Conditions For Determinacy Research Articles

A new moment determinacy condition for probability distributions

В этой статье мы предлагаем условие на вероятностное распределение, которое позволяет нам однозначно определить распределение по всем его моментам. Это условие применимо как к случаю Гамбургера (распределения на всей действительной прямой), так и к случаю Стилтьеса (распределения на положительной полупрямой). Предложенное условие легко проверяется и связано как с условием Лина, так и с обратным условием Крейна. Кроме того, мы приводим еще одно условие определенности для проблем моментов Гамбургера и Стилтьеса, которое похоже на условие Лина, но не требует обратного условия Крейна.

A unified approach to determinacy conditions with regime switching

The conditions that ensure the existence of a unique stable equilibrium — determinacy conditions — for rational expectations models with Markov switching depend on the stability concept, contrasting with standard linear rational expectations models. In this paper, we offer a unified framework for the two commonly used stability concepts: boundedness and mean-square stability. We derive determinacy conditions for both concepts based on simple metrics. Qualitatively, we show that mean-square stable solutions are always at least as many as bounded solutions. We then apply and discuss our results in two monetary models.

Inflation targeting, output stabilization, and real indeterminacy in monetary models with an interest rate rule

AbstractCentral banks set the nominal interest rate to target inflation and stabilize output. In monetary models, monetary policy affects output directly via the wealth effect. I show that in these models, the response of the central bank to fluctuations in output may induce real indeterminacy even if the Taylor principle is satisfied. I find that the determinacy conditions depend on the interest elasticity of output and generally, the Taylor principle is neither necessary nor sufficient for determinacy. This is in stark contrast with the New Keynesian model where a sufficiently strong policy response to inflation or output usually ensures determinacy.

On equilibrium determinacy in overlapping generations models with money

This paper provides a detailed analysis of the local determinacy of monetary and non-monetary steady states in Tirole (1985)’s classical two-period overlapping generations model with capital and production. We show that the sufficient condition for local determinacy in endowment economies provided by Scheinkman (1980) does not generalize to models with production: there are robust examples with arbitrary utility functions in which the non-monetary steady state is locally determinate or indeterminate. In contrast, the monetary steady state is locally determinate under fairly weak conditions.

Information technology of synthesis of liquid dosing process control

Problem. Currently, different solutions are available on the global market for liquid dosing. There is no universal technology, as the same substances can be dosed using different types of equipment. Therefore, manufacturers face the complex task of determining the most optimal kind of equipment to achieve their goals. These issues are a complex multi-criteria scientific problem, and to effectively address them, it is necessary to develop a technology for synthesizing a liquid dosing control system using multi-criteria optimization methods in different conditions of information determinacy. Goal. The paper aims to increase the efficiency of liquid dosing control by developing information technology for the control system synthesizing. The object of the paper is the process of information technology development for synthesizing the liquid dosing control system. The subject of the paper is the models for the selection of hardware and software for the liquid dosing control system. Methodology. The study analyses and provides a classification of liquid dosing technology and analyses existing liquid dosing control systems. A structural model of information technology for synthesising a liquid dosing control system is developed, and criteria for selecting the elements of the liquid dosing control system are justified. A model for selecting PLC and SCADA systems for synthesising the liquid dosing control system is also developed using hierarchical analysis methods and multi-criteria evaluation and optimisation. Results. The paper resulted in the following: analysis and classification of liquid dosing technology; analysis of existing liquid dosing control systems; development of a structural model of the information technology of synthesising a liquid dosing control system; justification of criteria for selecting the elements of the liquid dosing control system, and the development of a model for selecting PLC and SCADA systems for the synthesis of the liquid dosing control system using hierarchical analysis methods and multi-criteria evaluation and optimisation. Originality. Further development of the methods of hierarchy analysis and multi-criteria assessment and optimization has been achieved by applying them to a specific field – the development of models for selecting hardware and software for the liquid dosing process control system. Practical value. The proposed information technology of synthesising a liquid dosing control system, as well as the mathematical models for selecting hardware and software for the liquid dosing process control system, will reduce the time and cost required to develop such a system.

Inflation response in a New Keynesian model with money illusion

AbstractThis study investigates the role of money illusion (MI) in a dynamic stochastic general equilibrium model. We introduce MI such that households, in their intertemporal optimization, erroneously recognize nominal variables as real ones. We find that first, our model could exhibit money nonneutrality in the long run; second, the Taylor principle is a sufficient condition for determinacy but not a necessary condition; third, the response to output in monetary policy rule matters for the model not to exhibit money nonneutrality in the long run; and finally, MI could flatten the slope that represents the output‐inflation trade‐off.

Optimal monetary policy with [formula omitted

We study the optimal monetary policy problem in a New Keynesian economy with a zero lower bound (ZLB) on the nominal interest rate, when the steady state natural rate (r∗) becomes permanently negative. We show that the optimal policy aims to approach gradually a new steady state with positive average inflation. Around that steady state, the optimal policy implies well defined (second-best) paths for inflation and output in response to shocks to the natural rate. Under plausible calibrations, the optimal policy implies that the nominal rate remains at its ZLB most of the time. Despite the latter feature, the central bank can implement the optimal outcome as a unique equilibrium by means of an appropriate nonlinear interest rate rule. In order to establish that result, we derive sufficient conditions for local determinacy in a general model with endogenous regime switches.

A Unified Approach to Determinacy Conditions with Regime Switching

A Unified Approach to Determinacy Conditions with Regime Switching

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.

Non‐classical Tauberian and Abelian type criteria for the moment problem

AbstractThe aim of this paper is to provide some new criteria for the determinacy problem of the Stieltjes moment problem. We first give a Tauberian type criterion for moment indeterminacy that is expressed purely in terms of the asymptotic behavior of the moment sequence (and its extension to imaginary lines). Under an additional assumption this provides a converse to the classical Carleman's criterion, thus yielding an equivalent condition for moment determinacy. We also provide a criterion for moment determinacy that only involves the large asymptotic behavior of the distribution (or of the density if it exists), which can be thought of as an Abelian counterpart to the previous Tauberian type result. This latter criterion generalizes Hardy's condition for determinacy, and under some further assumptions yields a converse to the Pedersen's refinement of the celebrated Krein's theorem. The proofs utilize non‐classical Tauberian results for moment sequences that are analogues to the ones developed in [8] and [3] for the bi‐lateral Laplace transforms in the context of asymptotically parabolic functions. We illustrate our results by studying the time‐dependent moment problem for the law of log‐Lévy processes viewed as a generalization of the log‐normal distribution. Along the way, we derive the large asymptotic behavior of the density of spectrally‐negative Lévy processes having a Gaussian component, which may be of independent interest.

Existence and Uniqueness of Solutions to Dynamic Models with Occasionally Binding Constraints

We present the first necessary and sufficient conditions for there to be a unique perfect-foresight solution to an otherwise linear dynamic model with occasionally binding constraints, given a fixed terminal condition. We derive further results on the existence of a solution in the presence of such terminal conditions. These results give determinacy conditions for models with occasionally binding constraints, much as Blanchard and Kahn (1980) did for linear models. In an application, we show that widely used New Keynesian models with endogenous states possess multiple perfect foresight equilibrium paths when there is a zero lower bound on nominal interest rates, even when agents believe that the central bank will eventually attain its long-run, positive inflation target. This illustrates that a credible long-run inflation target does not render the Taylor principle sufficient for determinacy in the presence of the zero lower bound. However, we show that price level targeting does restore determinacy providing agents believe that inflation will eventually be positive.

Heart Rate Variability of Children with Mitral Valve Prolapse in Orthostatic Test

The purpose of the research was to study the state of autonomic regulation in prepubertal children with mitral valve prolapse during an orthostatic test Materials and methods. The study involved 2 groups: the main – 26 children aged 10-11 years with mitral valve prolapse, and a control group – 22 relatively healthy children. The adaptive mechanisms were monitored by analyzing heart rate variability. All children participated in a cardiorhythmic examination at rest lying down and during an active orthostatic test. Results and discussion. Among the indicators that had significant differences, the indicators of regulatory process adequacy index and mode amplitude should be noted. In the group of children with mitral valve prolapse, an increase of the regulatory process adequacy index indicated the predominance of the functioning of the sinus node over the activity of the sympathetic division of the autonomic nervous system. An increase in the adequacy index and mode amplitude indicates the connection of the central structures of rhythm control (subcortical rhythms) during a change in body position. Stress index also increased. This index of tension of regulatory systems shows the activity of the mechanisms of sympathetic regulation, the state of central regulation. Children in the control group had a well-coordinated response of the sympathetic nervous system to the orthostatic test: the low frequency spectrum and very low frequency indicators increased. While in main group, the value of low frequency spectrum (the work of the sinus node) increased, the value of very low frequency (the reaction of the central structures of the nervous system) decreased. This indicates dysfunction of the most important reactions, which also affects the daily activities of children, increases the risk of mitral valve prolapse complications. Conclusion. In children with mitral valve prolapse, the absence of a pronounced typical reaction to an ortho test is a reflection of an adaptive-regulatory overstrain in conditions of morphological determinacy of connective tissue dysplasia, which are trying to ensure the adequacy of intracardiac hemodynamics. The data obtained will be useful for predicting the reaction of the body of children with mitral valve prolapse to physical activity of varying intensity

Determinacy and classification of Markov-switching rational expectations models

In a general class of Markov-switching rational expectations models, this study derives necessary and sufficient conditions for determinacy, indeterminacy and the case of no stable solution. Classification of the models into these three mutually disjoint and exhaustive subsets is completely characterized by only one particular solution known as the minimum of modulus solution in the mean-square stability sense. The rationale behind this result comes from the novel finding that the solution plays the same role as what the generalized eigenvalues do for linear rational expectations models. Moreover, the solution has its own identification condition that does not require examining the entire solution space. The accompanying solution procedure is therefore computationally efficient, and as tractable as standard solution methodologies for linear rational expectations models. The proposed methodology unveils several important implications for determinacy in the regime-switching framework that differ from the linear model counterpart.

Determinacy and E-stability with Interest Rate Rules at the Zero Lower Bound

This paper examines the uniqueness and learnability of rational expectations equilibrium when the policy rate is occasionally pegged at the zero lower bound (ZLB). We consider a model that features recurring, transient ZLB regimes and compare various interest rate rules which respond to inflation, price level, and average inflation in addition to output. In this environment, determinacy conditions ensure a unique equilibrium, given the recurrence of ZLB events, and E-stability conditions can rule out deflationary spirals under learning. We fi nd that price level targeting, including nominal income targeting as a special case, most effectively promotes determinacy and E-stability among the policy frameworks, while the economy under a standard inflation targeting rule is prone to indeterminacy. Average inflation targeting can promote determinacy and E-stability very effectively, provided that the measure of average inflation is sufficiently backward looking.

E-stability vis-à-vis determinacy in regime-switching models

This paper examines E-stability, determinacy, and indeterminacy in a general class of regime-switching models with lagged endogenous variables. Using determinacy conditions from Cho (2016, 2020), our first result extends McCallum (2007) to models with time-varying parameters: the unique mean-square stable equilibrium is E-stable if agents have current information and one-period-ahead decision rules. Further, we address the existence of E-stable non-fundamental equilibria, and find that Iteratively E-stable equilibria of indeterminate switching models can exist. Finally, we show that indeterminate New Keynesian models with persistent, recurring interest rate peg regimes admit Iteratively E-stable equilibria. In special cases, the Iterative E-stability condition coincides with the Long Run Taylor Principle.

Does My Model Predict a Forward Guidance Puzzle?

We provide sufficient conditions for when a rational expectations structural model predicts bounded responses of endogenous variables to forward guidance announcements. The conditions coincide with a special case of the well-known (E)xpectation-stability conditions that govern when agents can learn a Rational Expectations Equilibrium. The conditions are distinct from the determinacy conditions and are applicable in a wide variety of models including models with sunspots or Markov-switching. We show how the conditions can diagnose features of a model that contribute to the Forward Guidance Puzzle and reveal how to construct well-behaved forward guidance predictions in standard medium-scale New Keynesian environments.

New Checkable Conditions for Moment Determinacy of Probability Distributions

We have analyzed some conditions which are essentially involved in deciding whether or not a probability distribution is unique (moment-determinate) or nonunique (moment-indeterminate) by its moments. We suggest new conditions concerning both absolutely continuous and discrete distributions. By using the new conditions, which are easily checkable, we either establish new results or extend previous ones in both the Hamburger case (distributions on the whole real line) and the Stieltjes case (distributions on the positive half-line). Specific examples illustrate the results as well as the relationship between the new conditions and previously available conditions.

New checkable conditions for moment determinacy of probability distributions

Проанализированы некоторые условия, которые играют существенную роль при выяснении, однозначно ли данное вероятностное распределение определяется своими моментами. Мы предлагаем новые условия как для абсолютно непрерывных, так и для дискретных распределений. Используя эти новые, легко проверяемые условия, мы устанавливаем новые результаты или обобщаем уже существующие как в случае Гамбургера (распределения на всей действительной оси), так и в случае Стилтьеса (распределения на положительной полуоси). Специфические примеры иллюстрируют как результаты, так и соотношения между новыми и ранее доступными условиями.

Necessary and Sufficient Conditions for Determinacy of Asymptotically Stationary Equilibria in OLG Models

We propose a criterion for determining whether a local policy analysis can be made in a given equilibrium in an overlapping generations model. The criterion can be applied to models with infinite past and future as well as those with a truncated past. The equilibrium is not necessarily a steady state; for example, demographic and type composition of the population or individuals’ endowments can change over time. However, asymptotically, the equilibrium should be stationary. The two limiting stationary paths at either end of the timeline do not have to be the same. If they are, conditions for local uniqueness are far more stringent for an economy with a truncated past as compared to its counterpart with an infinite past. In addition, we illustrate our main result using a textbook model with a single physical good, a two-period life-cycle and a single type of consumer. In this model we show how to calculate a response to a policy change using the implicit function theorem.

Determinacy and Classification of Markov-Switching Rational Expectations Models

In a general class of Markov-switching rational expectations models, this study derives necessary and sufficient conditions for determinacy, indeterminacy and the case of no stable solution. Classification of the models into these three mutually disjoint and exhaustive subsets is completely characterized by the most stable solution in the mean-square stability sense. The rationale behind this result comes from the novel finding that the most stable solution plays the same role as what the generalized eigenvalues do for linear rational expectations models. Moreover, the solution has its own identification condition that does not require examining the entire solution space. The accompanying solution procedure is therefore computationally efficient, and as tractable as standard solution methodologies for linear rational expectations models. The proposed methodology unveils several important implications for determinacy in the regime-switching framework that differ from the linear model counterpart.