Randomness, Determinism and Undecidability in the Economic cycle Theory

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.