## D91 Intertemporal Consumer Choice; Life Cycle Models and Saving

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#### Keywords

- Labor income risk (3)
- Portfolio choice (3)
- Health shocks (2)
- Stochastic mortality risk (2)
- stochastic differential utility (2)
- Bayes-Lernen (1)
- Bayesian learning (1)
- Capital-Asset-Pricing-Modell (1)
- Consumption hump (1)
- FBSDE (1)

- Consumption habits and humps (2013)
- We show that the optimal consumption of an individual over the life cycle can have the hump shape (inverted U-shape) observed empirically if the preferences of the individual exhibit internal habit formation. In the absence of habit formation, an impatient individual would prefer a decreasing consumption path over life. However, because of habit formation, a high initial consumption would lead to high required consumption in the future. To cover the future required consumption, wealth is set aside, but the necessary amount decreases with age which allows consumption to increase in the early part of life. At some age, the impatience outweighs the habit concerns so that consumption starts to decrease. We derive the optimal consumption strategy in closed form, deduce sufficient conditions for the presence of a consumption hump, and characterize the age at which the hump occurs. Numerical examples illustrate our findings. We show that our model calibrates well to U.S. consumption data from the Consumer Expenditure Survey.

- Stochastic differential utility as the continuous-time limit of recursive utility (2013)
- We establish a convergence theorem that shows that discrete-time recursive utility, as developed by Kreps and Porteus (1978), converges to stochastic differential utility, as introduced by Dufffie and Epstein (1992), in the continuous-time limit of vanishing grid size.

- Financial sophistication in the older population (2012)
- This paper examines data on financial sophistication among the U.S. older population, using a special-purpose module implemented in the Health and Retirement Study. We show that financial sophistication is deficient for older respondents (aged 55+). Specifically, many in this group lack a basic grasp of asset pricing, risk diversification, portfolio choice, and investment fees. Subpopulations with particular deficits include women, the least educated, persons over the age of 75, and non-Whites. In view of the fact that people are increasingly being asked to take on responsibility for their own retirement security, such lack of knowledge can have serious implications.

- Life insurance demand under health shock risk (2014)
- This paper studies the life cycle consumption-investment-insurance problem of a family. The wage earner faces the risk of a health shock that significantly increases his probability of dying. The family can buy term life insurance with realistic features. In particular, the available contracts are long term so that decisions are sticky and can only be revised at significant costs. Furthermore, a revision is only possible as long as the insured person is healthy. A second important and realistic feature of our model is that the labor income of the wage earner is unspanned. We document that the combination of unspanned labor income and the stickiness of insurance decisions reduces the insurance demand significantly. This is because an income shock induces the need to reduce the insurance coverage, since premia become less affordable. Since such a reduction is costly and families anticipate these potential costs, they buy less protection at all ages. In particular, young families stay away from life insurance markets altogether.

- Critical illness insurance in life cycle portfolio problems (2014)
- I analyze a critical illness insurance in a consumption-investment model over the life cycle. I solve a model with stochastic mortality risk and health shock risk numerically. These shocks are interpreted as critical illness and can negatively affect the expected remaining lifetime, the health expenses, and the income. In order to hedge the health expense effect of a shock, the agent has the possibility to contract a critical illness insurance. My results highlight that the critical illness insurance is strongly desired by the agents. With an insurance profit of 20%, nearly all agents contract the insurance in the working stage of the life cycle and more than 50% of the agents contract the insurance during retirement. With an insurance profit of 200%, still nearly all working agents contract the insurance, whereas there is little demand in the retirement stage.

- Consumption-investment problems with stochastic mortality risk (2014)
- I numerically solve realistically calibrated life cycle consumption-investment problems in continuous time featuring stochastic mortality risk driven by jumps, unspanned labor income as well as short-sale and liquidity constraints and a simple insurance. I compare models with deterministic and stochastic hazard rate of death to a model without mortality risk. Mortality risk has only minor effects on the optimal controls early in the life cycle but it becomes crucial in later years. A diffusive component in the hazard rate of death has no significant impact, whereas a jump component is desired by the agent and influences optimal controls and wealth evolution. The insurance is used to ensure optimal bequest such that there is no accidental bequest. In the absence of the insurance, the biggest part of bequest is accidental.

- On the welfare cost of consumption fluctuations in the presence of memorable goods (2013)
- We propose a new classification of consumption goods into nondurable goods, durable goods and a new class which we call “memorable” goods. A good is memorable if a consumer can draw current utility from its past consumption experience through memory. We construct a novel consumption-savings model in which a consumer has a well-defined preference ordering over both nondurable goods and memorable goods. Memorable goods consumption differs from nondurable goods consumption in that current memorable goods consumption may also impact future utility through the accumulation process of the stock of memory. In our model, households optimally choose a lumpy profile of memorable goods consumption even in a frictionless world. Using Consumer Expenditure Survey data, we then document levels and volatilities of different groups of consumption goods expenditures, as well as their expenditure patterns, and show that the expenditure patterns on memorable goods indeed differ significantly from those on nondurable and durable goods. Finally, we empirically evaluate our model’s predictions with respect to the welfare cost of consumption fluctuations and conduct an excess-sensitivity test of the consumption response to predictable income changes. We find that (i) the welfare cost of household-level consumption fluctuations may be overstated by 1.7 percentage points (11.9% points as opposed to 13.6% points of permanent consumption) if memorable goods are not appropriately accounted for; (ii) the finding of excess sensitivity of consumption documented in important papers of the literature might be entirely due to the presence of memorable goods.

- Fiscal policy and MPC heterogeneity (2013)
- We use responses to survey questions in the 2010 Italian Survey of Household Income and Wealth that ask consumers how much of an unexpected transitory income change they would consume. We find that the marginal propensity to consume (MPC) is 48 percent on average, and that there is substantial heterogeneity in the distribution. We find that households with low cash-on-hand exhibit a much higher MPC than affluent households, which is in agreement with models with precautionary savings where income risk plays an important role. The results have important implications for the evaluation of fiscal policy, and for predicting household responses to tax reforms and redistributive policies. In particular, we find that a debt-financed increase in transfers of 1 percent of national disposable income targeted to the bottom decile of the cash-on-hand distribution would increase aggregate consumption by 0.82 percent. Furthermore, we find that redistributing 1% of national disposable income from the top to the bottom decile of the income distribution would boost aggregate consumption by 0.33%.

- Asset pricing and consumption-portfolio choice with recursive utility and unspanned risk (2014)
- We study consumption-portfolio and asset pricing frameworks with recursive preferences and unspanned risk. We show that in both cases, portfolio choice and asset pricing, the value function of the investor/representative agent can be characterized by a specific semilinear partial differential equation. To date, the solution to this equation has mostly been approximated by Campbell-Shiller techniques, without addressing general issues of existence and uniqueness. We develop a novel approach that rigorously constructs the solution by a fixed point argument. We prove that under regularity conditions a solution exists and establish a fast and accurate numerical method to solve consumption-portfolio and asset pricing problems with recursive preferences and unspanned risk. Our setting is not restricted to affine asset price dynamics. Numerical examples illustrate our approach.

- Consumption and wage humps in a life-cycle model with education (2014)
- he observed hump-shaped life-cycle pattern in individuals' consumption cannot be explained by the classical consumption-savings model. We explicitly solve a model with utility of both consumption and leisure and with educational decisions affecting future wages. We show optimal consumption is hump shaped and determine the peak age. The hump results from consumption and leisure being substitutes and from the implicit price of leisure being decreasing over time; more leisure means less education, which lowers future wages, and the present value of foregone wages decreases with age. Consumption is hump shaped whether the wage is hump shaped or increasing over life.