Title

aprub -- Estimate the upper bound on the average persuasion rate

Syntax

aprub depvar treatrvar instrvar [covariates] [if] [in] [, model(string) title(string)]

Options

option Description

model(string) Regression model when covariates are present
title(string) Title

Description

aprub estimates the upper bound on the average persuasion rate (APR).
varlist should include depvar treatrvar instrvar covariates in order.
Here, depvar is binary outcomes (y), treatrvar is binary treatment (t),
instrvar is binary instruments (z), and covariates (x) are optional.

There are two cases: (i) covariates are absent and (ii) covariates are present.

- Without x, the upper bound (theta_U) on the APR is defined by

theta_U = /{1 - E[B|z=0]},

where A = 1(y=1,t=1)+1-1(t=1) and
B = 1(y=1,t=0).

The estimate and its standard error are obtained by the following procedure:

1. E[A|z=1] is estimated by regressing A on z.

2. E[B|z=0] is estimated by regressing B on z.

3. theta_U is computed using the estimates obtained above.

4. The standard error is computed via STATA command nlcom.

- With x, the upper bound (theta_U) on the APR is defined by

theta_U = E[theta_U_num(x)]/E[theta_U_den(x)],

where

theta_U_num(x) = E[A|z=1,x] - E[B|z=0,x]

and

theta_U_den(x) = 1 - E[B|z=0,x].

The estimate is obtained by the following procedure.

If model("no_interaction") is selected (default choice),

1. E[A|z=1,x] is estimated by regressing A on z and x.

2. E[B|z=0,x] is estimated by regressing B on z and x.

Alternatively, if model("interaction") is selected,

1. E[A|z=1,x] is estimated by regressing A on x given z = 1.

2. E[B|z=0,x] is estimated by regressing B on x given z = 0.

Ater step 1, both options are followed by:

3. For each x in the estimation sample, theta_U_num(x) and theta_U_den(x) are evaluated.

4. The estimates of theta_U_num(x) and theta_U_den(x) are averaged to estimate theta_U.

When covariates are present, the standard error is missing because an analytic formula for the standard error is complex.
Bootstrap inference is implemented when this package's command persuasio is called to conduct inference.

Options

model(string) specifies a regression model.

This option is only relevant when x is present.
The dependent variable is
either A or B.
The default option is "no_interaction" between z and x.
When "interaction" is selected, full interactions between z and x are allowed.

title(string) specifies a title.

Remarks

It is recommended to use this package's command persuasio instead of calling aprub directly.

Examples

We first call the dataset included in the package.

. use GKB_persuasio, clear

The first example estimates the upper bound on the APR without covariates.

. aprub voteddem_all readsome post

The second example adds a covariate.

. aprub voteddem_all readsome post MZwave2

The third example estimates the upper bound by the covariate.

. by MZwave2,sort: aprub voteddem_all readsome post

Stored results

Scalars

e(N): sample size

e(ub_coef): estimate of the upper bound on the average persuasion rate

e(ub_se): standard error of the upper bound on the average persuasion rate

Macros

e(outcome): variable name of the binary outcome variable

e(treatment): variable name of the binary treatment variable

e(instrument): variable name of the binary instrumental variable

e(covariates): variable name(s) of the covariates if they exist

e(model): regression model specification ("no_interaction" or "interaction")

Functions:

e(sample): 1 if the observations are used for estimation, and 0 otherwise.

Authors

Sung Jae Jun, Penn State University, <sjun@psu.edu>

Sokbae Lee, Columbia University, <sl3841@columbia.edu>

License

GPL-3

References

Sung Jae Jun and Sokbae Lee (2022),
Identifying the Effect of Persuasion,
arXiv:1812.02276 [econ.EM]

Version

0.2.1 20 November 2022