CONWUTATIONALECONONUCSYSTEMS Advances in Computational Economics VOLUMES SERIES EDITORS Hans Amman, University ofAmsterdam, Amsterdam, The Netherlands Anna Nagumey, University of Massachusetts at Amherst, USA EDITORIAL BOARD Anantha K Duraiappah, European University Institute John Geweke, University of Minnesota Manfred Gilli, University ofGeneva Kenneth L Judd, Stanford University David Kendriek, University ofTexas at Austin Daniel MeFadden, University ofCali/ornia at Berkeley Ellen MeGrattan, Duke University Reinhard Neck, Universität Bielefeld Adrian R Pagan, Australian National University John Rust, University ofWisconsin Bere Rustem, University ofLondon HaI R Varian, University of Michigan The titles published in this series are listed at the end of this volume Computational Economic Systems Models, Methods & Econometrics edited by Manfred Gilli University ofGeneva, Switzerland SPRINGER-SCIENCE+BUSINESS MEDIA, B.V A C.I.P Catalogue record for this book is available from the Library of Congress ISBN 978-90-481-4655-0 ISBN 978-94-015-8743-3 (eBook) DOI 10.1007/978-94-015-8743-3 Printed on acid-free paper All Rilzhts Reserved © 1996 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1996 Softcover reprint ofthe hardcover 1st edition 1996 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner TABLE OF CONTENTS Preface List of Contributors vii IX Part One: Modeling Computational Economic Systems Evolutionary Games and Genetic Algorithms Christopher R Birchenhall The Emergency and Evolution of Self-Organized Coalitions Arthur de Vany Smart Systems and Simple Agents: Industry Pricing by Parallel and Genetic Strategies Raymond Board and Peter A Tinsley A Distributed Parallel Genetic Algorithm: An Application from Economic Dynamics Paul M Beaumont and Pa trick T Bradshaw Multi-Item Stochastic Inventory Models with Constraints and their Parallel Computation Yuan Wang and Yuafan Deng Building and Solving Multicriteria Models Involving Logical Conditions R.L V Pinto and Berc Rustem 25 51 81 103 123 Part Two: Computational Methods in Econometrics Wavelets in Econometrics: An Application to Outlier Testing Seth A Greenblatt Linear Versus Nonlinear Information Processing: A Look at Neutral Networks Emilio Barucci, Giampiero M Gallo and Leonardo Landi Solving Triangular Seemingly Unrelated Regression Equations Models on Massively Parallel Systems Erricos J Kontoghiorghes and E Dinenis Maximum Likelihood Estimation of Nonlinear Rational Expectations Models by Orthogonal Polynomial Projection Methods Mario J Miranda 139 161 191 203 vi Structural Breaks and GAReR Modelling Stephen G Hall and Martin Sola Block Distributed Methods for Solving Multicountry Econometric Models ion Faust and Ralph Tryon Efficient Solution of Linear Equations Arising in a Nonlinear Economic Model Are Magnus Bruaset Solving Path-dependent Rational Expectations Models Using the Fair-Taylor Method F.J Henk Don and Rudy M.G van Stratum Author Index Subject Index 217 229 243 257 271 277 Preface The approach to many problems in economic analysis has drastically changed with the development and dissemination of new and more efficient computational techniques The present volume constitutes a selection of papers presented at the IFAC-Meeting on 'Computational Methods in Economics and Finance', organized by Hans Amman and Ben; Rustem in June 1994 in Amsterdam The selected contributions illustrate the use of new computatiollal methods and computing teehniques, such as parallel proeessing, to solve eeonomic problems Part I of the volume is dedieated to modelling eomputational economic systems The eontributions present eomputational methods to investigate the evolution of the behaviour of eeonomic agents Christopher Birehenhall diseusses the applieation of various forms of genetic algorithms to simple games and eompares the out comes with theory and experimental evidence Arthur de Vany analyzes sequential and Edgeworth recontracting eore formation with imprecise information, using the Boltzmann maehine as a model to study the evolution of eoalitions Board and Tinsley foeus on the organization of interindustry communications for adjustment of producer prices using parallel Jacobi iterations and genetic algorithms Beaumont and Bradshaw also explore the use of genetic algorithms in computational economics In particular, they present a distributed parallel genetic algorithm whieh is quite effective at solving complex optimization problems as it avoids converging on suboptimal solutions Wang and Deng develop a multiitem, multi-period, double-random inventory model and demonstrate the application of distributed memory MIMD parallel computers to solve such models Following the prineiples of behavioral realism, Pinto and Rustem present a multiple eriteria decision support system for the construction and solution of multicriteria models involving logical conditions Papers in Part Ir concern new eomputational approaches to econometrie problems Seth Greenblatt gives an application of wavelets to outlier detection Barucci, Gallo and Landi compare the information processing capabilities of different architectures of neural networks to those of standard linear techniques Kontoghiorghes and Dinensis propose an efficient parallel iterative algorithm, based on orthogonal transformations, to solve triangular seemingly unrelated regression equation models on massively parallel computers Mario Miranda presents a nested fixed-point algorithm for computing the full information maximum likelihood estimators of a nonlinear rational expectations model using orthogonal polynomial projection methods Hall and Sola propose a generalization of the standard GARCH model which allows diserete switching Follows a set ofpapers which diseuss viii approaches for the solution of nonlinear rational expectation models Faust and Tryon present variations on the Fair-Taylor algorithm exploiting the block structure of multi-country, rational expectations macroeconometric models to solve them in a distributed processing environment Are Magnus Bruaset discusses efficient methods for solving certain linear systems which arise in the solution process of nonlinear economic models Don and Stratum present a way to solve path-dependent rational expectations systems numerically using Fair-Taylor's method If the stationary state of the system is path-dependent Fair-Taylor's method may fail to converge to the correct solution They avoid this problem by rewriting the original model in terms of scaled variables We are grateful to Hans Amman and Ber~ Rustem, the organizers of the Amsterdam conference, for having provided researchers in the computational economics area with this excellent opportunity to exchange their experiences In particular this conference provided the basis for continuing intellectual exchanges in this field with the setting up of the foundation of the Society of Computational Economics The Amsterdam conference certainly significantly contributed to assessing computational economics as a now established field in economics Manfred Gilli Department of Econometrics, University of Geneva, Geneva, Switzerland List of Contributors Emilio Barucci DIMADEFAS, University of Florence, Italy Paul M Beaumont Supercomputer Computations Research Institute, Florida State University, Tallahassee, FL, USA Christopher R Birchenhall School of Economic Studies, University of Manchester, United Kingdom Raymond Board Federal Reserve Board, Washington, DC, USA Patrick T Bradshaw Supercomputer Computations Research Institute, Florida State University, Tallahassee, FL, USA Are Magnus Bruaset SINTEF Applied Mathematics, Oslo, Norway Yuafan Deng Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong E Dinenis Centre for Insurance and Investment Studies, City University Business School, London, Uni ted Kingdom F J Henk Don Central Planning Bureau, The Hague, and University of Amsterdam, The Netherlands Jon Faust Federal Reserve Board, Washington, DC, USA Giampiero M Gallo Department of Statistics, University of Florence, Italy Seth A Greenblatt Cent re for Quantitative Economics and Computing, Department of Economics, University of Reading, United Kingdom x Stephen G Hall Centre for Economic Forecasting, London Business School, United Kingdom Erricos J Kontoghiorghes Centre for Insurance and Investment Studies, City University Business School, London, United Kingdom Leonardo Landi Department of Information Systems, University of Florence, Italy Mario J Miranda Department of Agricultural Economics and Rural Sociology, Ohio State University, Columbus, OH, USA Rodrigo L V Pinto Department of Computing, Imperial College, London, United Kingdom Ben; Rustem Department of Computing, Imperial College, London, United Kingdom Martin Sola Birkbeck College, London, United Kingdom Rudy M G van Stratum Central Planning Bureau, The Hague, The Netherlands Peter A Tinsley Federal Reserve Board, Washington, DC, USA Ralph Tryon Federal Reserve Board, Washington, DC, USA Arthur de Vany Institute for Mathematical Behavioral Sciences, University of California, Irvine, CA, USA Yuan Wang Center for Scientific Computing, State University of New York, Stony Brook, NY, USA 268 F.J.H DON AND R.M.G VAN STRATUM TABLE Results of model of Figure 2, K(0)=1.00, D(0)=0.399 t C -1 - o 0.546 0.546 0.546 0.546 0.546 C' D D' DP !K I'K jK G G* I 1* K 0.652 0.643 0.635 0.627 0.621 0.399 0.520 0.630 0.732 0.825 0.520 0.630 0.732 0.825 0.911 0.399 0.520 0.630 0.732 0.825 0.911 0.044 0.042 0.040 0.039 0.037 1.000 0.025 0.025 0.025 0.025 0.025 -0.956 0.017 0.015 0.014 0.012 0.269 0.269 0.269 0.269 0.269 0.321 0.317 0.313 0.309 0.306 0.258 0.257 0.257 0.256 0.255 0.247 0.247 0.247 0.247 0.247 1.000 1.048 1.093 1.135 1.175 99 0.546 0.546 1.838 1.838 1.838 0.025 0.025 0.000 0.269 0.269 0.247 0.247 1.644 100 0.546 0.546 1.838 1.838 1.838 0.025 0.025 0.000 0.269 0.269 0.247 0.247 1.644 t K' -1 - o 1.644 1.644 1.644 1.644 1.644 KP Kr A A' 1.000 1.048 1.093 1.135 1.175 1.212 1.644 1.644 1.644 1.644 1.644 -3.043 -2.982 -2.928 -2.880 -2.838 1.000 -2.055 -2.084 -2.110 -2.136 -2.159 ~ -4.043 -0.927 -0.844 -0.770 -0.702 1.227 1.227 1.227 1.227 1.227 1.000 1.028 1.042 1.055 1.068 1.080 0.227 0.199 0.185 0.172 0.159 0.500 0.488 0.478 0.469 0.461 1.000 0.390 0.390 0.390 0.390 0.390 -0.500 0.098 0.088 0.079 0.071 99 1.644 1.644 1.644 -2.454 -2.454 0.000 1.227 1.227 0.000 0.390 0.390 0.000 100 1.644 1.644 1.644 -2.454 -2.454 0.000 1.227 1.227 0.000 0.390 0.390 0.000 running a current account deficit Debt accumulates during this phase Eventuaily, net output rises sufficiently so that the trade balance shows a surplus In steady state the current account must be balanced The trade surplus is offset by interest payments on debt." The constant level of consumption is such that the present discounted value of net output minus consumption equals the initial value of debt, or equivalently that the present discounted value of current and future trade surpluses is zero A lower initial stock of capital then implies a lower present discounted value of net output Given the same initial value of debt, the constant level of total consumption declines ACKNOWLEDGEMENTS The authors gratefully acknowledge the helpful comments of Nick Draper and Berend Hasseiman SOLVING PATH-DEPENDENT MODELS 269 References Blanchard, O.J and S Fischer, 1989, Lectures on macroeconomics, The MIT Press Cooper, R.N and J.D Sachs, 1984, 'Borrowing abroad: the debtor's perspective', in G.N Smith and J.T Cuddington (Eds.), International debt and development countries Don, F.J.H., 1990, 'Some issues in solving large sparse systems of equations', Journal 0/ Economic Dynamics and Control14, 313-325 Don, F.J.H and G.M Gallo, 1987, 'Solving large sparse systems of equations in econometric models', Journal 0/ Forecasting 6, 167-180 Fair, R.C and J.B Taylor, 1983, 'Solution and maximum likelihood estimation of dynamic nonlinear rational expectations models', Econometrica 51, 1169-1185 Laffargue, J-P., 1990, 'Resolution d'un modele macroeconomique avec anticipations rationelles', Annales d'Economie et de Statistique 17, 97-119 AUTHORINDEX Abreu, D., 17 Alpert, B.K., 151 Amari, S., 177 Arifovic, J., Armstrong, J., 229, 231, 234 Arthur, B., 27,29,48 Ashby, S.F., 245 Atkinson, K.E., 208, 211 Aubin, J., 31, 32 Auscher, P., 144 Avriel, M., 108 Axelsson, 0., 246 Blanchard, O.J., 59, 230, 266 Blinder, A., 53 Bolerslev, T., 217 Booker, L., 85 Born, J., 85 Bots, A., 162 Boucekkine, R., 229, 234 Bowman, V.J., 124, 131, 133 Box, G.E.P., 164, 165 Boyd, J., 93 Bradshaw, P., 91, 92 Bresnahan, T., 27, 30 Brillet, J., 237 Brock, W., 93 Brown, C., 86 Bruaset, A.M., 246, 250 Brunner, A.D., 218 Bulirsch, R., 52 Bunch, J.R., 255 Bunn, J., 48 Byrd, R.H., 108, 114 Baldi, P., 28 Ball, 1., 66 Barnard, E., 167, 169, 186 Barnett, V., 153 Barron, A.R., 166 Barucci, E., 169 Bates, J.M., 185 Baum, E.B., 28, 169 Beaumont, P., 87, 91, 92 Becker, G., 52 Beguelin, A., 86 Belew, R., 95 Belsley, D.A., 78, 159 Bentz, Y., 172 Bera, A.K., 165 Berner, R., 230 Bertsekas, D.P., 104 Beylkin, G., 1.51, 153 Bianchini, R., 86 Binmore, K., 10, 20 Birchenhall, C., 69 Black, R., 229, 231, 234 Blair, C.E., 126 Cai, J., 218 Caplin, A., 53 Carlton, D., 53 Cavalier, T.M., 126 Chervonenkis, A.Y., 169 Choie, Y.-J., 167 Chopra, A., 30 Christiano, L., 89, 92 Chui, C.K., 158 Clark, P., 230 Clarke, M.R.B., 192, 196 Cohen, A., 144 Coifman, R., 151, 153 Coleman, W., 93 271 272 Concus, P., 245 Cooper, R.N., 258 Cuddington, J.T., 269 Daubechies, 1., 144, 145, 159 David, H.A., 154-156 David, P., 27, 48 Davis, L., 100 Day, R., 30 De Jong, K., 85 De Vany, A., 27 Deaton, A., 211 Decro, M., 125 DeI Bimbo, A., 167 Demostene, R., 162 Dert, C.L., 108, 114 Devore, R.A., 153 Diebold, F.X., 217, 226 Domowitz, 1., 58 Don, F.J.H., 233, 260, 265 Dongarra, J.J., 86, 246 Donoho, D.1., 152, 153 Doya, K., 168 Drost, F.C., 217 Dudkin, 1., 65 Duff, 1.8., 246 Dwivedi, T.D., 192 Dyer, J.8., 123, 132 Dyer, R.F., 125 Eckard, E., 59 Edgeworth, F., 33, 40 Edison, H., 230 Ehrhardt, R., 103 Ellison, G., 31, 32, 48 Engle, R.F., 165, 217 Evtushenko, Y.G., 108 Fair, R.C., 203-205, 211-214, 229, 257 Farrell, J., 27, 30 Faust, J., 234,235,238 Feldman, J., 35 Ferguson, A., 25 Fischer, S., 266 Fisher, J., 89, 92 Fisher, P., 52, 231-233 Flannery, B.P., 208, 211 Forman, E.H., 125 Forrest, S., 29, 30, 83 Foufoula-Georgiou, E., 159 Freeland, J.R., 103 Friedman, D., 10 Funaro, D., 94 Gagnon, J., 230 Gallo, G.M., 233, 265 Garbely, M., 233 Garey, M., 68 Geist, A., 70, 86 Gelatt, C., 83 Gilbert, J.R., 247, 252 Giles, D.E.A., 192, 200 Gilli, M., 233, 235 Ginzberg, M., 123 Glauber, J.W., 211 Gode, D., 52 Goffe, W.L., 139 Goldberg, D.E., 4, 77, 83 Goldfeld, S.M., 212 Golub, G.H., 192, 245, 248 Goodhart, C.A.E., 227 Gordon, R., 53, 59 Gorges-Schleuter, M., 85, 86 Granger, C.W.J., 164, 177, 185, 186 Green, E., 58 Greenstein, S., 27 Greenwald, B., 53 Grefenstette, J., 87 Gucht,D van, 82, 85 Gustafson, 1., 246 Guttorp, P., 153 Haan, den W., 93 Hadley, G., 103 273 Hall, R., 79 Hall, S.G., 218 Hamilton, J.D., 217-219, 221, 222, 226 Hammarling, S.J., 194 Hansen, L.P., 204, 207, 214 Harvey, A.C., 218 Hashem, S., 185 HaussIer, D., 169 Hawkins, D.M., 153 Hayek, F., 25 Heller, W.P., 177 Helmberger, P.G., 211 Henry, S.G.B., 227 Hernandez-Cata, E., 230 Hestenes, M.R., 245 Hinton, G.E., 167 Holland, J.H., 13,82-84 Hollinger, P., 234 Holly, S., 52 Hooker, J.N., 126 Hopfield, J., 34 Horn, R., 59 Hornik, K., 161, 166-169 Huang, G., 65 Hubbard, G., 58 Huberman, B.A., 168 Hughes Hallett, A., 52, 231, 233 Hughes, T., 31 Hunt, D.J., 195 Jain, R., 167 Jarque, C.M., 165 Jenkins, G.M., 164 Jeroslow, R.G., 126 Jog, P., 82, 85 Johnson, C., 59 Johnson, D., 68 Johnstone, I.M., 152, 153 Judd, K.L., 88, 93, 97, 207, 208 Juillard, M., 229, 234 JiJi, J., 65 Kahn, C., 230 Kahneman, D., 132 Kan, A.H.G., 108, 110, 114 Kandori, M., 10 Karp, R., 68 Kasanen, E., 133 Katz, D., 26 Kauffman, S., 27, 30 Kehagias, A., 167 Kerkyacharian, G., 152, 153 Keynes, J., 58 Kim, C., 218 Kimbrough, S.E., 126 Kirkpatrick, S., 83 Klein, 1., 229 Kok, A.G.D., 103 KaIen, J.F., 168, 170 Kontoghiorghes, E.J., 192,194,196, 197 Korhonen, P., 131-133 Korotkich, V.V., 108 Kourouklis, S., 192, 200 Koza, J.R., 17,83 Kuan, C.-M., 167, 168 Kumar, P., 159 Kwon, H.C., 221 Kwon, Y., 167 Laan, G van der, 234 Laffargue, J.-P., 229, 234, 258 Lahiri, K., 192 Lamoreux, C.G., 217 Landi, L., 167, 169 Laroque, G., 211 Lastrapes, W.D., 217 Laxton, D., 229,231, 234 Lee, C.-N., 167 Lee, R.M., 126 Lee, T.-H., 164 Lee, Y., 170, 172 Lemarechal, C., 82 Leshno, M., 161 274 Lewis, T., 153 Liebowitz, S., 30 Lindskog, G., 246 Lippmann, R.P., 168, 169 Liu, T., 177 Ljung, T., 165 Lofti, V., 132 Long, E.M.R., 194 Lowe, J.K., 126 Lu, W., 65 Lucas, C., 127 Luder, B.J., 153 Mühlenbein, H., 85 MacQueen, K.S., 195 Mailath, G.J., 10 Mallat, S.G., 140, 141, 143, 144, 150, 153 Mancheck, B., 86 Manderick, B., 85 Mani, G., 185 Mankiw, G., 66 Mansur, A., 234 Manteuffel, T.A., 245 Marcet, A., 93 Margolis, S., 30 Marquez, J., 230 Martin, P.W., 194 Mass, W., 166 Masson, P., 230 Mathias, K., 86 Matsushima, H., 17 Maynard Smith, McClelland, J., 33, 36 McCoy, E.J., 153 McCulloch, J.H., 221 McKinnon, K.I.M., 124, 126, 127, 129 Means, G., 57, 58, 61 Meier, D.C., 162 Meredith, G., 230 Miller, R., 79 Miranda, M.J., 207, 211 Mirman, 1., 93 Mitchell, W., 57 Mitra, G., 127 Mladineo, R.H., 108 Moler, C., 247, 252 Moody, J., 177 Moody, S., 127 Moskowitz, H., 131, 132 Mozer, M.C., 170 Murata, N., 177 Mustafa, M.A., 125 Muth, J.F., 205 Myung Won Kim, 170, 172 Nason, G.P., 149, 153 Nelson, D., 217 Nemhauser, G.L., 100 Nijman, T.E., 217 Okuna-Fujiwara, M., 20 Ortega, J., 231 Ostermark, R., 133 Paige, C.C., 192, 200 Pardalos, P.M., 126 Parkinson, D., 195 Patel, N., 82 Pauletto, G., 233, 235 Pearlmutter, B.A., 167 Peierls, T., 252 Perdval, D.B., 153 Perron, P., 217 Perry, M., 63 Pesaran, B., 227 Pesaran, M.H., 164 Peterson, B., 59 Peterson, R., 103 Pfeifer, R., 162 Picard, D., 152, 153 Pigou, A., 58 Pinkus, A., 161 Poddig, T., 162 275 Pollack, J.B., 170 Porter, R., 58 Portues, E.L., 103 Poston, T., 167 Potapov, M.A., 108 Potter, S.M., 164 Prasnikar, V., 20 Press, W.H., 208,211 Qualls, D., 59 Quandt, R.E., 212 Radcliffe, N., 85 Rarnanathan, R., 186 Refenes, A.N., 172 Revankar, N.S., 200 Rheinboldt, W., 231 Rinnooy Kan, A.H.G., 100 Rioul, 0., 140 Rob, R., 10 Roberts, D.M., 103 Rokhlin, V., 151, 153 Rose, D., 229, 231, 234 Rose, D.J., 255 Roternberg, J., 53, 54,58 Roth, A.R., 20 Rudin, W., 141, 142 Ruiz, E., 218 Rurnelhart, D.E., 33, 36,167, 168 Rustern, B., 135 Ryvkin, A., 65 Sachs, J.D., 258 Sah, R., 31, 32 Saloner, G., 27, 30, 58 Sang-Hoon Oh, 170, 172 Santini, S., 167 Sargent, T.J., 53, 207 Saylor, P.E., 245 Schaffer, J.D., 100, 101 Scheier, C., 162 Schrnalensee, R., 53, 79 Schrnidt, P., 192 Schnabel, R.B., 108, 114 Schnitger, G., 166 Schocken, S., 161 Schornish, M., 85 Schraudolph, N., 87, 95 Schreiber, R., 247, 252 Seber, G.A.F., 196 Sefton, M., 17 Sentana, E., 218 Shapiro, H., 26 Silver, E.A., 103 Singleton, K.J., 204, 214 Srnith, G.N., 269 Srnith, R., 82 Sola, M., 227 Sontag, E.D., 166, 170, 183 Sorensen, D.C., 246 Soyster, A.L., 126 Spiessens, P., 85 Spivakovsky, 1., 234 Spulbur , D., 53 Srivastava, V.K., 192,200 Starkweather, T., 86 Stevens, G., 230 Stewart, T.J., 132 Stiefel, E., 245 Stiglitz, J., 31, 32, 53 Stoer, J., 52 Stohr, E., 123 Strang, G., 147 Straub, P., 15 Sugden, R., 30 Suh, J., 82, 85 Sunder, S., 52 Sunderan, V., 86 Susrnel, R., 217-219,221,222,226 Syrnansky, S., 230, 238 Tanese, R., 86 Tateher, J., 79 Taylor, J.B., 88,203-205,207,211 214,229,230,257 276 Teräsvirta, T., 164 Tesler, L.G., 192 Teukolsky, S.A., 208, 211 Theil, H., 178 Timmer, G.T., 114 TinsIey, P., 56 Tobin, J., 58 Todd, M.J., 100 Tom, A., 108 Tryon, R., 230, 234, 235, 238 Tsai, W., 65 Tsiddon, D., 66 Tveito, A., 250 Tversky, A., 132 Uhlig, H., 88, 207 Vakhutinsky, 1., 65 Van Loan, C.F., 192,245,248 Vapnik, V.N., 169 Varga, R., 231 Vecchi, M, 83 Vennemo, H., 243, 244, 247 Vetterling, W.T., 208, 211 Vial, P., 144 Viitanen, S., 108 Villers de, J., 169, 186 Vincke, P., 124, 130 Vorst, H.A van der, 245, 246,250 WaIden, A.T., 153 Wallenius, H., 130-133 Waterson, M., 67 Weigend, A.S., 168 Werbos, P.J., 166, 167 Whalley, J., 234 White, H., 164, 167, 168, 220, 221 Whitin, T., 103 Whitley, D., 86 Wierzbicki, A.P., 133 Williams, H.P., 124, 126, 127, 129 Williams, J.C., 211 Williams, R.J., 167 Willig, R., 79 Wilson, G., 233 Wolfram, S., 247 Working, H., 212 Wright, B.D., 211 Va, V., 161 Yavaq, A., 17 Yoshizawa, S., 177 Yuan, L., 87 Zabinsky, Z., 82 Zamir, S., 20 Zapranis, A.D., 172 Zeleny, M., 133 Zellner, A., 192, 195 Zenios, S.A., 104 Zionts, S., 125, 132, 133 Zipser, D., 167 Zwol, W van, 162 SUBJECT INDEX behavioral convergence, 132 realism, 131-133 BiCGSTAB, 245-247,250 binary choiee, 36 block diagonal matrix, 243, 246, 250, 254 boundary value problem, 258 boundedly rational, 25 Box-Jenkins model, 162 Active Memory Technology, 196 adaptation, 30, 35 adaptive, 26, 29, 30, 32,35 algorithm banded elimination, 248 BiCGSTAB, 245-247,250 block Gauss-Seidel, 232 block Jacobi, 232, 233 column sweep, 194 distributed Jacobi, 235 Fair-Taylor, 229,232,257,258, 260, 261, 263 first-order iterative, 230, 231 Gauss-Seidel, 214, 231 genetic, 69, 81-84 hili-climbing, 82 quadratic, 212 iterative tSURE, 195 Jacobi, 52,231 multicriteria, 134 nested fixed point, 203 Newton, 211,214, 230-232,244, 260, 265 parallel Jacobi, 59, 70 pattern search, 110 renumbering, 248 reverse Cuthili-McKee ordering, 248 two level, 24.5 arbitrage equation, 211 ARCH process, 218 architecture, 28, 31, 32,48 aspiration level, 124, 133 Chebyshev approximation, 208, 210 coefficient, 210 norm, 124, 133 polynomial, 93, 208 coalition, 27,29-31,33,34,36-43, 45-48 efficient, 31, 36 emergent, 29 evolution of, 26, 36, 37, 39,41 formation of, 36 fragmented, 39 fuzzy, 31, 32, 45 globally optimal, 42 noisy evolution of, 40 noisy selection of, 45 random, 41 self-organized, 26, 36 structure, 27, 29, 33-35,42 value, 27 coding arithmetie, geometrie, mixed, collocation nodes, 207 basis functions, 92 basis polynomial, 207 277 278 column sweep, 194 commodity storage, 205, 211, 212, 214 communication cost, 68 inter-industry, 64, 65 model,59 compatibility, 28, 29, 33 compatible choice, 28, 29, 35, 37 computer system 486 PC, 238 AMT DAP51O, 192, 195 RP9000 735-48Z, 247 IBM RISC, 86 Intel Paragon, 103 MIMD, 103, 104 SIMD, 192 Solbourne 704/6E, 237 Sun, 69, 134 conditional expectation, 206 conjectural variation, 72 connectionist, 35 constraint, 26, 32-37,48 convergence, 87, 250, 251, 254 coordination, 26, 28-31,33,37,38, 42,43 cost communication, 68 holding, 105 ordering, 105 shortage, 106 covariance matrix, 192, 194, 199, 200 singular, 191 crossover, 5, 84 cubic spline, 90 DAP, 192, 195, 196, 199 decision support system, 123 denoising, 152 derivative analytic, 210 finite difference, 210 diagnostic testing, 153 direct search, 110, 114 direct solver, 245,252,254 distributed Jacobi algorithm, 235 distributed parallel genetic algorithm, 82 distributed processing, 85, 233 economic organization emergence of, 26 evolution of, 26 efficiency, 115 efficient solution, 124 emergence, 26 emergent computation, 29 property, 25 end-conddition, 260 end-condition, 258, 259 estimation maximum likelihood, 203-206, 208, 209, 211-214 method of momemts, 212 switching GARCR, 221 estimator linear unbiased, BL UE, 192 quasi maximum likelihood, 220 Euler equation, 88 residual, 89, 90 evaluation, 84 evolution, 30,31,34,36-42,45-47 evolutionary model, execution time model, 191, 192, 196-199 extended path method, 203, 204, 212, 213 Fair-Taylor algorithm, 229, 232, 235, 237, 257, 258, 260, 261, 263 feedback, 29,30, 36 279 first-order iterative algorithm, 231 fitness, 7, 33, 83 fixed-point algorithm, 203 forecasting performance, 176 forma analysis, 85 Fourier transform, 146 Fredholm equation, 99 function assembly method, 112 game coordination, 15, 26, 36, 47, 48 evolutionary, 10 network coordination, 31 symmetrie, 9, 30 GARCH model, 217 GAUCSD,87 Gauss-Legendre quadrature, 91 Gauss-Seidel algorithm, 214, 231 Gaussian elimination, 247, 254 GENESIS, 87 genetic algorithm, 4, 69, 76, 81 genetic drift, 85 global optimum, 27, 34, 37, 39, 41, 42,82,83,87 GQOPT,212 graph,28 Gray encoding, 91 Hamilton model, 218 Hamilton-Markov switching model, 218 hill-climbing, 35, 82 Householder transformations, 196, 197 hypercube, 28, 32,48 hysteresis, 258-260, 263, 264 1/0 matrix, 59 idempotent matrix, 194 ill-conditioned matrix, 96 ill-conditioned system, 96, 98, 252 image compression, 150 input-output pricing, 67 institutions, 25, 30, 48 integer programming, 126 Intel Paragon, 103, 104 interactive interface, 124 internalize, 27 inventory control systems, 103 cost, 103, 118 level, 105 model, 103 multi-item models, 104 island model, 86 iterative solver, 245, 246, 250 Jacobi algorithm, 52, 231 Jacobian, 243, 244, 247, 259 Lagrangian, 261 Lahey Fortran compiler, 212 landscape, 27, 31, 38,41,46,47 learning, 11,35, 166 least squares generalised, 192 ordinary, 195 three-stage, 199 Leontief matrix, 59 open system, 59 likelihood funetion, 206 analytic derivatives of, 209 linear unbiased estimator, 192 load balancing, 87 loeal interactions, 28 loeal optimum, 27, 37, 48 logic modelling, 124 logic programming, 125 logic-based language, 124, 128 logical eondition, 127 logical inferenee, 126 LU decomposition, 245,247 maeroeconometric model 280 MULTIMOD, 230, 238 MX-4, 229, 234 RE-7, 229-231,234 massively parallel, 191, 192, 199 Mathematica, 247 mating, 84 Matlab, 247, 252 matrix banded, 247 block diagonal, 243, 246, 250, 254 factorization, 247 partitioning, 70 permutation, 245, 250 scaling, 251,254 maximum likelihood estimation, 203206, 208, 209, 211-214 media selection problem, 124 message passing, 57 method extended path, 203, 204, 212, 213 Fair-Taylor, 257, 258, 260, 261, 263 function assembly, 112 hill-climbing, 82 Newton, 260, 265 ofmoments, 204, 205, 211-214 polynomial projection, 203-205, 207,211-214 preconditioned iterative, 246 pruning, 168 scaling, 261 sparse direct, 243,254 Spectral-Galerkin, 93 symbolic inference, 126 MIMD computer, 103, 104 mixed-integer programming, 124 model adjustment cost, 53 ARIMA,164 ARMA,I77 Box-Jenkins, 162 connectionist of coalition, 32 Cooper and Sachs, 261 disaggregated pricing, 54 extended information set, 162, 175,179 GARCH,217 optimal borrowing, 261 optimal growth, 82, 88 path-dependent, 257 rational expectations, 229,230, 257 univariate linear, 163 VAR, 55 multi-country models, 229 multicriteria problem, 123, 130, 131 MULTIMOD, 230, 238 multiple criteria decision support systems, 123 multiresolution analysis, 140 mutation, 5, 84 MX-4, 230 NAG,134 neighbors, 28, 29, 31-33, 35-37, 39,40 network,26,28-30,32-35,37,40, 41,48 neural network, 32-34,48, 166 block-structured, 167 multi-Iayer feedforward, 166 Newton's method, 208, 211, 232, 244,246,251,265 noise, 29, 31, 36, 41, 48 NP-complete, 68, 126 ob server , 26, 29 optimal growth model, 82, 88 optimization constrained, 108 global, 82, 83, 87, 108 order, 25, 26, 29-31,36, 43,48 order statistic, 154, 156 281 orthogonal basis, 94 orthogonal transformations, 191, 192, 199 outlier testing, 153, 155 parallel genetic algorithm, 85 parallel implementation, 191 parallel Jacobi algorithm, 59, 70 path-dependent search, 27 pattern search, 108 permutation matrix, 245, 250 pivoting, 245, 248 policy function, 89 polynomial approximation, 89 polynomial projection method, 203205,207,211-214 preconditioner, 246, 247, 249 predieate calculus, 126 preference function, 131 preference structure, 124 pricing, 51 asymmetrie adjustment, 56 in distributed production, 57 producer, 52 problem representation, 124 proposition al calculus, 126 pruning techniques, 168 PVM, 70, 86 QR decomposition, 192, 195, 196 quadratic cost function, 167 quasi-maximum likelihood estimator, 220 rational expectations, 203-207,211, 214,229,230,257 rational polynomial approximation, 94 RE-7,230 regression backward stepwise, 196, 197 inconsistent equation, 194 regression model seemingly unrelated, SURE, 191 triangular seemingly unrelated, tSURE,191 residual diagnostic, 165 residual norm, 251, 252 resource allocation problem, 124 reverse Cuthill-McKee ordering, 248 robust decision making, 133 rootfinding problem, 207 scaling function, 146 schemata theorem, 84 score matrix, 220 search, 31, 34,47 adaptive, 31, 82, 83 random,83 undirected, 29 search pattern, 110 search space, 27 selection, self-organized, 25, 26 service rate constraint, 107 signals, 27, 31, 32, 34, 35, 37,40, 41 SIMD computer, 192, 195 SIMPC, 263, 265 simulation, 108 simultaneous action, 32, 35 smoothing, 152 software package FortLP,135 C,134 C++,69 Fortran-Plus Enhanced, 195 GAUCSD,87 GENESIS, 87 GQOPT, 212 Lahey Fortran compiler, 212 MatClass, 69 Mathematiea, 247 Matlab, 247, 252, 254 Motif,135 282 NAG, 134 PVM, 70, 86 SIMPC, 263, 265 SunPro SPARCompiler , 69 TROLL portable, 234,237,244, 247,254 sparse linear systems, 243, 244 sparse matrix, 151 sparsity pattern, 245, 254 Spectral-Galerkin method, 93 speedup, 87, 116 squashing function, 166, 170 stationary state, 257-260,262,264266 steady state, 257, 268 stochastic communication, 74 stochastic process, 205 SURE model, 191 switching GARCH estimation, 221 symbolic inference method, 126 technology, 26, 33 trade-off, 131 training set, 166 TROLL, portable, 234, 237, 244, 247, 254 ultimatum game, 20 utility function, 123 intertemporal, 261 V-C dimension, 169 Vandermonde matrix, 96 wavelet construction of, 145, 146 Haar, 149, 155 Advances in Computational Economics A Nagurney: Network Economics A Variational Inequality Approach 1993 ISBN 0-7923-9293-0 A.K Duraiappah: Global Warming and Economic Development A Holistic Approach to International Policy Co-operation and Co-ordination 1993 ISBN 0-7923-2149-9 D.A Belsley (ed.): Computational Techniques for Econometrics and Economic Analysis 1993 ISBN 0-7923-2356-4 W.W Cooper and A.B Whinston (eds.): New Directions in Computational Economics 1994 ISBN 0-7923-2539-7 M Gilli (ed.): Computational Economic Systems Models, Methods & Econometrics 1996 ISBN 0-7923-3869-3 KLUWER ACADEMIC PUBLISHERS - DORDRECHT / BOSTON / LONDON ... The titles published in this series are listed at the end of this volume Computational Economic Systems Models, Methods & Econometrics edited by Manfred Gilli University ofGeneva, Switzerland SPRINGER-SCIENCE+BUSINESS... Computational Economics The Amsterdam conference certainly significantly contributed to assessing computational economics as a now established field in economics Manfred Gilli Department of Econometrics, ... Logical Conditions R.L V Pinto and Berc Rustem 25 51 81 103 123 Part Two: Computational Methods in Econometrics Wavelets in Econometrics: An Application to Outlier Testing Seth A Greenblatt Linear