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Why a Simple Herding Model May Generate the Stylized Facts of Daily Returns: Explanation and Estimation
(2012)

Reiner Franke
Frank Westerhoff
 The paper proposes an elementary agentbased asset pricing model that, invoking the
two trader types of fundamentalists and chartists, comprises four features: (i) price determination
by excess demand; (ii) a herding mechanism that gives rise to a macroscopic
adjustment equation for the market fractions of the two groups; (iii) a rush towards fundamentalism
when the price misalignment becomes too large; and (iv) a stronger noise
component in the demand per chartist trader than in the demand per fundamentalist
trader, which implies a structural stochastic volatility in the returns. Combining analytical
and numerical methods, the interaction between these elements is studied in the
phase plane of the price and a majority index. In addition, the model is estimated by
the method of simulated moments, where the choice of the moments reflects the basic
stylized facts of the daily returns of a stock market index. A (parametric) bootstrap
procedure serves to set up an econometric test to evaluate the model’s goodnessoffit,
which proves to be highly satisfactory. The bootstrap also makes sure that the estimated
structural parameters are well identified.