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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

### 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.
Alexis Lazaridis

### 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.
Alexis Lazaridis

### 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

### 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

### 6. Advanced Time Series Modeling

Abstract
Consider the following linear relation:
$${{y}_{i}}={{b}_{1}}+{{b}_{2}}{{x}_{i}}+{{u}_{i}}$$
(6.1)
Alexis Lazaridis

### 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.
Alexis Lazaridis

### 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.
Alexis Lazaridis

### 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.
Alexis Lazaridis

### 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

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