Structural macroeconometric analysis and new HANK-type models with extremely high dimensionality require fast and robust methods to efficiently deal with occasionally binding constraints (OBCs), especially since major developed economies have again hit the zero lower bound on nominal interest rates. This paper shows that a linear dynamic rational expectations system with OBCs, depending on the expected duration of the constraint, can be represented in closed form. Combined with a set of simple equilibrium conditions, this can be exploited to avoid matrix inversions and simulations at runtime for significant gains in computational speed. An efficient implementation is provided in Python programming language. Benchmarking results show that for medium-scale models with an OBC, more than 150,000 state vectors can be evaluated per second. This is an improvement of more than three orders of magnitude over existing alternatives. Even state evaluations of large HANK-type models with almost 1000 endogenous variables require only 0.1 ms.

We present the first necessary and sufficient conditions for there to be a unique perfect-foresight solution to an otherwise linear dynamic model with occasionally binding constraints, given a fixed terminal condition. We derive further results on the existence of a solution in the presence of such terminal conditions. These results give determinacy conditions for models with occasionally binding constraints, much as Blanchard and Kahn (1980) did for linear models. In an application, we show that widely used New Keynesian models with endogenous states possess multiple perfect foresight equilibrium paths when there is a zero lower bound on nominal interest rates, even when agents believe that the central bank will eventually attain its long-run, positive inflation target. This illustrates that a credible long-run inflation target does not render the Taylor principle sufficient for determinacy in the presence of the zero lower bound. However, we show that price level targeting does restore determinacy providing agents believe that inflation will eventually be positive.

'This practical review assesses several approaches to solving medium- and large-scale dynamic stochastic general equilibrium (DSGE) models featuring occasionally binding constraints. In such models, global solution methods are not possible because of the curse of dimensionality. This causes the modeller to look elsewhere for methods that can handle the significant non-linearities and non-differentiable functions that inequality constraints represent. The paper discusses methods-including Newton-type solvers under perfect foresight, the piecewise linear algorithm (OccBin), regime-switching models (RISE) and the news shocks approach (DynareOBC) - and compares the results from a simple borrowing constraints model obtained using projection methods, providing example MATLAB code. The study focuses on the news shocks method, which I find produces higher accuracy than other methods and allows the modeller to study multiple equilibria and determinacy issues'--Abstract, page ii.

This book is a compilation of a selected subset of research articles presented at the Eighth INFORMS Computing Society Conference, held in Chandler, Arizona, from January 8 to 10, 2003. The articles in this book represent the diversity and depth of the interface between ORiMS (operations research and the management sciences) and CS/AI (computer science and artificial intelligence ). This volume starts with two papers that represent the reflective and integrative thinking that is critical to any scientific discipline. These two articles present philosophical perspectives on computation, covering a variety of traditional and newer methods for modeling, solving, and explaining mathematical models. The next set includes articles that study machine learning and computational heuristics, and is followed by articles that address issues in performance testing of solution algorithms and heuristics. These two sets of papers demonstrate the richness of thought that takes place at the ORiMS and CSI AI interface. The final set of articles demonstrates the usefulness of these and other methods at the interface towards solving problems in the real world, covering e-commerce, workflow, electronic negotiation, music, parallel computation, and telecommunications. The articles in this collection represent the results of cross-fertilization between ORiMS and CSI AI, making possible advances that could have not been achieved in isolation. The continuing aim ofthe INFORMS Computing Society and this research conference is to invigorate and further develop this interface.

An accessible introduction to optimization analysis using spreadsheets Updated and revised, Optimization Modeling with Spreadsheets, Third Edition emphasizes model building skills in optimization analysis. By emphasizing both spreadsheet modeling and optimization tools in the freely available Microsoft® Office Excel® Solver, the book illustrates how to find solutions to real-world optimization problems without needing additional specialized software. The Third Edition includes many practical applications of optimization models as well as a systematic framework that illuminates the common structures found in many successful models. With focused coverage on linear programming, nonlinear programming, integer programming, and heuristic programming, Optimization Modeling with Spreadsheets, Third Edition features: An emphasis on model building using Excel Solver as well as appendices with additional instructions on more advanced packages such as Analytic Solver Platform and OpenSolver Additional space devoted to formulation principles and model building as opposed to algorithms New end-of-chapter homework exercises specifically for novice model builders Presentation of the Sensitivity Toolkit for sensitivity analysis with Excel Solver Classification of problem types to help readers see the broader possibilities for application Specific chapters devoted to network models and data envelopment analysis A companion website with interactive spreadsheets and supplementary homework exercises for additional practice Optimization Modeling with Spreadsheets, Third Edition is an excellent textbook for upper-undergraduate and graduate-level courses that include deterministic models, optimization, spreadsheet modeling, quantitative methods, engineering management, engineering modeling, operations research, and management science. The book is an ideal reference for readers wishing to advance their knowledge of Excel and modeling and is also a useful guide for MBA students and modeling practitioners in business and non-profit sectors interested in spreadsheet optimization.