Essentials of Applied Econometrics

Essentials of Applied Econometrics

ESSENTIALS OF APPLIED ECONOMETRICS

Aaron Smith

J. Edward Taylor

UNIVERSITY OF CALIFORNIA PRESS

University of California Press, one of the most distinguished university presses in the United States, enriches lives around the world by advancing scholarship in the humanities, social sciences, and natural sciences. Its activities are supported by the UC Press Foundation and by philanthropic contributions from individuals and institutions. For more information, visit www.ucpress.edu.

University of California Press

Oakland, California

© 2017 by The Regents of the University of California

Library of Congress Cataloging-in-Publication Data

Names: Smith, Aaron, author. | Taylor, J. Edward, author.

Title: Essentials of applied econometrics / Aaron Smith, J. Edward Taylor.

Description: Oakland, California : University of California Press, [2017] | Includes index. | Description based on print version record and CIP data provided by publisher; resource not viewed.

Identifiers: LCCN 2016018912 (print) | LCCN 2016018067 (ebook) | ISBN 9780520963290 (ebook) | ISBN 9780520288331 (pbk. : alk. paper)

Subjects: LCSH: Econometrics—Textbooks.

Classification: LCC HB139 (print) | LCC HB139 .S6255 2017 (ebook) | DDC 330.01/5195—dc23

LC record available at https://lccn.loc.gov/2016018912

Manufactured in the United States of America

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Contents

Preface

Acknowledgments

About the Authors

1 Introduction to Econometrics

What is Econometrics?

Step 1: What Do You Want to Do?

Step 2: Formulate Your Research Design and Specify the Econometric Model

Step 3: Apply Statistical Theory

An Illustration with the Population Mean

Putting It Together: Poverty and Test Scores

From Statistics to Econometrics

2 Simple Regression

The Least-Squares Criterion

Estimating a Simple Regression Model of Academic Performance

The R²

Beyond Simple Regression

3 Multiple Regression

The Multiple Regression Model

When Does the MR Estimator Collapse to the SR Estimator?

Back to API and FLE (and PE, Too)

From Two to Many Explanatory Variables: The General Multiple Regression Model

Perfect Multicollinearity

Interpreting MR Coefficients

Using Matrix Algebra to Estimate a Multiple Regression Model

4 Generalizing from a Sample

Three Steps to Generalizing from a Sample

Step 1: Define Your Population and Research Goal

Step 2: Make Assumptions about Your Population (and How Your Sample Represents It)

Step 3: Compute Statistics to Measure OLS Accuracy

Data Types

5 Properties of Our Estimators

An Experiment in Random Sampling

BLUE Estimators

The Sample Mean

The OLS Regression

Multiple Regression

Back to Schools and Free Lunch

Consistent Estimators

Properties of the Regression Line (or Plan, or Hyperplane)

6 Hypothesis Testing and Confidence Intervals

Hypothesis Testing

Hypothesis Testing with Small Samples

Confidence Intervals

What Determines Confidence Interval Width?

How Large a Sample is Large Enough?

Hypothesis Testing and Confidence Intervals in Multiple Regressions

Presenting Your Results

7 Predicting in a Nonlinear World

Getting the Model Right

How Could We Get the Model Wrong?

What If the True Model is Nonlinear?

Testing Functional Forms

8 Best of BLUE I: Cross-Section Data and Heteroskedasticity (Assumption CR2)

The Problem of Heteroskedasticity

Testing for Heteroskedasticity

Fixing the Problem

Back to Climate Change

9 Best of Blue II: Correlated Errors (Assumption CR3)

Time-Series Data: Autocorrelation

Ignoring Autocorrelation

How to Test for Autocorrelation

Fixing Autocorrelation

An Ex Post Error-Correction Method: Newey-West

Ex Ante: Using What We Know to Improve on OLS

Clustered and Spatial Data

10 Sample Selection Bias (Assumption CR1)

What If We Have a Nonrepresentative Sample?

How Does It Happen?

How Sample Selection Bias Affects Regression Models

What to Do About It

Self-Selection

Experiments

11 Identifying Causation

Why Care About Causation?

A New Classical Regression Assumption

The Endogeneity Problem

Measurement Error

X and Y Jointly Determined

Omitted Variables

12 Instrumental Variables: A Solution to the Endogeneity Problem

What Are Instrumental Variables?

The Quest for Good Instruments

The Gold Standard: Randomized Treatments

A Brave New World

Appendix: Critical Values for Commonly Used Tests in Econometrics

Notes

Index

Preface

This book was designed to give students the tools they need to carry out econometric analysis in the modern world. Most textbooks assume that the purpose of econometrics is to formulate a true mathematical model of a piece of the economy or to estimate whether a change in one variable causes change in another. Many students are unsure what to do if they cannot justify the often unrealistic assumptions required of a true model or a causal effect. If the model is misspecified, does this mean it is useless? If we cannot convincingly justify causality, are we wasting our time?

Much work in practice does not have such grand goals. Google does not usually care about doing airtight tests of whether one variable causes another. It is more interested in using (often very large) data sets to find correlations and predict people’s behavior. Estimating correlations and performing predictions are very different goals to formulating true models and establishing causality. We believe our book is unique among intermediate econometrics texts at making this distinction clear.

Traditional econometrics textbooks also confound two distinct sets of assumptions that econometricians make. Some of these assumptions address how your data sample represents the whole population (sampling theory) and some of these assumptions address how economic variables relate to each other (causal analysis). Most textbooks lump these assumptions together, which makes it unclear where one ends and the other begins. However, if your goal is correlation or prediction, then you need the sampling theory assumptions but not the causal analysis assumptions.

Our book begins with sampling theory: how to use a sample to make inferences about a whole population. We address causality as a distinct topic in the last two chapters of the book. In between, we cover the critical topics that are an essential part of any econometrics course, including properties of estimators, hypothesis testing, dealing with nonlinear relationships, heteroskedasticity, correlated errors, and sampling bias. These are essentials of applied econometrics regardless of whether the goal of your research concerns correlation, prediction, or causation.

The book covers essential econometric theory but with an emphasis on the best practices for estimating econometric models. It stresses the importance of being explicit about the purpose of the analysis, i.e., the population we want our analysis to inform us about and whether our goal is to establish correlation, predict outcomes, or demonstrate causation. Real-world examples are used throughout to illuminate the concepts presented while stimulating student interest in putting econometric tools to use.

THE GENESIS OF REBELTEXT

It was Winter Quarter 2012. The memory of student protests and pepper spray still permeated the air above the UC Davis quad. Ed gritted his teeth and told the campus bookstore to order up 125 copies of an undergraduate econometrics textbook at $150 a shot. (That’s a gross of $18,750 just from one class.)

Over dinner that night, Ed’s 20-year-old son, Sebastian, just back from occupying the Port of Oakland, said he spent $180 on a new edition calculus text required for his course. Sebastian’s little brother, Julian, exclaimed: That’s obscene. Sebastian responded, You’re right. Basic calculus hasn’t changed in decades. You don’t need new editions to learn calculus.

Before dinner was over, Ed’s two kids had ambushed him and made him promise never, ever, to assign an expensive textbook to his students again.

So, what do you want me to do then, write one? Ed asked them.

Exactly, they answered in unison.

And get a good title for it, Ed’s wife, Peri, added.

The next day, RebelText was born. What’s RebelText?

First, it’s affordable. It costs as little as one-fifth the price of a normal textbook. Second, it’s concise. It covers what one can hope to get through in a quarter- or semester-long course. Third, it’s more compact than most textbooks. Being both affordable and compact, you can carry it around with you. Write in it. Don’t worry about keeping the pages clean, because at this price there’s no need to resell it after the class is through (or worry about whether there will still be a market for your edition). This RebelText will naturally evolve as needed to keep pace with the field, but there will never, ever, be a new edition just for profits’ sake.

WHO SHOULD USE THIS BOOK AND HOW

When we sat down to write Essentials of Applied Econometrics, we wanted a compact book for an upper-division undergraduate econometrics class. That is primarily what this is. The knowledge in this book should prime any undergraduate for further study or to venture out into the real world with an appreciation for the essential concepts and tools of econometrics. More than a textbook, this can be a helpful basic reference in applied econometrics for any graduate student, researcher, or practitioner.

RebelText was created to make learning and teaching as efficient as possible. We need to learn the essentials of the subject. We do not want to wade through thick textbooks in order to locate what we need to know, constantly wondering what will and won’t be on the next test. We especially do not want to pay for a big textbook that we don’t come close to finishing in the course! Because it is concise, there is no reason not to read and study every word of Essentials of Applied Econometrics. All of it could be on the test. Master it, and you will be conversant enough to strike up a conversation with anyone who does econometrics, and you’ll have the basic tools to do high-quality applied econometric work. Think of this book as presenting the best practices and state-of-the-art methods for doing econometrics. By mastering it, you’ll also have the conceptual and intuitive grounding you need in order to move on to higher-level econometrics courses. You’ll probably find yourself referring back to it from time to time, so keep it on your shelf!

STUDENT RESOURCES ONLINE

Essentials of Applied Econometrics is intended to be used interactively with online content. We encourage you to visit our living website, http://www.ucpress.edu/go/appliedeconometrics, where you will find an Econometrics Rosetta Stone showing how to use some of the most popular software packages to do econometric analysis. You will also find a variety of interesting data sets, study questions, and online appendices for our book. We welcome your suggestions for other online content you discover on your own! When we use the textbook, the website becomes a center of class activity.

INSTRUCTOR RESOURCES ONLINE

A set of instructor resources including test questions and images for lecture presentations are available for download with permission of the publisher. If you are teaching with Essentials of Applied Econometrics, consider contributing your ideas about novel uses of the book and website, interesting data sets, programs, and projects to the RebelText movement. To find out how, visit rebeltext.org and click on contributing to RebelText.

Acknowledgments

This book would not have happened without our families and students. Ed gives special thanks to Sebastian and Julian, who shamed him into launching the RebelText project; to his wife Peri Fletcher, who believed in this project from the start; to Laika, who managed to eat only a couple early drafts of our manuscript; and to UC Davis undergraduate Quantitative Methods (ARE 106) students, who were our guinea pigs and cheerleaders while this book was being written. Aaron thanks his wife Heather and daughter Hayley for their enduring patience and inspiration while he labored on this book. He also thanks Heather for teaching him about California school finance and thereby providing us with the main example we use in the book. Abbie Turiansky was instrumental in helping us put together the very first draft of many of the chapters in this book. Michael Castelhano, Justin Kagin, Dale Manning, and Karen Thome provided valuable research assistance at various stages of this project. We are greatly indebted to Jan Camp at Arc Light Books, who helped us launch the first RebelTexts as print-on-demand books.

Aaron Smith and J. Edward Taylor

Davis, California, 2016

About the Authors

Aaron Smith’s first real job was teaching econometrics (not counting working on the family farm in New Zealand where he grew up). In 1994, just before heading off to graduate school, he taught an econometrics class much like the one you’re probably taking with this book. It was a scary and invigorating experience—he must have enjoyed it because he’s still doing it all these years later! He is currently a professor of Agricultural and Resource Economics at UC Davis, where he has been since 2001 after earning his PhD in Economics from UC San Diego. When not teaching, he does research on policy, prices, and trading in agricultural, energy, and financial markets. Recent project topics include identifying which traders in commodity futures markets seem to know where prices are headed, estimating how the recent growth in the use of ethanol made from corn as an ingredient in gasoline has affected food and gas prices, and understanding commodity booms and busts. His research has won the Quality of Communication, Quality of Research Discovery, and Outstanding American Journal of Agricultural Economics Article Awards from the Agricultural and Applied Economics Association. You can learn more about Aaron at his website: asmith.ucdavis.edu.

J. Edward Taylor loves teaching economics, especially econometrics, microeconomics, and economic development. He’s been doing it for about 25 years now at UC Davis, where he is a professor in the Agricultural and Resource Economics Department. He’s also done a lot of economic research. At last count, he had published about 150 articles, book chapters, and books on topics ranging from labor economics, international trade, immigration, biodiversity, and poverty—and more than 20,000 citations on Google Scholar. He’s in Who’s Who in Economics, the list of the world’s most cited economists; a Fellow of the Agricultural and Applied Economics Association (AAEA), and recent editor of the American Journal of Agricultural Economics (AJAE). Nearly everything Ed does involves applied econometrics. He has presented his findings to the US Congress, the United Nations, the World Bank, and governments around the world, and he is published in journals ranging from The American Economic Review to Science. His recent book, Beyond Experiments in Development Economics: Local Economy-Wide Impact Evaluation (Oxford University Press, 2014), won the AAEA Quality of Communication Award. You can learn more about Ed at his website: jetaylor.ucdavis.edu.

CHAPTER 1

Introduction to Econometrics

It is interesting that people try to find meaningful patterns in things that are essentially random.

—Data, Star Trek

LEARNING OBJECTIVES

Upon completing the work in this chapter, you will be able to:

▸ Define and describe the basics of econometrics

▸ Describe how to do an econometric study

Jaime Escalante was born in Bolivia in 1930. He immigrated to the United States in the 1960s, hoping for a better life. After teaching himself English and working his way through college, he became a teacher at Garfield High School in East Los Angeles. Jaime believed strongly that higher math was crucial for building a successful career, but most of the students at Garfield High, many of whom came from poor backgrounds, had very weak math skills. He worked tirelessly to transform these kids into math whizzes. Incredibly, more than a quarter of all the Mexican-American high school students who passed the AP calculus test in 1987 were taught by Jaime.

Hollywood made a movie of Jaime’s story called Stand and Deliver. If you haven’t seen that movie, you’ve probably seen one of the other dozens with a similar plot. An inspiring and unconventional teacher gets thrown into an unfamiliar environment filled with struggling or troubled kids. The teacher figures out how to reach the kids, they perform well in school, and their lives change forever.

We all have stories of an inspiring teacher we once had. Or a terrible teacher we once had. Meanwhile, school boards everywhere struggle with the question of how to teach kids and turn them into economically productive adults. Do good teachers really make all the difference in our lives? Or do they merely leave us with happy memories? Not every school can have a Jaime Escalante. Is more funding for public schools the answer? Smaller class sizes? Better incentives for teachers? Technology?

Econometrics can provide answers to big questions like these.

WHAT IS ECONOMETRICS?

Humans have been trying to make sense of the world around them for as long as anyone knows. Data bombard our senses: movements in the night sky, the weather, migrations of prey, growth of crops, spread of pestilence. We have evolved to have an innate curiosity about these things, to seek patterns in the chaos (empirics), then explanations for the patterns (theories). Much of what we see around us is random, but some of it is not. Sometimes our lives have depended on getting this right: predicting where to find fish in the sea (and being smart enough to get off the sea when a brisk nor’easter wind starts to blow), figuring out the best time to plant a crop, or intervening to arrest the spread of a plague. A more complex world gives us ever more data we have to make sense of, from climate change to Google searches to the ups and downs of the economy.

Econometrics is about making sense of economic data (literally, it means economy measurement). Often, it is defined as the application of statistics to economic data, but it is more than that. To make sense of economic data, we usually need to understand something about the unseen processes that create these data. For example, we see differences in people’s earnings and education (years of completed schooling). Econometric studies consistently find that there is a positive relationship between the two variables. Can we use people’s schooling to predict their earnings? And if we increase people’s schooling, can we say that their earnings will increase?

These are two different questions, and they get at the hardest part of econometrics—distilling causation from correlation. We may use an econometric model to learn that people with a college degree earn more than those without one. That is a predictive, or correlative, relationship. We don’t know whether college graduates earn more because of useful things they learned in college—that is, whether college causes higher earnings. College graduates tend to have high IQ, and they might have earned a lot regardless of whether or not they went to college. Mark Twain (who was not educated beyond elementary school) once said: I’ve never let my school interfere with my education. He might have had a point.

Often, an econometrician’s goal is to determine whether some variable, X, causes an outcome, Y. But not all of econometrics is about causation. Sometimes we want to generate predictions and other times test a theory. Clearly defining the purpose of an econometrics research project is the first step toward getting credible and useful results. The second step is to formulate your research design and specify your econometric model, and the final step is to apply statistical theory to answer the question posed in step 1.

Most of your first econometrics course focuses on step 3, but don’t forget steps 1 and 2! Throughout the book, we will remind you of these steps. Next, we discuss each of the three steps to put the rest of the book in context.

STEP 1: WHAT DO YOU WANT TO DO?

The first step in doing econometrics is to define the purpose of the modeling. It is easy to skip this step, but doing so means your analysis is unlikely to be useful.

Your purpose should be concrete and concise. I want to build a model of the economy is not enough. What part of the economy? What do you want to learn from such a model? Often, if you can state your purpose in the form of a question, you will see whether you have defined it adequately.

Here are some examples.

Do Good Teachers Produce Better Student Outcomes?

To estimate whether good teachers improve life outcomes, we first need to measure teacher quality. In a 2014 study, Raj Chetty, John Friedman, and Jonah Rockoff constructed measures of how much an above-average teacher improves students’ test scores over what they would have been with an average teacher. These are called value-added (VA) measures of teacher quality and were estimated using detailed data on elementary school records from a large urban school district. This research was deemed so important that it was presented in not one but two papers in the most prestigious journal in economics, the American Economic Review.¹

Chetty and his coauthors used econometrics with their VA measures to show that replacing an average teacher with a teacher whose VA is in the top 5% would increase students’ earnings later in life by 2.8%. This might seem small, but the average 12-year-old in the United States can expect lifetime earnings of $522,000,² so a 2.8% earnings bump is worth about $14,500 per student. Multiply that by 20 kids per classroom and an excellent teacher starts to look really valuable. It works the other way too—teachers with low VA potentially have large negative effects on lifetime earnings.

Does the Law of Demand Hold for Electricity?

In microeconomic theory, the law of demand predicts that when the price of a good rises, demand for the good falls. Does this theoretical prediction hold up in the real world? Is the own-price elasticity of demand really negative? How large is it? Finding a negative correlation between price and demand is consistent with economic theory; finding the opposite is not.

Katrina Jessoe and David Rapson asked this question using data on residential electricity consumption.³ They conducted an experiment in which they divided homes randomly into three groups. The first group faced electricity prices that jumped by 200–600% on certain days of the year. The second group faced the same price rises but also were given an electronic device that told them in real time how much electricity they were using. The third group was the control group: they experienced no change in their electricity prices.

Jessoe and Rapson used econometrics to estimate that consumers in the first group did not change their consumption significantly compared with the control group—they had a price elasticity of demand close to zero. However, the second group had a price elasticity of demand of −0.14. Conclusion: the law of demand holds for electricity, but only if consumers know how much electricity they are using in real time. Without this knowledge, they don’t know how much electricity is used when they run the air conditioner or switch on a light, so they don’t respond to a price change.

Is It Possible to Forecast Stock Returns?

Lots of people think they can make money in the stock market. We often receive emails informing us of the next greatest stock tip. Business TV channels are full of people yelling about how to make money in the stock market. Every time the market crashes, there’s a great story about the genius investor who saw it all coming and made money during the crash.⁴ But if it’s so easy to make money in the stock market, why isn’t everyone doing it?

Based on the theory of efficient financial markets, many economists cast a skeptical eye on claims that the stock market is highly predictable. If everyone knew the market was going to go up, then it would have already done so.