Types of Experiments¶
| Type | Free from Self-Selection | External Validity | Example | LATE | ||
|---|---|---|---|---|---|---|
| RCT (Randomized Control Trials) | ✅ | ⚠️ | Only for compliers | |||
| Natural/ Quasi | A situation where the researcher does not assign treatment to individuals Treatment is “as if” random, as implicit randomization occurs | ❌ | ✅ | |||
| Regression Discontinuity Design | Discrete treatment status determined by an underlying continuous variable, which is used for quasi experiments Assumption: People right before and after threshold are identical Running/forcing variable: Index/measure that determines eligibility Cutoff/cutpoint: threshold that formally assigns access to program Limitations - Requires lots of data in the neighborhood of the threshold - Poor generalizability: The validity of the results is usually restricted to this region - Throws away the lot of information in the non-random parts - Doesn’t allow building structural causal model | Uni admission cutoff provides a natural experiment on uni education. Students just above/below are likely to be very similar. For these students, uni education is “as if” random. Comparing these students (ones that went to uni/not) produces an estimate of the causal effect of college education. |  | People in the bandwidth | ||
| Differences-in-Differences | 2 time-series process \(y_1\) and \(y_2\) have the factors affecting them |  | ||||
| Instrumental Variables | IV technique helps work around simultaneous causal relationships - Education -> Earnings -> Education -> ... - Supply → Demand → Supply → ... | Only for compliers |
Compliance¶
| Type | What they do when assigned to control group \(T=0\) | What they do when assigned to treatment group \(T=1\) |
|---|---|---|
| Compliers | \(T=0\) | \(T=1\) |
| Always takers | \(T=1\) | \(T=1\) |
| Never takers | \(T=1\) | \(T=1\) |
| Defiers | \(T=0\) | \(T=1\) |
Differences-in-Differences¶
Let
- Control: \(y_0\) be the time series with \(x=0\)
- Treated: \(y_1\) be the time series with \(x=1\)
- \(D_t\) be the difference of the 2 series
\[ \begin{aligned} y_{0t} &= f(t) + \beta_1 (T=0) \\ &= f(t) \\ y_{1t} &= f(t) + \beta_1 (T=1) \\ D_t &= (y_1 - y_0)_t \end{aligned} \]
Assumptions¶
- Parallel trends: \(f_1(t) = f_0(t)\)
- confirmed by evaluating regions without the treatment
- No differential timing: Check Goodman-Bacon decomposition
- Absence treatment: no other variables
- Difference between the treatment & the control group is time-invariant
- any difference in their difference must be due to the treatment effect.
Why not other way?¶
- Wrong ways: Impossible to know if change happened because of treatment or naturally
- Only comparing treatment group before/after
- Only comparing treatment/control group at a particular time
RDD¶
Threats¶
Manipulation¶
People may change behavior when they know of the cutoff
Discontinuity exists in the running variable even without any treatment
Check with McCrary Density Plot
Non-Compliance¶
People on the margin of the cutoff may/may not get treatment, by misrepresenting the running variable - Some people may not want treatment even though they crossed the cutoff - Others may request access to the above discarded treatment spots
This is different from manipulation, where the actual running variable comes out different
For eg: Misreporting income
Types¶
| \(T\) | |||
|---|---|---|---|
| Sharp | \(\begin{cases} 1, & z \ge z_0\\ 0, & \text{o.w}\end{cases}\) | ||
| Fuzzy | \(\begin{cases} , & z \ge z_0\\ , & \text{o.w}\end{cases}\) | Doubly-local effect: CACE only around cutoff Useful when there is non-compliance Use above/below threshold as instrument |  |
What to Choose¶
