Stats Regression instrumentalvariables

Home › Stats-Regression › Instrumental variables

InstrumentalVariables

Instrumental-variables regression: two-stage least squares, LIML and two-step GMM, at linearmodels parity.

public static class InstrumentalVariables

Example — one exogenous regressor, one endogenous, two instruments.

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);

IvSummary summary = InstrumentalVariables.TwoStageLeastSquares(design);

double effect = summary.Coefficients[2];     // => 1.9054825408…
double error = summary.StandardErrors[2];    // => 0.0310248100…
double strength = summary.FirstStage[0].PartialRSquared;  // => 0.9933…

Remarks — the coefficients run as linearmodels reports them: the constant when IvOptions.WithIntercept adds it, the exogenous regressors, then the endogenous ones. The default covariance is robust, as the reference's fit() is, where OrdinaryLeastSquares defaults to the unadjusted one as statsmodels does: each follows its own reference.

The three estimators share one design and one options record, and an option the fit would not read is refused rather than ignored: IvOptions.Fuller outside LIML, the GmmWeight options outside GMM, and a kernel or bandwidth without the kernel covariance or weight that reads it.

Applies to — net10.0, netstandard2.0.

See also — IvSummary, IvOptions, the instrumental-variables index.

Members

Member	What it does
InstrumentalVariables.TwoStageLeastSquares	Fits two-stage least squares.
InstrumentalVariables.Liml	Fits limited-information maximum likelihood, with Fuller's correction.
InstrumentalVariables.Gmm	Fits two-step GMM with a chosen weight matrix.