1. 1 Introduction In economics, one often observes time series that exhibit different patterns of qualitative behavior, both regular and irregular, symmetric and asymmetric. There exist two different perspectives to explain this kind of behavior within the framework of a dynamical model. The traditional belief is that the time evolution of the series can be explained by a linear dynamic model that is exogenously disturbed by a stochastic process. In that case, the observed irregular behavior is explained by the influence of external random shocks which do not necessarily have an economic reason. A more recent theory has evolved in economics that attributes the patterns of change in economic time series to an underlying nonlinear structure, which means that fluctua tions can as well be caused endogenously by the influence of market forces, preference relations, or technological progress. One of the main reasons why nonlinear dynamic models are so interesting to economists is that they are able to produce a great variety of possible dynamic outcomes - from regular predictable behavior to the most complex irregular behavior - rich enough to meet the economists' objectives of modeling. The traditional linear models can only capture a limited number of possi ble dynamic phenomena, which are basically convergence to an equilibrium point, steady oscillations, and unbounded divergence. In any case, for a lin ear system one can write down exactly the solutions to a set of differential or difference equations and classify them."

Migration, commuting, and tourism are prominent phenomena demonstrating the political and economic relevance of the spatial choice behavior of households. The identification of the determinants and effects of the households' location choice is necessary for both entrepreneurial and policy planners who attempt to predict (or regulate) the future demand for location-specific commodities, such as infrastructure, land, or housing, and the supply of labor. Microeconomic studies of the spatial behavior of individuals have typically focused upon the demand for a single, homogeneous, yet location-specific com 2 modity (such as land or housing ) or their supply of labor3 and investigated the formation of location-specific prices and wages in the presence of transportation and migration costs or analyzed the individual-and location-specific character istics triggering spatial rather than quantitative or temporal adjustments. In contrast to many theoretical analyses, empirical studies of the causes or con sequences of individual demand for location-specific commodities have often considered several "brands" of a heterogeneous good that are offered at various locations, are perfect substitutes, and may be produced by varying production 4 technologies. lCf. Alonso (1964) 2Cf. Muth (1969). 3Cf. Sjaastad (1962) and Greenwood (1975)."

As a new type of technique, simplicial methods have yielded extremely important contributions toward solutions of a system of nonlinear equations. Theoretical investigations and numerical tests have shown that the performance of simplicial methods depends critically on the triangulations underlying them. This monograph describes some recent developments in triangulations and simplicial methods. It includes the D1-triangulation and its applications to simplicial methods. As a result, efficiency of simplicial methods has been improved significantly. Thus more effective simplicial methods have been developed.

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 brings together a wide range of topics and perspectives in the growing field of Classification and related methods of Exploratory and Multivariate Data Analysis. It gives a broad view on the state ofthe art, useful for those in the scientific community who gather data and seek tools for analyzing and interpreting large sets of data. As it presents a wide field of applications, this book is not only of interest for data analysts, mathematicians and statisticians, but also for scientists from many areas and disciplines concerned with real data, e. g. , medicine, biology, astronomy, image analysis, pattern recognition, social sciences, psychology, marketing, etc. It contains 79 invited or selected and refereed papers presented during the Fourth Bi- ennial Conference of the International Federation of Classification Societies (IFCS'93) held in Paris. Previous conferences were held at Aachen (Germany), Charlottesville (USA) and Edinburgh (U. K. ). The conference at Paris emerged from the elose coop- eration between the eight members of the IFCS: British Classification Society (BCS), Classification Society of North America (CSNA), Gesellschaft fur Klassifikation (GfKl), J apanese Classification Society (J CS), Jugoslovenska Sekcija za Klasifikacije (JSK), Societe Francophone de Classification (SFC), Societa. Italiana di Statistica (SIS), Vereniging voor Ordinatie en Classificatie (VOC), and was organized by INRIA ("Institut National de Recherche en Informatique et en Automatique"), Rocquencourt and the "Ecole Nationale Superieure des Telecommuni- cations," Paris.

A discussion of various aspects of dynamic behavior of empirical macroeconomic, and in particular, macroeconometric models, is presented in this book. The book addresses in depth several theoretical and practical aspects concerning the modeling and analysis of long-run equilibrium behavior, adjustment dynamics and stability. Tools are developed to identify and interpret the main determinants of the dynamics of models. The tools involve, among others, error-correction mechanisms, eigenvalue analysis, feedback closure rules, graph theory, learning behavior, steady-state analysis, and stochastic simulation. Their usefulness is demonstrated by interesting applications to a number of well-known national and multi-national models.

'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.

Many models in this volume can be used in solving portfolio problems, in assessing forecasts, in understanding the possible effects of shocks and disturbances.

The papers collected in this volume are contributions to T.I.Tech./K.E.S. Conference on Nonlinear and Convex Analysis in Economic Theory, which was held at Keio University, July 2-4, 1993. The conference was organized by Tokyo Institute of Technology (T. I. Tech.) and the Keio Economic Society (K. E. S.) , and supported by Nihon Keizai Shimbun Inc .. A lot of economic problems can be formulated as constrained optimiza tions and equilibrations of their solutions. Nonlinear-convex analysis has been supplying economists with indispensable mathematical machineries for these problems arising in economic theory. Conversely, mathematicians working in this discipline of analysis have been stimulated by various mathematical difficulties raised by economic the ories. Although our special emphasis was laid upon "nonlinearity" and "con vexity" in relation with economic theories, we also incorporated stochastic aspects of financial economics in our project taking account of the remark able rapid growth of this discipline during the last decade. The conference was designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who were seeking for effective mathematical weapons for their researches. Thirty invited talks (six of them were plenary talks) given at the conf- ence were roughly classified under the following six headings : 1) Nonlinear Dynamical Systems and Business Fluctuations, . 2) Fixed Point Theory, 3) Convex Analysis and Optimization, 4) Eigenvalue of Positive Operators, 5) Stochastic Analysis and Financial Market, 6) General Equilibrium Analysis.

As large physical capital stock projects need long periods to be built, a time-to-build specification is incorporated in factor demand models. Time-to-build and adjustment costs dynamics are identified since by the first moving average dynamics, whereas by the latter autoregressive dynamics are induced. Empirical evidence for time-to-build is obtained from data from the Dutch construction industry and by the estimation result from the manufacturing industry of six OECD countries.

This book presents a review of recent developments in the theory and construction of index numbers using the stochastic approach, demonstrating the versatility of this approach in handling various index number problems within a single conceptual framework. It also contains a brief, but complete, review of the existing approaches to index numbers with illustrative numerical examples.;The stochastic approach considers the index number problem as a signal extraction problem. The strength and reliability of the signal extracted from price and quantity changes for different commodities depends on the messages received and the information content of the messages. The most important applications of the new approach are to be found in the context of measuring rate of inflation and fixed and chain base index numbers for temporal comparisons and for spatial inter-country comparisons - the latter generally require special index number formulae that result in transitive and base invariant comparisons.

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."

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.

This book provides advanced theoretical and applied tools for the implementation of modern micro-econometric techniques in evidence-based program evaluation for the social sciences. The author presents a comprehensive toolbox for designing rigorous and effective ex-post program evaluation using the statistical software package Stata. For each method, a statistical presentation is developed, followed by a practical estimation of the treatment effects. By using both real and simulated data, readers will become familiar with evaluation techniques, such as regression-adjustment, matching, difference-in-differences, instrumental-variables, regression-discontinuity-design, and synthetic control method, and are given practical guidelines for selecting and applying suitable methods for specific policy contexts. The second revised and extended edition features two new chapters on some recent development of difference-in-differences. Specifically, chapter 5 introduces advanced difference-in-differences methods when many times are available and treatment can be either time-varying or fixed at a specific time. Chapter 6 introduces the synthetic control method, a treatment effect estimation approach suitable when only one unit is treated. Both chapters present applications using the software Stata.

This Fourth Edition updates the "Solutions Manual for Econometrics" to match the Sixth Edition of the Econometrics textbook. It adds problems and solutions using latest software versions of Stata and EViews. Special features include empirical examples replicated using EViews, Stata as well as SAS. The book offers rigorous proofs and treatment of difficult econometrics concepts in a simple and clear way, and provides the reader with both applied and theoretical econometrics problems along with their solutions. These should prove useful to students and instructors using this book.

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.

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.

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 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 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 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.

Methods for Estimation and Inference in Modern Econometrics provides a comprehensive introduction to a wide range of emerging topics, such as generalized empirical likelihood estimation and alternative asymptotics under drifting parameterizations, which have not been discussed in detail outside of highly technical research papers. The book also addresses several problems often arising in the analysis of economic data, including weak identification, model misspecification, and possible nonstationarity. The book's appendix provides a review of some basic concepts and results from linear algebra, probability theory, and statistics that are used throughout the book. Topics covered include: Well-established nonparametric and parametric approaches to estimation and conventional (asymptotic and bootstrap) frameworks for statistical inference Estimation of models based on moment restrictions implied by economic theory, including various method-of-moments estimators for unconditional and conditional moment restriction models, and asymptotic theory for correctly specified and misspecified models Non-conventional asymptotic tools that lead to improved finite sample inference, such as higher-order asymptotic analysis that allows for more accurate approximations via various asymptotic expansions, and asymptotic approximations based on drifting parameter sequences Offering a unified approach to studying econometric problems, Methods for Estimation and Inference in Modern Econometrics links most of the existing estimation and inference methods in a general framework to help readers synthesize all aspects of modern econometric theory. Various theoretical exercises and suggested solutions are included to facilitate understanding.

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.

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.

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.