Equilibrium Indeterminacy Research Articles

Arbitrage in automated market makers

One of the most interesting applications of blockchain is given by the automated market makers (AMMs). In the paper, we discuss how arbitrage activity between the AMMs and the other exchange nodes can affect the volumes of assets in liquidity pools of constant function AMMs. In particular, we argue that arbitrage superimposes to the constant function in determining the liquidity volumes within the same AMM and across different AMMs. Yet, despite representing an additional condition in the model, equilibrium arbitrage is typically not unique because it may depend on several elements, such as the amount of liquidity in the system and the number of exchange nodes. Hence, the paper discusses how the constant function and arbitrage jointly determine the relationship across the assets’ liquidity volume in the pool but not a unique value for such volumes unless further constraints are introduced. Therefore, a platform interested in predicting the pool’s liquidity volumes may face indeterminacy as to which equilibrium would prevail. Though arbitrage has been discussed in related literature, equilibrium indeterminacy does not seem to have been pointed out.

Industry clusters and macroeconomic (in)stability

Abstract While the competitive behavior of firms with regard to entry and exit activities serves as a driving force behind the business cycle, little attention has been paid to the issue of industry clusters when discussing belief-driven cyclical fluctuations. Faced with this deficiency, this study analyzes the possibility of the emergence of equilibrium indeterminacy from the perspective of industrial organization. By analyzing the effects of endogenous overhead costs in the market, this paper finds that belief-driven business cycle fluctuations are related to industry clusters. More specifically, a stronger spillover effect or a less pronounced congestion effect tends to increase the likelihood of local indeterminacy.

Unconventional policy instruments in the New Keynesian model

Abstract 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 that, in addition to the effect of conventional interest rate policy, may enter the Phillips curve, the investment–saving (IS) curve, and the welfare function, thus influencing inflation and output. The paper 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 reduces the zone of equilibrium indeterminacy and may reduce the volatility of the economy. However, in some circumstances, committing to not use the second instrument may be welfare-improving (a result akin to Rogoff (Journal of International Economics 18(3-4), 199–217, 1985) example of counterproductive coordination). We also show that the optimal central banker should be both aggressive against inflation and interventionist in using the unconventional policy instrument, and we analyze the optimal central banker’s preferences when social preferences would yield equilibrium indeterminacy.

Catenary configuration and geometric stiffness matrix of inextensible cables: Analytical high-order asymptotic solutions for parametric design

The analytical and geometric study of catenary curves is a classic matter of applied mathematical modeling. The paper systematizes a methodological strategy to achieve fully analytical solutions for the mechanical problem of determining the equilibrium configuration assumed by inextensible inclined cables under gravitational loads. By developing a two-step perturbation scheme, the statically indeterminate equilibrium problem is asymptotically formulated, and asymptotic solutions are obtained in the form of convergent polynomial series of terms with increasing orders of smallness. As a major achievement, the asymptotic analytical solutions are explicit functions of the governing parameters and automatically satisfy the integral compatibility condition, which traditionally requires a numerical solution to assess the hyperstatic unknowns. The mathematical conditions for the existence of admissible solutions and asymptotic consistency of the perturbation scheme are provided, while the characteristic properties of the asymptotic series are recognized or demonstrated. Parametric analyses successfully verify the high approximation accuracy achievable by high-order asymptotic series, truncated to a large but finite number of terms. With the aim of extending the methodology to the largest possible variety of cable structure applications, a fully analytical, although asymptotic, expression of the geometric stiffness matrix of inextensible inclined cables is determined. Parametric analyses confirm that high-order asymptotic expressions can accurately approximate the exact stiffness matrix assessed numerically. This achievement opens up viable opportunities for analytically studying and parametrically designing complex cable structures (including collaborations with other structural elements), within the framework of the direct stiffness method. Finally, the feasibility and effectiveness of the asymptotic direct stiffness method are successfully verified by solving in a fully-analytical way a paradigmatic static problem for the catenary cable-stayed beam.

Inflation gap persistence, indeterminacy, and monetary policy

Empirical literature has documented that the persistence of the gap between inflation and its trend declined after the Volcker disinflation. Previous studies into the source of the decline in inflation gap persistence have offered competing views while sidestepping the possibility of equilibrium indeterminacy. We examine the source of the decline by estimating a medium-scale dynamic stochastic general equilibrium model using Bayesian methods that allow for indeterminacy. We show that the Fed's change from a passive to an active policy response to the inflation gap or a decrease in firms' probability of price change can fully account for the decline in inflation gap persistence by ruling out indeterminacy that induces persistent economic 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.

Cost channel, determinacy, and monetary policy in a two-country new Keynesian model

This study examines the role of the cost channel of monetary policy in a two-country new Keynesian model. The results demonstrate that the presence of the cost channel significantly affects worldwide equilibrium determinacy. A greater foreign cost channel widens worldwide equilibrium indeterminacy when home and foreign central banks respond strongly to inflation and the output gap. This phenomenon is exacerbated when a greater cost channel exists simultaneously in both countries. • We examine determinacy analysis in a two-country model with a cost channel. • The degree of the cost channel affects worldwide equilibrium determinacy. • The central bank s stronger reaction to inflation exacerbates indeterminacy. • This result is worsened whencost channels become more severe in both countries.

A tractable overlapping generations structure for quantitative DSGE models

This paper develops a novel tractable overlapping generations (OLG) structure whose aggregate equations resemble a model of an infinitely lived representative agent, except that there are no aggregate transversality conditions in the OLG economy. The main assumptions are complete markets and time-invariant (but age-dependent) consumption shares of age-groups. The tractability of the OLG structure here distinguishes it from conventional OLG models – the present structure is suitable for quantitative dynamic stochastic general equilibrium (DSGE) macro models. Importantly, the OLG structure here maintains key predictions of standard OLG models, namely the possibility of low real interest rates and of equilibrium indeterminacy. • This paper develops a novel tractable overlapping generations (OLG) structure. • Aggregate equations resemble a model of an infinitely lived representative agent. • However, there are no aggregate transversality conditions in the OLG economy. • The OLG structure here is much more tractable than conventional OLG models. • Thus, the present OLG structure is suitable for quantitative DSGE macro models.

Indeterminacy and imperfect information

We study equilibrium determination in an environment where two types of agents have different information sets: Fully informed agents observe histories of all exogenous and endogenous variables. Less informed agents observe only a strict subset of the full information set and need to solve a dynamic signal extraction problem to gather information about the variables they do not directly observe. Both types of agents know the structure of the model and form expectations rationally. In this environment, we identify a new channel that generates 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 monetary policy models where an imperfectly informed central bank follows an interest rate rule.

The Taylor Rule in Egypt: Is it Optimal? Is there Equilibrium Determinacy?

We investigate Egypt's Taylor rule (interest rate targeting) between 1976 and 2019 by including the main economic variables in its reaction function. Using the Taylor principle, we investigate Egypt’s monetary policy optimality. To this end, we conduct the generalized method of moments (GMM) estimation procedure with different Taylor rule specifications to deal with potential endogeneity among variables. Our GMM estimates reveal that the partial adjustment coefficient is of considerable magnitude, indicating the explanatory power of policy inertia on many total variations in the current values of the nominal interest rate in Egypt. Furthermore, the inflation gap coefficient violates the Taylor principle, making the policy procyclical and inflation "spiral" and inducing divergence from the long-run equilibrium. Therefore, Egypt's Taylor rule, and thus monetary policy, reflects the indeterminacy of equilibrium and is a passive and destabilizing policy. Besides, the output gap coefficient was unexpectedly found to be insignificant.

Necessary and sufficient conditions for determinacy of asymptotically stationary equilibria in OLG models

We propose a criterion for verifying whether an equilibrium of an overlapping-generations model is amenable to local policy analysis, i.e., is determinate. The criterion is applicable for a generic set of parameters of the model, and in case of indeterminacy, it indicates the nature of the problem: multiplicity of equilibria or their absence for near-by parameters.The criterion can be applied to models with infinite past and future as well as to those with a truncated past. The baseline equilibrium is not required to be a steady state, and economic parameters, for example endowments, can change over time. However, asymptotically, the equilibrium should be stationary, though the two limiting paths at either end of the time-line do not have to be the same. If they are, conditions for local uniqueness of equilibrium are far more stringent for an economy with a truncated past as compared to its counterpart with an infinite past.We illustrate our main result using a text-book model with a single physical good and a two-period life-cycle. There, price growth paths that start at one steady state and end up at another constitute indeterminate equilibria for all parameters.

Real indeterminacy and dynamics of asset price bubbles in general equilibrium

We show that both real indeterminacy and asset price bubble may appear in an infinite-horizon exchange economy with infinitely lived agents and an imperfect financial market. We explain how the asset structure and heterogeneity (in terms of preferences and endowments) affect the existence and the dynamics of asset price bubbles as well as the equilibrium indeterminacy. Moreover, this paper bridges the literature on bubbles in models with infinitely lived agents and that in overlapping generations models.

Endogenous fluctuations and international business cycles

AbstractWe introduce equilibrium indeterminacy into a two‐country incomplete asset model with imperfect competition to analyze the role of self‐fulfilling expectations or beliefs in explaining international business cycles. We find that, when self‐fulfilling beliefs are correlated with technology shocks, the model can account for the countercyclical behaviour observed for the terms of trade and real net exports while simultaneously generating higher volatilities relative to output, as in the data. The choice of the labour‐supply elasticity is shown to be critical for generating a negative correlation between the real exchange rate and relative consumption, thereby resolving the Backus–Smith puzzle.

Currency substitution as an automatic stabilizer

AbstractIn the presence of frictions, the existing literature shows that currency substitution is detrimental for domestic aggregate stability. This paper singles out the role of currency substitution and shows that diversified currency holdings operate as an automatic stabilizer that mitigates belief-driven cyclical fluctuations in Farmer’s (1997) indeterminate monetary economy. When the foreign inflation rate is lower than the domestic inflation rate, the model’s steady state always displays saddle-path stability. Hence, equilibrium indeterminacy originally present in the domestic country is entirely removed in the presence of diversified currency holdings. When the foreign inflation rate is higher than the domestic inflation rate, then depending on the degrees of currency substitution and relative risk aversion, indeterminacy is either impossible or the requisite level of the foreign inflation rate for indeterminacy is too high to square with data. The stabilizing effect of diversified currency holdings on domestic aggregate stability is robust to whether domestic and foreign currencies display as Edgeworth substitutes or complements, or are additively separable in the household’s preferences.

Equilibrium indeterminacy and sunspot tales

We argue that dynamic indeterminacy in structural models can help rationalize statistical regularities regarding higher-order properties of macroeconomic time series. Without departing from the Gaussian rational expectations paradigm, we formally establish that any indeterminate equilibrium model admits a linear recursion with multiplicative noise representation. This allows self-fulfilling expectations (sunspots) to enhance endogenous propagation forces that trigger high-probability extreme changes in model variables, while also inducing time variation in conditional volatilities. As a result, even modest, short-lived exogenous shocks can produce large and persistent macroeconomic effects. Using a workhorse New Keynesian framework, we investigate the ability of such a general mechanism to account for observed fat-tailed behavior and volatility clusters in the inflation series over the Great Inflation period of US macroeconomic history.

Policy Regime Shifts In China

Using an estimated DSGE model with monetary and fiscal policy interactions and allowing for equilibrium indeterminacy, I find that a passive monetary and passive fiscal policy regime fits Chinese economy best. However, if money is introduced in the economy, things would be different before and after 2012. Specifically, the active monetary and passive fiscal policy prevailed before 2012 and passive monetary and passive fiscal policy fitted after 2012 in China. Besides, government spending has different impact before and after 2012 according to the model.

Asset Prices and Standing Facilities in a Monetary Economy

This paper develops a general equilibrium model of money and banking in which the central bank opens a discount window and pays an interest rate on reserves. With aggregate uncertainty about liquidity demands, banks exhaust their monetary reserves and access to the discount window in some states of nature. Changing the interest-rate corridor, defined as the difference between the discount and the deposit rates, generates responses in the bank's portfolio choice, asset prices, welfare, and the liquidity structure of assets' yields. The discount window policy can be a potential source of both the indeterminacy of equilibria and instability of asset prices.

PROGRESSIVE TAXATION AND MACROECONOMICS (IN)STABILITY UNDER HOUSEHOLD HETEROGENEITY

It has been shown that progressive income taxation may stabilize an otherwise standard representative-agent real business cycle model with an indeterminate steady state against aggregate fluctuations caused by agents’ animal spirits. By contrast, within an identical model that allows for sustained economic growth, progressive taxation could lead to equilibrium indeterminacy and sunspot-driven fluctuations. In the context of household heterogeneity that gives rise to income and asset inequality, the fiscal authority has (at least) two options of setting the baseline level of taxable income: (i) the economy-wide average level of income and (ii) the economy’s steady-state level of per capita income. I show that the adoption of a fiscal rule (i) invalidates the effects that a progressive tax can exert on the model’s local stability properties. Progressive income taxation thus no longer operates as an automatic stabilizer that mitigates belief-driven cyclical fluctuations in a no-growth economy, nor as an automatic destabilizer that leads to local indeterminacy in a sustained-growth economy. If a tax policy rule (ii) is instead adopted, then the existing literature’s findings of the (de)stabilizing roles of progressive taxation are robust to the inclusion of household heterogeneity.

EQUILIBRIUM INDETERMINACY, ENDOGENOUS ENTRY AND EXIT, AND INCREASING RETURNS TO SPECIALIZATION

This paper systematically examines the interrelations between equilibrium indeterminacy, endogenous entry and exit of intermediate input firms, and increasing returns to specialization within two versions of a parsimonious one-sector monopolistically competitive RBC model. The technology for producing an intermediate good is postulated to display internal increasing returns to scale in our benchmark framework, whereas positive productive externalities are considered in the alternative setting. We analytically show that either formulation will exhibit belief-driven cyclical fluctuations provided the equilibrium wage-hours locus is positively sloped and steeper than the household’s labor supply curve. We also find that ceteris paribus our alternative macroeconomy is more susceptible to indeterminacy and sunspots than the baseline counterpart.

Capacity choice, monetary trade, and the cost of inflation

Both buyers and sellers in decentralized markets make investments ex ante that constrain trading possibilities ex post: buyers decide in advance how much money to carry, while sellers decide how much inventory to stock. We show that the interaction between these choices naturally leads to indeterminacy of equilibrium. When neither inflation nor the scrap value of unsold goods is high, there is a continuum of equilibria in which buyers and sellers coordinate on their choices of money balances and capacity. Furthermore, at low inflation rates, traded quantities are pinned down by the seller’s capacity choice, and inflation therefore has no effect on output and welfare. We also contrast our results with other environments with strategic complementarities and discuss how they depend on the pricing mechanism.