Quasi-Experiments I


Winter 2023

Course surveys due April 12, 11:59 PM


  • Two more weeks left!

  • Final projects due April 21

  • Groups need to meet with instructor one more time before April 19

  • Extra office hour times April 13-19

  • Every group member needs to be in at least one group meeting to receive group meeting grade

Last time

  • Learning from experiments

  • Good to understand what works, but not why or where

  • Need to think about support factors

  • Scaling up, drilling down

  • Today: Observational causal data strategies

Types of data strategy

Data strategy
Inquiry Observational Experimental
Descriptive Sample survey List experiment
Causal Quasi-experiment Survey/field experiment

Types of data strategy

Data strategy
Inquiry Observational Experimental
Descriptive Sample survey List experiment
Causal Quasi-experiment Survey/field experiment

Challenges to causal interpretations

1. Reverse causation

  • Instead of \(Z\) causing \(Y\), \(Y\) causes \(Z\)
  • Simultaneity: \(Z\) causes \(Y\) and vice versa


Students who are likely to participate enroll in Political Science courses more often

Challenges to causal interpretations

2. Omitted variable bias

  • There is an unobserved factor \(X\) that explains the relationship between \(Z\) and \(Y\)


  • We believe that more education increases income

  • But having smart parents increases both education and income

Challenges to causal interpretations

3. Selection bias

  • Individuals sort into condition \(Z\) in a manner that predicts outcome \(Y\)
  • Treatment and control are not comparable


  • Always-takers are more likely to participate in the TUP program

Challenges to causal interpretations

1. Reverse causation

2. Omitted variable bias

3. Selection bias

  • Random assignment avoids this in expectation

  • Hard to overcome with observational causal data strategies

  • Need to pretend that we can analyze data as if it was an experiment


  • Answer strategies that produce data as-if they were drawn from an experiment

  • Natural experiment: Random assignment outside of the researcher control

  • Example: Choosing municipalities at random for auditing

  • Quasi-experiment: Conditions are assigned in a manner that is sufficiently orthogonal to potential outcomes

Examples of quasi-experiment

  • Benefits eligible only to people under a certain income

  • Institutional variation based on arbitrary population thresholds

  • Winning an election by a narrow margin

  • Being barely inside/outside an administrative border

  • Unexpected events

Regression discontinuity designs

  • Three ingredients:
  1. Score (running variable)

  2. Cutoff (threshold)

  3. Treatment (at least two conditions)

Visual representation

As a graph

Example: Hoekstra (2019)

  • Question: Effect of higher education on earnings

  • Challenge: Selection bias

  • Solution: Focus on attendance at US state flagship university among 28-33 year olds

  • Outcome: Earnings

  • Score: SAT test scores

  • Cutoff: Admission cutoff

  • Treatment: Attending flagship university

Treatment take-up


How do you get an estimate?

  • Two approaches to RDD data:
  1. Local randomization

  2. Continuity-based

Local randomization

  • Potential outcomes are not random because they depend on the score (and other things)

  • However, around the cutoff, treatment assignment is as good as random

  • So we can pretend we have an experiment within a bandwidth around the cutoff

Bandwidth tradeoff

RDD assumptions

1. Continuity

Score is continuous at the cutoff

2. Comparability

Units are comparable at or around the cutoff

  • These imply no manipulation and no selection bias
  • Local randomization is sufficient but not necessary to satisfy these assumptions

Continuity-based approach

  • Treatment assignment is deterministic at the cutoff

  • But usually too few or no units at the cutoff

  • Task: Approximate the gap at the cutoff as best as possible

  • This becomes a line drawing problem

Line drawing: Parametric

Line drawing: Nonparametric

Line drawing: Bandwidth

RDDs in balance


  • Intuitive design

  • Widely applicable

  • Easy to visualize


  • Results are highly local

  • Scale up? Drill down?

  • Too many moving parts

  • Software automates most of the decisions

  • Ideally, results are consistent under different approaches

Next Week

Quasi-experiments II

Focus on: Difference-in-differences design

Break time!