Precautionary Saving and Endogenous Labor Supply with and without Intertemporal Expected Utility

We analyze precautionary saving behavior in a framework with labor and nonlabor income risks, an endogenous supply of labor, and a representation of preferences that disentangles attitudes toward risk, attitudes toward intertemporal substitution, and ordinal preferences for consumption and leisure. This preference structure allows us to disentangle and to describe in an intuitive way the different forces that determine precautionary saving “in the small” and “in the large.”     

Comparative precautionary saving under higher-order risk and recursive utility

Measuring and comparing the precautionary saving motive rest almost exclusively on the expected utility framework, and only focus on income risk or coefficients of the Arrow–Pratt type. We generalize the standard approach by characterizing comparative precautionary saving under recursive utility for increases in income risk and increases in risk on the saving return, including higher-order risk effects. We express the comparisons in terms of precautionary premia. In addition, we define a new class of preference coefficients, and derive the associated conditions to predict a stronger precautionary motive. The coefficients provide a detailed picture of the preferences sustaining precautionary saving and could be useful in applications.     

Comparative Ambiguity Aversion in Intertemporal Decisions

This article examines the effects of ambiguity aversion on intertemporal decisions when there is ambiguity about a future state. Compared to the existing literature, we allow for a three-way separation between intertemporal substitution, risk aversion, and ambiguity aversion. Holding risk preferences, beliefs, and time preferences fixed, we explore how a change in ambiguity aversion increases the strength of the current willingness to pay. We apply our results to saving, self-protection, and self-insurance problems.     

Risk aversion, intertemporal substitution, and the aggregate investment-uncertainty relationship

We analyze the role of risk aversion and intertemporal substitution in a simple dynamic general equilibrium model of investment and savings. Our main finding is that risk aversion cannot by itself explain a negative relationship between aggregate investment and aggregate uncertainty, as the effect of increased uncertainty on investment also depends on the intertemporal elasticity of substitution. In particular, the relationship between aggregate investment and aggregate uncertainty is positive even if agents are very risk averse, as long as the elasticity of intertemporal substitution is low. A negative investment-uncertainty relationship requires that the relative risk aversion and the elasticity of intertemporal substitution are both relatively high or both relatively low. We also show that the implications of our model are consistent with the available empirical evidence.     

Optimal savings distortions with recursive preferences

This paper derives an intertemporal optimality condition for economies with private information, focusing on a class of recursive preferences. By comparing it to the situation where agents can freely save in a risk-free asset market, we derive the optimal savings distortions necessary for constrained optimality. Our recursive preferences are homogeneous and satisfy a balanced-growth condition, while allowing us to separate the role of risk aversion and intertemporal elasticity of substitution. We perform some quantitative exercises that disentangle the respective roles played by these two parameters in optimal distortions and the implied welfare gains.     

Robust consumption and portfolio choice for time varying investment opportunities

This paper examines a continuous-time intertemporal consumption and portfolio choice problem for an investor with recursive preferences. The investor worries about model misspecification and seeks robust decision rules. The expected excess return of a risky asset follows a mean-reverting process. I find that whether the concern about model misspecification decreases the total demand for equities largely depends on risk aversion and the attitude toward intertemporal substitution. When the elasticity of intertemporal substitution is about 1 and risk aversion is moderate, the aversion to model uncertainty increases the proportion of wealth invested in equities. The calibration analysis based on detection-error probabilities shows that the quantitative effect of robustness is almost negligible.     

Endogenous Life‐Cycle Housing Investment and Portfolio Allocation

This paper develops a life‐cycle portfolio allocation model to address the effects of housing investment on the portfolio allocation of households. The model employs a comprehensive housing investment structure, Epstein–Zin recursive preferences, and a stock market entry cost. Furthermore, rather than resorting to calibration we estimate the value of the relative risk aversion and elasticity of intertemporal substitution. The model shows that housing investment has a strong crowding out effect on investment in risky assets throughout the life‐cycle. We further find that the effect of the presence of housing investment on households portfolio allocation is larger than the effect of having EZ recursive preferences.     

Changes in risk and the demand for saving

How does risk affect saving? Empirical work typically examines the effects of detectible differences in risk within the data. How these differences affect saving in theoretical models depends on the metric one uses for risk. For labor-income risk, second-degree increases in risk require prudence to induce increased saving demand. However, prudence is not necessary for first-degree risk increases and not sufficient for higher-degree risk increases. For increases in interest-rate risk, a precautionary effect and a substitution effect need to be compared. This paper provides necessary and sufficient conditions on preferences for an Nth-degree change in risk to increase saving.     

The term structure of interest rates in a DSGE model with recursive preferences

A dynamic stochastic general equilibrium (DSGE) model in which households have Epstein and Zin recursive preferences is solved with perturbation. The parameters governing preferences and technology are estimated by maximum likelihood using macroeconomic data and the term structure of interest rates. The estimates imply a large risk aversion, an elasticity of intertemporal substitution higher than one, and substantial adjustment costs. Furthermore, the paper identifies the tensions within the model by estimating it on subsets of these data. The analysis concludes by pointing out potential extensions that may improve the model's fit.     

Precautionary saving and partially observed income

I propose an intertemporal precautionary saving model in which the agent's labor income is subject to (possibly correlated) shocks with different degrees of persistence and volatility. However, he only observes his total income, not individual components. I show that partial observability of individual components of income gives rise to additional precautionary saving due to estimation risk, the error associated with estimating individual components of income. This additional precautionary saving is higher, when estimation risk is greater. Compared with a precautionary agent who is otherwise identical, but ignores estimation risk, the rational agent consumes less at the beginning of his life, but consumes more later, because of larger wealth accumulated from savings for estimation risk. The utility cost of ignoring estimation risk is also quantified in closed form.     

Asset pricing under quantile utility maximization

“Focus on the downside, and the upside will take care of itself” is a famous quote among professional investors. By considering an agent who follows this advice, we reproduce the first and second moments of stock returns, risk-free rate and consumption growth. The agent's behavior toward risk is analogous to a relative risk aversion of about 3 under expected utility, the elasticity of intertemporal substitution is about 0.5 and the time discount factor is below 1. In particular, the proposed model separates time and risk preferences in an innovative way.     

Precautionary Saving of Chinese and U.S. Households

We employ a model of precautionary saving to study why household saving rates are high in China and low in the United States. The use of recursive preferences gives a convenient decomposition of saving into precautionary and nonprecautionary components. Over 80% of China's saving rate and nearly all U.S. saving arises from the precautionary motive. The difference between U.S. and Chinese household income growth rates is vastly more important than income risk for explaining the saving rates. The key mechanism is that precautionary savers have target wealth‐to‐income ratios, and rapid income growth necessitates high saving rates to maintain the ratio.     

Generalized Disappointment Aversion and Asset Prices

We characterize generalized disappointment aversion (GDA) risk preferences that can overweight lower‐tail outcomes relative to expected utility. We show in an endowment economy that recursive utility with GDA risk preferences generates effective risk aversion that is countercyclical. This feature comes from endogenous variation in the probability of disappointment in the representative agent's intertemporal consumption‐saving problem that underlies the asset pricing model. The variation in effective risk aversion produces a large equity premium and a risk‐free rate that is procyclical and has low volatility in an economy with a simple autoregressive endowment‐growth process.     

Strong Increases in Downside Risk Aversion

A ranking of risk preferences is of economic interest insofar as it leads to unambiguous comparative statics predictions, and for this to be the case, the ranking must be a strict partial ordering. The ranking by greater risk aversion meets this demand at the second order, and yields a variety of well-known predictions concerning the effect of greater risk aversion on demands for insurance and risky assets, among many other applications. There has been less success at the third order, where ranking preferences by aversion to downside risk has not produced a strict partial ordering. The problem is that account has not been taken of the fact that an increase in downside risk aversion must induce changes in risk aversion as well. We propose a definition of stronger downside risk aversion that does yield a strict partial ordering by requiring a nested increase in both second- and third-order risk aversion, so that v is more strongly downside risk averse than u if v is more risk averse and more downside risk averse than u. We demonstrate that v being more strongly downside risk averse than u is characterized by v never liking any change in the probability distribution for y that induces a third-order stochastic dominance deterioration in the distribution for u(y). We apply the definition to obtain intuitive comparative statics predictions in the precautionary saving problem, and relate the definition to alternatives proposed in the literature.     

Asset pricing in production economies with extrapolative expectations

Introducing extrapolative bias into a standard production-based model with recursive preferences reconciles salient stylized facts about business cycles (low consumption volatility, high investment volatility relative to output) and financial markets (high equity premium, volatile stock returns, low and smooth risk-free rate) with plausible levels of risk aversion and intertemporal elasticity of substitution. Furthermore, the model captures return predictability based upon dividend yield, Q, and investment. Intuitively, extrapolative bias increases the variation in the wealth–consumption ratio, which is heavily priced under recursive preferences; adjustment costs decrease the covariance between marginal utility and asset returns. Empirical support for key implications of the model is also provided.     

Insurance demand in the presence of loss-dependent background risk

We analyze insurance demand when insurable losses come with an uninsurable zero-mean background risk that increases in the loss size. If the individual is risk vulnerable, loss-dependent background risk triggers a precautionary insurance motive and increases optimal insurance demand. Prudence alone is sufficient for insurance demand to increase in two cases: the case of fair insurance and the case where the smallest possible loss exceeds a certain threshold value (referred to as the large loss case). We derive conditions under which insurance demand increases or decreases in initial wealth. In the large loss case, prudence determines whether changes in the background risk lead to more insurance demand. We generalize this result to arbitrary loss distributions and find conditions based on decreasing third-degree Ross risk aversion, Arrow–Pratt risk aversion, and Arrow–Pratt temperance.     

On the Intertemporal Elasticity of Substitution under Nonhomothetic Utility

In this note, we use a model with nonseparable and nonhomothetic preferences to estimate the intertemporal elasticity of substitution (IES). We show that, while the homothetic utility model may induce a bias that increases the elasticity of substitution between nondurables and durables, the estimated IES remains positive and significant.     

When does uncovered interest parity hold?

A consensus is emerging that returns to the currency carry trade are driven by two factors. One of these is probably consumption risk but there is widespread disagreement about the identity of the remaining factor. This paper bolsters the case for volatility being the unknown factor. A structural model that specifies that monetary volatility is the second factor is tested for 56 monetary regimes using the artificial economy methodology. The negative slope in the Fama regression arises when monetary volatility is low and the precautionary savings motive dominates the intertemporal substitution motive. When monetary volatility is high, the Fama slope is positive in line with uncovered interest parity. We conclude that, given the predominance of precautionary savings, the degree of monetary volatility explains whether uncovered interest parity holds.