Follow the median: revisiting bubbles and cycles

Abstract

Under very general conditions, the best predictor of any random variable’s observed time series is not its mean but its median. Hence, if we aim to model a variable with a skewed (a.k.a. asymmetric) probability distribution, so mean and median diverge, it is the model’s predicted median path that must be compared to that variable’s observed time series. Thus e.g. rational economic agents base their decisions on their target variables’ expected (a.k.a. mean) paths, which must as a result follow certain rules (mainly no arbitrage); but, if those variables are skewedly distributed, irrational-looking observations may not reflect irrationality, for the median is not subject to the rules rationality imposes on the mean. Yet economic models rarely pose this hypothesis and, when they do, their skewness assumptions often present major theoretical and/or empirical drawbacks. This paper proposes instead to assume normally distributed (hence symmetric) random perturbations and then rely on economics’ standard nonlinear assumptions (e.g. diminishing returns, decreasing marginal utility, etc.) to skew relevant variables’ distributions endogenously. (.../...)