anderson_rubin

class weak_instruments.anderson_rubin.ARTestResult(ar_stat: float, p_val: float)

Bases: object

Stores results for the Anderson-Rubin (AR) test.

ar_stat

The Anderson-Rubin test statistic.

Type:

float

p_val

The p-value for the test statistic.

Type:

float

summary()

Prints a summary of the Anderson-Rubin test results in a tabular format.

__getitem__(key)

Allows dictionary-like access to ARTestResult attributes.

__repr__()

Returns a string representation of the ARTestResult object.

summary()

Prints a summary of the Anderson-Rubin test results in a tabular format.

weak_instruments.anderson_rubin.ar_test(Y: ndarray, X: ndarray, Z: ndarray, b: ndarray, talk: bool = False) → ARTestResult

Calculates the Jackknife Anderson-Rubin (AR) test with cross-fit variance as described in Mikusheva and Sun (2022).

Parameters:

  • Y (np.ndarray) – A 1-D numpy array of the dependent variable (N,).

  • X (np.ndarray) – A 2-D numpy array of the endogenous regressors (N, L).

  • Z (np.ndarray) – A 2-D numpy array of the instruments (N, K), where K > L.

  • b (np.ndarray) – A 1-D numpy array of the parameter values to test (L,).

  • talk (bool, optional) – If True, provides detailed output for debugging purposes. Default is False.

Returns:

An object containing the following attributes:

  • ar_stat (float): The Anderson-Rubin test statistic.

  • p_val (float): The p-value for the test statistic.

Return type:

ARTestResult

Raises:

ValueError – If the dimensions of Y, X, Z, or b are inconsistent or invalid.

Notes

  • The Anderson-Rubin test is a robust inference method for instrumental variables models, particularly in the presence of many or weak instruments.

  • This implementation uses a jackknife approach with cross-fit variance estimation as recommended by Mikusheva and Sun (2022).

  • The function computes the AR test statistic and its p-value under the null hypothesis that the parameter vector b is the true value.

  • The test is robust to weak identification and is valid even when the number of instruments is large relative to the sample size.

Example

>>> import numpy as np
>>> from weak_instruments.anderson_rubin import ar_test
>>> Y = np.array([1, 2, 3])
>>> X = np.array([[1], [2], [3]])
>>> Z = np.array([[1, 0], [0, 1], [1, 1]])
>>> b = np.array([0.5])
>>> result = ar_test(Y, X, Z, b)
>>> print(result)