Bayesian Estimation of the Heuristic Switching Model

In these experiments participants predict an evolution of the endogenous time series of price of the financial asset. The price is a function of the average of the participants' forecasts. A peculiar feature of these experiments is that the resulting time series may vary qualitatively even under the same treatment: in some cases, the convergence to the fundamental price is observed, while in other cases the price exhibits volatility and repeated patterns of bubbles and crashes.

To explain this variety of outcomes Anufriev and Hommes (2012) propose the Heuristic Switching Model where participants follow behavioural prediction heuristics and switch between them based on their past performance. In this paper we take Bayesian approach to estimate such a model on the available data from the previous learning-to-forecast experiments. The observed variable is the individual numerical point forecasts.

In the experiment individuals may condition their forecasts on the price from the previous rounds displayed on the screen. We assume that the individual point forecasts are generated by certain unobserved behavioural forecasting heuristics (e.g., adaptive, trend-following, constant, rational) and that individuals may switch between these heuristics.

The probabilities of switching are conditioned on the past performances of the rules. We model the process of switching with hidden Markov Model. We estimate the parameters of the rules and the probabilities of choosing a specific rule by an individual at a given time using MCMC Gibbs sampler. Depending on the treatment (functional form of price determination) we observed prevalence of different sets of heuristics.