Title

calc4persuasio -- Calculate the effect of persuasion when
information on Pr(y=1|z) and optimally Pr(t=1|z) for each z=0,1 is available

Syntax

calc4persuasio y1 y0 e1 e0

Description

calc4persuasio calculates the effect of persuasion when
information on Pr(y=1|z) and optimally Pr(t=1|z) for each z=0,1 is available.
The inputs to this command are y1, y0, e1 and e0. They are all scalars
and refer to the estimates of Pr(y=1|z=1), Pr(y=1|z=0),
Pr(t=1|z=1), and Pr(t=1|z=0), where (y, t, z)
are binary outcomes, binary treatments, and binary instruments, respectively.

The outputs of this command are the lower and upper bounds on the average persuasion rate (APR)
as well as the lower and upper bounds on the local persuasion rate (LPR).

There are two cases: (i) all four inputs are given and (ii) only y1 and y0 are given.

In case (i), calc4persuasio provides the following bounds.

- The lower bound on the APR is defined by

(y1 - y0)/(1 - y0).

- The upper bound on the APR is defined by

/{1 - max(0, y0 - e0)}.

- The lower bound on the LPR is defined by

max{(y1 - y0)/(1 - y0), (y1 - y0)/(e1 - e0)}.

- The upper bound on the LPR is simply 1.

In case (ii), calc4persuasio provides the following bounds.

- The lower bound on both the APR and LPR is defined by

(y1 - y0)/(1 - y0).

- The upper bound on both the APR and LPR is simply 1.

Remarks

The purpose of calc4persuasio is to provide bound estimates of both average and local persuasion rates
when summary statistics on Pr(y=1|z) and/or Pr(t=1|z) for each z=0,1 are available.

Examples

We first call the dataset included in the package.

. use GKB_persuasio, clear

We now compute summary statistics.

. foreach var in voteddem_all readsome {

foreach treat in 0 1 {

sum `var' if post == `treat'

scalar `var'_treat' = r(mean)

}

}

Then, we calculate the bound estimates on the APR and LPR.

. calc4persuasio voteddem_all_1 voteddem_all_0 readsome_1 readsome_0

Finally, we compare this with the following.

. calc4persuasio voteddem_all_1 voteddem_all_0

Stored results

Scalars

r(apr_lb): estimate of the lower bound on the average persuasion rate

r(apr_ub): estimate of the upper bound on the average persuasion rate

r(lpr_lb): estimate of the lower bound on the local persuasion rate

r(lpr_ub): estimate of the upper bound on the local persuasion rate

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