Sample data alone never suffice to draw conclusions about populations. Inference always requires assumptions about the population and sampling process. Statistical theory has revealed much about how strength of assumptions affects the precision of point estimates, but has had much less to say about how it affects the identification of population parameters. Indeed, it has been commonplace to think of identification as a binary event - a parameter is either identified or not - and to view point identification as a pre-condition for inference. Yet there is enormous scope for fruitful inference using data and assumptions that partially identify population parameters. This book explains why and shows how. The book presents in a rigorous and thorough manner the main elements of Charles Manski's research on partial identification of probability distributions. One focus is prediction with missing outcome or covariate data. Another is decomposition of finite mixtures, with application to the analysis of contaminated sampling and ecological inference. A third major focus is the analysis of treatment response. Whatever the particular subject under study, the presentation follows a common path. The author first specifies the sampling process generating the available data and asks what may be learned about population parameters using the empirical evidence alone. He then ask how the (typically) setvalued identification regions for these parameters shrink if various assumptions are imposed. The approach to inference that runs throughout the book is deliberately conservative and thoroughly nonparametric. Conservative nonparametric analysis enables researchers to learn from the available data without imposing untenable assumptions. It enables establishment of a domain of consensus among researchers who may hold disparate beliefs about what assumptions are appropriate. Charles F. Manski is Board of Trustees Professor at Northwestern University. He is author of Identification Problems in the Social Sciences and Analog Estimation Methods in Econometrics. He is a Fellow of the American Academy of Arts and Sciences, the American Association for the Advancement of Science, and the Econometric Society.

This conference brought together an international group of fisheries economists from academia, business, government, and inter-governmentalagencies, to consider a coordinated project to build an econometric model of the world trade in groundfish. A number of the conference participants had just spent up to six weeks at Memorial University of Newfoundland working and preparing papers on the project. This volume presents the papers that these scholars produced, plus additional papers prepared by other conference participants. In addition, various lectures and discussionswhich were transcribed from tapes made of the proceedings are included. The introductory essay explains the genesis of the conference, describes the approach taken to modelling the groundfish trade, very briefly summarizes the technical papers, and describes future plans. The project is continuing as planned, and a second conference was held in St. John's in August 1990. The conference was a NATO Advanced Research Workshop and we wish to thank the ScientificAffairs Division ofNATO for their financial support. Additional financial support was received from the Canadian Centre for Fisheries Innovation in St. John's, the Department of Fisheries and Oceans of the Government of Canada, the Department of Fisheries of the Government of Newfoundland and Labrador, Memorial University of Newfoundland and Air Nova; we acknowledge with appreciation their help.

Experiences with Financial Liberalization provides a broad spectrum of policy experiences relating to financial liberalization around the globe since the 1960s. There is a sizable body of theoretical and aggregative empirical literature in this area, but there is little work documenting and analyzing the experiences of individual countries and/or sets of countries. This book is divided into four parts by geographical region - Africa, Asia and Latin America, Central and Eastern Europe, and the Middle East. Aggregative econometric studies cannot substitute for country-wide studies in allowing the researcher to draw lessons for the future, and this volume adds to this relatively small body of literature.

Louis Phlips The stabilisation of primary commodity prices, and the related issue of the stabilisation of export earnings of developing countries, have traditionally been studied without reference to the futures markets (that exist or could exist) for these commodities. These futures markets have in turn been s udied in isolation. The same is true for the new developments on financial markets. Over the last few years, in particular sine the 1985 tin crisis and the October 1987 stock exchange crisis, it has become evident that there are inter actions between commodity, futures, and financial markets and that these inter actions are very important. The more so as trade on futures and financial markets has shown a spectacular increase. This volume brings together a number of recent and unpublished papers on these interactions by leading specialists (and their students). A first set of papers examines how the use of futures markets could help stabilising export earnings of developing countries and how this compares to the rather unsuccessful UNCTAD type interventions via buffer stocks, pegged prices and cartels. A second set of papers faces the fact, largely ignored in the literature, that commodity prices are determined in foreign currencies, with the result that developing countries suffer from the volatility of exchange rates of these currencies (even in cases where commodity prices are relatively stable). Financial markets are thus explicitly linked to futures and commodity markets."

Many problems in statistics and econometrics offer themselves naturally to
the use of optimization heuristics. Standard methods applied to highly
complex problems often produce approximate results, of unknown quality,
based on heavy assumptions. Optimization heuristic methods provide
powerful results to many complex problems. combined with relatively
simple implementation.

• Offers a self-contained introduction to optimization heuristics in econometrics and statistics
• Features many examples of optimization heuristic methods applied to real problems
• Includes detailed coverage of the threshold accepting heuristic
• Provides suggestions for further reading

This book was mainly written while I stayed at the Catholic University of Louvain. Professor Anton P. Barten was the one who did not only give me a warm welcome in Louvain, but also supported my research with most valuable comments and constructive criticisms. In addition I benefitted from dis cussions with Erik Schokkaert, Denis de Crombrugghe and Jo Baras on various subjects, such as the small-sample correction of Chapter 9. The arduous task of transferring my neat handwriting into a readable typescript was excellently taken care of by Brs. E. Crabbe and notably Brs. F. Duij sens, even after working hours. Mrs. A. Molders prevented me of making serious abuse of the English language. My admiration for Carien, finally, is an exponential function of the patience and enthusiasm with which she sup ported my research. Chapter I is a general introduction to the subject of linkage models, and it contains few mathematical elaborations. Chapters 2 to 4 use more, but elementary, mathematics, and treat several aspects related to the deriva tion, interpretation and estimation of linkage models. Chapter 2 deals vii tll the theory of import allocation models, Chapter J treats the problem of defining and interpreting elasticities of substitution, while Chapter 4 is concerned with the econometric problems related to the estimation of mul tivariate models with linear restrictions, such as import allocation models."

Continuous-time econometrics is no longer an esoteric subject although most still regard it as such, so much so that it is hardly mentioned in standard textbooks on econometrics. Thanks to the work done in the last 20 years, both the theoretical and the applied side are by now well developed. Methods of estimation have been theoretically elaborated and practically implemented through computer programs. Continuous-time macroeconometric models for different countries have been constructed, estimated and used. Being myself involved in these developments, it was with great pleasure that I accepted the invitation to organize a session on continuous-time econometrics in the context of the International Symposium on Economic Modelling (jointly organized by the University of Urbino and the book series International Studies in Economic Modelling, and co-sponsored by the Consiglio Nazionale delle Ricerche). The reaction of 'continuists' from all over the world was so enthusiastic that I was able to arrange two sessions, one on the theory and the other on the applications. The symposium was held in Urbino on 23-25 July 1990. The papers presented in Urbino have been revised in the light of the discussion at the symposium and the referees' comments. Hence, what is published here should become another standard reference in the field of continuous-time econometrics.

Understanding the structure of a large econometric model is rather like the art of winetasting or like the art of playing a musical instrument. The quality of a wine results from a complex combination of various elements such as its colour which should be clear and crystalline, its smell which can be decomposed into a general aroma and a variety of particular characteristics, more or less persistent depending on the type and the age of the wine, its taste, of course, which again is a complex system whose equilibrium and charm depend on the whole set of ingredients: alcohol, tannin, glycerine, sugar, acidity . . . Similarly, a clarinetist's musicianship depends on the quality of his instrument, on his embouchure, fingering, tonguing and articu lation techniques, on his sense for rhythm, phasing and tone colour. However, the enchantment produced by a Romanee-Conti or by a brilliant performance of Brahm's F minor sonata for clarinet and piano arises from a process which is at the same time time much simpler and much more complex than the straightforward juxtaposition of individual causal relations. In recent years econometricians and macro-economists have been challenged by the problem of keeping abreast with an ever increasing number of increasingly more complex large econometric models. The necessity of developing systematic analytical tools to study the often implicit and hidden structure of these models has become more evident.

This book is the first volume of the International Series in Economic Model ing, a series designed to summarize current issues and procedures in applied modeling within various fields of economics and to offer new or alternative approaches to prevailing problems. In selecting the subject area for the first volume, we were attracted by the area to which applied modeling efforts are increasingly being drawn, regional economics and its associated subfields. Applied modeling is a broad rubric even when the focus is restricted to econometric modeling issues. Regional econometric modeling has posted a record of rapid growth during the last two decades and has become an established field of research and application. Econometric models of states and large urban areas have become commonplace, but the existence of such models does not signal an end to further development of regional econ ometric methods and models. Many issues such as structural specification, level of geographic detail, data constraints, forecasting integrity, and syn thesis with other regional modeling techniques will continue to be sources of concern and will prompt further research efforts. The chapters of this volume reflect many of these issues. A brief synopsis of each contribution is provided below: Richard Weber offers an overview of regional econometric models by discussing theoretical specification, nature of variables, and ultimate useful ness of such models. For an illustration, Weber describes the specification of the econometric model of New Jersey."

This book deals with the methods and practical uses of regression and factor analysis. An exposition is given of ordinary, generalized, two- and three-stage estimates for regression analysis, the method of principal components being applied for factor analysis. When establishing an econometric model, the two ways of analysis complement each other. The model was realized as part of the 'Interplay' research project concerning the economies of the European Common Market countries at the Econometrics Department of the Tilburg School of Economics. The Interplay project aims at: a. elaborating more or less uniformly defined and estimated models; b. clarifying the economic structure and the economic policy possible with the linked models of the European Community countries. Besides the model for the Netherlands published here, the models for Belgium, Italy, West Germany and the United Kingdom are ready for linking and for publishing later on. The econometric model presented in this book and upon which the Interplay model is based comprises eleven structural and twenty-one definitional equations; it is estimated with ordinary, two- and three-stage least squares. The analysis of the model is directed at eliminating multicollinearity, accor ding to D.E. Farrar's and R. Glauber's method. In practice, however, complete elimination of multicollinearity leads to an exclusion of certain relations which is not entirely satisfactory. Economic relations can be dealt with more fully by analyzing the variables involved in detail by factor analysis. In this study factor analysis is also a suitable method for a comparative analysis of different periods."

Econometric theory, as presented in textbooks and the econometric literature generally, is a somewhat disparate collection of findings. Its essential nature is to be a set of demonstrated results that increase over time, each logically based on a specific set of axioms or assumptions, yet at every moment, rather than a finished work, these inevitably form an incomplete body of knowledge. The practice of econometric theory consists of selecting from, applying, and evaluating this literature, so as to test its applicability and range. The creation, development, and use of computer software has led applied economic research into a new age. This book describes the history of econometric computation from 1950 to the present day, based upon an interactive survey involving the collaboration of the many econometricians who have designed and developed this software. It identifies each of the econometric software packages that are made available to and used by economists and econometricians worldwide.

A function is convex if its epigraph is convex. This geometrical structure has very strong implications in terms of continuity and differentiability. Separation theorems lead to optimality conditions and duality for convex problems. A function is quasiconvex if its lower level sets are convex. Here again, the geo metrical structure of the level sets implies some continuity and differentiability properties for quasiconvex functions. Optimality conditions and duality can be derived for optimization problems involving such functions as well. Over a period of about fifty years, quasiconvex and other generalized convex functions have been considered in a variety of fields including economies, man agement science, engineering, probability and applied sciences in accordance with the need of particular applications. During the last twenty-five years, an increase of research activities in this field has been witnessed. More recently generalized monotonicity of maps has been studied. It relates to generalized convexity off unctions as monotonicity relates to convexity. Generalized monotonicity plays a role in variational inequality problems, complementarity problems and more generally, in equilibrium prob lems."

National income estimates date back to the late 17th century, but only in the half-century since the Second World War have economic accounts developed in their present form, becoming an indispensable tool for macroeconomic analysis, projections and policy formulation. Furthermore, it was in this period that the United Nations issued several versions of a system of national accounts (SNA) to make possible economic comparisons on a consistent basis. The latest version, SNA 1993, published in early 1994, occasioned this collection of essays and commentaries. The three chief objectives of the volume are: to enhance understanding of socioeconomic accounts generally and of SNA 1993 in particular; to offer a critique of SNA 1993, including constructive suggestions for future revisions of the system, making it even more useful for its national and international purposes; and to serve as a textbook, or book of readings in conjunction with SNA 1993, for courses in economic accounts.

Drawing on the author's extensive and varied research, this book provides readers with a firm grounding in the concepts and issues across several disciplines including economics, nutrition, psychology and public health in the hope of improving the design of food policies in the developed and developing world. Using longitudinal (panel) data from India, Bangladesh, Kenya, the Philippines, Vietnam, and Pakistan and extending the analytical framework used in economics and biomedical sciences to include multi-disciplinary analyses, Alok Bhargava shows how rigorous and thoughtful econometric and statistical analysis can improve our understanding of the relationships between a number of socioeconomic, nutritional, and behavioural variables on a number of issues like cognitive development in children and labour productivity in the developing world. These unique insights combined with a multi-disciplinary approach forge the way for a more refined and effective approach to food policy formation going forward. A chapter on the growing obesity epidemic is also included, highlighting the new set of problems facing not only developed but developing countries. The book also includes a glossary of technical terms to assist readers coming from a variety of disciplines.

The purpose of this volume is to honour a pioneer in the field of econometrics, A. L. Nagar, on the occasion of his sixtieth birthday. Fourteen econometricians from six countries on four continents have contributed to this project. One of us was his teacher, some of us were his students, many of us were his colleagues, all of us are his friends. Our volume opens with a paper by L. R. Klein which discusses the meaning and role of exogenous variables in struc tural and vector-autoregressive econometric models. Several examples from recent macroeconomic history are presented and the notion of Granger-causality is discussed. This is followed by two papers dealing with an issue of considerable relevance to developing countries, such as India; the measurement of the inequality in the distribution of income. The paper by C. T. West and H. Theil deals with the problem of measuring inequality of all components of total income vvithin a region, rather than just labour income. It applies its results to the regions of the United States. The second paper in this group, by N. Kakwani, derives the large-sample distributions of several popular inequality measures, thus providing a method for drawing large-sample inferences about the differences in inequality between regions. The techniques are applied to the regions of Cote d'Ivoire. The next group of papers is devoted to econometric theory in the context of the dynamic, simultaneous, linear equations model. The first, by P. J."

In plying their trade, social scientists often are confronted with significant phenomena that appear incapable of measurement. Past practice would suggest that the way to deal with these cases is to work harder at finding appropriate measures so that standard quantitative analysis can still be applied. Professor Katzner's approach, however is quite different. Rather than concentrating on the construction of measures, he raises the question of how such phenomena can be investigated and understood in the absence of numerical gauges to represent them.

At the time of this volume's publication in 1985, general equilibrium modelling had become a significant area of applied economic research. Its focus was to develop techniques to facilitate economy-wide quantitative assessment of allocative and distributional impacts on policy changes. UK Tax Policy and Applied General Equilibrium Analysis was the first book-length treatment of the development and application of an applied general equilibrium model of the Walrasian type, constructed to analyse UK taxation and subsidy policy. As a whole, UK Tax Policy and Applied General Equilibrium Analysis offers the reader two things. First, it gives a detailed account of the development of an applied general equilibrium model of the UK. Second, it provides results of model experiments which have been designed to inform the policy debate, not only in the UK but also in other countries. It should thus be of interest to both researchers and students undertaking research in the applied general equilibrium area and to policy makers concerned with tax reform.

Giovanni Castellani Rector of the University of Venice This book contains the Proceedings of the Conference on "Economic Policy and Control Theory" which was held at the University of Venice (Italy) on 27 January-l February 1985. The goal of the Conference was to survey the main developments of control theory in economics, by emphasizing particularly new achievements in the analysis of dynamic economic models by con trol methods. The development of control theory is strictly related to the development of science and technology in the last forty years. Control theory was indeed applied mainly in engineering, and only in the sixties economists started using control methods for analys ing economic problems, even if some preliminary economic applica tions of calculus of variations, from which control theory was then developed, date back to the twenties. Applications of control theory in economics also had to solve new, complicated, problems, like those encountered in optimal growth models, or like the determination of the appropriate inter temporal social welfare function, of the policy horizon and the relative final state of the system, of the appropriate discount factor. Furthermore, the uncertainty characterizing economic models had to be taken into account, thus giving rise to the development of stochastic control theory in economics."

Thi s book ari ses from The Fourth European Coll oqui urn on Theoret i ca 1 and Quant itat i ve Geography wh i ch was he 1 din Ve 1 dhoven, The Netherlands in September 1985. It contains a series of papers on spatial choice dynamics and dynamical spatial systems which were presented at the colloquium, together with a few other soll icited ones. The book is intended primarily as a state-of-the art review of mainly European research on these two fastly growing problem areas. As a consequence of this decision, the book contains a selection of papers that differs in terms of focus, level of sophistication and conceptual background. Evidently, the dissimination of ideas and computer software is a time-related phenomenon, which in the European context is amplified by differences in language, the profile of geography and the formal training of geographers. The book reflects such differences. It would have been impossible to produce this book without the support of the various European study groups on theoretical and quantitative geography. Without their help the meetings from which this volumes originates would not have been held in the first place. We are also indebted to the Royal Dutch Academy of Science for partly funding the colloquium, and to SISWO and TNOjPSC for providing general support in the organisation of the conference.

o. Guvenen, University of Paris IX-Dauphine The aim of this publication is to present recent developments in international com modity market model building and policy analysis. This book is based mainly on the research presented at the XlIth International Conference organised by the Applied Econometric Association (AEA) which was held at the University of Zaragoza in Spain. This conference would not have been possible with out the cooperation of the Department of Econometrics of the University of Zaragoza and its Chairman A.A. Grasa. I would like to express my thanks to all contributors. I am grateful to J.H.P. Paelinck, J.P. Ancot, A.J. Hughes Hallett and H. Serbat for their constructive contributions and comments concerning the structure of the book. vii INTRODUCTION o. Guvenen The challenge of increasing complexity and global interdependence at the world level necessitates new modelling approaches and policy analysis at the macroeconomic level, and for commodities. The evaluation of economic modelling.follows the evolution of international economic phenomena. In that interdependent context there is a growing need for forecasting and simulation tools in the analysis of international primary com modity markets."

These proceedings, from a conference held at the Federal Reserve Bank of St. Louis on October 17-18, 1991, attempted to layout what we currently know about aggregate economic fluctuations. Identifying what we know inevitably reveals what we do not know about such fluctuations as well. From the vantage point of where the conference's participants view our current understanding to be, these proceedings can be seen as suggesting an agenda for further research. The conference was divided into five sections. It began with the formu lation of an empirical definition of the "business cycle" and a recitation of the stylized facts that must be explained by any theory that purports to capture the business cycle's essence. After outlining the historical develop ment and key features of the current "theories" of business cycles, the conference evaluated these theories on the basis of their ability to explain the facts. Included in this evaluation was a discussion of whether (and how) the competing theories could be distinguished empirically. The conference then examined the implications for policy of what is known and not known about business cycles. A panel discussion closed the conference, high lighting important unresolved theoretical and empirical issues that should be taken up in future business cycle research. What Is a Business Cycle? Before gaining a genuine understanding of business cycles, economists must agree and be clear about what they mean when they refer to the cycle."