Limited information capacity as a source of inertia

We derive optimal time-dependent adjustment rules from Shannon's (1948) Information Theory. In a continuous-time LQ prediction problem with a costly rate of information acquisition-processing, the optimal prediction evolves smoothly, but jumps at an optimally chosen frequency, when fresh information accrues. A more volatile and persistent target raises the information rate required to maintain a sampling frequency. This cost-effect moderates and may even reverse the benefit-effect on the value of information, so optimal inertia is unresponsive to and nonmonotonic in the predictability of the environment. Conventional models with a fixed cost per observation imply no such cost-effect, so inertia rises quickly in the predictability of the environment. (C) 2003 Elsevier B.V. All rights reserved.