Optimal Rules under Adjustment Cost and Infrequent Information

A large number of microeconomic decision variables such as investments, prices, inventories or employment are characterized by intermittent large adjustments. The behavior of those variables has been often modeled as following state-dependent rules. The optimality of such state-dependent rules depends crucially on the continuous observation of the relevant state, an assumption which is far from being fulfilled in practice. We propose an alternative model, where at least part of information about the relevant state variable is infrequent. We study several alternatives. We start with the special case where innovations are infrequent, but are readily observed. Only in this case are optimal rules state-dependent. We then explore the common case of infrequent and delayed information. It may arrive at deterministic times, like periodic macroeconomic statistics, or stochastically, when some events trigger announcements. Part of the relevant information may be continuously observed, while the other part is only observed infrequently. The resulting rules are time and state dependent, characterized by trigger and target points that are functions of the time spent since the last time of information arrival. We derive the conditions which characterize the optimal rules and provide numerical algorithms for each case