Determination Of Equilibrium Research Articles

Technological change and monetary policy in a sticky-price model

We developed a sticky-price model that introduces the factors of (a) the non-separability of consumption and labor in the utility function and (b) a technological change induced by the investment of profits, to analyze the determinacy of equilibrium. We found that while engaging in inflation targeting increases the probability of determinacy, engaging in share-price targeting decreases the probability of determinacy in a standard sticky-price model; engaging in both inflation targeting and share-price targeting can increase the probability of determinacy in our model.

FISCAL POLICY UNDER BALANCED BUDGET AND INDETERMINACY: A NEW KEYNESIAN PERSPECTIVE

We investigate the effect of fiscal policy on equilibrium determinacy in a New Keynesian economy with rule-of-thumb (liquidity-constrained) consumers and capital accumulation by focusing on the inter-action between monetary policy and taxation under the assumption of balanced budget. Our main finding is that taxation of firms' monopoly rents enforce the Taylor principle – the prescription that the nominal interest rate must respond more than one for a unitary change in inflation – as a criterion for equilibrium determinacy.

A Critical Remark on the Determinacy of Equilibrium in Woodford’s 'Interest and Prices'

The New Neoclassical Synthesis (NNS) epitomized by Michael Woodford's Interest and Prices (2003) is based on a system of three equations that determines the short-run dynamics of output, inflation and interest-rates. Using a feedback-rule of the interest rate to change in inflation and output gaps, Woodford is able to show that the model converges to the equilibrium. But the mathematical procedure he uses to achieve this important result is formally allowable but logically not correct. This paper presents a brief critique of the Woodford’s strategy and shows that applying the ”classical criteria” for the determinacy of an equilibrium do not alter the main conclusion of Woodford’s framework.

Learning About Inflation Measures for Interest Rate Rules

Empirical evidence suggests that goods are highly heterogeneous with respect to the degree of price rigidity. We develop a DSGE model featuring heterogeneous nominal rigidities across two sectors to study the equilibrium determinacy and stability under adaptive learning for interest rate rules that respond to inflation measures differing in their degree of price stickiness. We find that rules responding to headline inflation measures that assign a positive weight to the inflation of the sector with low price stickiness are more prone to generate macroeconomic instability than rules that respond exclusively to the inflation of the sector with high price stickiness. By this we mean that they are more prone to induce non-learnable fundamental-driven equilibria, learnable self-fulfilling expectations equilibria, and equilibria where fluctuations are unbounded. We discuss how our results depend on the elasticity of substitution across goods, the degree of heterogeneity in price rigidity, as well as on the timing of the rule.

Learning About Inflation Measures for Interest Rate Rules

Empirical evidence suggests that goods are highly heterogeneous with respect to the degree of price rigidity. We develop a DSGE model featuring heterogeneous nominal rigidities across two sectors to study the equilibrium determinacy and stability under adaptive learning for interest rate rules that respond to inflation measures differing in their degree of price stickiness. We find that rules responding to headline inflation measures that assign a positive weight to the inflation of the sector with low price stickiness are more prone to generate macroeconomic instability than rules that respond exclusively to the inflation of the sector with high price stickiness. By this we mean that they are more prone to induce non-learnable fundamental-driven equilibria, learnable self-fulfilling expectations equilibria, and equilibria where fluctuations are unbounded. We discuss how our results depend on the elasticity of substitution across goods, the degree of heterogeneity in price rigidity, as well as on the timing of the rule.

Monetary Policy, Determinacy, and Learnability in a Two-Block World Economy

We study how determinacy and learnability of worldwide rational expectations equilibrium may be affected by monetary policy in a simple, two country, New Keynesian framework under both fixed and flexible exchange rates. We find that open economy considerations may alter conditions for determinacy and learnability relative to closed economy analyses, and that new concerns can arise in the analysis of classic topics such as the desirability of exchange rate targeting and monetary policy cooperation.

Monetary Policy, Determinacy, and Learnability in a Two‐Block World Economy

We study how determinacy and learnability of worldwide rational expectations equilibrium may be affected by monetary policy in a simple, two‐country, New Keynesian framework under both fixed and flexible exchange rates. We find that open economy considerations may alter conditions for determinacy and learnability relative to closed economy analyses and that new concerns can arise in the analysis of classic topics such as the desirability of exchange rate targeting and monetary policy cooperation.

Trend Inflation, Taylor Principle and Indeterminacy

Even low levels of trend inflation substantially affect the dynamics of a basic new Keynesian DSGE model when monetary policy is conducted by a contemporaneous Taylor rule. Positive trend inflation shrinks the determinacy region. Neither the Taylor principle, which requires the inflation coefficient to be greater than one, nor the generalized Taylor principle, which requires that in the long run the nominal interest rate should be raised by more than the increase in inflation, is a sufficient condition for local determinacy of equilibrium. This finding holds for different types of Taylor rules, inertial policy rules and price indexation schemes. Therefore, regardless of the theoretical set up, the monetary literature on Taylor rules cannot disregard average inflation in both theoretical and empirical analysis.

Trend Inflation, Taylor Principle, and Indeterminacy

Positive trend inflation shrinks the determinacy region of a basic New Keynesian dynamic stochastic general equilibrium model when monetary policy is conducted by a contemporaneous interest rate rule. Neither the Taylor principle, which requires the inflation coefficient to be greater than one, nor the generalized Taylor principle, which requires that the nominal interest rate to be raised by more than the increase in inflation in the long run, is a sufficient condition for local determinacy of equilibrium. This finding holds for different types of Taylor rules, inertial policy rules, and price indexation schemes. Therefore, regardless of the theoretical setup, the monetary literature on interest rate rules cannot disregard average inflation in both theoretical and empirical analyses.

ON INTEREST RATE POLICY AND EQUILIBRIUM STABILITY UNDER INCREASING RETURNS: A NOTE

Bullard and Mitra [Journal of Monetary Economics 49 (2002), 1105–1130] find that, in a New Keynesian economy without capital and under four variants of the Taylor rule, the Taylor principle is sufficient to guarantee both determinacy and E-stability of equilibrium in most cases. Xiao [Macroeconomic Dynamics 12 (2008), 22–49] claims that with capital and mild increasing returns the Taylor principle cannot guarantee either determinacy or E-stability with any of the four rules. In this paper we show that in the Calvo-type sticky price models a second-order condition for profit maximization must be satisfied in firms' pricing decision problem, and we point out that the examples given in Xiao's paper to support his conclusion violate this condition. After imposing this condition, we find that increasing returns have little effect on determinacy and E-stability under two of the policy rules but significant effects under the other two. These results are obtained in models both with and without capital.

An Interest Rate Peg Might Be Better than You Think

Active interest rate policy is frequently recommended based on its merits in reducing macroeconomic volatility and being a simple and transparent policy device. In a standard New Keynesian model,we show that an even simpler policy, namely an interest rate peg, can be welfare enhancing: The minimum state variable solution and an autoregessive solution under a peg can lead to lower welfare losses than the unique solution under an active interest rate rule. Given that a peg is usually blamed to facilitate endogenous fluctuations, we further show that a peg can be implemented in a way that ensures equilibrium determinacy.

Interest rate pass-through, monetary policy rules and macroeconomic stability

In this paper we analyze equilibrium determinacy in a sticky price model in which the pass-through from policy rates to retail interest rates is sluggish and potentially incomplete. In addition, we empirically characterize and compare the interest rate pass-through process in the euro area and the U.S. We find that if the pass-through is incomplete in the long run, the standard Taylor principle is insufficient to guarantee equilibrium determinacy. Our empirical analysis indicates that this result might be particularly relevant for bank-based financial systems as for instance that in the euro area.

Financial stability, interest-rate smoothing and equilibrium determinacy

This paper examines the interaction between monetary policy and financial stability and provides an assessment of the implications of banks’ risk management practices for monetary policy. By considering the desire of the central bank to stabilize different types of the “basis” risk as a contribution to financial stability, we derive a set of plausible interest-rate rules characterized by either backward or forward interest-rate smoothing. The paper investigates the determinacy conditions of the rational expectations equilibria obtained under such rules. Contrary to what previously found in the literature, we find that the practice of smoothing interest rates backward does not in general alleviate problems of equilibrium indeterminacy. Moreover, basis risk stabilization may lead to policy rules embedding “forward” interest-rate smoothing, where a new kind of indeterminacy may arise following excessive concern for financial stability.

Learning about monetary policy rules when the cost-channel matters

We study how monetary policy may affect determinacy and expectational stability (E-stability) of rational expectations equilibrium when the cost channel of monetary policy matters. Focusing on instrumental Taylor-type rules and optimal target rules, we show that standard policies can induce indeterminacy and expectational instability when the cost channel is present. A naïve application of the traditional Taylor principle could be misleading, and expectations-based reaction function under discretion does not always induce determinate and E-stable equilibrium. This result contrasts with the findings of Bullard and Mitra [2002. Learning about monetary policy rules. Journal of Monetary Economics 49, 1105–1129] and Evans and Honkapohja [2003. Expectations and stability problem for optimal monetary policies. Review of Economic Studies 70, 807–824] for the standard new Keynesian model. The ability of the central bank to commit to an optimal policy is an antidote to these problems.

Real wage rigidity and the Taylor principle

This paper investigates conditions for equilibrium determinacy in the basic new Keynesian model with real wage rigidity. The determinacy region is increased under forward-looking rules and the Taylor principle continues to ensure equilibrium uniqueness under current-looking rules.

When Does Determinacy Imply Expectational Stability?

In the recent literature on monetary and fiscal policy design, adoption of policies that induce both determinacy and learnability of equilibrium has been considered fundamental to economic stabilization. We study the connections between determinacy of rational expectations equilibrium, and expectational stability or learnability of that equilibrium, in a general class of purely forward-looking models. We ask what types of economic assumptions drive differences in the necessary and sufficient conditions for the two criteria. We apply our result to a relatively general New Keynesian model. Our framework is sufficiently flexible to encompass lags in information, a cost channel for monetary policy, and either Euler equation or infinite horizon approaches to learning. We are able to isolate conditions under which determinacy does and does not imply learnability, and also conditions under which long horizon forecasts make a clear difference to conclusions about expectational stability. The sharpest result is that informational delays break equivalence connections between determinacy and learnability.

Two‐Sector Growth Models with Productive Public Goods: Equilibrium (In)determinacy

In existing two‐sector, human capital‐based endogenous growth models with social constant returns, local equilibrium indeterminacy emerges based upon either differential factor tax rates or sector‐specific externalities. Two primary results are established in this paper. First, once there are productive public goods, the two existing mechanisms are not robust in establishing local indeterminacy. Second, with the congestion effect in the use of public services, local indeterminacy is regained.

Determinacy of Interest Rate Rules with Bond Transaction Services in a Cashless Economy

Canzoneri and Diba (2004) show that the Taylor principle is not a panacea for equilibrium determinacy in a model where bonds and money provide liquidity services to households. We consider a cashl ...

Generic determinacy of Nash equilibrium in network-formation games

This paper proves the generic determinacy of Nash equilibrium in network-formation games: for a generic assignment of utilities to networks, the set of probability distributions on networks induced by Nash equilibria is finite.

THE COST CHANNEL OF MONETARY POLICY AND INDETERMINACY

We study the conditions that guarantee equilibrium determinacy in a standard sticky price model augmented with a cost channel. A central bank that assigns some positive weight to the output gap in its reaction function makes the economymore proneto multiple equilibria relative to the standard case. The value of the threshold on the interest rate response to inflation isabove oneand depends on the fraction of firms that need to borrow their bills payment.