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."

This book provides a game theoretic model of interaction among VoIP telecommunications providers regarding their willingness to enter peering agreements with one another. The author shows that the incentive to peer is generally based on savings from otherwise payable long distance fees. At the same time, termination fees can have a countering and dominant effect, resulting in an environment in which VoIP firms decide against peering. Various scenarios of peering and rules for allocation of the savings are considered. The first part covers the relevant aspects of game theory and network theory, trying to give an overview of the concepts required in the subsequent application. The second part of the book introduces first a model of how the savings from peering can be calculated and then turns to the actual formation of peering relationships between VoIP firms. The conditions under which firms are willing to peer are then described, considering the possible influence of a regulatory body.

In applications, and especially in mathematical finance, random time-dependent events are often modeled as stochastic processes. Assumptions are made about the structure of such processes, and serious researchers will want to justify those assumptions through the use of data. As statisticians are wont to say, "In God we trust; all others must bring data."
This book establishes the theory of how to go about estimating not just scalar parameters about a proposed model, but also the underlying structure of the model itself. Classic statistical tools are used: the law of large numbers, and the central limit theorem.Researchers have recently developed creative and original methods to use these tools in sophisticated (but highly technical) ways to reveal new details about the underlying structure. For the first time in book form, the authors present these latest techniques, based on research from the last 10 years. They include new findings.

This book will be of special interest to researchers, combining the theory of mathematical finance with its investigation using market data, and it will also prove to be useful in a broad range of applications, such as to mathematical biology, chemical engineering, and physics. "

Since its establishment in the 1950s the American Economic Association's Committee on Economic Education has sought to promote improved instruction in economics and to facilitate this objective by stimulating research on the teaching of economics. These efforts are most apparent in the sessions on economic education that the Committee organizes at the Association's annual meetings. At these sessions economists interested in economic education have opportunities to present new ideas on teaching and research and also to report the findings of their research. The record of this activity can be found in the Proceedings of the American Eco nomic Review. The Committee on Economic Education and its members have been actively involved in a variety of other projects. In the early 1960s it organized the National Task Force on Economic Education that spurred the development of economics teaching at the precollege level. This in turn led to the development of a standardized research instrument, a high school test of economic understanding. This was followed later in the 1960s by the preparation of a similar test of understanding college economics. The development of these two instruments greatly facilitated research on the impact of economics instruction, opened the way for application of increasingly sophisticated statistical methods in measuring the impact of economic education, and initiated a steady stream of research papers on a subject that previously had not been explored."

This book is based on an international conference organised by the Applied Econo- metric Association (AEA) on International Macroeconomic Modelling which was held in Brussels at the Commission of the European Communities in December 1983. On behalf of the Applied Econometric Association, we would like to extend our thanks to all participants and contributors. This conference would not have been possible without the cooperation and support of the Commission of the European Economic Communities and of its Directorate General for Economics and Financial Affairs (DGII) staff, in particular M. Emerson, A. Dramais, and also H. Serbat of the Paris Chamber of Commerce and Industry. Our thanks go also to J.P. Ancot for his constructive comments concerning the structure of this book. We are grateful to M. Russo, R. Maldague and Y. Ullmo for opening the con- ference with their stimulating review and comments on the use of international macroeconomic models; and to R. Bird, A.M. Costa, A. Crockett, H. Guitton, J.C. Milleron, J. Paelinck, J. Waelbroeck for chairing the scientific sessions. P. Artus F. Gagey O. Guvenen vi INTRODUCTION The main focus of this book is to present recent developments in the construction and use of international macroeconometric models. Four main aspects are selected: (i) analysis of trade linkages and exchange rate determination; (ii) modelling and simulating the international economy; (iii) international policy coordination; (iv) the use of international macroeconomic models.

This book has taken form over several years as a result of a number of courses taught at the University of Pennsylvania and at Columbia University and a series of lectures I have given at the International Monetary Fund. Indeed, I began writing down my notes systematically during the academic year 1972-1973 while at the University of California, Los Angeles. The diverse character of the audience, as well as my own conception of what an introductory and often terminal acquaintance with formal econometrics ought to encompass, have determined the style and content of this volume. The selection of topics and the level of discourse give sufficient variety so that the book can serve as the basis for several types of courses. As an example, a relatively elementary one-semester course can be based on Chapters one through five, omitting the appendices to these chapters and a few sections in some of the chapters so indicated. This would acquaint the student with the basic theory of the general linear model, some of the prob lems often encountered in empirical research, and some proposed solutions. For such a course, I should also recommend a brief excursion into Chapter seven (logit and pro bit analysis) in view of the increasing availability of data sets for which this type of analysis is more suitable than that based on the general linear model.

The field of econometrics has gone through remarkable changes during the last thirty-five years. Widening its earlier focus on testing macroeconomic theories, it has become a rather comprehensive discipline concemed with the development of statistical methods and their application to the whole spectrum of economic data. This development becomes apparent when looking at the biography of an econometrician whose illustrious research and teaching career started about thirty-five years ago and who will retire very soon after his 65th birthday. This is Gerd Hansen, professor of econometrics at the Christian Albrechts University at Kiel and to whom this volume with contributions from colleagues and students has been dedicated. He has shaped the econometric landscape in and beyond Germany throughout these thirty-five years. At the end of the 1960s he developed one of the first econometric models for the German econ omy which adhered c10sely to the traditions put forth by the Cowles commission."

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."

Recent economic history suggests that a key element in economic growth and development for many countries has been an aggressive export policy and a complementary import policy. Such policies can be very effective provided that resources are used wisely to encourage exports from industries that can be com petitive in the international arena. Also, import protection must be used carefully so that it encourages infant industries instead of providing rents to industries that are not competitive. Policy makers may use a variety of methods of analysis in planning trade policy. As computing power has grown in recent years increasing attention has been give to economic models as one of the most powerful aids to policy making. These models can be used on the one hand to help in selecting export industries to encourage and infant industries to protect and on the other hand to chart the larger effects ofttade policy on the entire economy. While many models have been developed in recent years there has not been any analysis of the strengths and weaknesses of the various types of models. Therefore, this monograph provides a review and analysis of the models which can be used to analyze dynamic comparative advantage."

The availability of financial data recorded on high-frequency level has inspired a research area which over the last decade emerged to a major area in econometrics and statistics. The growing popularity of high-frequency econometrics is driven by technological progress in trading systems and an increasing importance of intraday trading, liquidity risk, optimal order placement as well as high-frequency volatility. This book provides a state-of-the art overview on the major approaches in high-frequency econometrics, including univariate and multivariate autoregressive conditional mean approaches for different types of high-frequency variables, intensity-based approaches for financial point processes and dynamic factor models. It discusses implementation details, provides insights into properties of high-frequency data as well as institutional settings and presents applications to volatility and liquidity estimation, order book modelling and market microstructure analysis.

This book grew out of a 'Doctorat D'Etat' thesis presented at the University of Dijon-Institut Mathematique Economiques (lME). It aims to show that quantity rationing theory provides the means of improving macroeconometric modelling in the study of struc- tural changes. The empirical results presented in the last chapter (concerning Portuguese economy) and in the last Appendix (con- cerning the French economy), although preliminary, suggested that the effort is rewarding and should be continued. My debts are many. An important part of the research work was accomplished during my visit to the Institut National de la Statistique et des Etudes Economiques (lNSEE, Paris), where I have beneficted from stimulating discussions (particularly with P. Villa) and infor- matical support. I have also received comments and suggestions from R. Quandt, J.-J. Laffont, P. Kooiman and P.-Y. Henin. I am specially indebted to P. Balestra for encouraging and valuable discussions, particularly in the field of econometric methods. My thanks go also to an anonymous referee. His constructive criticism and suggestions resulted in a number of improvements to an earlier version of this book. I cannot forget my friend A. Costa from BP A (Porto) who has helped me in the preparation of this work. Last but not least, I would like to thank my wife for her encouragement and patience throughout these years. Of course, I am the only one responsible for any remaining errors.

Econometrics of Health Care - which we have sometimes called 'medico metrics' - is a field in full expansion. The reasons are numerous: our knowl edge of quantitative relations in the field of health econometrics is far from being perfect, a large number of analytical difficulties - combining medical (latent factors, e. g. ) and economic facts (spatial behaviour, e. g. ) are faced by the research worker, medical and pharmaceutical techniques change rapidly, medical costs rocket more than proportionally with available resources, of being tightened. medical budgets are in the process So it is not surprising that the practice of 'hygieconometrics' - to produce a neologism - is more and more included in the programmes of econometri cians. The Applied Econometrics Association has devoted to the topic two symposia in less than three years (Lyons, February 1983; Rotterdam, December 1985), without experiencing any difficulties in getting valuable papers: on econometrics of risks and medical insurance, on the measurement of health status and of efficiency of medical techniques, on general models allowing simulation. These were the themes for the second meeting, but other aspects of medical-economic problems had presented themselves already to the analyst: medical decision making and its consequences, the behaviour of the actors - patients and physicians -, regional medicometrics and what not: some of them have been covered by the first meeting. Finally, in July 1988 took place in Lyons the Fourth International Conference on System Science in Health Care; it should not be astonishing ."

hen my husband died in 1973 I had to go through his W papers. Some of them were still in manuscript form and had never before been published. I selected several of these, plus a number of other articles that had appeared in periodicals but were no longer in print. This book is the result. At my request Richard Ebeling wrote an introduction which he has done in great detail. The depth of Ebeling's understanding of my husband's work is certainly apparent in his writing. I am pleased to have the Ludwig von Mises Institute present this volume to the public. Margit von Mises New York City September 1989 vii Introduction I I n the 1920s and the 1930s, Ludwig von Mises was recognized as one of the leading economic theorists on the European Conti nent. I F. A. Hayek has said that Mises's critique of the possibilities for economic calculation under socialism had "the most profound impression on my generation . . . . To none of us '" who read his] book Socialism] when it appeared was the world ever the same again., 2 Lord Lionel Robbins, in introducing the Austrian School literature on money and the trade cycle to English-speaking readers in 1931, emphasized the "marvelous renaissance" the "School of Vienna" had experienced "under the leadership of . . . Professor Mises."

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.

Measuring productive efficiency for nonprofit organizations has posed a great challenge to applied researchers today. The problem has many facets and diverse implications for a number of disciplines such as economics, applied statistics, management science and information theory. This monograph discusses four major areas, which emphasize the applied economic and econometric as. pects of the production frontier analysis: A. Stochastic frontier theory, B. Data envelopment analysis, C. Clustering and estimation theory, D. Economic and managerial applications Besides containing an up-to-date survey of the mos. t recent developments in the field, the monograph presents several new results and theorems from my own research. These include but are not limited to the following: (1) interface with parametric theory, (2) minimax and robust concepts of production frontier, (3) game-theoretic extension of the Farrell and Johansen models, (4) optimal clustering techniques for data envelopment analysis and (5) the dynamic and stochastic generalizations of the efficiency frontier at the micro and macro levels. In my research work in this field I have received great support and inspiration from Professor Abraham Charnes of the University of Texas at Austin, who has basically founded the technique of data envelopment analysis, developed it and is still expanding it. My interactions with him have been most fruitful and productive. I am deeply grateful to him. Finally, I must record my deep appreciation to my wife and two children for their loving and enduring support. But for their support this work would not have been completed.

The book develops the capabilities arising from the cooperation between mathematicians and statisticians working in insurance and finance fields. It gathers some of the papers presented at the conference MAF2010, held in Ravello (Amalfi coast), and successively, after a reviewing process, worked out to this aim.

In the autumn of 1961 Jan Salomon ('Mars') Cramer was appointed to the newly established chair of econometrics at the University of Amsterdam. This volume is published to commemorate this event. It is well-known how much econometrics has developed over the period under consideration, the 25 years that elapsed between 1961 and 1986. This is specifically true for the areas in which Cramer has been actively interested. We mention the theory and measurement of consumer behaviour; money and income; regression, correla tion and forecasting. In the present volume this development will be high lighted. Sixteen contributions have been sollicited from scholars all over the world who have belonged to the circle of academic friends of Cramer for a shorter or longer part of the period of 25 years. The contributions fall broadly speaking into the four areas mentioned above. Theory and measurement of consumer behaviour is represented by four papers, whereas a fifth paper deals with a related area. Richard Blundell and Costas Meghir devote a paper to the estimation of Engel curves. They apply a discrete choice model to British (individual) data from the Family Expenditure Survey 1981. Their aim is to assess the impact of individual characteristics such as income, demographic structure, location, wages and prices on commodity expenditure."

Lawrence Klein, University of Pennsylvania Jaime Marquez, Federal Reserve BoarrI* All examination of the economics literature over the last twenty years reveals a marked tendency towards polarisation. On the one hand, there has been a propensity to develop theoretical models which have little connection with either empirical verification or problems requiring immediate attention. On the other iland, empirical analyses are generally typified by testing for its own sake, with limited examination of the implications of the results. As a result, the number of papers confronting theory with facts towards the solution of economic problems has been on the decline for years. To fill this growing gap in the literature, we have invited a number of authors to write papers using both theoretical and empirical techniques to address current issues of interest to the profession at large: the US trade deficit and the global implications of policies that attempt to reduce it, the international ramifications of the debt crisis, the international oil market and its implications for the US oil industry, and the development of new econometric techniques. In addressing these issues, each author has approached the subject matter from an eclectic standpoint - that is, avoiding strict adherence to a given doctrine.

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."

The econometric consequences of nonstationary data have wide ranging im plications for empirical research in economics. Specifically, these issues have implications for the study of empirical relations such as a money demand func tion that links macroeconomic aggregates: real money balances, real income and a nominal interest rate. Traditional monetary theory predicts that these nonsta tionary series form a cointegrating relation and accordingly, that the dynamics of a vector process comprised of these variables generates distinct patterns. Re cent econometric developments designed to cope with nonstationarities have changed the course of empirical research in the area, but many fundamental challenges, for example the issue of identification, remain. This book represents the efforts undertaken by the authors in recent years in an effort to determine the consequences that nonstationarity has for the study of aggregate money demand relations. We have brought together an empirical methodology that we find useful in conducting empirical research. Some of the work was undertaken during the authors' sabbatical periods and we wish to acknowledge the generous support of Arizona State University and Michigan State University respectively. Professor Hoffman wishes to acknowledge the support of the Fulbright-Hays Foundation that supported sabbattical research in Europe and separate support of the Council of 100 Summer Research Program at Arizona State University."

Statistical Methods in Econometrics is appropriate for beginning graduate courses in mathematical statistics and econometrics in which the foundations of probability and statistical theory are developed for application to econometric methodology. Because econometrics generally requires the study of several unknown parameters, emphasis is placed on estimation and hypothesis testing involving several parameters. Accordingly, special attention is paid to the multivariate normal and the distribution of quadratic forms. Lagrange multiplier tests are discussed in considerable detail, along with the traditional likelihood ration and Wald tests. Characteristic functions and their properties are fully exploited. Also asymptotic distribution theory, usually given only cursory treatment, is discussed in detail.
The book assumes a working knowledge of advanced calculus (including integral calculus) basic probability and statistics, and linear algebra. Important properties from matrix algebra are summarized in the appendix. Numerous examples, exercises, and practice problems are included.
Key Features
* Covers both multivariate analysis and matrix algebra
* Focuses on newer tests of hypotheses such as the Lagrange multiplier test
* Discusses characteristic functions in depth
* Material has evolved during 15 years of classroom instruction