Applied Econometrics Using the SAS System E-Book

Vivek Ajmani

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 407

Veröffentlichungsjahr: 2011

Beschreibung

The first cutting-edge guide to using the SAS® system for the analysis of econometric data Applied Econometrics Using the SAS® System is the first book of its kind to treat the analysis of basic econometric data using SAS®, one of the most commonly used software tools among today's statisticians in business and industry. This book thoroughly examines econometric methods and discusses how data collected in economic studies can easily be analyzed using the SAS® system. In addition to addressing the computational aspects of econometric data analysis, the author provides a statistical foundation by introducing the underlying theory behind each method before delving into the related SAS® routines. The book begins with a basic introduction to econometrics and the relationship between classical regression analysis models and econometric models. Subsequent chapters balance essential concepts with SAS® tools and cover key topics such as: * Regression analysis using Proc IML and Proc Reg * Hypothesis testing * Instrumental variables analysis, with a discussion of measurement errors, the assumptions incorporated into the analysis, and specification tests * Heteroscedasticity, including GLS and FGLS estimation, group-wise heteroscedasticity, and GARCH models * Panel data analysis * Discrete choice models, along with coverage of binary choice models and Poisson regression * Duration analysis models Assuming only a working knowledge of SAS®, this book is a one-stop reference for using the software to analyze econometric data. Additional features include complete SAS® code, Proc IML routines plus a tutorial on Proc IML, and an appendix with additional programs and data sets. Applied Econometrics Using the SAS® System serves as a relevant and valuable reference for practitioners in the fields of business, economics, and finance. In addition, most students of econometrics are taught using GAUSS and STATA, yet SAS® is the standard in the working world; therefore, this book is an ideal supplement for upper-undergraduate and graduate courses in statistics, economics, and other social sciences since it prepares readers for real-world careers.

Leseprobe

CONTENTS

Preface

Acknowledgements

1 Introduction to Regression Analysis

1.1 Introduction

1.2 Matrix Form of the Multiple Regression Model

1.3 Basic Theory of Least Squares

1.4 Analysis of Variance

1.5 The Frisch–Waugh Theorem

1.6 Goodness of Fit

1.7 Hypothesis Testing and Confidence Intervals

1.8 Some Further Notes

2 Regression Analysis Using Proc IML and Proc Reg

2.1 Introduction

2.2 Regression Analysis Using Proc IML

2.3 Analyzing the Data Using Proc Reg

2.4 Extending the Investment Equation Model to the Complete Data Set

2.5 Plotting the Data

2.6 Correlation Between Variables

2.7 Predictions of the Dependent Variable

2.8 Residual Analysis

2.9 Multicollinearity

3 Hypothesis Testing

3.1 Introduction

3.2 Using SAS to Conduct the General Linear Hypothesis

3.3 The Restricted Least Squares Estimator

3.4 Alternative Methods of Testing the General Linear Hypothesis

3.5 Testing for Structural Breaks in Data

3.6 The CUSUM Test

3.7 Models with Dummy Variables

4 Instrumental Variables

4.1 Introduction

4.2 Omitted Variable Bias

4.3 Measurement Errors

4.4 Instrumental Variable Estimation

4.5 Specification Tests

5 Nonspherical Disturbances and Heteroscedasticity

5.1 Introduction

5.2 Nonspherical Disturbances

5.3 Detecting Heteroscedasticity

5.4 Formal Hypothesis Tests to Detect Heteroscedasticity

5.5 Estimation of β Revisited

5.6 Weighted Least Squares and FGLS Estimation

5.7 Autoregressive Conditional Heteroscedasticity

6 Autocorrelation

6.1 Introduction

6.2 Problems Associated with OLS Estimation Under Autocorrelation

6.3 Estimation Under the Assumption of Serial Correlation

6.4 Detecting Autocorrelation

6.5 Using SAS to Fit the AR Models

7 Panel Data Analysis

7.1 What is Panel Data?

7.2 Panel Data Models

7.3 The Pooled Regression Model

7.4 The Fixed Effects Model

7.5 Random Effects Models

8 Systems of Regression Equations

8.1 Introduction

8.2 Estimation Using Generalized Least Squares

8.3 Special Cases of the Seemingly Unrelated Regression Model

8.4 Feasible Generalized Least Squares

9 Simultaneous Equations

9.1 Introduction

9.2 Problems with OLS Estimation

9.3 Structural and Reduced Form Equations

9.4 The Problem of Identification

9.5 Estimation of Simultaneous Equation Models

9.6 Hausman’s Specification Test

10 Discrete Choice Models

10.1 Introduction

10.2 Binary Response Models

10.3 Poisson Regression

11 Duration Analysis

11.1 Introduction

11.2 Failure Times and Censoring

11.3 The Survival and Hazard Functions

11.4 Commonly Used Distribution Functions in Duration Analysis

11.5 Regression Analysis with Duration Data

12 Special Topics

12.1 Iterative FGLS Estimation Under Heteroscedasticity

12.2 Maximum Likelihood Estimation Under Heteroscedasticity

12.3 Harvey’s Multiplicative Heteroscedasticity

12.4 Groupwise Heteroscedasticity

12.5 Hausman–Taylor Estimator for the Random Effects Model

12.6 Robust Estimation of Covariance Matrices in Panel Data

12.7 Dynamic Panel Data Models

12.8 Heterogeneity and Autocorrelation in Panel Data Models

12.9 Autocorrelation in Panel Data

Appendix A Basic Matrix Algebra for Econometrics

A.1 Matrix Definitions

A.2 Matrix Operations

A.3 Basic Laws of Matrix Algebra

A.4 Identity Matrix

A.5 Transpose of a Matrix

A.6 Determinants

A.7 Trace of a Matrix

A.8 Matrix Inverses

A.9 Idempotent Matrices

A.10 Kronecker Products

A.11 Some Common Matrix Notations

A.12 Linear Dependence and Rank

A.13 Differential Calculus in Matrix Algebra

A.14 Solving a System of Linear Equations in Proc IML

Appendix B Basic Matrix Operations in Proc IML

B.1 Assigning Scalars

B.2 Creating Matrices and Vectors

B.3 Elementary Matrix Operations

B.4 Comparison Operators

B.5 Matrix-Generating Functions

B.6 Subset of Matrices

B.7 Subscript Reduction Operators

B.8 The Diag and VecDiag Commands

B.9 Concatenation of Matrices

B.10 Control Statements

B.11 Calculating Summary Statistics in Proc IML

Appendix C Simulating the Large Sample Properties of the OLS Estimators

Appendix D Introduction to Bootstrap Estimation

D.1 Introduction

D.2 Calculating Standard Errors

D.3 Bootstrapping in SAS

D.4 Bootstrapping in Regression Analysis

Appendix E Complete Programs and Proc IML Routines

E.1 Program 1

E.2 Program 2

E.3 Program 3

E.4 Program 4

E.5 Program 5

E.6 Program 6

E.7 Program 7

E.8 Program 8

E.9 Program 9

E.10 Program 10

E.11 Program 11

E.12 Program 12

E.13 Program 13

E.14 Program 14

E.15 Program 15

E.16 Program 16

E.17 Program 17

References

Index

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Library of Congress Cataloging-in-Publication Data:

Ajmani, Vivek B.

Applied econometrics using the SAS system / Vivek B. Ajmani.p. cm.

Includes bibliographical references and index.

ISBN 978-0-470-12949-4 (cloth)

1. Econometrics–Computer programs. 2. SAS (Computer file) I. Title.

HB139.A46 2008

330.0285’555–dc22

2008004315

To My Wife, Preeti, and My Children, Pooja and Rohan

PREFACE

The subject of econometrics involves the application of statistical methods to analyze data collected from economic studies. The goal may be to understand the factors influencing some economic phenomenon of interest, to validate a hypothesis proposed by theory, or to predict the future behavior of the economic phenomenon of interest based on underlying mechanisms or factors influencing it.

Although there are several well-known books that deal with econometric theory, I have found the books by Badi H. Baltagi, Jeffrey M. Wooldridge, Marno Verbeek, and William H. Greene to be very invaluable. These four texts have been heavily referenced in this book with respect to both the theory and the examples they have provided. I have also found the book by Ashenfelter, Levine, and Zimmerman to be invaluable in its ability to simplify some of the complex econometric theory into a form that can easily be understood by undergraduates who may not be well versed in advanced statistical methods involving matrix algebra.

When I embarked on this journey, many questioned me on why I wanted to write this book. After all, most economic departments use either Gauss or STATA to do empirical analysis. I used SAS Proc IML extensively when I took the econometric sequence at the University of Minnesota and personally found SAS to be on par with other packages that were being used. Furthermore, SAS is used extensively in industry to process large data sets, and I have found that economics graduate students entering the workforce go through a steep learning curve because of the lack of exposure to SAS in academia. Finally, after using SAS, Gauss, and STATA for my own personal work and research, I have found that the SAS software is as powerful or flexible compared to both Gauss and STATA.

There are several user-written books on how to use SAS to do statistical analysis. For instance, there are books that deal with regression analysis, logistic regression, survival analysis, mixed models, and so on. However, all these books deal with analyzing data collected from the applied or social sciences, and none deals with analyzing data collected from economic studies. I saw an opportunity to expand the SAS-by-user books library by writing this book.

I have attempted to incorporate some theory to lay the groundwork for the techniques covered in this book. I have found that a good understanding of the underlying theory makes a good data analyst even better. This book should therefore appeal to both students and practitioners, because it tries to balance the theory with the applications. However, this book should not be used as a substitute in place of the well-established texts that are being used in academia. As mentioned above, the theory has been referenced from four main texts: Baltagi (2005), Greene (2003), Verbeek (2004), and Wooldridge (2002).

This book assumes that the reader is somewhat familiar with the SAS software and programming in general. The SAS help manuals from the SAS Institute, Inc. offer detailed explanation and syntax for all the SAS routines that were used in this book. Proc IML is a matrix programming language and is a component of the SAS software system. It is very similar to other matrix programming languages such as GAUSS and can be easily learned by running simple programs as starters. Appendixes A and B offer some basic code to help the inexperienced user get started. All the codes for the various examples used in this book were written in a very simple and direct manner to facilitate easy reading and usage by others. I have also provided detailed annotation with every program. The reader may contact me for electronic versions of the codes used in this book. The data sets used in this text are readily available over the Internet. Professors Greene and Wooldridge both have comprehensive web sites where the data are available for download. However, I have used data sets from other sources as well. The sources are listed with the examples provided in the text. All the data (except the credit card data from Greene (2003)) are in the public domain. The credit card data was used with permission from William H. Greene at New York University.

The reliance on Proc IML may be a bit confusing to some readers. After all, SAS has well-defined routines (Proc Reg, Proc Logistic, Proc Syslin, etc.) that easily perform many of the methods used within the econometric framework. I have found that using a matrix programming language to first program the methods reinforces our understanding of the underlying theory. Once the theory is well understood, there is no need for complex programming unless a well-defined routine does not exist.

It is assumed that the reader will have a good understanding of basic statistics including regression analysis. Chapter 1 gives a good overview of regression analysis and of related topics that are found in both introductory and advance econometric courses. This chapter forms the basis of the analysis progression through the book. That is, the basic OLS assumptions are explained in this chapter. Subsequent chapters deal with cases when these assumptions are violated. Most of the material in this chapter can be found in any statistics text that deals with regression analysis. The material in this chapter was adapted from both Greene (2003) and Meyers (1990).

Chapter 2 introduces regression analysis in SAS. I have provided detailed Proc IML code to analyze data using OLS regression. I have also provided detailed coverage of how to interpret the output resulting from the analysis.The chapter ends with a thorough treatment of multicollinearity. Readers are encouraged to refer to Freund and Littell (2000) for a thorough discussion on regression analysis using the SAS system.

Chapter 3 introduces hypothesis testing under the general linear hypothesis framework. Linear restrictions and the restricted least squares estimator are introduced in this chapter. This chapter then concludes with a section on detecting structural breaks in the data via the Chow and CUSUM tests. Both Greene (2003) and Meyers (1990) offer a thorough treatment of this topic.

Chapter 4 introduces instrumental variables analysis. There is a good amount of discussion on measurement errors, the assumptions that go into the analysis, specification tests, and proxy variables. Wooldridge (2002) offers excellent coverage of instrumental variables analysis.

Chapter 5 deals with the problem of heteroscedasticity. We discuss various ways of detecting whether the data suffer from heteroscedasticity and analyzing the data under heteroscedasticity. Both GLS and FGLS estimations are covered in detail. This chapter ends with a discussion of GARCH models. The material in this chapter was adapted from Greene (2003), Meyers (1990), and Verbeek (2004).

Chapter 6 extends the discussion from Chapter 5 to the case where the data suffer from serial correlation. This chapter offers a good introduction to autocorrelation. Brocklebank and Dickey (2003) is excellent in its treatment of how SAS can be used to analyze data that suffer from serial correlation. On the other hand, Greene (2003), Meyers (1990), and Verbeek (2004) offer a thorough treatment of the theory behind the detection and estimation techniques under the assumption of serial correlation.

Chapter 7 covers basic panel data models. The discussion starts with the inefficient OLS estimation and then moves on to fixed effects and random effects analysis. Baltagi (2005) is an excellent source for understanding the theory underlying panel data analysis while Greene (2003) offers an excellent coverage of the analytical methods and practical applications of panel data.

Seemingly unrelated equations (SUR) and simultaneous equations (SE) are covered in Chapters 8 and 9, respectively. The analysis of data in these chapters uses Proc Syslin and Proc Model, two SAS procedures that are very efficient in analyzing multiple equation models. The material in this chapter makes extensive use of Greene (2003) and Ashenfelter, Levine and Zimmerman (2003).

Chapter 10 deals with discrete choice models. The discussion starts with the Probit and Logit models and then moves on to Poisson regression. Agresti (1990) is the seminal reference for categorical data analysis and was referenced extensively in this chapter.

Chapter 11 is an introduction to duration analysis models. Meeker and Escobar (1998) is a very good reference for reliability analysis and offers a firm foundation for duration analysis techniques. Greene (2003) and Verbeek (2004) also offer a good introduction to this topic while Allison (1995) is an excellent guide on using SAS to analyze survival analysis/duration analysis studies.

Chapter 12 contains special topics in econometric analysis. I have included discussion on groupwise heterogeneity, Harvey’s multiplicative heterogeneity, Hausman–Taylor estimators, and heterogeneity and autocorrelation in panel data.

Appendixes A and B discuss basic matrix algebra and how Proc IML can be used to perform matrix calculations. These two sections offer a good introduction to Proc IML and matrix algebra useful for econometric analysis. Searle (1982) is an outstanding reference for matrix algebra as it applies to the field of statistics.

Appendix C contains a brief discussion of the large sample properties of the OLS estimators. The discussion is based on a simple simulation using SAS.

Appendix D offers an overview of bootstrapping methods including their application to regression analysis. Efron and Tibshirani (1993) offer outstanding discussion on bootstrapping techniques and were heavily referenced in this section of the book.

Appendix E contains the complete code for some key programs used in this book.

St. Paul, MN

VIVEK B. AJMANI

ACKNOWLEDGMENTS

I owe a great debt to Professors Paul Glewwe and Gerard McCullough (both from University of Minnesota) for teaching me everything I know about econometrics. Their instruction and detailed explanations formed the basis for this book. I am also grateful to Professor William Greene (New York University) for allowing me to access data from his text Econometric Analysis, 5th edition, 2003. The text by Greene is widely used to teach introductory graduate level classes in econometrics for the wealth of examples and theoretical foundations it provides. Professor Greene was also kind enough to nudge me in the right direction on a few occasions while I was having difficulties trying to program the many routines that have been used in this book.

I would also like to acknowledge the constant support I received from many friends and colleagues at Ameriprise Financials. In particular, I would like to thank Robert Moore, Ines Langrock, Micheal Wacker, and James Eells for reviewing portions of the book.

I am also grateful to an outside reviewer for critiquing the manuscript and for providing valuable feedback. These comments allowed me to make substantial improvements to the manuscript. Many thanks also go to Susanne Steitz-Filler for being patient with me throughout the completion of this book.

In writing this text, I have made substantial use of resources found on the World Wide Web. In particular, I would like to acknowledge Professors Jeffrey Wooldridge (Michigan State University) and Professor Marno Verbeek (RSM Erasmus University, the Netherlands) for making the data from their texts available on their homepages.

Although most of the SAS codes were created by me, I did make use of two programs from external sources. I would like to thank the SAS Institute for giving me permission to use the % boot macros. I would also like to acknowledge Thomas Fomby (Southern Methodist University) for writing code to perform duration analysis on the Strike data from Kennan (1984).

Finally, I would like to thank my wife, Preeti, for “holding the fort” while I was busy trying to crack some of the codes that were used in this book.

St. Paul, MN

VIVEK B. AJMANI