In this project, we study the life-cycle consumption choice of an agent who can endogenously improve his education level. First, we start with a parsimonious model where the agent can decide upon his optimal consumption and how to allocate his leisure time. This stylized model allows us to tease out the effect of an endogenous education choice. In his leisure time, the agent can either relax, which increases his utility, or spend time on educating himself, which leads to disutility and costs. There are however, future benefits from a higher education level, since the agent’s potential salary increases in this level. In line with the literature, we first assume that the agent has Cobb-Douglas utility from consumption and leisure time. We conjecture that the structure of the model allows us to solve the model in closed-form, so that we can perform extensive comparative statics. We can study whether an endogenous education choice leads to a consumption hump, an empirical fact that has drawn the attention of several researchers (see, e.g., Browning, Crossley (2001), Gourinchas, Parker (2002), Feigenbaum (2008)). We expect to find a new explanation for the existence of a consumption hump in life-cycle patterns. We plan to calibrate this model to consumption data (e.g. PSID) so that we can analyze whether the model can create a realistic peak point of consumption expenditures.
Second, we extend our stylized model to include financial assets and unspanned labor income to explore the effects of education on a full blown life-cycle model with a working phase and a retirement phase. We expect to address several interesting research questions: What are the feedback effects of education choice on financial decisions? How are saving motives for retirement affected by education choice? How is education choice influenced by unspanned labor income?
Our project is both innovative and challenging. Although several authors include education information into life-cycle consumption-portfolio problems, mostly education is treated as an exogenous characteristic that cannot be influenced by the agent (see state of the art). By contrast, we study a model that is able to explain reasons for “lifelong learning”. Our model also delivers an endogenous explanation for age-dependent wage levels. Solving is challenging since we have to apply involved stochastic control and numerical methods.
The observed hump-shaped consumption pattern of individuals over their life cycle cannot be explained by the classical consumption-savings model. We have thus solved an extended model with utility depending on both consumption and leisure and with endogenous educational decisions affecting future wages.
To start with, we study a model with certainty. We can show that optimal consumption has the observed hump shape and we pin down the peak age. We have currently finished a first draft of a working paper.
In a second stage, we extend the deterministic model to include assets modelled stochastically as well as unspanned labor income. We are still able to solve the model explicitly in special cases where either the stock or the income process is deterministic or the Brownian motions of the stock and the income process are perfectly correlated. Furthermore, we are able to alter the wage dynamics and utility specifications such that the model allows for a reduction in dimensionality to make a numerical solution more accessible.
A heuristic approach based on Bick, Kraft and Munk (2012) has been implemented to solve the full blown model numerically. Simulations show, that the approximate solution generated by this class of numerical algorithms is potentially inaccurate and reliable error bounds for the calculated policies cannot be obtained easily. In order to evaluate the accuracy and to ensure convergence to the real solution a supplementary numerical algorithm is currently being implemented that is based on the method proposed by Munk and Soerensen (2010). To solve the full-blown model, a numerical algorithm is being implemented that is based on the method proposed by Munk and Soerensen (2010).