Feiv

Feiv(
    FixestFormula,
    data,
    ssc_dict,
    drop_singletons,
    drop_intercept,
    weights,
    weights_type,
    collin_tol,
    lookup_demeaned_data,
    solver='scipy.linalg.solve',
    demeaner=None,
    lookup_preconditioner=None,
    store_data=True,
    copy_data=True,
    lean=False,
    context=0,
    sample_split_var=None,
    sample_split_value=None,
)

Non user-facing class to estimate an IV model using a 2SLS estimator.

Inherits from the Feols class. Users should not directly instantiate this class, but rather use the feols() function. Note that no demeaning is performed in this class: demeaning is performed in the FixestMulti class (to allow for caching of demeaned variables for multiple estimation).

Parameters

Name	Type	Description	Default
Y	np.ndarray	Dependent variable, a two-dimensional np.array.	required
X	np.ndarray	Independent variables, a two-dimensional np.array.	required
endgvar	np.ndarray	Endogenous Indenpendent variables, a two-dimensional np.array.	required
Z	np.ndarray	Instruments, a two-dimensional np.array.	required
weights	np.ndarray	Weights, a one-dimensional np.array.	required
coefnames_x	list	Names of the coefficients of X.	required
coefnames_z	list	Names of the coefficients of Z.	required
collin_tol	float	Tolerance for collinearity check.	required
solver	Literal['np.linalg.lstsq', 'np.linalg.solve', 'scipy.linalg.solve', 'scipy.sparse.linalg.lsqr']	“scipy.sparse.linalg.lsqr”], default is “scipy.linalg.solve”. Solver to use for the estimation.	'scipy.linalg.solve'
demeaner	Optional[AnyDemeaner]	Resolved typed demeaner configuration.	None
weights_name	Optional[str]	Name of the weights variable.	required
weights_type	Optional[str]	Type of the weights variable. Either “aweights” for analytic weights or “fweights” for frequency weights.	required

Attributes

Name	Type	Description
_Z	np.ndarray	Processed instruments after handling multicollinearity.
_weights_type_feiv	str	Type of the weights variable defined in Feiv class. Either “aweights” for analytic weights or “fweights” for frequency weights.
_coefnames_z	list	Names of coefficients for Z after handling multicollinearity.
_collin_vars_z	list	Variables identified as collinear in Z.
_collin_index_z	list	Indices of collinear variables in Z.
_is_iv	bool	Indicator if instrumental variables are used.
_support_crv3_inference	bool	Indicator for supporting CRV3 inference.
_support_iid_inference	bool	Indicator for supporting IID inference.
_tZX	np.ndarray	Transpose of Z times X.
_tXZ	np.ndarray	Transpose of X times Z.
_tZy	np.ndarray	Transpose of Z times Y.
_tZZinv	np.ndarray	Inverse of transpose of Z times Z.
_beta_hat	np.ndarray	Estimated regression coefficients.
_Y_hat_link	np.ndarray	Predicted values of the regression model.
_u_hat	np.ndarray	Residuals of the regression model.
_scores	np.ndarray	Scores used in the regression.
_hessian	np.ndarray	Hessian matrix used in the regression.
_bread	np.ndarray	Bread matrix used in the regression.
_pi_hat	np.ndarray	Estimated coefficients from 1st stage regression
_X_hat	np.ndarray	Predicted values of the 1st stage regression
_v_hat	np.ndarray	Residuals of the 1st stage regression
_model_1st_stage	Any	feols object of 1st stage regression. It contains various results and diagnostics from the fixed effects OLS regression.
_endogvar_1st_stage	np.ndarray	Unweihgted Endogenous independent variable vector
_Z_1st_stage	np.ndarray	Unweighted instruments vector to be used for 1st stage
_non_exo_instruments	list	List of instruments name excluding exogenous independent vars.
__p_iv	scalar	Number of instruments listed in _non_exo_instruments
_f_stat_1st_stage	scalar	F-statistics of First Stage regression for evaluation of IV weakness. The computed F-statistics test the following null hypothesis : # H0 : beta_{z_1} = 0 & … & beta_{z_{p_iv}} = 0 where z_1, …, z_{p_iv} # are the instrument variables # H1 : H0 does not hold Note that this F-statistics is adjusted to heteroskedasticity / clusters if users set specification of variance-covariance matrix type
_eff_F	scalar	Effective F-statistics of first stage regression as in Olea and Pflueger 2013
_data	pd.DataFrame	The data frame used in the estimation. None if arguments lean = True or store_data = False.

Raises

Name	Type	Description
	ValueError	If Z is not a two-dimensional array.

Examples

Feiv is returned by feols() when the formula includes an IV part, i.e. depvar ~ exog | fe | endog ~ instrument.

import pyfixest as pf

fit = pf.feols("Y ~ X2 | f1 | X1 ~ Z1", pf.get_data())
fit.tidy()

	Estimate	Std. Error	t value	Pr(>|t|)	2.5%	97.5%
Coefficient
X2	-0.174227	0.017599	-9.899554	0.0	-0.208764	-0.139689
X1	-0.992187	0.104775	-9.469663	0.0	-1.197801	-0.786574

The first stage F-statistic is stored on the fitted object.

fit._f_stat_1st_stage

647.2703851604904

See the instrumental variables tutorial for details.

Methods

Name	Description
Feiv.IV_Diag	Implement IV diagnostic tests.
Feiv.IV_weakness_test	Implement IV weakness test (F-test).
Feiv.demean	Demean instruments and endogeneous variable.
Feiv.drop_multicol_vars	Drop multicollinear variables in matrix of instruments Z.
Feiv.eff_F	Compute Effective F stat (Olea and Pflueger 2013).
Feiv.first_stage	Implement First stage regression.
Feiv.get_fit	Fit a IV model using a 2SLS estimator.
Feiv.to_array	Transform estimation DataFrames to arrays.
Feiv.wls_transform	Transform variables for WLS estimation.

Feiv.IV_Diag

IV_Diag(statistics=None)

Implement IV diagnostic tests.

Notes

This method covers diagnostic tests related with IV regression. We currently have IV weak tests only. More test will be updated in future updates!

Parameters

Name	Type	Description	Default
statistics	list[str]	List of IV diagnostic statistics	None

Example

The following is an example usage of this method:

::: {#4a7c1a7c .cell execution_count=3}
``` {.python .cell-code}
import numpy as np
import pandas as pd
from pyfixest.estimation import feols

# Set random seed for reproducibility
np.random.seed(1)

# Number of observations
n = 1000

# Simulate the data
# Instrumental variable
z = np.random.binomial(1, 0.5, size=n)
z2 = np.random.binomial(1, 0.5, size=n)

# Endogenous variable
d = 0.5 * z + 1.5 * z2 + np.random.normal(size=n)

# Control variables
c1 = np.random.normal(size=n)
c2 = np.random.normal(size=n)

# Outcome variable
y = 1.0 + 1.5 * d + 0.8 * c1 + 0.5 * c2 + np.random.normal(size=n)

# Cluster variable
cluster = np.random.randint(1, 50, size=n)
weights = np.random.uniform(1, 3, size=n)

# Create a DataFrame
data = pd.DataFrame({
    'd': d,
    'y': y,
    'z': z,
    'z2': z2,
    'c1': c1,
    'c2': c2,
    'cluster': cluster,
    'weights': weights
})

vcov_detail = "iid"

# Fit OLS model
fit_ols = feols("y ~ 1 + d + c1 + c2", data=data, vcov=vcov_detail)

# Fit IV model
fit_iv = feols("y ~ 1 + c1 + c2 | d ~ z", data=data,
         vcov=vcov_detail,
         weights="weights")
fit_iv.first_stage()
F_stat_pf = fit_iv._f_stat_1st_stage
fit_iv.IV_Diag()
F_stat_eff_pf = fit_iv._eff_F

print("(Unadjusted) F stat :", F_stat_pf)
print("Effective F stat :", F_stat_eff_pf)
```

::: {.cell-output .cell-output-stdout}
```
(Unadjusted) F stat : 52.81535560457474
Effective F stat : 48.61288119858675
```
:::
:::

Feiv.IV_weakness_test

IV_weakness_test(iv_diag_statistics=None)

Implement IV weakness test (F-test).

This method covers hetero-robust and clustered-robust F statistics. It produces two statistics:

• self._f_stat_1st_stage: F statistics of first stage regression
• self._eff_F: Effective F statistics (Olea and Pflueger 2013) of first stage regression

Notes

“self._f_stat_1st_stage” is adjusted to the specification of vcov. If vcov_detail = “iid”, F statistics is not adjusted, otherwise it is always adjusted.

Parameters

Name	Type	Description	Default
iv_diag_statistics	list	List of IV weakness statistics	None

Feiv.demean

demean()

Demean instruments and endogeneous variable.

Feiv.drop_multicol_vars

drop_multicol_vars()

Drop multicollinear variables in matrix of instruments Z.

Feiv.eff_F

eff_F()

Compute Effective F stat (Olea and Pflueger 2013).

Feiv.first_stage

first_stage()

Implement First stage regression.

Feiv.get_fit

get_fit()

Fit a IV model using a 2SLS estimator.

Feiv.to_array

to_array()

Transform estimation DataFrames to arrays.

Feiv.wls_transform

wls_transform()

Transform variables for WLS estimation.