Finite-Order VAR Representation of Linear Rational Expectations Models: In a Nutshell

Let G be a nilpotent group with finite abelian ranks (e.g. let G be a finitely generated nilpotent group) and suppose φ is an automorphism of G of finite order m. If γ and ψ denote the associated maps of G given by \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\gamma :g \mapsto g^{ - 1} \cdot g\phi and \psi :g \mapsto g \cdot g\phi \cdot g\phi ^2 \cdots \cdot \cdot g\phi ^{m - 1} for g \in G,$$ \end{document} then Gγ · kerγ and Gψ · ker ψ are both very large in that they contain subgroups of finite index in G.

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Rational Expectations and Inflation

10.23943/princeton/9780691158709.001.0001 ◽

2017 ◽

Cited By ~ 51

Author(s):

Thomas J. Sargent

Keyword(s):

World War I ◽

French Revolution ◽

Rational Expectations ◽

Ronald Reagan ◽

Fiscal Policies ◽

Economic Policies ◽

Budget Deficits ◽

Nobel Lecture ◽

Economic Decisions ◽

The French Revolution

This collection of essays uses the lens of rational expectations theory to examine how governments anticipate and plan for inflation, and provides insight into the pioneering research for which the author was awarded the 2011 Nobel Prize in economics. Rational expectations theory is based on the simple premise that people will use all the information available to them in making economic decisions, yet applying the theory to macroeconomics and econometrics is technically demanding. This book engages with practical problems in economics in a less formal, noneconometric way, demonstrating how rational expectations can satisfactorily interpret a range of historical and contemporary events. It focuses on periods of actual or threatened depreciation in the value of a nation's currency. Drawing on historical attempts to counter inflation, from the French Revolution and the aftermath of World War I to the economic policies of Margaret Thatcher and Ronald Reagan, the book finds that there is no purely monetary cure for inflation; rather, monetary and fiscal policies must be coordinated. This fully expanded edition includes the author's 2011 Nobel lecture, “United States Then, Europe Now.” It also features new articles on the macroeconomics of the French Revolution and government budget deficits.

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Finite-order Integration Weights Can be Dangerous

Computational Methods in Applied Mathematics ◽

10.2478/cmam-2007-0015 ◽

2007 ◽

Vol 7 (3) ◽

pp. 239-254 ◽

Cited By ~ 3

Author(s):

I.H. Sloan

Keyword(s):

Function Space ◽

Finite Order ◽

Small Subset ◽

Worst Case ◽

Integration Rule ◽

Dimensional Lattice ◽

3 Dimensional ◽

Sum Of Functions ◽

Integration Rules

Abstract Finite-order weights have been introduced in recent years to describe the often occurring situation that multivariate integrands can be approximated by a sum of functions each depending only on a small subset of the variables. The aim of this paper is to demonstrate the danger of relying on this structure when designing lattice integration rules, if the true integrand has components lying outside the assumed finiteorder function space. It does this by proving, for weights of order two, the existence of 3-dimensional lattice integration rules for which the worst case error is of order O(N¯½), where N is the number of points, yet for which there exists a smooth 3- dimensional integrand for which the integration rule does not converge.

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On Commutation Properties of the Composition Relation of Convergent and Divergent Permutations (Part I)

Tatra Mountains Mathematical Publications ◽

10.2478/tmmp-2014-0002 ◽

2014 ◽

Vol 58 (1) ◽

pp. 13-22

Author(s):

Roman Wituła ◽

Edyta Hetmaniok ◽

Damian Słota

Keyword(s):

Finite Order ◽

Convergent Series ◽

The Other ◽

Other Hand ◽

The Family ◽

Composition Relation ◽

The Continuum

Abstract In the paper we present the selected properties of composition relation of the convergent and divergent permutations connected with commutation. We note that a permutation on ℕ is called the convergent permutation if for each convergent series ∑an of real terms, the p-rearranged series ∑ap(n) is also convergent. All the other permutations on ℕ are called the divergent permutations. We have proven, among others, that, for many permutations p on ℕ, the family of divergent permutations q on ℕ commuting with p possesses cardinality of the continuum. For example, the permutations p on ℕ having finite order possess this property. On the other hand, an example of a convergent permutation which commutes only with some convergent permutations is also presented.

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