The Wages of Schooling

Legend tells of a legendary econometrician whose econometric skills were the stuff of legend.

Masters at Work

This chapter completes our exploration of paths from cause to effect with a multifaceted

investigation of the causal effect of schooling on wages. Good questions are the foundation of our work, and the question of whether increased education really increases earnings is a classic. Masters have tackled the schooling question with all tools in hand, except, ironically, random assignment. The answers they’ve fashioned are no less interesting for being incomplete.

6.1 Schooling, Experience, and Earnings

British World War II veteran Bertie Gladwin dropped out of secondary school at age 14, though he still found work as a radio communication engineer in the British intelligence service. In his sixties, Bertie returned to school, completing a BA in psychology. Later, Bertie earned a В Sc in microbiology, before embarking on a Master’s degree in military intelligence, completed at the age of 91. Bertie has since been considering study for a PhD.-

It’s never too late to learn something new. Unlike Bertie Gladwin, however, most students complete their studies before establishing a career. College students spend years buried in books and tuition bills, while many of their high school friends who didn’t go to college may have started work and gained a measure of financial independence. In return for the time-consuming toil and expense of college, college graduates hope to be rewarded with higher earnings down the road. Hopes and dreams are one thing; life follows many paths. Are the forgone earnings and tuition costs associated with a college degree worthwhile? That’s a million dollar question, and our interest in it is more than personal. Taxpayers subsidize college attendance for students around the world, a policy motivated in part by the view that college is the key to economic success.

Economists call the causal effect of education on earnings the returns to schooling. This term invokes the notion that schooling is an investment in human capital, with a monetary payoff similar to that of a financial investment. Generations of masters have estimated the economic returns to schooling. Their efforts illustrate four of our tools: regression, DD, IV, and RD.

’Metrics master Jacob Mincer pioneered efforts to quantify the return to schooling using regression.- Working with U. S. census data, Mincer ran regressions like

where In Y{ is the log annual earnings of man z, S;- is his schooling (measured as years spent studying), and Xt is his years of work experience. Mincer defined the latter as age minus years of schooling minus 6, a calculation that counts all years since graduation as years of work. Masters call X{ calculated in this way potential experience. It’s customary to control for a quadratic function of potential experience to allow for the fact that, although earnings increase with experience, they do so at a decreasing rate, eventually flattening out in middle age.

Mincer’s estimates of equation (6.1) for a sample of about 31,000 nonfarm white men in the 1960 Census look like

image073 Подпись: (6.2)

In Yi = a 4- .070 S; + (.002)

With no controls, p = .07. This estimate comes from a model built with logs, so p = .07 implies average earnings rise by about 7% with each additional year of schooling (the appendix to Chapter 2 discusses regression models with logs on the left-hand side). With potential experience included as a control variable, the estimated returns increase to about.11.

The model with potential experience controls for the fact that those with more schooling typically have fewer years of work experience, since educated men usually start full-time work later (that is, after their schooling is completed). Because S;- and Xt are negatively correlated, the OVB formula tells us that omitting experience, which has a positive effect on earnings, leads to a lower estimate of the returns to schooling than we can expect in long regressions that include experience controls. Mincer’s estimates imply that white men with a given level of experience enjoy an 11% earnings advantage for each additional year of education. It remains to be seen, however, whether this is a causal effect.-

Of Singers, Fencers, and PhDs: Ability Bias

Equation (6.1) compares men with more and fewer years of schooling, while holding their years of work experience fixed. Is control for potential experience sufficient for ceteris to be paribus? In other words, at a given experience level, are more – and less-educated workers equally able and diligent? Do they have the same family connections that might offer a leg up in the labor market? Such claims seem hard to swallow. Like other masters, we’re pretty highly educated ourselves. And we’re smarter, harder working, and better bred than most of those who didn’t stick it out in the schooling department, or so we tell ourselves. The good qualities that we imagine we share with other highly educated workers are also associated with higher earnings, complicating the causal interpretation of regression estimates like those in equation Г6.2У

We can hope to improve on these simple regression estimates by controlling for attributes correlated with schooling, variables we’ll call Af (short for “ability”). Ignoring the experience term for now and focusing on other sources of OVB, the resulting long

regression can be written as

Подпись:In Yt = Cf! + p! S, + yAi + e{.

The OVB formula tells us that the short regression slope from a model with no controls, ps, is related to the long regression slope in model Г6.3І by the formula

P* = P1 + $ASY>

ability bias

where <5as is the slope from a bivariate regression of Af on S;-. As always, short (ps) equals long (pl) plus the regression of omitted (from short) on included (<5AS) times the effect of omitted in long (y). In this context, the difference between short and long is called ability bias since the omitted variable is ability.

Which way does ability bias go? We’ve defined Af so that у in the long regression is positive (otherwise, we’d call Af dis-ability). Surely <5AS is positive as well, implying

upward ability bias: we expect the short regression ps to exceed the more controlled pl. After all, our London School of Economics and MIT students tend to be high ability, at least in the sense of having high test scores and good grades in high school. On the other hand, some people cut their schooling short so as to pursue more immediately lucrative activities. Sir Mick Jagger abandoned his pursuit of a degree at the London School of Economics in 1963 to play with an outfit known as the Rolling Stones. Jagger got no satisfaction, and he certainly never graduated from college, but he earned plenty as a singer in a rock and roll band. No less impressive, Swedish epee fencer Johan Harmenberg left MIT after 2 years of study in 1979, winning a gold medal at the 1980 Moscow Olympics, instead of earning an MIT diploma. Harmenberg went on to become a biotech executive and successful researcher. These examples illustrate how people with high ability—musical, athletic, entrepreneurial, or otherwise—may be economically successful without the benefit of an education. This suggests that $AS> and hence ability bias, can be negative as easily as positive.

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