Instrument relevance and exogeneity diagnostics

Identification needs \(E[U|Z] = 0\) (exogeneity) together with variation in X that Z explains (relevance). Both are reported and they fail in different ways: a weak but valid instrument gives large variance, while a strong but invalid one gives confident nonsense. Exogeneity is NOT testable without further restrictions – the returned correlation is a diagnostic against a supplied residual, not a test, and the key is named accordingly. Mirrors morie.fn.hrzinst.

Usage

morie_instrument_check(X, Z, U = NULL, y = NULL)

Arguments

X

numeric endogenous regressor(s).

Z

numeric instrument(s), same number of rows as X.

U

residuals for the exogeneity diagnostic.

y

response; residuals are formed by 2SLS when U is omitted.

Value

list: first_stage_r2, first_stage_F, relevant, corr_U_Z, exogeneity_testable, n, n_instruments, method.

References

Horowitz, Ch. 5, Sec. 5.3.

Examples

set.seed(1)
z <- rnorm(200)
morie_instrument_check(z + rnorm(200), z)$relevant
#> [1] TRUE