I. Magnus, p

Name: Econometric - initial course.

The textbook contains a systematic presentation of the foundations of econometrics and is written on the basis of lectures that the authors have read for a number of years in the Russian Economic School and Higher School of Economics. Linear regression models are studied in detail (the least squares method, hypotheses, heterosduction, autocorrelation errors, model specification). Individual chapters are devoted to systems of simultaneous equations, the maximum truthful method in regression models, models with discrete and limited dependent variables.
In the sixth edition of the book added three new chapters. The head of the "panel data" complements the book to a complete list of topics, traditionally included in modern basic econometric courses. Chapter "Pre-testing" and "Econometric Financial Markets" are also added, which will be useful for those who are interested in theoretical and applied aspects of econometrics. The number of exercises is significantly increased. Enabled exercises with real data available to the reader on the Book Web site.
For students, graduate students, teachers, as well as experts in the applied economy and finance.

Econometrics (along with microeconomics and macroeconomics) is among the basic disciplines of modern economic education. What is econometrics? When you deal with live, developing science, it always causes difficulty when trying to give a brief description of its subject and methods. Is it possible to say that econometric is the science of economic dimensions, as its name suggests? Of course, it is possible, but then the question arises which sense to invest in the term "economic dimensions". This is similar to how to identify mathematics as a science of numbers. Therefore, not trying to develop this problem in more detail, we give the statements of recognized authorities in the economy and econometric.

1. Introduction
1.1. Models
1.2. Types of models
1.3. Data types
2. Model of paired regression
2.1. Cruvinary fitting
2.2. Method of least squares (MNC)
2.3. Linear regression model with two variables
2.4. Theorem Gauss Markova. Evaluation Error Dispersion A2
2.5. Statistical properties of MNK estimates of regression parameters. Checking the hypothesis B \u003d BO-trust intervals for regression coefficients
2.6. Analysis of the variation of the dependent variable in regression. The determination coefficient Y2.
2.7. Assessment of the maximum likelihood of regression coefficients
Exercises
3. Multiple regression model
3.1. Basic hypothesis
3.2. Least square method. Theorem Gauss Markova
3.3. Statistical properties of MNK estimates
3.4. Analysis of the variation of the dependent variable in regression. R2 coefficients and adjusted R
3.5. Check hypotheses. Trust intervals and trust areas
Exercises
4. Various aspects of multiple regression
4.1. Multicollinarity
4.2. Fictive variables
4.3. Private correlation
4.4. Model specification
Exercises
5. Some generalizations of multiple regression
5.1. Stochastic regressors
5.2. Generalized Method of the Smaliest Squares
5.3. Affordable generic method of least squares
Exercises
6. Heterosedalism and time correlation
6.1. Heterosedastic
6.2. Correlation in time
Exercises
7. Forecasting in regression models
7.1. Unconditional forecasting
7.2. Conditional forecasting
7.3. Forecasting in the presence of autorgan errors
Exercises
8. Instrumental variables
8.1. The consistency of estimates obtained using instrumental variables
8.2. Effect of measurement errors
8.3. Dual-step method of smallest squares
8.4. Test Hausman
Exercises
9. Regression equations
3.1. Externally not related equations
9.1. Systems of simultaneous equations
Exercises
10. Method of maximum believing in regression models
10.1. Introduction
10.2. Mathematical apparatus 246.
10.3. Estimation of the maximum truthfulness of the parameters of multidimensional normal distribution
10.4. Properties of maximum truth estimates
10.5. Assessment of maximum truth-like in a linear model
10.6. Check hypotheses in linear model, I
10.7. Check hypotheses in linear model, II
10.8. Nonlinear restrictions
Exercises
11. Temporary rows
11.1. Models of distributed lags
11.2. Dynamic models
11.3. Single roots and cointegration
11.4 Boxing Jenkins Models (ARIMA)
11.5. Garch Model
Exercises
12. Discrete dependent variables and censored samples
12.1. Binary and multiple selection models
12.2. Models with trimmed and censored samples
Exercises
13. Panel data
13.1 Introduction
13.2. Designations and main models
13.3. Fixed Effect Model
13.4. Random
13.5. Quality fit
13.6. Select model
13.7. Dynamic models
13.8. Binary selection model with panel data
13.9. The generalized method of moments
Exercises
14. Preliminary testing: Introduction
14.1. Introduction
14.2. Formulation of the problem
14.3. Main result
14.4. Pretest estimate
14.5. WALS-Evaluation
14.6. Equivalence theorem
14.7. Pre-testing and the effect of "Untilization"
14.8. The effect of "Untilization". One auxiliary parameter
14.9. Selection of the model: from common to particular and private to the general
14.10. The effect of "Untilization". Two auxiliary parameters
14.11. Forecasting and pre-testing
14.12. Generalizes
14.13. Other questions
Exercises
15. Econometric Financial Markets
15.1. Introduction
15.2. Financial market efficiency hypothesis
15.3. Optimization of securities portfolio
15.4. Test on the inclusion of new assets in an effective portfolio
15.5. Optimal portfolio in the presence of a risk-free asset
15.6. Financial Assent Assessment Models
Exercises
16. Prospects for econometrics
1,6.1. Introduction
16.2. What actually does an econometrist practice?
16.3. Econometrics and physics
16.4. Econometrics and Mathematical Statistics
16.5. Theory and practice
16.6. Econometric method
16.7. Weak link
16.8. Aggregation
16.9. How to use other works
16.10. Conclusion
Application la. Linear algebra
1. Vector space
2. Vector LP Space
3. Linear addiction
4. Linear subspace
5. Base. Dimension
6. Linear operators
7. Matrix
8. Operations with matrices
9. Invariants of matrices: trail, determinant
10. Rank Matrix
11. Reverse matrix
12. Linear equations
13. Own numbers and vectors
14. Symmetric matrices
15. Positively defined matrices
16. Idmpotent matrices
17. Block matrices
18. The work of the Kononker
19. Differentiation by vector argument
Exercises
Application MS. Theory of Probability and Mathematical Statistics
1. Random variables, random vectors
2. Conditional distributions
3. Some special distributions
4. Multidimensional normal distribution
5. The law of large numbers. Central Limit Theorem.
6 Basic concepts and objectives of mathematical statistics
7. Evaluation of parameters
8. Checking hypotheses
Appendix EP. Overview of econometric packages
1. The origin of the packages. Windows version. Graphics
2. On some packages
3. Practical experience
Appendix Art. Short English-Russian Dictionary of Terms
The application is. Tables
Literature
Subject index

UDC 330.43 (075.8)
BBK 65V6Я73

Magnus Ya.R., Katyshev P.K., Recipers A.A.
Econometrics. Starting course: studies. - 8th ed., Act. - M.:, 2007. - 504 p.

ISBN 978-5-7749-0473-0

The chapter "panel data" complements the book to a complete list of topics traditionally included in modern basis courses of econometrics. Chapters "Pre-testing" and "financial market econometrics" will be useful for those who are interested in theoretical and applied aspects of econometrics. The number of exercises is significantly increased. Enabled exercises with real data available to the reader on the Book Web site.

For students, graduate students, teachers, as well as experts in the applied economy and finance.

Table of contents of the opening word Preface to the first edition of the preface to the third edition of the Preface to the Sixth Edition 1. Introduction 1.1. Models 1.2. Types of models 1.3. Data Types 2. Steam Recession Model 2.1. Curve 2.2. Method of least squares (MNC) 2.3. Linear regression model with two variables 2.4. Theorem Gauss Markov. Evaluation of dispersion errors A2 2.5. Statistical properties of MNK estimates of regression parameters. Checking the hypothesis B \u003d BO-trust intervals for regression coefficients 2.6. Analysis of the variation of the dependent variable in regression. Determination coefficient Ya2 2.7. Assessment of the maximum likelihood of the regression coefficients Exercise 3. Model of multiple regression 3.1. Basic hypothesis 3.2. Least square method. Theorem Gaussa Markova 3.3. Statistical properties of MNK estimates 3.4. Analysis of the variation of the dependent variable in regression. R2 coefficients and adjusted R 3.5. Check hypotheses. Trust intervals and trust areas of exercise 4. Various aspects of multiple regression 4.1. Multicollery 4.2. Fictive variables 4.3. Private correlation 4.4. Specification of the exercise model 5. Some generalizations of multiple regression 5.1. Stochastic regressors 5.2. The generalized method of smallest squares 5.3. Available generalized method of smaller squares exercise 6. Heterosedalism and time correlation 6.1. Heterosedalism 6.2. Correlation by time Exercise 7. Prediction in regression models 7.1. Unconditional forecasting 7.2. Conditional forecasting 7.3. Forecasting in the presence of autorganship errors exercise 8. Tool variables 8.1. The consistency of estimates obtained using instrumental variables 8.2. The effect of measurement errors 8.3. Two-step method of least squares 8.4. Test Hausman exercise 9. Systems of regression equations 3.1. Externally not related equations 9.1. Systems of simultaneous exercise equations 10. Method of maximum believing in regression models 10.1. Introduction 10.2. Mathematical apparatus 246 10.3. Assessment of the maximum likelihood of parameters of multidimensional normal distribution 10.4. The properties of estimates of the maximum believing 10.5. Assessment of maximum truthfulness in linear model 10.6. Checking the hypotheses in the linear model, I 10.7. Checking the hypotheses in the linear model, II 10.8. Nonlinear exercise restrictions 11. Temporary rows 11.1. Models of distributed lags 11.2. Dynamic models 11. 3. Single roots and co-integration 11.4 Boxing-Jenkins model (ARIMA) 11.5. Garch Exercise Models 12. Discrete dependent variables and censored samples 12.1. Models of binary and multiple selection 12.2. Models with trimmed and censored samples of exercise 13. Panel data 13.1 Introduction 13.2. Designations and main models 13.3. Model with fixed effect 13.4. Model with a random effect 13.5. The quality of fitting 13.6. Select model 13.7. Dynamic models 13.8. Binary selection models with panel data 13.9. Generalized Momentity Moments Exercise 14. Preliminary Testing: Introduction 14.1. Introduction 14.2. Setting the problem 14.3. Main result 14.4. Pretest-score 14.5. Wals-score 14.6. Equivalence Theorem 14.7. Pre-testing and the effect of "Untilization" 14.8. The effect of "Untilization". One auxiliary parameter 14.9. Selection of the model: from total to private and private to total 14.10. The effect of "Untilization". Two auxiliary parameters 14.11. Forecasting and pre-testing 14.12. Generalizations 14.13. Other issues of exercise 15. Financial market econometrics 15.1. Introduction 15.2. Hypothesis of the effectiveness of the financial market 15.3. Optimization of the securities portfolio 15.4. Test on the inclusion of new assets in an effective portfolio 15.5. The optimal portfolio in the presence of a risk-free asset 15.6. Models of evaluation of financial assets Exercises 16. Outlook Econometrics 1,6.1. Introduction 16.2. What actually does an econometrist practice? 16.3. Econometrics and physics 16.4. Econometrics and mathematical statistics 16.5. Theory and practice 16.6. Econometric method 16.7. Weak link 16.8. Aggregation 16.9. How to use other works 16.10. Conclusion Appendixa Linear algebra 1. Vector space 2. Vector space LP 3. Linear dependence 4. Linear subspace 5. Basis. Dimension 6. Linear operators 7. Matrix 8. Operations with matrices 9. Invariants of matrices: trail, determinant 10. Rang of the matrix 11. Reverse matrix 12. Systems of linear equations 13. Own numbers and vectors 14. Symmetric matrices 15. Positively defined matrices 16 . Idmpotent matrices 17. Block matrices 18. Production of a kerel 19. Differentiation according to the vector argument exercise application MS. Probability Theory and Mathematical Statistics 1. Random variables, random vectors 2. Conditional distributions 3. Some special distributions 4. Multidimensional normal distribution 5. The law of large numbers. Central Limit Theorem 6 Basic Concepts and Objectives of Mathematical Statistics 7. Evaluation of Parameters 8. Checking the hypotheses application EP. Overview of econometric packages 1. The origin of the packages. Windows version. Graphics 2. On some packages 3. Experience of practical work Appendix Art. Short English-Russian dictionary terms app TA. Tables Literature Subject

6th ed., Pererab. and add. - M.: Case, 2004. - 576 p.

In the sixth edition of the book added three new chapters. The head of the "panel data" complements the book to a complete list of topics, traditionally included in modern basic econometric courses. Chapter "Pre-testing" and "Econometric Financial Markets" are also added, which will be useful for those who are interested in theoretical and applied aspects of econometrics. The number of exercises is significantly increased. Enabled exercises with real data available to the reader on the Book Web site.

For students, graduate students, teachers, as well as applied economics and finance specialists

Format: djvu.

The size: 5.9 MB.

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The size: 21, 7 MB

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Table of contents
Opening word 10.
Preface to first edition 13
Preface to the Third Edition 18
Preface to the sixth edition 23
1. Introduction 26.
1.1. Models 26.
1.2. Types of models 28.
1.3. Data Types 30.
2. Steam regression model 32
2.1. Circle adjustment 32.
2.2. Method of least squares (MNC) 34
2.3. Linear regression model with two variables 38
2.4. Theorem Gauss Markov. Evaluation Dispersion Errors A2 41
2.5. Statistical properties of MNK estimates of regression parameters. Check hypothesis B \u003d BO-trust intervals for regression coefficients 46
2.6. Analysis of the variation of the dependent variable in regression. Coefficient of determination y2 51
2.7. Estimation of the maximum affordability of regression coefficients 55
Exercises 58.
3. Multiple regression model 67
3.1. Basic hypothesis 68.
3.2. Least square method. Theorem Gaussa Markova 69
3.3. Statistical properties of MNK estimates 72
3.4. Analysis of the variation of the dependent variable in regression. R2 coefficients and adjusted R ^, 74
3.5. Check hypotheses. Trust intervals and trust areas 78 "
Exercises 88.
4. Various aspects of multiple regression 108
4.1. Multicollarity 109;
4.2. Fictive variables 112.
4.3. Private correlation 118.
4.4. Model Specification 124.
Exercises 135.
5. Some generalizations of multiple regression 148
5.1. Stochastic regressors 149.
5.2. The generic method of least squares .... 154
5.3. Available generalized method of least squares 160
Exercises 163.
6. Heterosedalism and time correlation 167
6.1. Heterosdasticity 168.
6.2. Correlation by time 184
Exercises 192.
7. Forecasting in regression models 204
7.1. Unconditional forecasting 205.
7.2. Conditional forecasting 208.
7.3. Forecasting in the presence of autorgan errors 209
Exercises 211.
eight . Tool variables 212.
8.1. Wealth of estimates obtained using instrumental variables 213
8.2. Effect of measurement errors 214
8.3. Two-having method of least squares .... 215
8.4. Test Hausman 217.
Exercises 218.
9. Regression equations 220 systems
3.1. Externally not related equations 221
9.1. Systems of simultaneous equations 224
Exercises 241.
10. Method of maximum believing in regression models 244
10.1. Introduction 245.
10.2. Mathematical apparatus 246.
10.3. Assessment of the maximum truthfulness of the parameters of multidimensional normal distribution. . 248.
10.4. Properties of maximum truth estimates. 249.
10.5. Assessment of maximum truthful in linear model 250
10.6. Check hypotheses in linear model, I 253
10.7. Check hypotheses in linear model, II 257
10.8. Nonlinear limitations 258.
Exercises 260.
11. Temporary rows 264
11.1. Models of distributed lags 266
11.2. Dynamic models 268.
11.3. Single roots and co-integration 276
11.4 Boxing Jenkins (ARIMA) 28
11.5. GARCH Model 3.
Exercises 3J.
12. Discrete dependent variables and censored samples 3
12.1. Models of binary and multiple selection ... 3!
12.2. Models with trimmed and censored samples 3.
Exercises 3;
13. Panel data 31
13.1 Introduction 3.
13.2. Designations and main models 3
13.3. Model with fixed effect 3
13.4. Model with random effect 31
13.5. Quality fitting Z1.
13.6. Select model 3 "
13.7. Dynamic models 3.
13.8. Binary selection models with panel data 3
13.9. Generic Mother Mode 3
Exercises 39.
14. Preliminary testing: Introduction 39
14.1. Introduction 3!
14.2. Setting the problem 40.
14.3. Main result 40 "
14.4. PRETEST-RATION 4 $
14.5. Wals-score 40
14.6. Equivalence Theorem 4.
14.7. Pre-testing and the effect of "Untilization" 407
14.8. The effect of "Untilization". One auxiliary parameter 412
14.9. Selection of the model: from total to private and from private to total 415
14.10. The effect of "Untilization". Two auxiliary parameters 419
11. Prediction and pre-testing 425
.12. Generalizations 429.
13. Other questions 432
Exercises 434.
15. Financial Market Econometrics 435
11,5.1. Introduction 436.
15.2. Hypothesis of the effectiveness of the financial market. . . 438.
15.3. Optimization of securities portfolio 446
15.4. Test on the inclusion of new assets in an effective portfolio 450
15.5. Optimal portfolio in the presence of a risk-free asset 456
15.6. Financial assessment models 461
Exercises 471.
16. Prospects for Econometrics 472
1,6.1. Introduction 472.
16.2. What actually does an econometrist practice? .... 473.
16.3. Econometrics and physics 474
16.4. Econometrics and mathematical statistics. . . 475.
16.5. Theory and Practice 476
16.6. Econometric method 477.
16.7. Weak link 480.
1.6.8. Aggregation 481.
16.9. How to use other works 481
16.10. Conclusion 482.
Application la. Linear algebra 484.
1. Vector space 484
2. Vector space LP 485
3. Linear dependence 485
4. Linear subspace 486
5. Base. Dimension 486.
6. Linear operators 487
7. Matrix 488.
8. Operations with matrices 489
9. Matrix invariants: Trail, determinant 492
10. Rank Matrix 494
11. Reverse Matrix 495
12. Linear Equations 496 systems
13. Owls and vectors 496
14. Symmetric matrices 498
15. Positively defined matrices 500
16. Idmpotent matrices 502
17. Block matrices 503
18. Production of the Krakekera 504
19. Differentiation according to the vector argument. . 505.
Exercises 507.
Application MS. Probability Theory and Mathematical Statistics 509
1. Random variables random vectors 509
2. Conditional distributions 516
3. Some special distributions 518
4. Multidimensional normal distribution 524
5. The law of large numbers. Central Limit Theorem 528
6 Basic concepts and objectives of mathematical statistics 531
7. Evaluation of parameters 533
8. Check hypothesis 539
Appendix EP. Overview of econometric packages 542
1. The origin of the packages. Windows version. Graphics 543.
2. About some packages 544
3. Practical work experience 546
Appendix Art. Short English-Russian Dictionary of Terms 547
The application is. Tables 555.
Literature 561.
Subject 570.

Compared with the 1997 edition, the book includes three new chapters on the method of maximum believing in regression models, temporary rows and models with discrete and limited dependent variables. The number of examples from the Russian economy, tasks and exercises is significantly increased.

For students, graduate students, teachers, as well as experts in the applied economy and finance.

"Econometrics makes a quantitative analysis of real economic phenomena, based on the current development of theory and observations related to the methods of obtaining conclusions" (Samuelson).

"The main task of econometrics is to fill the empirical content of a priori economic reasoning" (Klein).

"The goal of econometrics is the empirical conclusion of economic laws. Econometrics complements the theory using real data for checking and clarifying the postulated relationships "(Maleno).

This book is addressed primarily to students, first starting to study econometrics, and has two goals. First, we want to prepare the reader to applied research in the field of economics. Secondly, we think it will be useful to students who are going to in-depth to study the theory of econometrics in the future. No preliminary knowledge about econometrics is required. However, it is assumed to become acquainted with the courses of linear algebra, the theory of probabilities and mathematical statistics in the initial volume (for example, Gelfand, 1971; Ilyin, Poznyak, 1984; Ventcel, 1964). We also assume that the reader owns mathematical analysis within the standard course of the technical university.

There are several excellent econometric textbooks in English. For example, the book (Greene, 1997) can rightly be considered an "econometric encyclopedia" - it contains almost all sections of modern econometrics. In the textbook (Goldberger, 1990), more attention is paid to the formal mathematical side of econometrics. Very successful, modern and balanced from the point of view of theory and applications is, in our opinion, the book (Johnston and Dinardo, 1997). It should also be noted textbooks (Griffits, Hill and Judge, 1993) and (Pindyck and Rubinfeld, 1991), oriented readers who do not have strong mathematical training and equipped with a large number of examples and exercises. A good complement to standard textbooks can serve as a book (Kennedy, 1998), where the main emphasis is on the content side of the econometric analysis and which contains a large number of interesting exercises. It is also necessary to mention the book (Hamilton, 1994), where the theory of temporary series is also described in a high mathematical level, and the book (Stewart, 1991) containing successful and compact sections on the theory of temporary series.

Therefore, it may be necessary to bring some arguments in favor of writing a new book instead of a simple translation of one of the existing textbooks. Our book is based on the material of lectures that one of the authors (Ya. Magnus) read as an initial course of econometrics on a master program for students of the Russian Economic School (RSH) in March-April 1993. Two other author (P. Katyshev, and . Perceptive) conducted practical classes. The intensive 7-week course included the foundations of econometrics. It was the first year of the existence of the Russian Economic School. In subsequent years, the authors collaborated in creating a program of all three econometric courses for students of the first year of study in RSH. In the process of work, we, in particular, amounted to examples from the Russian economy, which used instead of traditionally considered examples from the economies of Western Europe and the United States. In the end, we came to be convinced that it would be desirable to have a textbook written specifically for Russian students, and reworked the course program in an independent book. This book is thus the result of a five-year experience of teaching econometrics for Russian students.

Chapters 2-4 contain a classic theory of linear regression models. This material is the core of econometrics, and students must master it well before proceeding to the study of the rest of the book. Chapter 2 discusses the simplest model with two regressors, Chapter 3 is devoted to multidimensional models. In a certain sense, head 2 is redundant, but from a pedagogical point of view it is extremely useful to study the regression models with two variables. Then, for example, you can do without a matrix algebra, in a two-dimensional case it is easier to understand the graphical interpretation of regression. Chapter 4 contains several additional sections (the problem of multicollinearity, fictitious variables, model specification), but its material can also be attributed to the standard bases of econometrics.

In chapters 5-9, some generalizations of the standard multiple regression model are studied, such as stochastic regressors, a generalized method of smallest squares, heterosduction and autocorrelation of residues, an affordable generalized method of smallest squares, prediction, method of instrumental variables. Surprisingly in the theory of econometrics that at this level, most of the theorems of the standard kernel of the theory (chapter 2-4) remain fair, at least approximately or asymptotically, when the conditions theorems are weakened. We strongly recommend constantly correlate the results of chapters 5-9 with the main results set forth in chapters 2-4.

Chapter 10 contains the theory of systems of simultaneous equations, i.e. The case when the model contains more than one equation. There are problems with which an econometrist can occur in practical work.

The book includes several applications, including an overview of econometric packages and a brief English-Russian dictionary of terms.

Our experience shows that the material of chapters 1-7 is enough for the 7-week course for 6 hours per week, and the material of chapters 1-10 is for a standard single-grader. We received good results with the following course structure: two two-hour lectures per week and one seminar (in more small subgroups), but other course structures are also possible.

Students

The problem of tasks is the key to the study of mathematics, statistics, as well as econometrics. Our teachers told us about this when we were students, and we repeat it here. And that's right! For students with orientation on practical activity, experiments with data are needed. Delete several observations from your data and see what happens to your estimates and why. Add explaning variables and see how your estimates and forecasts will change. In general, experiment. A student focused on studying the theory must ask himself a question, for some reason, or another condition of the theorem is necessary. Why the theorem ceases to be fair if you delete or change one of the conditions. Find countemen.

Teachers

It is important that all students have the required mathematical and statistical level of training at the beginning of the course. If this is not the case, the course should begin with a review of the necessary concepts of linear algebra and mathematical statistics. Chapters 2-4 should stand at the beginning of the course. There is a certain freedom in choosing further if the time does not allow to include the entire book to the course. In the event of a shortage of time, stochastic regressors can be postponed (clause 5.1) and the tests for heterosfeasting (but not the concept of heterosfeasting) for the next course. Chapters 7-10 contain special, but important sections that can be included in the course with a certain degree of details, depending on the tastes of the teacher.

We will be grateful for any comments, reports on typos, obscure places, errors in this book.

Thanks

We are in a huge debt to five generations of students of the Russian economic school, which in the course of studying the course gave a lot of critical comments used by us when working on a book. Without them, this book would never be written.

We are grateful to graduates of Rash Vladislav Kargin and Alexey Attzkom, who prepared an example for the book at the market of apartments in Moscow, as well as students of Roshe Elena Pichoy and Gauhar turmukhambetova, the efforts of which they managed to avoid many typos. We are also grateful to our colleague Alexander Salanikov who took the work of editing manuscripts. In the work on the manuscript, P. Katyshev and A. Perestec received financial support from the Russian Humanitarian Scientific Foundation, the project 96-02-16011a.

Tilburg / Moscow, March 1997