Investment and Monetary Policy: Learning and Determinacy of Equilibrium

We explore determinacy and expectational stability (learnability) of rational expectations equilibrium (REE) in New Keynesian (NK) models that include capital. Using a consistent calibration across three different models—labor‐only, firm‐specific capital, or an economy‐wide rental market for capital, we provide a clear picture of when REE is determinate and learnable and when it is not under a variety of monetary policy rules. Our findings make a case for greater optimism concerning the use of such rules in NK models with capital. While Bullard and Mitra’s (2002, 2007) findings for the labor‐only NK model do not always extend to models with capital, we show that determinate and learnable REE can be achieved in NK models with capital if there is (i) plausible capital adjustment costs, (ii) some weight given to output in the policy rule, and/or (iii) a policy of interest rate smoothing.     

Robust monetary policy with imperfect knowledge

We examine the performance and robustness properties of monetary policy rules in an estimated macroeconomic model in which the economy undergoes structural change and where private agents and the central bank possess imperfect knowledge about the true structure of the economy. Policymakers follow an interest rate rule aiming to maintain price stability and to minimize fluctuations of unemployment around its natural rate but are uncertain about the economy's natural rates of interest and unemployment and how private agents form expectations. In particular, we consider two models of expectations formation: rational expectations (RE) and learning. We show that in this environment the ability to stabilize the real side of the economy is significantly reduced relative to an economy under RE with perfect knowledge. Furthermore, policies that would be optimal under perfect knowledge can perform very poorly if knowledge is imperfect. Efficient policies that take account of private learning and misperceptions of natural rates call for greater policy inertia, a more aggressive response to inflation, and a smaller response to the perceived unemployment gap than would be optimal if everyone had perfect knowledge of the economy. We show that such policies are quite robust to potential misspecification of private sector learning and the magnitude of variation in natural rates.     

Inflation targeting: What inflation rate to target?

In an economy with nominal rigidities in both an intermediate good sector and a finished good sector, and thus with a natural distinction between CPI and PPI inflation rates, a benevolent central bank faces a tradeoff between stabilizing the two measures of inflation, a final output gap and, unique to our model, a real marginal cost gap in the intermediate sector, so that optimal monetary policy is second-best. We discuss how to implement the optimal policy with minimal information requirement and evaluate the robustness of these simple rules when the central bank may not know the exact sources of shocks or nominal rigidities. A main finding is that a simple hybrid rule under which the short-term interest rate responds to CPI inflation and PPI inflation results in a welfare level close to the optimum, whereas policy rules that ignore PPI inflation or PPI sector shocks can result in significant welfare losses.     

Asymmetric Preferences and the Stability Problem for Optimal Monetary Policy Rules

This paper evaluates the stability properties of optimal monetary policy rules when professionals under adaptive learning have asymmetric preferences. The asymmetric preferences require volatility estimates in real time. An expectations‐based rule can stabilize the economy, while a fundamentals‐based rule leads to instability.     

Inflation targeting and nominal-income-growth targeting: When and why are they suboptimal?

We compare optimal and simple interest-rate rules. Our model features optimizing agents, monopolistic competition in both product and labor markets, and one-period nominal contracts (for wages alone or for both wages and prices) signed before shocks are known. Exact solutions ensure that we obtain correct welfare rankings. Optimal rules maximize the unconditional expected utility of the representative agent with commitment subject to the information set of the policymaker. Even with monopolistic distortions, the optimal full-information rule makes the economy mimic the hypothetical full-flexibility equilibrium. Strict versions of inflation targeting, nominal-income-growth targeting, and other such simple rules are suboptimal under both full and partial information but flexible versions are optimal under certain partial-information assumptions. Nominal-income-growth targeting dominates inflation targeting for plausible parameter values.     

Learnability and monetary policy: A global perspective

The recent literature on monetary policy design has emphasized the importance of equilibrium determinacy and learnability in the choice of policy rules. This paper contains an analysis of the learnability of the equilibrium in a class of simple, micro-founded models in which the policy authority uses a Taylor-type monetary policy rule. Unlike previous analyses, the model economy is not linearized about a steady state—instead, a global perspective is adopted. Globally, the nonlinear model economy can possess rational expectations equilibria other than the steady state consistent with the inflation target of the monetary authorities. These include a second, low inflation ‘liquidity trap’ steady state, periodic equilibria, and sunspot equilibria. The main results in the paper characterize the conditions under which these alternative equilibria maybe stable under adaptive learning, even when the policy rule obeys the Taylor principle. The stability of multiple equilibria is associated with policy rules which are forecast-based. An important finding is that backward-looking Taylor-type policy rules can guarantee that the unique learnable equilibrium is the steady state associated with the inflation target of the monetary authority.     

Monetary policy under model and data-parameter uncertainty

Empirical Taylor rules are much less aggressive than those derived from optimization-based models. This paper analyzes whether accounting for uncertainty across competing models and (or) real-time data considerations can explain this discrepancy. It considers a central bank that chooses a Taylor rule in a framework that allows for an aversion to the second-order risk associated with facing multiple models and measurement-error configurations. The paper finds that if the central bank cares strongly enough about stabilizing the output gap, this aversion leads to significant declines in the coefficients of the Taylor rule even if the central bank's loss function assigns little weight to reducing interest rate variability. Furthermore, a small degree of aversion can generate an optimal rule that matches the empirical Taylor rule.     

Adaptive learning, forecast-based instrument rules and monetary policy

This paper argues that recently popular forecast-based instrument rules for monetary policy may fail to stabilize economic fluctuations. In a New Keynesian model of output gap and inflation determination in which private agents face multi-period decision problems, but have non-rational expectations and learn over time, if the monetary authority adopts a forecast-based instrument rule and responds to observed private forecasts then this class of policies frequently induce divergent learning dynamics. A central bank that correctly understands private behavior can mitigate such instability by responding to the determinants of private forecasts. This suggests gathering information on the determinants of expectations to be useful.     

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 by the central bank 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.     

Fiscal Adjustment and Inflation Targeting in Less Developed Countries

Inflation targeting may not be viable in less developed countries (LDCs) where policymakers rely too heavily on cuts in infrastructure investment to balance the budget. Using a mix of analytical and numerical methods, we demonstrate that the equilibrium ceases to be saddle point stable under active policy when infrastructure cuts account for 30–70% of fiscal adjustment and the return on infrastructure exceeds a comparatively low threshold value. The result is robust to the form of the Taylor rule, the degree of real wage flexibility, the initial level of debt, the choice of a balanced‐budget or debt‐targeting rule, and the q‐elasticity of private investment spending.     

Optimal Continuation versus the Timeless Perspective in Monetary Policy

The timeless‐perspective approach suggests that policymakers implement in each period policy actions conforming to a rule that would have been fully optimal to adopt in the distant past. A motivating advantage is that policy henceforth would continue by recommending the same optimality conditions if reconsidered, thereby enhancing credibility. We argue that continuation can alternatively be achieved with better results, on average, in terms of policymakers' objectives, by implementing in each period the time‐invariant policy that is optimal from the viewpoint of the contemporary understanding of objectives and constraints, but while ignoring the conditions that happen to prevail at the time.     

Instability of sunspot equilibria in real business cycle models under adaptive learning

We provide conditions under which a general, reduced-form class of real business cycle (RBC) models has rational expectations equilibria that are both indeterminate and stable under adaptive learning. Indeterminacy of equilibrium allows for the possibility that non-fundamental “sunspot” variable realizations can be used to drive the model, and several researchers have offered calibrated structural models where sunspot shocks play such a role. However, we show that the structural restrictions researchers have adopted lead to reduced-form systems that are always unstable under adaptive learning dynamics, thus calling into question the plausibility of these sunspot-driven RBC models.     

Nowcasting and the Taylor Rule

Actual federal funds rates in the U.S. have, at times, deviated from the recommendations of a simple Taylor rule. This paper proposes a “nowcasting” Taylor rule that preserves the form of the Taylor rule but encompasses realistic assumptions on information observable to policymakers. Because contemporaneous inflation rates and output gaps are not observable at the time policy is set, policymakers must form “nowcasts.” The optimal nowcast will depend, in part, on forecast uncertainty whenever policymakers have asymmetric costs to over‐ and underpredicting inflation and output. Empirical evidence shows that actual policy rates are consistent with those recommended by a nowcasting Taylor rule.     

The Value of Interest Rate Stabilization Policies When Agents Are Learning

We examine the expectational stability (E-stability) of rational expectations equilibrium in the "New Keynesian" model where monetary policy is optimally derived and interest rate stabilization is added to the central bank's traditional objectives of inflation and output stabilization. We consider both the case where the central bank lacks a commitment technology and the case of full commitment. We show that for both cases, optimal policy rules yield rational expectations equilibria that are E-stable for a wide range of empirically plausible parameter values. These findings stand in contrast to Evans and Honkapohja's findings for optimal monetary policy rules in environments where interest rate stabilization is not a central bank objective.     

Learning to profit with discrete investment rules

The learning of optimal discrete investment rules is analysed and related to the problem of forecasting financial returns. The aim is twofold: to characterize some 'good' learning methods for agents using investment rules of this form and to explain why many observed investment rules such as technical trading rules are discrete. A consistent estimator for discrete investment rules is used and it is shown, using simulations, that direct estimation of investment rules is preferable to the estimation of forecasting models to be used in such rules. This model and the associated results indicate there are a number of reasons why it may be easier to learn a good discrete investment rule than to learn a continuous rule; this provides a partial explanation of why discrete investment rules are used so widely.     

Optimality of the Friedman Rule in an Overlapping Generations Model with Spatial Separation

Recent models with spatial separation and limited communication suggest that the Friedman rule may not be optimal. This is important in light of the disparity between theory and practice concerning optimal monetary policy. We take a close look at these models and show that intergenerational transfers are key to the suboptimality of the Friedman rule. The Friedman rule is a necessary condition for achieving the efficient allocation in equilibrium. We also show that the Friedman rule is chosen whenever agents can implement mutually beneficial arrangements.     

Monetary Policy Response to Oil Price Shocks

How should monetary authorities react to an oil price shock? This paper shows that in a noncompetitive economy, policies that perfectly stabilize prices entail large welfare costs, hence explaining the reluctance of policymakers to enforce them. The policy trade‐off is nontrivial because oil (energy) is an input to both production and consumption. As welfare‐maximizing policies are hard to implement and communicate, I derive a simple interest rate rule that depends only on observables but mimics the optimal plan in all dimensions. The optimal rule is hard on core inflation but accommodates oil price changes.     

Flexible Majority Rules for Central Banks

We propose a flexible majority rule for central-bank committees where the size of the majority depends monotonically on the change in interest rate within a particular time frame. Small changes in the interest rate require a small share, while larger changes require a larger share of supporting votes. We show that flexible majority rules are superior to simple majority rules.     

Simple versus optimal rules as guides to policy

This paper compares the performance of different policy rules. Our comparisons focus on simple feedback rules versus rules which are optimal, given knowledge of the correct economic structure and the appropriate loss function for the policymaker. First, we compare rule performance when the correct model is not known. Second, we compare rule performance with respect to the frequency-specific behavior for variables of interest. Taken as a whole, our results indicate how the case for a model-specific optimal rule can break down when one relaxes the assumption that the true model is known as well as the assumption that the appropriate loss function is known. Links are made to the literature on monetary policy.