The (Un)identification of Continuous-Action Rational Inattention Decision Models

In this paper, we discuss some properties of optimal consideration set in binary state continuous-action rational inattention decision problems. First, we show that it is the form of the utility function that determines the form of posterior distribution, i.e. whether it is a binary distribution or a triple or quadruple distribution, etc. Besides, we will also show that the posterior distribution may not be resulted after information acquisition in some circumstances. Second, we show that the optimal consideration set is essentially the optimal action strategies. Therefore, without further conditions, the rational inattention decision model is unidentifiable. Third, in order to identify the rational inattention decision model, we introduce another condition to the model. The discrete actions after information acquisition that satisfy the endogenously-determined probability (optimal action strategies) should satisfy the properties of probabilities, and therefore the discrete actions should also follow an exogenous probability distribution. This idea is tested by an example with quadratic utility function. Through this example, we find that under this condition, the optimal consideration set can be identified. The elements in the optimal consideration set, or equivalently the discrete signals after information acquisition, exhibit a curve or curves.