Regression Discontinuity: Causal Inference at the Threshold

You are sitting in a government office in Santiago in 2003, and a spreadsheet is open on your screen. Chile's Ministry of Education has asked you to evaluate the Beca Presidente de la República, a national merit scholarship that covers university tuition for students who score above a certain threshold on the national university entrance exam. The program costs the government hundreds of millions of pesos annually, and legislators want to know: does it actually work? Does receiving this scholarship translate into higher earnings a decade later, or does it simply reward students who would have succeeded regardless?

You pull up two files. The first belongs to Valentina. She scored 70 on the qualifying exam, cleared the cutoff by exactly one point, and received the scholarship. Ten years later, she earns 2.4 million pesos per month as a civil engineer. The second file belongs to Rodrigo. He scored 69, missed the cutoff by one point, and received nothing. Ten years later, he earns 1.1 million pesos per month working in sales.

The difference is stark: 1.3 million pesos per month, roughly 118 percent of Rodrigo's salary. A politician looking at this would call it a triumph. The scholarship worked.

But you pause. Before you write that into your report, you have to answer a harder question. Is that income gap caused by the scholarship, or was it always going to exist because Valentina was simply the stronger student? She scored higher on the exam. She may have had better teachers, more disciplined study habits, a stronger aptitude for mathematics. Even without a single peso of government support, she might have found a way to attend university and become an engineer. Rodrigo, meanwhile, might have plateaued in sales regardless of whether anyone handed him a tuition waiver.

This is the central problem you face: selection bias. The students who received the scholarship are not a random sample of Chilean teenagers. They are, by construction, the students who scored highest. Comparing their outcomes to non-recipients does not isolate the effect of the scholarship. It conflates the scholarship's effect with the pre-existing advantages that got those students above the cutoff in the first place.

You need a smarter comparison. And it turns out, it is hiding inside the data you already have.