Generalised weak instrument test

Tests for weak instruments with multiple endogenous regressors using the generalised minimum eigenvalue statistic of Lewis and Mertens (2025). The test is robust to heteroskedasticity and autocorrelation and nests the classical Stock-Yogo (2005) test as a special case. The function is a direct port from the Matlab codes by Lewis and Mertens (2025)

Usage

gweakivtest(
  y,
  Y,
  X,
  Z,
  cov_type = "EHW",
  alfa = 0.05,
  tau = 0.1,
  points = 1000L,
  target = "beta",
  crit = "abs"
)

Arguments

y

Regressand (T x 1 numeric vector or matrix).

Y

Endogenous regressors (T x N numeric matrix).

X

Exogenous regressors (T x Nx numeric matrix). A constant column is added automatically if one is absent or if X has zero columns.

Z

Instruments (T x K numeric matrix). Requires K >= N.

cov_type

HAR covariance estimator: "EHW" (Eicker-Huber-White, default) or "NW" (Newey-West with Lazarus et al. (2018) bandwidth).

alfa

Nominal significance level (default 0.05).

tau

Bias tolerance: maximum acceptable relative (or absolute, see crit) bias of the 2SLS estimator (default 0.10).

points

Number of random starting points for the Stiefel manifold optimisation used to compute the sharp critical value when K > N + 1 (default 1000).

target

Either "beta" (default) to test the full coefficient vector, or a positive integer j <= N to target the single coefficient beta_j.

crit

Bias criterion: "abs" (absolute bias, default) or "rel" (relative bias). "abs" requires the error covariance matrix; "rel" does not.

Value

A named list with the following elements:

nobs

Number of complete observations used.

beta_2SLS

2SLS point estimate(s).

target

Description of the targeted parameter.

criterion

Bias criterion used ("abs" or "rel").

gmin_generalized

Generalised minimum eigenvalue test statistic (Lewis-Mertens).

gmin_generalized_critical_value

Sharp critical value via Stiefel optimisation.

gmin_generalized_critical_value_simplified

Conservative simplified critical value (closed-form bound).

stock_yogo_test_statistic

Stock-Yogo test statistic under the Nagar approximation.

stock_yogo_critical_value_nagar

Stock-Yogo critical value under the Nagar approximation.

References

Lazarus, E., Lewis, D. J., Stock, J. H. and Watson, M. W. (2018). HAR inference: recommendations for practice. Journal of Business & Economic Statistics, 36(4), 541–559.

Lewis, D. J. and Mertens, K. (2025). A robust test for weak instruments for 2SLS with multiple endogenous regressors. The Review of Economic Studies, DOI: 10.1093/restud/rdaf103.

Stock, J. H. and Yogo, M. (2005). Testing for weak instruments in linear IV regression. In D. W. K. Andrews and J. H. Stock (Eds.), Identification and inference for econometric models: essays in honor of Thomas Rothenberg, pp. 80–108. Cambridge University Press.