Source code for statsmodels.stats.oaxaca

# TODO Non-Linear Regressions can be used
# TODO Further decomposition of the two_fold parameters i.e.
# the delta method for further two_fold detail
"""
Author: Austin Adams

This class implements Oaxaca-Blinder Decomposition. It returns
a OaxacaResults Class:

OaxacaBlinder:
Two-Fold (two_fold)
Three-Fold (three_fold)

OaxacaResults:
Table Summary (summary)

Oaxaca-Blinder is a statistical method that is used to explain
the differences between two mean values. The idea is to show
from two mean values what can be explained by the data and
what cannot by using OLS regression frameworks.

"The original use by Oaxaca's was to explain the wage
differential between two different groups of workers,
but the method has since been applied to numerous other
topics." (Wikipedia)

The model is designed to accept two endogenous response variables
and two exogenous explanitory variables. They are then fit using
the specific type of decomposition that you want.

The method was famously used in Card and Krueger's paper
"School Quality and Black-White Relative Earnings: A Direct Assessment" (1992)

General reference for Oaxaca-Blinder:

B. Jann "The Blinder-Oaxaca decomposition for linear
regression models," The Stata Journal, 2008.

Econometrics references for regression models:

E. M. Kitagawa  "Components of a Difference Between Two Rates"
Journal of the American Statistical Association, 1955.

A. S. Blinder "Wage Discrimination: Reduced Form and Structural
Estimates," The Journal of Human Resources, 1973.
"""
from textwrap import dedent

import numpy as np

from statsmodels.regression.linear_model import OLS
from statsmodels.tools.tools import add_constant


[docs]class OaxacaBlinder: """ Class to perform Oaxaca-Blinder Decomposition. Parameters ---------- endog : array_like The endogenous variable or the dependent variable that you are trying to explain. exog : array_like The exogenous variable(s) or the independent variable(s) that you are using to explain the endogenous variable. bifurcate : {int, str} The column of the exogenous variable(s) on which to split. This would generally be the group that you wish to explain the two means for. Int of the column for a NumPy array or int/string for the name of the column in Pandas. hasconst : bool, optional Indicates whether the two exogenous variables include a user-supplied constant. If True, a constant is assumed. If False, a constant is added at the start. If nothing is supplied, then True is assumed. swap : bool, optional Imitates the STATA Oaxaca command by allowing users to choose to swap groups. Unlike STATA, this is assumed to be True instead of False cov_type : str, optional See regression.linear_model.RegressionResults for a description of the available covariance estimators cov_kwds : dict, optional See linear_model.RegressionResults.get_robustcov_results for a description required keywords for alternative covariance estimators Notes ----- Please check if your data includes at constant. This will still run, but will return incorrect values if set incorrectly. You can access the models by using their code as an attribute, e.g., _t_model for the total model, _f_model for the first model, _s_model for the second model. Examples -------- >>> import numpy as np >>> import statsmodels.api as sm >>> data = sm.datasets.ccards.load() '3' is the column of which we want to explain or which indicates the two groups. In this case, it is if you rent. >>> model = sm.OaxacaBlinder(df.endog, df.exog, 3, hasconst = False) >>> model.two_fold().summary() Oaxaca-Blinder Two-fold Effects Unexplained Effect: 27.94091 Explained Effect: 130.80954 Gap: 158.75044 >>> model.three_fold().summary() Oaxaca-Blinder Three-fold Effects Endowments Effect: 321.74824 Coefficient Effect: 75.45371 Interaction Effect: -238.45151 Gap: 158.75044 """ def __init__( self, endog, exog, bifurcate, hasconst=True, swap=True, cov_type="nonrobust", cov_kwds=None, ): if str(type(exog)).find("pandas") != -1: bifurcate = exog.columns.get_loc(bifurcate) endog, exog = np.array(endog), np.array(exog) self.two_fold_type = None self.bifurcate = bifurcate self.cov_type = cov_type self.cov_kwds = cov_kwds self.neumark = np.delete(exog, bifurcate, axis=1) self.exog = exog self.hasconst = hasconst bi_col = exog[:, bifurcate] endog = np.column_stack((bi_col, endog)) bi = np.unique(bi_col) self.bi_col = bi_col # split the data along the bifurcate axis, the issue is you need to # delete it after you fit the model for the total model. exog_f = exog[np.where(exog[:, bifurcate] == bi[0])] exog_s = exog[np.where(exog[:, bifurcate] == bi[1])] endog_f = endog[np.where(endog[:, 0] == bi[0])] endog_s = endog[np.where(endog[:, 0] == bi[1])] exog_f = np.delete(exog_f, bifurcate, axis=1) exog_s = np.delete(exog_s, bifurcate, axis=1) endog_f = endog_f[:, 1] endog_s = endog_s[:, 1] self.endog = endog[:, 1] self.len_f, self.len_s = len(endog_f), len(endog_s) self.gap = endog_f.mean() - endog_s.mean() if swap and self.gap < 0: endog_f, endog_s = endog_s, endog_f exog_f, exog_s = exog_s, exog_f self.gap = endog_f.mean() - endog_s.mean() bi[0], bi[1] = bi[1], bi[0] self.bi = bi if hasconst is False: exog_f = add_constant(exog_f, prepend=False) exog_s = add_constant(exog_s, prepend=False) self.exog = add_constant(self.exog, prepend=False) self.neumark = add_constant(self.neumark, prepend=False) self.exog_f_mean = np.mean(exog_f, axis=0) self.exog_s_mean = np.mean(exog_s, axis=0) self._f_model = OLS(endog_f, exog_f).fit( cov_type=cov_type, cov_kwds=cov_kwds ) self._s_model = OLS(endog_s, exog_s).fit( cov_type=cov_type, cov_kwds=cov_kwds )
[docs] def variance(self, decomp_type, n=5000, conf=0.99): """ A helper function to calculate the variance/std. Used to keep the decomposition functions cleaner """ if self.submitted_n is not None: n = self.submitted_n if self.submitted_conf is not None: conf = self.submitted_conf if self.submitted_weight is not None: submitted_weight = [ self.submitted_weight, 1 - self.submitted_weight, ] bi = self.bi bifurcate = self.bifurcate endow_eff_list = [] coef_eff_list = [] int_eff_list = [] exp_eff_list = [] unexp_eff_list = [] for _ in range(0, n): endog = np.column_stack((self.bi_col, self.endog)) exog = self.exog amount = len(endog) samples = np.random.randint(0, high=amount, size=amount) endog = endog[samples] exog = exog[samples] neumark = np.delete(exog, bifurcate, axis=1) exog_f = exog[np.where(exog[:, bifurcate] == bi[0])] exog_s = exog[np.where(exog[:, bifurcate] == bi[1])] endog_f = endog[np.where(endog[:, 0] == bi[0])] endog_s = endog[np.where(endog[:, 0] == bi[1])] exog_f = np.delete(exog_f, bifurcate, axis=1) exog_s = np.delete(exog_s, bifurcate, axis=1) endog_f = endog_f[:, 1] endog_s = endog_s[:, 1] endog = endog[:, 1] two_fold_type = self.two_fold_type if self.hasconst is False: exog_f = add_constant(exog_f, prepend=False) exog_s = add_constant(exog_s, prepend=False) exog = add_constant(exog, prepend=False) neumark = add_constant(neumark, prepend=False) _f_model = OLS(endog_f, exog_f).fit( cov_type=self.cov_type, cov_kwds=self.cov_kwds ) _s_model = OLS(endog_s, exog_s).fit( cov_type=self.cov_type, cov_kwds=self.cov_kwds ) exog_f_mean = np.mean(exog_f, axis=0) exog_s_mean = np.mean(exog_s, axis=0) if decomp_type == 3: endow_eff = (exog_f_mean - exog_s_mean) @ _s_model.params coef_eff = exog_s_mean @ (_f_model.params - _s_model.params) int_eff = (exog_f_mean - exog_s_mean) @ ( _f_model.params - _s_model.params ) endow_eff_list.append(endow_eff) coef_eff_list.append(coef_eff) int_eff_list.append(int_eff) elif decomp_type == 2: len_f = len(exog_f) len_s = len(exog_s) if two_fold_type == "cotton": t_params = (len_f / (len_f + len_s) * _f_model.params) + ( len_s / (len_f + len_s) * _s_model.params ) elif two_fold_type == "reimers": t_params = 0.5 * (_f_model.params + _s_model.params) elif two_fold_type == "self_submitted": t_params = ( submitted_weight[0] * _f_model.params + submitted_weight[1] * _s_model.params ) elif two_fold_type == "nuemark": _t_model = OLS(endog, neumark).fit( cov_type=self.cov_type, cov_kwds=self.cov_kwds ) t_params = _t_model.params else: _t_model = OLS(endog, exog).fit( cov_type=self.cov_type, cov_kwds=self.cov_kwds ) t_params = np.delete(_t_model.params, bifurcate) unexplained = (exog_f_mean @ (_f_model.params - t_params)) + ( exog_s_mean @ (t_params - _s_model.params) ) explained = (exog_f_mean - exog_s_mean) @ t_params unexp_eff_list.append(unexplained) exp_eff_list.append(explained) high, low = int(n * conf), int(n * (1 - conf)) if decomp_type == 3: return [ np.std(np.sort(endow_eff_list)[low:high]), np.std(np.sort(coef_eff_list)[low:high]), np.std(np.sort(int_eff_list)[low:high]), ] elif decomp_type == 2: return [ np.std(np.sort(unexp_eff_list)[low:high]), np.std(np.sort(exp_eff_list)[low:high]), ]
[docs] def three_fold(self, std=False, n=None, conf=None): """ Calculates the three-fold Oaxaca Blinder Decompositions Parameters ---------- std: boolean, optional If true, bootstrapped standard errors will be calculated. n: int, optional A amount of iterations to calculate the bootstrapped standard errors. This defaults to 5000. conf: float, optional This is the confidence required for the standard error calculation. Defaults to .99, but could be anything less than or equal to one. One is heavy discouraged, due to the extreme outliers inflating the variance. Returns ------- OaxacaResults A results container for the three-fold decomposition. """ self.submitted_n = n self.submitted_conf = conf self.submitted_weight = None std_val = None self.endow_eff = ( self.exog_f_mean - self.exog_s_mean ) @ self._s_model.params self.coef_eff = self.exog_s_mean @ ( self._f_model.params - self._s_model.params ) self.int_eff = (self.exog_f_mean - self.exog_s_mean) @ ( self._f_model.params - self._s_model.params ) if std is True: std_val = self.variance(3) return OaxacaResults( (self.endow_eff, self.coef_eff, self.int_eff, self.gap), 3, std_val=std_val, )
[docs] def two_fold( self, std=False, two_fold_type="pooled", submitted_weight=None, n=None, conf=None, ): """ Calculates the two-fold or pooled Oaxaca Blinder Decompositions Methods ------- std: boolean, optional If true, bootstrapped standard errors will be calculated. two_fold_type: string, optional This method allows for the specific calculation of the non-discriminatory model. There are four different types available at this time. pooled, cotton, reimers, self_submitted. Pooled is assumed and if a non-viable parameter is given, pooled will be ran. pooled - This type assumes that the pooled model's parameters (a normal regression) is the non-discriminatory model. This includes the indicator variable. This is generally the best idea. If you have economic justification for using others, then use others. nuemark - This is similar to the pooled type, but the regression is not done including the indicator variable. cotton - This type uses the adjusted in Cotton (1988), which accounts for the undervaluation of one group causing the overevalution of another. It uses the sample size weights for a linear combination of the two model parameters reimers - This type uses a linear combination of the two models with both parameters being 50% of the non-discriminatory model. self_submitted - This allows the user to submit their own weights. Please be sure to put the weight of the larger mean group only. This should be submitted in the submitted_weights variable. submitted_weight: int/float, required only for self_submitted, This is the submitted weight for the larger mean. If the weight for the larger mean is p, then the weight for the other mean is 1-p. Only submit the first value. n: int, optional A amount of iterations to calculate the bootstrapped standard errors. This defaults to 5000. conf: float, optional This is the confidence required for the standard error calculation. Defaults to .99, but could be anything less than or equal to one. One is heavy discouraged, due to the extreme outliers inflating the variance. Returns ------- OaxacaResults A results container for the two-fold decomposition. """ self.submitted_n = n self.submitted_conf = conf std_val = None self.two_fold_type = two_fold_type self.submitted_weight = submitted_weight if two_fold_type == "cotton": self.t_params = ( self.len_f / (self.len_f + self.len_s) * self._f_model.params ) + (self.len_s / (self.len_f + self.len_s) * self._s_model.params) elif two_fold_type == "reimers": self.t_params = 0.5 * (self._f_model.params + self._s_model.params) elif two_fold_type == "self_submitted": if submitted_weight is None: raise ValueError("Please submit weights") submitted_weight = [submitted_weight, 1 - submitted_weight] self.t_params = ( submitted_weight[0] * self._f_model.params + submitted_weight[1] * self._s_model.params ) elif two_fold_type == "nuemark": self._t_model = OLS(self.endog, self.neumark).fit( cov_type=self.cov_type, cov_kwds=self.cov_kwds ) self.t_params = self._t_model.params else: self._t_model = OLS(self.endog, self.exog).fit( cov_type=self.cov_type, cov_kwds=self.cov_kwds ) self.t_params = np.delete(self._t_model.params, self.bifurcate) self.unexplained = ( self.exog_f_mean @ (self._f_model.params - self.t_params) ) + (self.exog_s_mean @ (self.t_params - self._s_model.params)) self.explained = (self.exog_f_mean - self.exog_s_mean) @ self.t_params if std is True: std_val = self.variance(2) return OaxacaResults( (self.unexplained, self.explained, self.gap), 2, std_val=std_val )
[docs]class OaxacaResults: """ This class summarizes the fit of the OaxacaBlinder model. Use .summary() to get a table of the fitted values or use .params to receive a list of the values use .std to receive a list of the standard errors If a two-fold model was fitted, this will return unexplained effect, explained effect, and the mean gap. The list will always be of the following order and type. If standard error was asked for, then standard error calculations will also be included for each variable after each calculated effect. unexplained : float This is the effect that cannot be explained by the data at hand. This does not mean it cannot be explained with more. explained : float This is the effect that can be explained using the data. gap : float This is the gap in the mean differences of the two groups. If a three-fold model was fitted, this will return characteristic effect, coefficient effect interaction effect, and the mean gap. The list will be of the following order and type. If standard error was asked for, then standard error calculations will also be included for each variable after each calculated effect. endowment effect : float This is the effect due to the group differences in predictors coefficient effect : float This is the effect due to differences of the coefficients of the two groups interaction effect : float This is the effect due to differences in both effects existing at the same time between the two groups. gap : float This is the gap in the mean differences of the two groups. Attributes ---------- params A list of all values for the fitted models. std A list of standard error calculations. """ def __init__(self, results, model_type, std_val=None): self.params = results self.std = std_val self.model_type = model_type
[docs] def summary(self): """ Print a summary table with the Oaxaca-Blinder effects """ if self.model_type == 2: if self.std is None: print( dedent( f"""\ Oaxaca-Blinder Two-fold Effects Unexplained Effect: {self.params[0]:.5f} Explained Effect: {self.params[1]:.5f} Gap: {self.params[2]:.5f}""" ) ) else: print( dedent( """\ Oaxaca-Blinder Two-fold Effects Unexplained Effect: {:.5f} Unexplained Standard Error: {:.5f} Explained Effect: {:.5f} Explained Standard Error: {:.5f} Gap: {:.5f}""".format( self.params[0], self.std[0], self.params[1], self.std[1], self.params[2], ) ) ) if self.model_type == 3: if self.std is None: print( dedent( f"""\ Oaxaca-Blinder Three-fold Effects Endowment Effect: {self.params[0]:.5f} Coefficient Effect: {self.params[1]:.5f} Interaction Effect: {self.params[2]:.5f} Gap: {self.params[3]:.5f}""" ) ) else: print( dedent( f"""\ Oaxaca-Blinder Three-fold Effects Endowment Effect: {self.params[0]:.5f} Endowment Standard Error: {self.std[0]:.5f} Coefficient Effect: {self.params[1]:.5f} Coefficient Standard Error: {self.std[1]:.5f} Interaction Effect: {self.params[2]:.5f} Interaction Standard Error: {self.std[2]:.5f} Gap: {self.params[3]:.5f}""" ) )