iv.sensemakr implements a suite of sensitivity analysis tools for instrumental variable estimates, as discussed in Cinelli, C. and Hazlett, C. (2025) “An Omitted Variable Bias Framework for Sensitivity Analysis of Instrumental Variables”, Biometrika (doi:10.1093/biomet/asaf004; PDF).
News
Package website is now online.
Paper published in Biometrika. You can find a free version here..
Watch the video of the talk at PCIC.
Watch the video of the talk at JSM.
Development version
To install the development version on GitHub make sure you have the package devtools installed.
# install.packages("devtools")
devtools::install_github("carloscinelli/iv.sensemakr")Please also make sure you have the latest version of sensemakr installed.
# install.packages("devtools")
devtools::install_github("carloscinelli/sensemakr")Basic usage
# loads package
library(iv.sensemakr)
# loads dataset
data("card")
# prepares data
y <- card$lwage # outcome
d <- card$educ # treatment
z <- card$nearc4 # instrument
x <- model.matrix( ~ exper + expersq + black + south + smsa + reg661 + reg662 +
reg663 + reg664 + reg665+ reg666 + reg667 + reg668 + smsa66,
data = card) # covariates
# fits IV model
card.fit <- iv_fit(y,d,z,x)
# see results
card.fit
#>
#> Instrumental Variable Estimation
#> (Anderson-Rubin Approach)
#> =============================================
#> IV Estimates:
#> Coef. Estimate: 0.132
#> t-value: 2.33
#> p-value: 0.02
#> Conf. Interval: [0.025, 0.285]
#> Note: H0 = 0, alpha = 0.05, df = 2994.
#> =============================================
#> See summary for first stage and reduced form.
# runs sensitivity analysis
card.sens <- sensemakr(card.fit, benchmark_covariates = c("black", "smsa"))
# see results
card.sens
#>
#> Sensitivity Analysis for Instrumental Variables
#> (Anderson-Rubin Approach)
#> =============================================================
#> IV Estimates:
#> Coef. Estimate: 0.132
#> t-value: 2.33
#> p-value: 0.02
#> Conf. Interval: [0.025, 0.285]
#>
#> Sensitivity Statistics:
#> Extreme Robustness Value: 0.000523
#> Robustness Value: 0.00667
#>
#> Bounds on Omitted Variable Bias:
#> Bound Label R2zw.x R2y0w.zx Lower CI Upper CI Crit. Thr.
#> 1x black 0.00221 0.0750 -0.0212 0.402 2.59
#> 1x smsa 0.00639 0.0202 -0.0192 0.396 2.57
#>
#> Note: H0 = 0, q >= 1, alpha = 0.05, df = 2994.
#> =============================================================
#> See summary for first stage and reduced form.
# sensitivity contour plot
plot(card.sens, lim = 0.09)
# latex code for sensitivity table
ovb_minimal_reporting(card.sens, outcome_label = "lwage", treatment_label = "educ")
#> \begin{table}[!h]
#> \centering
#> \begin{tabular}{lrrrrrr}
#> \multicolumn{7}{c}{Outcome: \textit{lwage}} \\
#> \hline \hline
#> Treatment: & Est. & Lower CI & Upper CI & t-value & $XRV_{q = 1, \alpha = 0.05}$ & $RV_{q = 1, \alpha = 0.05}$ \\
#> \hline
#> \textit{educ} & 0.132 & 0.025 & 0.285 & 2.327 & 0.1\% & 0.7\% \\
#> \hline
#> df = 2994 & & \multicolumn{5}{r}{ \small \textit{Bound (1x black)}: $R^2_{Z\sim W| {\bf X}}$ = 0.2\%, $R^2_{Y(0)\sim W| Z, {\bf X}}$ = 7.5\%} \\
#> \end{tabular}
#> \end{table}
# html code for sensitivity table
ovb_minimal_reporting(card.sens, format = "pure_html",
outcome_label = "lwage", treatment_label = "educ")| Outcome: lwage | ||||||
|---|---|---|---|---|---|---|
| Treatment | Est. | Lower CI | Upper CI | t-value | XRVq = 1, α = 0.05 | RVq = 1, α = 0.05 |
| educ | 0.132 | 0.025 | 0.285 | 2.327 | 0.1% | 0.7% |
| Note: df = 2994; Bound ( 1x black ): R2Z~W|X = 0.2%, R2Y(0)~W|Z,X = 7.5% | ||||||