Estimation of a forward-looking monetary policy rule: A time-varying parameter model using ex post data

In this paper, we consider estimation of a time-varying parameter model for a forward-looking monetary policy rule, by employing ex post data. A Heckman-type (1976. The common structure of statistical models of truncation, sample selection, and limited dependent variables and a simple estimator for such models. Annals of Economic and Social Measurement 5, 475-492) two-step procedure is employed in order to deal with endogeneity in the regressors. This allows us to econometrically take into account changing degrees of uncertainty associated with the Fed's forecasts of future inflation and GDP gap when estimating the model. Even though such uncertainty does not enter the model directly, we achieve efficiency in estimation by employing the standardized prediction errors for inflation and GDP gap as bias correction terms in the second-step regression. We note that no other empirical literature on monetary policy deals with this important issue. Our empirical results also reveal new aspects not found in the literature previously. That is, the history of the Fed's conduct of monetary policy since the early 1970s can in general be divided into three subperiods: the 1970s, the 1980s, and the 1990s. The conventional division of the sample into pre-Volcker and Volcker-Greenspan periods could mislead the empirical assessment of monetary policy.     

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.     

Determinacy, Learnability, and Monetary Policy Inertia

We show how monetary policy inertia can help alleviate problems of indeterminacy and non-existence of stationary equilibrium observed for some commonly studied monetary policy rules. We also find that inertia promotes learnability of equilibrium. The context is a simple, forward-looking model of the macroeconomy widely used in the rapidly expanding literature in this area. We conclude that this might be an important reason why central banks in the industrialized economies display considerable inertia when adjusting monetary policy in response to changing economic conditions.     

International dimensions of optimal monetary policy

This paper provides a baseline general equilibrium model of optimal monetary policy among interdependent economies with monopolistic firms and nominal rigidities. An inward-looking policy of domestic price stabilization is not optimal when firms’ markups are exposed to currency fluctuations. Such a policy raises exchange rate volatility, leading foreign exporters to charge higher prices vis-à-vis increased uncertainty in the export market. As higher import prices reduce the purchasing power of domestic consumers, optimal monetary rules trade off a larger domestic output gap against lower consumer prices. Optimal rules in a world Nash equilibrium lead to less exchange rate volatility relative to both inward-looking rules and discretionary policies, even when the latter do not suffer from any inflationary (or deflationary) bias. Gains from international monetary cooperation are related in a non-monotonic way to the degree of exchange rate pass-through.     

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.     

The Effects of Monetary Policy on Unemployment Dynamics under Model Uncertainty: Evidence from the United States and the Euro Area

This paper explores the role that the imperfect knowledge of the structure of the economy plays in the uncertainty surrounding the effects of rule-based monetary policy on unemployment dynamics in the euro area and the United States. We employ a Bayesian model averaging procedure on a wide range of models which differ in several dimensions to account for the uncertainty that the policymaker faces when setting the monetary policy and evaluating its effect on real economy. We find evidence of a high degree of dispersion across models in both policy rule parameters and impulse response functions. Moreover, monetary policy shocks have very similar recessionary effects on the two economies with a different role played by the participation rate in the transmission mechanism. Finally, we show that a policymaker who does not take model uncertainty into account and selects the results on the basis of a single model may come to misleading conclusions not only about the transmission mechanism, but also about the differences between the euro area and the United States, which are on average essentially small.     

Uncovering the Hit List for Small Inflation Targeters: A Bayesian Structural Analysis

We estimate underlying structural macroeconomic policy objectives of three of the earliest explicit inflation targeters within the context of a small open economy dynamic stochastic general equilibrium model. We assume central banks set policy optimally, such that we can reverse engineer policy objectives from observed time series data. Joint tests of the posterior distributions of these policy preference parameters suggest that the central banks are very similar in their overall objective. None of the central banks show a concern for stabilizing the real exchange rate. All three central banks share a concern for minimizing the volatility in the change in the nominal interest rate. We also show that the resulting optimal policy rule responds to exchange rate movements, even in the case where the central banks do not explicitly care about exchange rate stabilization. This result is also corroborated by results from an alternative simple-rule characterization and estimation of central bank behavior. These last two findings point to the pitfalls of making inferences, from the level of ad hoc simple rules, about what central banks may care about.     

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.     

Optimal Constrained Interest-Rate Rules

We show that if policymakers compute the optimal unconstrained interest-rate rule within a Taylor-type class, they may be led to rules that generate indeterminacy and/or instability under learning. This problem is compounded by uncertainty about structural parameters since an optimal rule that is determinate and stable under learning for one calibration may be indeterminate or unstable under learning under a different calibration. We advocate a procedure in which policymakers restrict attention to rules constrained to lie in the determinate learnable region for all plausible calibrations, and that minimize the expected loss, computed using structural parameter priors, subject to this constraint.     

An investigation of the gains from commitment in monetary policy

We propose a simple framework for analyzing a continuum of monetary policy rules characterized by differing degrees of credibility, in which commitment and discretion become special cases of what we call quasi-commitment. The monetary policy authority is assumed to formulate optimal commitment plans, to be tempted to renege on them, and to succumb to this temptation with a constant exogenous probability known to the private sector. By interpreting this probability as a continuous measure of the (lack of) credibility of the monetary policy authority, we investigate the welfare effect of a marginal increase in credibility. Our main finding is that, in a simple model of the monetary transmission mechanism, most of the gains from commitment accrue at relatively low levels of credibility.     

The extensive margin and monetary policy

The creation of new firms, referred to as the extensive margin, is a significant but overlooked dimension of monetary policy. A monetary VAR documents that monetary policy has significant effects on firm creation. An analytically tractable model combining sticky prices and firm entry shows that entry alters the transmission of monetary policy innovations, acting much like a type of investment in more standard models. Monetary policy rules that offset the uncertainty of productivity shocks can raise the mean level of entry and thereby welfare, suggesting a new motivation for stabilization policy.     

Optimal Monetary Policy with Countercyclical Credit Spreads

We study optimal monetary policy in a New‐Keynesian Dynamic Stochastic General Equilibrium (DSGE) model with a credit channel and relationship lending in banking. We show that borrowers' bank‐specific (deep) habits give rise to countercyclical credit spreads, which, in turn, make optimal monetary policy depart substantially from price stability, under both discretion and commitment. Our analysis shows that the welfare costs of setting monetary policy under discretion (with respect to the optimal Ramsey plan) and of using simpler suboptimal policy rules are strictly increasing in the magnitude of deep habits in credit markets and market power in banking.     

Optimal Fiscal Policy Rules in a Monetary Union

This paper investigates the importance of fiscal policy in providing macroeconomic stabilization in a monetary union. We use a microfounded New Keynesian model of a monetary union, which incorporates persistence in inflation and non-Ricardian consumers, and derive optimal simple rules for fiscal authorities. We find that fiscal policy can play an important role in reacting to inflation, output, and the terms of trade, but that not much is lost if national fiscal policy is restricted to react, on the one hand, to national differences in inflation and, on the other hand, to either national differences in output or changes in the terms of trade. However, welfare is reduced if national fiscal policy responds only to output, ignoring inflation.     

Learning,Monetary Policy,and Asset Prices

We explore the stability properties of interest rate rules granting an explicit response to stock prices in a New Keynesian DSGE model where the presence of non‐Ricardian households makes stock prices nonredundant for the business cycle. We find that responding to stock prices enlarges the policy space for which the equilibrium is both determinate and E‐stable (learnable). In particular, the Taylor principle ceases to be necessary, and determinacy/E‐stability is granted also by mildly passive policy rules. Our results appear to be more prominent in economies featuring a lower elasticity of substitution across differentiated products and/or more rigid labor markets.     

Technical analysis: An asset allocation perspective on the use of moving averages

In this paper, we analyze the usefulness of technical analysis, specifically the widely employed moving average trading rule from an asset allocation perspective. We show that, when stock returns are predictable, technical analysis adds value to commonly used allocation rules that invest fixed proportions of wealth in stocks. When uncertainty exists about predictability, which is likely in practice, the fixed allocation rules combined with technical analysis can outperform the prior-dependent optimal learning rule when the prior is not too informative. Moreover, the technical trading rules are robust to model specification, and they tend to substantially outperform the model-based optimal trading strategies when the model governing the stock price is uncertain.     

Monetary and Fiscal Policy Switching

A growing body of evidence finds that policy reaction functions vary substantially over different periods in the United States. This paper explores how moving to an environment in which monetary and fiscal regimes evolve according to a Markov process can change the impacts of policy shocks. In one regime monetary policy follows the Taylor principle and taxes rise strongly with debt; in another regime the Taylor principle fails to hold and taxes are exogenous. An example shows that a unique bounded non-Ricardian equilibrium exists in this environment. A computational model illustrates that because agents' decision rules embed the probability that policies will change in the future, monetary and tax shocks always produce wealth effects. When it is possible that fiscal policy will be unresponsive to debt at times, active monetary policy (like a Taylor rule) in one regime is not sufficient to insulate the economy against tax shocks in that regime and it can have the unintended consequence of amplifying and propagating the aggregate demand effects of tax shocks. The paper also considers the implications of policy switching for two empirical issues.     

The Cost of Nominal Rigidity in NNS Models

We present a model with Calvo wage and price setting, capital formation, and estimated rules for government spending and monetary policy. Our model captures many aspects of U.S. data, including the volatility that has been observed in various efficiency gaps. We estimate the cost of nominal rigidity—welfare under flexible wages and prices minus welfare with nominal rigidities—to be as much as 3% of consumption each period. Since there are interest rate rules that virtually eliminate this cost, our model suggests that—contrary to Lucas's (2003) assertion—there is considerable room for improvement in demand management policy.     

Optimal simple and implementable monetary and fiscal rules

Welfare-maximizing monetary- and fiscal-policy rules are studied in a model with sticky prices, money, and distortionary taxation. The Ramsey-optimal policy is used as a point of comparison. The main findings are: the size of the inflation coefficient in the interest-rate rule plays a minor role for welfare. It matters only insofar as it affects the determinacy of equilibrium. Optimal monetary policy features a muted response to output. Interest-rate rules that feature a positive response to output can lead to significant welfare losses. The welfare gains from interest-rate smoothing are negligible. Optimal fiscal policy is passive. The optimal monetary and fiscal rule combination attains virtually the same level of welfare as the Ramsey-optimal policy.     

Optimal monetary policy in a small open economy with staggered wage and price contracts

We study optimal monetary policy for a small open economy in a model where both domestic prices and wages are sticky due to staggered contracts. The simultaneous presence of the two forms of nominal rigidities introduces an additional trade-off between domestic inflation and the output gap. We derive a second-order approximation to the average welfare losses that can be expressed in terms of the unconditional variances of the output gap, domestic price inflation, and wage inflation. As a consequence, the optimal policy seeks to minimize a weighted average of these variances. We analyze welfare implications of several alternative simple policy rules, and find that domestic price inflation targeting generates relatively large welfare losses, whereas CPI inflation targeting performs nearly as well as the optimal rule.     

Optimal Monetary Policy Rules and House Prices: The Role of Financial Frictions

We probe the scope for reacting to house prices in simple and implementable monetary policy rules, using a New Keynesian model with a housing sector and financial frictions on the household side. We show that the social‐welfare‐maximizing monetary policy rule features a reaction to house price variations, when the latter are generated by housing demand or financial shocks. The sign and size of the reaction crucially depend on the degree of financial frictions in the economy. When the share of constrained agents is relatively small, the optimal reaction is negative, implying that the central bank must move the policy rate in the opposite direction with respect to house prices. However, when the economy is characterized by a sufficiently high average loan‐to‐value ratio, then it becomes optimal to counter house price increases by raising the policy rate.