Non-standard central bank loss functions, skewed risks, and the certainty equivalence principle

This paper sets out to investigate the role of additive uncertainty under plausible non-standard central bank loss functions over future inflation. Building on a substantial body of evidence in the economic psychology literature, this paper postulates (i) period-by-period loss functions that are non-convex, i.e. displaying diminishing or non-increasing sensitivity to losses, and (ii) non-linear weighing of probabilities, hence departing from the expected utility paradigm. In addition, a simple and plausible form of non-time separability of the central bank's inter-temporal loss function is also considered in the analysis. The main conclusion of the study is that if the additive uncertainty is caused by a non-Normal distributed additive shock, for instance if the probability distribution of the shock is skewed, then with these departures from the quadratic function the principle of certainty equivalence does not hold. Thus, it appears that with additive uncertainty of the non-Normal type the assumption of a quadratic loss function for the central banker may not be as innocuous as it is commonly regarded. Conversely, non-time separability of the central bank inter-temporal loss function as studied in this paper does not determine i style="mso-bidi-font-style: normal">per se any departure from certainty equivalence. Moreover, no evidence is found of an optimal policy gradualism as a response to increased additive uncertainty even under the non-standard loss functions considered in this paper.