Determination Of Equilibrium Research Articles

MONETARY FEEDBACK RULES AND EQUILIBRIUM DETERMINACY IN PURE EXCHANGE OVERLAPPING GENERATIONS MODELS

This paper considers a pure exchange overlapping generations model in which the money-growth rate is endogenous and follows a feedback rule. Different specifications for the monetary policy rule are analyzed, namely a so-called current, forward, or backward-looking feedback rule, depending on whether the monetary authority uses the actual, expected, or last observed values of the inflation rate to set the monetary policy. We study how the responsiveness of the policy rule with respect to inflation affects the determinacy of the monetary equilibrium. A policy rule is called aggressive (moderate) if it responds strongly (moderately) to inflation deviations from the target. We show how aggressive feedback rules, depending on the considered timing, can reinforce mechanisms that lead to indeterminacy or may lead the inflation rate to fluctuate around the monetary equilibrium at which monetary policy is aggressive. Aleaning against the windpolicy seems to be more desirable from an equilibrium determinacy point of view. On the contrary, aleaning with the windpolicy could not be the recommended policy for the Central Bank.

Global Determinacy Under Monetary and Fiscal Policy Switchings

This paper examines equilibrium determinacy in the context of a structural regime switching macro model with monetary and fiscal policy switching. We first show theoretically and in practice that the long-run Taylor principle proposed by Davig and Leeper (2007) is necessary but not sufficient for determinacy in mean-square stability sense. We then show that stochastic switching in policy stances substantially changes the determinacy region. On the one hand, a unique stable equilibrium under regime switching may exist when monetary and fiscal policies are both recurrently passive or active. On the other hand, a switch between two alternative policy combinations which imply determinacy under two fixed-regimes often requires a large swing in fiscal policy in order to achieve global determinacy, ruling out some traditionally determinate equilibria. Finally, we show that money growth management can be an alternative to active fiscal policy in a zero lower-bound scenario in order to lead the economy to global determinacy.

Bad Luck, Bad Policy, or Learning? A Markov-Switching Approach to Understanding Postwar U.S. Macroeconomic Dynamics

In this paper we analyze changes in the Federal Reserve behavior and objectives since the 1960s justified by potentially evolving beliefs — through a real-time learning process — about the structure of the economy and shifts in policymakers preferences in the late 1970s. In addition, we allow for changes in the volatility of the structural shocks in a medium scale Markov-switching DSGE model. We evaluate the relative contribution of each narrative to the explanation of the Great Inflation and the Great Moderation. We argue that the interplay between central bank learning and a shift in policy makers’ preferences explains movements in the monetary instrument, and regulates equilibrium determinacy in the economy. We find evidence of “bad” policy consistent with equilibrium indeterminacy during the 1970s and “good” policy during the Great Moderation. In addition, the model captures non-policy related high volatility periods clustered around the late 1960’s through the 1970s, specifically supply side shocks that behaved as destabilizing forces driving macroeconomic fluctuations. To conclude, we observe that a change in monetary policy objectives, assumptions about policymakers’ learning process, and Markov-switching volatility are key to fit the model to the U.S. post-war data.

Financial Factors and Monetary Policy: Determinacy and Learnability of Equilibrium

This paper contributes to the debate whether central banks should respond to asset prices, credit spreads and other financial factors in setting monetary policy, by evaluating determinacy and expectational stability of equilibria under various monetary policy rules. With adaptive learning, beliefs constitute an additional set of state variables, which may require more than a response to inflation, that has traditionally been argued in the literature as sufficient to achieve central bank objectives under rational expectations. Furthermore, financial frictions are introduced by extending the determinacy and adaptive learning methodology embodied in Bullard and Mitra (2002) and Bullard and Mitra (2007), beyond the New Keynesian modelling framework by incorporating a Financial Accelerator (Bernanke, Gertler and Gilchrist 1999). A key result is that monetary policy rules responding to lagged asset prices and credit volume have less desirable determinacy and learnability characteristics than responding to current asset prices and credit spreads. This conclusion dovetails with recent research such as Gilchrist and Zakrajsek (2011) and Gilchrist and Zakrajsek (2012), who show that signals derived from credit spreads contain information which help explain business cycle fluctuations and demonstrate that a credit spread augmented monetary policy rule dampens cycle variability. Another result is that the conclusions in both Bullard and Mitra (2002) and Bullard and Mitra (2007) are robust to a New Keynesian model with financial frictions.

CONSUMPTION EXTERNALITIES AND MONETARY POLICY WITH LIMITED ASSET MARKET PARTICIPATION

This article explores the interaction between consumption externalities and limited asset market participation (LAMP) in the standard New‐Keynesian model. We assess the performance of simple Taylor‐type interest rate rules with respect to (a) equilibrium determinacy, (b) the model's ability to simultaneously generate output and inflation volatility similar to the pre‐Volcker era, and (c) the model's response to a technology shock. We find that when individual preferences are affected by average household consumption (Aggregate Consumption Externality), stronger externalities increase the range of LAMP for which multiple equilibria arise even if the policy rule satisfies the Taylor principle. The interaction of LAMP and externalities can generate vast inflation/output relative volatility in line with the one observed in the data in the 1970s. According to our analysis, consumption externalities also affect the responses of endogenous variables to total factor productivity shocks. (JEL E4, E5)

On the desirability of nominal GDP targeting

This paper evaluates the welfare properties of nominal GDP targeting in the context of a New Keynesian model with both price and wage rigidity. In particular, we compare nominal GDP targeting to inflation and output gap targeting as well as to a conventional Taylor rule. These comparisons are made on the basis of welfare losses relative to a hypothetical equilibrium with flexible prices and wages. Output gap targeting is the most desirable of the rules under consideration, but nominal GDP targeting performs almost as well. Nominal GDP targeting is associated with smaller welfare losses than a Taylor rule and significantly outperforms inflation targeting. Relative to inflation targeting and a Taylor rule, nominal GDP targeting performs best conditional on supply shocks and when wages are sticky relative to prices. Nominal GDP targeting may outperform output gap targeting if the gap is observed with noise, and has more desirable properties related to equilibrium determinacy than does gap targeting.

Determinacy and learnability of equilibrium in a small-open economy with sticky wages and prices

In a small-open economy model with nominal wage and price rigidities, it has been argued that, in terms of welfare losses, the monetary policy rule that responds to consumer price index (CPI) inflation performs better than rules that react to competing inflation measures. From the viewpoint of determinacy and learnability of rational expectations equilibrium (REE), this paper suggests that the rule that responds to CPI inflation does not increase the Central Bank's ability to promote the convergence of an economy to a determinate and learnable REE nor improves the speed of this convergence when compared with rules that react to contending inflation measures.

Fiscal policy lag and equilibrium determinacy in a continuous-time New Keynesian model

It has been suggested that local equilibrium determinacy can be achieved by applying active monetary policies combined with passive fiscal policies in discrete-time New Keynesian (NK) models that include a fiscal policy rule with a time lag in the policy response. However, indeterminacy can occur even under such policies in models with money in the production function. In this paper, we first confirm that these results hold in a continuous-time NK model without a policy lag. Furthermore, we present the case of a fiscal policy lag that is capable of avoiding indeterminacy.

Unconventional Policy Instruments in the New Keynesian Model

This paper analyzes the use of unconventional policy instruments in New Keynesian setups in which the ‘divine coincidence’ breaks down. The paper discusses the role of a second instrument and its coordination with conventional interest rate policy, and presents theoretical results on equilibrium determinacy, the inflation bias, the stabilization bias, and the optimal central banker’s preferences when both instruments are available. We show that the use of an unconventional instrument can help reduce the zone of equilibrium indeterminacy and the volatility of the economy. However, in some circumstances, committing not to use the second instrument may be welfare improving (a result akin to Rogoff (1985a) example of counterproductive coordination). We further show that the optimal central banker should be both aggressive against inflation, and interventionist in using the unconventional policy instrument. As long as price setting depends on expectations about the future, there are gains from establishing credibility by using any instrument that affects these expectations.

When Ricardo Meets Chamberlin: A Simple Dynamic Model of Monopolistic Competition

We develop a dynamic model of monopolistic competition which sheds light on how the interplay between the degree of product differentiation and intertemporal elasticity of substitution affects the steady-state equilibrium. Consumers love variety and split their labor endowment between wage labor, which brings immediate income, and producing capital, which yields a rent in the future. The impact of the elasticity of substitution across varieties on the market outcome depends crucially on whether consumption today and consumption tomorrow are gross substitutes or gross complements. The case of Cobb-Douglas intertemporal utility is a borderline situation, when the market outcome is invariant to the degree of product differentiation. We also fully characterize the unique steady-state equilibrium path and show that the key dynamic properties of the model, such as local stability and determinacy of equilibrium, also hinge mainly on the interplay between the intra- and intertemporal elasticities of substitution.

Do credit market imperfections justify a central bank׳s response to asset price fluctuations?

Do credit market imperfections justify a central bank׳s response to asset price fluctuations? This study addresses this question from the perspective of equilibrium determinacy. In the model we use, prices are sticky and the working capital of firms is subject to asset values because of a lack of commitment. If credit market imperfections exist to a small degree, the Taylor principle is a necessary and sufficient condition for equilibrium determinacy, and monetary policy response to asset price fluctuations is good from the perspective of equilibrium determinacy. However, if credit market imperfections exist to a large degree such that the collateral constraint is binding, then the Taylor principle no longer guarantees equilibrium determinacy, and monetary policy response to asset price fluctuations becomes a source of equilibrium indeterminacy. We find that the existence of credit market imperfections makes it unsuitable to initiate a monetary policy response to deal with asset price fluctuations. We also find that reductions in credit market imperfections can enlarge the indeterminacy region of the model parameters.

Determinacy of equilibrium in outcome game forms

We show the generic finiteness of the number of probability distributions on outcomes induced by Nash equilibria for two-person game forms such that either (i) one of the players has no more than two strategies or (ii) both of the players have three strategies, and (iii) for outcome game forms with three players, each with at most two strategies. Finally, we exhibit an example of a game form with three outcomes and three players for which the Nash equilibria of the associated game induce a continuum of payoffs for an open non-empty set of utility profiles.

A New Keynesian model with staggered price and wage setting under learning

This paper provides a study of the implications for economic dynamics when the central bank sets its nominal interest rate target in response to variations in wage inflation. I provide results on the existence, uniqueness, and stability under learning of rational expectations equilibrium for alternative specifications of the manner in which monetary policy responds to economic shocks when nominal rigidities are present. Monopolistically competitive producers set prices via staggered price contracts, and households set nominal wages in the same fashion. In this setting, the conditions for determinacy and learnability of rational expectations equilibrium differ from a model where only prices are sticky. I find that when the central bank responds to wage and price inflation and to the output gap, a Taylor principle for wage and price inflation arises that is related to stability under learning dynamics. In other words, a moderate reaction of the interest rate to wage inflation helps to avoid instability under learning and indeterminacy.

On the inherent instability of private money

A primary concern in monetary economics is whether a purely private monetary regime is consistent with macroeconomic stability. I show that a competitive regime is inherently unstable due to the properties of endogenously determined limits on private money creation. Precisely, there is a continuum of equilibria characterized by a self-fulfilling collapse of the value of private money and a persistent decline in the demand for money. I associate these equilibrium allocations with self-fulfilling banking crises. It is possible to formulate a fiscal intervention that results in the global determinacy of equilibrium, with the property that the value of private money remains stable. Thus, the goal of monetary stability necessarily requires some form of government intervention.

Determinacy of Equilibrium in a New Keynesian Model with Monetary Policy Lag

We use the New Keynesian continuous-time framework to theoretically investigate the effects of a lag in a central bank’s response to economic fluctuations (i.e., monetary policy lag) on local equilibrium determinacy. In the case of a policy without lag, equilibrium is indeterminate even though a central bank’s policy response is sufficiently active. However, in the case of a policy with lag, an active monetary policy can contribute to local equilibrium determinacy if the lag is modest.

On the Inherent Instability of Private Money

A primary concern in monetary economics is whether a purely private monetary regime is consistent with macroeconomic stability. I show that a competitive regime is inherently unstable due to the properties of endogenously determined limits on private money creation. Precisely, there is a continuum of equilibria characterized by a self-fulfilling collapse of the value of private money and a persistent decline in the demand for money. I associate these equilibrium allocations with self-fulfilling banking crises. It is possible to formulate a fiscal intervention that results in the global determinacy of equilibrium, with the property that the value of private money remains stable. Thus, the goal of monetary stability necessarily requires some form of government intervention.

On stable outcomes of approval, plurality, and negative plurality games

We prove two results on the generic determinacy of Nash equilibrium in voting games. The first one is for negative plurality games. The second one is for approval games under the condition that the number of candidates is equal to three. These results are combined with the analogous one obtained in De Sinopoli (Games Econ Behav 34:270–286, 2001) for plurality rule to show that, for generic utilities, three of the most well-known scoring rules, plurality, negative plurality and approval, induce finite sets of equilibrium outcomes in their corresponding derived games—at least when the number of candidates is equal to three. This is a necessary requirement for the development of a systematic comparison amongst these three voting rules and a useful aid to compute the stable sets of equilibria Mertens (Math Oper Res 14:575–625, 1989) of the induced voting games. To conclude, we provide some examples of voting environments with three candidates where we carry out this comparison.

Determinacy of Equilibrium in Outcome Game Forms

Determinacy of Equilibrium in Outcome Game Forms

Currency substitution, risk premia and the Taylor principle

This paper studies the equilibrium determinacy properties of a simple interest rate rule in a small open economy subject to currency substitution (i.e., the use of a foreign currency for domestic transactions) and risk premia on foreign borrowing. It shows that if currencies are substitute in the provision of liquidity services the rule׳s response to inflation has to be sufficiently above unity for the equilibrium to be locally determinate. This reinforced Taylor principle requirement appears to be more binding in economies characterized by a larger elasticity of currency substitution, more debt-elastic country risk premia, and intermediate degrees of dollarization in transactions.

Monetary Policy and the Transaction Role of Money in the US

The declining importance of money in transactions can explain the well-known fact that U.S. interest rate policy was passive in the pre-Volcker period and active after 1982. We generalise a standard cashless New Keynesian model (Woodford2003) by incorporating an explicit transaction role for money. In the pre-Volcker period, we estimate that money did play an important role and determinacy required a passive interest rate policy. However, after 1982, money no longer played an important role in facilitating transactions. Correspondingly, the conventional view prevails and an active policy ensured equilibrium determinacy.