  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.
