Socioeconomic interaction and swings in business confidence indicators

We propose a stochastic model of interactive formation of individual expectations regarding the business climate in an industry. Our model is motivated by a business climate survey conducted since 1960 in Germany by the Ifo-institute (www.ifo.de). In accordance with the data structure of this survey, in our model there is associated to each economic agent (business manager) a random variable with a three-element state space representing her possible types of expectations. The evolution of individual expectations in a finite population is then modeled as a spatio-temporal stochastic process with local interaction between agents. An appropriate structure of the interaction between agents in our setting turns out to be provided by a Festinger function (in physics called energy function or Hamiltonian) of the Blume-Capel type. Time series of the fractions of agents holding each type of expectations are obtained for the model by Monte Carlo simulations. We find that our model reproduces some generic features of the empirical time series obtained from the German business-climate data, in particular the occurrence of abrupt large but rare swings. In our model, such swings occur as spontaneous phase changes, between macroscopic states.