Optimal and Myopic Information Acquisition

We consider the problem of optimal dynamic information acquisition from many correlated information sources. Each period, the decision-maker jointly takes an action and allocates a fixed number of observations across the available sources. His payoff depends on the actions taken and on an unknown state. In the canonical setting of jointly normal information sources, we show that the optimal dynamic information acquisition rule proceeds myopically after finitely many periods. If signals are acquired in large blocks each period, then the optimal rule turns out to be myopic from period 1. These results demonstrate the possibility of robust and "simple" optimal information acquisition, and simplify the analysis of dynamic information acquisition in a widely used informational environment

Efficient Algorithms for Optimal Control of Quantum Dynamics: The "Krotov'' Method unencumbered

Efficient algorithms for the discovery of optimal control designs for coherent control of quantum processes are of fundamental importance. One important class of algorithms are sequential update algorithms generally attributed to Krotov. Although widely and often successfully used, the associated theory is often involved and leaves many crucial questions unanswered, from the monotonicity and convergence of the algorithm to discretization effects, leading to the introduction of ad-hoc penalty terms and suboptimal update schemes detrimental to the performance of the algorithm. We present a general framework for sequential update algorithms including specific prescriptions for efficient update rules with inexpensive dynamic search length control, taking into account discretization effects and eliminating the need for ad-hoc penalty terms. The latter, while necessary to regularize the problem in the limit of infinite time resolution, i.e., the continuum limit, are shown to be undesirable and unnecessary in the practically relevant case of finite time resolution. Numerical examples show that the ideas underlying many of these results extend even beyond what can be rigorously proved.Comment: 19 pages, many figure

Vehicle Choices, Miles Driven, and Pollution Policies

Mobile sources contribute large percentages of each pollutant, but technology is not yet available to measure and tax emissions from each vehicle. We build a behavioral model of household choices about vehicles and miles traveled. The ideal-but-unavailable emissions tax would encourage drivers to abate emissions through many behaviors, some of which involve market transactions that can be observed for feasible market incentives (such as a gas tax, subsidy to new cars, or tax by vehicle type). Our model can calculate behavioral effects of each such price and thus calculate car choices, miles, and emissions. A nested logit structure is used to model discrete choices among different vehicle bundles. We also consider continuous choices of miles driven and the age of each vehicle. We propose a consistent estimation method for both discrete and continuous demands in one step, to capture the interactive effects of simultaneous decisions. Results are compared with those of the traditional sequential estimation procedure.

Search Costs and Medicare Plan Choice

There is increasing evidence suggesting that Medicare beneficiaries do not make fully informed decisions when choosing among alternative Medicare health plans. To the extent that deciphering the intricacies of alternative plans consumes time and money, the Medicare health plan market is one in which search costs may play an important role. To account for this, we split beneficiaries into two groups--those who are informed and those who are uninformed. If uninformed, beneficiaries only use a subset of covariates to compute their maximum utilities, and if informed, they use the full set of variables considered. In a Bayesian framework with Markov Chain Monte Carlo (MCMC) methods, we estimate search cost coefficients based on the minimum and maximum statistics of the search cost distribution, incorporating both horizontal differentiation and information heterogeneities across eligibles. Our results suggest that, conditional on being uninformed, older, higher income beneficiaries with lower self-reported health status are more likely to utilize easier access to information.Search, Medicare Health Plan Choice, Discrete Choice Models, Bayesian Methods