Chaos and Unpredictability in Dynamic Social Problems
Abstract: We study a dynamic model environmental protection in which
the level of pollution is a state variable that strategically links
policy making periods. Policymakers maximize their incumbents'
utilities: they have heterogeneous preferences on how to pollute, and
they do not fully internalize the cost of pollution. This type of
political economy model is often reduced to a "modified planner's
problem" and yields predictions that are qualitatively similar to the
planners' solution, albeit with a bias: too much pollution in the
steady state (or, in other applications, too little public goods, too
much debt, etc.). We highlight conditions under which this reduction
is not possible, and the dynamic time inconsistency in the social
choice generated by the political process generates a novel source of
distortions. Under these conditions, there are equilibria in which,
for a generic economy and starting from a generic initial condition,
the state evolves in complex cycles, or unpredictable chaotic
dynamics. Depending on the fundamentals of the economy, these
equilibria may generate ergodic distributions that consistently
overshoot the planner's steady state, or that fluctuate around it.
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