Numerical Methods in Life-Cycle Portfolio Choice with Labor Income, Housing and Biometric Risk

Project Start:01/2013
Category: Household Finance
Funded by:LOEWE

Empirical studies have documented that the consumption expenditures of individuals typically show an inverted U-shape over the life cycle, increasing up to the age of 45-50 years and then decreasing over the remaining lifetime. So far, standard, frictionless consumption-savings models have not been able to generate this hump in consumption: if an individual’s subjective time preference rate is higher (lower) than the risk-adjusted and expected returns on investments, consumption is expected to decrease (increase) monotonically over the entire lifetime.

Known explanations of the consumption hump include borrowing constraints, income uncertainty and precautionary savings, endogenous labor supply with hump-shaped wages, variations in household size, mortality risk, and consumer durables serving as collateral. Our purpose is to add a new, simple explanation of the hump without questioning any of the existing explanations.

Key Findings

− If an individual’s preferences exhibit habit formation, the empirically observed hump in lifetime consumption can naturally materialize from a tradeoff between impatience and concerns about the effects of current consumption on future habit levels and thus future minimum consumption.

− These habit concerns cause a large reduction in the otherwise very high consumption early in life, but a smaller reduction in the otherwise medium-sized consumption in middle age. In some circumstances, a hump-shaped consumption path emerges.

− 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 the consumption hump and the sensitivity of the optimal consumption path to the values of key parameters of our model.

− We show that our "parsimonious model" provides a nice match with consumption patterns derived from the 1980-2003 Consumer Expenditure Surveys in the United States.


Related Published Papers

Author/sTitleYearProgram AreaKeywords
Holger Kraft, Claus Munk, Frank Thomas Seifried, Sebastian WagnerConsumption Habits and Humps
Economic Theory
2017 Household Finance Consumption hump, life-cycle utility maximization, habit formation, impatience
Holger Kraft, Claus Munk, Sebastian WagnerHousing Habits and Their Implications for Life-Cycle Consumption and Investment
Review of Finance
2018 Household Finance Habit formation, life-cycle household decisions, housing expenditure share, consumption hump, stock market participation, renting vs. owning home, human capital