In the framework of small-scale agent-based financial market models, the paper starts out from the concept of structural stochastic volatility, which derives from different noise levels in the demand of fundamentalists and chartists and the time-varying market shares of the two groups. It advances several different specifications of the endogenous switching between the trading strategies and then estimates these models by the method of simulated moments (MSM), where the choice of the moments reflects the basic stylized facts of the daily returns of a stock market index. In addition to the standard version of MSM with a quadratic loss function, we also take into account how often a great number of Monte Carlo simulation runs happen to yield moments that are all contained within their empirical confidence intervals. The model contest along these lines reveals a strong role for a (tamed) herding component. The quantitative performance of the winner model is so good that it may provide a standard for future research.