Interpreting ramsey reset test eviews

Table B-1 Critical Values of the t-Distribution

Level of Significance

Degrees of Freedom

One-Sided: 10% Two-Sided: 20%

5% 10%

2.5% 5%

1% 2%

0.5% 1%

1 3.078 6.314 12.706 31.821 63.657 2 1.886 2.920 4.303 6.965 9.925 3 1.638 2.353 3.182 4.541 5.841 4 1.533 2.132 2.776 3.747 4.604 5 1.476 2.015 2.571 3.365 4.032 6 1.440 1.943 2.447 3.143 3.707 7 1.415 1.895 2.365 2.998 3.499 8 1.397 1.860 2.306 2.896 3.355 9 1.383 1.833 2.262 2.821 3.250 10 1.372 1.812 2.228 2.764 3.169 11 1.363 1.796 2.201 2.718 3.106 12 1.356 1.782 2.179 2.681 3.055 13 1.350 1.771 2.160 2.650 3.012 14 1.345 1.761 2.145 2.624 2.977 15 1.341 1.753 2.131 2.602 2.947 16 1.337 1.746 2.120 2.583 2.921 17 1.333 1.740 2.110 2.567 2.898 18 1.330 1.734 2.101 2.552 2.878 19 1.328 1.729 2.093 2.539 2.861 20 1.325 1.725 2.086 2.528 2.845 21 1.323 1.721 2.080 2.518 2.831 22 1.321 1.717 2.074 2.508 2.819 23 1.319 1.714 2.069 2.500 2.807 24 1.318 1.711 2.064 2.492 2.797 25 1.316 1.708 2.060 2.485 2.787 26 1.315 1.706 2.056 2.479 2.779 27 1.314 1.703 2.052 2.473 2.771 28 1.313 1.701 2.048 2.467 2.763 29 1.311 1.699 2.045 2.462 2.756 30 1.310 1.697 2.042 2.457 2.750 40 1.303 1.684 2.021 2.423 2.704 60 1.296 1.671 2.000 2.390 2.660 120 1.289 1.658 1.980 2.358 2.617

(Normal) ∞ 1.282 1.645 1.960 2.326 2.576

Source: Reprinted from Table IV in Sir Ronald A. Fisher, Statistical Methods for Research Workers, 14th ed. (copyright © 1970, University of Adelaide) with permission of Hafner, a division of the Macmillan Publishing Company, Inc.

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USING ECONOMETRICS

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S E V E N T H E D I T I O N

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USING ECONOMETRICS A P R A C T I C A L G U I D E

A. H. Studenmund Occidental College

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Bruce K. Johnson Centre College

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CONTENTS

Preface xiii

Chapter 1 An Overview of Regression Analysis 1 1.1 What Is Econometrics? 1 1.2 What Is Regression Analysis? 5 1.3 The Estimated Regression Equation 14 1.4 A Simple Example of Regression Analysis 17 1.5 Using Regression Analysis to Explain Housing Prices 20 1.6 Summary and Exercises 23 1.7 Appendix: Using Stata 30

Chapter 2 Ordinary Least Squares 35 2.1 Estimating Single-Independent-Variable

Models with OLS 35 2.2 Estimating Multivariate Regression Models with OLS 40 2.3 Evaluating the Quality of a Regression Equation 49 2.4 Describing the Overall Fit of the Estimated Model 50 2.5 An Example of the Misuse of R 2 55 2.6 Summary and Exercises 57 2.7 Appendix: Econometric Lab #1 63

Chapter 3 Learning to Use Regression Analysis 65 3.1 Steps in Applied Regression Analysis 66 3.2 Using Regression Analysis to Pick Restaurant Locations 73 3.3 Dummy Variables 79 3.4 Summary and Exercises 83 3.5 Appendix: Econometric Lab #2 89

Chapter 4 The Classical Model 92 4.1 The Classical Assumptions 92 4.2 The Sampling Distribution of βn 100 4.3 The Gauss–Markov Theorem and the Properties

of OLS Estimators 106 4.4 Standard Econometric Notation 107 4.5 Summary and Exercises 108

ix

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x CONTENTS

Chapter 5 Hypothesis Testing and Statistical Inference 115 5.1 What Is Hypothesis Testing? 116 5.2 The t-Test 121 5.3 Examples of t-Tests 129 5.4 Limitations of the t-Test 137 5.5 Confidence Intervals 139 5.6 The F-Test 142 5.7 Summary and Exercises 147 5.8 Appendix: Econometric Lab #3 155

Chapter 6 Specification: Choosing the Independent Variables 157

6.1 Omitted Variables 158 6.2 Irrelevant Variables 165 6.3 An Illustration of the Misuse of Specification Criteria 167 6.4 Specification Searches 169 6.5 An Example of Choosing Independent Variables 174 6.6 Summary and Exercises 177 6.7 Appendix: Additional Specification Criteria 184

Chapter 7 Specification: Choosing a Functional Form 189 7.1 The Use and Interpretation of the Constant Term 190 7.2 Alternative Functional Forms 192 7.3 Lagged Independent Variables 202 7.4 Slope Dummy Variables 203 7.5 Problems with Incorrect Functional Forms 206 7.6 Summary and Exercises 209 7.7 Appendix: Econometric Lab #4 217

Chapter 8 Multicollinearity 221 8.1 Perfect versus Imperfect Multicollinearity 222 8.2 The Consequences of Multicollinearity 226 8.3 The Detection of Multicollinearity 232 8.4 Remedies for Multicollinearity 235 8.5 An Example of Why Multicollinearity Often Is Best Left

Unadjusted 238 8.6 Summary and Exercises 240 8.7 Appendix: The SAT Interactive Regression

Learning Exercise 244

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xiCONTENTS

Chapter 9 Serial Correlation 273 9.1 Time Series 274 9.2 Pure versus Impure Serial Correlation 275 9.3 The Consequences of Serial Correlation 281 9.4 The Detection of Serial Correlation 284 9.5 Remedies for Serial Correlation 291 9.6 Summary and Exercises 296 9.7 Appendix: Econometric Lab #5 303

Chapter 10 Heteroskedasticity 306 10.1 Pure versus Impure Heteroskedasticity 307 10.2 The Consequences of Heteroskedasticity 312 10.3 Testing for Heteroskedasticity 314 10.4 Remedies for Heteroskedasticity 320 10.5 A More Complete Example 324 10.6 Summary and Exercises 330 10.7 Appendix: Econometric Lab #6 337

Chapter 11 Running Your Own Regression Project 340 11.1 Choosing Your Topic 341 11.2 Collecting Your Data 342 11.3 Advanced Data Sources 346 11.4 Practical Advice for Your Project 348 11.5 Writing Your Research Report 352 11.6 A Regression User’s Checklist and Guide 353 11.7 Summary 357 11.8 Appendix: The Housing Price Interactive Exercise 358

Chapter 12 Time-Series Models 364 12.1 Distributed Lag Models 365 12.2 Dynamic Models 367 12.3 Serial Correlation and Dynamic Models 371 12.4 Granger Causality 374 12.5 Spurious Correlation and Nonstationarity 376 12.6 Summary and Exercises 385

Chapter 13 Dummy Dependent Variable Techniques 390 13.1 The Linear Probability Model 390 13.2 The Binomial Logit Model 397 13.3 Other Dummy Dependent Variable Techniques 404 13.4 Summary and Exercises 406

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xii CONTENTS

Chapter 14 Simultaneous Equations 411 14.1 Structural and Reduced-Form Equations 412 14.2 The Bias of Ordinary Least Squares 418 14.3 Two-Stage Least Squares (2SLS) 421 14.4 The Identification Problem 430 14.5 Summary and Exercises 435 14.6 Appendix: Errors in the Variables 440

Chapter 15 Forecasting 443 15.1 What Is Forecasting? 444 15.2 More Complex Forecasting Problems 449 15.3 ARIMA Models 456 15.4 Summary and Exercises 459

Chapter 16 Experimental and Panel Data 465 16.1 Experimental Methods in Economics 466 16.2 Panel Data 473 16.3 Fixed versus Random Effects 483 16.4 Summary and Exercises 484

Appendix A Answers 491

Appendix B Statistical Tables 517

Index 531

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PREFACE

Econometric education is a lot like learning to fly a plane; you learn more from actually doing it than you learn from reading about it.

Using Econometrics represents an innovative approach to the understand- ing of elementary econometrics. It covers the topic of single-equation lin- ear regression analysis in an easily understandable format that emphasizes real-world examples and exercises. As the subtitle A Practical Guide implies, the book is aimed not only at beginning econometrics students but also at regression users looking for a refresher and at experienced practitioners who want a convenient reference.

What’s New in the Seventh Edition?

Using Econometrics has been praised as “one of the most important new texts of the last 30 years,” so we’ve retained the clarity and practicality of previous editions. However, we’re delighted to have made a number of substantial improvements in the text.

The most exciting upgrades are:

1. Econometric Labs: These new and innovative learning tools are optional appendices that give students hands-on opportunities to bet- ter understand the econometric principles that they’re reading about in the chapters. The labs originally were designed to be assigned in a classroom setting, but they also have turned out to be extremely valu- able for readers who are not in a class or for individual students in classes where the labs aren’t assigned. Hints on how best to use these econometric labs and answers to the lab questions are available in the instructor’s manual on the Using Econometrics Web site.

2. The Use of Stata throughout the Text: In our opinion, Stata has become the econometric software package of choice among economic researchers. As a result, we have estimated all the text examples and exercises with Stata and have included a short appendix to help stu- dents get started with Stata. Beyond this, we have added a complete guide to Using Stata to our Web site. This guide, written by John Perry of Centre College, explains in detail all the Stata commands needed to replicate the text’s equations and answer the text’s exercises. However, even though we use Stata extensively, Using Econometrics is not tied to

xiii

A01_STUD2742_07_SE_FM.indd 13 08/02/16 3:01 PM

Stata or any other econometric software, so the text works well with all standard regression packages.

3. Expanded Econometric Content: We have added coverage of a number of econometric tests and procedures, for example the Breusch-Pagan test and the Prais–Winsten approach to Generalized Least Squares. In addition, we have expanded the coverage of even more topics, for example the F-test, confidence intervals, the Lagrange Multiplier test, and the Dickey–Fuller test. Finally, we have simplified the notation and improved the clarity of the explanations in Chapters 12–16, particu- larly in topics like dynamic equations, dummy dependent variables, instrumental variables, and panel data.

4. Answers to Many More Exercises: In response to requests from instruc- tors and students, we have more than tripled the number of exercises that are answered in the text’s appendix. These answers will allow stu- dents to learn on their own, because students will be able to attempt an exercise and then check their answers against those in the back of the book without having to involve their professors. In order to continue to provide good exercises for professors to include in problem sets and exams, we have expanded the number of exercises contained in the text’s Web site.

5. Dramatically Improved PowerPoint Slides: We recognize the impor- tance of PowerPoint slides to instructors with large classes, so we have dramatically improved the quality of the text’s PowerPoints. The slides replicate each chapter’s main equations and examples, and also pro- vide chapter summaries and lists of the key concepts in each chapter. The PowerPoint slides can be downloaded from the text’s Web site, and they’re designed to be easily edited and individualized.

6. An Expanded and Improved Web Site: We believe that this edition’s Web site is the best we’ve produced. As you’d expect, the Web site includes all the text’s data sets, in easily downloadable Stata, EViews, Excel, and ASCII formats, but we have gone far beyond that. We have added Using Stata, a complete guide to the Stata commands needed to estimate the book’s equations; we have dramatically improved the PowerPoint slides; and we have added answers to the new economet- ric labs and instructions on how best to use these labs in a classroom setting. In addition, the Web site also includes an instructor’s manual, additional exercises, extra interactive regression learning exercises, and additional data sets. But why take our word for it? Take a look for your- self at http://www.pearsonhighered.com/studenmund

xiv PREFACE

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http://www.pearsonhighered.com/studenmund
Features

1. Our approach to the learning of econometrics is simple, intuitive, and easy to understand. We do not use matrix algebra, and we relegate proofs and calculus to the footnotes or exercises.

2. We include numerous examples and example-based exercises. We feel that the best way to get a solid grasp of applied econometrics is through an example-oriented approach.

3. Although most of this book is at a simpler level than other economet- rics texts, Chapters 6 and 7 on specification choice are among the most complete in the field. We think that an understanding of specification issues is vital for regression users.

4. We use a unique kind of learning tool called an interactive regression learning exercise to help students simulate econometric analysis by giving them feedback on various kinds of decisions without relying on computer time or much instructor supervision.

5. We’re delighted to introduce a new innovative learning tool called an econometric lab. These econometric labs, developed by Bruce Johnson of Centre College and tested successfully at two other institutions, are optional appendices aimed at giving students hands-on experi- ence with the econometric procedures they’re reading about. Students who complete these econometric labs will be much better prepared to undertake econometric research on their own.

The formal prerequisites for using this book are few. Readers are assumed to have been exposed to some microeconomic and macroeconomic theory, basic mathematical functions, and elementary statistics (even if they have forgotten most if it). Students with little statistical background are encour- aged to begin their study of econometrics by reading Chapter 17, “Statistical Principles,” on the text’s Web site.

Because the prerequisites are few and the statistics material is self-contained, Using Econometrics can be used not only in undergraduate courses but also in MBA-level courses in quantitative methods. We also have been told that the book is a helpful supplement for graduate-level econometrics courses.

The Stata and EViews Options

We’re delighted to be able to offer our readers the chance to purchase the student version of Stata or EViews at discounted prices when bundled with the textbook. Stata and EViews are two of the best econometric software

xvPREFACE

A01_STUD2742_07_SE_FM.indd 15 08/02/16 3:01 PM

programs available, so it’s a real advantage to be able to buy them at sub- stantial savings.

We urge professors to make these options available to their students even if Stata or EViews aren’t used in class. The advantages to students of owning their own regression software are many. They can run regressions when they’re off-campus, they will add a marketable skill to their résumé if they learn Stata or EViews, and they’ll own a software package that will allow them to run regressions after the class is over if they choose the EViews option.

Acknowledgments

This edition of Using Econometrics has been blessed by superb contribu- tions from Ron Michener of the University of Virginia and Bruce Johnson of Centre College. Ron was the lead reviewer, and in that role he commented on every section and virtually every equation in the book, creating a 132-page magnum opus of textbook reviewing that may never be surpassed in length or quality.

Just as importantly, Ron introduced us to Bruce Johnson. Bruce wrote the first drafts of the econometric labs and three other sections, made insight- ful comments on the entire revision, helped increase the role of Stata in the book, and proofread the manuscript. Because of Bruce’s professional exper- tise, clear writing style, and infectious enthusiasm for econometrics, we’re happy to announce that he will be a coauthor of the 8th and subsequent edi- tions of Using Econometrics.

This book’s spiritual parents were Henry Cassidy and Carolyn Summers. Henry co-authored the first edition of Using Econometrics as an expansion of his own work of the same name, and Carolyn was the text’s editorial con- sultant, proofreader, and indexer for four straight editions. Other important professional contributors to previous editions were the late Peter Kennedy, Nobel Prize winner Rob Engle of New York University, Gary Smith of Pomona College, Doug Steigerwald of the University of California at Santa Barbara, and Susan Averett of Lafayette College.

In addition, this edition benefitted from the evaluations of a talented group of professional reviewers:

Lesley Chiou, Occidental College Dylan Conger, George Washington University Leila Farivar, Ohio State University Abbass Grammy, California State University, Bakersfield

xvi PREFACE

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Jason Hecht, Ramapo College Jin Man Lee, University of Illinois at Chicago Noelwah Netusl, Reed College Robert Parks, Washington University in St. Louis David Phillips, Hope College John Perry, Centre College Robert Shapiro, Columbia University Phanindra Wunnava, Middlebury College

Invaluable in the editorial and production process were Jean Berming- ham, Neeraj Bhalla, Adrienne D’Ambrosio, Marguerite Dessornes, Christina Masturzo, Liz Napolitano, Bill Rising, and Kathy Smith. Providing crucial emotional support during an extremely difficult time were Sarah Newhall, Barbara Passerelle, Barbara and David Studenmund, and my immediate family, Jaynie and Connell Studenmund and Brent Morse. Finally, I’d like to thank my wonderful Occidental College colleagues and students for their feedback and encouragement. These particularly included Lesley Chiou, Jack Gephart, Jorge Gonzalez, Andy Jalil, Kate Johnstone, Mary Lopez, Jessica May, Cole Moniz, Robby Moore, Kyle Yee, and, especially, Koby Deitz.

A. H. Studenmund

xviiPREFACE

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1

1.1 What Is Econometrics?

1.2 What Is Regression Analysis?

1.3 The Estimated Regression Equation

1.4 A Simple Example of Regression Analysis

1.5 Using Regression to Explain Housing Prices

1.6 Summary and Exercises

1.7 Appendix: Using Stata

An Overview of Regression Analysis

1.1 What Is Econometrics?

“ Econometrics is too mathematical; it’s the reason my best friend isn’t majoring in economics.”

“ There are two things you are better off not watching in the making: sausages and econometric estimates.”1

“ Econometrics may be defined as the quantitative analysis of actual economic phenomena.”2

“ It’s my experience that ‘economy-tricks’ is usually nothing more than a justification of what the author believed before the research was begun.”

Obviously, econometrics means different things to different people. To beginning students, it may seem as if econometrics is an overly complex obstacle to an otherwise useful education. To skeptical observers, econometric

Chapter 1

1. Ed Leamer, “Let’s take the Con out of Econometrics,” American Economic Review, Vol. 73, No. 1, p. 37.

2. Paul A. Samuelson, T. C. Koopmans, and J. R. Stone, “Report of the Evaluative Committee for Econometrica,” Econometrica, 1954, p. 141.

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2 CHAPTER 1 AN OVERVIEW OF REGRESSION ANALYSIS

results should be trusted only when the steps that produced those results are completely known. To professionals in the field, econometrics is a fascinat- ing set of techniques that allows the measurement and analysis of economic phenomena and the prediction of future economic trends.

You’re probably thinking that such diverse points of view sound like the statements of blind people trying to describe an elephant based on which part they happen to be touching, and you’re partially right. Econometrics has both a formal definition and a larger context. Although you can easily memorize the formal definition, you’ll get the complete picture only by understanding the many uses of and alternative approaches to econometrics.

That said, we need a formal definition. Econometrics—literally, “economic measurement”—is the quantitative measurement and analysis of actual economic and business phenomena. It attempts to quantify economic reality and bridge the gap between the abstract world of economic theory and the real world of human activity. To many students, these worlds may seem far apart. On the one hand, economists theorize equilibrium prices based on carefully conceived marginal costs and marginal revenues; on the other, many firms seem to operate as though they have never heard of such concepts. Econometrics allows us to examine data and to quantify the actions of firms, consumers, and governments. Such measurements have a number of different uses, and an examination of these uses is the first step to understanding econometrics.

Uses of Econometrics

Econometrics has three major uses:

1. describing economic reality

2. testing hypotheses about economic theory and policy

3. forecasting future economic activity

The simplest use of econometrics is description. We can use econometrics to quantify economic activity and measure marginal effects because econo- metrics allows us to estimate numbers and put them in equations that previ- ously contained only abstract symbols. For example, consumer demand for a particular product often can be thought of as a relationship between the quantity demanded 1Q2 and the product’s price 1P2, the price of a substitute 1Ps2, and disposable income 1Yd2. For most goods, the relationship between consumption and disposable income is expected to be positive, because an increase in disposable income will be associated with an increase in the consumption of the product. Econometrics actually allows us to estimate that