/*** Title ----- {phang}{cmd:lpr4ytz} {hline 2} Estimate the local persuasion rate Syntax ------ > {cmd:lpr4ytz} _depvar_ _treatrvar_ _instrvar_ [_covariates_] [_if_] [_in_] [, {cmd:model}(_string_) {cmd:title}(_string_)] ### Options | _option_ | _Description_ | |-------------------|-------------------------| | {cmd:model}(_string_) | Regression model when _covariates_ are present | | {cmd: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 {cmd:LPR} = {Pr({it:y}=1|{it:z}=1)-Pr({it:y}=1|{it:z}=0)}/{Pr[{it:y}=0,{it:t}=0|{it:z}=0]-Pr[{it:y}=0,{it:t}=0|{it:z}=1]}. 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-{it:y})*(1-{it: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 {cmd:LPR} = E[{cmd:LPR_num}({it:x}]/E[{cmd:LPR_den}({it:x}] where {p 4 8 2} {cmd:LPR_num}({it:x}) = Pr({it:y}=1|{it:z}=1,{it:x}) - Pr({it:y}=1|{it:z}=0,{it:x}) and {p 4 8 2} {cmd:LPR_den}({it:x}) = Pr[{it:y}=0,{it:t}=0|{it:z}=0,{it:x}] - Pr[{it:y}=0,{it:t}=0|{it:z}=1,{it:x}]. The estimate is obtained by the following procedure. If {cmd: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-{it:y})*(1-{it: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, {cmd:LPR}({it:x}) does not depend on _x_, because of the linear regression model specification. Alternatively, if {cmd:model}("interaction") is selected, {p 4 8 2} 1. Pr({it:y}=1|{it:z},{it:x}) is estimated by regressing {it:y} on _x_ given _z_ = 0,1. {p 4 8 2} 2. Pr[{it:y}=0,{it:t}=0|{it:z},{it:x}] is estimated by regressing (1-{it:y})*(1-{it:t}) on _x_ given _z_ = 0,1. {p 4 8 2} 3. Pr({it:t}=1|{it:z},{it:x}) is estimated by regressing _t_ on _x_ given _z_ = 0,1. {p 4 8 2} 4. For each _x_ in the estimation sample, both {cmd:LPR_num}({it:x}) and {cmd:LPR_den}({it:x}) are evaluated. {p 4 8 2} 5. Then, the sample analog of {cmd: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 ------- {cmd: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. {cmd: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, Sokbae Lee, Columbia University, License ------- GPL-3 References ---------- Sung Jae Jun and Sokbae Lee (2022), Identifying the Effect of Persuasion, [arXiv:1812.02276 [econ.EM]](https://arxiv.org/abs/1812.02276) Version ------- 0.2.1 20 November 2022 ***/ capture program drop lpr4ytz program lpr4ytz, eclass sortpreserve byable(recall) version 16.1 syntax varlist (min=3) [if] [in] [, model(string) title(string)] marksample touse gettoken Y varlist_without_Y : varlist gettoken T varlist_without_YT : varlist_without_Y gettoken Z X : varlist_without_YT quietly levelsof `Y' if "`r(levels)'" != "0 1" { display "`Y' is not a 0/1 variable" error 450 } quietly levelsof `T' if "`r(levels)'" != "0 1" { display "`T' is not a 0/1 variable" error 450 } quietly levelsof `Z' if "`r(levels)'" != "0 1" { display "`Z' is not a 0/1 variable" error 450 } display " " display as text "{hline 65}" display "{bf:lpr4ytz:} Estimating the Local Persuasion Rate" display as text "{hline 65}" display " " display " - Binary outcome: `Y'" display " - Binary treatment: `T'" display " - Binary instrument: `Z'" display " - Covariates (if exist): `X'" display " " * generate variables used in estimating the LPR tempvar case_id den_lpr gen `case_id' = _n /* generate temporary Case ID */ gen `den_lpr' = (1-`Y')*(1-`T') * if there are no covariates (X) or no interaction terms between Z and X if "`X'" == "" | "`model'" == "" | "`model'" == "no_interaction" { quietly { reg `Y' `Z' `X' if `touse' local nobs = e(N) est store num_reg reg `den_lpr' `Z' `X' if `touse' est store den_reg suest num_reg den_reg, vce(cluster `case_id') * estimate of the local persuation rate nlcom (local_persuasion_rate: ([num_reg_mean]`Z')/(-[den_reg_mean]`Z')) } tempname b V lpr se matrix `b' = r(b) matrix `V' = r(V) ereturn post `b' `V', obs(`nobs') esample(`touse') ereturn display, nopv scalar `lpr' = r(table)[1,1] scalar `se' = r(table)[2,1] display " " display "Note: It is recommended to use {bf:persuasio} for causal inference." display " " ereturn scalar lpr_coef = `lpr' ereturn scalar lpr_se = `se' ereturn local outcome `Y' ereturn local treatment `T' ereturn local instrument `Z' ereturn local covariates `X' ereturn local model `model' } * if there are interaction terms between Z and X if "`X'" != "" & "`model'" == "interaction" { tempvar `Y'_1 `Y'_0 `T'_1 `T'_0 `den_lpr'_1 `den_lpr'_0 quietly { foreach var in `Y' `T' `den_lpr' { foreach value in 0 1 { reg `var' `X' if `Z'==`value' & `touse' predict ``var'_`value'' if `touse' replace ``var'_`value'' = min(max(``var'_`value'',0),1) } } } tempvar thetahat_num thetahat_den gen `thetahat_num' = ``Y'_1' - ``Y'_0' gen `thetahat_den' = ``den_lpr'_0' - ``den_lpr'_1' tempname lpr_num lpr_den quietly sum `thetahat_num' if `touse' scalar `lpr_num' = r(mean) quietly sum `thetahat_den' if `touse' scalar `lpr_den' = r(mean) local nobs = r(N) tempname lpr b se scalar `lpr' = `lpr_num'/`lpr_den' scalar `se' = . matrix `b' = `lpr' matrix colnames `b' = local_persuasion_rate ereturn post `b', obs(`nobs') esample(`touse') ereturn display, nopv display " " display "Notes: It is recommended to use {bf:persuasio} for causal inference." display " Standard errors are missing if model-interaction option is selected." display " " ereturn scalar lpr_coef = `lpr' ereturn scalar lpr_se = `se' ereturn local outcome `Y' ereturn local treatment `T' ereturn local instrument `Z' ereturn local covariates `X' ereturn local model `model' } display "Reference: Jun and Lee (2022), arXiv:1812.02276 [econ.EM]" end