally do not think through a complete action plan. Instead, individuals prioritize their thinking and leave deliberations on less important decisions to the time or event when they arise.     

An essay on the Life Cycle: Characterizing intertemporal behavior with uncertainty,human capital,taxes, durables,imperfect capital markets,and non-separable preferences

This paper formulates a general characterization of a household's portfolio choice and savings behavior in an environment with uncertain future interest rates, prices, wages, and factors influencing tastes. Savings may be invested in three types of assets: financial assets; human capital, which is non-tradable; and consumer durables, in which investment may be partially irreversible. Risk-return relations determine the optimal allocation of resources across assets at a point in time. The optimal intertemporal allocation of resources is determined by a restriction on the planned growth rate for the marginal utility of after-tax wealth, where growth rates depend on rates of time preference and measures of long-term riskless rates of interest. Given special assumptions, this marginal utility follows a martingale process as a consequence of optimizing behavior. Pricing formulae are developed for evaluating shifts in uncertain future income, wage, and price profiles. The relations characterizing portfolio and savings behavior presented here do not rely on particular distributional assumptions; they account for all forms of uncertainty including wage uncertainty induced by human capital investment; they allow for the non-marketability of assets; and the main results apply for very general functional form assumptions for preferences. In later sections, results are extended to incorporate income taxes and to account for a wide variety of imperfections in asset markets.     

Cost Benefit Analysis with Uncertain Cash Flow and Project Life

When future cash flows and the lives of capital projects are known, the optimal solution is usually one of choosing the project that maximizes net present value of future returns on the project. In many situations, however, the information needed for cost-benefit analysis is not known with certainty. Recent cost-benefit models have tried to introduce some realism by assuming future cash flows are unknown but are subject to known probability laws. However, not much has been done on relaxing the assumption of known project life. This paper proposes a framework to include the assumption of uncertain project life and future cash flows in cost-benefit decision making. The method follows from some known techniques from the actuarial literature that to a large extent is underappreciated in cost-benefit analysis.     

True indexes and rational habit formation

In this paper we discuss the construction of true indexes when tastes change endogenously. True indexes take the substitution possibilities of the consumer to a changing economic situation into account when equating the utility level of a particular period to the utility level attained in the base period through an appropriate change in income or the wage level. When tastes change endogenously, the current decision depends on the past history of consumption but, by the same token, the future path of consumption will depend on the current choice. In a true index, these intertemporal links of the current decision have to be taken into account. For a particular specification of the habit formation process, this is achieved by an appropriate transformation of prices and expenditures. A true intertemporal wage index is computed for the period 1946–1967 in the U.S. Because of increasing needs and intertemporal rationality, this index is roughly constant and equal to 1: real wages remained constant!     

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.     

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.     

The effect of acute pain on risky and intertemporal choice

Pain is a highly salient and attention-demanding experience that motivates people to act. We investigated the effect of pain on decision making by delivering acute thermal pain to participants’ forearm while they made risky and intertemporal choices involving money. Participants (n = 107) were more risk seeking under pain than in a no-pain control condition when decisions involved gains but not when they involved equivalent losses. Pain also resulted in greater preference for immediate (smaller) over future (larger) monetary rewards. We interpret these results as a motivation to offset the aversive, pain-induced state, where monetary rewards become more appealing under pain than under no pain and when delivered sooner rather than later. Our findings add to the long-standing debate regarding the role of intuition and reflection in decision making.     

Repeated Experimentation to Learn About a Flow-Pollutant Threshold

We examine in discrete time the management of a flow pollutant that causes damage when it crosses a fixed but unknown threshold. The manager sequentially chooses a pollution level that allows learning about the threshold, thereby improving future decisions. If crossed, damage can be reversed at some cost. We analyze the conditions under which experimentation is optimal, and explore how experimentation depends on restoration costs, information about the threshold, and the discount rate. Our results suggest that the level of experimentation, defined as the difference between the optimal activity with and without learning, is non-monotonic in costs and decreasing in the discount rate. We identify two stopping boundaries for the experiment, depending on cost levels compared to the lower bound of the threshold’s interval. We show that when costs are high the stopping boundary under an infinite number of decisions is the same as when there are only two decision moments. A computational extension to more than two decisions suggests that an optimal sequence of experiments can cross the same threshold several times before experimentation ceases. These results shed light on a large class of environmental decision problems that has not been examined in the literature.     

Consistent Planning Under Uncertain Lifetime

This paper considers the problem of intertemporal planning when changing tastes result in inconsistent plans. This problem has been considered in the literature under the assumption of a lifetime certainty. Some of the solutions proposed in the literature exhibit certain undesirable properties such as incoherence and lack of Pareto-optimality. This paper proposes a procedure for solving the intertemporal dilemma when lifetime is uncertain. The proposed solution is coherent and Pareto-optimal, and is, in fact, valid for the case of certain as well as uncertain lifetime. [020]     

Beyond the Stern Review: Lessons from a risky venture at the limits of the cost-benefit analysis

This paper argues that debates amongst economists triggered by the Stern Review are partly relevant, focusing on key parameters translating real ethical issues, and partly misplaced in that they do not consider enough other determinants of climate change damages: i) the specifications of the utility function used for the assessments (preference for the environment, preference for smooth growth paths), ii) the interplay between uncertainty and the sequentiality of the decision, and iii) whether the growth engines behind the integrated assessment models can account for transient disequilibrium and sub-optimality. We derive some suggestions for any future research agenda in integrated assessment modelling, whatever the position of the analysts about the relevance of the intertemporal optimisation framework and the Bayesian approach to uncertainty in the climate affair.     

Intertemporal Permit Trading for the Control of Greenhouse Gas Emissions

This paper integrates two themes in the intertemporal permitliterature through the construction of an intertemporal bankingsystem for a pollutant that creates both stock and flow damages. A permit banking system for the special case of a pollutant thatonly causes stock damages is also developed. This latter,simpler case corresponds roughly to the greenhouse gas emissionreduction regime proposed by the U.S. Department of State as ameans of fulfilling the U.S. commitment to the FrameworkConvention on Climate Change. This paper shows that environmentalregulators can achieve the socially optimal level of emissionsand output through time by setting the correct total sum ofallowable emissions, and specifying the correct intertemporaltrading ratio for banking and borrowing. For the case ofgreenhouse gases, we show that the optimal growth rate of permitprices, and therefore the optimal intertemporal trading rate, hasthe closed-form solution equal to the ratio of current marginalstock damages to the discounted future value of marginal stockdamages less the decay rate of emissions in the atmosphere. Given a non-optimal negotiated emission path we then derive apermit banking system that has the potential to lower net socialcosts by adjusting the intertemporal trading ratio taking intoaccount the behavior of private agents. We use a simplenumerical simulation model to illustrate the potential gains fromvarious possible banking systems.     

On Intertemporal Subsidy-Free Prices and Economic Depreciation: Constrained Market Pricing Revisited

The constrained market pricing approach to regulating monopolies maintains that prices should be subsidy-free, lying between the often expansive bounds of stand alone and incremental costs. For a simple two-good/two-period model of a monopolist subject to a zero profit constraint, it is shown that subsidy-free prices are those which rise to the amortized opportunity cost of the currently optimal asset configuration required to meet both current and future demand, providing—in some circumstances—justification for accelerated depreciation. Such intertemporal subsidy-free prices recognize that the stand alone cost of existing assets to current consumers depends on the value of those assets to future consumers. Hence, if a feasible resale price for the fixed costs of capacity exists within or between periods, then intertemporal stand alone costs and intertemporal incremental costs are driven to equality.     

Optimal monetary policy in a small open economy with inflation and output persistence

We study optimal monetary policy for a small open economy in a model where both inflation and output show persistence. We incorporate habit formation into intertemporal consumption decision and modify the Calvo price setting to include indexation to past inflation. The message conveyed from this study can be viewed as twofold. First, full stabilization of domestic prices or the output gap is not optimal policy. This is because stabilization of the output gap leads to serial correlation in domestic inflation, whereas under full stabilization of domestic prices the output gap displays some serial correlation. It is, however, shown that at the zero inflation steady state, stabilizing domestic prices is equivalent to stabilizing the output gap. Second, in the presence of foreign income shock inflation and the output gap are more stable under flexible CPI inflation targeting than under other alternative policy regimes considered.     

Nonseparable preferences and optimal social security systems

In this paper, we consider economies in which agents are privately informed about their skills, which evolve stochastically over time. We require agents' preferences to be weakly separable between the lifetime paths of consumption and labor. However, we allow for intertemporal nonseparabilities in preferences like habit formation. In this environment, we derive a generalized version of the Inverse Euler Equation and use it to show that intertemporal wedges characterizing optimal allocations of consumption can be strictly negative. We also show that preference nonseparabilities imply that optimal differentiable asset income taxes are necessarily retrospective in nature. We show that under weak conditions, it is possible to implement a socially optimal allocation using a social security system in which taxes on wealth are linear, and taxes/transfers are history-dependent only at retirement. The average asset income tax in this system is zero.     

Risk taking with additive and multiplicative background risks

We examine the effects of background risks on optimal portfolio choice. Examples of background risks include uncertain labor income, uncertainty about the terminal value of fixed assets such as housing and uncertainty about future tax liabilities. While some of these risks are additive and have been amply studied, others are multiplicative in nature and have received far less attention. The simultaneous effect of both additive and multiplicative risks has hitherto not received attention and can explain some paradoxical choice behavior. We rationalize such behavior and show how background risks might lead to seemingly U-shaped relative risk aversion for a representative investor.     

MULTIATTRIBUTE UTILITY THEORY,INTERTEMPORAL UTILITY,AND CORRELATION AVERSION

Convenient assumptions about qualitative properties of the intertemporal utility function have generated counterintuitive implications for the relationship between atemporal risk aversion and the intertemporal elasticity of substitution. If the intertemporal utility function is additively separable, then the latter two concepts are the inverse of each other. We review a theoretical specification with a long lineage in the literature on multi‐attribute utility and use this theoretical structure to guide the design of a series of experiments that allow us to identify and estimate intertemporal correlation aversion. Our results show that subjects are correlation averse over lotteries with intertemporal income profiles.