Pairing Off

One sample average is the loneliest number that you’ll ever do. Luckily, we’re usually concerned with two. We’re especially keen to compare averages for subjects in experimental treatment and control groups. We reference these averages with a compact notation, writing Y1 for Avgn[YilDi = 1] and Y0 for Avgn[YilDi = 0]. The treatment group mean, Y1, is the average for the n1 observations belonging to the treatment group, with Y° defined similarly. The total sample size is n = n0 + n1.

For our purposes, the difference between Y1 and Y0 is either an estimate of the causal effect of treatment (if Y is an outcome), or a check on balance (if Y is a covariate). To keep the discussion focused, we’ll assume the former...

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Just DDo It: A Depression Regression

The simplest DD calculation involves only four numbers, as in equations (5.1) and (5.2). In practice, however, the DD recipe is best cooked with regression models fit to samples of more than four data points, such as the 12 points plotted in Figure 5.2. In addition to allowing for more than two periods, regression DD neatly incorporates data on more than two cross-sectional units, as we’ll see in a multistate analysis of the MLDA in Section 5.2. Equally important, regression DD facilitates statistical inference, often a tricky matter in a DD setup (for details, see the appendix to this chapter).

The regression DD recipe associated with Figure 5.2 has three ingredients:

(i) A dummy for the treatment district, written TREATd, where the subscript d reminds us that this varies across distric...

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Regression Anatomy and the OVB Formula

The most interesting regressions are multiple; that is, they include a causal variable of interest, plus one or more control variables. Equation (2.2). for example, regresses log earnings on a dummy for private college attendance in a model that controls for ability, family background, and the selectivity of schools that students have applied to and been admitted to. We’ve argued that control for covariates in a regression model is much like matching. That is, the regression coeffiicent on a private school dummy in a model with controls is similar to what we’d get if we divided students into cells based on these controls, compared public school and private school students within these cells, and then took an average of the resulting set of conditional comparisons...

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Rustling Sheepskin in the Lone Star State

Schooling means many things, and every educational experience is different. But economists look at diverse educational experiences and see them all as creating human capital: a costly investment in skills from which we also expect to see a return. Some students, like Bertie Gladwin, enjoy school for its own sake and show little interest in economic returns. But many more probably see their schooling as stressful, tiring, and expensive. In addition to tuition costs, time spent in school could have been spent working. Many college students spend relatively little on tuition, but all full-time students pay an opportunity cost...

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Masters of ’Metrics: The Remarkable Wrights

The IV method was invented by economist Philip G. Wright, assisted by his son, Sewall, a geneticist. Philip wrote frequently about agricultural markets. In 1928, he published The Tariff on Animal and Vegetable Oils.— Most of this book is concerned with the question of whether the steep tariffs on farm products imposed in the early 1920s benefited domestic producers. A 1929 reviewer noted that “Whatever the practical value of the intricate computation of elasticity of demand and supply as applied particularly to butter in this

chapter, the discussion has high theoretical value.”—

In competitive markets, shifting supply and demand curves simultaneously generate equilibrium prices and quantities...

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A Tale of Two Colleges

Students who attended a private four-year college in America paid an average of about $29,000 in tuition and fees in the 2012-2013 school year. Those who went to a public university in their home state paid less than $9,000. An elite private education might be better in many ways: the classes smaller, the athletic facilities newer, the faculty more distinguished, and the students smarter. But $20,000 per year of study is a big difference. It makes you wonder whether the difference is worth it.

The apples-to-apples question in this case asks how much a 40-year-old Massachusetts – born graduate of, say, Harvard, would have earned if he or she had gone to the University of Massachusetts (U-Mass) instead...

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