tsls¶
- weak_instruments.tsls.TSLS(Y: ndarray[tuple[int, ...], dtype[float64]], X: ndarray[tuple[int, ...], dtype[float64]], Z: ndarray[tuple[int, ...], dtype[float64]], W: ndarray[tuple[int, ...], dtype[float64]] | None = None, talk: bool = False) TSLSResult ¶
Two-Stage Least Squares (2SLS) estimator for weak instruments.
- Parameters:
Y (NDArray[np.float64]) – A 1-D numpy array of the dependent variable (N,).
X (NDArray[np.float64]) – A 2-D numpy array of the endogenous regressors (N, L). Do not include the constant.
Z (NDArray[np.float64]) – A 2-D numpy array of the instruments (N, K), where K >= L. Do not include the constant.
W (NDArray[np.float64], optional) – A 2-D numpy array of the exogenous controls (N, G). Do not include the constant. Default is None.
talk (bool, optional) – If True, provides detailed output for teaching / debugging purposes. Default is False.
- Returns:
- An object containing the following attributes:
beta (NDArray[np.float64]): The estimated coefficients for the model.
r_squared (float): The R-squared value for the model.
adjusted_r_squared (float): The adjusted R-squared value for the model.
f_stat (float): The F-statistic for the model.
standard_errors (NDArray[np.float64]): The robust standard errors for the estimated coefficients.
root_mse (float): The root mean squared error.
pvals (list of float): p-values for coefficients.
tstats (list of float): t-statistics for coefficients.
cis (list of tuple): Confidence intervals for coefficients.
- Return type:
- Raises:
ValueError – If the dimensions of Y, X, or Z are inconsistent or invalid.
RuntimeWarning – If the number of instruments (columns in Z) is not greater than the number of regressors (columns in X).
Notes
The TSLS estimator is a classic instrumental variable estimator.
- The function performs two stages:
The first stage projects X onto the space spanned by Z (and W if provided).
The second stage regresses Y on the fitted values from the first stage.
Additional statistics such as R-squared, adjusted R-squared, and F-statistics are calculated for model evaluation.
If the number of endogenous regressors is 1, first-stage statistics (R-squared and F-statistic) are also computed.
Example
>>> import numpy as np >>> from weak_instruments.tsls import TSLS >>> Y = np.array([1, 2, 3]) >>> X = np.array([[1], [2], [3]]) >>> Z = np.array([[1, 0], [0, 1], [1, 1]]) >>> result = TSLS(Y, X, Z) >>> print(result.summary())
- class weak_instruments.tsls.TSLSResult(beta: ndarray[tuple[int, ...], dtype[float64]], r_squared: float = None, adjusted_r_squared: float = None, f_stat: float = None, standard_errors: ndarray[tuple[int, ...], dtype[float64]] = None, root_mse: float = None, pvals: ndarray[tuple[int, ...], dtype[float64]] | None = None, tstats: ndarray[tuple[int, ...], dtype[float64]] | None = None, cis: ndarray[tuple[int, ...], dtype[float64]] = None)¶
Bases:
object
Stores results for the TSLS estimator.
- beta¶
Estimated coefficients from the TSLS regression.
- Type:
NDArray[np.float64]
- r_squared¶
R-squared value.
- Type:
float
- adjusted_r_squared¶
Adjusted R-squared value.
- Type:
float
- f_stat¶
F-statistic for the model.
- Type:
float
- standard_errors¶
Robust standard errors.
- Type:
NDArray[np.float64]
- root_mse¶
Root mean squared error.
- Type:
float
- pvals¶
p-values for coefficients.
- Type:
NDArray[np.float64] or None
- tstats¶
t-statistics for coefficients.
- Type:
NDArray[np.float64] or None
- cis¶
Confidence intervals for coefficients.
- Type:
NDArray[np.float64] or None
- summary()¶
Prints a summary of the TSLS results in a tabular format similar to statsmodels OLS.