# Inference on Average Overall Effect Parameters

`overall.Rd`

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

## 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.

## Value

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.

## 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.

## 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)
#> est HAC_SE HAC_CI_L HAC_CI_U wild_SE wild_CI_L wild_CI_U bw
#> AOEY 0.8557528 0.09429867 0.6709308 1.0405748 NA NA NA 8
#> AOED 0.6449039 0.03744014 0.5715226 0.7182852 NA NA NA 8
#> ADED 0.3551812 0.02213500 0.3117974 0.3985650 NA NA NA 8
#> LAOE 2.4093413 0.27637076 1.8676646 2.9510181 NA NA NA 8
#> size
#> AOEY 2000
#> AOED 2000
#> ADED 2000
#> LAOE 2000
```