# Create a binary instrumental variables design

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))

## Arguments

N | An integer. Sample size. |
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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 |

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

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

outcome_sd | A non negative number. Standard deviation on Y. |

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). |

## Value

A simple instrumental variables design.

## 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.

## 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) # }