TwoSLS

Closed-form linear IV / two-stage least squares

from _api_doc_utils import *

1 Where it fits

Group: Causal inference

TwoSLS estimates linear instrumental-variables models. With endogenous regressors \(X_e\), exogenous controls \(X_c\), instruments \(Z\), and outcome \(y\), it runs the projection of the second-stage design on the instrument span and then estimates

\[ y = \alpha + X_e\beta_e + X_c\beta_c + u. \]

It supports multiple endogenous regressors and excluded instruments.

2 Python API

Constructor: cm.TwoSLS

Call fit(x_endog, x_exog, z, y). The predict(x) method expects a second-stage design matrix matching the fitted endogenous+exogenous columns. The robust linear covariance options match OLS: vanilla, hc1, newey_west, and cluster.

print(inspect.signature(cm.TwoSLS))

()

cls = cm.TwoSLS
display(HTML(html_table(["Public method"], public_methods(cls))))

Public method
bootstrap(self, /, n_bootstrap, seed=None)
fit(self, /, x_endog, x_exog, z, y)
fit_sketch(self, /, x_endog, x_exog, z, y, sketch_size, seed=None)
fit_weighted(self, /, x_endog, x_exog, z, y, sample_weight)
predict(self, /, x)
summary(self, /, vcov='hc1', lags=None, clusters=None)

3 Minimal example

rng=np.random.default_rng(9); n=400
z=rng.normal(size=(n,2)); x_exog=rng.normal(size=(n,1)); v=rng.normal(size=(n,1)); u=.6*v[:,0]+rng.normal(scale=.4,size=n)
x_endog=z@np.array([[.8],[-.4]])+.2*x_exog+v; y=.5+1.2*x_endog[:,0]-.7*x_exog[:,0]+u
model=cm.TwoSLS(); model.fit(x_endog,x_exog,z,y)
print(model.summary()["coef"])
print(model.summary(vcov="newey_west", lags=3)["coef_se"])

[ 1.22456127 -0.6589091 ]
[0.04054546 0.03621148]

4 summary() contract

The table below is generated by fitting the live class in this repository and then inspecting summary(). Shapes are shown because most values are plain NumPy arrays or scalars.

rng=np.random.default_rng(109); n=120; z=rng.normal(size=(n,2)); x_exog=rng.normal(size=(n,1)); v=rng.normal(size=(n,1)); x_endog=z@np.array([[.8],[-.4]])+.2*x_exog+v; y=.5+1.2*x_endog[:,0]-.7*x_exog[:,0]+.6*v[:,0]+rng.normal(size=n)*.4
model=cm.TwoSLS(); model.fit(x_endog,x_exog,z,y)
summary = model.summary()
display(HTML(html_table(["summary() key", "shape"], summary_shape_rows(summary))))

summary() key	shape
intercept	()
coef	(2,)
intercept_se	()
coef_se	(2,)
vcov_type	()