Consumption Dynamics in Mixed-Income Neighborhoods with Connected Households

We investigate the dynamics of household consumption in a setting in which households are connected across income classes. Low- and high-income households form preferences endogenously, conditional on their own and their neighbor's past consumption. The modeling effort relies on a stochastic dynamic model of interdependent consumer choice in which the demand for commodities evolves according to a non-linear difference equation with stochastic initial states. The analysis targets a region of the parameter space that corresponds to salient features of a mixed-income neighborhood in which households are connected. Standard methods of asymptotic analysis of dynamic systems (e.g. bifurcation analysis) are combined with numerical simulation, statistical modelling of extreme events and statistical estimation techniques to investigate the dynamics. From the mathematical point of view, our analysis reveals the existence of intricate bifurcation pattern, coexistence of multiple attractors, complex basins and long transients. The essential economic finding states that key features of household consumption vary significantly in the influence the high-income households exert on the preference formation of the low-income households. In particular, we find that the prevalence of long transients, i.e. long waiting times before convergence to asymptotic states occur, is inversely related to the type of connectedness considered. We demonstrate that the dynamics of the consumption trajectory evolving over an extended time period before it settles on long-run simple consumption pattern, may not at all be captured by an asymptotic state. Thus, policies targeting the economies in mixed-income neighborhoods that are solely based on information about long-run consumption states, might trigger unwanted, unanticipated effects.