Topic & Objectives
In this project, we study the life-cycle consumption choice of an agent who can endogenously improve his education level. It has been empirically documented that consumption expenditures of individuals are hump shaped over the life cycle with a peak around the age of 45-50 years. These findings contrast the classical, frictionless life-cycle consumption-savings models that predict either a monotonically increasing, monotonically decreasing, or flat consumption profile depending on parameter values. We present and explicitly solve a parsimonious and transparent model in which the optimal consumption of the individual can exhibit a hump-shaped life-cycle pattern.
The key model feature generating the consumption hump is endogenous educational decisions. The agent decides how much time to spend on education. He benefits from education since it has a lasting positive effect on the wages he earns. On the other hand, by spending time on education the agent forgoes leisure, which leads to disutility. In addition, education might require a monetary investment by the agent. The endogenously determined price of leisure relative to consumption varies over life. Enjoying an extra hour of leisure means spending one hour less on education, which reduces wages in all future. The present value of the foregone wages is larger for young than for old agents. Therefore, the relative price of leisure decreases over life. The consumption bundle of perishable goods and leisure is optimally tilted towards more perishable consumption and less leisure early in life, but less perishable consumption and more leisure later in life. When we embed this mechanism in a setting where the return on savings exceeds the agent's subjective time preference rate, a hump-shaped pattern for perishable consumption emerges.
- In contrast to the classical frictionless life-cycle consumption-savings models, consumption expenditures of individuals have been documented to be hump shaped over the life cycle. We find that this consumption hump can be explained without risk or frictions by the introduction of endogenous educational decisions.
- We find that for realistic parameter values in a continuous time portfolio optimization problem with education, the empirical observation of increasing consumption rates until the age of 48 with a slight drop after retirement can be reproduced. Additionally, we find that the model is flexible enough to generate monotonically increasing as well as hump shaped wage profiles with different peak ages that are documented in different empirical studies.
- Our findings link the literature on consumption humps and the effects of educational decisions on wages and welfare. Our results question the need of government interventions to reduce or remove frictions like borrowing constraints that are the leading explanation in the first strain of literature. Alternatively, we find that through the effect of educational decisions on future wages, the price of leisure relative to consumption of goods decreases over life, and this can twist the consumption pattern from being monotonically increasing in the corresponding model without education and leisure into the hump-shaped profile observed in the data.
|53||Holger Kraft, Claus Munk, Frank Thomas Seifried, Mogens Steffensen||Consumption and Wage Humps in a Life-Cycle Model with Education||2014||Household Finance||Education, leisure, consumption hump, wage hump|