rlassomodels.RlassoIV

class rlassomodels.RlassoIV(*, select_X=True, select_Z=True, post=True, sqrt=False, fit_intercept=True, cov_type='nonrobust', x_dependent=False, random_state=None, lasso_psi=False, prestd=False, n_corr=5, max_iter=2, conv_tol=0.0001, n_sim=5000, c=1.1, gamma=None, solver='cd', cd_max_iter=1000, cd_tol=1e-10, cvxpy_opts=None, zero_tol=0.0001)

Rigorous Lasso for instrumental-variable estimation in the presence of high-dimensional instruments and/or controls. Uses the post-double-selection (PDS) and post-regularization (CHS) methods for estimation, see references below.

Parameters

select_X: bool, optional (default: True)

Whether to use lasso/post-lasso for feature selection of high-dim controls.

select_Z: bool, optional (default: True)

Whether to use lasso/post-lasso for feature selection of high-dim instruments.

post: bool, default=True

If True, post-lasso is used to estimate betas. Note that post will only affect the results for the post-regularization (CHS) method and not those of post-double-selection (pds).

sqrt: bool, default=False

If True, sqrt lasso criterion is minimized: loss = ||y - X @ beta||_2 / sqrt(n) see: Belloni, A., Chernozhukov, V., & Wang, L. (2011). Square-root lasso: pivotal recovery of sparse signals via conic programming. Biometrika, 98(4), 791-806.

fit_intercept: bool, default=True

If True, unpenalized intercept is estimated.

cov_type: str, default=”nonrobust”

Type of covariance matrix. “nonrobust” - nonrobust covariance matrix “robust” - robust covariance matrix “cluster” - cluster robust covariance matrix

x_dependent: bool, default=False

If True, the less conservative lambda is estimated by simulation using the conditional distribution of the design matrix.

n_sim: int, default=5000

Number of simulations to be performed for x-dependent lambda calculation.

random_state: int, default=None

Random seed used for simulations if x_dependent is True.

lasso_psi: bool, default=False

If True, post-lasso is not used to obtain the residuals during the iterative estimation procedure.

prestd: bool, default=False

If True, the data is prestandardized instead of on the fly by penalty loadings. Currently only supports homoscedastic case.

n_corr: int, default=5

Number of correlated variables to be used in the for initial calculation of the residuals.

c: float, default=1.1

slack parameter used for lambda calculation. From Hansen et.al. (2020): “c needs to be greater than 1 for the regularization event to hold asymptotically, but not too high as the shrinkage bias is increasing in c.”

gamma: float, optional=None

Regularization parameter. If not provided gamma is calculated as 0.1 / np.log(n_samples)

max_iter: int, default=2

Maximum number of iterations to perform in the iterative estimation procedure.

conv_tol: float, default=1e-4

Tolerance for the convergence of the iterative estimation procedure.

solver: str, default=”cd”

Solver to be used for the iterative estimation procedure. “cd” - coordinate descent “cvxpy” - cvxpy solver

cd_max_iter: int, default=10000

Maximum number of iterations to perform in the shooting algorithm.

cd_tol: float, default=1e-10

Tolerance for the coordinate descent algorithm.

cvxpy_opts: dict, default=None

Options to be passed to the cvxpy solver. See cvxpy documentation for more details: https://www.cvxpy.org/tutorial/advanced/index.html#solve-method-options

zero_tol: float, default=1e-4

Tolerance for the rounding of the coefficients to zero.

References

Chernozhukov, V., Hansen, C., & Spindler, M. (2015).

Post-selection and post-regularization inference in linear models with many controls and instruments. American Economic Review, 105(5), 486-90.

Belloni, A., Chernozhukov, V., & Hansen, C. (2014).

Inference on treatment effects after selection among high-dimensional controls. The Review of Economic Studies, 81(2), 608-650.

Ahrens, A., Hansen, C. B., & Schaffer, M. (2019).

PDSLASSO: Stata module for post-selection and post-regularization OLS or IV estimation and inference.

Attributes

results_: dict[“PDS”, “CHS”]

Dictionary containing the 2-stage-least-squares estimates. Values are linearmodels.iv.IV2SLS objects. See: https://bashtage.github.io/linearmodels/iv/iv/linearmodels.iv.model.IV2SLS.html https://bashtage.github.io/linearmodels/iv/examples/basic-examples.html

X_selected_: dict[list[str]]

List of selected controls for each stage in the estimation.

Z_selected_: list[str]

List of selected instruments.

valid_vars_: list[str]

List of variables for which standard errors and test statistics are valid.

fit(X, y, D_exog=None, D_endog=None, Z=None)

Fit the model.

Parameters

X: array-like, shape (n_samples, n_controls)

Control variables. Potentially high-dimensional.

y: array-like, shape (n_samples,)

Outcome/dependent variable.

D_exog: array-like, shape (n_samples, n_exog)

Low-dimensionnal exogenous regressors. On which inference is performed.

D_endog: array-like, shape (n_samples, n_endog)

Endogenous regressors. On which inference is performed.

Z: array-like, shape (n_samples, n_instruments)

Instruments. Potentially high-dimensional.

Returns

selfobject

Returns the instance itself.

summary()

Produces a summary of the results.