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

binary_iv_designer(N = 100, type_probs = c(1/3, 1/3, 1/3, 0),
assignment_probs = c(0.5, 0.5, 0.5, 0.5), a_Y = 1, b_Y = 0,
d_Y = 0, outcome_sd = 1, a = c(1, 0, 0, 0) * a_Y, b = rep(b_Y,
4), d = rep(d_Y, 4), args_to_fix = NULL)

## Arguments

N An integer. Sample size. A vector of four numbers in [0,1]. Probability of each complier type (always-taker, never-taker, complier, defier). 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 real number. Constant in Y equation. Assumed constant across types. Overridden by a if specified. A real number. Effect of X on Y equation. Assumed constant across types. Overridden by b if specified. A real number. Effect of Z on Y. Assumed constant across types. Overridden by d if specified. A real number. The standard deviation of the outcome. A vector of four numbers. Constant in Y equation for each complier type (always-taker, never-taker, complier, defier). A vector of four numbers. Slope on X in Y equation for each complier type (always-taker, never-taker, complier, defier). A vector of four numbers. Slope on Z in Y equation for each complier type (non zero implies violation of exclusion restriction). 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))# NOT RUN {
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)# NOT RUN {
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)# NOT RUN {
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)# NOT RUN {
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)# NOT RUN {
diagnose_design(binary_iv_design_5)
# }


## Author

DeclareDesign Team