The intrinsic comparative dynamics of infinite horizon optimal control problems with a time-varying discount rate and time-distance discounting

The intrinsic comparative dynamics of a ubiquitous class of optimal control problems with a time-varying discount rate and time-distance discounting are derived and shown to be characterized by a positive semidefinite matrix. It is also shown that the said comparative dynamics are invariant to the functional form of the discount rate function and the type of agent. Consequently, if one limits econometric testing to the basic comparative dynamics of the given class of control problems, one cannot determine (i) the functional form of the discount rate function used by an agent, and thus if an agent is a time-consistent or time-inconsistent decision maker, or (ii) if an agent commits to a plan of action or takes into account the changing nature of his preferences when choosing a plan.