Title

lpr4ytz -- Estimate the local persuasion rate

Syntax

lpr4ytz 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

lpr4ytz estimates the local persuasion rate (LPR).
varlist should include depvar treatrvar instrvar covariates in order.
Here, depvar is binary outcomes (y), treatrvar is binary treatments (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 LPR is defined by

LPR = /.

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

1. The numerator of the LPR is estimated by regressing y on z.

2. The denominator is estimated by regressing (1-y)*(1-t) on z.

3. The LPR is obtained as the ratio.

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

- With x, the LPR is defined by

LPR = E[LPR_num(x]/E[LPR_den(x]

where

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

and

LPR_den(x) = Pr[y=0,t=0|z=0,x] - Pr[y=0,t=0|z=1,x].

The estimate is obtained by the following procedure.

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

1. The numerator of the LPR is estimated by regressing y on z and x.

2. The denominator is estimated by regressing (1-y)*(1-t) on z and x.

3. The LPR is obtained as the ratio.

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

Note that in this case, LPR(x) does not depend on x, because of the linear regression model specification.

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

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

2. Pr[y=0,t=0|z,x] is estimated by regressing (1-y)*(1-t) on x given z = 0,1.

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

4. For each x in the estimation sample, both LPR_num(x) and LPR_den(x) are evaluated.

5. Then, the sample analog of LPR is constructed.

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 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 lpr4ytz directly.

Examples

We first call the dataset included in the package.

. use GKB_persuasio, clear

The first example estimates the LPR without covariates.

. lpr4ytz voteddem_all readsome post

The second example adds a covariate.

. lpr4ytz voteddem_all readsome post MZwave2

The third example allows for interactions between x and z.

. lpr4ytz voteddem_all readsome post MZwave2, model("interaction")

Stored results

Scalars

e(N): sample size

e(lpr_coef): estimate of the local persuasion rate

e(lpr_se): standard error of the estimate of the local 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