Risk-Sensitive Consumption and Savings under Rational Inattention

Abstract

This paper studies the consumption-savings behavior of households who have risk-sensitive preferences and su¤er from limited information-processing capacity (rational inattention or RI). We …nd that the model displays a wide range of observational equivalence properties, implying that consumption and savings data cannot distinguish between models with risksensitivity, robustness, rational inattention, or rational expectations, in any combination. We then show that the welfare costs from RI are much larger for risk-sensitive households than any other observationally-equivalent settings. Thus, a potential method for testing risk-sensitivity vs. robustness is to ask agents how much they would pay to receive better information about the state of the world.

Signal Extraction and Rational Inattention

“…They also established the observational equivalence between the two preferences within the LQG setting. Luo and Young (2010a) extend this equivalence to RI settings.…”

Robustness, information–processing constraints, and the current account in small open economies

“…As shown in Luo (2008) and Luo and Young (2010), in order to facilitate the introduction of RB and RI we reduce the above multivariate model with a general income process to a univariate model with iid innovations to permanent income s t that can be solved in closed-form. Specifically, if s t is defined as a new state variable, we can reformulate the above PIH model as…”

“…40 To obtain (33), we use the fact that the entropy of a Gaussian random variable is equal to half of its logarithm variance plus a constant term. 41 Convergence requires that κ > log (R) ≈ R − 1; see Luo and Young (2010) for a discussion. 42 The RB-RI model proposed in this paper encompasses the hidden state model discussed in Hansen et al (2002) and Hansen and Sargent (2007b); the main difference is that none of the states in the RB-RI model are perfectly observable (or controllable).…”

“…(42) and (43), we can see that imperfect state observation due to RI can amplify the importance of model uncertainty measured by Σ in determining consumption and precautionary savings. Before proceeding, we want to draw a distinction between the model proposed above and similar ones used in Luo and Young (2010) and Luo et al (2011). In those other papers, agents were assumed to trust the Kalman filter they use to process information, meaning that decisions were only robust to misspecification of the income process.…”

“…We think that it is a way to distinguish CARA preference and RB. 13 See Hansen and Sargent (2007a) and Luo and Young (2010) for detailed comparisons of the two models. In our ICA model, it seems more plausible to have different degrees of robustness (ϑ) across countries than to assume different degrees of risk sensitivity (i.e., enhanced risk aversion) across countries to explain the observed different joint behavior of consumption and current accounts in emerging and developed economies.…”