Expectations, Learning and Monetary Policy: An Overview of Recent Research

Expectations about the future are central for determination of current macroeconomic outcomes and the formulation of monetary policy. Recent literature has explored ways for supplementing the benchmark of rational expectations with explicit models of expectations formation that rely on econometric learning. Some apparently natural policy rules turn out to imply expectational instability of private agents?learning. We use the standard New Keynesian model to illustrate this problem and survey the key results about interest-rate rules that deliver both uniqueness and stability of equilibrium under econometric learning. We then consider some practical concerns such as measurement errors in private expectations, observability of variables and learning of structural parameters required for policy. We also discuss some recent applications including policy design under perpetual learning, estimated models with learning, recurrent hyperinflations, and macroeconomic policy to combat liquidity traps and deflation.Imperfect knowledge, learning, interest-rate setting, fluctuations, stability, determinacy.

Expectations, learning and monetary policy: an overview of recent research

Expectations about the future are central for determination of current macroeconomic outcomes and the formulation of monetary policy. Recent literature has explored ways for supplementing the benchmark of rational expectations with explicit models of expectations formation that rely on econometric learning. Some apparently natural policy rules turn out to imply expectational instability of private agents’ learning. We use the standard New Keynesian model to illustrate this problem and survey the key results for interest-rate rules that deliver both uniqueness and stability of equilibrium under econometric learning. We then consider some practical concerns such as measurement errors in private expectations, observability of variables and learning of structural parameters required for policy. We also discuss some recent applications, including policy design under perpetual learning, estimated models with learning, recurrent hyperinflation, and macroeconomic policy to combat liquidity traps and deflation.imperfect knowledge; learning; interest-rate setting; fluctuations; stability; determinacy

Automata games for multiple-model checking

3-valued models have been advocated as a means of system abstraction such that verifications and refutations of temporal-logic properties transfer from abstract models to the systems they represent. Some application domains, however, require multiple models of a concrete or virtual system. We build the mathematical foundations for 3-valued property verification and refutation applied to sets of common concretizations of finitely many models. We show that validity checking for the modal mu-calculus has the same cost (EXPTIME-complete) on such sets as on all 2-valued models, provide an efficient algorithm for checking whether common concretizations exist for a fixed number of models, and propose using parity games on variants of tree automata to efficiently approximate validity checks of multiple models. We prove that the universal topological model in [M. Huth, R. Jagadeesan, and D. A. Schmidt. A domain equation for refinement of partial systems. Mathematical Structures in Computer Science, 14(4):469-505, 5 August 2004] is not bounded complete. This confirms that the approximations aforementioned are reasonably precise only for tree-automata-like models, unless all models are assumed to be deterministic. © 2006 Elsevier B.V. All rights reserved

Equilibria, Fixed Points, and Complexity Classes

Many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind. Examples include Nash equilibria in games; market equilibria; computing optimal strategies and the values of competitive games (stochastic and other games); stable configurations of neural networks; analysing basic stochastic models for evolution like branching processes and for language like stochastic context-free grammars; and models that incorporate the basic primitives of probability and recursion like recursive Markov chains. It is not known whether these problems can be solved in polynomial time. There are certain common computational principles underlying different types of equilibria, which are captured by the complexity classes PLS, PPAD, and FIXP. Representative complete problems for these classes are respectively, pure Nash equilibria in games where they are guaranteed to exist, (mixed) Nash equilibria in 2-player normal form games, and (mixed) Nash equilibria in normal form games with 3 (or more) players. This paper reviews the underlying computational principles and the corresponding classes

On some reduced order models for packed separation processes

The use of packed-bed separation columns as a liquid-gas contact system in absorption and distillation has steadily increased in the chemical and process industries and with it the need for tools for their adequate design and control. The mathematical models for packed separation columns are known for their large dimensionality. This can pose a problem when one considers the design and/or optimisation of systems involving more than one column or a single large column. The use of reduced-order models came as an answer to this problem. Reduced-order models presented to date do not rigorously solve the mass transfer subproblem. Four generalised steady-state reduced-order models for separation processes in packed columns are developed and compared in this work. The models are based on the two film theory of mass transfer and the more rigorous of them have as a starting point one of the so called rate based methods. The mass and energy transfer rates across the vapour liquid interface are evaluated by means of different approximate solutions of the Maxwell-Stefan equations for steady-state, unidirectional mass transfer. The differential equations of the models are converted into algebraic equations through the application of the orthogonal collocation procedure on the spatial variable. The resulting system of algebraic equations is subsequently solved using a modification of the Powell hybrid method. Three case studies dealing with distillation columns are presented but the models are easily modified to work with other separation processes (e.g., absorption). The results of the simulations indicated a clear advantage when using more rigorous methods for the computation of the interphase mass transfer rates. Their inclusion in the reduced-order models improved the convergence characteristics of the solution with respect to the number of collocation points and also increased the robustness of the models in converging towards the solution. These improvements were obtained without increasing significantly the time spent in the simulations when compared with a model using an effective diffusivity approach in the evaluation of the mass transfer rates

Moment matching versus Bayesian estimation: Backward-looking behaviour in the new-Keynesian three-equations model

The paper considers an elementary New-Keynesian three-equations model and contrasts its Bayesian estimation with the results from the method of moments (MM), which seeks to match the model-generated second moments of inflation, output and the interest rate to their empirical counterparts. Special emphasis is placed on the degree of backward-looking behaviour in the Phillips curve. While, in line with much of the literature, it only plays a marginal role in the Bayesian estimations, MM yields values of the price indexation parameter close to or even at its maximal value of one. These results are worth noticing since the matching thus achieved is entirely satisfactory. The matching of some special (and even better) versions of the model is econometrically evaluated by a model comparison test. --inflation persistence,autocovariance profiles,goodness-of-fit,model comparison

Effects of short-term thinking on investment and implications for macroeconomic policies

In this thesis, after a brief introduction, three papers on the effects of short-term thinking on the economy are presented, where short-term thinking is defined to encompass both short-termistic incentive structures as well as imperfectly forward-looking expectations. The first paper studies the impact of short-termistic incentives for managers of American corporations on their decisions regarding the capital mix of their companies. The second paper presents a New Keynesian model with rigid wages and myopic expectations and assesses the performance of simple monetary policy rules. The final chapter uses a medium-scale dynamic stochastic general equilibrium model to study to what extent multipliers of government investment depend, inter alia, on the forward-lookingness of agents' expectations.In der vorliegenden Arbeit werden nach einer kurzen Einleitung drei Aufsätze zu den Effekten kurzfristigen Denkens auf die Ökonomie betrachtet. Unter "kurzfristigem Denken" werden sowohl kurzfristige Anreizsysteme als auch unvollkommen vorausschauende Erwartungen subsumiert. Der erste Aufsatz untersucht die Auswirkungen kurzfristiger Anreizsysteme bei Managern US-amerikanischer Unternehmen auf die Wahl ihres Kapitalstocks. Der zweite Aufsatz beleuchtet im Rahmen eines neukeynesianischen Modells mit Lohnrigiditäten die Stabilisierungseigenschaften unterschiedlicher einfacher geldpolitischer Regeln, wenn Wirtschaftssubjekte myopische Erwartungen aufweisen. Im Rahmen des letzten Aufsatzes wird mittels eines dynamischen stochastischen allgemeinen Gleichgewichtsmodells untersucht, inwiefern der Ausgabenmultiplikator auf öffentliche Investitionen davon abhängt, wie vorausschauend die Erwartungen der Wirtschaftssubjekte sind

Essays in Empirical Macroeconomics

This thesis consists of three self-contained chapters in empirical macroeconomics and analyzes important issues related to monetary policy and labor supply. The first chapter deals with the problem of weak identification in the estimation of inflation dynamics and a monetary policy rule. We suggest constructing additional instruments by estimating factors from a large macroeconomic data set. The rationale underlying the use of the factor-augmented instrument set is that a central banker relies on a large information set in his forecasts of important macroeconomic variables. In the final two parts of this thesis, the focus shifts to the aggregation and estimation of labor supply elasticities. The second chapter develops an aggregation procedure for the Frisch elasticity of labor supply. The exact size of this particular elasticity matters a lot when macroeconomists try to assess the quantitative implications of certain types of policies on employment and hours worked. A particular emphasis is laid on worker heterogeneity in observables and unobservables and applicability to an individual labor supply function with non-employment as a possible outcome. The third chapter treats the estimation of micro elasticities of labor supply for the entire conditional hours distribution. Not only economists but also policy-makers are interested in estimates of the Marshallian and the Hicks elasticities: the responsiveness of hours worked to changes in the wage rate induced by tax increases determines the amount of tax revenue raised

Competitive optimisation on timed automata

Timed automata are finite automata accompanied by a finite set of real-valued variables called clocks. Optimisation problems on timed automata are fundamental to the verification of properties of real-time systems modelled as timed automata, while the control-program synthesis problem of such systems can be modelled as a two-player game. This thesis presents a study of optimisation problems and two-player games on timed automata under a general heading of competitive optimisation on timed automata. This thesis views competitive optimisation on timed automata as a multi-stage decision process, where one or two players are confronted with the problem of choosing a sequence of timed moves—a time delay and an action—in order to optimise their objectives. A solution of such problems consists of the “optimal” value of the objective and an “optimal” strategy for each player. This thesis introduces a novel class of strategies, called boundary strategies, that suggest to a player a symbolic timed move of the form (b, c, a)— “wait until the value of the clock c is in very close proximity of the integer b, and then execute a transition labelled with the action a”. A distinctive feature of the competitive optimisation problems discussed in this thesis is the existence of optimal boundary strategies. Surprisingly perhaps, many competitive optimisation problems on timed automata of practical interest admit optimal boundary strategies. For example, optimisation problems with reachability price, discounted price, and average-price objectives, and two-player turn-based games with reachability time and average time objectives. The existence of optimal boundary strategies allows one to work with a novel abstraction of timed automata, called a boundary region graph, where players can use only boundary strategies. An interesting property of a boundary region graph is that, for every state, the set of reachable states is finite. Hence, the existence of optimal boundary strategies permits us to reduce competitive optimisation problem on a timed automaton to the corresponding competitive optimisation problem on a finite graph