Can heterogeneous agent models explain the alleged mispricing of the S&P 500?

Tests of excessive volatility along the lines of Shiller (1981) and Leroy and Porter (1981) count among the most convincing pieces of evidence against the validity of the time-honored efficient market hypothesis. Recently, using Shiller s distinction between ex-ante rational (fundamental) price and ex-post rational price, Schmitt and Westerhoff (2017) have demonstrated that the difference between S&P 500 market prices and their ex-post counterparts exhibits a bi-modal distribution speaking for the prevalence of long periods of either undervaluation or overvaluation. Schmitt and Westerhoff (2017) also show that this new stylized fact is shared by a large set of nonlinear behavioral models of speculative interactions between heterogeneous market participants. Most of these models allow some form of chartist or fundamentalist strategy, and the more recent members of this family of models also allow for agents switching between both alternatives according to some fitness criterion. Here I go one step further exploring which (if any) of this legacy of behavioral models fits best the data. I discuss econometric issues in the estimation of these highly complex nonlinear models, and estimate the parameters of different versions of seven canonical models. As it turns out, most of these models perform not better than a linear chartist-fundamentalist model, and often their fit is worse than the fit of this benchmark. Among the models considered here, the one proposed by Franke and Westerhoff (2012) is the only exception. Estimation of the model confidence set indicates that this model is not outperformed by other candidates, and depending on the setting and the confidence level, it is often found to be the single member of the model confidence set.