overall function

Inference on Average Overall Effect Parameters

Inference on the average overall effect of the IV on the outcome, that on the treatment receipt, and the local average overall effect in the presence of network spillover of unknown form

overall(Y, D, Z, S, A, K = 1, bw = NULL, B = NULL, alp = 0.05)

Arguments

• Y: An n-dimensional outcome vector
• D: An n-dimensional binary treatment vector
• Z: An n-dimensional binary instrumental vector
• S: An n-dimensional logical vector to indicate whether each unit belongs to the sub-population S
• A: An n times n symmetric binary adjacency matrix
• K: A scalar to indicate the range of neighborhood used for constructing the interference set. Default is 1.
• bw: A scalar of the bandwidth used for the HAC estimation and the wild bootstrap. If bw = NULL, the rule-of-thumb bandwidth proposed by Leung (2022) is used. Default is NULL.
• B: The number of bootstrap repetitions. If B = NULL, the wild bootstrap is skipped. Default is NULL.
• alp: The significance level. Default is 0.05.

Returns

A data.frame containing the following elements: - est: The parameter estimate

• HAC_SE: The standard error computed by the network HAC estimation

• HAC_CI_L: The lower bound of the confidence interval computed by the network HAC estimation

• HAC_CI_U: The upper bound of the confidence interval computed by the network HAC estimation

• wild_SE: The standard error computed by the wild bootstrap

• wild_CI_L: The lower bound of the confidence interval computed by the wild bootstrap

• wild_CI_U: The upper bound of the confidence interval computed by the wild bootstrap

• bw: The bandwidth used for the HAC estimation and the wild bootstrap

• size: The size of the subpopulation S

Details

The overall() function estimates the average overall effect of the IV on the outcome, that on the treatment receipt, and the local average overall effect via inverse probability weighting in the approximate neighborhood interference framework. The function also computes the standard errors and the confidence intervals for the target parameters based on the network HAC estimation and the wild bootstrap. For more details, see Hoshino and Yanagi (2023). The lengths of Y, D, Z, S and of the row and column of A must be the same. K must be a positive integer. bw must be NULL or a non-negative number. B must be NULL or a positive number. alp must be a positive number between 0 and 0.5.

Examples

# Generate artificial data
set.seed(1)
n <- 2000
data <- latenetwork::datageneration(n = n)

# Arguments
Y   <- data$Y
D   <- data$D
Z   <- data$Z
S   <- rep(TRUE, n)
A   <- data$A
K   <- 1
bw  <- NULL
B   <- NULL
alp <- 0.05

# Estimation
latenetwork::overall(Y = Y,
                     D = D,
                     Z = Z,
                     S = S,
                     A = A,
                     K = K,
                     bw = bw,
                     B = B,
                     alp = alp)

References

Hoshino, T., & Yanagi, T. (2023). Causal inference with noncompliance and unknown interference. arXiv preprint arXiv:2108.07455.

Leung, M.P. (2022). Causal inference under approximate neighborhood interference. Econometrica, 90(1), pp.267-293.