Home › Stats-Regression › Instrumental-variables data

IvCovarianceType

How an instrumental-variables fit estimates the covariance of its coefficients: linearmodels' four.

public enum IvCovarianceType

Members — Unadjusted assumes one variance for every error, s²·(x̂ᵀx̂)⁻¹. Robust is White's estimator over the projected regressors, and the default. Kernel lets the errors be correlated along the row order as well, weighting lags by IvOptions.Kernel up to its bandwidth. Clustered lets errors correlate inside a cluster and treats clusters as independent; it needs the overloads that take labels.

Example — the same fit under two covariances.

using Lodestar.Stats.Regression;
using Lodestar.Stats.Regression.Instrumental;

double[] response = [3.1, 4.0, 5.2, 4.4, 6.9, 7.1, 6.0, 8.8, 9.1, 8.2, 10.7, 11.3];
double[] exogenous = [0.2, -1.0, 0.5, 1.3, -0.4, 0.9, -1.2, 0.1, 1.7, -0.6, 0.8, -0.3];
double[] endogenous = [1.0, 1.4, 2.1, 1.8, 3.0, 3.3, 2.6, 3.9, 4.2, 3.7, 4.9, 5.4];
double[] instruments =
    [0.9, 0.1, 1.5, -0.3, 2.2, 0.4, 1.7, 0.8, 3.1, -0.2, 3.3, 0.6,
     2.4, 1.1, 3.8, -0.5, 4.1, 0.9, 3.5, 0.2, 4.6, -0.1, 5.2, 0.7];

var design = new IvDesign(response, exogenous, 1, endogenous, 1, instruments, 2);

int[] clusters = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6];
IvSummary robust = InstrumentalVariables.TwoStageLeastSquares(design);
IvSummary clustered = InstrumentalVariables.TwoStageLeastSquares(
    design, clusters, new IvOptions { CovarianceType = IvCovarianceType.Clustered });

double robustError = robust.StandardErrors[2];        // => 0.0310248100…
double clusteredError = clustered.StandardErrors[2];  // => 0.0192193492…

Remarks — its own type rather than CovarianceType, whose HC1 to HC3 have no counterpart in the reference. The clustered covariance takes its small-sample factor G/(G−1)·(n−1)/(n−k) only when Debiased is set, as the reference's does; statsmodels applies the same factor by default. Under every choice the coefficients are read against the normal unless Debiased is set, including Unadjusted.

Applies to — net10.0, netstandard2.0.

See also — IvOptions, KernelType.