Equilibrium Indeterminacy Research Articles

Going the Extra Mile: Effort by Workers and Job‐Seekers

AbstractIn the search‐and‐matching model, equilibrium indeterminacy obtains when wages respond strongly to a labor market tightening, and hiring is very elastic. We introduce two types of effort into such a model. Variable labor effort gives rise to short‐run increasing returns to hours in production. This amplifies profit expectations and firms' hiring incentives expanding the indeterminacy region. Variable search effort makes workers search more intensively in a tighter labor market. The procyclical nature of the resource cost of searching stabilizes firms' inclination to hire, shrinking the indeterminacy region. Indeterminacy disappears completely when vacancy posting costs are replaced with hiring costs.

Generic determinacy among stationary overlapping generations

For simplicity or realism, determinacy analysis for overlapping-generations models typically aggregates all conceivable commodities into a fixed, finite number of types. Analysis finds robust examples with indeterminate equilibria, which suggests indeterminacy may be significant among overlapping generations. But does robust indeterminacy exist despite that simplifying aggregation? or because of aggregation? We suggest the latter with a generic determinacy theorem for overlapping-generations models with idealized competitive markets for a continuum of commodities in discrete or continuous time. And aggregating the continuum of commodities into a finite number of types transforms some of those generic, determinate models into ostensibly-robust indeterminacy examples.

Persistent dynamics in (in)determinate equilibrium rational expectations models

Equilibrium indeterminacy in rational expectations models is often claimed to produce higher time series persistence relative to determinacy. Proceeding by means of a simple linear stochastic model, I formally show that, for reasonable parameter configurations, there exists an uncountable (continuously infinite) set of indeterminate equilibria in low-order AR(MA) representation, which exhibit strictly lower persistence than their determinate counterpart. Implications for empirical studies concerned with, e.g., testing for indeterminacy and macroeconomic forecasting are discussed.

On the indeterminacy of equilibrium in an endogenous growth model with non-separable preferences

This paper studies equilibrium indeterminacy in an extended version of the two-sector endogenous growth model by Mino (1999) by allowing alternative specifications for leisure. When utility depends on pure leisure, indeterminacy may only emerge if consumption and leisure are Edgeworth complements. We obtain the necessary and sufficient conditions for indeterminacy from the arbitrage condition on the two assets of the economy: consumption and human capital. When qualified leisure is considered, indeterminacy does not arise.

ON ENDOGENOUS BUSINESS CYCLES UNDER INCREASING RETURNS TO VARIETY AND SECTOR‐SPECIFIC EXTERNALITY

We examine the theoretical as well as quantitative interrelations between endogenous business cycles, increasing returns to product variety and sector‐specific productive externalities within a two‐sector real business cycle model. In a calibrated version of our benchmark closed‐economy setting, the threshold level of investment externalities needed for equilibrium indeterminacy is found to be monotonically increasing in the degree of market competitiveness. We also study the model's local stability properties (i) when the parameters that govern the level of intermediate‐good producers' market power and the strength of variety effects are disentangled; and (ii) in the context of a small open economy. (JEL E30, E32, O41)

Income Taxation Rules and Stability of a Small Open Economy

This paper examines the stability of a small open economy under alternative income taxation rules. Using a one-sector real business cycle model with external increasing returns, we show that if the income tax schedule is linear, the small open economy will not generate equilibrium indeterminacy, but it exhibits a diverging behavior under certain conditions. In this case, an appropriate choice of nonlinear tax on the factor income may recover the saddle-point stability. We also reveal that if the taxation on the interest income on financial assets is regressive, then the small open economy may exhibit equilibrium indeterminacy. In this situation, a progressive tax rule on the interest income can contribute to eliminating sunspot-driven fluctuations.

Monetary policy and macroeconomic stability revisited

A large literature has established the view that the Fed's change from a passive to an active policy response to inflation led to U.S. macroeconomic stability after the Great Inflation of the 1970s. We revisit this view by estimating a generalized New Keynesian model using a full-information Bayesian method that allows for indeterminacy of equilibrium and adopts a sequential Monte Carlo algorithm. The estimated model empirically outperforms canonical New Keynesian models that confirm the literature's view. It also points to substantial uncertainty about whether the policy response to inflation was active or passive during the Great Inflation. More importantly, a more active policy response to inflation alone does not suffice for explaining the U.S. macroeconomic stability, unless it is accompanied by a change in either trend inflation or policy responses to the output gap and output growth. This extends the literature by emphasizing the importance of the changes in other aspects of monetary policy in addition to its response to inflation.

Do inflation-targeting central banks adjust inflation targets to meet the target?

Under inflation targeting, central banks are supposed to set an inflation target in advance and then try to make the actual inflation reach the target. However, central banks may have an incentive to adjust their targets to meet their goals. Panel data analysis with a sample of 19 inflation-targeting countries show that changes in the inflation target significantly and positively respond to the deviation of the inflation rate from the target in the previous period. This result supports the idea that inflation-targeting central banks adjust the inflation target to meet the target when they miss it. Further analysis suggests that such a relationship is more evident in central banks with low credibility or weak performance compared with high credibility or strong performance. Finally, we show that such behavior of central banks can lead to equilibrium indeterminacy in the standard New Keynesian model. Further, such behavior renders achieving equilibrium determinacy harder for central banks even in more realistic models. This result may imply that when central banks respond to missed inflation targets by adjusting their targets and to enhance the credibility and stabilize the inflation rate, they may end up destabilizing inflation expectations and the inflation rate.

Computing sunspot solutions to rational expectations models with timing restrictions

Abstract Rational expectations (RE) frameworks featuring informational constraints are becoming increasingly popular in macroeconomic research. A recent strand of literature has explored the analytics of RE models with informational subperiods, in which the occurrence of exogenous shocks is period-specific and decision makers condition their own choices and expectations upon a sequence of nested information sets (timing restrictions). Assuming the unrestricted (full information) RE model satisfies saddle-path stability, this paper provides (i) necessary and sufficient conditions for existence of an uncountably infinite set of linearly perturbed solutions to its restricted (informationally constrained) counterpart, and (ii) an algorithm for computing the full set of sunspot solutions when equilibrium indeterminacy occurs.

Indeterminacy and Imperfect information

We study equilibrium determination in an environment where two kinds of agents have different information sets: The fully informed agents know the structure of the model and observe histories of all exogenous and endogenous variables. The less informed agents observe only a strict subset of the full information set. All types of agents form expectations rationally, but agents with limited information need to solve a dynamic signal extraction problem to gather information about the variables they do not observe. In this environment, we identify a new channel that leads to equilibrium indeterminacy: Optimal information processing of the less informed agent introduces stable dynamics into the equation system that lead to self-fulling expectations. For parameter values that imply a unique equilibrium under full information, the limited information rational expectations equilibrium is indeterminate. We illustrate our framework with a monetary policy problem where an imperfectly informed central bank follows an interest rate rule.

Arbitrary initial conditions and the dimension of indeterminacy in linear rational expectations models

Indeterminate equilibrium rational expectations (RE) models are ubiquitous in both theoretical and applied work in dynamic macroeconomics. The issue of characterizing the exact dimension of indeterminacy—i.e. of deriving the full set of causal and stable solutions to linear RE models—has only recently been addressed in the context of general and multivariate settings. This paper complements existing results by identifying bounds on the observable dimension of indeterminacy of linear RE models in the presence of arbitrary initial conditions. Implications for the estimation of indeterminate equilibrium RE models are discussed.

Indeterminate equilibrium growth with product and R&D spillovers

The paper revisits an endogenously growing economy à la Romer (1990) to explore the possibility of local and global indeterminacy where, along with the usual R&D spillover, a manufacturing sector generates a product spillover on R&D. When the product spillover facilitates R&D, the dynamic market equilibrium is unique and determinate. However, when the product spillover is strongly negative on R&D, multiple balanced market equilibria emerge and are therefore globally indeterminate. Furthermore, global indeterminacy coexists with local indeterminacy under the joint condition on the intertemporal elasticity of substitution of consumption. Local indeterminacy also emerges when the product spillover is mildly negative in tandem with a high intertemporal elasticity of substitution. Hence, a dynamic market economy with product spillovers in the R&D sector enriches the understanding of observable growth phenomena, including business and growth cycles and income and growth disparity, among countries with the same economic fundamentals.

A NOTE ON ROBUST MONETARY POLICY AND NON-ZERO TREND INFLATION

This paper studies how model uncertainty influences economic fluctuation when trend inflation is high. We introduce Hansen and Sargent’s [(2008) Robustness, Princeton University Press] robust control techniques into a New Keynesian model with non-zero trend inflation. We reveal the following three points. First, we find that robust monetary policy responds more aggressively. This aggressiveness increases with trend inflation. Second, as the trend inflation rises, the response of macroeconomic variables is larger under robust policy. Third, stronger robustness tends to lead to indeterminate equilibrium as trend inflation increases. Consequently, the economy might be volatile when trend inflation is high due to robustness from the view of both variance and determinacy. We interpret the results as indicating that the model uncertainty might be the one of the factors causing large macroeconomic fluctuations when trend inflation is high.

AN EXPERIMENTAL STUDY OF UNCERTAINTY IN COORDINATION GAMES

AbstractGlobal games and Poisson games have been proposed to address equilibrium indeterminacy in Common Knowledge Coordination games. The present study investigates in a controlled setup, using as controls Common Knowledge games, whether idiosyncratic uncertainty about economic fundamentals (Global games) or uncertainty about the number of actual players (Poisson games) may influence subjects' behavior. We find that uncertainty about the number of actual players has more influence on subjects' behavior than idiosyncratic uncertainty about economic fundamentals. Furthermore, subjects' behavior under Poisson population‐size uncertainty is closer to the respective theoretical prediction than subjects' behavior under idiosyncratic uncertainty about economic fundamentals.

AN ESTIMATED DSGE MODEL WITH A DEFLATION STEADY STATE

Benhabib et al. [(2001) Journal of Economic Theory 96, 40–69] argue that there exists a deflation steady state when the zero lower bound on the nominal interest rate is considered in a Taylor-type monetary policy rule. This paper estimates a medium-scale DSGE model with a deflation steady state for the Japanese economy during the period from 1999 to 2013, when the Bank of Japan conducted a zero interest rate policy and the inflation rate was almost always negative. Although the model exhibits equilibrium indeterminacy around the deflation steady state, a set of specific equilibria is selected by Bayesian methods. According to the estimated model, positive shocks to households’ preferences and wage markup, and a negative shock to monetary policy do not necessarily have an inflationary effect, in contrast to a standard model with a targeted-inflation steady state. An economy in the deflation equilibrium could experience unexpected volatility because of sunspot fluctuations, but it turns out that sunspot shocks have a limited effect on Japan’s output fluctuations and rather contribute to stabilizing the economy after the global financial crisis.

Financial contracting with enforcement externalities

We study the negative feedback loop between the aggregate default rate and the efficacy of enforcement in a model of debt-financed entrepreneurial activity. The novel feature of our model is that enforcement capacity is accumulated ex ante and thus subject to depletion ex post. We characterize the effect of shocks that deplete enforcement resources on the aggregate default rate and credit supply. In the model default decisions by entrepreneurs are strategic complements, leading to multiple equilibria. We propose a global game selection to overcome equilibrium indeterminacy and show how shocks that deplete enforcement capacity can lead to a spike in the aggregate default rate and trigger credit rationing.

Progressive taxation as an automatic destabilizer under endogenous growth

It has been shown that in an otherwise standard one-sector real business cycle model with an indeterminate steady state under laissez faire, sufficiently progressive income taxation may stabilize the economy against aggregate fluctuations caused by agents’ animal spirits. We show that this previous finding can be overturned within an identical model which allows for sustained endogenous growth. Specifically, progressive taxation may operate like an automatic destabilizer that leads to equilibrium indeterminacy and sunspot-driven cyclical fluctuations in an endogenously growing macroeconomy. This instability result is obtained under two tractable progressive tax policy formulations that have been considered in the existing literature.

A NOTE ON NOMINAL GDP TARGETING AND MACROECONOMIC (IN)STABILITY

Benhabib and Farmer show that in a laissez-faire one-sector real business cycle model under aggregate increasing returns, under sufficiently high degrees of productive externality, the demand-side effect in the labor market triggered by agents' expectations about the economy's future outweighs the supply-side effect, making agents' expectations become self-fulfilling. This paper analytically demonstrates that the conduct of monetary policy under nominal gross domestic product (GDP) targeting reinforces the supply-side effect in the labor market, thereby making belief-driven aggregate fluctuations more difficult to occur. This reinforcement effect on labor supply is absent under nominal consumption targeting and inflation targeting. Hence, under these two monetary regimes, the necessary and sufficient conditions for the economy to display equilibrium indeterminacy and sunspot fluctuations are identical to those in Benhabib and Farmer's laissez-faire economy. The results are robust to an endogenous growth extension of the model, implying that targeting the nominal GDP growth rate is more desirable than targeting the nominal consumption growth rate or the inflation rate in terms of macroeconomic stability.

Indeterminacy and fundamental reduced form representations of DSGE models

AbstractDynamic stochastic general equilibrium (DSGE) models are known to exhibit indeterminacy—that is, equilibrium nonuniqueness—under realistic parameterizations. This paper studies how the potential for indeterminacy impacts on the possibility of recovering a DSGE model's structural shocks via empirical vector autoregressions (VARs), which in turn requires the model's reduced form representation to be fundamental. By means of a simple example, we first establish that indeterminacy is neither necessary nor sufficient for (non)fundamental representations to arise. We then investigate the relationship between indeterminacy and nonfundamentalness in the context of a general class of linearized DSGE models, which nests the New Keynesian framework as a special case. It is shown that an indeterminate equilibrium model may generically admit a fundamental moving average representation, even when its determinate counterpart always involves nonfundamentalness. As a main implication, checking for existence of a VAR representation of a DSGE model's equilibria cannot be regarded as an indirect test for the indeterminacy hypothesis.

The full set of solutions of linear rational expectations models

This article characterises the dimension of indeterminacy of linear rational expectations (LRE) models and derives their full set of solutions. It extends the analysis of indeterminate equilibria in Lubik and Schorfheide (2003) where some equilibria are incorrectly classified as indeterminate even though they entail the same observable outcome.