o_delta_boot_inf {robomit}

Bootstrapped mean delta* and confidence intervals

Description

Provides the mean and confidence intervals of bootstrapped delta*s, i.e., the degree of selection on unobservables relative to observables (with respect to the treatment variable) that would be necessary to eliminate the result (following Oster 2019).

Usage

o_delta_boot_inf(y, x, con, m = "none", w = NULL, id = "none", time = "none",
beta = 0, R2max, sim, obs, rep, CI, type, useed = NA, data)

Arguments

y

Name of the dependent variable (as string).

x

Name of the independent treatment variable (i.e., variable of interest; as string).

con

Name of related control variables. Provided as string in the format: "w + z +...".

m

Name of unrelated control variables (m; see Oster 2019; as string; default is m = "none").

w

weights (only for weighted estimations). Warning: For weighted panel models R can report different R-square than Stata, leading deviation between R and Stata results.

id

Name of the individual id variable (e.g. firm or farm; as string). Only applicable for fixed effect panel models.

time

Name of the time id variable (e.g. year or month; as string). Only applicable for fixed effect panel models.

beta

beta for which delta*s should be estimated (default is beta = 0)..

R2max

Maximum R-square for which delta*s should be estimated.

sim

Number of simulations.

obs

Number of draws per simulation.

rep

Bootstrapping either with (= TRUE) or without (= FALSE) replacement

CI

Confidence intervals, indicated as vector. Can be and/or 90, 95, 99.

type

Model type (either lm or plm; as string).

useed

User defined seed.

data

Dataset.

Details

Provides the mean and confidence intervals of bootstrapped delta*s, i.e., the degree of selection on unobservables relative to observables (with respect to the treatment variable) that would be necessary to eliminate the result (following Oster 2019). Bootstrapping can either be done with or without replacement. The function supports linear cross-sectional (see lm objects in R) and fixed effect panel (see plm objects in R) models.

Value

Returns tibble object, which includes the mean and confidence intervals of bootstrapped delta*s.

References

Oster, E. (2019). Unobservable Selection and Coefficient Stability: Theory and Evidence. Journal of Business & Economic Statistics, 37, 187-204.

Examples

# load data, e.g. the in-build mtcars dataset
data("mtcars")
data_oster <- mtcars

# preview of data
head(data_oster)

# load robomit
require(robomit)

# compute the mean and confidence intervals of estimated bootstrapped delta*s
o_delta_boot_inf(y = "mpg",            # dependent variable
                 x = "wt",             # independent treatment variable
                 con = "hp + qsec",    # related control variables
                 beta = 0,             # beta
                 R2max = 0.9,          # maximum R-square
                 sim = 100,            # number of simulations
                 obs = 30,             # draws per simulation
                 rep = FALSE,          # bootstrapping with or without replacement
                 CI = c(90,95,99),     # confidence intervals
                 type = "lm",          # model type
                 useed = 123,          # seed
                 data = data_oster)    # dataset