Title

aprlb -- Estimate the lower bound on the average persuasion rate

Syntax

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

Options

option Description

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

Description

aprlb estimates the lower bound on the average persuasion rate (APR).
varlist should include depvar instrvar covariates in order.
Here, depvar is binary outcomes (y), 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 lower bound (theta_L) on the APR is defined by

theta_L = /{1 - Pr(y=1|z=0)}.

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

1. Pr(y=1|z=1) and Pr(y=1|z=0) are estimated by regressing y on z.

2. theta_L is computed using the estimates obtained above.

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

- With x, the lower bound (theta_L) on the APR is defined by

theta_L = E[theta_L_num(x)]/E[theta_L_den(x)],

where

theta_L_num(x) = Pr(y=1|z=1,x) - Pr(y=1|z=0,x)

and

theta_L_den(x) = 1 - Pr(y=1|z=0,x).

The estimate is obtained by the following procedure.

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

1. Pr(y=1|z,x) is estimated by regressing y on z and x.

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

1a. Pr(y=1|z=1,x) is estimated by regressing y on x given z = 1.

1b. Pr(y=1|z=0,x) is estimated by regressing y on x given z = 0.

Ater step 1, both options are followed by:

2. For each x in the estimation sample, theta_L_num(x) and theta_L_den(x) are evaluated.

3. The estimates of theta_L_num(x) and theta_L_den(x) are averaged to estimate theta_L.

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 of y on z and x.

This option is only relevant when x is present.
The default option is "no_interaction" between z and x.
When "interaction" is selected, full interactions between z and x are allowed;
this is accomplished by estimating Pr(y=1|z=1,x) and Pr(y=1|z=0,x), separately.

title(string) specifies a title.

Remarks

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

Examples

We first call the dataset included in the package.

. use GKB_persuasio, clear

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

. aprlb voteddem_all post

The second example adds a covariate.

. aprlb voteddem_all post MZwave2

The third example estimates the lower bound by the covariate.

. by MZwave2, sort: aprlb voteddem_all post

Stored results

Scalars

e(N): sample size

e(lb_coef): estimate of the lower bound on the average persuasion rate

e(lb_se): standard error of the lower bound on the average persuasion rate

Macros

e(outcome): variable name of the binary outcome 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