This paper addresses the statistical properties of time series driven by rational bubbles à la Blanchard and Watson (1982). Using insights on the behavior of multiplicative stochastic processes, we demonstrate that the tails of the unconditional distribution emerging from such bubble processes follow power-laws (exhibit hyperbolic decline). More precisely, we find that rational bubbles predict ...

We extend the model of rational bubbles of [Blanchard, 1979] and [Blanchard and Watson, 1982] to arbitrary dimensions d: a number d of market time series are made linearly interdependent via d × d stochastic coupling coefficients. We first show that the no-arbitrage condition imposes that the non-diagonal impacts of any asset i on any other asset j = i has to vanish on average, i.e., must exhib...

The fiscal theory of price determination asserts that the price level is determined by the ratio of nominal public debt to the present value of real primary surpluses. To show its fragility, we describe a cash-in-advance economy with infinitely lived real productive assets. The fiscal theory does not hold since speculative bubbles partly restore the classical indeterminacy result.

We propose that imitation between traders and their herding behaviour not only lead to speculative bubbles with accelerating over-valuations of financial markets possibly followed by crashes, but also to “anti-bubbles” with decelerating market devaluations following all-time highs. For this, we propose a simple market dynamics model in which the demand decreases slowly with barriers that progre...

The Nasdaq fell another ≈ 10% on Friday the 14’th of April 2000 signaling the end of a remarkable speculative high-tech bubble starting in spring 1997. The closing of the Nasdaq at 3321 corresponds to a total loss of over 35% since its all-time high of 5133 on the 10’th of March 2000. Similarities to the speculative bubble preceding the infamous crash of October 1929 are quite striking: The bel...

Episodes of market crashes have fascinated economists for centuries. Although many academics, practitioners and policy makers have studied questions related to collapsing asset price bubbles, there is little consensus yet about their causes and effects. This review and essay evaluates some of the hypotheses offered to explain the market crashes that often follow asset price bubbles. Starting fr...