Optimal Control Theory for Undergraduates

Dynamic optimization is widely used in financial economics, macroeconomics and resource economics. This is accounting for some tension between the undergraduate and graduate teaching of economics because most undergraduate programs still concentrate on static economic analysis. This paper shows how, with the help of the Microsoft Excel Solver tool, the principles of dynamic economics can be taught to students with minimal knowledge of calculus. As it is assumed that the reader has no prior knowledge of optimal control theory, some attention is paid to the main concepts of dynamic optimization.Optimal Control Theory, Economic Education, Microsoft Excel

Optimal Control Theory for Undergraduates Using the Microsoft Excel Solver Tool

Dynamic optimisation is widely used in financial economics, macroeconomics and resource economics. This accounts for friction between the undergraduate and graduate teaching of economics because most undergraduate programmes still concentrate on static economic analysis. This paper shows how, with the help of the Microsoft Excel Solver tool, the principles of dynamic economics can be taught to students with minimal knowledge of calculus. As it is assumed that the reader has no prior knowledge of optimal control theory, some attention is paid to the main concepts of dynamic optimisation.

The Genuine Savings Criterion and the Value of Population

Arrow, Dasgupta and Maler demonstrate thatin any dynamic model of the economy with changing population, population should properly be one of the state variables of the system. It enters both in the maxim and, at least under total utilitarianism, and into the production function in one way or another. If population growth is exponential and there are constant returns to scale, then a simple transformation to per capita variables can be used to eliminate one state variable. However, this simple transformation cannot be made if growth is not exponential, as it obviously is not and cannot be. If the growth of population is exogenous, then introducing it into the system does not affect the optimal policy. However, if one asks whether the system is sustainable, in the sense of at least maintaining total welfare (integral of discounted utilities), then the criterion is that the value of the rates of change of the state variables is non-negative, so that the shadow price of population becomes relevant. In this paper, we derive explicit formulas in a simple model, showing that the rate of growth of per capita capital is not the correct formula but must have other terms added to it. We also study the question under an alternative criterion of long-run average utilitarianism.

Employment, Dynamic Deterrence and Crime

Using monthly panel data we solve and estimate, using maximum likelihood techniques, an explicitly dynamic model of criminal behavior where current criminal activity adversely affects future employment outcomes. This acts as 'dynamic deterrence' to crime: the threat of future adverse effects on employment payoffs when caught committing crimes reduces the incentive to commit them. We show that this dynamic deterrence effect is strong in the data. Hence, policies which weaken dynamic deterrence will be less effective in fighting crime. This suggests that prevention is more powerful than redemption since the latter weakens dynamic deterrence as anticipated future redemption allows criminals to look forward to negating the consequences of their crimes. Static models of criminal behavior neglect this and hence sole reliance on them can result in misleading policy analysis.

Stochastic Optimal Control Modeling of Debt Crises

What is an optimal or a sustainable external debt - for a country, region or sector? How should one monitor and evaluate debt to preclude a crisis? We use stochastic optimal control/dynamic programming to derive an optimal debt. The deviation of the actual from the optimal will serve as a Warning Signal of a crisis. There is a correspondence between Hamilton-Jacobi-Bellman equation of Dynamic Programming and the static Mean-Variance (M-V) analysis in finance. A graphic analysis of M-V is helpful to explain the implications of DP. An explicit example is the US Agricultural debt crisis.stochastic optimal control, debt, international finance, US agricultural crisis, Mean-Variance analysis, Hamilton-Jacobi-Bellaman equation

Heterogeneity in Returns to Work Experience: A Dynamic Model of Female Labor Force Participation

This paper provides structural estimates of heterogeneous returns to work experience for Japanese married women. A dynamic model of labor force participation is used to account for dynamic selfselection into employment. Heterogeneity is incorporated into the model in a way that allows for the multidimensional skill heterogeneity in employment and home production and for the individual-specific slope and curvature of experience effect on earnings. The structural estimates and their comparison to the reduced-form estimates highlight the importance of dynamic self-selection into employment and heterogeneity in returns to work experience.

Heterogeneity in Returns to Work Experience : A Dynamic Model of Female Labor Force Participation

This paper provides structural estimates of heterogeneous returns to work experience for Japanese married women. A dynamic model of labor force participation is used to account for dynamic self-selection into employment. Heterogeneity is incorporated into the model in a way that allows for the multidimensional skill heterogeneity in employment and home production and for the individual-specific slope and curvature of experience effect on earnings. The structural estimates and their comparison to the reduced-form estimates highlight the importance of dynamic self-selection into employment and heterogeneity in returns to work experience.heterogeneous returns, Japan, labour, multidimensional skill heterogeneity in employment, structual estimates