Randomness, Determinism and Undecidability in the Economic Cycle Theory

Ignacio Escañuela ROMANA



The scientific literature that studies the Business cycles contains a historical debate between random and deterministic models. On the one hand, models built with explanatory variables follow a stochastic trajectory and produce, through transmission mechanisms, the studied cycles. Its rationale: the so-called Slutsky-Yule effect. In addition, models in which the system phase at time T fixes, applying the “ceteris paribus condition”, the phase at time t + 1. The cycle would be the product of variables, making it possible to predict and enabling economic policies to combat recessions. The thesis of this work is as follows. The application of the theorems of Chaitin of undecidability shows that it is not possible to conclude such debate. It is impossible to determine with absolute certainty whether the observed cycles follow a deterministic or stochastic model. To reach this result, I outline the fundamental theories of the business cycle, providing a classification and examples of mathematical models. I review the definition of randomness, and I consider the demonstration of Chaitin about the impossibility of deciding whether a data set is stochastic or not. A consequence, he says, of Gödel incompleteness theorems. I conclude considering a string of economic data, aggregated or not, as random or deterministic, depends on the theory. This applies to all cyclical phenomena of any nature. Specific mathematical models have observable consequences. But probabilism and determinism are only heuristic programs that guide the knowledge progress.

Key words: Randomness, Business cycle theories, Undecidability, Heuristic.

JEL: B40, D50, E32.


Randomness, Business cycle theories, Undecidability, Heuristic.

Full Text:


Álvarez Vázquez, N.J. (1996). Introducción a la evolución de la metodología de la econometría. Madrid: UNED.

Álvarez Vázquez, N.J. (2004). Econometría II. Análisis de modelos econométricos de series temporales. Madrid: Ediciones Académicas.

Azariadis, C. (1981). Self-fulfilling prophecies. Journal of Economic Theory, 25(3), 380-396. doi. 10.1016/0022-0531(81)90038-7

Azariadis, C., Kaas, L. & Wen, Y. (2015). Self-fulfilling credit cycles. Federal Reserve Bank of St. Louis, Working Paper 2015(005A). doi. 10.2139/ssrn.2166087

Barnett, V. (2006). Chancing an interpretation: Slutsky’s random cycles revisited. The European Journal of the History of Economic Thought, 13(3), 411-432. doi. 10.1080/09672560600875596

Benhabib, J. & Farmer, R.E.A (1994). Indeterminacy and increasing returns. Journal of Economic Theory, 63(1), 19-41. doi. 10.1006/jeth.1994.1031

Benhabib, J. & Farmer, R.E.A (1999). Indeterminacy and sunspots in macroeconomics. In Handbook of Macroeconomics, 1(A), (pp. 387–448), Amsterdam: North Holland. doi. 10.1016/s1574-0048(99)01009-5

Benhabib, J. & Nishimura, K. (1998). Indeterminacy and sunspots with constant returns. Journal of Economic Theory, 81(1), 58-96. doi. 10.1006/jeth.1998.2414

Bjork, R.A. (1989). Retrieval inhibition as an adaptive mechanism in human memory. In Roediger, H.L. & Craik, F.I.M. (Eds.), Varieties of memory and consciousness: Essays in honour of Endel Tulving (pp. 309-330). Hillsdale, NJ: Erlbaum.

Blanchard, O.J. & Kiyotaki, N. (1987). Monopolistic competition and the effect of aggregate demand. American Economic Review, 77(4), 647-66.

Bricmont, J. (2004). Determinism, chaos and quantum mechanics.

Bridgman, P.W. (1927). The logic of modern physics. New York: Macmillan.

Calude, C.S. (2002). Incompleteness, complexity, randomness and beyond. Centre for Discrete Mathematics and Theoretical Computer Science, Research Report 166.

Calude, C.S. & Stay, M.A. (2004). From Heisenberg to Gödel via Chaitin. Centre for Discrete Mathematics and Theoretical Computer Science, Research Report 235.

Chaitin, G.J. (1975). Randomness and mathematical proof. Scientific American, 232(5), 47-52. doi. 10.1038/scientificamerican0575-47

Chaitin, G.J. (2004), Meta math!. The quest for Omega. Retrieved from arXiv:math/0404335v7 [math.HO]. doi. 10.5860/choice.43-4073

Chaitin, G.J. (2006). The limits of reason. Scientific American, 294(3), 74-81. doi. 10.1038/scientificamerican0306-74

Chari, V.V., Kehoe, P.J. & McGrattan, E.R. (2009). New Keynesian models: Not yet useful for policy analysis. American Economic Journal: Macroeconomics, 1(1), 242-266. doi. 10.1257/mac.1.1.242

Chatterjee, S. (2000). From cycles to shocks: Progress in business-cycle theory. Federal Reserve Bank of Philadelphia, Business Review, 3, 27-37.

Cho, J.O & Cooley, T.F. (1991). The business cycle with nominal contracts. Economic Theory, 6(1), 13-33.

Cho, J.O. & Cooley, T.F. (1994). Employment and hours over the business cycle. Journal of Economic Dynamics and Control, 18(2), 411-432. doi. 10.1016/0165-1889(94)90016-7

Diebold, F.X. & Rudebusch, G. (1996). Measuring business cycles: A modern perspective. Review of Economics and Statistics, 78(1), 67-77. doi. 10.2307/2109848

Dobrescu, M. & Paicu, C.L. (2012). New approaches to business cycle theory in current economic science. Theoretical and Applied Economics, 19(7), 147-160.

Duffy, J. & Xiao, W. (2005). Instability of sunspot equilibria in real business cycle models under adaptative learning. JME Manuscript # 0438.

Ekkehard, E. & Stockhammer, E. (2003). Macroeconomic regimes. Business cycle theories reconsidered. Center for Empirical Macroeconomics, Working Paper 99.

Farmer, R.E.A. & Guo, J.T. (1994). Real business cycles and the animal spirits hypothesis. Journal of Economic Theory, 63(1), 42-72. doi. 10.1006/jeth.1994.1032

Farmer, R.E.A. (2012). The evolution of endogenous business cycles. NBER Working Paper 18284. doi. 10.3386/w18284

Farmer, R.E.A. & Platonov, K. (2016). Animal spirits in a monetary economy. NBER Working Paper, No. 22136. doi. 10.3386/w22136

Farmer, R.E.A. & Woodford, M. (1984). Self-fulfilling prophecies and the business cycle. CARESS Working Paper No.84-12.

Frey, G. (1972). La Matematización de nuestro universo. Madrid: G. Del Toro.

Frisch, R. (1931). A Method of decomposing an empirical series into its cyclical and progressive components. Journal of the American Statistical Association, 26(173), 73-78. doi. 10.2307/2277598

Frisch, R. (1933). Propagation problems and impulse problems in dynamic economics. (in Economic Essays in Honour of Gustav Cassel, Allen & Unwin, London, 1933, pp. 171–3, 181–90, 197–203 London: George Allen & Unwin LTD. doi. 10.1017/cbo9781139170116.032

Gali, J. & Rabanal, P. (2004). Technology shocks and aggregate fluctuations: How well does the RBS model fit postwar U.S. data? NBER Working Paper 10636. doi. 10.3386/w10636

Gillies, D.A. (1972). Operationalism. Synthese 25(1-2), 1-24. doi. 10.1007/bf00484997

Greenwald, B.C. & Stiglitz, J.E. (1986). Externalities in economies with imperfect information and incomplete markets. The Quaterly Journal of Economics, 101(2), 229-264. doi. 10.2307/1891114

Greenwald, B.C. & Stiglitz, J.E. (1993). Financial market imperfections and business cycles. The Quarterly Journal of Economics, 108 (1), 77-114. doi. 10.2307/2118496

Hairault, J.O. & Portier F. (1993). Money, new-Keynesian macroeconomics and the business cycle. European Economic Review, 37(8), 1533-1568. doi. 10.1016/0014-2921(93)90121-p

Hansen, L.P. (2014). Uncertainty outside and inside economic models. NBER Working Paper 20394. doi. 10.3386/w20394

Hausman, D.M. (1989). Economic methodology in a nutshell, The Journal of Economic Perspectives, 3(2), 115-127. doi. 10.1257/jep.3.2.115

Hempel, C.G. (1950). Problems and changes in the empiricist criterion of meaning. Revue Internationale De Philosophie, 41, 41-63.

Keynes, J.M. (2008). The general theory of employment, interest, and money. New Delhi: Atlantic Publishers.

Kindleberger, C.P. (1985). Bank failures: The 1930s and the 1980s. Proceedings, 6, 7-52.

King, R.G. & Plosser, C.I. (1984). Money, credit, and prices in a real business cycle. American Economic Review, 74(3), 363-380.

King, R.G., Plosser, C.I. & Rebelo, S.T. (1988). Production, growth and business cycles: I. The basic neoclassical model. Journal of Monetary Economics, 21(2-3), 195-232. doi. 10.1016/0304-3932(88)90030-x

Kondratieff, N.D. & Stolper, W.F., (1935). The long waves in economic life. The Review of Economics and Statistics, 17(6), 105-115. doi. 10.2307/1928486

Kuznets, S. (1929). Random events and cyclical oscillations, Journal of the American Statistical Association, 24(167), 258-275. doi. 10.2307/2276856

Kydland, F.E., & Prescott, E. C. (1982). Time to build and aggregate fluctuations. Econometrica, 50(6), 1345-1370. doi. 10.2307/1913386

Kydland, F.E. & Prescott, E.C. (1990). Business cycles: Real facts and a monetary myth. Federal Reserve Bank of Minneapolis, Quaterly Review 14(2), 3-18.

L'Ecuyer, P., Simard, R & Wegenkittl, S. (2002). Sparse serial tests of uniformity for random number generators. SIAM Journal on Scientific Computing, 24(2), 652–668. doi. 10.1137/s1064827598349033

Long, J.B. & Plosser, C.I. (1983). Real business cycles. Journal of Political Economy, 91(1), 39-69. doi. 10.1086/261128

Lucas, R.E.J. (1972). Expectations and the neutrality of money. Journal of Economic Theory, 4(2), 103-124. doi. 10.1016/0022-0531(72)90142-1

Lucas, R.E.J. (1977). Understanding business cycles. Carnegie-Rochester Conference Series on Public Policy, 5(1), 7-29. doi. 10.1016/0167-2231(77)90002-1

Mankiw, N.G. (1989). Real business cycles: A new Keynesian perspective. The Journal of Economic Perspectives, 3(3), 79-90. doi. 10.1257/jep.3.3.79

Mario Parra, C. & Suárez, J. A. (2006). Sobre dos teoremas de incompletez de Chaitin. Lecturas Matemáticas, 161-174.

McGough, B., Meng, Q. & Xue, J. (2013). Expectational stability of sunspot equilibria in non-convex economies. Journal of Economic Dynamics  Control, 37(6), 1126-1141. doi. 10.1016/j.jedc.2013.01.012

Minsky, H.P. (1986). Stabilizing an unstable economy. New Haven: Yale University Press.

Moran, P.A.P. (1949). The statistical analysis of the sunspot and Lynx cycles. The Journal of Animal Ecology, 18(1), 115-116. doi. 10.2307/1585

Moran, P.A.P. (1950). The oscillatory behaviour of moving averages. Proceedings of the Cambridge Philosophical Society, 46(2), 272-280. doi. 10.1017/s0305004100025731

Muth, J.F. (1961). Rational expectations and the theory of price movements. Econometrica, 29(3), 315-335. doi. 10.2307/1909635

Nagel, E. (2006). La estructura de la ciencia. Barcelona: Paidós.

Nelson, C. & Plosser, C. (1982). Trends and random walks in macroeconomic time series: Some evidence and implications. Journal of Monetary Economics, 10(2), 139-162. doi. 10.1016/0304-3932(82)90012-5

Oppers, S.E. (2002). The Austrian theory of business cycles: Old lessons for modern economic policy. IMF Working Paper 02/2. doi. 10.5089/9781451841770.001

Pollock, D.S.G. (1987). Methods of time-series analysis, Interdisciplinary Science Reviews 12(2),

Pollock, D.S.G. (2013). Cycles, syllogisms and semantics: Examining the idea of spurious cycles. Journal of Time Series Econometrics, 6(1), 81-102. doi. 10.1515/jtse-2012-0033

Prescott, E.C. (1986). Theory ahead of business cycle measurement. Quaterly Review, 10(4), 9-25.

Quine, W.V. (1951). Main trends in recent philosophy: Two dogmas of empiricism. The Philosophical Review, 60(1), 20-43. doi. 10.2307/2181906

Romer, D. (2006). Macroeconomía avanzada. Madrid: McGraw-Hill.

Romer, P.M. (1986). Increasing returns and long-run growth. The Journal of Political Economy, 94(5), 1002-1037. doi. 10.1086/261420

Russell, B. (1914). Our knowledge of the external world as a field for scientific method in Philosophy. London: George Allen  Unwin LTD. doi. 10.5962/bhl.title.2067

Sala-I-Martin, X. (1994). Apuntes de crecimiento económico. Barcelona: Antoni Bosch Editor.

Samuelson, P. (1958). An exact consumption-loan model of interest with or without the social contrivance of money. The Journal of Political Economy, 66(6), 467-482. doi. 10.1086/258100

Shell, K. (1977). Monnaie et allocation intertemporelle. Centre National de la Recherche Scientifique, Séminaire Malinvaud (Noviembre 21,1977).

Schmitt-Grohe, S. & Uribe, M. (2000). Price level determinacy and monetary policy under a balanced-budget requirement. Journal of Monetary Economics, 45(1), 211-246. doi. 10.1016/s0304-3932(99)00046-x

Schmitt-Grohe, S. (2000). Endogenous business cycles and the dynamics of output, hours, and consumption. American Economic Review, 90(5), 1136-1159. doi. 10.1257/aer.90.5.1136

Slutsky, E. (1937). The summation of random causes as the source of cyclic processes. Econometrica, 5(2), 105-146. doi. 10.2307/1907241

Sols, F. (2013). Uncertainty, incompleteness, chance, and design, in Intelligible Design, Manuel M. Carreira, M. M. & Julio A. Gonzalo, J. A. (eds.), World Scientific (Singapore, 2013). arXiv: 1301.7036. doi. 10.1142/9789814447614_0006

Spear, S. (1984). Sufficient conditions for the existence of sunspot equilibria. Journal of Economic Theory, 34(2), 360-370. doi. 10.1016/0022-0531(84)90149-2

Stadler, G.W. (1994). Real business cycles. Journal of Economics Literature, 32(4), 1750-1783.

Tobin, J. (1995). The natural rate as new classical macroeconomics. In R. Cross (ed.), The Natural Rate of Unemployment: Reflections on 25 years of the Hypothesis, Cambridge: Cambridge University Press, pp. 32–42. doi. 10.1017/cbo9780511559631.004

Volchan, S.B. (2002). What Is a random sequence? The Mathematical Association of America (109), 46-63. doi. 10.2307/2695767

Wen, Y. (1998). Capacity utilization under increasing returns to scale. Journal of Economic Theory, 81, 7-36. doi. 10.1006/jeth.1998.2412

Whitta-Jacobsen, H.J. (2002). Endogenous Keynesian business cycles. Institute of Economics, Discussion Papers, No. 2002(15).

Woodford, M. (1990). Learning to believe in sunspots. Econometrica, 58(2), 277-307. doi. 10.2307/2938205

Yule, G.U. (1926). Why do we sometimes get nonsense-correlations between time-series?. A Study in sampling and the nature of time-series. Journal of the Royal Statistical Society, 89(1), 1-63. doi. 10.2307/2341482

Zahringer, K.A. (2012). Monetary disequilibrium theory and business cycles: An Austrian critique. Quarterly Journal of Austrian Economics, 15(3), 304-330.

DOI: http://dx.doi.org/10.1453/jepe.v3i4.1083


  • There are currently no refbacks.


Journal of Economics and Political Economy - J. Econ. Pol. Econ. - JEPE - www.kspjournals.org

ISSN: 2148-8347. Editor : editor-jepe@kspjournals.org   Secretarial: secretarial@kspjournals.org   Istanbul - Turkey.

Copyright © KSP Journals