Create a binary instrumental variables design

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

Usage

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.

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.

Author

DeclareDesign Team

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)
}