Introduction to Instrumental Variables (IV)

Main Ideas

• Instrumental variables (IV) help estimate causal effects when treatment offers are randomized but actual participation is not. This situation is called incomplete random assignment.
• The example is a lottery for seats at KIPP Lynn, a popular charter school. The lottery randomly determines who is offered a seat, but families decide whether to accept. Some students who lose the lottery later attend anyway.
• Comparing students who attend KIPP with those who do not would be misleading: attendance is not random, and family characteristics—such as parental dedication—may affect both enrollment and achievement. This is selection bias.
• IV uses the random lottery offer to estimate the effect of attendance, accounting for the fact that some students do not follow their offer status.

IV Method and Terminology

The lesson describes IV as a chain:

1. Instrument: The variable that starts the chain. Here, it is winning the KIPP lottery.
2. First stage: The effect of the instrument on treatment. Here, it is how much winning increases the likelihood of attending KIPP.
3. Second stage: The effect of treatment on the outcome. Here, it is the effect of KIPP attendance on math scores—the causal effect of interest.
4. Reduced form: The effect of the instrument on the outcome. Here, it is the effect of winning the lottery on math scores.

Under the required assumptions:

Estimated effect of attendance on scores = reduced-form effect ÷ first-stage effect

KIPP Example

From 2005 to 2008, 371 fourth- and fifth-grade students applied to the KIPP Lynn lottery:

• 253 won a seat.
• 118 lost.

Winning did not guarantee attendance:

• About 78% of lottery winners attended KIPP.
• About 4% of lottery losers attended.
• The lottery therefore increased attendance by 74 percentage points—the first stage.

A year later, winners’ average math scores were about 0.36 standard deviations higher than losers’ scores—the reduced form. Dividing 0.36 by 0.74 gives an estimated attendance effect of about 0.48 standard deviations.

The estimate applies most directly to applicants whose attendance was changed by the lottery—not automatically to every student in Lynn. The instructor says it may nevertheless indicate what could happen when additional charter seats are added.

Three Assumptions Required for IV

1. A substantial first stage: The instrument must meaningfully change the treatment of interest. In this example, winning must make KIPP attendance substantially more likely.
2. Independence: The instrument must be as good as randomly assigned, so winners and losers are comparable in relevant characteristics. The lesson recommends checking balance in family backgrounds, aptitudes, and similar factors.
3. Exclusion restriction: The instrument must affect the outcome only through the treatment. For example, if winning itself made students happier and motivated them to study more regardless of which school they attended, that would be another pathway and would violate the assumption.

IV can address non-random take-up in lotteries and clinical research, and may also use naturally occurring variation that is as good as randomly assigned. The video briefly previews a future example involving whether having children early in a career affects women’s earnings, but does not develop that analysis here.

Speakers and Sources Featured

• Instructor / narrator — explains IV concepts and the KIPP example.
• Josh — introduces charter schools and the education question; the subtitles identify him only by first name.
• Kamal — asks about comparing lottery winners and about measuring math scores.
• Camilla — responds that school attendance is not random.
• Otto — reacts to the explanation of selection bias.
• Mother — appears in a brief emotional moment associated with the documentary footage.
• Unnamed students — provide short reactions and questions.
• Whispered voice — says “Instrumental variables.”
• Waiting for Superman — an award-winning documentary referenced in connection with families awaiting school-lottery results.