IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v377y2007i1p211-226.html
   My bibliography  Save this article

On feedback and stable price adjustment mechanisms

Author

Listed:
  • Fernandez-Anaya, Guillermo
  • Alvarez-Ramirez, Jose
  • Ibarra-Valdez, Carlos

Abstract

Given an excess demand function of an economy, say Z(p), a stable price adjustment mechanism (SPAM) guarantees convergence of solution path p(t,p0) to an equilibrium peq solution of Z(p)=0. Besides, all equilibrium points of Z(p) are asymptotically stable. Some SPAMs have been proposed, including Newton and transpose Jacobian methods. Despite this powerful stability property of SPAMs, their acceptation in the economics community has been limited by a lack of interpretation. This paper focuses on this issue. Specifically, feedback control theory is used to link SPAMs and price dynamics models with control inputs, which match the economically intuitive Walrasian Hypothesis (i.e., prices change with excess demand sign). Under mild conditions, it is shown the existence of a feedback function that transforms the price dynamics into a desired SPAM. Hence, a SPAM is interpreted as a fundamental (e.g., Walrasian) price dynamics under the action of a feedback function aimed to stabilize the equilibrium set of the excess demand function.

Suggested Citation

  • Fernandez-Anaya, Guillermo & Alvarez-Ramirez, Jose & Ibarra-Valdez, Carlos, 2007. "On feedback and stable price adjustment mechanisms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 211-226.
    • Handle: RePEc:eee:phsmap:v:377:y:2007:i:1:p:211-226
    DOI: 10.1016/j.physa.2006.10.088
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437106011563
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2006.10.088?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. N/A, 1976. "Chapter III. the World Economy," National Institute Economic Review, National Institute of Economic and Social Research, vol. 75(1), pages 33-63, February.
    2. Hommes, Cars H., 1991. "Adaptive learning and roads to chaos : The case of the cobweb," Economics Letters, Elsevier, vol. 36(2), pages 127-132, June.
    3. N/A, 1976. "Chapter I. The Home Economy," National Institute Economic Review, National Institute of Economic and Social Research, vol. 76(1), pages 6-24, May.
    4. Marcet, Albert & Sargent, Thomas J., 1989. "Convergence of least squares learning mechanisms in self-referential linear stochastic models," Journal of Economic Theory, Elsevier, vol. 48(2), pages 337-368, August.
    5. Schonhofer, Martin, 1999. "Chaotic Learning Equilibria," Journal of Economic Theory, Elsevier, vol. 89(1), pages 1-20, November.
    6. Mukherji, Anjan, 1995. "A Locally Stable Adjustment Process," Econometrica, Econometric Society, vol. 63(2), pages 441-448, March.
    7. Goeree, Jacob K. & Hommes, Cars & Weddepohl, Claus, 1998. "Stability and complex dynamics in a discrete tatonnement model," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 395-410, January.
    8. N/A, 1976. "Chapter II. The World Economy," National Institute Economic Review, National Institute of Economic and Social Research, vol. 78(1), pages 21-39, November.
    9. Taylor, John B, 1979. "Estimation and Control of a Macroeconomic Model with Rational Expectations," Econometrica, Econometric Society, vol. 47(5), pages 1267-1286, September.
    10. Neugart, Michael, 2004. "Complicated dynamics in a flow model of the labor market," Journal of Economic Behavior & Organization, Elsevier, vol. 53(2), pages 193-213, February.
    11. Sonnemans, Joep & Hommes, Cars & Tuinstra, Jan & van de Velden, Henk, 2004. "The instability of a heterogeneous cobweb economy: a strategy experiment on expectation formation," Journal of Economic Behavior & Organization, Elsevier, vol. 54(4), pages 453-481, August.
    12. Brown, Donald J., 1997. "Three Lectures on the Walrasian Hypotheses for Exchange Economies," Center Discussion Papers 28459, Yale University, Economic Growth Center.
    13. Jarsulic, Marc, 1993. "A nonlinear model of the pure growth cycle," Journal of Economic Behavior & Organization, Elsevier, vol. 22(2), pages 133-151, October.
    14. Smale, Steve, 1976. "A convergent process of price adjustment and global newton methods," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 107-120, July.
    15. N/A, 1976. "Chapter I. The Home Economy," National Institute Economic Review, National Institute of Economic and Social Research, vol. 78(1), pages 6-20, November.
    16. Hommes, Cars H. & Rosser,, J. Barkley, 2001. "Consistent Expectations Equilibria And Complex Dynamics In Renewable Resource Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 5(02), pages 180-203, April.
    17. N/A, 1976. "Chapter I. The Home Economy," National Institute Economic Review, National Institute of Economic and Social Research, vol. 77(1), pages 7-32, August.
    18. N/A, 1976. "Chapter II. The World Economy," National Institute Economic Review, National Institute of Economic and Social Research, vol. 76(1), pages 25-44, May.
    19. Samuelson, Paul A, 1976. "Economics of Forestry in an Evolving Society," Economic Inquiry, Western Economic Association International, vol. 14(4), pages 466-492, December.
    20. anonymous, 1976. "The economy in 1975," Federal Reserve Bulletin, Board of Governors of the Federal Reserve System (U.S.), issue Feb, pages 71-81.
    21. Saari, Donald G & Simon, Carl P, 1978. "Effective Price Mechanisms," Econometrica, Econometric Society, vol. 46(5), pages 1097-1125, September.
    22. N/A, 1976. "Chapter II. The World Economy," National Institute Economic Review, National Institute of Economic and Social Research, vol. 77(1), pages 33-49, August.
    23. Day, Richard H, 1982. "Irregular Growth Cycles," American Economic Review, American Economic Association, vol. 72(3), pages 406-414, June.
    24. Paul A. Samuelson, 1976. "Alvin Hansen as a Creative Economic Theorist," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(1), pages 24-31.
    25. Brown, D.J., 1997. "Three Lectures on the Walrasian Hypotheses for Exchange Economies," Papers 782, Yale - Economic Growth Center.
    26. Medio, Alfredo, 1991. "Continuous-time models of chaos in economics," Journal of Economic Behavior & Organization, Elsevier, vol. 16(1-2), pages 115-151, July.
    27. Jess Benhabib & Richard H. Day, 1981. "Rational Choice and Erratic Behaviour," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(3), pages 459-471.
    28. Mackey, Michael C., 1989. "Commodity price fluctuations: Price dependent delays and nonlinearities as explanatory factors," Journal of Economic Theory, Elsevier, vol. 48(2), pages 497-509, August.
    29. Taylor, John B., 1993. "Discretion versus policy rules in practice," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 39(1), pages 195-214, December.
    30. Negroni, Giorgio, 2003. "Adaptive expectations coordination in an economy with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 28(1), pages 117-140, October.
    31. Martin Schonhofer, "undated". "Chaotic Learning Equilibria," Computing in Economics and Finance 1997 121, Society for Computational Economics.
    32. Hommes, Cars H., 1994. "Dynamics of the cobweb model with adaptive expectations and nonlinear supply and demand," Journal of Economic Behavior & Organization, Elsevier, vol. 24(3), pages 315-335, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Feldstein, Martin, 1995. "The Effect of Marginal Tax Rates on Taxable Income: A Panel Study of the 1986 Tax Reform Act," Journal of Political Economy, University of Chicago Press, vol. 103(3), pages 551-572, June.
    2. Krätschmer, Volker, 2006. "Strong consistency of least-squares estimation in linear regression models with vague concepts," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 633-654, March.
    3. Feldstein, Martin, 1995. "The Effect of Marginal Tax Rates on Taxable Income: A Panel Study of the 1986 Tax Reform Act," Journal of Political Economy, University of Chicago Press, vol. 103(3), pages 551-572, June.
    4. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    5. Calzolari, Giorgio, 2012. "Econometric notes," MPRA Paper 71440, University Library of Munich, Germany.
    6. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    7. Buhong Zheng, 1997. "Statistical Inferences for Poverty Measures with Relative Poverty Rates," LIS Working papers 167, LIS Cross-National Data Center in Luxembourg.
    8. Tamotsu Onozaki, 2018. "Nonlinearity, Bounded Rationality, and Heterogeneity," Springer Books, Springer, number 978-4-431-54971-0, April.
    9. Cars H. Hommes, 2009. "Bounded Rationality and Learning in Complex Markets," Chapters, in: J. Barkley Rosser Jr. (ed.), Handbook of Research on Complexity, chapter 5, Edward Elgar Publishing.
    10. Cavalli, Fausto & Naimzada, Ahmad, 2015. "A tâtonnement process with fading memory, stabilization and optimal speed of convergence," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 116-129.
    11. Hommes, Cars H. & Rosser,, J. Barkley, 2001. "Consistent Expectations Equilibria And Complex Dynamics In Renewable Resource Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 5(02), pages 180-203, April.
    12. Orlando Gomes, 2010. "Ordinary Least Squares Learning And Nonlinearities In Macroeconomics," Journal of Economic Surveys, Wiley Blackwell, vol. 24(1), pages 52-84, February.
    13. M. Grazia Pittau & Roberto Zelli, 2001. "Income distribution in Italy: A nonparametric analysis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 10(1), pages 175-189, January.
    14. Gomes, Orlando, 2009. "Adaptive learning and complex dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1206-1213.
    15. Eric Ghysels & Norman R. Swanson & Myles Callan, 2002. "Monetary Policy Rules with Model and Data Uncertainty," Southern Economic Journal, John Wiley & Sons, vol. 69(2), pages 239-265, October.
    16. Dieci, Roberto & Westerhoff, Frank, 2010. "Interacting cobweb markets," Journal of Economic Behavior & Organization, Elsevier, vol. 75(3), pages 461-481, September.
    17. Hommes, Cars, 2018. "Carl’s nonlinear cobweb," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 7-20.
    18. Orlando Gomes, 2009. "The timing of information updates: a stability result," Economics Bulletin, AccessEcon, vol. 29(4), pages 2860-2869.
    19. Herings, P. Jean-Jacques & van der Laan, Gerard & Venniker, Richard, 1996. "The Transition from a Drèze Equilibrium to a Walrasian Equilibrium," LIDAM Discussion Papers IRES 1996013, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    20. Jan Tuinstra & Florian Wagener, 2007. "On learning equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(3), pages 493-513, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:377:y:2007:i:1:p:211-226. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.