Status,Risk-Taking and Intertemporal Substitution in an Endogenous Growth Model

This paper examines intertemporal risk-taking in a stochastically growing economy with externalities in human capital accumulation where agents have preferences for social status. In order to isolate the effects of status concerns on long-run expected growth, the analysis is embedded in a non-expected utility setting, which disentangles the effects from risk aversion and intertemporal substitution. We examine the interaction between status desire and risk, risk aversion and intertemporal substitution. The externalities generated by the status game are able to correct the allocative distortions from the knowledge spillovers.Acknowledgement The author would like to thank an anonymous referee for his valuable comments.     

Invariant risk attitudes

Concepts of constant absolute risk aversion and constant relative risk aversion have proved useful in the analysis of choice under uncertainty, but are quite restrictive, particularly when they are imposed jointly. A generalization of constant risk aversion, referred to as invariant risk aversion is developed. Invariant risk aversion is closely related to the possibility of representing preferences over state-contingent income vectors in terms of two parameters, the mean and a linearly homogeneous, translation-invariant index of riskiness. The best-known index with such properties is the standard deviation. The properties of the capital asset pricing model, usually expressed in terms of the mean and standard deviation, may be extended to the case of general invariant preferences.     

Intertemporal elasticity of substitution and risk aversion: are they related empirically?

This article examines the relationship between two types of preference: preference of intertemporal choices and preference towards risk. In the simplest form of the constant relative risk aversion utility function, the intertemporal elasticity of substitution (IES) and risk aversion have an inverse relationship. However, there is no empirical evidence that suggests this inverse relationship holds. We examine the relationship between risk aversion and IES using household consumption data from the Consumer Expenditure Survey during 1996–2010. Multiple risk domains are selected to represent risk preference, and for each domain, we consider some households to be more risk averse than others. We separately estimate IES for the more risk-averse and less risk-averse households. We find that the IES estimates are generally smaller for the more risk-averse households than for the less risk-averse households and that the difference is statistically significant in the majority of the financial domains. This finding supports the inverse relationship between the two parameters, although considerable heterogeneity is found across domains.     

Wealth inequality, preference heterogeneity and macroeconomic volatility in two-sector economies

We explore the link between wealth inequality, preference heterogeneity and macroeconomic volatility in a two-sector neoclassical growth model. First we prove that, if agents have homogeneous preferences, when the absolute risk tolerance is a strictly convex (concave) function, sufficiently high (low) levels of wealth inequality may lead to endogenous fluctuations in the neighborhood of the steady state. Second, we consider the effects of preference heterogeneity when agents are homogeneous with respect to their wealth. We show that when the utility function belongs to the HARA class, sufficiently high levels of preference heterogeneity may lead to endogenous fluctuations in the neighborhood of the steady state if the elasticity of intertemporal substitution in consumption is greater than one.     

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.     

社会地位、非期望效用函数、资产定价和经济增长

本文利用非期望偏好结构 ,讨论消费和资产收益的时间序列行为。在这种递归偏好结构中 ,投资者积累财富不仅仅为了消费 ,也为了财富所带来的社会地位 ,我们研究这一假设对消费、投资组合策略、证券市场价格以及经济增长的影响 ,并利用所得到的定价方程讨论风险溢金问题。     

Prudence, Intertemporal Substitution, and Savings under Uncertainty

This paper derives the relations between the coefficient of absolute prudence, the equivalent precautionary premium, risk aversion to concentration, and the normality and shift of current consumption under uncertainty, without the time-separable utility assumption. Examples show that Kimball's coefficient of absolute prudence does not fully characterize precautionary saving or saving behavior under uncertainty. It is proved that, whereas a higher rate of intertemporal substitution and a larger coefficient of absolute prudence imply more savings when current consumption is normal, a larger coefficient of intertemporal substitution and a smaller coefficient of absolute prudence imply more savings when current consumption is inferior. Received July 17, 2001; revised version received November 20, 2001     

Epstein–Zin Utility in DICE: Is Risk Aversion Irrelevant to Climate Policy?

Climate change involves uncertain probabilities of catastrophic risks, and very longterm consequences of current actions. Climate economics, therefore, is centrally concerned with the treatment of risk and time. Yet conventional assumptions about utility and optimal economic growth create a perverse connection between risk aversion and time preference, such that more aversion to current risks implies less concern for future outcomes, and vice versa. The same conflation of risk aversion and time preference leads to the equity premium puzzle in finance. A promising response to the equity premium puzzle, the recursive utility of Epstein and Zin, allows separation of risk aversion and time preference—at the cost of considerable analytic complexity. We introduce an accessible implementation of Epstein–Zin utility into the DICE model of climate economics, creating a hybrid “EZ-DICE” model. Using Epstein–Zin parameters from the finance literature and climate uncertainty parameters from the science literature, we find that the optimal climate policy in EZ-DICE calls for rapid abatement of carbon emissions; it is similar to standard DICE results with the discount rate set to equal the risk-free rate of return. EZ-DICE solutions are sensitive to the intertemporal elasticity of substitution, but remarkably insensitive to risk aversion. Insensitivity to risk aversion may reflect the difficulty of modeling catastrophic risks within DICE. Implicit in DICE are strong assumptions about the cost of climate stabilization and the certainty and speed of success; under these assumptions, risk aversion would in fact be unimportant. A more realistic analysis will require a subtler treatment of catastrophic climate risk.     

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.     

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.     

Intertemporal substitution, risk aversion and ambiguity aversion

Summary. This paper axiomatizes a form of recursive utility on consumption processes that permits a role for ambiguity as well as risk. The model has two prominent special cases: (i) the recursive model of risk preference due to Kreps and Porteus [18]; and (ii) an intertemporal version of multiple-priors utility due to Epstein and Schneider [8]. The generalization presented here permits a three-way separation of intertemporal substitution, risk aversion and ambiguity aversion.Received: 5 August 2003, Revised: 12 March 2004, JEL Classification Numbers: D80, D81, D90.I am grateful to Larry Epstein for his guidance and invaluable advice, and to a referee for helpful comments and suggestions.     

A SMOOTH AMBIGUITY MODEL OF THE COMPETITIVE FIRM

This paper examines the optimal production decision of the competitive firm under price uncertainty when the firm's preferences exhibit smooth ambiguity aversion. Ambiguity is modeled by a second‐order probability distribution that captures the firm's uncertainty about which of the subjective beliefs govern the price risk. Ambiguity preferences are modeled by the (second‐order) expectation of a concave transformation of the (first‐order) expected utility of profit conditional on each plausible subjective distribution of the price risk. Within this framework, we derive necessary and sufficient conditions under which the ambiguity‐averse firm optimally produces less in response either to the introduction of ambiguity or to greater ambiguity aversion when ambiguity prevails. In the case that the price risk is binary, we show that ambiguity and greater ambiguity aversion always adversely affect the firm's production decision.     

Epstein–Zin Utility,Asset Prices,and the Business Cycle Revisited

This paper discusses the advantages of Epstein and Zin (1989) (EZ) preferences when building dynamic stochastic general equilibrium (DSGE) models that are consistent with well‐known stylized facts of both the business cycle and asset markets. To this end, we combine EZ preferences with several building blocks from the DSGE literature that has tried to solve the equity premium puzzle and to replicate characteristic statistics of the labor market. Our goal is to guide researchers in this area to useful modeling devices and to discuss EZ preferences vis‐a‐vis the standard time‐additive expected utility function. EZ preferences separate the attitude toward risk from the attitude toward intertemporal substitution. We demonstrate that this additional degree of freedom allows us to closely match the empirical facts already in a frictionless production economy with endogenous labor supply. Our study follows Heer and Maußner (2013). We examine models that consider adjustment costs of capital accumulation, consumption habits, and frictions in the allocation of labor. Our empirical targets are estimated from German data.     

The intertemporal allocation of consumption,time preference,and life-history strategies

This paper studies the intertemporal allocation of consumption and time preference in both biological and economic framework. By incorporating intergenerational transfers to examine human life-history strategies, this study demonstrates that time discounting and mortality mirror the age-variation in the value of survival, which in turn depends on future reproduction and productive surplus. Consistent with empirical findings, the results suggest that our biologically endowed rate of time preference is positive, and is lowest in early adulthood, but increases thereafter. The results also offers a biological explanation for intertemporal loss aversion, indicating that time preference is higher when exchange transactions involve a reduction in current consumption than when they involve an increase in current consumption. In a broader perspective, this paper looks into the biological foundation of preferences and motivation. Establishing the foundation of preferences with biological models and incorporating the results into economic models enrich the understanding of our decision-making mechanism and behavior.     

Precautionary demand for foreign assets in Sudden Stop economies: An assessment of the New Mercantilism

Financial globalization had a rocky start in emerging economies hit by Sudden Stops. Foreign reserves have grown very rapidly since then, as if those countries were practicing a New Mercantilism that views foreign reserves as a war chest for defense against Sudden Stops. This paper conducts a quantitative assessment of this argument using a stochastic intertemporal equilibrium framework in which precautionary foreign asset demand is driven by output variability, financial globalization, and Sudden Stop risk. In this framework, credit constraints produce endogenous Sudden Stops. We find that financial globalization and Sudden Stop risk can explain the surge in reserves but output variability cannot. These results hold using the intertemporal preferences of the Bewley–Aiyagari–Hugget precautionary savings model or the Uzawa–Epstein setup with endogenous impatience.     

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.     

Risk Preferences and Environmental Uncertainty: Implications for Crop Diversification Decisions in Ethiopia

To the extent that diversifying income portfolio is used as a strategy for shielding against production risk, both individual risk aversion and weather uncertainty could affect crop diversification decisions. This paper is concerned with empirically assessing the effects of risk aversion and rainfall variability on farm level diversity. Unique panel data from Ethiopia consisting of experimentally generated risk aversion measures combined with rainfall data are employed in the analysis. The major contribution of this study is its explicit treatment of individual risk preferences in the decision to diversify, simultaneously controlling for environmental risk in the form of rainfall variability. Covariate shocks from rainfall variability are found to positively contribute to an increased level of diversity with individual risk aversion having a positive but less significant role. We find that rainfall variability in spring has a greater effect than rainfall variability summer??the major rainy season. This finding is in line with similar agronomic-meteorological studies. These results imply that in situ biodiversity conservation could be effective in areas with high rainfall variability. However, reduction in risk aversion, which is associated with poverty reduction, is likely to reduce in situ conservation.     

General equilibrium, wariness and efficient bubbles

Wary consumers overlook gains but not losses in remote sets of dates or states. As preferences are upper but not lower Mackey semi-continuous, Bewley?s (1972) [4] result on existence of equilibrium whose prices are not necessarily countably additive holds. Wariness is related to lack of myopia and to ambiguity aversion (and, therefore, to Bewley?s (1986) [6] work on Knightian uncertainty). Wary infinite lived agents have weaker transversality conditions allowing them to be creditors at infinity and for bubbles to occur in positive net supply assets completing the markets. There are efficient allocations that can only be implemented with asset bubbles.     

Risk and regret aversions on optimal bank interest margin under capital regulation

This paper examines the bank's optimal loan rate (and thus the bank's interest margin) under more stringent capital regulation when the bank is not only risk-averse but also regret-averse. Risk-averse preferences are characterized by an option-based utility function that includes disutility from the dislike of bank equity risk. Regret-averse preferences feature an option-based utility function that includes disutility from having chosen ex-post suboptimal alternatives. We show that an increase in bank capital requirement results in an increased margin under risk aversion dominating regret aversion, whereas it results in a reduced margin under regret aversion dominating risk aversion. The former holds when risk aversion domination stems from increasing risk-averse preference, but not from decreasing regret-averse preference, while the latter holds when regret aversion domination results from either decreasing risk-averse or increasing regret-averse preference. Risk aversion, as such, makes the bank more prudent and less prone to risk-taking, while regret aversion, as such, makes the bank less prudent and more prone to risk-taking.     

THE RISK‐FREE RATE IN A FINITE HORIZON MODEL WITH BEQUESTS

This paper studies the risk‐free rate in an overlapping generations economy with bequests. It is shown that the risk‐free rate depends on risk aversion, the elasticity of intertemporal substitution, the share of wealth invested in human wealth, life expectancy, and the preference for bequests. In a standard life‐cycle context, mortality increases the subjective time rate of discount, and thus increases the compensation required to postpone consumption. This latter effect is offset in a bequest‐driven model of the type considered here, leading to much more powerful income effects. In this sense, the model provides a bequest‐motive explanation for the risk‐free rate puzzle put forward by Weil in 1989.