Business cycle modeling between financial crises and black swans: Ornstein-Uhlenbeck stochastic process vs Kaldor deterministic chaotic model

Business cycles are oscillations in the economy because of recessions and expansions. In this paper we investigate the oscillation of the gross domestic product as a result of its relations with the other main macroeconomic variables such as capital, consumption, and investment. There is a long-standing debate about chaos and non-linear dynamics in economy and even the usefulness of those concepts has been questioned. Stochastic modeling has proven to be able to simulate reality fairly well. However, a stochastic behavior implies that reality is about exogenous randomness, while a chaotic behavior means that reality is deterministic and non-linearities are endogenous. Here we compare an Ornstein-Uhlenbeck stochastic process with a Kaldor-Kalecki deterministic chaotic model to understand which one fits better real data. We show that our chaotic model is able to represent reality as well as the stochastic model taken into consideration. Furthermore, our model may reproduce an extreme event (black swans).