Optimization in a Simulation Setting: Use of Function Approximation in Debt Strategy Analysis

Abstract

of the Bank of Canada for useful comments. We would also like to thank Jeremy Graveline from the University of Minnesota and Mark Reesor from the University of Western Ontario for helpful discussions. All thanks are without implication and we retain any and all responsibility for any remaining omissions or errors.iii AbstractThe stochastic simulation model suggested by Bolder (2003) for the analysis of the federal government's debt-management strategy provides a wide variety of useful information. It does not, however, assist in determining an optimal debt-management strategy for the government in its current form. Including optimization in the debt-strategy model would be useful, since it could substantially broaden the range of policy questions that can be addressed. Finding such an optimal strategy is nonetheless complicated by two challenges. First, performing optimization with traditional techniques in a simulation setting is computationally intractable. Second, it is necessary to define precisely what one means by an "optimal" debt strategy. The authors detail a possible approach for addressing these two challenges. They address the first challenge by approximating the numerically computed objective function using a function-approximation technique. They consider the use of ordinary least squares, kernel regression, multivariate adaptive regression splines, and projection-pursuit regressions as approximation algorithms. The second challenge is addressed by proposing a wide range of possible government objective functions and examining them in the context of an illustrative example. The authors' view is that the approach permits debt and fiscal managers to address a number of policy questions that could not be fully addressed with the current stochastic simulation engine.

Measuring International Migration in Azerbaijan

“…Sephton [64], determined that MARS method is more successful than probit method [65] to predict the recession. Similar to this study, Bolder and Rubin [66], concluded that MARS method gives better results to define the best debt strategy in comparison with Kernel regression analysis. Moreover, Muzır [67], made a study about credit risk of Turkish banks and defined that MARS method measures this risk better than the logistic regression [68] analysis.…”

Sovereign Risk and Asset and Liability Management: Conceptual Issues

“…While the SALM objective may be clearly stated, optimization of this objective crucially depends on the specification of the government's objective function. Simulation estimates based on various methods show that MARS outperforms other methods, particularly when the objective function is highly dimensional and nonlinear and there is a lack of a large number of observations (Bolder and Rubin, 2007). 19 Thus, given uncertainty about the complexity of the government's objective function, the MARS method allows significant flexibility in its estimation.…”

“…In their simulations,Bolder and Rubin (2007) compare estimates of the ordinary least squares (OLS), nonparametric kernel regression (NKR), the projection pursuit regression (PPR), and MARS. They find that the goodness of fit of the NKR and PPR methods deteriorate quickly for even simple parabolic functions as their dimension increases.…”

“…They find that the goodness of fit of the NKR and PPR methods deteriorate quickly for even simple parabolic functions as their dimension increases. MARS and OLS perform well when using conic-cosine functions and MARS outperforms OLS when fitting more complex functions, such as the Rosenbrock function.20 Bolder and Rubin (2007) have performed such simulations with data for Canada.…”

Combining Canadian Interest Rate Forecasts

“…The approach we selected is termed Multiple Adaptive Regression Splines (MARS), which is a function-approximation technique based on the recursivepartitioning algorithm. The basic idea behind this technique is to define piecewise linear spline functions on an overlapping partition of the domain (Bolder and Rubin (2007) provide a detailed description of the MARS algorithm). As such, the MARS combination scheme can be considered an example of a mathematically complicated nonparametric, nonlinear aggregation of our four alternative models.…”