Macro Seminar: Aleh Tsyvinski (Yale)

Abstract: The paper develops a methodology for analyzing policies whose effects feature hysteresis or path-dependency in stochastic models with forward looking optimizing agents. First, we propose a general class of functionals that permits significant tractability of the analysis and allows to decompose the optimality conditions into the current marginal effects of the policy and the conditional expectation of the future marginal effects of policies. Second, we characterize in closed form the dynamics of stochastic hysteresis elasticity that represents the change in the whole optimal policy process with the introduction of the hysteresis effects. Third, we determine the optimal policy process. The dynamics of the present marginal effects of policies, the effects of the past, are determined by the recently developed functional Itˆo’s lemma. The dynamics of the conditional expectation process of the future marginal effects of policies, the future effects, is given by a new total derivative formula for conditional expectation processes. The total derivative formula allows us to represent the evolution of the conditional expectation as a sum of the expected dynamics of hysteresis with respect to time, a form of a time derivative, and the expected dynamics of hysteresis with the shocks to the trajectory of the stochastic process, a form of a stochastic derivative. Even when a policy has a small contemporaneous impact, the effects of the past choices and the future actions may be significant.

Please contact Alan Olivi at a.olivi@ucl.ac.uk for the seminar link.