A macroeconomic disequilibrium model is developed for the Federal Republic of Germany. Starting with a microeconomic model of firm's behaviour, the optimal dynamic adjustment of employment and investment is derived. The model of the firm is complemented by an explicite aggregation procedure which allows to derive macroeconomic relations. The model is estimated with macroeconomic data for the Federal Republic of Germany. An important feature is the consistent introduction of dynamic adjustment into a model of the firm. A new method is the particular approach of a delayed adjustment of employment and investment. The estimation results show significant underutilizations of labour and capital and indicate the importance of supply constraints for imports and exports. As the most prominent result, they reveal the importance of the slow adjustment of employment and investment for the macroeconomic situation in Germany and especially for the persistence of high unemployment in the eighties.

It has been quite a challenge for econometricians to model economies in transition. There is no textbook at hand to master that task. Economic theory cannot be applied without adaptations to the characteristic change of a whole economic system. Regression analysis, taking into account past economic development only, is of limited use for the econometrician. Having econometric models at hand would be very helpful for an active economic policy to guide the transition process. Various scenarios representing strategies could be simulated in their consequences to the economy. The best alternative in respect to the government's objectives could be chosen. This very situation has born the idea of co-operation between L6dz and Frankfurt in 1990. There are problems of this kind in Poland and in Germany. The German situation is somewhat better than that of Poland as a relatively small centrally planned economy is being united with a substantial social market economy taking over a lot of the burden of the former mismanagement. Thus, it might be possible to share the experience in modelling the united Germany and preparing forecasts with the Polish model builders. In addition, it would be prOfitable for both model establishing teams to link their models in order to improve the forecasting potential. Moreover, the Polish partner has a broad national and international experience in econometric model building which makes co-operation smooth and fruitful. His experience in modelling countries with a centrally planned economy would also help to master the transition problems.

This graduate level textbook deals with analyzing and forecasting multiple time series. It considers a wide range of multiple time series models and methods. The models include vector autoregressive, vector autoregressive moving average, cointegrated, and periodic processes as well as state space and dynamic simultaneous equations models. Least squares, maximum likelihood, and Bayesian methods are considered for estimating these models. Different procedures for model selection or specification are treated and a range of tests and criteria for evaluating the adequacy of a chosen model are introduced. The choice of point and interval forecasts is considered and impulse response analysis, dynamic multipliers as well as innovation accounting are presented as tools for structural analysis within the multiple time series context. This book is accessible to graduate students in business and economics. In addition, multiple time series courses in other fields such as statistics and engineering may be based on this book. Applied researchers involved in analyzing multiple time series may benefit from the book as it provides the background and tools for their task. It enables the reader to perform his or her analyses in a gap to the difficult technical literature on the topic.

This study is a revised version of my doctoral dissertation at the Economics Department of the University of Munich. I want to take the opportunity to express my gratitude to some people who have helped me in my work. My greatest thanks go to the supervisor of this dissertation, Professor Claude Billinger. Bis ideas have formed the basis of my work. Be permanently sup ported it with a host of ideas, criticism and encouragement. Furthermore, he provided a stimulating research environment at SEMECON. This study would not have been possible in this form without the help of my present and former colleagues at SEMECON. I am indebted to Rudolf Kohne-Volland, Monika Sebold-Bender and Ulrich Woitek for providing soft ware and guidance for the data analysis. Discussions with them and with Thilo Weser have helped me to take many hurdles, particularly in the early stages of the project. My sincere thanks go to them all. I had the opportunity to present a former version of my growth model at a workshop of Professor Klaus Zimmermann. I want to thank all the parti cipants for their helpful comments. I also acknowledge critical and constructive comments from an anonymous referee. Table of Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Part I. Methodology 1. Importance of Stylized Facts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.1 Limitations of statistical testing. . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Evaluating economic models. . . . . . . . . . . . . . . . . . .. . . . 11 . . . . . . 2. Further Methodological Issues . . . . . . . . . . . . . . . . . .. . . . 13 . . . . . ."

This book reports new developments in applied econometrics. All papers originated in two international workshops that were organized in the University of Munich on July 6-7, 1989, and on January 11 - 12, 1990. Financial support for these conferences by the University of Munich and the Thyssen Foundation is gratefully acknowledged. Since then all papers were substantially revised and updated. We wish to thank all authors for their patience with the revisions and Thomas Bauer, Lucie Merkle and Gisela Loos for editorial help. The ftrst section of the book collects contributions that address new "Methodological Developments." Two of them deal with problems in microeconometrics, the other two consider multi-equation systems. Martin Kukuk and Gerd Ronning treat "Ordinal Variables in Microeconometric Models." They especially deal with the case of limited-dependent variable models where some exogenous variables are either measured on an interval scale or a nominal scale. They discuss and compare two methods to deal with the problem. In his paper on "Goodness of Fit in Qualitative Choice Models: Review and Evaluation," Klaus F. Zimmermann investigates methods to summarize the predictive quality of models that deal with discrete alternatives. For these models, a widely accepted measure for evaluation like the R2, as in the case of ordinary least squares, does not exist. The paper summarizes the literature and suggests reasonable choices for evaluation on the basis of large-scale Monte Carlo investigations.

In the recent years, the study of cointegrated time series and the use of error correction models have become extremely popular in the econometric literature. This book provides an analysis of the notion of (weak) exogeneity, which is necessary to sustain valid inference in sub-systems, inthe framework of error correction models (ECMs). In many practical situations, the applied econometrician wants to introduce "structure" on his/her model in order to get economically meaningful coefficients. For thispurpose, ECMs in structural form provide an appealing framework, allowing the researcher to introduce (theoretically motivated) identification restrictions on the long run relationships. In this case, the validity of the inference will depend on a number of conditions which are investigated here. In particular, we point out that orthogonality tests, often used to test for weak exogeneity or for general misspecification, behave poorly in finite samples and are often not very useful in cointegrated systems.

In contemporary labor economics increasing attention is paid to the fact that unemployment is not only a stock but also a flow phenomenon. The present micro-econometric study analyses the impact of important socio-economic characteristics on unemployment duration in West Germany. Based on a search theoretic framework unemployment duration is considered as a stochastic process whose evolution is influenced by economicand demographic variables like unemployment benefits, expected wage offers, training and age. This is modeled by application of the concept of the hazard rate which denotes the conditional exit rate from unemployment over time given elapsed unemployment duration. Contrasting more traditional models a semi-parametric approachis chosen which reduces the danger of mis-specification of the stochastic duration process. This procedure also is particularly suitable for the analysis of grouped observations on unemployment duration typically generated by longitudinal data sets as the German "Socio-Economic Panel" which is utilized for this study. Besides deriving a set of empirical results on unemployment duration in West Germanymethodological issues of duration analysis are considered with particular attention paid to the impact of the sample design. Also, important outcomes from search theory and findings from other hazard rate analysesare surveyed.

The responses to questions such as 'What is the explanation for changes in the unemployment rate?' frequently involve the presentation of a mathematical relationship, a function that relates one set of variables to another set of variables. It should become apparent that as one's understanding of functions, relationships, and variables becomes richer and more detailed, one's ability to provide explanations for economic phenomena becomes stronger and more sophisticated. The author believes that a student's intuition should be involved in the study of mathematical techniques in economics and that this intuition develops not so much from solving problems as from visualizing them. Thus the author avoids the definition-theorem-proof style in favor of a structure that encourages the student's geometric intuition of the mathematical results. The presentation of real numbers and functions emphasizes the notion of linearity. Consequently, linear algebra and matrix analysis are integrated into the presentation of the calculus of functions of several variables. The book concludes with a chapter on classical programming, and one on nonlinear and linear programming. This textbook will be of particular interest and value to graduate and senior undergraduate students of economics, because each major mathematical idea is related to an example of its use in economics.

`...an interesting and original contribution to the realist argument' The Times Higher Education Supplement.

'This most commendable volume brings together a set of papers which permits ready access to the means of estimating quantitative relationships using cointegration and error correction procedures. Providing the data to show fully the basis for calculation, this approach is an excellent perception of the needs of senior undergraduates and graduate students.' - Professor W.P. Hogan, The University of Sydney Applied economists, with modest econometric background, are now desperately looking for expository literature on the unit roots and cointegration techniques. This volume of expository essays is written for them. It explains in a simple style various tests for the existence of unit roots and how to estimate cointegration relationships. Original data are given to enable easy replications. Limitations of some existing unit root tests are also discussed.

1. 1 Integrating results The empirical study of macroeconomic time series is interesting. It is also difficult and not immediately rewarding. Many statistical and economic issues are involved. The main problems is that these issues are so interrelated that it does not seem sensible to address them one at a time. As soon as one sets about the making of a model of macroeconomic time series one has to choose which problems one will try to tackle oneself and which problems one will leave unresolved or to be solved by others. From a theoretic point of view it can be fruitful to concentrate oneself on only one problem. If one follows this strategy in empirical application one runs a serious risk of making a seemingly interesting model, that is just a corollary of some important mistake in the handling of other problems. Two well known examples of statistical artifacts are the finding of Kuznets "pseudo-waves" of about 20 years in economic activity (Sargent (1979, p. 248)) and the "spurious regression" of macroeconomic time series described in Granger and Newbold (1986, 6. 4). The easiest way to get away with possible mistakes is to admit they may be there in the first place, but that time constraints and unfamiliarity with the solution do not allow the researcher to do something about them. This can be a viable argument."

The 17th Symposium on Operations Research was held at UniversitAt der Bundeswehr Hamburg, August 25-28, 1992, as the annual meeting of the Gesellschaft fA1/4r Mathematik, A-konomie und Operations Research (GMA-OR). The aim of this book is to provide a timely and comprehensive documentation of the symposium's scientific activities. It contains extended abstracts of most of the papers presented there. The symposium fell into twelve sections and an overlapping cross-section workshop. The sections covered established fields of theory and application such as (1) Mathematical Modelling in OR, (2) Stochastic Models of OR, (3) Combinatorial Optimization and Discrete Mathematics, (4) Linear and Non-Linear Optimization, (5) Systems and Control Theory, (6) Decision Support and Information Systems, (7) Applications in Business and Economics, (8) Econometrics and Statistics, (9) Micro-Economics and Game Theory, Macro-Economics and Applied Economics, Decision Theory, Utility and Risk, Banking, Finance and Insurance. As a novelty and an experiment, a cross-section workshop on Environmental Systems and Economics had been included in the program which was devoted to a topic of current political and scientific interest.

This book describes a series of laboratory experiments (with a total of 167 independent subjects) on forecasting behavior. In all experiments, the time series to be forecasted was generated by an abstract econometric model involving two or three artificial exogenous variables. This designprovides an optimal background for rational expectations and least-squares learning. As expected, these hypotheses do not explain observed forecasting behavior satisfactorily. Some phenomena related to this lack of rationality are studied: Concentration on changes rather than levels, underestimation of changes and overvaluation of volatile exogenous variables. Some learning behavior is observed. Finally, some aspects of individual forecasts such as prominence of "round" number, dispersion, etc., are studied.

The book is an in-depth review of the theory and empirics of the demand for money and other financial assets. The different theoretical approaches to the portfolio choice problem are described, together with an up-to-date survey of the results obtained from empirical studies of asset choice behaviour. Both single-equation studies and the more complete multi-asset portfolio models, are analysed.

The main theorem of Linear Programming Duality, relating a "pri- mal" Linear Programming problem to its "dual" and vice versa, can be seen as a statement about sign patterns of vectors in complemen- tary subspaces of Rn. This observation, first made by R.T. Rockafellar in the late six- ties, led to the introduction of certain systems of sign vectors, called "oriented matroids". Indeed, when oriented matroids came into being in the early seventies, one of the main issues was to study the fun- damental principles underlying Linear Progra.mrning Duality in this abstract setting. In the present book we tried to follow this approach, i.e., rather than starting out from ordinary (unoriented) matroid theory, we pre- ferred to develop oriented matroids directly as appropriate abstrac- tions of linear subspaces. Thus, the way we introduce oriented ma- troids makes clear that these structures are the most general -and hence, the most simple -ones in which Linear Programming Duality results can be stated and proved. We hope that this helps to get a better understanding of LP-Duality for those who have learned about it before und a good introduction for those who have not.

High and persistent unemployment rates in Europe during the eighties gave rise to a lively discussion about the nature and causes of joblessness. Among other sources structural unemployment was blamed for the lack of response of unemployment to increasing aggregate demand. Renewed attention was thus devoted to an analysis of the magnitude and the development of structural unemployment as well to its possi ble determinants. In this literature, the Beveridge curve experienced a resurrection and, at first glance, it seemed to be an appropriate tool to analyse the aforementioned issues. However, it was soon recognized that the Beveridge curve, i. e. the relation between unemployment and vacancies, was anything but stable, thus requiring a care ful distinction between dynamic loops around a (stable?) long-run Beveridge curve and possible shifts due to, say, an increasing mismatch between labor supplied and demanded. The controversy is far from being settled at the time of this writing. This book contains a collection of hitherto unpublished papers which are devoted to a theoretical and econometric analysis of structural unemployment. The papers put considerable emphasis on the question to what extent the Beveridge curve can serve as an adequate tool for such studies. The countries under consideration are Germany and Austria. In what follows a very brief summary of each paper will be outlined. Franz and Siebeck present, at some length, a theoretical and econometric analysis of the Beveridge curve in Germany."

International commodity markets have traditionally attracted the attention of economists, econometricians, and policy makers especially in and following politically tumultuous times. For instance, the primary commodity price boom of 1973/74 and the subsequent period of highly volatile world market prices initiated increased research on commodity markets which quickly focused on possible price stabilization schemes, particularly on buffer stocks. Simultaneously, the issue clearly advanced in priority on the political agenda, such that the United Nations Conference on Trade and Development (UNCTAD) proposed an "Integrated Program for Commodities" (IPC) intended to stabilize the world market prices of ten so-called "core commodities"l (UNCTAD (1974, 1976a), Behrman (1979)). Many developing nations welcomed the IPC almost enthusiastically, but it did not receive more than lukewarm support by major industrialized countries, apparently due to the experience with some thirty international commodity agreements past World War II2. Critical evaluations have, among others, been presented by McNicol (1978), Gordon-Ashworth (1984), and Macbean & Nguyen (1987). The most detailed of these studies is Gordon-Ashworth's, who concludes that "on balance ... the performance of international commodity agreements has been too unreliable and their distributive effects too uneven to secure the development goals that have been set" (1984, p. 284)3. Consequently, the IPC turned out to be quite controversial a topic on the UNCTAD's 1976 meeting in Nairobi and has not been able to gain any impetus since. lThese were cocoa, coffee, copper, cotton, jute, rubber, sisal, sugar, tea, and tin.

This sequel to the author's "Early Development in Mathematical Economics" covers developments in this field after the appearance of Cournot's "Recherches" in 1838 and until the publication of Jevons' "Theory" in 1871.

This book presents a theory of the general dynamic economic equilibrium which is a development of the static theory of Walras and Pareto. The work has built up an analytical model of the effective, current movement of an economic system, founded on the logic of the individual changing programmes - a basis for finding out the laws of all types of endogenous and exogenous movements of the economy. Indeed, the model can be used in the treatment of the typical problems of dynamic economics, by means of the author's method of variational dynamic analysis.

This collection of papers describes advances in the measurement of innovation output, principally through the use of a new technique based on scanning of trade and technical journals. Experience in several countries is assessed and the strength and weaknesses of the technique discussed. The conclusion is that, taken together with recent advances in the design of questionnaires for postal surveys of innovation, this technique provides a radically improved data source for testing innovation theories and for effective policy analysis.

1. 1 Motivation and Definition of Topic To provide motivation and to help define the topic of this study, important links between specific areas of economic theory are first highlighted. (i) Learning and Rational Expectations Theory In a standard rational expectations setting, agents in equilibrium have all the information about the model that enables them to correctly forecast future payoff-relevant variables. What rational expectations theory in its standard form does not tell us is what happens outside a rational expectations equilibrium. Less than complete knowledge of the model is a possible way to represent a situation outside the rational expectations equilibrium. It is natural to assume that agents recognize error and optimally utilize all available external information to improve on their information level, i. e. learn. Based on the information acquired by learning they modify their behavior. Under certain conditions learning steers the economy to the rational expectations equilibrium (Spear (1989), Blume, Bray and Easley (1982), Townsend (1983". This literature shows that learning is a possible mechanism to acquire the necessary level of information that agents are assumed to possess in a rational expectations equilibrium and hence there is a clear link between rational expectations theory and the 2 theory of learning. This fact is also emphasized among others by Friedman (1975), Pesaran (1987) and DeCanio (1979). (ii) Rational Expectations and Econometrics The equilibrium consequences of the rational expectations hypothesis are discussed in a considerable body of literature - cf.

One of the major issues of policy makers in The Netherlands is to reduce the high unemployment rate. In 1988 economic growth was substantial in all OECD countries, which led to an increase in employment. The economic growth also induced extra labour supply, especially of married women, which altogether led to a smaller reduction in the unemployment rate than could have been expected in view of the economic growth (see Rapportage Arbeidsmarkt, 1989). The estimated official unemployment rate in 1988 is still 11. 0% of the total labour force. Therefore, there is a strong interest in policies that seek to increase employment (the demand side of the labour market) as well as in understanding the factors that influence labour supply. In this thesis we try to further such understanding by constructing a detailed model of household labour supply. The data we use relate t9 Dutch households in 1985. In that year the official rate of unemployment was 15. 9%. A distinguishing feature of Dutch labour supply is its very low level of female labour force participation, e. g. in 1985 it was only 35. 2%. Apart from Spain, which had a similar participation rate, most other industrialized OECD countries had a participation rate of around 60% (see OECD Labor Force Statistics).

The macro disequilibrium model for Switzerland presented in this study grew out of a research project which was generously financed by Swiss Natio- nal Science Foundation. I am indebted to Prof. Hans Wtirgler and Prof. Heidi Schelbert for encouraging and supporting this work in many ways. The present book is the revised version of a paper that was accepted as a "Habilitations- schrift" by the University of ZUrich. Part of the research leading to this book was done during a stay at Princeton University, where I benefited from a stimulating environment, the gratuitous use of facilities and the helpful advise of Richard E. Quandt. Earlier disequilibrium studies for Switzerland were discussed in various seminars (Princeton, Universite de Montreal, C.O.R.E., 1988 Conference on European Unemployment in Chelwood Gate, 2nd Conference on Disequilibrium Econometrics at INSEE, 1989 European Spring Meeting on Macroeconomics in Paris) and published in the 'European Economic Review' and 'Recherches Eco- nomiques de Louvain'. Numerous people - including A.S. Blinder, L. Salvas- Bronsard, J.H. Dreze, S.M. Goldfeld, C. Gourieroux, P. Kooiman, J.P. Lambert, G. Laroque, H.S. Rosen, H.R. Sneessens" J. Waelbroeck and anonymous referees of the two journals - provided constructive comments on these earlier papers. Their suggestions - as well as the critical remarks by a referee of Springer 'Lecture Notes' - are partly reflected in the present book.

In this book voter behavior is analyzed from an economist's point of view. The influence of an economy on voter behavior is investigated and this behavior is analyzed in the perspective commonly used by economists. Econom(etr)ic tools are applied in the analyses. The book contains empirical analyses linking demographic variables to voter turnout and party choice using cross-section data for the Netherlands. Attention is focused on whether turnout and party choice decisions are taken sequentially or simultaneously by voters. An empirical test supports the former. Using these results, behavioral models of party choice and voter turnout are developed. Existing econometric analyses of voting behavior are put on a more solid theoretical footing. In both models a group perspective is used, in line with increased attention for this perspective in economics and political science. Empirical applications of the party choice model allow for an estimation of relative preferences for public goods, using the revealed preference mechanism provided by voting (intention). An alternative method for detecting these preferences, a new survey design, is discussed as well. In the turnout model, attention is fo- cused on the role of "civic duty" in a group context.

The theory of economic development is a branch of economic dynamics. Any discussion of the theory must involve dynamics even though not all dynamic problems are necessarily related to economic development. The theory's primary locus is upon the nice paths of economic variables. Stationary states, which have been the main concern of modem economic development theory, are actually special cases of economic dynamics. In this study, we propose an economic development theory within the framework of input-output systems and neoclassical economics. No political problems will be dealt with, although this does not mean that questions such as why Japan had a higher growth rate than China in the past are not important. Similarly, rather than dealing with the psychological and institutional aspects of in economic development processes we only suggest ways (or methods, as Hicks would call them) for analyzing what determines economic development from the point of view of "pure" economics. Our main contribution to economic growth theory is that we investigate various nonlinear dynamic phenomena such as bifurcations and economic cycles. We emphasize that oscillations and structural changes are not rare but universal in a progressive economy. No economic system can be stabilized forever if change is permitted.