How Robust is Robust Control in the Time Domain?

By applying robust control the decision maker wants to make good decisions when his model is only a good approximation of the true one. Such decisions are said to be robust to model misspecification. In this paper it is shown that both a “probabilistically sophisticated” and a non-“probabilistically sophisticated” decision maker applying robust control in the time domain are indeed assuming a very special kind of “misspecification of the approximating model.” This is true when unstructured uncertainty à la Hansen and Sargent is used or when uncertainty is related to unknown structural parameters of the modelLinear quadratic tracking problem, optimal control, robust control, time-varying parameters

Robust monetary policy in a small open economy

This paper studies how a central bank’s preference for robustness against model misspecification affects the design of monetary policy in a New-Keynesian model of a small open economy. Due to the simple model structure, we are able to solve analytically solve the optimal robust policy rule, and separately ana-lyze the effects of robustness against misspecification concerning the determination of inflation, output and the exchange rate. We show that an increased central bank preference for robustness makes monetary policy respond more aggressively or more cautiously to shocks, depending on the type of shock and the source of misspecification.Knightian uncertainty; model uncertainty; robust control; min-max policies

Monetary policy in a small open economy with a preference for robustness

We use robust control techniques to study the effects of model uncertainty on monetary policy in an estimated, semi-structural, small-open-economy model of the U.K. Compared to the closed economy, the presence of an exchange rate channel for monetary policy not only produces new trade-offs for monetary policy, but it also introduces an additional source of specification errors. We find that exchange rate shocks are an important contributor to volatility in the model, and that the exchange rate equation is particularly vulnerable to model misspecification, along with the equation for domestic inflation. However, when policy is set with discretion, the cost of insuring against model misspecification appears reasonably small.Monetary policy

Robust Equilibrium Yield Curves

This paper studies the quantitative implications of the interaction between robust control and stochastic volatility for key asset pricing phenomena. We present an equilibrium term structure model in which output growth is conditionally heteroskedastic. The agent does not know the true model of the economy and chooses optimal policies that are robust to model misspecification. The choice of robust policies greatly amplifies the effect of conditional heteroskedasticity in consumption growth, improving the model's ability to explain asset prices. In a robust control framework, stochastic volatility in consumption growth generates both a state-dependent market price of model uncertainty and a stochastic market price of risk. We estimate the model using data from the bond and equity market, as well as consumtion data. We show that the model is consistent with key empirical regularities that characterize the bond and equity markets. We also characterize empirically the set of models the robust representative agent entertains, and show that this set is "small". In other words, it is statistically difficult to distinguish between models in this set.Yield curve, market price of uncertainty, robust control

Robustness

The standard theory of decision making under uncertainty advises the decision maker to form a statistical model linking outcomes to decisions and then to choose the optimal distribution of outcomes. This assumes that the decision maker trusts the model completely. But what should a decision maker do if the model cannot be trusted? Lars Hansen and Thomas Sargent, two leading macroeconomists, push the field forward as they set about answering this question. They adapt robust control techniques and apply them to economics. By using this theory to let decision makers acknowledge misspecification in economic modeling, the authors develop applications to a variety of problems in dynamic macroeconomics. Technical, rigorous, and self-contained, this book will be useful for macroeconomists who seek to improve the robustness of decision-making processes.decision-making, uncertainty, statistical models, control techniques, economic modeling, dynamic microeconomics, misspecification

Robust Equilibrium Yield Curves

This paper studies the quantitative implications of the interaction between robust control and stochastic volatility for key asset pricing phenomena. We present an equilibrium term structure model with a representative agent and an output growth process that is conditionally heteroskedastic. The agent does not know the true model of the economy and chooses optimal policies that are robust to model misspecification. The choice of robust policies greatly amplifies the effect of conditional heteroskedasticity in consumption growth, improving the model’s ability to explain asset prices. In a robust control framework, stochastic volatility in consumption growth generates both a state-dependent market price of model uncertainty and a stochastic market price of risk. We estimate the model using data from the bond and equity markets, as well as consumption data. We show that the model is consistent with key empirical regularities that characterize the bond and equity markets. We also characterize empirically the set of models the robust representative agent entertains, and show that this set is ?small?. That is, it is statistically difficult to distinguish between models in this set.Yield curves, Market price of Uncertainty, Robust control.

Walsh’s Contract and Transparency about Central Bank Preferences for Robust Control.

Within a New Keynesian model subject to misspecification, we examine the quadratic contracts in a delegation framework where government and private agents are uncertain about central bank preferences for model robustness. We show that, in the case of complete transparency, the optimal penalty is decreasing in terms of the preference for robustness. In effect, a central bank reacts more aggressively to supply shocks when the model misspecification grows larger. Furthermore, beginning from the equilibrium of perfect transparency and assuming that the average preference for robustness is sufficiently high, the central bank has then an incentive to be less transparent in order to reduce the optimal penalty. Under similar conditions, we also find that greater opacity will increase inflation and output variability.Walsh’s contract, robust control, model uncertainty, central bank transparency.

Approximate Models and Robust Decisions

Decisions based partly or solely on predictions from probabilistic models may be sensitive to model misspecification. Statisticians are taught from an early stage that "all models are wrong", but little formal guidance exists on how to assess the impact of model approximation on decision making, or how to proceed when optimal actions appear sensitive to model fidelity. This article presents an overview of recent developments across different disciplines to address this. We review diagnostic techniques, including graphical approaches and summary statistics, to help highlight decisions made through minimised expected loss that are sensitive to model misspecification. We then consider formal methods for decision making under model misspecification by quantifying stability of optimal actions to perturbations to the model within a neighbourhood of model space. This neighbourhood is defined in either one of two ways. Firstly, in a strong sense via an information (Kullback-Leibler) divergence around the approximating model. Or using a nonparametric model extension, again centred at the approximating model, in order to `average out' over possible misspecifications. This is presented in the context of recent work in the robust control, macroeconomics and financial mathematics literature. We adopt a Bayesian approach throughout although the methods are agnostic to this position

Methods for robust control

Robust control allows policymakers to formulate policies that guard against model misspecification. The principal tools used to solve robust control problems are state-space methods (see Hansen and Sargent 2006 and Giordani and Soderlind 2004). In this paper we show that the structural-form methods developed by Dennis (2006) to solve control problems with rational expectations can also be applied to robust control problems, with the advantage that they bypass the task, often onerous, of having to express the reference model in statespace form. Interestingly, because state-space forms and structural forms are not unique the two approaches do not necessarily return the same equilibria for robust control problems. We apply both state-space and structural solution methods to an empirical New Keynesian business cycle model and find that the differences between the methods are both qualitatively and quantitatively important. In particular, with the structural-form solution methods the specification errors generally involve changes to the conditional variances in addition to the conditional means of the shock processes.Robust control ; Monetary policy ; Econometric models

Learning, Expectations Formation, and the Pitfalls of Optimal Control Monetary Policy

This paper examines the robustness characteristics of optimal control policies derived under the assumption of rational expectations to alternative models of expectations. We assume that agents have imperfect knowledge about the precise structure of the economy and form expectations using a forecasting model that they continuously update based on incoming data. We find that the optimal control policy derived under the assumption of rational expectations can perform poorly when expectations deviate modestly from rational expectations. We then show that the optimal control policy can be made more robust by deemphasizing the stabilization of real economic activity and interest rates relative to inflation in the central bank loss function. That is, robustness to learning provides an incentive to employ a "conservative" central banker. We then examine two types of simple monetary policy rules from the literature that have been found to be robust to model misspecification in other contexts. We find that these policies are robust to empirically plausible parameterizations of the learning models and perform about as well or better than optimal control policies.Rational expectations, robust control, model uncertainty