Regulation and robust stabilization: a behavioral approach

In this thesis we consider a number of control synthesis problems within the behavioral approach to systems and control. In particular, we consider the problem of regulation, the H! control problem, and the robust stabilization problem. We also study the problems of regular implementability and stabilization with constraints on the input/output structure of the admissible controllers. The systems in this thesis are assumed to be open dynamical systems governed by linear constant coefficient ordinary differential equations. The behavior of such system is the set of all solutions to the differential equations. Given a plant with its to-be-controlled variable and interconnection variable, control of the plant is nothing but restricting the behavior of the to-be-controlled plant variable to a desired subbehavior. This restriction is brought about by interconnecting the plant with a controller (that we design) through the plant interconnection variable. In the interconnected system the plant interconnection variable has to obey the laws of both the plant and the controller. The interconnected system is also called the controlled system, in which the controller is an embedded subsystem. The interconnection of the plant and the controller is said to be regular if the laws governing the interconnection variable are independent from the laws governing the plant. We call a specification regularly implementable if there exists a controller acting on the plant interconnection variable, such that, in the interconnected system, the behavior of the to-becontrolled variable coincides with the specification and the interconnection is regular. Within the framework of regular interconnection we solve the control problems listed in the first paragraph. Solvability conditions for these problems are independent of the particular representations of the plant and the desired behavior.

Why are Federal Funds Rates so Smooth?

US monetary policy is characterized by a substantial degree of inertia. While in principle this may well be the outcome of an optimizing central bank behaviour, the ability of any derived policy rule to match the data relies on so large weights for interest rate smoothing into policy makers' preferences as to be theoretically flawed. In this paper we investigate whether such a puzzle can be interpreted as resulting from the concern of monetary authorities for potential misspecifications of the macroeconomic dynamics. Accordingly, we use a novel thick modeling approach to incorporate model uncertainty into the identification of central bank's preferences. The robust thick policy rule shows the kind of smoothness observed in the data without resorting to implausible values for the preference parameters.Model uncertainty, interest rate smoothing, Fed policy preferences, robust optimal monetary policy

The Performance and Robustness of Interest-Rate Rules in Models of the Euro Area

In this paper, we examine the performance and robustness of optimized interest-rate rules in four models of the euro area that differ considerably in terms of size, degree of aggregation, relevance of forward-looking behavioral elements, and adherence to microfoundations. Our findings are broadly consistent with results documented for models of the U.S. economy: backward-looking models require relatively more aggressive policies with, at most, moderate inertia; rules that are optimized for such models tend to perform reasonably well in forward-looking models, while the reverse is not necessarily true; and, hence, the operating characteristics of robust rules (i.e., rules that perform satisfactorily in all models) are heavily weighted towards those required by backward-looking models.macroeconomic modelling; model uncertainty; monetary policy rules; robustness; euro area

Does Model Uncertainty Lead to Less Central Bank Transparency?

This paper discusses the problem of monetary policy transparency in a simple static robust control framework. In this framework, we identify two sources of monetary policy uncertainty. First, we identify the uncertainty about the central bank’s inflation stabilization preferences, which affects the private sector’s inflation expectations and therefore the realized inflation and output. On the other hand, uncertainty means that central bank is unsure about its model, in the sense that there is a group of approximate models that it also considers as possibly true and its objective is to choose a rule that will work under a range of different model specifications. We find that robustness reveals the emergence of a precautionary behaviour of the central bank in the case of unstructured model uncertainty, reducing thus central bank’s willingness to choice a high degree of monetary policy transparency.central bank transparency, min-max policies, model uncertainty, robust control.

Optimal monetary and fiscal policy with a zero bound on nominal interest rates

I characterize optimal monetary and fiscal policy in a stochastic New Keynesian model when nominal interest rates may occasionally hit the zero lower bound. The benevolent policymaker controls the short-term nominal interest rate and the level of government spending. Under discretionary policy, accounting for fiscal stabilization policy eliminates to a large extent the welfare losses associated with the presence of the zero bound. Under commitment, the gains associated with the use of the fiscal policy tool remain modest, even though fiscal stabilization policy is part of the optimal policy mix

Input-output stabilization of linear systems on Z

A formal framework is set up for the discussion of generalized autoregressive with external input models of the form Ay__Bu, where A and B are linear operators, with the main emphasis being on signal spaces consisting of bounded sequences parametrized by the integers. Different notions of stability are explored, and topological notions such as the idea of a closed system are linked with questions of stabilizability in this very general context. Various problems inherent in using Z as the time axis are analyzed in this operatorial framework

Monetary Policy with Uncertain Central Bank Preferences for Robustness.

In this paper,we consider the transparency of monetary policy in a New Keynesian model with misspecification doubts. Model uncertainty allows us to identify a new source of central bank opacity, which refers to a lack of information about central bank’s preference for model robustness. Thus, taking into account this lack of transparency, we study its impacts on macroeconomic variables. We show that greater transparency can reduce the variability of output gap, inflation as well as that of their expected values.