Recursive Utility Model Research Articles

Welfare costs of suboptimal retiree decisions.

We make a novel investigation of welfare costs associated with various suboptimal decisions made by retirees, both analytically and numerically. We utilize a unique framework that incorporates recursive utility with housing, and also encompasses expected utility and recursive utility without housing as special cases. Our findings indicate that under-investment in stocks incurs lower welfare costs compared to an equivalent over-investment. Suboptimal allocations in bond holdings result in higher costs than similar misallocations in stocks. Choosing not to participate in the stock market is less detrimental than avoiding the bond market. Should retirees opt to simplify their decision-making by investing solely in one type of asset, it is less costly for them to invest exclusively in bonds. Overconsumption of housing is less costly than an equivalent underconsumption. Suboptimal consumption imposes the highest welfare cost. Decisions regarding consumption, housing, and savings are found to be more crucial than the choice of how to distribute liquid savings between stocks and bonds. Additionally, recursive utility model better captures retirees' preference for bonds over stocks than expected utility model. Our results, which are consistent across various parameter settings, provide valuable insights for academics and policymakers aiming to enhance retiree welfare.

Asset pricing with time preference shocks: Existence and uniqueness

This paper studies existence and uniqueness of recursive utility in asset pricing models with time preference shocks. We provide conditions that clarify existence and uniqueness for a wide range of models, including exact necessary and sufficient conditions for standard formulations. The conditions isolate the roles of preference parameters, as well as the different risks that drive the consumption and preference shock processes. By deriving and decomposing a stability coefficient for recursive utility models, we show how different parameters in the model interact to determine existence and uniqueness of solutions.

The impact of risk aversion and ambiguity aversion on annuity and saving choices

We analyze the impact of risk aversion and ambiguity aversion on the competing demands for annuities and bequeathable savings using a lifecycle recursive utility model. Our main finding is that risk aversion and ambiguity aversion have similar effects: an increase in either of the two reduces annuity demand and enhances bond holdings. We obtain this unequivocal result in the flexible intertemporal framework of Hayashi and Miao (2011) by assuming that the agent’s preferences are monotone with respect to first-order stochastic dominance. Our contribution is then twofold. First, from a decision-theoretic point of view, we show that monotonicity allows one to obtain clear-cut results about the respective roles of risk and ambiguity aversion. Second, from the insurance point of view, our result that the demand for annuities decreases with risk and ambiguity aversion stands in contrast with what is usually found with other insurance products. As such, it may help explain the low annuitization level observed in the data.

Measuring preferences over the temporal resolution of consumption uncertainty

Timing premia measure how much consumption people are willing to forgo to resolve all consumption uncertainty immediately. We develop a novel experiment to elicit these attitudes directly in a model-free way. On average, subjects forgo around 5% of their total consumption to resolve all uncertainty immediately. Recursive utility models postulate a structural link between timing premia and deep preference parameters. We elicit these preference parameters separately and estimate corresponding predicted timing premia. Comparing directly elicited and predicted timing premia allows us to test this structural link. Surprisingly, we find a negative correlation between predicted and elicited timing premia.

Necessary and Sufficient Conditions for Existence and Uniqueness of Recursive Utilities

ABSTRACTWe obtain exact necessary and sufficient conditions for existence and uniqueness of solutions of a class of homothetic recursive utility models postulated by Epstein and Zin. The conditions center on a single test value with a natural economic interpretation. The test sheds light on the relationship between valuation of cash flows, impatience, risk adjustment, and intertemporal substitution of consumption. We propose two methods to compute the test value when an analytical solution is not available. We further provide several applications.

The Impact of Risk and Ambiguity Aversion on Annuity and Saving Choices

We analyze the impact of risk and ambiguity aversion using a lifecycle recursive utility model. Both risk and ambiguity aversion are shown to reduce annuity demand and enhance bond holdings. We obtain this result using an intertemporal framework in which we can vary both risk and ambiguity aversion, while preserving preference monotonicity.

Recursive Preferences, the Value of Life, and Household Finance

We analyze lifecycle saving strategies using a recursive utility model calibrated to match empirical estimates for the value of a statistical life. We show that, with a positive value of life, risk aversion reduces savings and annuity purchase. Risk averse agents are willing to make an early death a not-so-adverse outcome by enjoying greater consumption when young and bequeathing wealth in case of death. We also find that greater risk aversion lowers stock market participation. We show that this model can rationalize low annuity demand while also matching empirically documented levels of wealth and private investments in stocks. Our findings stand in contrast to studies that implicitly assume a negative value of life.

Parameter interchangeability under recursive utility with housing

We investigate the interchangeability of two central elements of most macroeconomic models, the parameter of intertemporal substitution and time discount rate. We use a recursive utility model during retirement with housing, uncertain life time and risky stock prices since recursive utility is more flexible and general and includes expected utility as a special case. The retiree makes consumption, housing, stock and bond investment decisions. We first provide the analytical solution of retiree decisions. We realistically calibrate our model and simulate the stock returns. Our calibrated model mimics the consumption data for homeowners well. The model qualitatively explains decreasing stock and bond holdings after retirement. Then, we investigate the interchangeability of two important parameters, the parameter of intertemporal substitution and discount rate since they have similar effects on retiree decisions. We show that the parameters of intertemporal substitution and discount rate are not interchangeable analytically. Exploring the interchangeability of parameters is important and fruitful since interchangeable parameters will help to make estimation of some parameters easier. Interchangeability will simplify the solution.

Household Finance and the Value of Life

We analyze lifecycle saving strategies using a recursive utility model calibrated to match empirical estimates of the value of a statistical life. The novelty of our approach is that we require preferences to be monotone with respect to first order stochastic dominance. The framework we use can disentangle risk aversion and the intertemporal elasticity and can feature a positive value of life without placing constraints on the value of the risk aversion parameter or the intertemporal elasticity of substitution. We show that, with a positive value of life, risk aversion reduces savings, decreases stock market participation and decreases annuity purchase. Risk averse agents are willing to make an early death a not-so-adverse outcome by enjoying greater consumption when young and bequeathing wealth in case of death. The model can rationalize low annuity demand while also matching empirically documented levels of wealth and private investments in stocks.

Macroeconomic Bond Risks at the Zero Lower Bound

Close-to-zero interest rates challenge standard economic models in which zero lower bound (ZLB) is absent. We estimate a recursive utility model which features time-varying latent expected real growth, expected inflation, and stochastic inflation volatility. Using an approximate solution to bond prices, we show that the ZLB model successfully captures interest rates in a ZLB period, without a deterioration in fit to rates in normal times. Incorporating ZLB lowers the estimates of expected inflation and increases inflation volatility. It leads to large, negative and volatile shadow rates, large and volatile shadow risk premia, and small and volatile lift-off probabilities.

Comment on Halevy (2007) 'Ellsberg Revisited: An Experimental Study'

Halevy (2007) experimentally tests the prediction of the Recursive Non-Expected Utility (RNEU) model that there is a positive correlation between degree of ambiguity aversion and degree of preference on reduction of compound lotteries ROCL. Halevy (2007) claimed that the experimental result supports the RNEU. In this study, we use Halevy’s data and conduct further analysis based on subject’s ambiguity attitude types: ambiguity neutral, ambiguity averse, and ambiguity loving. We find striking different results. First, there is no significant relationship between degree of preference on ROCL and degree of ambiguity aversion. Second, subjects who prefer simple lotteries are not more likely to be ambiguity averse than subjects who prefer compound lotteries. Third, ambiguity averse subjects are not more likely to prefer simple lottery than those who are ambiguity seeking. In sum, there is no evidence that ambiguity aversion can be well explained by preference on reduction of compound lotteries.

Durable Goods, Inflation Risk, and Equilibrium Asset Prices

High expected inflation is known to predict low future real growth. We show that, relative to nondurable goods sectors of the economy, such predictability is significantly more pronounced in durable sectors. Consistent with this macroeconomic evidence, the equity returns of durable goods-producing firms have a larger negative exposure to expected inflation risks. We estimate a two-good recursive utility model that features persistent growth fluctuations and inflation nonneutrality for durable and nondurable consumption. Our model can quantitatively account for the levels and volatilities of bond and equity prices, and correlations of equity returns with bond returns and with expected inflation. Received January 25, 2012; accepted July 13, 2015 by Editor Geert Bekaert.

Durable Goods, Inflation Risk and the Equilibrium Term Structure

High expected inflation is known to have a negative impact on future real growth. We show that this effect is significantly more pronounced in durable relative to non-durable goods sectors of the economy. Consistent with this macroeconomic evidence, the equity returns of durable-goods-producing firms have a larger negative exposure to expected inflation risks. We estimate a recursive utility model which features persistent growth fluctuations and inflation non-neutrality for durable and non-durable consumption. Our model can quantitatively account for the key moments of nominal bond prices and the levels, volatilities, and exposures of equity returns to expected inflation and bond returns.

Comparing consumption-based asset pricing models: The case of an Asian city

Eight consumption-based asset pricing models are developed, estimated and compared their capacities in accounting for the asset markets in Hong Kong. Results based on conventional metrics or recently developed econometric techniques deliver similar results: introducing housing into the consumption-based models does not always improve the models’ performance; how it is introduced matters. Recursive utility model and its housing-augmented variant, which emphasize the importance of early resolution of uncertainty and long term risk, outperform alternative models in forecasting stock returns. Collateral constraint model outperforms in predicting housing return, suggesting the importance of imperfect capital market in the housing market.

An estimation of economic models with recursive preferences

This paper presents estimates of key preference parameters of the Epstein and Zin (1989, 1991) and Weil (1989) recursive utility model, evaluates the model's ability to fit asset return data relative to other asset pricing models, and investigates the implications of such estimates for the unobservable aggregate wealth return. Our empirical results indicate that the estimated relative risk aversion parameter ranges from 17 to 60, with higher values for aggregate consumption than for stockholder consumption, while the estimated elasticity of intertemporal substitution is above 1. In addition, the estimated model-implied aggregate wealth return is found to be weakly correlated with the Center for Research in Security Prices value-weighted stock market return, suggesting that the return to human wealth is negatively correlated with the aggregate stock market return.

Consumption-Based Asset Pricing with Loss Aversion

I incorporate loss aversion in a consumption-based asset pricing model with recursive preferences and solve for asset prices in closed-form. I find loss aversion increases expected returns substantially relative to the standard recursive utility model. This feature of my model improves the ability to match moments on asset prices. Further, I find loss aversion induces important nonlinearities into the expected excess returns as a function of the exposure to the consumption shocks. In particular, the elasticities of expected returns with respect to the exposure to the consumption shocks are greater for assets with smaller exposures to the shocks, thus generating interesting predictions for the cross-section of returns. I provide empirical evidence supporting this outcome. The model with loss aversion correctly predicts both a negative premium for skewness and a security market line, the excess returns as a function of the exposure to market risk, flatter than the CAPM.

Pricing innovations in consumption growth: A re-evaluation of the recursive utility model

We re-evaluate the cross-sectional asset pricing implications of the recursive utility function of Epstein and Zin (1989, 1991), using innovations in future consumption growth in our tests. Our empirical specification helps explain the size, value and momentum effects. Specifically, we find that (і) the beta associated with news about consumption growth has a systematic pattern: beta decreases along the size dimension and increases along the book-to-market and momentum dimensions, (іі) innovation in consumption growth is significantly priced in asset returns using both the Fama and MacBeth (1973) and the stochastic discount factor approaches, and (ііі) the model performs better than both the CAPM and Fama–French model.

Recursive utility in a Markov environment with stochastic growth.

Recursive utility models that feature investor concerns about the intertemporal composition of risk are used extensively in applied research in macroeconomics and asset pricing. These models represent preferences as the solution to a nonlinear forward-looking difference equation with a terminal condition. In this paper we study infinite-horizon specifications of this difference equation in the context of a Markov environment. We establish a connection between the solution to this equation and to an arguably simpler Perron-Frobenius eigenvalue equation of the type that occurs in the study of large deviations for Markov processes. By exploiting this connection, we establish existence and uniqueness results. Moreover, we explore a substantive link between large deviation bounds for tail events for stochastic consumption growth and preferences induced by recursive utility.

An Experimental Study of Attitude Towards Second Order Risk

This paper examines systematically the attitude towards compound lottery by introducing three variants of symmetric uniform mean-preserving spread into stage-1 risk in a choice-based experimental setting. We do not observe consistent aversion to mean-preserving spread in the stage-1 risk. More importantly, the observed behavioral patterns reject a number of axioms including reduction of compound lotteries, time neutrality, and stage-1 betweenness (independence), which sheds light on related recursive utility models. The overall data support two-stage rank-dependent utility with distinct convex probability weighting functions in two stages.

Intertemporal utility smoothing under uncertainty

This paper axiomatizes a recursive utility model that captures both intertemporal utility smoothing defined across time and ambiguity aversion defined over states. The resulting representation adapts Wakai (Econometrica 76:137–153, 2008) model of intertemporal utility smoothing as an aggregator function, where the utility of the certainty equivalent of future uncertainty is computed by Gilboa and Schmeidler (J Math Econ 18:141–153, 1989) multiple-priors utility. The model also permits the separation of intertemporal utility smoothing from ambiguity aversion.