Comparison of Optimal Control Solutions in a Labor Market Model

In this paper a variety of computational optimal control techniques are compared on a complicated nonlinear discrete-time model. We use a labor market model with the objective of trying to obtain an unemployment rate objective, using an active labor market program as a control. In reality the control is constrained as only limited proportion of the unemployment can attend the labor market program. A variety of computational optimal control techniques are applied. The techniques include numerically linearizing the model and using standard linear quadratic optimal control and applying this to the nonlinear model; model based predictive control; and stacking the model over time and using optimisation techniquesLabour market policies; Optimal Control.

REVERSE SHOOTING IN A MULTI-DIMENSIONAL SETTING

This paper investigates the properties of dynamic solutions that have been derived using the well-known reverse-shooting algorithm. Given an arbitrary large-scale model about which we have limited information, how successful is the algorithm likely to be in solving this model? We address this question using a range of investment models, both linear and non-linear. By extending the investment models to allow for multidimensional specifications of the capital stock, we are able to examine the computational efficiency of the reverse shooting algorithm as the dimensionality of the capital stock is allowed to increase. Our approach provides insights into how the complexity of the solutions to a broad range of macroeconomic models increases with the dimensionality of the models.Macroeconomics; Reverse shooting; Saddlepath instability; Computational techniques; Investment models

Solving Macroeconomic Models with "Off-the-Shelf" Software: An Example of Potential Pitfalls

When working with large-scale models or numerous small models, there can be a temptation to rely on default settings in proprietary software to derive solutions to the model. In this paper we show that, for the solution of non-linear dynamic models, this approach can be inappropriate. Alternative linear and non-linear specifications of a particular model are examined. One version of the model, expressed in levels, is highly non-linear. A second version of the model, expressed in logarithms, is linear. The dynamic solution of each model version has a combination of stable and unstable eigenvalues so that any dynamic solution requires the calculation of appropriate “jumps” in endogenous variables. We can derive a closed-form solution of the model, which we use as our "true" benchmark, for comparison with computational solutions of both linear and non-linear models. Our approach is to compare the "goodness of fit" of reverse-shooting solutions for both the linear and non-linear model, by comparing the computational solutions with the benchmark solution. Under the basic solution method with default settings, we show that there is significant difference between the computational solution for the non-linear model and the benchmark closed-form solution. We show that this result can be substantially improved using modifications to the solver and to parameter settings.Solving non-linear models, reverse-shooting, computational economics, computer software

Reverse-Shooting versus Forward-Shooting over a Range of Dimensionalities

This paper investigates the properties of dynamic solutions that have been derived using the well-known reverse-shooting and forwardshooting algorithms. Given an arbitrary large-scale model about which we have limited information, how successful are the algorithms likely to be in solving this model? We address this question using a range of investment models, both linear and non-linear. By extending the investment models to allow for multi-dimensional specifications of the capital stock, we are able to examine the computational efficiency of the competing algorithms as the dimensionality of the capital stock is allowed to increase. Our approach provides insights into how the complexity of the solutions to a broad range of macroeconomic models increases with the dimensionality of the models.Macroeconomics; Reverse-shooting; Forward-shooting; Saddlepath instability; Computational techniques; Investment models.

Information Visualization Of An Agent-Based Financial System Model

This paper considers the application of information visualization techniques to an agent-based model of a financial system. The minority game is a simple agent-based model which can be used to simulate the events in a real-world financial market. To aid understanding of this model, we can apply information visualization techniques. Treemap and sunburst are two such information visualization techniques, which previous research tells us can effectively represent information similar to that generated by the minority game. Another information visualization technique, called logical fisheye-lens, can be used to augment treemap and sunburst, allowing users to magnify areas of interest in these visualizations. In this paper, treemap and sunburst, both with and without fisheye-lens, are applied to the minority game, and their effectiveness is evaluated. This evaluation is carried out through an analysis of users performing various tasks on (simulated) financial market data using the visualization techniques. A subjective questionnaire is also used to measure the users’ impressions of the visualization techniques.Dynamic Models, Minority Game, Visualization

Space-filling Techniques in Visualizing Output from Computer Based Economic Models

One important factor concerning economic models is that frequently large amounts of data are produced. There is the research issue of how end-users (who may not be researchers or model developers) can be presented with this data so that maximum benefits can be attained from the data production. The usual approach with economic models is a series of tables or data series plots. In this paper we use space-filling information visualization techniques as an aid to user’s understanding of data from an economic model. Based upon evaluation of the effectiveness of existing treemap and sunburst techniques through user experimentation, we introduce two new space-filling visualization techniques. We also describe fisheye-lens techniques applicable to these new visualizations.User Interfaces, Information visualisation, Minority Game

Exploiting Model Structure to Solve the Dynamics of a Macro Model

This paper considers alternative approaches to solving the time-path of a representative agent model following an exogenous shock. The model has a number of important dynamic properties that are both common to a wide range of economic models and have important computational implications for solving the model. The paper compares the alternative approaches on a computational basis and shows that the best approach to solving the model is obtained by fully exploiting the model structure in a modified reverse shooting algorithm.Representative agent models, shooting methods, MATLAB