Bruce McGough

Using a Long-Term Interest Rate as the Monetary Policy Instrument

Using a short-term interest rate as the monetary policy instrument can be problematic near its zero bound constraint. An alternative strategy is to use a long-term interest rate as the policy instrument. We find when Taylor-type policy rules are used to set the long rate in a standard New Keynesian model, indeterminacy - that is, multiple rational expectations equilibria - may often result. However, a policy rule with a long rate policy instrument that responds in a forward-looking fashion to inflation expectations can avoid the problem of indeterminacy.

Multiple Equilibria in Heterogeneous Expectations Models

This paper fills an important gap in the literature on determinacy and existence of sunspot equilibria in stochastic linear self-referential models. The results in this paper demonstrate that heterogeneity in expectations may alter a models regions of determinacy. We show how to associate with a heterogeneous expectations model (HE-model) a rational expectations model (ARE-model), the solutions to which are the equilibria of the HE-model. This association recasts the analysis of determinacy in the HE-model to analysis of determinacy in the ARE-model. We proceed to study a forward looking model and find that the stability properties of rational expectations models may not be robust. In particular, we present new results showing that in some models even a very small fraction of non-rational agents may preclude rational agents from coordinating on sunspots. Also, we present parameterizations of the model in which sunspots exist in the heterogeneous model when they do not exist in the rational expectations version of the model.

Statistical Learning With Time-Varying Parameters

In their landmark paper, Bray and Savin note that the constant-parameters model used by their agents to form expectations is misspecified and that, using standard econometric techniques, agents may be able to determine the time-varying nature of the models parameters. Here, we consider the same type of model as employed by Bray and Savin except that our agents form expectations using a perceived model with parameters that vary with time. We assume agents use the Kalman filter to form estimates of these time-varying parameters. We find that, under certain restrictions on the structure of the stochastic process and on the value of the stability parameter, the model will converge to its rational expectations equilibrium. Further, the restrictions on the stability parameter required for convergence are identical to those found by Bray and Savin.

Indeterminacy and the Stability Puzzle in Non-Convex Economies

We extend common factor analysis to a multi-dimensional setting by considering a bivariate reduced form consistent with many Real Business Cycle type models. We show how to obtain new representations of sunspots and find that there are parameter regions in which these sunspots are stable under learning. However, once the parameters are restricted to coincide with those generated by certain standard models of indeterminacy, we find, under one information assumption, that no stable sunspots exist, and under another information assumption, that they exist only for a very small part of the indeterminacy region. This leads to the following puzzle: why does indeterminacy almost always imply instability in RBC-type models?

ADAPTIVE LEARNING IN REGIME-SWITCHING MODELS

We study adaptive learning in economic environments subject to recurring structural change. Stochastically evolving institutional and policymaking features can be described by regime-switching models with parameters that evolve according to finite state Markov processes. We demonstrate that in nonlinear models of this form, the presence of sunspot equilibria implies two natural schemes for learning the conditional means of endogenous variables: under mean value learning, agents condition on a sunspot variable that captures the self-fulfilling serial correlation in the equilibrium, whereas under vector autoregression learning (VAR learning), the self-fulfilling serial correlation must be learned. We show that an intuitive condition ensures convergence to a regime-switching rational expectations equilibrium. However, the stability of sunspot equilibria, when they exist, depends on whether agents adopt mean value or VAR learning: coordinating on sunspot equilibria via a VAR learning rule is not possible. To illustrate these phenomena, we develop results for an overlapping-generations model and a New Keynesian model.

Adaptive Learning, Endogenous Inattention, and Changes in Monetary Policy

This paper develops an adaptive learning formulation of an extension to the Ball, Mankiw, and Reis (2005) sticky information model that incorporates endogenous inattention. We show that, following an exogenous increase in the policymakers preferences for price vs. output stability, the learning process can converge to a new equilibrium in which both output and price volatility are lower.

Representations and Sunspot Stability

By endowing his agents with simple forecasting models, or representations, Woodford (1990) found that finite state Markov sunspot equilibria may be stable under learning. We show that common factor representations generalize to all sunspot equilibria the representations used by Woodford (1990). We find that if finite state Markov sunspots are stable under learning then all sunspots are stable under learning, provided common factor representations are used.

Implementing Optimal Monetary Policy in New-Keynesian Models with Inertia

We consider optimal monetary policy in New Keynesian models with inertia due to lagged effects of inflation and output. We characterize the conditions for the unconditionally optimal equilibrium and compare them with those identifying optimality from the timeless perspective. Implementation of optimal policy is considered via construction of suitable interest-rate rules. We characterize the collection of all interest-rate rules consistent with the optimal equilibrium, and we identify among them an expectations-based rule that guarantees uniqueness and stability under learning.

Microloans, education and growth

This paper constructs a two‐period overlapping generations model of human capital investment decisions where a microloan program designed to finance entrepreneurial activities is active. It is shown that, in the presence of human capital externalities, microloans that are small and have immediate repayment can be growth depressing, and welfare decreasing, through their effect on the opportunity cost of schooling. By increasing the opportunity cost of schooling, such microloans divert investment away from human capital: by failing to internalize the social returns to education, households’ individually optimal investment decisions in the face of microcredit availability act to depress the growth of the economy and result in suboptimal welfare outcomes. Conditions under which these negative effects can occur are identified and potential solutions are suggested.

INTRODUCTION TO THE SYMPOSIUM ON INEQUALITY, UNCERTAINTY, AND MACRO-FINANCIAL DYNAMICS: RECENT ECONOMIC EVENTS

The importance of understanding the relationship between macroeconomics and finance was brought into sharp relief by the recent financial crisis and ensuing recession. The papers collected in this Symposium and discussed in this Introduction attempt to shed light on this relationship. (JEL C14, C20, E30, G10)