March  2013, 18(2): 377-401. doi: 10.3934/dcdsb.2013.18.377

Hysteresis and post Walrasian economics

1. 

Department of Economics, University of Strathclyde, Glasgow G4 0GE, United Kingdom

2. 

Oxford Centre for Collaborative Applied Mathematics, University of Oxford, Oxford OX1 3LB, United Kingdom

3. 

32 Campus Drive, Department of Mathematical Sciences, University of Montana, Missoula, MT 59812, United States

4. 

Department of Applied Mathematics, University College, Cork

Received  September 2011 Revised  January 2012 Published  November 2012

The ``new consensus'' DSGE(dynamic stochastic general equilibrium) macroeconomic model has microfoundations provided by a single representative agent. In this model shocks to the economic environment do not have any lasting effects. In reality adjustments at the micro level are made by heterogeneous agents, and the aggregation problem cannot be assumed away. In this paper we show that the discontinuous adjustments made by heterogeneous agents at the micro level mean that shocks have lasting effects, aggregate variables containing a selective, erasable memory of the shocks experienced. This hysteresis framework provides foundations for the post-Walrasian analysis of macroeconomic systems.
Citation: Rod Cross, Hugh McNamara, Leonid Kalachev, Alexei Pokrovskii. Hysteresis and post Walrasian economics. Discrete & Continuous Dynamical Systems - B, 2013, 18 (2) : 377-401. doi: 10.3934/dcdsb.2013.18.377
References:
[1]

James A. Ewing, On the production of transient electric currents in iron and steel conductors by twisting them when magnetised or magnetising them when twisted,, Proceedings of the Royal Society of London, 33 (1881), 21. Google Scholar

[2]

James A. Ewing, On hysteresis in the relation of strain to stress,, Reports of the British Society for the Advancement of Science, 59 (1890), 502. Google Scholar

[3]

W. B. Haines, Studies in the physical properties of soil: V. The hysteresis effect in capillary properties, and the modes of moisture distribution associated therewith,, Journal of Agricultural Science, 20 (1930), 97. Google Scholar

[4]

R. A. Fisher, On the capillary forces in an ideal soil: Correction of formulae given by W. B. Haines,, Journal of Agricultural Science, 16 (1926), 492. doi: 10.1017/S0021859600007838. Google Scholar

[5]

W. B. Haines, Studies in the physical properties of soils. II. A note on the cohesion developed by capillary forces in an ideal soil,, Journal of Agricultural Science, 15 (1925), 529. doi: 10.1017/S0021859600082460. Google Scholar

[6]

G. A. Tompsett, L. Krogh, D. W. Griffin, and W. C. Conner, Hysteresis and scanning behavior of mesoporous molecular sieves,, Langmuir, 21 (2005), 8214. doi: 10.1021/la050068y. Google Scholar

[7]

P. Lorente, C. Delgado, M. Delmar, D. Henzel and J. Jalife, Hysteresis in the excitability of isolated guinea pig ventricular myocytes,, Circulation Research, 69 (1991), 1301. doi: 10.1161/01.RES.69.5.1301. Google Scholar

[8]

Mark S. Goldman, Joseph H. Levine, Guy Major, David W. Tank and H. S. Seung, Robust persistent neural activity in a model integrator with multiple hysteretic dendrites per neuron,, Cerebral Cortex, 13 (2003), 1185. Google Scholar

[9]

Mark A. Krasnosel'skii and Alexei V. Pokrovskii, "Systems with Hysteresis,", Springer-Verlag, (1989). Google Scholar

[10]

Isaak D. Mayergoyz, "Mathematical Models of Hysteresis,", Springer-Verlag, (1991). Google Scholar

[11]

Augusto Visintin, "Differential Models of Hysteresis,", Springer-Verlag, (1994). Google Scholar

[12]

M. Brokate and J. Sprekels, "Hysteresis and Phase Transitions,", Springer-Verlag, (1996). Google Scholar

[13]

Izaac D. Mayergoyz, "Mathematical Models of Hysteresis And Their Applications,", Elsevier, (2003). Google Scholar

[14]

Giorgio Bertotti and Isaak D. Mayergoyz, "The Science of Hysteresis,", Elsevier Academic Press, (2006). Google Scholar

[15]

Rod Cross, On the foundations of hysteresis in economic systems,, Economics and Philosophy, 9 (1993), 53. Google Scholar

[16]

Matthias Göcke, Various concepts of hysteresis applied in economics,, Journal of Economic Surveys, 16 (2002), 167. Google Scholar

[17]

R. Cross, M. Grinfeld and H. Lamba, Hysteresis and economics,, IEEE Control Systems Magazine, 29 (2009), 30. Google Scholar

[18]

Philip Mirowski, "More Heat than Light: Economics as Social Physics, Physics as Nature's Economics,", Cambridge University Press, (1989). Google Scholar

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David Colander, Hans Follmer, Armin Haas, Michael D. Goldberg, Katarina Juselius, Alan Kirman, Thomas Lux and Birgitte Sloth, The financial crisis and the systemic failure of academic economics,, University of Copenhagen Dept. of Economics Discussion Paper, (2009), 09. Google Scholar

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John Maynard Keynes, Poverty in plenty: Is the economic system self-adjusting?,, The Listener, (1934). Google Scholar

[22]

Oliver J. Blanchard, The state of macro,, MIT Dept. Economics Working Paper (SSRN eLibrary), (2008), 08. Google Scholar

[23]

K. D. Hoover, Microfoundations and the ontology of macroeconomics,, in, (2009), 386. Google Scholar

[24]

Alan Kirman, "Foreword,", in Colander [27], (). Google Scholar

[25]

Avinash K. Dixit and Robert S. Pindyck, "Investment Under Uncertainty,", Princeton University Press, (1994). Google Scholar

[26]

Alessandro Citanna, The dynamics of wealth distribution with asymmetric incentives and endogenous matching,, Economic Theory, 33 (2007), 243. doi: 10.1007/s00199-006-0133-3. Google Scholar

[27]

David Colander, editor, "Post Walrasian Macroeconomics: Beyond the Dynamic Stochastic General Equilibrium Model,'', Cambridge University Press, (2006). Google Scholar

[28]

Gonçalo L. Fonseca, The history of economic thought,, , (). Google Scholar

[29]

Irving Fisher, "Mathematical Investigation in the Theory of Value and Prices,", Yale University Press, (1925). Google Scholar

[30]

Alban William Phillips, Mechanical models in economic dynamics,, Economica, 17 (1950), 283. Google Scholar

[31]

Milton Friedman, The "plucking model'' of business fluctuations revisited,, Economic Enquiry, 31 (1993), 171. Google Scholar

[32]

James D. Hamilton, A new approach to the economic analysis of nonstationary time series and the business cycle,, Econometrica, 57 (1989), 357. doi: 10.2307/1912559. Google Scholar

[33]

Valerie Cerra and Sweta Chaman Saxena, Growth dynamics: the myth of economic recovery,, IMF Working Paper WP/05/147, (2005). Google Scholar

[34]

Guillermo A. Calvo, Alejandro Izquierdo and Ernesto Talvi, Phoenix miracles in emerging markets: Recovering without credit from systemic financial crises,, NBER Working Paper 12101, (1210). Google Scholar

[35]

Valerie Cerra and Sweta Chaman Saxena, Growth dynamics: The myth of economic recovery,, American Economic Review, 98 (2008), 439. Google Scholar

[36]

Ricardo Caballero, Emmanuel Farhi and Mohamad L. Hammour, Speculative growth: hints from the US economy ,, American Economic Review, 96 (2006), 1159. doi: 10.1257/aer.96.4.1159. Google Scholar

[37]

Charles P. Kindleberger, "Manias, Panics and Crashes: A History of Financial Crises,", Wiley, (2000). Google Scholar

[38]

Rod Cross, Hugh McNamara, Alexei V. Pokrovskii and Dmitrii Rachinskii, A new paradigm for modelling hysteresis in macroeconomic flows,, Physica B: Condensed Matter, 403 (2007), 231. Google Scholar

[39]

Ferenc Preisach, Über die magnetische nachwirkung,, Zeitschrift für Physik, 94 (1935), 277. Google Scholar

[40]

Louis Néel, Theories des lois d'aimantation de Lord Rayleigh. I: le déplacement d'une paroi isolée,, Cahiers de Physique, 12 (1942), 1. Google Scholar

[41]

Louis Néel, Theories des lois d'aimantation de Lord Rayleigh. II: Multiple domains et champ coercitif,, Cahiers de Physiqu, 13 (1943), 19. Google Scholar

[42]

Douglas H. Everett and William Ivo Whitton, A general approach to hysteresis,, Transactions of the Faraday Society, 48 (1952), 749. Google Scholar

[43]

Denis Flynn, Hugh McNamara, Phillip O'Kane and Alexei V. Pokrovskii, Application of the Preisach model to soil-moisture hysteresis,, in, (): 689. Google Scholar

[44]

Hugh McNamara, "Development and Analysis of Macroeconomic Models Incorporating Preisach Hysteresis,", PhD thesis, (2008). Google Scholar

[45]

Denis Flynn and Oleg Rasskazov, On the integration of an ODE involving the derivative of a preisach nonlinearity,, Journal of Physics: Conference Series, 22 (2005), 43. doi: 10.1088/1742-6596/22/1/003. Google Scholar

[46]

Joseph Alois Schumpeter, "Business Cycles: A Theoretical, Historical and Statistical Analysis of the Capitalist Process,", McGraw-Hill, (1939). Google Scholar

[47]

N. Gregory Mankiw, "Principles of Macroeconomics,", 4th edition, (2006). Google Scholar

[48]

Franklin M. Fisher, "Disequilibrium Foundations of Equilibrium Economics,", Economic Society Monographs. Cambridge University Press, (1989). Google Scholar

[49]

Laura Piscitelli, Michael Grinfeld, Harbir Lamba and Rod Cross, On entry and exit in response to aggregate shocks,, Applied Economics Letters, 6 (1999), 569. doi: 10.1080/135048599352619. Google Scholar

[50]

D. Flynn, O. Rasskazov, A. Zhezherun and M. Donnegan, "Systems with Hysteresis,", , (). Google Scholar

[51]

Julia Darby, Rod Cross and Laura Piscitelli, Hysteresis and unemployment: a preliminary investigation,, in, (): 667. Google Scholar

[52]

Conor Twomey, Hysteresis in consumer markets with focus on the mobile communications market,, in, (2008). Google Scholar

show all references

References:
[1]

James A. Ewing, On the production of transient electric currents in iron and steel conductors by twisting them when magnetised or magnetising them when twisted,, Proceedings of the Royal Society of London, 33 (1881), 21. Google Scholar

[2]

James A. Ewing, On hysteresis in the relation of strain to stress,, Reports of the British Society for the Advancement of Science, 59 (1890), 502. Google Scholar

[3]

W. B. Haines, Studies in the physical properties of soil: V. The hysteresis effect in capillary properties, and the modes of moisture distribution associated therewith,, Journal of Agricultural Science, 20 (1930), 97. Google Scholar

[4]

R. A. Fisher, On the capillary forces in an ideal soil: Correction of formulae given by W. B. Haines,, Journal of Agricultural Science, 16 (1926), 492. doi: 10.1017/S0021859600007838. Google Scholar

[5]

W. B. Haines, Studies in the physical properties of soils. II. A note on the cohesion developed by capillary forces in an ideal soil,, Journal of Agricultural Science, 15 (1925), 529. doi: 10.1017/S0021859600082460. Google Scholar

[6]

G. A. Tompsett, L. Krogh, D. W. Griffin, and W. C. Conner, Hysteresis and scanning behavior of mesoporous molecular sieves,, Langmuir, 21 (2005), 8214. doi: 10.1021/la050068y. Google Scholar

[7]

P. Lorente, C. Delgado, M. Delmar, D. Henzel and J. Jalife, Hysteresis in the excitability of isolated guinea pig ventricular myocytes,, Circulation Research, 69 (1991), 1301. doi: 10.1161/01.RES.69.5.1301. Google Scholar

[8]

Mark S. Goldman, Joseph H. Levine, Guy Major, David W. Tank and H. S. Seung, Robust persistent neural activity in a model integrator with multiple hysteretic dendrites per neuron,, Cerebral Cortex, 13 (2003), 1185. Google Scholar

[9]

Mark A. Krasnosel'skii and Alexei V. Pokrovskii, "Systems with Hysteresis,", Springer-Verlag, (1989). Google Scholar

[10]

Isaak D. Mayergoyz, "Mathematical Models of Hysteresis,", Springer-Verlag, (1991). Google Scholar

[11]

Augusto Visintin, "Differential Models of Hysteresis,", Springer-Verlag, (1994). Google Scholar

[12]

M. Brokate and J. Sprekels, "Hysteresis and Phase Transitions,", Springer-Verlag, (1996). Google Scholar

[13]

Izaac D. Mayergoyz, "Mathematical Models of Hysteresis And Their Applications,", Elsevier, (2003). Google Scholar

[14]

Giorgio Bertotti and Isaak D. Mayergoyz, "The Science of Hysteresis,", Elsevier Academic Press, (2006). Google Scholar

[15]

Rod Cross, On the foundations of hysteresis in economic systems,, Economics and Philosophy, 9 (1993), 53. Google Scholar

[16]

Matthias Göcke, Various concepts of hysteresis applied in economics,, Journal of Economic Surveys, 16 (2002), 167. Google Scholar

[17]

R. Cross, M. Grinfeld and H. Lamba, Hysteresis and economics,, IEEE Control Systems Magazine, 29 (2009), 30. Google Scholar

[18]

Philip Mirowski, "More Heat than Light: Economics as Social Physics, Physics as Nature's Economics,", Cambridge University Press, (1989). Google Scholar

[19]

David Colander, Hans Follmer, Armin Haas, Michael D. Goldberg, Katarina Juselius, Alan Kirman, Thomas Lux and Birgitte Sloth, The financial crisis and the systemic failure of academic economics,, University of Copenhagen Dept. of Economics Discussion Paper, (2009), 09. Google Scholar

[20]

Alfred Marshall, "Principles of Economics,", Macmillan, (1890). Google Scholar

[21]

John Maynard Keynes, Poverty in plenty: Is the economic system self-adjusting?,, The Listener, (1934). Google Scholar

[22]

Oliver J. Blanchard, The state of macro,, MIT Dept. Economics Working Paper (SSRN eLibrary), (2008), 08. Google Scholar

[23]

K. D. Hoover, Microfoundations and the ontology of macroeconomics,, in, (2009), 386. Google Scholar

[24]

Alan Kirman, "Foreword,", in Colander [27], (). Google Scholar

[25]

Avinash K. Dixit and Robert S. Pindyck, "Investment Under Uncertainty,", Princeton University Press, (1994). Google Scholar

[26]

Alessandro Citanna, The dynamics of wealth distribution with asymmetric incentives and endogenous matching,, Economic Theory, 33 (2007), 243. doi: 10.1007/s00199-006-0133-3. Google Scholar

[27]

David Colander, editor, "Post Walrasian Macroeconomics: Beyond the Dynamic Stochastic General Equilibrium Model,'', Cambridge University Press, (2006). Google Scholar

[28]

Gonçalo L. Fonseca, The history of economic thought,, , (). Google Scholar

[29]

Irving Fisher, "Mathematical Investigation in the Theory of Value and Prices,", Yale University Press, (1925). Google Scholar

[30]

Alban William Phillips, Mechanical models in economic dynamics,, Economica, 17 (1950), 283. Google Scholar

[31]

Milton Friedman, The "plucking model'' of business fluctuations revisited,, Economic Enquiry, 31 (1993), 171. Google Scholar

[32]

James D. Hamilton, A new approach to the economic analysis of nonstationary time series and the business cycle,, Econometrica, 57 (1989), 357. doi: 10.2307/1912559. Google Scholar

[33]

Valerie Cerra and Sweta Chaman Saxena, Growth dynamics: the myth of economic recovery,, IMF Working Paper WP/05/147, (2005). Google Scholar

[34]

Guillermo A. Calvo, Alejandro Izquierdo and Ernesto Talvi, Phoenix miracles in emerging markets: Recovering without credit from systemic financial crises,, NBER Working Paper 12101, (1210). Google Scholar

[35]

Valerie Cerra and Sweta Chaman Saxena, Growth dynamics: The myth of economic recovery,, American Economic Review, 98 (2008), 439. Google Scholar

[36]

Ricardo Caballero, Emmanuel Farhi and Mohamad L. Hammour, Speculative growth: hints from the US economy ,, American Economic Review, 96 (2006), 1159. doi: 10.1257/aer.96.4.1159. Google Scholar

[37]

Charles P. Kindleberger, "Manias, Panics and Crashes: A History of Financial Crises,", Wiley, (2000). Google Scholar

[38]

Rod Cross, Hugh McNamara, Alexei V. Pokrovskii and Dmitrii Rachinskii, A new paradigm for modelling hysteresis in macroeconomic flows,, Physica B: Condensed Matter, 403 (2007), 231. Google Scholar

[39]

Ferenc Preisach, Über die magnetische nachwirkung,, Zeitschrift für Physik, 94 (1935), 277. Google Scholar

[40]

Louis Néel, Theories des lois d'aimantation de Lord Rayleigh. I: le déplacement d'une paroi isolée,, Cahiers de Physique, 12 (1942), 1. Google Scholar

[41]

Louis Néel, Theories des lois d'aimantation de Lord Rayleigh. II: Multiple domains et champ coercitif,, Cahiers de Physiqu, 13 (1943), 19. Google Scholar

[42]

Douglas H. Everett and William Ivo Whitton, A general approach to hysteresis,, Transactions of the Faraday Society, 48 (1952), 749. Google Scholar

[43]

Denis Flynn, Hugh McNamara, Phillip O'Kane and Alexei V. Pokrovskii, Application of the Preisach model to soil-moisture hysteresis,, in, (): 689. Google Scholar

[44]

Hugh McNamara, "Development and Analysis of Macroeconomic Models Incorporating Preisach Hysteresis,", PhD thesis, (2008). Google Scholar

[45]

Denis Flynn and Oleg Rasskazov, On the integration of an ODE involving the derivative of a preisach nonlinearity,, Journal of Physics: Conference Series, 22 (2005), 43. doi: 10.1088/1742-6596/22/1/003. Google Scholar

[46]

Joseph Alois Schumpeter, "Business Cycles: A Theoretical, Historical and Statistical Analysis of the Capitalist Process,", McGraw-Hill, (1939). Google Scholar

[47]

N. Gregory Mankiw, "Principles of Macroeconomics,", 4th edition, (2006). Google Scholar

[48]

Franklin M. Fisher, "Disequilibrium Foundations of Equilibrium Economics,", Economic Society Monographs. Cambridge University Press, (1989). Google Scholar

[49]

Laura Piscitelli, Michael Grinfeld, Harbir Lamba and Rod Cross, On entry and exit in response to aggregate shocks,, Applied Economics Letters, 6 (1999), 569. doi: 10.1080/135048599352619. Google Scholar

[50]

D. Flynn, O. Rasskazov, A. Zhezherun and M. Donnegan, "Systems with Hysteresis,", , (). Google Scholar

[51]

Julia Darby, Rod Cross and Laura Piscitelli, Hysteresis and unemployment: a preliminary investigation,, in, (): 667. Google Scholar

[52]

Conor Twomey, Hysteresis in consumer markets with focus on the mobile communications market,, in, (2008). Google Scholar

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