get_encouragement_data

get_encouragement_data(N=4000, seed=1234)

Synthetic data for an A/B encouragement design IV application.

DGP

Instrument: assigned_treatment ~ Bernoulli(0.5) [randomized, exogenous] Fixed effect: user_type ∈ {0, 1, 2}

First stage (compliance): P(adopt | encouraged) = 0.70 (compliers + always-takers) P(adopt | not encouraged) = 0.15 (always-takers only) First-stage coefficient = 0.70 - 0.15 = 0.55

Outcome (structural equation): revenue = 5 + user_type_FE + TRUE_LATE*adopted_feature + N(0, 1) TRUE_LATE = 2.0 (effect on compliers)

Wald identity (exact by construction): ITT = E[Y|Z=1] - E[Y|Z=0] = 2.0 * 0.55 = 1.10 LATE = ITT / first_stage = 1.10 / 0.55 = 2.0 ✓

Parameters

Name	Type	Description	Default
N	int	Number of observations (users). Default is 4000.	`4000`
seed	int	Random seed. Default is 1234.	`1234`

Returns

Name	Type	Description
	pandas.DataFrame	Columns: `revenue`, `assigned_treatment`, `adopted_feature`, `user_type`.

Examples

import pyfixest as pf

data = pf.get_encouragement_data()

# instrument take-up with the randomized encouragement, LATE is 2.0
fit = pf.feols(
    "revenue ~ 1 | user_type | adopted_feature ~ assigned_treatment", data
)
fit.summary()

###

Estimation:  IV
Dep. var.: revenue, Fixed effects: user_type
sample: None = all
Inference:  iid
Observations:  4000

| Coefficient     |   Estimate |   Std. Error |   t value |   Pr(>|t|) |   2.5% |   97.5% |
|:----------------|-----------:|-------------:|----------:|-----------:|-------:|--------:|
| adopted_feature |      2.004 |        0.057 |    34.977 |      0.000 |  1.891 |   2.116 |
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