The Impact of External Events on the Emergence of Social Herding of Economic Sentiment

We investigate the impact of an exogenous environment on the emergence of social herding of economic sentiment. An interactions-driven dynamics of economic sentiment is modeled by an Ising model on a large (two-dimensional) square lattice. The individual states are called optimism and pessimism. The exogenous environment is modeled as a sequence of random events, which might have a positive or negative influence on economic sentiment. These exogenous events can be frequent or rare, have a lasting impact or a non-lasting impact. Impact of events is inhomogeneous over the lattice, as individuals might fail to perceive particular events. We introduce two notions of social herding: permanent herding refers to the situation where an ordered state (i.e. a state with an overwhelming majority of optimists or pessimists) persists over an infinite time horizon, while temporary herding refers to the situation where ordered states appear, persist for some time and decay. The parameter of the inter-agent interaction strength is such as to engender permanent herding without the influence of the environment. To investigate the impact of an environment we determine whether an initially ordered state decays. We consider two cases: in the first case positive and negative events have both the same empirical frequencies and strengths, while in the second case events have the same empirical frequencies but different strengths. (In the first case the environment is ``neutral''in the long term), In the neutral case we find temporary herding if events are sufficiently ``strong'' and/or perceived by a sufficiently large proportion of agents, and our results suggest that permanent herding occurs for small values of the parameters. In the ``non-neutral'' case we find only temporary herding.