# estimation.models.feiv_.Feiv { #pyfixest.estimation.models.feiv_.Feiv } ```python estimation.models.feiv_.Feiv( FixestFormula, data, ssc_dict, drop_singletons, drop_intercept, weights, weights_type, collin_tol, lookup_demeaned_data, solver='scipy.linalg.solve', demeaner=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()](/reference/estimation.api.feols.feols.qmd) 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 {.doc-section .doc-section-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\[\'np.linalg.lstsq\', \'np.linalg.solve\', \'scipy.linalg.solve\', \'scipy.sparse.linalg.lsqr\', \'jax\'\] | "scipy.sparse.linalg.lsqr", "jax"], 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 {.doc-section .doc-section-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 {.doc-section .doc-section-raises} | Name | Type | Description | |--------|------------|--------------------------------------| | | ValueError | If Z is not a two-dimensional array. | ## Methods | Name | Description | | --- | --- | | [IV_Diag](#pyfixest.estimation.models.feiv_.Feiv.IV_Diag) | Implement IV diagnostic tests. | | [IV_weakness_test](#pyfixest.estimation.models.feiv_.Feiv.IV_weakness_test) | Implement IV weakness test (F-test). | | [demean](#pyfixest.estimation.models.feiv_.Feiv.demean) | Demean instruments and endogeneous variable. | | [drop_multicol_vars](#pyfixest.estimation.models.feiv_.Feiv.drop_multicol_vars) | Drop multicollinear variables in matrix of instruments Z. | | [eff_F](#pyfixest.estimation.models.feiv_.Feiv.eff_F) | Compute Effective F stat (Olea and Pflueger 2013). | | [first_stage](#pyfixest.estimation.models.feiv_.Feiv.first_stage) | Implement First stage regression. | | [get_fit](#pyfixest.estimation.models.feiv_.Feiv.get_fit) | Fit a IV model using a 2SLS estimator. | | [to_array](#pyfixest.estimation.models.feiv_.Feiv.to_array) | Transform estimation DataFrames to arrays. | | [wls_transform](#pyfixest.estimation.models.feiv_.Feiv.wls_transform) | Transform variables for WLS estimation. | ### IV_Diag { #pyfixest.estimation.models.feiv_.Feiv.IV_Diag } ```python estimation.models.feiv_.Feiv.IV_Diag(statistics=None) ``` Implement IV diagnostic tests. #### Notes {.doc-section .doc-section-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 {.doc-section .doc-section-parameters} | Name | Type | Description | Default | |------------|-------------|----------------------------------|-----------| | statistics | list\[str\] | List of IV diagnostic statistics | `None` | #### Example {.doc-section .doc-section-example} The following is an example usage of this method: ```{python} 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) ``` ### IV_weakness_test { #pyfixest.estimation.models.feiv_.Feiv.IV_weakness_test } ```python estimation.models.feiv_.Feiv.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 {.doc-section .doc-section-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 {.doc-section .doc-section-parameters} | Name | Type | Description | Default | |--------------------|--------|--------------------------------|-----------| | iv_diag_statistics | list | List of IV weakness statistics | `None` | ### demean { #pyfixest.estimation.models.feiv_.Feiv.demean } ```python estimation.models.feiv_.Feiv.demean() ``` Demean instruments and endogeneous variable. ### drop_multicol_vars { #pyfixest.estimation.models.feiv_.Feiv.drop_multicol_vars } ```python estimation.models.feiv_.Feiv.drop_multicol_vars() ``` Drop multicollinear variables in matrix of instruments Z. ### eff_F { #pyfixest.estimation.models.feiv_.Feiv.eff_F } ```python estimation.models.feiv_.Feiv.eff_F() ``` Compute Effective F stat (Olea and Pflueger 2013). ### first_stage { #pyfixest.estimation.models.feiv_.Feiv.first_stage } ```python estimation.models.feiv_.Feiv.first_stage() ``` Implement First stage regression. ### get_fit { #pyfixest.estimation.models.feiv_.Feiv.get_fit } ```python estimation.models.feiv_.Feiv.get_fit() ``` Fit a IV model using a 2SLS estimator. ### to_array { #pyfixest.estimation.models.feiv_.Feiv.to_array } ```python estimation.models.feiv_.Feiv.to_array() ``` Transform estimation DataFrames to arrays. ### wls_transform { #pyfixest.estimation.models.feiv_.Feiv.wls_transform } ```python estimation.models.feiv_.Feiv.wls_transform() ``` Transform variables for WLS estimation.