Constant Elasticity Of Intertemporal Substitution Research Articles

CRRA utility and the sustainability of cooperation in infinitely-repeated games

In a symmetric infinitely-repeated game, where players have constant relative risk aversion (CRRA), or constant elasticity of intertemporal substitution, utility functions, it is shown that the critical discount factor required to sustain full cooperation is decreasing in the coefficient of relative risk aversion (increasing in the elasticity of intertemporal substitution). An application to cooperation in international environmental agreements (IEA) is presented and it is shown that the limit of the critical discount factor as the number of countries goes to infinity is equal to one (zero) if the coefficient of intertemporal inequality aversion is less (greater) than one. • Analyses infinitely-repeated game when players have CRRA utility functions. • Cooperation in infinitely-repeated games is easier the more risk-averse are players. • Application to International Environmental Agreement with many countries.

Intertemporal utility with heterogeneous goods and constant elasticity of substitution

We characterize intertemporal utility functions over heterogeneous goods that feature (i) a constant elasticity of substitution between goods at each point in time and (ii) a constant intertemporal elasticity of substitution for at least one of the goods. We find that a standard, stationary intertemporal utility function is consistent with these two properties if and only if it either is of the intertemporal constant elasticity of substitution (ICES) form, that is, if all elasticities of substitution are identical, or if the instantaneous utility function is Cobb–Douglas. We also characterize the families of stationary intertemporal utility functions that feature either (i) or (ii), but not the respective other property.

Intertemporal Utility with Heterogeneous Goods and Constant Elasticity of Substitution

We characterize intertemporal utility functions over heterogeneous goods that feature (i) a constant elasticity of substitution between goods at each point in time and (ii) a constant intertemporal elasticity of substitution for at least one of the goods. We find that a standard (stationary) intertemporal utility function is consistent with these two properties if and only if it either is of the intertemporal constant elasticity of substitution (ICES) form, that is, if all elasticities of substitution are identical, or if the instantaneous utility function is Cobb-Douglas. We also characterize the families of standard intertemporal utility functions that feature either (i) or (ii), but not the respective other property. The ICES utility function offers a simple and consistent solution for applications that use constant good-specific intertemporal substitutability. This is, for example, relevant for dual discounting of market and non-market goods.

Recursive Utility with Investment Gains and Losses: Existence, Uniqueness, and Convergence

We study the total utility of an agent in a model of narrow framing with constant elasticity of intertemporal substitution and relative risk aversion degree and with infinite time horizon. In a finite-state Markovian setting, we prove that the total utility uniquely exists when the agent derives nonnegative utility of gains and losses incurred by holding risky assets and that the total utility can be non-existent or non-unique otherwise. Moreover, we prove that the utility, when uniquely exists, can be computed by a recursive algorithm with any starting point. We then consider a portfolio selection problem with narrow framing and solve it by proving that the corresponding dynamic programming equation has a unique solution. Finally, we propose a new model of narrow framing in which the agent's total utility uniquely exists in general.

Dynamic choice with constant source-dependent relative risk aversion

An axiomatic characterization of recursive utility with source-dependent constant relative risk aversion (CRRA), constant elasticity of intertemporal substitution, constant rate of impatience and subjective beliefs is established. The utility form is a minimal extension of Epstein–Zin–Weil utility that allows the CRRA to depend on the source of risk, a dependence that admits an ambiguity aversion interpretation. Dual representations of the proposed recursive utility are discussed and shown to be useful in tackling the central planner problem and associated asset pricing applications. An appendix presents the continuous-time version of the utility form, which preserves the effect of ambiguity aversion under Brownian/Poisson uncertainty, despite its smoothness.

Some Properties of The Solution of The Ramsey Model

Abstract The main aim of this paper is to improve some results obtained by Smith. We provide here a closed-form solution for the Ramsey model. We prove that if the inverse of the constant elasticity of intertemporal substitution is different to the elasticity of output with respect to physical capital, then the economy described by this model reaches the unique steady-state equilibrium, for any starting values of per-capita consumption. The advantage of the paper over the existing paper is that the arguments here are not local, that is, our hypotheses are most generally possible. Consequently, we can obtain almost all other results as particular cases of our solution. Our approach clarifies why different starting values of per-capita consumption generates the same steady-state equilibrium, but of different periods of time. We also clarifiy some of previous result obtained by other authors as for example Luca Guerrini.

IS THE ELASTICITY OF INTERTEMPORAL SUBSTITUTION CONSTANT?

In all common models of inter-temporal allocation, the assumption of a constant elasticity of intertemporal substitution (EIS) imposes surprising limitations on within period budget allocations. Consequently, the constant EIS assumption can be tested with demand data. In fact, the EIS is pinned down completely by the shape of Engel curves: if the EIS is constant then the EIS can be estimated without variation in the interest rate. That a price elasticity can be estimated without variation in the relevant price illustrates just how strong the constant EIS assumption is. The constant EIS assumption is rejected by demand data.

Consumption Paths Under Prospect Utility in an Optimal Growth Model

This paper studies the Cass-Koopmans-Ramsey model of optimal economic growth in the presence of loss aversion and habit formation. The representative agent's preferences for consumption can be gradually varied between the standard constant intertemporal elasticity of substitution (CIES) case and Kahneman and Tversky's prospect utility. We find that the transitional dynamics of optimal consumption paths differ distinctly from the standard model, in particular consumption smoothing is more pronounced. We also show that prospect utility can cause the economy to remain in a steady state with low consumption and low capital.

Consumption paths under prospect utility in an optimal growth model

This paper studies the Cass-Koopmans-Ramsey model of optimal economic growth in the presence of loss aversion and habit formation. The representative agent's preferences for consumption can be gradually varied between the standard constant intertemporal elasticity of substitution (CIES) case and Kahneman and Tversky's prospect utility. We find that the transitional dynamics of optimal consumption paths differ distinctly from the standard model, in particular consumption smoothing is more pronounced. We also show that prospect utility can cause the economy to remain in a steady state with low consumption and low capital.

Income Effects, Wealth Effects, and Multiple Equilibria in Trade Models with Durable Goods*

We examine the conditions for multiplicity of equilibrium in a dynamic, two-country model of trade with a durable good of the type proposed by Shimomura (1993, 2004). If trade must balance in each period, we show that there will be a unique autarkic steady-state equilibrium and that the principle of comparative advantage will hold if the nondurable good is not inferior. A necessary condition for the existence of multiple steady-state equilibria with free trade is that the marginal propensity to consume a good be higher in the exporting country. We provide an example with three steady states where the “extreme” steady states are saddle points and the “middle” steady state will be either a source or a sink, depending on the intertemporal elasticity of substitution. If there is international lending, this example has the property that there is a range of initial endowments for which there are three distinct and Pareto-optimal (saddle) paths that can be equilibria. We also show that there must be a unique saddle path from any endowment point with international capital markets when preferences are identical, homothetic, and have constant intertemporal elasticity of substitution.

Precautionary Saving and Consumption Smoothing across Time and Possibilities

This paper examines how aversion to risk and aversion to intertemporal substitution determine the strength of the precautionary saving motive in a two-period model with Selden/Kreps-Porteus preferences. For small risks, we derive a measure of the strength of the precautionary saving motive which generalizes the concept of "prudence" introduced by Kimball (1990b). For large risks, we show that decreasing absolute risk aversion guarantees that the precautionary saving motive is stronger than risk aversion, regardless of the elasticity of intertemporal substitution. Holding risk preferences fixed, the extent to which the precautionary saving motive is stronger than risk aversion increases with the elasticity of intertemporal substitution. We derive sufficient conditions for a change in risk preferences alone to increase the strength of the precautionary saving motive and for the strength of the precautionary saving motive to decline with wealth. Within the class of constant elasticity of intertemporal substitution, constant-relative risk aversion utility functions, these conditions are also necessary.

Optimal Human Investment Allocation: A Note on Government Spending and Labor-Leisure Choice

This paper presents an analysis of government spending and optimal human investment allocation rate in the two sector model of an endogenous growth (education and good sectors), by comparing solutions between social planner maximization problem and decentralized competitive equilibrium, and by considering two types of utility functions: the Constant Inter-temporal Elasticity of Substitution (CIES) and the Constant Elasticity of Substitution (CES) with labor-leisure choice. The results show that the optimal rate of human investment allocation depends on the elasticity of inter-temporal substitution in which it describes insignificant changes when we use CIES or CES. Moreover, the optimal rate of human investment allocation both in social planner as well as decentralized competitive equilibrium are equivalent which suggest that Pareto optimum is prevailed

Interior Optimal Chaos with Arbitrarily Low Discount Rates

In this study, we demonstrate, for an arbitrarily small discount rate, the existence of a topologically chaotic policy function that lies in the interior of the technology set in a two-sector model with smooth production and utility functions. For this purpose, we adopt CES production functions and a utility function with a constant elasticity of intertemporal substitution. The two-sector model with those functions always has a policy function lying in the interior of the technology set (interior policy function). The existence of a scramble set of a policy function may be proved even in the case in which the discount rate is arbitrarily small. JEL Classification Number: 041.

On the Dynamics of Economic Growth

This paper examines the dynamics of economic growth. First, it demonstrates that the standard neoclassical growth model with constant elasticity of intertemporal substitution is not consistent with the patterns of development we observe in the real world, once we consider the initial conditions. Second, it examines an alternative growth model, which is consistent with endogenously determined initial conditions and also generates dynamics that are in accord with the historical patterns of growth rates, capital flows, savings rates and labor supply. The alternative model is a generalized version of the neoclassical growth model, with increasing rates of intertemporal substitution due to a Stone-Geary type of utility.

A Revealed Preference Analysis of Asset Pricing Under Recursive Utility

This paper considers a representative agent model of asset prices based on a recursive utility specification. A constant elasticity of intertemporal substitution is assumed but the risk-preference component of utility is restricted only by qualitative, non-parametric regularity conditions. A principal contribution is to determine the exhaustive implications of this semiparametric recursive utility model for the one-step ahead joint probability distribution for consumption growth and asset returns. It is also shown, in contrast to the claims of previous studies, that the generalization from expected utility to recursive utility contributes substantially to the resolution of the equity premium puzzle.

Precautionary Savings and the Permanent Income Hypothesis

This paper derives the explicit solution of a dynamic stochastic optimal consumption problem for infinitely-lived agents whose preferences exhibit, in the presence of non-diversifiable labour income uncertainty, a constant elasticity of intertemporal substitution and constant absolute risk aversion. The constancy of the elasticity of intertemporal substitution, which implies that marginal utility at zero consumption is infinite, guarantees that the non-negativity constraint on consumption is never binding along the optimal path. The assumption of constant absolute risk aversion allows an explicit computation of human wealth, and provides a simple representation of the precautionary savings motive.

The equity premium puzzle and the risk-free rate puzzle

This paper studies the implications for general equilibrium asset pricing of a class of Kreps-Porteus nonexpected utility preferences characterized by a constant intertemporal elasticity of substitution and a constant, but unrelated, coefficient of relative risk aversion. It is shown that relaxing the parametric restriction on tastes imposed by the time-additive expected utility specification does not suffice to solve the Mehra-Prescott (1985) equity premium puzzle. An additional puzzle — the risk-free rate puzzle — emerges instead: why is the risk-free rate so low if agents are so averse to intertemporal substitution?

Portfolio choice with non-expected utility in continuous time

Non-expected utility preferences, which can distinguish intertemporal substitution from attitudes towards risk, are extended to continuous time. The consumption/savings and portfolio problem is solved for constant intertemporal elasticity of substitution and constant relative risk aversion.