Taylor rules in the open economy

Taylor rules, which link short-term interest rates to fluctuations in inflation and output, have been shown to be a good guide (both positively and normatively) to the conduct of monetary policy. As a result they have been used extensively to model policy in the context of both closed and open economy models. Their determinacy properties have also been analysed in the context of closed and, to a more limited degree, in small open economy models. In this paper, we extend the analysis of the determinacy properties of Taylor rules to the case of a benchmark two-country model. When the rules are specified in terms of output-price inflation we confirm and extend the conventional results from the closed economy literature—satisfying the Taylor principle is the key to ensuring determinacy, although the presence of backward-looking price-setting can affect the determinacy properties of the two-country model. However, the conventional results do not hold when we replace output-price inflation with consumer price inflation in the specification of the rule. In this case, Taylor rules which satisfy the Taylor principle will be indeterminate, unless there is an unusually large home bias in consumption. Similar indeterminacy problems arise when one country targets CPI inflation and the other output-price inflation. In this case we show that, even if determinacy is achieved, large spillovers may occur between countries.     

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.     

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.     

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.     

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.     

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.     

Stabilising Taylor rules when the supply shock has a unit root

This paper studies the implication of unit root supply shocks for the Taylor rule. I find that, when supply shocks have a unit root, if a central bank wishes to guarantee the stationarity of inflation, then their interest rate reaction function should not respond to the output gap. Once the stationarity of inflation is guaranteed by the output-gap-response parameter, the “Taylor principle” can be applied for warranting determinacy of the dynamics.     

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.     

Monetary policy and stock price dynamics with limited asset market participation

We study a New-Keynesian DSGE model subject to limited asset market participation (LAMP) and assess whether monetary policy should respond to stock prices for what concerns the determinacy and the learnability (E-stability) of the Rational Expectations Equilibrium (REE). We find that interest rate rules granting a positive response to stock prices facilitate both the determinacy and the E-stability of the fundamental REE when the degree of LAMP is sufficiently large to generate an inverted aggregate demand channel of monetary policy transmission. Moreover, according to our analysis, policy rules responding to stock prices appear to perform better than more standard rules responding to output with respect to both equilibrium determinacy and aggregate welfare.     

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.     

Optimal monetary policy under Calvo pricing with Bertrand competition

We consider a NK model characterized by a small and fixed number of firms competing in prices à la Bertrand and we study the implications for monetary policy under both exogenous and endogenous market concentration. We find that the implied NKPC has a lower slope compared to a standard NK model with atomistic firms, and the determinacy region enlarges assuming a standard Taylor rule. We characterize the impact of competition on the optimal monetary rules within the linear-quadratic approach of Rotemberg–Woodford. The optimal monetary rule requires a less aggressive reaction to inflationary shocks compared to monopolistic competition, but an increase in competition, due to either an increase in substitutability between the goods or in the number of firms, makes it optimal to adopt a more aggressive reaction in front of inflationary shocks. Finally, more competition increases the gains from commitment.     

Central bank instruments, fiscal policy regimes, and the requirements for equilibrium determinacy

This paper examines the role of the monetary instrument choice for local equilibrium determinacy under sticky prices and different fiscal policy regimes. Corresponding to Benhabib et al.'s results for interest rate feedback rules [Benhabib, J., Schmitt-Grohé, S., Uribe, M., 2001. Monetary policy and multiple equilibria. American Economic Review 91, 167–185], the money growth rate should not rise by more than one for one with inflation when the primary surplus is raised with public debt. Under an exogenous primary surplus, money supply should be accommodating—such that real balances grow with inflation—to ensure local equilibrium determinacy. When the central bank links the supply of money to government bonds by controlling the bond-to-money ratio, an inflation stabilizing policy can be implemented for both fiscal policy regimes. Local determinacy is then ensured when the bond-to-money ratio is not extremely sensitive to inflation, or when interest payments on public debt are entirely tax financed, i.e., the budget is balanced.     

Heterogeneous expectations,indeterminacy, and postwar US business cycles

This paper estimates a New Keynesian model extended to include heterogeneous expectations: consumers and firms form either rational or boundedly-rational expectations. The inclusion of heterogeneous expectations alters the determinacy properties of the model, with the details of expectations potentially becoming more influential than the Taylor principle for equilibrium stability.The model is estimated with Bayesian techniques, using rolling windows and allowing the parameters to fall both in the determinacy and indeterminacy regions. The estimates reveal large shares of agents who depart from rational expectations. Heterogeneous expectations are decisively preferred by the data everywhere in the sample.Finally, the paper revisits the narrative that sees postwar US macroeconomic data as consistent with indeterminacy in the pre-1979 sample, with a switch to determinacy starting in the early 1980s, and it shows that it is overall robust to inclusion of heterogeneous expectations.     

Fiscal Rules,Interest Payments on Debt,and the Irrelevance of the Taylor Principle

We show that in New Keynesian models with non‐neutral government debt, the Taylor principle ceases to be relevant for equilibrium determinacy if the government follows a fiscal rule of levying taxes in proportion to its interest payments on existing debt. This is in contrast with previous studies, which typically have assumed that taxes respond to the level of debt, and have found either a confirmation or reversal of the Taylor principle depending on the feedback from debt to taxes. We find, instead, that the equilibrium effect of the interest rate on debt is crucial for determinacy. If, as in our model, taxes are raised in response to debt interest payments, the range of indeterminacy monotonically decreases with the fiscal feedback parameter. When interest payments are completely tax‐financed, indeterminacy is ruled out without any restrictions on monetary policy.     

Equilibrium Determinacy under Monetary and Fiscal Policies in an Overlapping Generations Model

This paper studies the issue of equilibrium determinacy under monetary and fiscal policy feedback rules in an optimizing general equilibrium model with overlapping generations and flexible prices. It is shown that equilibria may be determinate also when monetary and fiscal policies are both 'passive'. In particular, under passive monetary rules, equilibrium uniqueness is more likely to be verified when fiscal policies are less committed to public debt stabilization.     

基于金融稳定的非线性泰勒规则*——中国的经验证据

本文首先构建了金融稳定指数,并结合中国实际进行了验证,结果表明该指数能够较好地反映中国金融业的稳定状况;然后基于STR模型构建了考虑金融稳定的非线性泰勒规则模型,并以中国的经验数据进行了估计和检验。结果发现：以滞后一期产出缺口为转换变量的、考虑金融稳定的泰勒规则呈现出非线性特征;与不考虑金融稳定的非线性泰勒规则相比,以滞后一期产出缺口为转换变量的、考虑金融稳定的非线性泰勒规则,满足泰勒条件,在拟合优度方面表现更好,有助于中央银行在实现价格、产出目标的同时兼顾金融稳定。     

Friedman's Money Supply Rule vs. Optimal Interest Rate Policy

Using New Keynesian models, we compare Friedman's k‐percent money supply rule to optimal interest rate setting, with respect to determinacy, stability under learning and optimality. First we review the recent literature: open‐loop interest rate rules are subject to indeterminacy and instability problems, but a properly chosen expectations‐based rule yields determinacy and stability under learning, and implements optimal policy. We show that Friedman's rule also can generate equilibria that are determinate and stable under learning. However, computing the mean quadratic welfare loss, we find for calibrated models that Friedman's rule performs poorly when compared to the optimal interest rate rule.     

Monetary policy with sticky prices and segmented markets

Summary. We consider a sticky-price model with segmented asset markets, and examine its implications for monetary policy. Our finding is, first, that the response of the money supply growth rate to a money demand shock required to stabilize inflation is not affected by the existence of a liquidity effect, but the response of the nominal interest rate is. Second, when the monetary authority adopts a Taylor rule, whether or not it should be active to obtain local determinacy of equilibria depends on the existence of a liquidity effect. Our results suggest that the monetary authority should be careful about the existence and the degree of a liquidity effect particularly when the nominal interest rate is used as the policy instrument.Received: 11 February 2004, Revised: 1 November 2004 JEL Classification Numbers: E3, E4, E5.     

Determinacy, stock market dynamics and monetary policy inertia

We study equilibrium determinacy in a New-Keynesian model where the Central Bank responds to asset prices growth. Unlike Taylor-type rules that react to asset prices, the proposed alternative does not harm dynamic stability and in certain cases promotes determinacy by inducing interest-rate inertia.