mwivhet: Inference with Many Weak Instruments and Heterogeneity

Inference in a linear instrumental variable regression model with many potentially weak instruments, in the presence of heterogeneous treatment effects. The package implements procedures from Yap (2025).

Please refer to the website for comprehensive details and a demonstration of the package functions.

Installation

You can install the development version from GitHub with:

if (!requireNamespace("remotes")) {
  install.packages("remotes")
}
remotes::install_github("minhnngo/mwivhet")

Citation

If you use mwivhet, please cite: https://doi.org/10.48550/arXiv.2408.11193

Simulation Demo

Judge Example without Covariates

library(mwivhet)
# Demo for judge example without covariates

# Numerator
LMnum <- GetLM_nocov(df = dnc, X = X, e = e, groupZ = group)

# L3O Variance
LMVar <- L3Ovar_gloop_nocov(df = dnc, group = group, X = X, e = e, MX = MX, Me = Me)

# t-statistic for LM test (compare with std normal)
LMt <- LMnum / sqrt(LMVar)

# Confidence Intervals
# Get coefficients first, then values
CI_coefs <- GetCIcoef_nocov(df = dnc, groupZ = group, X = X, Y = Y, MX = MX, MY = MY)
CI <- GetCIvals(CI_coefs)

print(paste("LM Statistic:", LMt))
#> [1] "LM Statistic: -0.790957868876291"
print("Confidence Interval:")
#> [1] "Confidence Interval:"
print(CI)
#> [1] -1.9568467  0.4052406

Quarter-of-Birth Example with Covariates (1)

# Demo for QOB example with covariates

# Numerator
# group indexes every QOB and groupW combination
LMnum <- GetLM(df = dc, X = X, e = e, groupW = groupW, group = group)

# Variance
LMVar <- L3Ovar_gloop_cov(df = dc, group = group, groupW = groupW, X = X, e = e, 
                          MX = MX, Me = Me)

# t-statistic for LM test
LMt <- LMnum / sqrt(LMVar)

# Confidence Intervals (Fast method)
CI_coefs <- GetL3OCIcoef_fast(df = dc, groupW = groupW, group = group, X = X, 
                              Y = Y, MX = MX, MY = MY)
CI <- GetCIvals(CI_coefs)

print(paste("LM Statistic:", LMt))
#> [1] "LM Statistic: 0.503840615057238"
print("Confidence Interval:")
#> [1] "Confidence Interval:"
print(CI)
#> [1] -0.5115206  0.6889379

Quarter-of-Birth Example with Covariates (2)

# Demo for QOB example with covariates, using stored G and P. Slower but allows continuous W, Z
# Would give the same results as previous example

# Construct G and P using the package function
GP <- GetGP(group = dc$group, groupW = dc$groupW, n = nrow(dc))

# Numerator
# Note: as.numeric ensures it returns a scalar, not a 1x1 matrix
LMnum <- as.numeric(t(dc$e) %*% GP$G %*% dc$X)

# L3O Variance
LMVar <- L3Ovar_iloop_cov(X = dc$X, e = dc$e, P = GP$P, G = GP$G)

# t-statistic
LMt <- LMnum / sqrt(LMVar)

# Confidence Intervals
CI_coefs <- GetCIcoef_iloop(df = dc, P = GP$P, G = GP$G, X = X, Y = Y, MX = MX, 
                            MY = MY, Z = GP$Z, W = GP$W, noisy = FALSE)
CI <- GetCIvals(CI_coefs)

print(paste("LM Statistic:", LMt))
#> [1] "LM Statistic: 0.503840615057238"
print("Confidence Interval:")
#> [1] "Confidence Interval:"
print(CI)
#> [1] -0.5115206  0.6889379