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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[9]

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

[10]

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

[11]

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

[12]

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

[13]

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

[14]

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

[15]

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

[16]

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

[17]

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

[18]

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

[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.

[20]

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

[21]

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

[22]

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

[23]

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

[24]

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

[25]

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

[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.

[27]

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

[28]

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

[29]

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

[30]

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

[31]

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

[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.

[33]

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

[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).

[35]

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

[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.

[37]

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

[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.

[39]

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

[40]

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

[41]

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

[42]

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

[43]

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

[44]

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

[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.

[46]

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

[47]

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

[48]

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

[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.

[50]

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

[51]

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

[52]

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

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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[9]

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

[10]

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

[11]

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

[12]

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

[13]

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

[14]

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

[15]

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

[16]

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

[17]

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

[18]

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

[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.

[20]

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

[21]

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

[22]

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

[23]

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

[24]

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

[25]

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

[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.

[27]

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

[28]

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

[29]

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

[30]

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

[31]

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

[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.

[33]

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

[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).

[35]

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

[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.

[37]

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

[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.

[39]

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

[40]

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

[41]

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

[42]

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

[43]

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

[44]

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

[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.

[46]

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

[47]

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

[48]

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

[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.

[50]

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

[51]

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

[52]

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

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