Uncertainty and Economic Policy: Big Problems and Small Models

This article presents an introduction to the main existing analytical results relating to problems of uncertainty and economic policy. It addresses specifically the question of “caution” versus “intensity” in the use of instruments of economic policy under uncertainty in dynamic contexts. That question can be illustrated simply as follows: How should the monetary authority act when faced with increasing uncertainty about the impact of its policy actions? The starting point is the assumption that the Central Bank can influence nominal or real economic variables, for example, using its monetary instruments. But depending on the degree of stability of the economic agents’ behavior, or depending on changes in technology or in the institutional structure, the effect of some policy actions may be more or less uncertain. Therefore, when this uncertainty is increased: Should the Central Bank use its instruments more cautiously or, conversely, to apply them with more intensity? This question is probably as old as the art of economic policy. However, its formal treatment began with the seminal paper of Brainard in the late 1960s, and continues today. In this article, and by using a sequence of small models but of growing complexity, I progressively introduce the main existing analytical results so far, I present comparative conclusions, and I suggest future research lines. The derivation of various results is presented in this work within a unified methodological framework using feedback rules, feedback gain coefficients and Riccati equations. This allows a better understanding of the analytic progression, and also provides a methodological basis that can be useful to obtain new results. First, I review results pertaining to deterministic problems, beginning with the classic Tinbergen result for static models and its redefinition in dynamic models. Secondly, I present the problem of “caution” versus “intensity” in problems with parametric uncertainty in a context of optimal control. I present the results of Chow for the case of current uncertainty; those of Craine for the case of future uncertainty; those of Mercado for the case that both types of uncertainty arise simultaneously; and those of Athans, Ku and Gershwin in relation to the “uncertainty threshold principle”. Thirdly, I present the problem of “caution” versus “intensity” in problems with model uncertainty in a context of robust control, and I introduce the results derived by Gonzalez and Rodriguez for the cases of current and future uncertainty. The main conclusion is that the results depend on the type of uncertainty (parametric or model uncertainty), the timing of the uncertainty (current or future), and the time horizon (finite or infinite). For optimal control with parametric uncertainty in the parameter associated with the policy variable, the optimal policy response is more cautious in the case of an increase in current uncertainty, while it becomes more intense in the case of an increase in future uncertainty. For an infinite horizon, caution prevails. Contrasting, in the case of robust control with model uncertainty, the optimal policy response becomes more and more intense as uncertainty increases, but beyond a certain level of uncertainty, the response changes of behavior and becomes more and more cautious. And also in contrast to the case of optimal control, this response is the same for both current and future uncertainty, as well as in the case of an infinite horizon. Most problems I dealt with in this article are of the linear quadratic form, with one target variable and one policy instrument, a standard formulation used to deal with them so far. In that sense, there are a number of scarcely explored lines of research that go beyond that formulation, such us: multivariate models, models with rational expectations, models with passive learning (using Kalman filters) or active learning (Dual control), and models with functional forms different from the linear quadratic one.