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A NONLINEAR PROGRAMMING METHOD FOR DYNAMIC PROGRAMMING
- Yongyang Cai, Kenneth L. Judd, Thomas S. Lontzek, Valentina Michelangeli, Che-Lin Su
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- Journal:
- Macroeconomic Dynamics / Volume 21 / Issue 2 / March 2017
- Published online by Cambridge University Press:
- 18 January 2016, pp. 336-361
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A nonlinear programming formulation is introduced to solve infinite-horizon dynamic programming problems. This extends the linear approach to dynamic programming by using ideas from approximation theory to approximate value functions. Our numerical results show that this nonlinear programming is efficient and accurate, and avoids inefficient discretization.
Contributors
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- By Rose Teteki Abbey, K. C. Abraham, David Tuesday Adamo, LeRoy H. Aden, Efrain Agosto, Victor Aguilan, Gillian T. W. Ahlgren, Charanjit Kaur AjitSingh, Dorothy B E A Akoto, Giuseppe Alberigo, Daniel E. Albrecht, Ruth Albrecht, Daniel O. Aleshire, Urs Altermatt, Anand Amaladass, Michael Amaladoss, James N. Amanze, Lesley G. Anderson, Thomas C. Anderson, Victor Anderson, Hope S. Antone, María Pilar Aquino, Paula Arai, Victorio Araya Guillén, S. Wesley Ariarajah, Ellen T. Armour, Brett Gregory Armstrong, Atsuhiro Asano, Naim Stifan Ateek, Mahmoud Ayoub, John Alembillah Azumah, Mercedes L. García Bachmann, Irena Backus, J. Wayne Baker, Mieke Bal, Lewis V. Baldwin, William Barbieri, António Barbosa da Silva, David Basinger, Bolaji Olukemi Bateye, Oswald Bayer, Daniel H. Bays, Rosalie Beck, Nancy Elizabeth Bedford, Guy-Thomas Bedouelle, Chorbishop Seely Beggiani, Wolfgang Behringer, Christopher M. Bellitto, Byard Bennett, Harold V. Bennett, Teresa Berger, Miguel A. Bernad, Henley Bernard, Alan E. Bernstein, Jon L. Berquist, Johannes Beutler, Ana María Bidegain, Matthew P. Binkewicz, Jennifer Bird, Joseph Blenkinsopp, Dmytro Bondarenko, Paulo Bonfatti, Riet en Pim Bons-Storm, Jessica A. Boon, Marcus J. Borg, Mark Bosco, Peter C. Bouteneff, François Bovon, William D. Bowman, Paul S. Boyer, David Brakke, Richard E. Brantley, Marcus Braybrooke, Ian Breward, Ênio José da Costa Brito, Jewel Spears Brooker, Johannes Brosseder, Nicholas Canfield Read Brown, Robert F. Brown, Pamela K. Brubaker, Walter Brueggemann, Bishop Colin O. Buchanan, Stanley M. Burgess, Amy Nelson Burnett, J. Patout Burns, David B. Burrell, David Buttrick, James P. Byrd, Lavinia Byrne, Gerado Caetano, Marcos Caldas, Alkiviadis Calivas, William J. Callahan, Salvatore Calomino, Euan K. Cameron, William S. Campbell, Marcelo Ayres Camurça, Daniel F. Caner, Paul E. Capetz, Carlos F. Cardoza-Orlandi, Patrick W. Carey, Barbara Carvill, Hal Cauthron, Subhadra Mitra Channa, Mark D. Chapman, James H. Charlesworth, Kenneth R. Chase, Chen Zemin, Luciano Chianeque, Philip Chia Phin Yin, Francisca H. Chimhanda, Daniel Chiquete, John T. Chirban, Soobin Choi, Robert Choquette, Mita Choudhury, Gerald Christianson, John Chryssavgis, Sejong Chun, Esther Chung-Kim, Charles M. A. Clark, Elizabeth A. Clark, Sathianathan Clarke, Fred Cloud, John B. Cobb, W. Owen Cole, John A Coleman, John J. Collins, Sylvia Collins-Mayo, Paul K. Conkin, Beth A. Conklin, Sean Connolly, Demetrios J. Constantelos, Michael A. Conway, Paula M. Cooey, Austin Cooper, Michael L. Cooper-White, Pamela Cooper-White, L. William Countryman, Sérgio Coutinho, Pamela Couture, Shannon Craigo-Snell, James L. Crenshaw, David Crowner, Humberto Horacio Cucchetti, Lawrence S. Cunningham, Elizabeth Mason Currier, Emmanuel Cutrone, Mary L. Daniel, David D. Daniels, Robert Darden, Rolf Darge, Isaiah Dau, Jeffry C. Davis, Jane Dawson, Valentin Dedji, John W. de Gruchy, Paul DeHart, Wendy J. Deichmann Edwards, Miguel A. De La Torre, George E. Demacopoulos, Thomas de Mayo, Leah DeVun, Beatriz de Vasconcellos Dias, Dennis C. Dickerson, John M. Dillon, Luis Miguel Donatello, Igor Dorfmann-Lazarev, Susanna Drake, Jonathan A. Draper, N. Dreher Martin, Otto Dreydoppel, Angelyn Dries, A. J. Droge, Francis X. D'Sa, Marilyn Dunn, Nicole Wilkinson Duran, Rifaat Ebied, Mark J. Edwards, William H. Edwards, Leonard H. Ehrlich, Nancy L. Eiesland, Martin Elbel, J. Harold Ellens, Stephen Ellingson, Marvin M. Ellison, Robert Ellsberg, Jean Bethke Elshtain, Eldon Jay Epp, Peter C. Erb, Tassilo Erhardt, Maria Erling, Noel Leo Erskine, Gillian R. Evans, Virginia Fabella, Michael A. Fahey, Edward Farley, Margaret A. Farley, Wendy Farley, Robert Fastiggi, Seena Fazel, Duncan S. Ferguson, Helwar Figueroa, Paul Corby Finney, Kyriaki Karidoyanes FitzGerald, Thomas E. FitzGerald, John R. Fitzmier, Marie Therese Flanagan, Sabina Flanagan, Claude Flipo, Ronald B. 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Yee, Viktor Yelensky, Yeo Khiok-Khng, Gustav K. K. Yeung, Angela Yiu, Amos Yong, Yong Ting Jin, You Bin, Youhanna Nessim Youssef, Eliana Yunes, Robert Michael Zaller, Valarie H. Ziegler, Barbara Brown Zikmund, Joyce Ann Zimmerman, Aurora Zlotnik, Zhuo Xinping
- Edited by Daniel Patte, Vanderbilt University, Tennessee
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- Book:
- The Cambridge Dictionary of Christianity
- Published online:
- 05 August 2012
- Print publication:
- 20 September 2010, pp xi-xliv
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SOLVING LARGE-SCALE RATIONAL-EXPECTATIONS MODELS
- JESS GASPAR, KENNETH L. JUDD
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- Journal:
- Macroeconomic Dynamics / Volume 1 / Issue 1 / January 1997
- Published online by Cambridge University Press:
- 02 March 2005, pp. 45-75
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We explore alternative approaches to numerical solutions of large rational-expectations models. We discuss and compare several current alternatives, focusing on the trade-offs in accuracy, space, and speed. The models range from representative-agent models with many goods and capital stocks, to models of heterogeneous agents with complete or incomplete asset markets. The methods include perturbation and projection methods. We show that these methods are capable of analyzing moderately large models even when we use only elementary, general-purpose numerical methods.
3 - Solving Dynamic Stochastic Competitive General Equilibrium Models
- Edited by Timothy J. Kehoe, University of Minnesota, T. N. Srinivasan, Yale University, Connecticut, John Whalley, University of Western Ontario
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- Frontiers in Applied General Equilibrium Modeling
- Published online:
- 14 January 2010
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- 17 January 2005, pp 45-66
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Summary
ABSTRACT: The Scarf algorithm was the first practical, almost surely convergent method for computing general equilibria of competitive models. The current focus of much computational research is computing equilibrium of dynamic stochastic models. While many of these models are examples of Arrow–Debreu equilibria, Scarf's algorithm and subsequent homotopy methods cannot be applied directly, because they have an infinite number of commodities. Many methods have been proposed for solving dynamic models and some work well on simple examples. However, all have convergence problems and are not likely to perform as well in models with heterogeneous agents, multiple goods, joint production, and other features often present in general equilibrium models. This paper discusses weaknesses of standard methods for solving dynamic stochastic models. We then present an alternative Negishi-style approach that combines convergent methods for solving finite systems of equations with convergent dynamic programming methods to produce more reliable algorithms for dynamic analyses. The dynamic programming step presents the key challenge, because most practical dynamic programming methods have convergence problems, but we argue that shape-preserving approximation methods offer a possible solution.
The Scarf (1967) algorithm was the first practical, surely convergent method for computing general equilibrium prices and, equivalently, systems of nonlinear equations in ℝn. This was followed by the development of almost surely convergent homotopy methods for solving nonlinear equations. This work gave us reliable and efficient methods for solving finite-dimensional systems of equations.
7 - Computational Methods for Dynamic Equilibria with Heterogeneous Agents
- Edited by Mathias Dewatripont, Université Libre de Bruxelles, Lars Peter Hansen, University of Chicago, Stephen J. Turnovsky, University of Washington
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- Book:
- Advances in Economics and Econometrics
- Published online:
- 06 January 2010
- Print publication:
- 20 January 2003, pp 243-290
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Summary
INTRODUCTION
Computational methods have become increasingly important in the analysis of dynamic general equilibrium problems. These methods are being used, for example, to study the incidence of tax and monetary policies in dynamic models of growth, commodity storage inv arious models of agricultural commodity markets, and price formationindyn amic models of asset markets. Many early computational methods relied primarily on intuitive economic tatonnement stories, and produced moderately successful algorithms. Even when these methods worked, they were usually slow. Furthermore, as we know from general equilibrium theory, tatonnement methods may not converge even with good initial guesses. Inthe past decade, the computational literature has made more use of formal mathematical tools from numerical analysis and perturbation theory. This use has resulted inmore powerful algorithms that canattack increasingly complex problems. These developments are particularly important when we try to solve models with several agents. This essay reviews the key ideas used in recent work, gives some examples of their advantages, and indicates the likely directions future work will take.
It is particularly appropriate that the 2000 World Congress of the Econometric Society include a survey of recent computational literature, because computational methodology is inherently an important part of what is broadly called “econometrics.” Ragnar Frisch, in his editorial in the initial issue of Econometrica, defined econometrics as the “unification of the theoretical-quantitative and the empirical-quantitative approach to economic problems.”