Using the generalized method of moments, we estimate structural parameters related to relative-risk aversion, the discount rate of future utility, and the intertemporal elasticity of substitution in consumption for the Brazilian economy. Estimates are provided for three types of utility function based on the consumption capital asset pricing model: constant relative risk aversion utility, utility with external habit, and Kreps-Porteus utility. These results are analyzed and then compared to previous results using Brazilian and U.S. data. Moreover, we perform over-identifying restrictions tests of all estimated models to investigate the possible existence of the equity premium puzzle in Brazil. The overall results show that Brazilian consumers have a relatively high discount rate, a low intertemporal elasticity of substitution, and a high relative risk aversion coefficient. Also, there is no evidence of the existence of the equity premium puzzle in Brazil.

Optimality conditions for consumption behavior with liquidity constraints are obtained using the functional recurrence equation in Bellman’s dynamic programming and the generalized Hamiltonian function in Pontryagin’s maximum principle. The rejection of Hall’s random walk hypothesis is then established for liquidity constrained consumers. An explicit mathematical relation is formulated which demonstrates the effects of liquidity constraints on consumption, which implies that under certain conditions the liquidity constraint may shift the optimal consumption profile forward even when the rate of time preference exceeds the interest rate. Our analysis is further developed to time-varying interest rates. Using the Kuhn-Tucker conditions, we have shown the interactions between the time-varying interest rate, the utility discount rate and the severity of liquidity constraints. It is shown, using the coefficient of absolute risk aversion, that how the time-varying interest rate may affect optimal consumption through intertemporal elasticity of substitution. Simultaneous effects of the pure preference parameters, interest rates variations and the liquidity constraints on optimal consumption path are mathematically formulated. Limitations in optimal control applications in modeling optimal consumption with liquidity constraints in a stochastic environment are briefly examined.

An OLG model with exhaustible resources and solar energy is developed, and equilibrium time paths are characterized numerically using recursive methods. For the parameter values considered, resource prices increase over time, and extractions, output, and utility decline over time until a steady-state is reached. Decreasing the intertemporal elasticity of substitution or raising consumers' subjective discount rate hastens exhaustion of the resource stock. Market equilibrium can result in much quicker use of the stock than social optimality under a constant discount rate, with consequent higher utility for early generations and lower utility for future generations in contrast to social optimality.

Abstract Arguments about the appropriate discount rate often start by assuming a Utilitarian social welfare function with isoelastic utility, in which the consumption discount rate is a function of the (constant) elasticity of marginal utility along with the (much discussed) utility discount rate. In this model, the elasticity of marginal utility simultaneously reflects preferences for intertemporal substitution, aversion to risk, and aversion to (spatial) inequality. While these three concepts are necessarily identical in the standard model, this need not be so: well-known models already enable risk to be separated from intertemporal substitution. Separating the three concepts might have important implications for the appropriate discount rate, and hence also for long-term policy. This paper investigates these issues in the context of climate-change economics, by surveying the attitudes of over 3000 people to risk, income inequality over space and income inequality over time. The results suggest that individuals do not see the three concepts as identical, and indeed that preferences over risk, inequality and time are only weakly correlated. As such, relying on empirical evidence of risk or inequality preferences may not necessarily be an appropriate guide to specifying the elasticity of intertemporal substitution.

The average microenterprise in a developing country may have very high marginal returns to capital, according to several recent studies. Financial constraints are part of the explanation for how these high returns persist. But, given these constraints, it remains to explain the limited self-financing by the households running these businesses. In particular, little is known about the elasticity of intertemporal substitution (EIS) of poor households, which describes how quickly households save in response to rates of return higher than their rate of time preference. If poorer households have a

To justify substantial emission reductions, recent literature on cost-benefit analysis of climate change suggests discounting environment consumption with an environmental discount rate instead of a consumption discount rate that is usually used in cost-benefit analysis. The present study clarifies that whether or not this dual-rate discounting approach succeeds in justifying substantial emission reductions depends on whether or not environment and goods consumption are substitutes in the Hicks-Allen sense and in the Edgeworth-Pareto sense (substitutes in the Hicks-Allen sense implies the Hicksian goods demand to be increasing in the relative price of environmental goods, while substitutes in the Edgeworth-Pareto sense implies the marginal utility of goods consumption to be decreasing in environment consumption). Moreover, a low intratemporal elasticity of substitution between environment and goods consumption within a period contributes to a low environmental discount rate in comparison to the consumption discount rate, while a low intertemporal elasticity of substitution between composite consumption of different periods contributes to declining discount rates over time. Paper submitted to the special issue “Discounting the Long-Run Future and Sustainable Development”

This paper aims to develop an Islamic intertemporal model of the current account based on the prevailing theoretical and empirical literature of PVMCA (Obstfeld and Rogoff, 1996, Cerrato et al., 2014). The proposed model is based on the budget constraint of the present and future consumption, which depends on the obligatory Zakat from the income and assets, the return rate on the owned assets, the inheritance linking previous to subsequent generation. Using logarithmic utility function, featured by a unitary elasticity of intertemporal substitution and a unitary coefficient of relative risk aversion, we show through Euler equation of consumption that there is an inverse relationship between consumption growth from the last age to the first one and the Zakat rate on assets. The outcomes of this result are that the Zakat on assets disciplines the consumer to have more rationality in consumption, and allows additional marginal assets for future generations. By assuming a unitary subjective discount rate, we indicate that the more the return rate on assets is high, the more the consumption growth between today and tomorrow will be fast. Through the budget constraint, if Zakat rate on the Zakatable assets is greater than Zakat rate on income, this leads to a relative expansion in private consumption of the wealthy group. Besides, we point out that an increase in return rate on assets, can drive to increasing or decreasing current consumption, because the substitution and income ef