Follow the money: The monetary roots of bubbles and crashes

We propose a reduced form model for the Minskian dynamics of liquidity and of asset prices in terms of the so-called financial accelerator mechanism. In a nutshell, credit creation is driven by the market value of the financial assets employed as collateral in the bank loans. This leads to a self-reinforcing feedback between financial prices and liquidity that we model by coupled non–linear stochastic processes. We show that the resulting dynamics are characterized by a transient super- exponential growth qualifying a bubble regime. Unchecked, this would lead to a finite time singularity (FTS). The underlying singularity expresses the unsustainable dynamics of the corresponding econ- omy and announces a regime change, such as a crash. We propose to describe the dynamics of the crisis by the same coupled non–linear stochastic process with inverted signs, i.e., nonlinear negative feedbacks of value and money on their growth rates. Casting the financial accelerator dynamics into a simple macroeconomic model, we show that the cycle of booms and bursts of financial assets and liquidity determines economic recessions in the form of increasing aggregate default rates and decreas- ing GDP. Finally, by exploiting the implications of the proposed model on the dynamics of financial asset returns, we introduce a generalized GARCH process, called FTS-GARCH, that can provide an early warning identification of bubbles. Estimating the FTS-GARCH on well-known historical bubble episodes suggest the possibility to diagnose in real-time the presence of bubbles in financial time series.