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2015 | Buch

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Dynamic Systems in Management Science

Design, Estimation and Control

verfasst von: Alexis Lazaridis

Verlag: Palgrave Macmillan UK

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

Dynamic Systems in Management Science explores the important gaps in the existing literature on operations research and management science by providing new and operational methods which are tested in practical environment and a variety of new applications.

Inhaltsverzeichnis

Frontmatter

Vectors and Matrices Eigenvalues and Eigenvectors Singular Value Decomposition, the Generalized Inverse A Multi-purpose Computer Program

1. Prerequisites for Contemporary Econometrics and Systems Modelling

Abstract

For analytical purposes, it is much more convenient to express any economic relationships in terms of mathematical equations so that we can apply various estimation methods and optimization techniques to derive economic policy in quantitative terms. Below we provide a simple example in terms of a plain consumption function.

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Specification and Estimation The Ordinary Least Squares Method Basic Assumptions — Tests Required Marginal Effects, Elasticities, Predictions, Confidence Intervals Recursive Residuals and Relevant Statistics Use of Dummy Variables

Frontmatter

2. The Classical Linear Model. Specific Computations

Abstract

To simplify the presentation the six observations presented in Table 2.1 will be considered. It is pointed out that no econometric analysis can be conducted with six observations only. However, our attempt is to analytically demonstrate the estimation process we’ll describe next so that everything to be understood without any difficulty having these few observations.

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3. Dummy or Control Variables and Additional Tests

Abstract

We’ll see next the use of variables taking the value 1 or 0 (zero) as explanatory variables. Usually, but not necessarily these variables are denoted with the letter d. Note also that the situation or category marked with zero plays the role of the reference category.

Alexis Lazaridis

Backmatter

Remedies When Basic Assumptions are Violated Feasible Generalized Least Squares (FGLS) Estimators Extensions of Usual System Models Fixed Effects and Random Effects Models Models with Binary Dependent Variable Tests Required. Interpretation of the Results

4. Basic Assumptions: Further Considerations

Abstract

Basic assumptions have been stated explicitly or implicitly. In many textbooks, one of these assumptions has the form which implies that the rank of this fixed data matrix X should be equal to the number of its columns m. If X is rank-deficient then the determinant of (X’X) is zero so that vector b̂ is undefined. However, depending on the computer program used, one may obtain some estimation results for multivariate models due to rounding errors, particularly when the numbers are stored in single precision memory allocation and not double precision. Hence, proper tests are required as it is explained in the Appendix of this Part, in order to overcome this trap. It is recalled that we stated (4.1) in a more rigid form, assuming that (X’X) is positive definite, since such a matrix is always invertible, whereas a nonsingular matrix is not necessarily positive definite.

Alexis Lazaridis

5. Extension of the Usual System Models

Abstract

Pooled time, cross-section data contain information for cross-section entities (such as individuals, firms, households, countries etc.) over a number of time periods. The resultant models are usually referred to as panel data regression models.

Alexis Lazaridis

Time Series-Stationarity Vector Autoregressive (VAR) Models Co-Integration Analysis and Relevant Tests Singular Value Decomposition to Compute Co-Integration Vectors The Error Correction Models and Dynamic Simulation Models with Categorical Dependent Variable Count Models Survival Analysis Seemingly Unrelated Regression (SUR) Models

6. Advanced Time Series Modeling

Abstract

Consider the following linear relation:

$${{y}_{i}}={{b}_{1}}+{{b}_{2}}{{x}_{i}}+{{u}_{i}}$$

(6.1)

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7. Health Service Modeling and Multiple-Equations Models

Abstract

In these types of models,¹ the dependent variable is categorical,² taking values according to a Likert-type scale. As in the cases discussed in Chapter 5, if the error term is assumed to follow the logistic distribution, then an ordered logit model can be adopted. However, if the normal distribution is assumed, then an ordered probit model could be adopted. To see the details regarding the probability estimation from ordered models, we’ll consider the data presented in Table 7.1. The participants are asked to provide answers as to whether they are satisfied with the health services provided by the local health agent.

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Simultaneous Equation Models Model Identification Estimation Methods Dynamic Systems Optimal Control Systems with Random Parameters Analytical Applications

Frontmatter

8. Simultaneous Equation Models and Dynamic Systems

Abstract

We discussed at the end of Chapter 7 one type of multiple equation model (SUR). Here we’ll present a second type of such models known as simultaneous equation models. A preliminary type of such a model was adopted at the beginning of Chapter 1, where the structural model described by Equations (1.1)–(1.3) was presented; finally the obtained reduced form was shown in (1.13). This was an attempt for a first familiarization with simultaneous equation models, where explanatory variables from one equation can be dependent variables in other equations. Note that each endogenous explanatory variable is explicitly specified in the relevant structural equation. It is recalled that in each structural equation endogenous explanatory variables are correlated with the corresponding disturbance term, which implies that OLS estimates are inconsistent. Thus other estimation methods should be employed when estimating the parameters of the structural form of such a model. The most popular one is a single-equation method, namely two stage least squares (2SLS). However, more efficient methods can be employed using the entire model, which has the form presented in Equations (7.11)–(7.11a) of Chapter 7.

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9. Optimal Control of Linear Dynamic Systems

Abstract

Pontryagin and his associates developed the maximum principle for solving continuous-data control problems. Basically the maximum (or minimum) principle provides a set of local necessary conditions for optimality. According to this method, variables analogous to the Lagrange multipliers should be introduced. These variables are often called the co-state or adjoint-system variables. A scalar-value function H, which generally is a function of x,p,u (state, co-state, control vector) and t, named Hamiltonian function of the problem, is also considered.

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10. Optimal Control of Dynamic Systems with Random Parameters

Abstract

We presented in the previous chapter the solution to an optimal control problem when the parameters of the matrices of system transition equation are considered constant. The solution is obtained by solving the Riccati-type Equations (9.67)–s(9.67g) presented in Chapter 9 backwards in time. However, if the system parameters are taken as random variables, then a more complicated method of solution should be adopted which is analytically presented next.

Alexis Lazaridis

Backmatter

Titel: Dynamic Systems in Management Science
verfasst von: Alexis Lazaridis
Verlag: Palgrave Macmillan UK
Electronic ISBN: 978-1-137-50892-8
Print ISBN: 978-1-349-70170-4
DOI: https://doi.org/10.1057/9781137508928