Mourifie-Wan (2017) test for instrument validity

Reformulates the testable implications of Kitagawa (2015) as a set of conditional moment inequalities and tests them in the intersection- bounds framework of Chernozhukov, Lee, and Rosen (2013). Without covariates x, iv_mw tests the same inequalities as iv_kitagawa and reduces exactly to the variance-weighted Kitagawa test. With covariates, iv_mw estimates the conditional CDFs F(y, d | X = x, Z = z) nonparametrically via series regression, computes plug-in heteroscedasticity-robust standard errors, and takes the sup over (y, x) of the variance-weighted positive-part violation. Critical values come from a multiplier bootstrap with adaptive moment selection in the style of Andrews and Soares (2010).

Usage

iv_mw(object, ...)

# Default S3 method
iv_mw(
  object,
  d,
  z,
  x = NULL,
  basis_order = 3L,
  x_grid_size = 20L,
  y_grid_size = 50L,
  adaptive = TRUE,
  grid = NULL,
  n_boot = 1000,
  alpha = 0.05,
  weights = NULL,
  parallel = TRUE,
  ...
)

# S3 method for class 'fixest'
iv_mw(
  object,
  x = NULL,
  basis_order = 3L,
  x_grid_size = 20L,
  y_grid_size = 50L,
  adaptive = TRUE,
  grid = NULL,
  n_boot = 1000,
  alpha = 0.05,
  weights = NULL,
  parallel = TRUE,
  ...
)

# S3 method for class 'ivreg'
iv_mw(
  object,
  x = NULL,
  basis_order = 3L,
  x_grid_size = 20L,
  y_grid_size = 50L,
  adaptive = TRUE,
  grid = NULL,
  n_boot = 1000,
  alpha = 0.05,
  weights = NULL,
  parallel = TRUE,
  ...
)

Arguments

object: For the default method: a numeric outcome vector. For the fixest and ivreg methods: a fitted instrumental variable model from fixest::feols or ivreg::ivreg().
...: Further arguments passed to methods.
d: Binary 0/1 treatment vector (default method only).
z: Discrete instrument (numeric or factor, default method only).
x: Optional numeric vector, matrix, or data frame of covariates. If supplied, the test is conditional on the first numeric column of x. If NULL, the test reduces to the unconditional Mourifie-Wan test.
basis_order: Polynomial order of the series-regression basis used to estimate F(y, d | X, Z). Default 3L (cubic). Set to "auto" to select the basis order by 5-fold cross-validation over the candidates 2, 3, 4, 5 with squared-error loss on the indicator regression. When "auto" is used, the bootstrap becomes post-selection-valid: the test statistic is compared to the maximum of the bootstrap statistics across the candidate orders, which controls size at the nominal level against any selection rule but is mildly conservative relative to a fixed-order test. Runtime with "auto" is approximately four times the fixed-order path.
x_grid_size: Number of quantile points of x at which to evaluate the conditional CDFs. Default 20.
y_grid_size: Number of quantile points of y at which to evaluate the inequalities. Default 50.
adaptive: Logical. If TRUE (default), the bootstrap uses the adaptive moment selection of Andrews-Soares (2010) with tuning parameter kappa_n = sqrt(log(log(n))). If FALSE, uses the plug-in least-favourable critical value (conservative).
grid: Deprecated. Ignored; use y_grid_size and x_grid_size instead.
n_boot: Number of multiplier-bootstrap replications. Default 1000.
alpha: Significance level for the returned verdict. Default 0.05.
weights: Optional survey weights. A non-negative numeric vector of length equal to the sample size. Scaled internally so the mean weight is 1.0 (preserving effective sample-size interpretation). Applied to the empirical CDFs, the bootstrap multiplier process, and the variance-weighted standard errors.
parallel: Logical. Run bootstrap replications in parallel on POSIX systems via parallel::mclapply. Default TRUE.

Value

An object of class iv_test; see iv_kitagawa for element descriptions. Additional elements:

conditional: Logical, whether covariates were supplied.
kappa_n: Andrews-Soares tuning parameter used (NA if not applicable).

Details

The CLR framework targets conditional moment inequalities of the form E[m(W; theta) | X] <= 0 for all X. Applied to Kitagawa's (2015) inequalities, the relevant moments are the positive-part differences of the conditional joint CDFs F(y, d | X, Z) for each (d, z_low, z_high, y, x) index. iv_mw estimates F(y, d | X, Z) by series regression of the indicator 1{Y <= y, D = d} on a polynomial basis of X within each Z cell. Robust standard errors come from the heteroscedasticity-consistent sandwich of the series regression. Critical values are drawn by multiplier bootstrap: the bootstrap process reuses the plug-in SE denominator and perturbs the residuals by Rademacher weights, projected back through the basis. Adaptive moment selection includes only moments whose observed studentised statistic is within kappa_n of the inequality boundary, giving tighter critical values when some inequalities are strictly slack.

References

Mourifie, I. and Wan, Y. (2017). Testing Local Average Treatment Effect Assumptions. Review of Economics and Statistics, 99(2), 305-313. doi:10.1162/REST_a_00622

Chernozhukov, V., Lee, S., and Rosen, A. M. (2013). Intersection Bounds: Estimation and Inference. Econometrica, 81(2), 667-737. doi:10.3982/ECTA8718

Imbens, G. W. and Angrist, J. D. (1994). Identification and Estimation of Local Average Treatment Effects. Econometrica, 62(2), 467-475. doi:10.2307/2951620

Examples

# \donttest{
set.seed(1)
n <- 500
z <- sample(0:1, n, replace = TRUE)
d <- rbinom(n, 1, 0.3 + 0.4 * z)
y <- rnorm(n, mean = d)
iv_mw(y, d, z, n_boot = 200, parallel = FALSE)
#> 
#> ── Mourifie-Wan (2017) ─────────────────────────────────────────────────────────
#> Sample size: 500
#> Statistic: "0.916", p-value: "1"
#> Verdict: cannot reject IV validity at 0.05
# }