Moment-inequality criterion and confidence set — morie_bnd_moment

Chernozhukov, Hong and Tamer (2007). The sample criterion Q_n(theta) = sum_j [sqrt(n) gbar_j / sd_j]_+^2 counts only VIOLATED inequalities, so deep inside the identified set – where every sample moment is negative – it is EXACTLY zero. The confidence region is the level set of Q_n under a multiplier bootstrap of the RECENTRED moments: the null sits at the boundary of the binding inequalities, not at the sample slack, and skipping the recentring makes the cutoff grow with slack.

Usage

morie_bnd_moment_inequality(
  data,
  g,
  theta_grid,
  alpha = 0.05,
  B = 500,
  seed = 0
)

Arguments

data: observations, rows passed to g.
g: function(data, theta) returning an (n, J) matrix oriented so the model says E[g_j] <= 0.
theta_grid: candidate parameter values.
alpha: miss probability.
B: multiplier-bootstrap draws.
seed: bootstrap seed.

Value

list: theta_grid, criterion, critical_value, in_confidence_set, set_estimate, confidence_set_bounds, n, J, method.

References

Chernozhukov, Hong and Tamer (2007), Econometrica 75:1243-1284; Andrews and Soares (2010), Econometrica 78:119-157.

Examples

set.seed(1)
d <- cbind(stats::rnorm(50, 1), stats::rnorm(50, 3))
g <- function(d, th) cbind(d[, 1] - th, th - d[, 2])
morie_bnd_moment_inequality(d, g, c(2))$criterion
#> [1] 0