Z_validity_test: A Test for Instrument Validity

In CarrThomas/TestforInstrumentValidity: A Test for Instrument Validity

Description

Z_validity_test performs the test for instrument validity described in Kitagawa (2015) in the case of a binary treatment, an instrument that can take many values, and no conditioning covariates.

Usage

Z_validity_test(Y, D, Z, Z_order, xis, B = 500, alpha = c(0.1, 0.05, 0.01))

Arguments

Y	A vector containing observations of the outcome variable.
D	A vector containing observations of the treatment variable.
Z	A vector containing observations of the instrument variable.
Z_order	A vector containing the unique values of the instrument variable ordered so that the propensity score is increasing with the value of the instrument. For example, if the instrument takes values 1, 2, 3 and we belive that P(D=1|Z=1) < P(D=1|Z=2) < P(D=1|Z=3), then Z_order would be c(1, 2, 3).
xis	A vector containing values of the trimming constant. Individual entries should be >0. For example, c(0.05, 0.1, 0.3, 0.5).
B	The number of bootstrap iterations when constructing standard errors. Defaults to 500.
alpha	A vector of significance levels for which critical values will be calculated. Each entry should be between 0 and 1. By default, critical values are returned for the 10%, 5% and 1% levels of significance.

Details

a

Value

Returns a list with entries

teststat	A vector with length(xis) entries containing the value of the test statistic corresponding to each value of the trimming constant.
pvals	A vector of with length(xis) containing the p-value corresponding to each value of the trimming constant.
cvs	A matrix with length(alpha) rows and length(xis) columns. Entry (i,j) is the critical value for significance level alpha[i] when the trimming constant is xis[j].

Examples

## Example where the null is valid

set.seed(1234);
Z <- c(rep(1, 1000), rep(0, 1000));
D <- rbinom(2000, 1, 1 / 2);
Y <- D + rnorm(2000);

xis <- c(sqrt(0.005 * (1 - 0.005)), sqrt(0.05 * (1 - 0.05)), sqrt(0.1 * (1 - 0.1)), 1);
Z_validity_test(Y, D, Z, c(0, 1), xis)

# Returns
$teststat
[1] 3.1702131 2.1545545 1.5652476 0.4695743

$pvals
[1] 0.710 0.912 0.978 0.984

$cvs
        [,1]     [,2]     [,3]     [,4]
90% 3.855944 3.449081 3.218573 1.274559
95% 4.036757 3.693522 3.532302 1.408723
99% 4.245746 4.039350 3.953901 1.677051

## Example where the null is not valid

set.seed(5678);
Z <- c(rep(1, 1000), rep(0, 1000));
D <- rbinom(2000, 1, 0.55 * Z + 0.45 * (1 - Z));
Y <- (1 - D * (1 - Z)) * rnorm(2000) + D * (1 - Z) * rnorm(2000, -0.7, 1);

xis <- c(sqrt(0.005 * (1 - 0.005)), sqrt(0.05 * (1 - 0.05)), sqrt(0.1 * (1 - 0.1)), 1);
Z_validity_test(Y, D, Z, c(0, 1), xis)

# Returns
$teststat
[1] 7.261042 7.261042 7.261042 2.593839

$pvals
[1] 0 0 0 0

$cvs
        [,1]     [,2]     [,3]     [,4]
90% 3.868514 3.466813 3.282482 1.299155
95% 4.059778 3.718391 3.624888 1.431084
99% 4.331277 4.254834 4.018666 1.744133

CarrThomas/TestforInstrumentValidity documentation built on July 1, 2020, 12:05 a.m.