Predicting the Unpredictable: Forecastable Bubbles and Business Cycles under Rational Expectations

Abstract

A popular interpretation of the Rational Expectations/Efficient Markets hypothesis states that, if it holds, market valuations must follow a random walk; hence, the hypothesis is frequently criticized on the basis of empirical evidence against such a prediction. Yet this reasoning incurs what we could call the 'fallacy of probability diffusion symmetry': although market efficiency does indeed imply that the mean (i.e. 'expected') path must rule out any cyclical or otherwise arbitrage-enabling pattern, if the probability diffusion process is asymmetric the observed path will most closely resemble not the mean but the median, which is not subject to this condition. In this context, this paper develops an efficient markets model where the median path of Tobin's q ratio displays regular, periodic cycles of bubbles and crashes reflecting an agency problem between investors and producers. The model is tested against U.S. market data, and its results suggest that such a regular cycle does indeed exist and is statistically significant. The aggregate production model in Gracia (Uncertainty and Capacity Constraints: Reconsidering the Aggregate Production Function, 2011) is then put forward to show how financial fluctuations can drive the business cycle by periodically impacting aggregate productivity and, as a consequence, GDP growth. JEL E22, E23, E32, G12, G14

The Cycle of Rents: A Model of Rational Bull-and-Bear Cycles in an Efficient Market

“…An obvious extension would be to expand this model into a general-equilibrium framework to explore its implications from a macroeconomic perspectivea direction already outlined to some extent in Gracia (2012), albeit under very restrictive assumptions regarding the potential sources of the rents' cycle (which in that specific paper was assumed to result from agency rents' behavior). Another logical next step would of course be to test the model's predictions against empirical data (along the lines of the tests already conducted in Gracia 2011 and 2012).…”

“…The most direct precedents of the model put forward in this paper are Gracia (2005), (2011) and (2012). Specifically, Gracia (2005) puts forward an efficient markets' valuation model based on agency rents leading a predator-prey cycle along the median path of a company's solvency ratio and, complementarily to this, Gracia (2012) provides empirical evidence that a cycle of these characteristics could indeed explain the long-term valuation cycle observable in both Tobin's Q and Shiller's CAPE data series. Gracia (2011), on the other hand, develops the production function we use in this paper by deriving it from a set of strictly neoclassical axioms, and then performs a battery of empirical tests showing it to be a better fit to observed data than the Cobb-Douglas function (in fact rejecting the Cobb-Douglas specification at 99% confidence).…”

“…Unfortunately, the economic papers where the observed path's link to the median instead of the mean is explicitly acknowledged and used to draw some relevant conclusions are few and far between (although there are some e.g. Roll 1992, Gracia 2005and Gracia 2012, which effectively, if not formally, leaves unchallenged the popular fallacy of treating observed data as if any arbitrage opportunities observed in them were also to be found in the expected path.…”

“…we resort (followingGracia 2005 andGracia 2012) to a widely used one: the geometric Brownian motion with drift = ( + ), where represents a stochastic function, t designates time, , ∈ ℜ are real constants and is a Wiener process such that 0 ≡ 0 (for the point in time = 0 chosen as the reference) and = √ , where is a standardized normallydistributed (i.e. symmetrical) function such that ~(0,1).…”