Browsing by Author "Caputo, Michael R."

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A Dual Approach to the Derivation of Feedback Demand Functions for Capital-Accumulating Agents
(University of Gothenburg, 2024-05) Bolin, Kristian; Caputo, Michael R.; Department of Economics
An optimal control model of a consumer is developed that accounts for the consumption of many goods and services, the accumulation of wealth, a state variable that affects instantaneous preferences and wealth accumulation, and contains several canonical models as special cases. Formulas are provided for the feedback consumption functions in terms of certain partial derivatives of a consumer’s lifetime indirect utility function, thereby obviating the need to solve the necessary conditions of Pontryagin or the Hamilton-Jacobi-Bellman equation. The intrinsic qualitative properties of the optimal control model in differential form are derived, and an example of how to implement the results for econometric purposes is provided as well.
Child Human Capital – The Importance of Parenting Style
(2019-08) Bolin, Kristian; Caputo, Michael R.; Department of Economics, University of Gothenburg
Investments in the human capital of children during their upbringing determine the opportunities available in adulthood. Recognizing that the parent-child interaction plays a significant role in the accumulation of child human capital, we develop a differential game in which the parent may invest directly in child human capital and the child consumes goods that influence the accumulation of their human capital. We compare the accumulation of child human capital between three different parenting styles, formalized as three different solution concepts to the differential game: (i) the parent and the child maximizes a joint utility function (cooperative solution), (ii) the parent announces a strategy dependent on time only (open-loop Stackelberg), (iii) the parent’s strategy depends on the accrued amount of human capital (feedback Stackelberg). We show that under rather general assumptions the open-loop Stackelberg equilibrium is time consistent, and coincides with a feedback Stackelberg equilibrium. Using cooperative parenting as a benchmark, we find that less or more child human capital may be accumulated over the family’s planning horizon under “open-loop Stackelberg” parenting, depending on parental and child preferences for human capital and wealth at the terminal time of the family’s planning horizon, and on the extent to which child consumption influences the accumulation of their human capital. In particular, if the child’s preference for terminal time wealth is strong enough, more human capital will be accumulated under “open-loop Stackelberg” parenting.
Consumption and Investment Demand when Health Evolves Stochastically
(2017-10) Bolin, Kristian; Caputo, Michael R.; Dept. of Economics, University of Gothenburg
The health capital model of Grossman (1972) is extended to account for uncertainty in the rate at which a stock of health depreciates. Two versions of the model are contemplated, one with a fully functioning financial market and the other in its absence. The comparative dynamics of the consumption and health-investment demand functions are studied in both models in a general setting, where it is shown that the key to deriving refutable results is to determine how a parameter or state variable affects the lifetime marginal utilities of health and wealth. To add further bite to the results, a stochastic control problem is solved for its feedback consumption and health-investment demand functions, thereby yielding estimable structural demand functions.
Non-Life-Threatening Ailments and Rational Patience
(2019-08) Bolin, Kristian; Caputo, Michael R.; Department of Economics, University of Gothenburg
The time at which a rational patient might choose an elective medical procedure for a non-life-threatening ailment is contemplated. The resulting model is purposely uncomplicated but general, and accounts for several basic factors that might affect such a decision. One such factor is that a patient cannot know with certainty the degree to which the medical procedure will be successful. Even so, patients have information about the expected outcome of the procedure and its risk, and about how the expected outcome and risk are affected by medical technological progress and surgeon experience. The effect of changes in exogenous variables on the timing of the medical procedure and on patient welfare are investigated. It is shown that risk averse and prudent patients behave in an unambiguous manner in response to changes in all of the exogenous variables.
Optimal Investment in Health when Lifetime is Stochastic, or, Rational Agents do not Often Follow Health Agency Recommendations
(2018-08) Bolin, Kristian; Caputo, Michael R.; Dept. of Economics, University of Gothenburg
A health-capital model is contemplated which accounts for the consumption of many goods, a stock of health and investment in it, as well as an agent’s random lifetime and accumulation of wealth. It is shown that if an agent maximizes the expected discounted value of lifetime utility, or if an agent maximizes the expected value of their lifetime, then an agent does not follow the health-investment policy that minimizes the conditional probability of dying at each point in time, in general. What is more, simple and intuitive sufficient, and necessary and sufficient, conditions are identified whereby such agents investment more or less in their health than said policy.