Developing Econometrics E-Book

Hengqing Tong

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 775

Veröffentlichungsjahr: 2011

Beschreibung

Statistical Theories and Methods with Applications to Economics and Business highlights recent advances in statistical theory and methods that benefit econometric practice. It deals with exploratory data analysis, a prerequisite to statistical modelling and part of data mining. It provides recently developed computational tools useful for data mining, analysing the reasons to do data mining and the best techniques to use in a given situation. * Provides a detailed description of computer algorithms. * Provides recently developed computational tools useful for data mining * Highlights recent advances in statistical theory and methods that benefit econometric practice. * Features examples with real life data. * Accompanying software featuring DASC (Data Analysis and Statistical Computing). Essential reading for practitioners in any area of econometrics; business analysts involved in economics and management; and Graduate students and researchers in economics and statistics.

Leseprobe

Contents

Foreword

Preface

Importance of econometrics for business analytics

How this book came into being

For whom the book is written

Some special features of the book

The organization of the book

Acknowledgements

Chapter 1 Introduction

1.1 Nature and scope of econometrics

1.2 Types of economic problems, types of data, and types of models

1.3 Pattern recognition and exploratory data analysis

1.4 Econometric modeling: The roadmap of this book

Electronic references for Chapter 1

Chapter 2 Independent variables in linear regression models

2.1 Brief review of linear regression

2.2 Selection of independent variable and stepwise regression

2.3 Multivariate data transformation and polynomial regression

2.4 Column multicollinearity in design matrix and ridge regression

2.5 Recombination of independent variable and principal components regression

Electronic references for Chapter 2

Chapter 3 Alternative structures of residual error in linear regression models

3.1 Heteroscedasticity: Consequences and tests for its existence

3.2 Generalized linear model with covariance being a diagonal matrix

3.3 Autocorrelation in a linear model

3.4 Generalized linear model with positive definite covariance matrix

3.5 Random effects and variance component model

Electronic references for Chapter 3

Chapter 4 Discrete variables and nonlinear regression model

4.1 Regression model when independent variables are categorical

4.2 Models with categorical or discrete dependent variables

4.3 Nonlinear regression model and its algorithm

4.4 Nonlinear regression models in practice

Electronic references for Chapter 4

Chapter 5 Nonparametric and semiparametric regression models

5.1 Nonparametric regression and weight function method

5.2 Semiparametric regression model

5.3 Stochastic frontier regression model

Electronic references for Chapter 5

Chapter 6 Simultaneous equations models and distributed lag models

6.1 Simultaneous equations models and inconsistency of OLS estimators

6.2 Statistical inference for simultaneous equations models

6.3 The concepts of lag regression models

6.4 Finite distributed lag models

6.5 Infinite distributed lag models

Electronic references for Chapter 6

Chapter 7 Stationary time series models

7.1 Auto-regression model AR(p)

7.2 Moving average model MA(q)

7.3 Auto-regressive moving-average process ARMA(p, q)

Electronic references for Chapter 7

Chapter 8 Multivariate and nonstationary time series models

8.1 Multivariate stationary time series model

8.2 Nonstationary time series

8.3 Cointegration and error correction

8.4 Autoregression conditional heteroscedasticity in time series

8.5 Mixed models of multivariate regression with time series

Electronic references for Chapter 8

Chapter 9 Multivariate statistical analysis and data analysis

9.1 Model of analysis of variance

9.2 Other multivariate statistical analysis models

9.3 Customer satisfaction model and path analysis

9.4 Data analysis and process

Electronic references for Chapter 9

Chapter 10 Summary and further discussion

10.1 About probability distributions: Parametric and non-parametric

10.2 Regression

10.3 Model specification and prior information

10.4 Classical theory of statistical inference

10.5 Computation of maximum likelihood estimates

10.6 Specification searches

10.7 Resampling and sampling distributions – the bootstraps method

10.8 Bayesian inference

Electronic references for Chapter 10

Index

This edition first published 2011© 2011 John Wiley & Sons, Ltd

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Library of Congress Cataloging-in-Publication Data

Tong, Hengqing, 1971–Developing econometrics / Hengqing Tong, T. Krishna Kumar, Yangxin Huang.p. cm.Includes bibliographical references and index.

ISBN 978-0-470-68177-0 (cloth) – ISBN 978-1-119-96090-41. Econometrics. 2. Econometric models. 3. Data mining. I. Kumar, T. Krishna. II. Huang, Yang Xin. III. Title.HB139.T66 2011330.01′5195–dc23

2011024956

A catalogue record for this book is available from the British Library.

Print ISBN: 978-0-470-68177-0ePDF ISBN: 978-1-119-95424-8oBook ISBN: 978-1-119-95423-1ePub ISBN: 978-1-119-96090-4Mobi ISBN: 978-1-119-96091-1

Foreword

Econometrics was defined by the Econometric Society as a science devoted to the advancement of economic theory in relation to mathematics and statistics. With mathematical statistics as theoretical basis, and with the regression model as basic framework, econometrics provides a quantitative description of economic phenomenon by describing the internal relationships among economic data. It is also used to predict or forecast the economic scene under alternate hypothetical scenarios in order to aid us in designing economic policies. Econometrics is the better half, and the scientific half, of economics. It is a science like other sciences such as physics and chemistry, a Nobel Prize in economics has been awarded since 1969, and most of the works of the awardees happened to be in econometrics.

More recently, using new data mining tools, econometrics enabled companies to squeeze the last bit of knowledge from information to gain a competitive advantage over other companies competing with them. So far, many of the econometrics books in the English language at advanced undergraduate and graduate levels have been aimed at the graduate students and researchers of the western countries. The competition for the knowledge industry is throwing up vast opportunities for econometrics in the academic and business worlds of the emerging Asian countries. Only some of the successful books have been brought out as Asian editions with Asian co-authors who tend to be teachers and not researchers. At present, the teaching and research level on econometrics in countries like China, India, Singapore, and South Korea has improved significantly, and a number of high-level econometrics research works come from this part of the world. There is some time lag in adapting the latest developments in statistical theories and methods into econometrics. Brazil, Russia, India, and China (BRIC Countries) are emerging as the new growth centers. There is therefore a need to have a different kind of book that not only bridges the gap between recent statistical theories and methods and econometrics but also provides examples from problems arising in these emerging economies.

The contents and quality of this book are comparable approximately to some classical econometrics books that are currently available. With particular emphasis on mathematical analysis of econometric models, and a focus on robust modeling and Bayesian methods, this book covers advanced developments to an extent that they are relevant to econometrics.

The book draws heavily from the teaching and research experience of all the authors in China, India, and the United States. In particular it draws from the extensive teaching, research, and consultancy experience of some of the authors in India and China. It is commendable that almost all of the statistical theories and methods discussed in the book are illustrated through computer software prepared by the principal author. This book is a much revised and updated version of a similar book written by some of these authors in the Chinese language that was well received in China. I hope the book will be well received and found useful by graduate students, researchers, and teachers not only in the Asian countries but also in the advanced industrialized countries of the west. I congratulate the authors and the publisher for the timely introduction of this kind of book.

As a person who founded the Indian Econometric movement in India in 1960, and who made contributions to statistical science expounded in this book it gives me immense pleasure to write the foreword for this book.

C. R. Rao

(Calyampudi Radhakrishna Rao)

October 2011

Preface

The economies of the world are developing, and so are the theories and methods of econometrics. This book, called Developing Econometrics, written by authors coming from the developing countries, makes a sincere effort to reflect these developments.

In recent years countries have been grouped differently and are being given different names, as new industrialized economies, emerging economies and BRIC (Brazil, Russia, India, and China). They are creating a competitive spirit amongst themselves and are trading with the advanced industrialized countries. With increasing globalization and trade, increasing world competition, and increasing availability of large volumes of data, the need is being felt more and more to unlock the mysteries of uncertainty hidden in the chest of statistical tools and data.

Besides, there is a new emerging econometrics that is called by different names, business analytics being the most popular. In this book we attempt to realign econometrics with business analytic needs, and with recent trends in statistical theories and methods. The practitioner applying econometrics to business and public policy will thus, we hope, be equipped with the best possible tools for the pattern-recognition and predictions required for policy intervention so as to make our world a better place to live in.

Importance of econometrics for business analytics

‘Uncertain knowledge plus knowledge of the amount of uncertainty equals usable knowledge’ observed C.R. Rao. All decision makers in scientific investigations, business and public policy search continuously for better and better usable knowledge. Rajeeva Karandikar, the Director of the Chennai Mathematics Institute, advised graduate students of statistics in Bangalore to learn economics not only to apply statistics to economic problems but also to enrich statistics through the development of new statistical tools designed to address economic issues. Nothing can give a better fillip to developing cutting-edge statistical theories and methods than the need to use them for competitive advantage in a globally competitive business world. In recent years, and under recessionary conditions, businesses the world over have been looking for new ways of reducing costs and increasing revenues in the face of uncertainty. One such way is to squeeze as much useful information (usable knowledge) as possible from the volumes of data on consumer preferences and consumer complaints on product quality, production, sales, as well as operations data from various companies over time.

How this book came into being

There are several econometric textbooks that deal mostly with econometrics as statistical methods applied to the domain of economics. Most of these books covered the subject quite well both in depth and breadth. Courses on econometrics in business schools mostly use some of these textbooks written primarily for graduate students in economics departments. There are a few exceptions. Most of these texts are written by authors who teach and do research in the western industrialized countries. With globalization and the growth of the emerging economies western countries as well as emerging economies have felt a need to have some business applications from these emerging economies, preferably from those who had taught and done research in those countries. It is in this context that one of us, Tong, felt that he should write an English language textbook on econometrics, building upon his successful Chinese textbook on econometrics. Huang, co-author of Tong’s Chinese language book, who teaches in the United States, agreed to join him in this new venture. Their proposal went before James Murphy of Wiley. On the basis of a preliminary review Murphy realized that most of the examples were drawn from China and a few from the US, but another major emerging economy, India, had been left out. He felt it desirable to have some examples from India, and to have a broader perspective. He thus felt it desirable to involve an Indian author who had been teaching econometrics to business students in India. This is how Kumar was asked to join the team.

For whom the book is written

The book is ideally suited as a graduate text to a course in a business school on econometrics or business analytics. It can serve as a textbook on econometrics for graduate students in the economics department of a typical school of arts and sciences. It can also serve as a reference book for mathematicians and statisticians who look for financially lucrative opportunities in the business world in the area of business analytics. Teachers, students, and researchers in the emerging economies such as the BRIC countries (Brazil, Russia, India, and China) may find the book a welcome addition to the existing textbooks. Teachers, students, and researchers in the western countries will also find it useful. The book presents a unified approach to statistical modeling in economics and business. This unified approach treats data as sample information, with the truth behind the data being known only partially. Such a perspective makes it necessary to specify a probability distribution for the observed data. Inferences regarding that distribution can be drawn either using the classical approach or the Bayesian approach, or as the authors prefer an eclectic approach. The classical approach presumes the existence of a prior knowledge that is deterministic while the Bayesian approach assumes the prior knowledge to be stochastic. If you are a teacher and want to have a text that incorporates Bayesian econometrics and nonparametric inference you will find this book useful.

Various recent developments in statistical theories and methods, such as nonparametric and semi-parametric methods, are more general versions of specifying the underlying probability distribution of the observed data than the purely parametric specification. This unified treatment brings home the importance of entertaining alternate specifications of the econometric models and of choosing the best among them for squeezing the most information from the observed data. If you are a teacher who is interested in teaching econometrics with a business perspective so that the students have a ready use, soon after their graduation, for the skills developed in the course, you will find this book useful.

Some special features of the book

There is a tendency among many econometrics teachers and students to treat econometrics as an already developed statistical tool that can be applied to economics and business, and hence emphasize which statistical tool should be used in a given specific situation. From the same perspective the standard statistical computing software required to practice econometrics is almost always imported from outside. In this book we make a sincere attempt to integrate economic problems with mathematical and statistical modeling and developing computer software. In this process we hope we have been able to help the reader to modify, and even build new models, methods and computer software to solve a variety of new problems that cannot be adequately solved employing present day methods. Such an approach is needed in order to arrive at better and better models if business analytics is to succeed in a competitive world. This is why this book can be of immense use to consultants in business analytics.

The book comes with computer software called Data Analysis and Statistical Computing (DASC). The architecture of DASC is different from other statistical software. It is simple to learn and to use. There is an illustrative example and an illustrative data set for each menu function in DASC. It is made user-friendly with menus that help accomplish various statistical computations needed for statistical inference/decision making. Some of the specialized topics are delegated to Electronic References that are available on the website created for the readers of this book. Each chapter is preceded by a chapter summary that presents a brief preview of what one can find in that chapter. As a ready reference, at the end of each chapter, there is a list of contents of the Electronic References that are pertinent to that chapter.

Software DASC and the Electronic References can be downloaded from websitehttp://public.whut.edu.cn/slx/English/Login1.htm

The organization of the book

Keeping in mind the economic and business as the domain of the application of statistics, Chapter 1 gives a broad overview of the types of problems one might encounter, and the types of data that each such problem context will throw up.

The linear regression model is the work horse of econometrics. Which variables are to be used in standard linear multiple regressions and in what functional forms are discussed in Chapter 2. Normally if the model is properly chosen one would expect the errors to have a Normal distribution with constant variance. In general when the model is specified a priori it may happen that the conditional variance will be non-constant. How to handle that situation is the topic of Chapter 3. What are normally termed as a dummy variable or limited dependent variable models are termed discrete or categorical variable models in this book. This is because that is how the variables appear in econometric models. These models are discussed in Chapter 4. In econometrics some situations call for models that are nonlinear in parameters. These are also discussed in Chapter 4. A general specification of the conditional distribution and conditional mean may lead one to specify the econometric models as non-parametric or semi-parametric models. This topic engages us in Chapter 5.

Economic models can be classified into three major segments, partial equilibrium models, general equilibrium models, and disequilibrium models. Formulating an economic problem in any of these forms requires econometric models that involve a system of regression equations, one each for each simultaneously determined endogenous economic variable. Disequilibrium models deal with adjustment towards the equilibrium. These adjustment mechanisms, such as adaptive expectations and partial adjustment involve formulation of models with distributed lags. Chapter 6 deals with simultaneous equation models and models with distributed lags.

As explained in Chapter 1 the econometric models we build depend on the form in which the data come to us. Most economic data, and especially high frequency financial data, come to us in the form of time series. Chapter 7 covers univariate stationary time series models. Chapter 8 deals with both non-stationary time series and multivariate time series (to capture the general equilibrium approach to economic modeling). In Chapter 9 we cover a variety of topics, such as the General Linear Model with error distributions belonging to non-Normal distributions, robust regression, multivariate analysis, analysis of variance, causal modeling and path analysis, etc.

The conditional probability distribution of a dependent variable, conditional on the assigned values of the independent variables, can be characterized by its moments. It is for this reason that one normally focuses attention in econometrics on the conditional mean of that distribution as a single parametric multiple regression model. With the business analytic perspective in mind there is a need to have in our tool kit a variety of models, Bayesian, non-Bayesian, parametric and non-parametric, etc., so as to allow for the possibility that the pattern in data is in a flexible form to fit the data better than a single parametric model. Chapter 10 provides this integrated view of all the material covered in the book.

It is the prerogative of an instructor to structure a course as he or she wishes and hence we do not intend to suggest how these chapters can be structured to suit different types of courses.

Hengqing Tong

(Department of Mathematics, Wuhan University of Technology, China)

T. Krishna Kumar

(Samkhya Analytica India Pvt Ltd., Bangalore, and Adjunct Professor, Indian Institute of Management, Bangalore, India)

Yangxin Huang

(Department of Epidemiology and Biostatistics at the University of South Florida, USA)

August 20, 2011

Acknowledgements

Many people contributed to this work. We are most indebted to the major original contributors to statistical science and economic theory who inspired us. We are indebted to our teachers. We thank Professor C.R. Rao, a living legend in statistics, for agreeing to see various chapter outlines and a few sample chapters and write a Foreword for the book. We thank B.L.S. Prakasa Rao for going through the first draft of Chapter 10 and offering his comments and suggestions for improvement. We thank our students who helped us in checking the mathematical derivations and numerical statistical computations. Special mention may be made here of Kumar’s doctoral students of Indian Institute of Management, Bangalore, Jayarama Holla and Puja Guha, of Tong’s doctoral and postgraduate students of Wuhan University of Technology, Yuan Wan, Yang Ye, Yichao Pan, Fangmei Wang, Yan Gong, Yingbi Zhang, Yajie Cheng, Shudan Lu, Wei Wan, Wenjuan Wang and Li Guo, and of Huang’s student and associate of University of South Florida, Ralph Carpenter and Ren Chen. Special thanks are due to Dr Qiaoling Tong, Dr Tianzhen Liu, Dr Qiaohui Tong, Dr Xing Xie and Sha Wang for programing the DASC software. Kumar thanks Nirmala for her help during the last stage of proof reading the galley proofs. Kumar thanks Ramarao Annavarapu for his valuable comments on the drafts of various parts of the manuscript written by him. Kumar’s contribution is based on the graduate course in econometrics taught by him for several years at Indian Institute of Management as an Adjunct Professor. He thanks various batches of students who provided excellent feedback on what is relevant and what is not. He thanks Indian Institute of Management for providing him the necessary infrastructure. Kumar also thanks Cranes Software International Limited for supplying him with SYSTAT 12 free of cost to check the calculations used in our illustrative examples using our own DASC software.

We thank the editorial support and encouragement provided to us by editors James Murphy, Richard Davies, and Susan Barclay, along with other editorial staff working in the Statistics division of Wiley, Kathryn Sharples, Ilaria Meliconi and Heather Kay. Special thanks are due to James Murphy for bringing together the authors, Tong and Kumar, from two different countries who had not known each other. Ilaria Meliconi and Kathryn Sharples deserve thanks for bearing the pressures from the authors and the difficulties in getting the technical reviews of the manuscript as quickly as the authors wanted it. Our sincere thanks go to Richard Davies who managed so efficiently the tight time schedule and technical processing of the manuscript for printing. The final stages of print-setting and print-layout are quite crucial in the making of a book. The authors thank Prachi Sinha Sahay and Britto Fleming Joe for an excellent and speedy job of print-setting and publishing.

We thank our wives – Pingxi Cai (Tong), Usha (Kumar), and Liuyan Yan (Huang) for bearing with our preoccupation with our work on the manuscript, subtracting time from the family. No words are adequate to express Kumar’s gratitude to his wife Usha for the encouragement she gave him to go ahead with the writing for this book. Usha’s encouragement is our source of strength for the success of this book.

Kumar thanks the Department of Information and Decision Sciences, College of Business Administration, University of Illinois, Chicago for availing him of its library facilities as a Visiting Scholar. This facility became critically important as Kumar moved to Chicago during the final phases of preparing the manuscript.

The research work of Tong reported in this book was supported by the National Natural Science Foundation of China (30570611, 60773210).