GV249 Seminar WT3: Randomised Experiments

Lennard Metson

2025-02-04

🧪 Types of experiments

Distinctions can be murky

What counts as the field?
Hybrid approaches: lab-in-field, lab-in-cloud, field with survey outcomes
Relevant question: To what extent is the treatment linked to the outcome and obviously part of a study?

🧪 Which type of experiment? 1

🧪 Which type of experiment? 2

Lawson and Greene (2014) Making Clientelism Work, Comparative Politics

🧪 Which type of experiment? 3

Ryan (2013) An Experimental Study of Persuasive Social Communication, Political Communication

🎲 Why randomise?

Revision from AT Week 5 (causality):

\(ATE = \text{mean}(Y_i^1) - \text{mean}(Y_i^0)\)
Switching equation: \(Y_i = D_i \cdot Y_i^1 + (1 - D_i) \cdot Y_i^0\)
If you randomise \(D_i\), you get a random sample of potential outcomes
(P)ATE Vs (S)ATE

🎲 Why randomise?

\(SE(ATE)\) comes from the hypothetical distribution of ATEs under different random assignments

🎲 Types of randomisation

Simple versus complete:

Simple: subject-by-subject randomly assign to a condition
Complete: define the number of subjects who will be in each condition, then randomly allocate subjects to those “places”

🎲 Types of randomisation

Blocked: (1) (non-randomly) divide subjects into the groups you are using as “blocks”; (2) conduct random assignment within those blocks
- Reduces (randomisation) sampling variation
- Useful for sub-group comparisons

📊 Estimating the ATE

Treatment effect = difference-in-means between treatment and control groups:
- \(\text{mean}(Y_i | D_i = 1) - \text{mean}(Y_i | D_i = 0)\)
- OLS: \(Y_i = \alpha + \beta \cdot D_i + \epsilon_i\)

☝️ Assumptions

Independence: the (revealed) potential outcome is independent
Excludability: the only difference between groups is the treatment
Non-interference: experimental subjects do not affect one another’s potential outcomes

💻 Example from last week’s lab