An inventory of simple monetary policy rules in a New Keynesian macroeconomic model

We derive necessary and sufficient conditions for simple monetary policy rules that guarantee equilibrium determinacy in the New Keynesian monetary model. Our modeling framework is derived from a fully specified optimization model that is amenable to analytical characterisation. The monetary rules analyzed are variants of the basic Taylor rules ranging from simple inflation targeting (current, forward, backward) to canonical Taylor rules with and without inertial nominal interest rates. We establish that determinacy obtains for a wide range of policy parameters, especially when the monetary authority targets output and smoothes interest rates. Contrary to other results in the literature, we do not find a case for super-inertial interest rate policy.     

Evaluating inflation targeting as a monetary policy objective for India

This study formulates a small open economy model for India with exchange rate as a prominent channel of monetary policy. The model is estimated using the Instrumental Variable-Generalized Methods of Moments (IV-GMM) estimator and evaluated through simulations. This study compares different cases of domestic and CPI inflation targeting, strict and flexible inflation targeting, and simple Taylor type rules. The analysis highlights the unsuitability of simple Taylor-type monetary rules in stabilizing the Indian economy and suggests that discretionary optimization works better in stabilizing this economy. There seems to be a trade-off between output gap stabilization and exchange rate stabilization in flexible domestic inflation targeting and CPI inflation targeting respectively. However, flexible domestic inflation targeting seems a better alternative from an overall macro stabilization perspective in India where financial markets are still not sufficiently integrated to ensure quick transmission of interest rate impulses and existence of rigidities in the economy.     

Stabilizing Taylor rules and determinacy under unit root supply shocks: A re-examination

I revisit the stabilizing and determinacy properties of Taylor-type policy rules in the canonical New Keynesian model when allowing for a unit root in the supply shock process. While able to offset inflationary pressure from non-stationary disturbances, interest-rate feedback rules that are unresponsive to fluctuations in the output gap necessarily produce unstable dynamics and explosive volatility for the latter. Specifically, rules fulfilling the Taylor principle are found to enforce the unique (non-stationary) equilibrium featuring well-anchored inflation expectations and immunity to sunspots; yet there exists no equilibrium predicting stationary behavior for both the inflation and output gap series, irrespective of whether the policy stance induces determinacy or indeterminacy. I show this property survives the adoption of forecast-based instrument rules, and also explore the relationship between Taylor-type rules and optimal discretionary policies in this particular New Keynesian environment.     

Wicksellian Rules and the Taylor Principle: Some Practical Implications*

In this paper, we derive and compare the determinacy regions of price-level targeting rules (Wicksellian rules) and Taylor rules in a standard New Keynesian model. We conclude that Wicksellian rules do not require the Taylor principle to hold in order to induce determinacy. Our results have two implications. First, in a univariate setting, the estimation of simple Taylor rules when the true rule is Wicksellian can lead to the erroneous conclusion that the equilibrium is indeterminate. Second, indeterminacy is ruled out when using system-based methods, but it can be concluded that the central bank is less averse to inflation movements than it actually is.     

Optimal monetary policy for a small open economy

This paper focuses on the design of monetary policy rules for a small open economy. The model features optimizing behavior, general equilibrium and price stickiness. The real exchange rate is shown to affect the firm's real marginal cost, aggregate supply and aggregate demand. The welfare objective depends on the openness of the economy, and the optimal policy rule differs from that which obtains in a closed economy. The inflation versus output gap stabilization trade-off is caused by the real exchange rate. The implied optimal monetary policy regime is domestic inflation target coupled with controlled floating of the real exchange rate.     

Does it matter (for equilibrium determinacy) what price index the central bank targets?

What inflation rate should the central bank target? We address determinacy issues related to this question in a two-sector model in which prices can differ in equilibrium. We assume that the degree of nominal price stickiness can vary across the sectors and that labor is immobile. The contribution of this paper is to demonstrate that a modified Taylor Principle holds in this environment. If the central bank elects to target sector one, and if it responds with a coefficient greater than unity to price movements in this sector, then this policy rule will ensure determinacy across all sectors. The results of this paper have at least two implications. First, the equilibrium-determinacy criterion does not imply a preference to any particular measure of inflation. Second, since the Taylor Principle applies at the sectoral level, there is no need for a Taylor Principle at the aggregate level.     

Monetary Policy and Exchange Rate Volatility in a Small Open Economy

We lay out a small open economy version of the Calvo sticky price model, and show how the equilibrium dynamics can be reduced to a simple representation in domestic inflation and the output gap. We use the resulting framework to analyse the macroeconomic implications of three alternative rule-based policy regimes for the small open economy: domestic inflation and CPI-based Taylor rules, and an exchange rate peg. We show that a key difference among these regimes lies in the relative amount of exchange rate volatility that they entail. We also discuss a special case for which domestic inflation targeting constitutes the optimal policy, and where a simple second order approximation to the utility of the representative consumer can be derived and used to evaluate the welfare losses associated with the suboptimal rules.     

MONETARY POLICY REGIME SWITCHES AND MACROECONOMIC DYNAMICS*

This article considers the determinacy and distributional consequences of regime switching in monetary policy. Although switching in the inflation target does not affect determinacy, switches in the inflation response can cause indeterminacy. Satisfying the Taylor principle period by period is neither necessary nor sufficient for determinacy when inflation responses switch; indeterminacy can arise if monetary policy responds too aggressively to inflation in the active regime. Inflation target switches primarily impact the level of inflation, whereas inflation response switches primarily impact the volatility. Expecting an inflation target switch has minor effects on volatility, whereas expecting an inflation response switch raises volatility more substantially.     

When does the cost channel pose a challenge to inflation targeting central banks?

In a sticky-price model where firms finance their production inputs, there is both a lower and an upper bound on the central bank's inflation response necessary to rule out the possibility of self-fulfilling inflation expectations. This paper shows that real wage rigidities decrease this upper bound, but coefficients in the range of those on the Taylor rule place the economy well within the determinacy region. However, when there is time-variation in the share of firms who finance their inputs (i.e. Markov-switching) then inflation targeting interest rate rules frequently result in indeterminacy, even if the central bank also targets output. Adding a nominal growth target to the policy rule can often alleviate this indeterminacy and therefore anchor inflation expectations.     

ADAPTIVE LEARNING AND MONETARY POLICY IN AN OPEN ECONOMY: LESSONS FROM JAPAN

Abstract. Motivated by Japan's economic experiences in recent decades, we incorporate adaptive learning into an open economy dynamic stochastic general equilibrium model to examine the volatility and welfare impact of alternative monetary policies. Comparing four Taylor‐styled policy rules that reflect Japan's monetary policy debates, we first show that imperfect knowledge and the associated learning process induce higher volatility in the economy and that explicit exchange rate stabilization is unwarranted. Moreover, contrary to results under the rational expectation paradigm, we find that while tight inflation controls raise output volatility, they can improve overall welfare under learning by smoothing inflation fluctuations.     

Should a central bank react to food inflation? Evidence from an estimated model for Chile

We examine whether food price shocks are a major source of macroeconomic fluctuations. We estimate a small open economy DSGE model using an alternative Taylor rule applied to Chilean data. The empirical evidence suggests that food inflation played a non-trivial role in shaping Chile's de facto monetary policy actions. Consistent with its commitment to price stability, the central bank increases the policy rate in reaction to food inflation. Despite an immediate monetary policy reaction to a food price shock, the policy rate gradually tapers off. This is due to a second-round effect on non-food inflation propagated by the food price shock. A main finding is that monetary policy that targets headline inflation is welfare improving.     

Optimal Monetary Policy with Price and Wage Rigidities

In this paper, I search for an optimal configuration of parameters for variants of the Taylor rule by using an accurate second‐order welfare‐based method within a fully microfounded dynamic stochastic model, with price and wage rigidities, without capital accumulation. A version of the model with distortionary taxation is also explicitly tested. The model is solved up to second‐order solution. Optimal rules are obtained by maximizing a conditional welfare measure, differently from what has been done in the current literature. Optimal monetary policy functions turn out to be characterized by inflation targeting parameter lower than in empirical studies. In general, the optimal values for monetary policy parameters depend on the degree of nominal rigidities and on the role of fiscal policy. When nominal rigidities are higher, optimal monetary policy becomes more aggressive to inflation. With a tighter fiscal policy, optimal monetary policy turns out to be less aggressive to inflation. Impulse‐response functions based on second‐order model solution show a non‐affine pattern when the economy is hit by shocks of different magnitude .     

Bubble-free policy feedback rules

We consider a broad class of linear dynamic stochastic rational-expectations models made of a finite number N of structural equations for N+1 endogenous variables and to be closed by one policy feedback rule. We design, for any model of this class and any stationary VARMA solution of that model, a “bubble-free” policy feedback rule ensuring that this solution is not only the unique stationary solution of the closed model, but also its unique solution. We apply these results to locally linearisable models of the monetary transmission mechanism and obtain interest-rate rules that not only ensure the local determinacy of the targeted equilibrium in the neighbourhood of the steady state considered, but also prevent the economy from gradually leaving this neighbourhood.     

Trend inflation and macroeconomic stability in a small open economy

This paper estimates a small open economy New Keynesian model for Australia with positive trend inflation while allowing for multiple equilibria. We first show the extent to which positive trend inflation can shrink the determinacy region. We then conduct a Bayesian estimation over two separate periods: from 1983Q1 to 1993Q1, covering the pre-inflation-targeting regime, and from 1993Q2 to 2018Q4, covering the inflation-targeting regime. We find that Australian monetary policy before the adoption of inflation-targeting permitted multiple equilibria and self-fulfilling inflation expectations to arise, resulting in exacerbated macroeconomic volatility. The implementation of inflation-targeting in Australia in the early 1990s successfully eradicated equilibrium multiplicity and sunspot shocks, and thereby drove the economy towards greater stability.     

Wealth in utility,the Taylor principle and determinacy

Wealth in the utility function leads to the discounting to consumer’s Euler equation, enlarging determinacy regions and making it easier for the monetary authority to ensure equilibrium determinacy. We show that a passive policy rule which adjusts nominal interest rate by less than one-for-one in response to the inflation rate is able to rule out equilibrium indeterminacy, if properly specified, due to the presence of the demand channel of the Taylor principle and equilibrium determinacy. Furthermore, the extent to which monetary policy rule can be passive in order to avoid indeterminacy depends critically on the degree of preference over wealth as well as the underlying structures and parameters of the model.     

Foreign output shocks,monetary rules and macroeconomic volatilities in small open economies

The 2008 financial crisis is marked by the drop in output of major industrial countries which affected small open economies in various degrees. We examine the role of three different types of monetary policy rules in mitigating or exacerbating the effects of a negative foreign output shock on key macroeconomic variables of a small open economy by numerically solving a dynamic stochastic general equilibrium (DSGE) model. We find that compared to the Taylor rule, small open economies that follow either fixed exchange rate regime or strict inflation targeting tend to stabilize real exchange rate and inflation at the expense of substantial instability in the real economy.     

TAYLOR RULE REACTION COEFFICIENTS AND REAL EXCHANGE RATE PERSISTENCE

Recent literature has established a link between the persistence of real exchange rates and the degree of inertia in Taylor rule monetary policy reactions functions. This paper provides a different view on this link by investigating how the size of Taylor rule reaction coefficients impacts the adjustment dynamics of the real exchange rate. Within a stylized sticky‐price open‐economy macro model, it is demonstrated that a stronger interest rate reaction to inflation in the Taylor rule raises the convergence speed of the real exchange rate. Conversely, raising the coefficient on the output gap or attending to the exchange rate in an open‐economy version of the Taylor rule slows down real exchange rate adjustment. In all cases, more rapid convergence comes at the cost of stronger initial real exchange rate misalignments in the wake of monetary policy shocks.     

Firms’ money demand and monetary policy

Standard New Keynesian models for monetary policy analysis are ‘cashless’. When the nominal interest rate is the central bank's operating instrument, the LM equation is endogenous and, it is argued, can be ignored. The modern theoretical and quantitative debate on the importance of money for monetary policy conduct, however, overlooks firms’ money demand. Working in an otherwise canonical New Keynesian setup, we show that macroeconomic dynamics are critically affected by the firms’ money demand choice. Under the conventional Taylor‐rule framework, we prove that equilibrium determinacy may require either an active interest rate policy, overreacting to inflation, or a passive interest rate policy, underreacting to inflation, depending on the elasticity of production with respect to cash balances. We then develop a numerical analysis to evaluate our theoretical results. We find that macroeconomic stability is more likely to occur under an active, but not overly aggressive, monetary policy stance. We also examine the dynamic effects of forward‐looking feedback rules. We show that, in this policy regime, indeterminacy is likely to be induced by both active and passive rules, even for relatively low productivity effects of money.     

INTEREST RATE RULES AND WELFARE IN OPEN ECONOMIES

This paper analyses the welfare performance of a set of five alternative interest rate rules in an open economy stochastic dynamic general equilibrium model with nominal rigidities. A rule with a lagged interest rate term, high feedback on inflation and low feedback on output is found to yield the highest welfare for a small open economy. This result is robust across different degrees of openness, different sources of home and foreign shocks, alternative foreign monetary rules and different specifications for price-setting behaviour. The same rule emerges as both the Nash and cooperative equilibria in a two-country version of the model.