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.

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...