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Randomness, Determinism and Undecidability in the Economic Cycle Theory
Abstract
Abstract
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.Keywords
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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
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