Learning, Expectations, and Endogenous Business Cycles

Doshchyn, Artur and Giommetti, Nicola (2013): Learning, Expectations, and Endogenous Business Cycles.

Abstract

We show that business cycles can emerge and proliferate endogenously in the economy due to the way economic agents learn, form their expectations, and make decisions regarding savings and production for future periods. There are no exogenous shocks of any kind to productivity or any other fundamental parameters of the economy, in contrast to Real Business Cycle models. To our knowledge this thesis is the first attempt to formally introduce adaptive learning and expectation errors as an autonomous source of endogenous business cycles.

We develop a simple, growth-less macroeconomic model, in which agents do not have perfect foresight, learn adaptively to form expec- tations, and solve limited inter-temporal optimization models. The theoretical possibility of cycles largely arises from the nonlinearity of the actual law of motion of price, in particular from the fact that agents always overpredict (underpredict) future prices when they are higher (lower) than equilibrium level. Even though the main version of the model is based on households having a simple logarithmic utility func- tion, we also show that the results hold when a more generic Hyperbolic Absolute Risk Aversion utility function is chosen. Money stock is neutral in the long run in either case.

We conduct simulations in models with agents having both simple logarithmic and HARA utility functions. Following Thomas Sargent (1993), we assume agents to be “rational econometricians” using various econometric adaptive learning tools: Auto ARIMA, VAR and AR(2) models. In all simulations, output and other economic variables indeed display cyclical fluctuations around their equilibrium levels.

Both converging and diverging cycles may be obtained in simulations with Auto ARIMA models, while the VAR learning tool leads to diverging fluctuations in the majority of cases, suggesting that making agents consider several variables increases instability, at least in our setting. It is also observed that higher frequency of model switching is usually accompanied with increasing amplitude of cycles, suggesting the hypothesis that economic crises may happen when agents make drastic revisions of their beliefs about how the economy works. Only converging cycles can be obtained with AR(2), however in this case the economy may get trapped in a so called “false equilibrium”, with output way below or above the true equilibrium level. Even though this is not formally an equilibrium, the convergence towards the true one is so slow that exogenous shocks may be needed to move the economy back on track. This result is in line with the Keynesian view that the economy may remain in a depressed state for quite a long period of time, and active government intervention may be required to speed up the recovery.

Within the developed framework we analyze whether active mone- tary policy (i.e. changes in money stock) can be used for stabilization purposes. It turns out that in the simple case, when agents have loga- rithmic utility function, shifts in money supply can have real effects on the economy only if they are unexpected by agents, or if future price expectations are not adjusted exactly proportionally to the announced monetary interventions. We also show that the second case is not sus- tainable within the adaptive learning environment, so that monetary policy may become ineffective in the long run when, and if, learning is complete.

We prove, however, that monetary interventions always have real effects in the short run in the setting with a more generic HARA utility function. Still, it is highly questionable whether the central bank is able to accurately assess the consequences of its own actions, as that would require it knowing precisely the actual law of motion of the economy, current market’s expectations, and agents’ reaction to news about the upcoming monetary interventions, which, moreover, can change over time.

• Item Type: MPRA Paper
• Language: English
• Keywords: learning; expectations; endogenous business cycles; monetary policy
• Subjects: D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D83 - Search ; Learning ; Information and Knowledge ; Communication ; Belief ; Unawareness; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D84 - Expectations ; Speculations; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E32 - Business Fluctuations ; Cycles; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E37 - Forecasting and Simulation: Models and Applications; E - Macroeconomics and Monetary Economics > E5 - Monetary Policy, Central Banking, and the Supply of Money and Credit > E52 - Monetary Policy

References

Andolfatto, D. (1996). Business cycles and labor-market search. American Economic Review, 86(1):112–32.

Barro, R. J. (1980). A capital market in an equilibrium business cycle model. Econometrica, 48(6):1393–1417.

Beaudry, P. and Portier, F. (2004). An exploration into Pigou’s theory of cycles. Journal of Monetary Economics, 51(6):1183–1216.

Benhabib, J. and Farmer, R. E. (1999). Indeterminacy and sunspots in macroeconomics. In Taylor, J. B. and Woodford, M., editors, Handbook of Macroeconomics, Handbook of Macroeconomics, chapter 6, pages 387–448. Elsevier.

Black, F. (1982). General equilibrium and business cycles. National Bureau of Economic Research, NBER Working Paper No. 950.

Brunner, K., Cukierman, A., and Meltzer, A. H. (1983). Money and economic activity, inventories and business cycles. Journal of Monetary Economics, 11(3):281–319.

Buiter, W. (2009). The unfortunate uselessness of most ‘state of the art’ academic monetary economics. Financial TImes. Willem Buier’s Maverecon.

Cellarier, L. L. (2008). Least squares learning and business cycles. Journal of Economic Behavior and Organization, 68(3-4):553–564.

Cogley, T. and Nason, J. M. (1995). Output dynamics in real-business-cycle models. American Economic Review, 85(3):492–511.

Cuthbertson, K. and Nitzsche, D. (2004). Quantitative Financial Economics: Stocks, Bonds and Foreign Exchange. Wiley, 2nd edition. Dosi, G., Fagiolo, G., and Andrea, R. (2006). An evolutionary model of endogenous business cycles. Computational Economics, 27(1):3–34.

Elmendorf, D. W. (1996). The effect of interest-rate changes on household saving and consumption: a survey. Board of Governors of the Federal Reserve System (U.S.), Finance and Economics Discussion Series: 96-27.

Eusepi, S. and Preston, B. (2011). Expectations, learning, and business cycle fluctuations. American Economic Review, 101(6):2844–2872.

Evans, G. W. and Honkapohja, S. (2001). Learning and Expectations in Macroeconomics. Frontiers of Economic Research. Princeton University Press.

Evans, G. W. and Honkapohja, S. (2009). Learning and macroeconomics. Annual Review of Economics, 1(5):421–451.

Farmer, R. E. A. and Guo, J.T. (1994). Real business cycles and the animal spirits hypothesis. Journal of Economic Theory, 63(1):42–72.

Grandmont, J.-M. (1985). On endogenous competitive business cycles. Econometrica, 53(5):995–1045.

Hansen, G. D. (1985). Indivisible labor and the business cycle. Journal of Monetary Economics, 16(3):309–327.

Hayek, F. (1931). Prices and Production. 2nd ed. Routledge, London. Hicks, J. R. (1950). A Contribution to the Theory of the Trade Cycle. Clarendon Press, Oxford.

Howitt, P. and McAfee, R. P. (1992). Animal spirits. American Economic Review, 82(3):493–507.

Huang, K. X., Liu, Z., and Zha, T. (2009). Learning, adaptive expectations and technology shocks. Economic Journal, 119(536):377–405.

Jaimovich, N. and Rebelo, S. (2007). Behavioral theories of the business cycle. Journal of the European Economic Association, 5(2-3):361–368. Juglar, C. (1862). Des Crises commerciales et leur retour periodique en France, en Angleterre, et aux Etats-Unis. Guillaunim, Paris.

Keynes, J. M. (1936). The General Theory of Employment, Interest and Money. Macmillan, London.

Kydland, F. E. and Prescott, E. . (1982). Time to build and aggregate fluctuations. Econometrica, 50(6):1345–1370.

Lengnick, M. (2011). Agent-based macroeconomics - a baseline model. Economics Working Papers, Christian-Albrechts-University of Kiel, Department of Economics, No. 2011-04.

Long, J. B. and Plosser, C. L. (1983). Real business cycles. Journal of Political Economy, 91(1):39–69.

Lucas, R. J. (1972). Expectations and the neutrality of money. Journal of Economic Theory, 4(2):103–124.

Lucas, R. J. (1973). Some international evidence on output-inflation tradeoffs. American Economic Review, 63(3):326–334.

Lucas, R. J. (1975). An equilibrium model of the business cycle. Journal of Political Economy, 83(5):1113–1144.

Lucas, R. J. (1976). Econometric policy evaluation: A critique. Carnegie- Rochester Conference Series on Public Policy, 1(1):19–46.

Malthus, T. R. (1836). Principles of Political Economy. 2rd ed. William Pickering, London.

Marcet, A. and Sargent, T. J. (1989). Convergence of least squares learning mechanisms in self-referential linear stochastic models. Journal of Economic Theory, 48(2):337–368.

Merz, M. (1995). Search in the labor market and the real business cycle. Journal of Monetary Economics, 36(2):269–300.

Milani, F. (2011). Expectation shocks and learning as drivers of the business cycle. Economic Journal, 121(552):379–401.

Mises, L. (1912). The Theory of Money and Credit. (H.E. Batson, trans.) Liberty Fund, Indianapolis, 1981.

Mitchell, W. C. (1927). Business Cycles: The Problem and Its Setting. National Bureau of Economic Research.

Mortensen, D. T. and Pissarides, C. A. (1994). Job creation and job destruction in the theory of unemployment. Review of Economic Studies, 61(3):397–415.

Muth, J. F. (1961). Rational expectations and the theory of price movements. Econometrica, 29(6):315–335.

Paul, O. (2003). The us business cycle: an agent-based model of heterogenous firms operating under uncertainty. Society for Computational Economics, Computing in Economics and Finance 2003, N.90.

Pigou, A. C. (1927). Industrial Fluctuations. Macmillan, London. Prescott, E. C. (1986). Theory ahead of business cycle measurement. Carnegie-Rochester Conference Series on Public Policy.

Ricardo, D. (1817). On the Principles of Political Economy and Taxation. 3rd ed. John Murray, London, 1821.

Samuelson, P. A. (1939). Interactions between the multiplier analysis and the principle of acceleration. The Review of Economics and Statistics, 25(Autumn):11–44.

Sargent, T. J. (1993). Bounded Rationality in Macroeconomics. Oxford University Press, Oxford.

Sargent, T. J. and Wallace, N. (1975). ‘rational’ expectations, the optimal monetary instrument, and the optimal money supply rule. Journal of Political Economy, 85(1):163–190.

Say, J.-B. (1803). A Treatise on Political Economy or the Production, Distribution and Consumption of Wealth. A.M. Kelley Publishers, New York, 1971.

Schumpeter, J. A. (1912). Theorie der wirtschaftlichen Entwicklung. Dunker & Humblot, Leipzig.

Schumpeter, J. A. (1939). Business Cycles: A Theoretical, Historical, and Statistical Analysis of the Capitalist Process. McGraw-Hill, New York and London.

Sismondi, J. C. L. (1819). New Principles of Political Economy: Of Wealth and Its Relation to Population. (R. Hyse, trans. and ed.) Transaction Publishers, New Brunswick, 1991.

Wen, Y. (2001). Understanding self-fulfilling rational expectations equi- libria in real business cycle models. Journal of Economic Dynamics and Control, 25(8):1221–1240.

Williams, N. (2003). Adaptive learning and business cycles. Manuscript, Princeton University.

Woodford, M. (1990). Learning to believe in sunspots. Econometrica, 58(2):277–307.