Title

persuasio4yz -- Conduct causal inference on persuasive effects for binary outcomes y and binary instruments z

Syntax

persuasio4yz depvar instrvar [covariates] [if] [in] [, level(#) model(string) method(string) nboot(#) title(string)]

Options

option Description

level(#) Set confidence level; default is level(95)
model(string) Regression model when covariates are present
method(string) Inference method; default is method("normal")
nboot(#) Perform # bootstrap replications
title(string) Title

Description

persuasio4yz conducts causal inference on persuasive effects.

It is assumed that binary outcomes y and binary instruments z are observed.
This command is for the case when persuasive treatment (t) is unobserved,
using an estimate of the lower bound on the average persuasion rate (APR) via
this package's command aprlb.

varlist should include depvar instrvar covariates in order. Here, depvar is binary outcomes (y), instrvar is binary instruments (z), and covariates (x) are optional.

When treatment t is unobserved, the upper bound on the APR is simply 1.

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 confidence interval 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.

4. Then, a confidence interval for the APR is set by

[ est - cv * se , 1 ],

where est is the estimate, se is the standard error, and cv is the one-sided standard normal critical value (e.g., cv = 1.645 for level(95)).

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

theta_L = E[theta_L(x)],

where

theta_L(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.

4. A bootstrap confidence interval for the APR is set by

[ bs_est(alpha) , 1 ],

where bs_est(alpha) is the alpha quantile of the bootstrap estimates of theta_L
and 1 - alpha is the confidence level.

The bootstrap procedure is implemented via STATA command bootstrap.

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.

level(#) sets confidence level; default is level(95).

method(string) refers the method for inference.

The default option is method("normal").
By the naure of identification, one-sided confidence intervals are produced.

1. When x is present, it needs to be set as method("bootstrap");
otherwise, the confidence interval will be missing.

2. When x is absent, both options yield non-missing confidence intervals.

nboot(#) chooses the number of bootstrap replications.

The default option is nboot(50).
It is only relevant when method("bootstrap") is selected.

title(string) specifies a title.

Remarks

It is recommended to use nboot(#) with # at least 1000.
A default choice of 50 is meant to check the code initially
because it may take a long time to run the bootstrap part.
The bootstrap confidence interval is based on percentile bootstrap.
Normality-based bootstrap confidence interval is not recommended
because bootstrap standard errors can be unreasonably large in applications.

Examples

We first call the dataset included in the package.

. use GKB_persuasio, clear

The first example conducts inference on the APR without covariates, using normal approximation.

. persuasio4yz voteddem_all post, level(80) method("normal")

The second example conducts bootstrap inference on the APR.

. persuasio4yz voteddem_all post, level(80) method("bootstrap") nboot(1000)

The third example conducts bootstrap inference on the APR with a covariate, MZwave2, interacting with the instrument, post.

. persuasio4yz voteddem_all post MZwave2, level(80) model("interaction") method("bootstrap") nboot(1000)

Stored results

Matrices

e(apr_est): (1*2 matrix) bounds on the average persuasion rate in the form of [lb, 1]

e(apr_ci): (1*2 matrix) confidence interval for the average persuasion rate in the form of [lb_ci, 1]

Macros

e(cilevel): confidence level

e(inference_method): inference method: "normal" or "bootstrap"

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