Builds a design with one instrument, one binary explanatory variable, and one outcome.

## Arguments

- N
An integer. Sample size.

- type_probs
A vector of four numbers in [0,1]. Probability of each complier type (always-taker, never-taker, complier, defier).

- assignment_probs
A vector of four numbers in [0,1]. Probability of assignment to encouragement (Z) for each complier type (always-taker, never-taker, complier, defier). Under random assignment these are normally identical since complier status is not known to researchers in advance.

- a_Y
A real number. Constant in Y equation. Assumed constant across types. Overridden by

`a`

if specified.- b_Y
A real number. Effect of X on Y equation. Assumed constant across types. Overridden by

`b`

if specified.- d_Y
A real number. Effect of Z on Y. Assumed constant across types. Overridden by

`d`

if specified.- outcome_sd
A real number. The standard deviation of the outcome.

- a
A vector of four numbers. Constant in Y equation for each complier type (always-taker, never-taker, complier, defier).

- b
A vector of four numbers. Slope on X in Y equation for each complier type (always-taker, never-taker, complier, defier).

- d
A vector of four numbers. Slope on Z in Y equation for each complier type (non zero implies violation of exclusion restriction).

- args_to_fix
A character vector. Names of arguments to be args_to_fix in design.

## Value

A simple instrumental variables design with binary instrument, treatment, and outcome variables.

## Details

A researcher is interested in the effect of binary X on outcome Y. The relationship is confounded because units that are more likely to be assigned to X=1 have higher Y outcomes. A potential instrument Z is examined, which plausibly causes X. The instrument can be used to assess the effect of X on Y for units whose value of X depends on Z if Z does not negatively affect X for some cases, affects X positively for some, and affects Y only through X.

See vignette online for more details on estimands.

## Examples

```
# Generate a simple iv design: iv identifies late not ate
binary_iv_design_1 <- binary_iv_designer(N = 1000, b = c(.1, .2, .3, .4))
if (FALSE) {
diagnose_design(binary_iv_design_1)
}
# Generates a simple iv design with violation of monotonicity
binary_iv_design_2 <- binary_iv_designer(type_probs = c(.1,.1,.6, .2), b_Y = .5)
if (FALSE) {
diagnose_design(binary_iv_design_2)
}
# Generates a simple iv design with violation of exclusion restriction
binary_iv_design_3 <- binary_iv_designer(d_Y = .5, b_Y = .5)
if (FALSE) {
diagnose_design(binary_iv_design_3)
}
# Generates a simple iv design with violation of randomization
binary_iv_design_4 <- binary_iv_designer(N = 1000, assignment_probs = c(.2, .3, .7, .5), b_Y = .5)
if (FALSE) {
diagnose_design(binary_iv_design_4)
}
# Generates a simple iv design with violation of first stage
binary_iv_design_5 <- binary_iv_designer(type_probs = c(.5,.5, 0, 0), b_Y = .5)
if (FALSE) {
diagnose_design(binary_iv_design_5)
}
```