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Dynamic Economics: Optimization by the Lagrange Method

Gregory C. Chow

Published in print:
1997
Published Online:
October 2011
ISBN:
9780195101928
eISBN:
9780199855032
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195101928.001.0001
Subject:
Economics and Finance, Financial Economics

This work provides a unified and simple treatment of dynamic economics using dynamic optimization as the main theme, and the method of Lagrange multipliers to solve dynamic economic problems. The ... More


Optimal Resource Allocations

Lars Peter Hansen and Thomas J. Sargent

in Recursive Models of Dynamic Linear Economies

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691042770
eISBN:
9781400848188
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691042770.003.0005
Subject:
Economics and Finance, History of Economic Thought

This chapter describes a planning problem that generates competitive equilibrium allocations and compares two methods for solving it. The first method uses state- and date-contingent Lagrange ... More


Optimal Programming

S. N. Afriat

in Logic of Choice and Economic Theory

Published in print:
1987
Published Online:
November 2003
ISBN:
9780198284611
eISBN:
9780191595844
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198284616.003.0024
Subject:
Economics and Finance, Microeconomics

This is the first of five chapters on optimal programming (the typical mathematics of economics) and related issues as related to choice making. It introduces the general ideas of optimal programming ... More


Entropy Maximization

Amos Golan

in Foundations of Info-Metrics: Modeling, Inference, and Imperfect Information

Published in print:
2017
Published Online:
November 2017
ISBN:
9780199349524
eISBN:
9780199349555
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199349524.003.0004
Subject:
Economics and Finance, Econometrics

In this chapter I develop the essential maximum entropy procedure, which is an inversion procedure for inferring an unknown probability distribution function from incomplete information. The ... More


Dynamic Optimization in Discrete Time

GREGORY C. CHOW

in Dynamic Economics: Optimization by the Lagrange Method

Published in print:
1997
Published Online:
October 2011
ISBN:
9780195101928
eISBN:
9780199855032
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195101928.003.0002
Subject:
Economics and Finance, Financial Economics

In dynamic economics, a set of equations are used to describe how state variables undergo dynamic evolution. This set of equations is used in maximizing a specific objective function that proves to ... More


The principles of mechanics before Hertz

JESPER LÜTZEN

in Mechanistic Images in Geometric Form: Heinrich Hertz's 'Principles of Mechanics'

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567370
eISBN:
9780191717925
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567370.003.0002
Subject:
Physics, History of Physics

The period until 1860 saw a steady flow of interesting new theoretical discoveries in mechanics, even in the area of mechanics of systems of finitely many mass points. Moreover, there was a continued ... More


Testing and Evaluation

David F. Hendry

in Dynamic Econometrics

Published in print:
1995
Published Online:
November 2003
ISBN:
9780198283164
eISBN:
9780191596384
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198283164.003.0013
Subject:
Economics and Finance, Econometrics

The non‐central chi‐squared distribution frequently results when hypothesis testing, so the large‐sample properties of such tests are analysed for sequences of local alternatives. Test power depends ... More


Economic Growth

GREGORY C. CHOW

in Dynamic Economics: Optimization by the Lagrange Method

Published in print:
1997
Published Online:
October 2011
ISBN:
9780195101928
eISBN:
9780199855032
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195101928.003.0003
Subject:
Economics and Finance, Financial Economics

Through dynamic programming, the Bellman equation could be set up from a simple optimal growth model that is subject to a constraint function which involves variables that denote consumption, capital ... More


Models in Finance

GREGORY C. CHOW

in Dynamic Economics: Optimization by the Lagrange Method

Published in print:
1997
Published Online:
October 2011
ISBN:
9780195101928
eISBN:
9780199855032
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195101928.003.0007
Subject:
Economics and Finance, Financial Economics

Using stochastic differential equations instead of utilizing stochastic difference equations, most of the models involved in finance follow Merton’s work and are developed in continuous time. In this ... More


A Commodity Space

Lars Peter Hansen and Thomas J. Sargent

in Recursive Models of Dynamic Linear Economies

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691042770
eISBN:
9781400848188
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691042770.003.0006
Subject:
Economics and Finance, History of Economic Thought

This chapter describes a concept of value that will be used to formulate a model in which the decisions of agents are reconciled in a competitive equilibrium. It describes a commodity space in which ... More


Scattering by a Bounded Inhomogeneity

Peter Monk

in Finite Element Methods for Maxwell's Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198508885
eISBN:
9780191708633
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508885.003.0011
Subject:
Mathematics, Numerical Analysis

This chapter continues the approximation of the field scattered by a bounded object. In this case, a penetrable scatterer (i.e., not a perfect conductor) is considered and the analysis of the ... More


A Complete Info-Metrics Framework

Amos Golan

in Foundations of Info-Metrics: Modeling, Inference, and Imperfect Information

Published in print:
2017
Published Online:
November 2017
ISBN:
9780199349524
eISBN:
9780199349555
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199349524.003.0009
Subject:
Economics and Finance, Econometrics

In this chapter I develop the complete info-metrics framework for inferring problems and theories under all types of uncertainty and missing information. That framework allows for uncertainty in the ... More


Testing linearity against parametric alternatives

Timo Teräsvirta, Dag Tjøstheim, and W. J. Granger

in Modelling Nonlinear Economic Time Series

Published in print:
2010
Published Online:
May 2011
ISBN:
9780199587148
eISBN:
9780191595387
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199587148.003.0005
Subject:
Economics and Finance, Econometrics

The topic of this chapter is testing linearity of a model when the alternative is a parametric nonlinear model nesting a linear model. The case leading to standard asymptotic inference is discussed ... More


Convex Programming

S. N. Afriat

in Logic of Choice and Economic Theory

Published in print:
1987
Published Online:
November 2003
ISBN:
9780198284611
eISBN:
9780191595844
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198284616.003.0025
Subject:
Economics and Finance, Microeconomics

This is the second of five chapters on optimal programming (the typical mathematics of economics) and related issues as related to choice making. It introduces convexity conditions, and shows where ... More


Constrained Lagrangian Mechanics

Peter Mann

in Lagrangian and Hamiltonian Dynamics

Published in print:
2018
Published Online:
August 2018
ISBN:
9780198822370
eISBN:
9780191861253
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198822370.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter builds on the previous two chapters to tackle constrained systems, using Lagrangian mechanics and constrained variations. The first section deals with holonomic constraint equations ... More


Stress response in the presence of local constraints on the deformation

David J. Steigmann

in Finite Elasticity Theory

Published in print:
2017
Published Online:
December 2017
ISBN:
9780198567783
eISBN:
9780191746536
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198567783.003.0006
Subject:
Mathematics, Applied Mathematics

Chapter 6 develops the structure of the stress response in the presence of material constraints on the basis of the Lagrange-multiplier rule. Examples given include incompressibility and ... More


Lagrangian Mechanics

Jennifer Coopersmith

in The Lazy Universe: An Introduction to the Principle of Least Action

Published in print:
2017
Published Online:
June 2017
ISBN:
9780198743040
eISBN:
9780191802966
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198743040.003.0006
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, History of Physics

It is demonstrated how d’Alembert’s Principle can be used as the basis for a more general mechanics – Lagrangian Mechanics. How this leads to Hamilton’s Principle (the Principle of Least Action) is ... More


Adding a Dimension

A. R. P. Rau

in The Beauty of Physics: Patterns, Principles, and Perspectives

Published in print:
2014
Published Online:
December 2014
ISBN:
9780198709916
eISBN:
9780191780189
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198709916.003.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Dimensional considerations are a powerful, integral part of physics. Starting with the familiar linear dimension, physics expands the idea in different ways. The essence of even complicated problems ... More


Maximum Likelihood Estimation

M. Hashem Pesaran

in Time Series and Panel Data Econometrics

Published in print:
2015
Published Online:
March 2016
ISBN:
9780198736912
eISBN:
9780191800504
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198736912.003.0009
Subject:
Economics and Finance, Econometrics

One important tool of estimation and hypothesis testing in econometrics is maximum likelihood (ML) estimation and the various testing procedures associated with it, namely, the likelihood ratio (LR), ... More


The superiority of the LM test in a class of econometric models where the Wald test performs poorly

Jun Ma and Charles R. Nelson

in Unobserved Components and Time Series Econometrics

Published in print:
2015
Published Online:
January 2016
ISBN:
9780199683666
eISBN:
9780191763298
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199683666.003.0014
Subject:
Economics and Finance, Econometrics

In models having a representation y=γ‎·g(β‎,x) + ɛ the standard Wald test for β‎ has systematically been the wrong size in finite samples when the identifying parameter γ‎ is small relative to its ... More


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