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An agent-based “proof of principle” for Walrasian macroeconomic theory

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If the economy were always in macroeconomic equilibrium then perhaps the full-employment money-and-growth models of recent vintage would suffice to explain the time paths of the money wage and the price level. But since any actual economy is almost continuously out of equilibrium we need also to study wage and price dynamics under arbitrary conditions.

(Phelps 1968, p. 678).

Abstract

Macroeconomic models are typically solved through the imposition of a top-down general equilibrium solution constraining agents’ rational behavior. This is customarily obtained by recurring, explicitly or not, to the Walrasian auctioneer artifice. In this paper we aim at contributing to the small but burgeoning literature that deals with the consequences of removing it from the start by means of agent-based techniques. We let the textbook full-employment neoclassical macroeconomic model be populated by a large number of bounded-rational, autonomous agents, who are repeatedly engaged in decentralized transactions in interrelated markets. We set up a computational laboratory to perform several experiments, whose designs differ as regards the way we treat learning on the one side, and the institutional arrangement determining who—between firms and workers—is bound to bear the risk associated to incomplete markets on the other one. We show that our fully decentralized multi-market system admits the possibility to attain the Walrasian full-employment solution, but also that serious coordination failures emerge endogenously as learning mechanisms and institutional settings are varied.

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Notes

  1. For standard handbook treatment, see e.g. Wickens (2008, Chap. 2–4).

  2. The logical inversion between price formation and actual trades at the root of the Walrasian approach to macroeconomics does not depend on the market structure. It holds true also for monopolistic competition models, where transactions occur only after the Bertrand-Nash equilibrium price has been somehow calculated by all players.

  3. Leijonhufvud (1993, 2006) and Howitt (2006) strongly advocate this approach for macroeconomic analysis.

  4. Tesfatsion (2006) argues that agent-based models could also be used to provide: (i) empirical understanding; (ii) normative understanding; (iii) methodological advancement.

  5. On this point see also Howitt (2012).

  6. One characterized, in the parlance of John Maurice Clark, by an irrational passion for dispassionate rationality.

  7. See Axtell (2005) for an introduction to this issue, as well as for some computational analysis linked to the literature on Edgeworth k-lateral re-contracting schemes, which were originally conceived as a valid alternative to Walrasian microfoundations of macroeconomic analysis (Weintraub 1977), but that have apparently felt into oblivion thereafter.

  8. See Colander et al. (2008) and (2009) for two recent items from a quite long list. A comprehensive parade of arguments is presented in Colander (2006).

  9. For a growing economy, stationarity should be clearly defined in terms of great ratios.

  10. See, for instance, Lian and Plott (1998) and Noussair et al. (2007).

  11. A comprehensive discussion this issue can be found in chapters 1 and 2 of Delli Gatti et al. (2011).

  12. The collection of papers contained in Colander (2006) provides a definition and a comprehensive discussion of the topic.

  13. See Theorems 3.7 and 3.8 in Kulkarni (1995).

  14. A third obvious possibility is that the ergodic distribution is degenerate, in that the absorbing class contains just one state.

  15. Of course, the result one obtains from allowing agents to learn according to different mechanisms is univocal when the Markov chain admits just one aborbing class C.

  16. In our simulations, observed actions and payoffs are evaluated by means of a moving average over the last three periods. Different orders do not return significantly differences.

  17. The codes can be downloaded from the website http://www.gaffeo.altervista.org/research.html

  18. A different, but mutually compatible, interpretation can be offered along the lines developed by Witt (1997), who discusses how fluctuations in aggregate activity are in fact fully coherent with the idea of spontaneous order developed by Friedrich A. Hayek. Further explorations in this direction are left for further research.

  19. The repetitions with different seeds have been performed for the model with a parameterization identical to the one presented in Table 1.

  20. In order to save space, from now on we will present only results for selected variables. The whole set of results is available upon request.

  21. This result is particularly interesting given that, as reported in Table 2, the first and second moments of the distributions associated to this variable are very similar under the various scenarios. The dissimilarity between distributions must therefore be attributed to the moments higher than the second one.

  22. We limit the Montercarlo exercise in this section to a sample size equal to 100 due to its computational expensiveness. This explain the small deviations of averages from the ones reported in Table 2.

References

  • Ashraf Q, Gershman B, Howitt P (2013) How inflation affects macroeconomic performance: an agent-based computational investigations, mimeo, Brown University

  • Axtell R (2005) The complexity of exchange. Econ J 115:F193–F210

    Article  Google Scholar 

  • Blanchard O (2009) The state of macro. Annu Rev Econ 1:209–228

    Article  Google Scholar 

  • Blanchard O, Kiyotaki N (1987) Monopolistic competition and the effect of aggregate demand. Am Econ Rev 77:647–666

    Google Scholar 

  • Borio C, Disyatat P (2010) Unconventional monetary policies: an appraisal. Manch Sch 78:53–89

    Google Scholar 

  • Bosch-Domènech A, Sunder S (2000) Tracking the invisible hand: convergence of double auctions to competitive equilibrium. Comput Econ 16:257–284

    Article  Google Scholar 

  • Bowles S, Gintis H (2000) Walrasian economics in retrospect. Q J Econ 115:1411–1439

    Article  Google Scholar 

  • Clower R, Howitt P (1998) Keynes and the classics: an end of century view. In: Ahiakpor J (ed) Keynes and the classics reconsidered. Kluwer, Boston

    Google Scholar 

  • Colander D (ed) (2006) Post Walrasian macro: beyond the DSGE model. Cambridge University Press, Cambridge

    Google Scholar 

  • Colander D, Föllmer H, Goldberg M, Haas A, Juselius F, Kirman A, Lux T, Sloth B (2009) The financial crisis and the systemic failure of academic economics, Kiel Institute for the World Economy Working Paper 1489

  • Colander D, Howitt P, Kirman A, Leijonhufvud A, Mehrling P (2008) Beyond DSGE models: toward an empirically based macroeconomics. Am Econ Rev 98:236–240

    Article  Google Scholar 

  • Davis D, Holt C (1996) Markets with posted prices: recent results from the laboratory. Investig Econ 20:291–320

    Google Scholar 

  • Delli Gatti D, Desiderio S, Gaffeo E, Cirillo P, Gallegati M (2011) Macroeconomics from the bottom-up. Springer, Berlin

    Book  Google Scholar 

  • Diamond P (1971) A model of price adjustment. J Econ Theory 3:156–168

    Article  Google Scholar 

  • Dopfer K (2004) The economic agent as rule maker and rule user: Homo sapiens oeconomicus. J Evol Econ 14:177–196

    Article  Google Scholar 

  • Dosi G, Fagiolo G, Roventini A (2010) Schumpeter meeting Keynes: a policy-friendly model of endogenous growth and business cycles. J Econ Dyn Control 34:1748–1767

    Article  Google Scholar 

  • Epstein J (2006) Generative social science. Studies in agent-based computational modeling. Princeton University Press, Princeton

    Google Scholar 

  • Galand G (2009) The neutrality of money revisited with a bottom-up approach: decentralization, limited information and bounded rationality. Comput Econ 33:337–360

    Article  Google Scholar 

  • Gintis H (2007) The dynamics of general equilibrium. Econ J 117:1280–1309

    Article  Google Scholar 

  • Gintis H (2012) Agent-based models as Markov processes: theory and application to the dynamics of market exchange. Santa Fe Institute and Central European University, Mimeo

    Google Scholar 

  • Gode D, Sunder S (1993) Allocative efficiency of markets with zero intelligence (ZI) traders: markets as a partial substitute for individual rationality. J Polit Econ 101:119–137

    Article  Google Scholar 

  • Golman R, Page S (2010) Basins of attraction and equilibrium selection under different learning rules. J Evol Econ 20:49–72

    Article  Google Scholar 

  • Grazzini J (2012) Analysis of the emergent properties: stationarity and ergodicity. J Artif Soc Soc Simul 15(2):7

    Google Scholar 

  • Hall R (1991) Booms and recessions in a noisy economy. Yale University Press, New Heaven

    Google Scholar 

  • Hodgson J (1997) The ubiquity of habits and rules. Camb J Econ 21:663–684

    Article  Google Scholar 

  • Hopkins E, Seymour R (2002) The stability of price dispersion under seller and consumer learning. Int Econ Rev 19:46–76

    Google Scholar 

  • Howitt P (2006) Coordination issues in long-run growth. In: Tesfatsion L, Judd K (eds) Handbook of computational economics: agent-based computational economics. Elsevier, Amsterdam

    Google Scholar 

  • Howitt P (2012) What have central bankers learned from modern macroeconomic theory? J Macroecon 34:11–22

    Article  Google Scholar 

  • Izquierdo L, Izquierdo S, Galàn J, Santos J (2009) Techniques to understand computer simulations: Markov chain analysis. J Artif Soc Soc Simul 12(1):6

    Google Scholar 

  • Ketchman J, Smith V, Williams A (1984) A comparison of posted-offer and double-auction pricing institutions. Rev Econ Dyn 51:595–614

    Google Scholar 

  • Kulkarni V (1995) Modeling and analysis of stochastic systems. Chapman & Hall, New York

    Google Scholar 

  • LeBaron B, Tesfatsion L (2008) Modeling macroeconomies as open-ended dynamic systems of interacting agents. Am Econ Rev 98:256–260

    Article  Google Scholar 

  • Leijonhufvud A (1993) Towards a not-too-rational macroeconomics. South Econ J 60:1–13

    Article  Google Scholar 

  • Leijonhufvud A (2006) Agent-based macro. In: Tesfatsion L, Judd K (eds) Handbook of computational economics: agent-based computational economics. Elsevier, Amsterdam

    Chapter  Google Scholar 

  • Lian P, Plott C (1998) General equilibrium, markets, macroeconomics and money in a laboratory experimental environment. Econ Theory 12:21–75

    Article  Google Scholar 

  • Lucas R, Sargent T (1979) After Keynesian macroeconomics. Fed Reserv Bank Minneap Q Rev 3:1–16

    Google Scholar 

  • Mayr E (1988) Toward a new philosophy of biology: observations of an evolutionist. Harvard University Press, Cambridge

    Google Scholar 

  • Meaning J, Zhu F (2011) The impact of recent central bank asset purchase programmes. BIS Q Rev 3:73–83

    Google Scholar 

  • Murphy K, Shleifer A, Vishny R (1989) Industrialization and the big push. J Polit Econ 97:1003–1026

    Article  Google Scholar 

  • Noussair C, Plott C, Riezman R (2007) Production, trade, prices, exchange rates and equilibration in large experimental economies. Eur Econ Rev 51:49–76

    Article  Google Scholar 

  • Phelps E (1968) Money-wage dynamics and labor-market equilibrium. J Polit Econ 76:678–711

    Article  Google Scholar 

  • Phelps E (1969) The new microeconomics in inflation and employment theory. Am Econ Rev 59:147–160

    Google Scholar 

  • Phelps E (2007) Macroeconomics for a modern economy. Am Econ Rev 97:543–561

    Article  Google Scholar 

  • Phelps E et al (1970) Microeconomic foundations of employment and inflation. Norton, New York

    Google Scholar 

  • Plot C (1986) The posted-offer trading institution. Science 232:732–738

    Article  Google Scholar 

  • Saari D (1985) Iterative price mechanism. Econometrica 53:1117–1131

    Article  Google Scholar 

  • Saari D (1992) The aggregated excess demand function and other aggregation procedures. Econ Theory 2:359–388

    Article  Google Scholar 

  • Saari D, Simon P (1978) Effective price mechanism. Econometrica 46:1097–1125

    Article  Google Scholar 

  • Salop S, Stiglitz J (1977) Bargains and ripoffs: a model of monopolistically competitive price dispersion. Rev Econ Stud 44:493–510

    Article  Google Scholar 

  • Smith V (1981) An empirical study of decentralized institutions of monopoly restraint. In: Quirk J, Horwich G (eds) Essays in contemporary fields of economics in honor of E. T. Weiler (1914–1979). Purdue University Press, West Lafayette

    Google Scholar 

  • Smith V (1982) Microeconomic systems as an experimental science. Am Econ Rev 72:923–955

    Google Scholar 

  • Sprigg J Jr, Ehlen M (2007) Comparative dynamics in an overlapping-generation model: the effects of quasi-rational discrete choice on finding and maintaining Nash equilibrium. Comput Econ 29:69–96

    Article  Google Scholar 

  • Tesfatsion L (2006) Agent-based computational economics: a constructive approach to economic theory. In: Tesfatsion L, Judd K (eds) Handbook of computational economics: agent-based computational economics. Elsevier, Amsterdam

    Google Scholar 

  • Vanberg V (2002) Rational choice vs. program-based behavior: alternative theoretical approaches and their relevance for the study of institutions. Ration Soc 14:7–53

    Article  Google Scholar 

  • Vriend N (2000) An illustration of the essential difference between individual and social leraning, and its consequences for computational analysis. J Econ Dyn Control 24:1–19

    Article  Google Scholar 

  • Weintraub R (1977) The microfoundations of macroeconomics: a critical survey. J Econ Lit 15:1–23

    Google Scholar 

  • Wickens M (2008) Macroeconomic theory. A dynamic general equilibrium approach. Princeton University Press, Princeton

    Google Scholar 

  • Witt U (1997) The Hayekian puzzle: spontaneous order and the business cycle. Scott J Polit Econ 44:44–58

    Article  Google Scholar 

  • Woodford M (2009) Convergence in macroeconomics: elements of the new synthesis. Am Econ J 1:267–279

    Google Scholar 

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Authors and Affiliations

  1. Department of Economics, University of Trento, Via Inama 5, 38100, Trento, Italy

    Edoardo Gaffeo

  2. Università Politecnica delle Marche, Ancona, Italy

    Mauro Gallegati

  3. University of Waterloo, Waterloo, Canada

    Umberto Gostoli

Authors
  1. Edoardo Gaffeo
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  2. Mauro Gallegati
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  3. Umberto Gostoli
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Correspondence to Edoardo Gaffeo.

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Gaffeo, E., Gallegati, M. & Gostoli, U. An agent-based “proof of principle” for Walrasian macroeconomic theory. Comput Math Organ Theory 21, 150–183 (2015). https://doi.org/10.1007/s10588-014-9180-7

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