Welcome to regpyhdfe’s documentation!
Introduction
This package provides a semi-convenient way of performing regression with high dimensional fixed effects in python.
To use this, Your data must be in a pandas dataframe. Please see Examples and Tutorial sections for instructions.
Limitations
Does not work with Weighting (yet).
In order to change address this, one would have to change the underyling model used for regressions. This is currently standard OLS from statsmodels, which does not support weighting. Statsmodels has other linear regression objects which do support weighting, but those have their own issues (Weighted Linear Regression does not support all kinds of weighting, Generalized Linear Models lacks appropriate summary statistics etc.)
Replication of Stata not _quite_ identical when using clustering
By not quite I mean an F-Value of 114.8 v.s. 114.58 etc.:
# OLS Regression Results
# =======================================================================================
# Dep. Variable: ttl_exp R-squared (uncentered): 0.454
# Model: OLS Adj. R-squared (uncentered): -623.342
# Method: Least Squares F-statistic: 114.8
# Date: Sun, 07 Feb 2021 Prob (F-statistic): 4.28e-08
# Time: 19:42:56 Log-Likelihood: -29361.
# No. Observations: 12568 AIC: 5.873e+04
# Df Residuals: 11 BIC: 5.874e+04
# Df Model: 2
# Covariance Type: cluster
# ==============================================================================
# coef std err t P>|t| [0.025 0.975]
# ------------------------------------------------------------------------------
# wks_ue 0.0307 0.016 1.975 0.074 -0.004 0.065
# tenure 0.8514 0.066 12.831 0.000 0.705 0.997
# ==============================================================================
# Omnibus: 2467.595 Durbin-Watson: 1.819
# Prob(Omnibus): 0.000 Jarque-Bera (JB): 8034.980
# Skew: 0.993 Prob(JB): 0.00
# Kurtosis: 6.376
# ==============================================================================
# ==============================================================================
#
# V.S.
#
# ==============================================================================
# ==============================================================================
# HDFE Linear regression Number of obs = 12,568
# Absorbing 1 HDFE group F( 2, 11) = 114.58
# Statistics robust to heteroskedasticity Prob > F = 0.0000
# R-squared = 0.6708
# Adj R-squared = 0.5628
# Number of clusters (idcode) = 3,102 Within R-sq. = 0.4536
# Number of clusters (year) = 12 Root MSE = 2.8836
#
# (Std. Err. adjusted for 12 clusters in idcode year)
# ------------------------------------------------------------------------------
# | Robust
# ttl_exp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
# -------------+----------------------------------------------------------------
# wks_ue | .0306653 .0155436 1.97 0.074 -.0035459 .0648765
# tenure | .8513953 .0663892 12.82 0.000 .7052737 .9975169
# _cons | 3.784107 .4974451 7.61 0.000 2.689238 4.878976
# ------------------------------------------------------------------------------
A note of interest is that the fewer degrees of freedom are involved, the worse this discrepancy is, here is an example where clustering leads to just two degrees of freedom in the residuals, so basically as bad as the discrepancy can be:
# OLS Regression Results
#=======================================================================================
#Dep. Variable: ttl_exp R-squared (uncentered): 0.454
#Model: OLS Adj. R-squared (uncentered): -6866.766
#Method: Least Squares F-statistic: 1.354e+04
#Date: Sun, 07 Feb 2021 Prob (F-statistic): 0.00608
#Time: 20:32:41 Log-Likelihood: -29361.
#No. Observations: 12568 AIC: 5.873e+04
#Df Residuals: 1 BIC: 5.874e+04
#Df Model: 2
#Covariance Type: cluster
#==============================================================================
# coef std err t P>|t| [0.025 0.975]
#------------------------------------------------------------------------------
#wks_ue 0.0307 0.004 7.483 0.085 -0.021 0.083
#tenure 0.8514 0.013 66.321 0.010 0.688 1.015
#==============================================================================
#Omnibus: 2467.595 Durbin-Watson: 1.819
#Prob(Omnibus): 0.000 Jarque-Bera (JB): 8034.980
#Skew: 0.993 Prob(JB): 0.00
#Kurtosis: 6.376
#==============================================================================
#==============================================================================
#
# v.s.
#
#==============================================================================
#==============================================================================
# HDFE Linear regression Number of obs = 12,568
# Absorbing 1 HDFE group F( 2, 1) = 7212.19
# Statistics robust to heteroskedasticity Prob > F = 0.0083
# R-squared = 0.6708
# Adj R-squared = 0.5628
# Number of clusters (union) = 2 Within R-sq. = 0.4536
# Number of clusters (idcode) = 3,102 Root MSE = 2.8836
#
# (Std. Err. adjusted for 2 clusters in union idcode)
# ------------------------------------------------------------------------------
# | Robust
# ttl_exp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
# -------------+----------------------------------------------------------------
# wks_ue | .0306653 .0043113 7.11 0.089 -.024115 .0854455
# tenure | .8513953 .0132713 64.15 0.010 .6827674 1.020023
# _cons | 3.784107 .0531894 71.14 0.009 3.108272 4.459942
# ------------------------------------------------------------------------------
#
# Absorbed degrees of freedom:
# -----------------------------------------------------+
# Absorbed FE | Categories - Redundant = Num. Coefs |
# -------------+---------------------------------------|
# idcode | 3102 3102 0 *|
# -----------------------------------------------------+
The T-values are still quite similar, but the F-statistic is completely wrong. It is my understanding that one is not really supposed to use clustering when fewer than 30 clusters are present. This yields:
#HDFE Linear regression Number of obs = 12,568
#Absorbing 1 HDFE group F( 2, 29) = 5953.94
#Statistics robust to heteroskedasticity Prob > F = 0.0000
# R-squared = 0.6708
# Adj R-squared = 0.5628
# Within R-sq. = 0.4536
#Number of clusters (delete_me) = 30 Root MSE = 2.8836
# (Std. Err. adjusted for 30 clusters in delete_me)
#------------------------------------------------------------------------------
# | Robust
# ttl_exp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
#-------------+----------------------------------------------------------------
# wks_ue | .0306653 .0054123 5.67 0.000 .0195959 .0417346
# tenure | .8513953 .0078384 108.62 0.000 .8353639 .8674267
# _cons | 3.784107 .0467015 81.03 0.000 3.688592 3.879622
#------------------------------------------------------------------------------
#Absorbed degrees of freedom:
#-----------------------------------------------------+
# Absorbed FE | Categories - Redundant = Num. Coefs |
#-------------+---------------------------------------|
# idcode | 3102 0 3102 |
#-----------------------------------------------------+
# OLS Regression Results
#=======================================================================================
#Dep. Variable: ttl_exp R-squared (uncentered): 0.454
#Model: OLS Adj. R-squared (uncentered): -235.820
#Method: Least Squares F-statistic: 7905.
#Date: Sun, 07 Feb 2021 Prob (F-statistic): 2.03e-40
#Time: 22:00:43 Log-Likelihood: -29361.
#No. Observations: 12568 AIC: 5.873e+04
#Df Residuals: 29 BIC: 5.874e+04
#Df Model: 2
#Covariance Type: cluster
#==============================================================================
# coef std err t P>|t| [0.025 0.975]
#------------------------------------------------------------------------------
#wks_ue 0.0307 0.005 6.529 0.000 0.021 0.040
#tenure 0.8514 0.007 125.159 0.000 0.837 0.865
#==============================================================================
#Omnibus: 2467.595 Durbin-Watson: 1.819
#Prob(Omnibus): 0.000 Jarque-Bera (JB): 8034.980
#Skew: 0.993 Prob(JB): 0.00
#Kurtosis: 6.376
#==============================================================================
Oh dear. What about 100?
The simplest fix would be to manually calculate these metrics - residuals and coefficients are all correct, which should give us all the information to calculate appropriately adjusted metrics. This would involve finding the method that Stata packages use, finding a reference for the method and implementing it as specified.
regpyhdfe package
Submodules
regpyhdfe.regpyhdfe module
- class regpyhdfe.regpyhdfe.Regpyhdfe(df, target, predictors, absorb_ids=[], cluster_ids=[], drop_singletons=True, intercept=False)[source]
Bases:
object- __init__(df, target, predictors, absorb_ids=[], cluster_ids=[], drop_singletons=True, intercept=False)[source]
Regression wrapper for PyHDFE.
- Parameters:
df (pandas Dataframe) – dataframe containing referenced data which includes target, predictors and absorb and cluster.
target (string) – name of target variable - the y in y = X*b + e.
predictors (string or list of strings) – names of predictors, the X in y = X*b + e.
absorb_ids (string or list of strings) – names of variables to be absorbed for fixed effects.
cluster_ids (string or list of strings) – names of variables to be clustered on.
drop_singletons (bool) – indicates whether to drop singleton groups. Defaults is True, same as stata. Setting to False is equivalent to passing keepsingletons to reghdfe.
- regpyhdfe.regpyhdfe.summary(self, regpyhdfe, yname=None, xname=None, title=None, alpha=0.05)[source]
Summarize the Regression Results.
- Parameters:
yname (str, optional) – Name of endogenous (response) variable. The Default is y.
xname (list[str], optional) – Names for the exogenous variables. Default is var_## for ## in the number of regressors. Must match the number of parameters in the model.
title (str, optional) – Title for the top table. If not None, then this replaces the default title.
alpha (float) – The significance level for the confidence intervals.
- Returns:
Instance holding the summary tables and text, which can be printed or converted to various output formats.
- Return type:
Summary
See also
statsmodels.iolib.summary.SummaryA class that holds summary results.
regpyhdfe.utils module
- regpyhdfe.utils.add_intercept(X)[source]
Prepends a column of 1s (an intercept column) to a a 2D numpy array.
- Parameters:
X (numpy array) – 2D numpy array.
- Returns:
X with an appended column of 1s.
- regpyhdfe.utils.get_np_columns(df, columns, intercept=False)[source]
Helper used to retreive columns as numpy array.
- Parameters:
df (pandas dataframe) – dataframe containing desired columns
columns (list of strings) – list of names of desired columns. Must be a list even if only 1 column is desired.
intercept (bool) – set to True if You’d like resulting numpy array to have a column of 1s appended to it.
- Returns:
2D numpy array with columns of array consisting of feature vectors, i.e. the first column of the result is a numpy vector of the first column named in columns argument.
- regpyhdfe.utils.sklearn_to_df(sklearn_dataset)[source]
Converts (as well as it can) an sklearn dataset to a Pandas dataframe.
- Parameters:
sklearn_dataset (sklearn.utils.Bunch) – this parameter is usually the result of using sklearn to quickly get a dataset, e.g. the object resulting from calling sklearn.load_datasets.load_boston().
- Returns:
Pandas dataframe df where df[‘target’] is the target variable in the original dataset.
Tutorial
Installation
Should work with just pip install regpyhdfe.
Load in data
We need a pandas dataframe. For the purposes of this example You can go to https://github.com/lod531/regPyHDFE/blob/main/data/cleaned_nlswork.dta and download the cleaned nlswork dataset. This dataset contains entries that can be acquired in stata by typing use nlswork, except rows containing NA values have already been dropped (hence cleaned_nlswork.dta, rather than nlswork.dta).
Once You have a file, importing the data is as simple as
import pandas as pd
# load dataframe
df = pd.read_stata('path/to/cleaned_nlswork.dta')
Pandas has other import functions if You have a file in a different format, e.g. pd.read_csv.
Regress
Target is of course the target variable.
Predictors are… Predictors.
absorb_ids are names of variables to be absorbed as high dimensional fixed effects
cluster_ids are names of variables containing cluster information (i.e. if there are N clusters, then each row of a cluster variables contains one of N distinct values.)
target = "ln_wage"
predictors = ["hours", "tenure", "ttl_exp"]
absorb_ids = ["year", "idcode"]
cluster_ids = ["year"]
from regpyhdfe import Regpyhdfe
model = Regpyhdfe(df=df, target=target, predictors=predictors,
absorb_ids=absorb_ids,
cluster_ids=cluster_ids)
results = model.fit()
Examine results
At the time of writing, the results object is of type statsmodels.regression.linear_model.RegressionResults, documentation for which can be viewed here.
The statsmodels.regression.linear_model.RegressionResults` object has a variety of statistics, but chances are all You’re looking is a summary, like so:
print(results.summary())
The output of that looks like
OLS Regression Results
=======================================================================================
Dep. Variable: ln_wage R-squared (uncentered): 0.059
Model: OLS Adj. R-squared (uncentered): -1313.428
Method: Least Squares F-statistic: 185.2
Date: Thu, 14 Jan 2021 Prob (F-statistic): 2.09e-08
Time: 13:21:24 Log-Likelihood: 766.62
No. Observations: 12568 AIC: -1527.
Df Residuals: 9 BIC: -1505.
Df Model: 3
Covariance Type: cluster
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
hours -0.0017 0.001 -3.371 0.001 -0.003 -0.001
tenure 0.0109 0.003 3.858 0.000 0.005 0.016
ttl_exp 0.0348 0.003 12.650 0.000 0.029 0.040
==============================================================================
Omnibus: 1709.175 Durbin-Watson: 2.171
Prob(Omnibus): 0.000 Jarque-Bera (JB): 21109.707
Skew: -0.174 Prob(JB): 0.00
Kurtosis: 9.340 Cond. No. 6.87
==============================================================================
Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors are robust to cluster correlation (cluster)
And for Your convenience the whole script is
import pandas as pd
# load dataframe
df = pd.read_stata('/path/to/cleaned_nlswork.dta')
target = "ln_wage"
predictors = ["hours", "tenure", "ttl_exp"]
absorb_ids = ["year", "idcode"]
cluster_ids = ["year"]
from regpyhdfe import Regpyhdfe
model = Regpyhdfe(df=df, target=target,
predictors = predictors,
absorb_ids=absorb_ids,
cluster_ids=cluster_ids)
results = model.fit()
print(results.summary())
Examples
Installation
pip install regpyhdfe, simple as that.
Examples
The examples consist of two parts: the python code and the comments.
The python code(s) are minimal examples of a regression. One could simply copy/paste the code, change the dataset and the features of regression and have a working script.
The comments consists of two parts: first part is an identical regression using the reghdfe package in stata. The second part is the output of a corresponding python regression using regPyHDFE. Those comments are there for comparison purposes.
Timing information is trivial and at this time not included - both stata and python run instantly on a laptop CPU.
Using fixed effects only
These examples do not use clustering. As You can see, all that’s really needed is a pandas dataframe. Then simply pass in the arguments in appropriate order (or simply pass named arguments. For details on parameters look at the Regpyhdfe object documentation)
import pandas as pd
import numpy as np
from regpyhdfe import Regpyhdfe
from sklearn.datasets import load_boston
def sklearn_to_df(sklearn_dataset):
df = pd.DataFrame(sklearn_dataset.data, columns=sklearn_dataset.feature_names)
df['target'] = pd.Series(sklearn_dataset.target)
return df
df = sklearn_to_df(load_boston())
df.to_stata("boston.dta")
# . reghdfe target CRIM ZN INDUS NOX AGE, absorb(CHAS RAD)
# (MWFE estimator converged in 3 iterations)
#
# HDFE Linear regression Number of obs = 506
# Absorbing 2 HDFE groups F( 5, 491) = 21.93
# Prob > F = 0.0000
# R-squared = 0.3887
# Adj R-squared = 0.3712
# Within R-sq. = 0.1825
# Root MSE = 7.2929
#
# ------------------------------------------------------------------------------
# target | Coef. Std. Err. t P>|t| [95% Conf. Interval]
# -------------+----------------------------------------------------------------
# CRIM | -.2089114 .0491012 -4.25 0.000 -.3053857 -.1124371
# ZN | .0679261 .0183051 3.71 0.000 .03196 .1038922
# INDUS | -.2279553 .0860909 -2.65 0.008 -.3971074 -.0588033
# NOX | -9.424849 5.556005 -1.70 0.090 -20.34133 1.49163
# AGE | -.0140739 .0183467 -0.77 0.443 -.0501215 .0219738
# _cons | 31.24755 2.53596 12.32 0.000 26.26487 36.23022
# ------------------------------------------------------------------------------
#
# Absorbed degrees of freedom:
# -----------------------------------------------------+
# Absorbed FE | Categories - Redundant = Num. Coefs |
# -------------+---------------------------------------|
# CHAS | 2 0 2 |
# RAD | 9 1 8 |
# -----------------------------------------------------+
# target~CRIM + ZN + INDUS + NOX + AGE, absorb(CHAS, RAD)
# OLS Regression Results
# =======================================================================================
# Dep. Variable: target R-squared (uncentered): 0.183
# Model: OLS Adj. R-squared (uncentered): 0.158
# Method: Least Squares F-statistic: 21.93
# Date: Mon, 11 Jan 2021 Prob (F-statistic): 7.57e-20
# Time: 20:30:53 Log-Likelihood: -1715.7
# No. Observations: 506 AIC: 3441.
# Df Residuals: 491 BIC: 3463.
# Df Model: 5
# Covariance Type: nonrobust
# ==============================================================================
# coef std err t P>|t| [0.025 0.975]
# ------------------------------------------------------------------------------
# CRIM -0.2089 0.049 -4.255 0.000 -0.305 -0.112
# ZN 0.0679 0.018 3.711 0.000 0.032 0.104
# INDUS -0.2280 0.086 -2.648 0.008 -0.397 -0.059
# NOX -9.4248 5.556 -1.696 0.090 -20.341 1.492
# AGE -0.0141 0.018 -0.767 0.443 -0.050 0.022
# ==============================================================================
# Omnibus: 172.457 Durbin-Watson: 0.904
# Prob(Omnibus): 0.000 Jarque-Bera (JB): 532.297
# Skew: 1.621 Prob(JB): 2.59e-116
# Kurtosis: 6.839 Cond. No. 480.
# ==============================================================================
#
# Notes:
# [1] R² is computed without centering (uncentered) since the model does not contain a constant.
# [2] Standard Errors assume that the covariance matrix of the errors is correctly specified.
model = Regpyhdfe(df, 'target', ['CRIM', 'ZN', 'INDUS', 'NOX', 'AGE'], ['CHAS', 'RAD'])
results = model.fit()
print("target~CRIM + ZN + INDUS + NOX + AGE, absorb(CHAS, RAD)")
print(results.summary())
import pandas as pd
import numpy as np
from regpyhdfe import Regpyhdfe
# details about dataset can be found at https://www.kaggle.com/crawford/80-cereals
df = pd.read_stata('/home/abom/Desktop/regPyHDFE/data/cereal.dta')
# . reghdfe rating fat protein carbo sugars, absorb(shelf)
# (MWFE estimator converged in 1 iterations)
#
# HDFE Linear regression Number of obs = 77
# Absorbing 1 HDFE group F( 4, 70) = 54.98
# Prob > F = 0.0000
# R-squared = 0.7862
# Adj R-squared = 0.7679
# Within R-sq. = 0.7586
# Root MSE = 6.7671
#
# ------------------------------------------------------------------------------
# rating | Coef. Std. Err. t P>|t| [95% Conf. Interval]
# -------------+----------------------------------------------------------------
# fat | -5.684196 .8801468 -6.46 0.000 -7.439594 -3.928799
# protein | 3.740386 .8430319 4.44 0.000 2.059012 5.42176
# carbo | -.7892276 .2041684 -3.87 0.000 -1.196429 -.3820266
# sugars | -2.03286 .2179704 -9.33 0.000 -2.467588 -1.598132
# _cons | 64.49503 4.92674 13.09 0.000 54.66896 74.3211
# ------------------------------------------------------------------------------
#
# Absorbed degrees of freedom:
# -----------------------------------------------------+
# Absorbed FE | Categories - Redundant = Num. Coefs |
# -------------+---------------------------------------|
# shelf | 3 0 3 |
# -----------------------------------------------------+
# rating ~ fat + protein + carbo + sugars, absorb(shelf)
# OLS Regression Results
# =======================================================================================
# Dep. Variable: rating R-squared (uncentered): 0.759
# Model: OLS Adj. R-squared (uncentered): 0.734
# Method: Least Squares F-statistic: 54.98
# Date: Mon, 11 Jan 2021 Prob (F-statistic): 6.89e-21
# Time: 20:45:37 Log-Likelihood: -252.82
# No. Observations: 77 AIC: 513.6
# Df Residuals: 70 BIC: 523.0
# Df Model: 4
# Covariance Type: nonrobust
# coef std err t P>|t| [0.025 0.975]
# ------------------------------------------------------------------------------
# fat -5.6842 0.880 -6.458 0.000 -7.440 -3.929
# protein 3.7404 0.843 4.437 0.000 2.059 5.422
# carbo -0.7892 0.204 -3.866 0.000 -1.196 -0.382
# sugars -2.0329 0.218 -9.326 0.000 -2.468 -1.598
# ==============================================================================
# Omnibus: 5.613 Durbin-Watson: 1.801
# Prob(Omnibus): 0.060 Jarque-Bera (JB): 7.673
# Skew: 0.179 Prob(JB): 0.0216
# Kurtosis: 4.504 Cond. No. 5.84
# ==============================================================================
residualized = Regpyhdfe(df, 'rating', ['fat', 'protein', 'carbo', 'sugars'], ['shelf'])
results = residualized.fit()
print("rating ~ fat + protein + carbo + sugars, absorb(shelf)")
print(results.summary())
import pandas as pd
import numpy as np
from regpyhdfe import Regpyhdfe
# show variable labels
#pd.read_stata('/home/abom/Desktop/regPyHDFE/nlswork.dta', iterator=True).variable_labels()
# Load data
df = pd.read_stata('/home/abom/Desktop/regPyHDFE/data/cleaned_nlswork.dta')
df['hours_log'] = np.log(df['hours'])
# . reghdfe ln_wage hours_log, absorb(idcode year)
# (dropped 884 singleton observations)
# (MWFE estimator converged in 8 iterations)
#
# HDFE Linear regression Number of obs = 12,568
# Absorbing 2 HDFE groups F( 1, 9454) = 0.50
# Prob > F = 0.4792
# R-squared = 0.7314
# Adj R-squared = 0.6430
# Within R-sq. = 0.0001
# Root MSE = 0.2705
#
# ------------------------------------------------------------------------------
# ln_wage | Coef. Std. Err. t P>|t| [95% Conf. Interval]
# -------------+----------------------------------------------------------------
# hours_log | -.0058555 .0082759 -0.71 0.479 -.022078 .010367
# _cons | 1.736618 .0292873 59.30 0.000 1.679208 1.794027
# ------------------------------------------------------------------------------
#
# Absorbed degrees of freedom:
# -----------------------------------------------------+
# Absorbed FE | Categories - Redundant = Num. Coefs |
# -------------+---------------------------------------|
# idcode | 3102 0 3102 |
# year | 12 1 11 |
# -----------------------------------------------------+
# ln_wage ~ hours_log, absorb(idcode, year)
# OLS Regression Results
# =======================================================================================
# Dep. Variable: ln_wage R-squared (uncentered): 0.000
# Model: OLS Adj. R-squared (uncentered): -0.329
# Method: Least Squares F-statistic: 0.5006
# Date: Mon, 11 Jan 2021 Prob (F-statistic): 0.479
# Time: 21:07:22 Log-Likelihood: 386.59
# No. Observations: 12568 AIC: -771.2
# Df Residuals: 9454 BIC: -763.7
# Df Model: 1
# Covariance Type: nonrobust
# ==============================================================================
# coef std err t P>|t| [0.025 0.975]
# ------------------------------------------------------------------------------
# hours_log -0.0059 0.008 -0.708 0.479 -0.022 0.010
# ==============================================================================
# Omnibus: 1617.122 Durbin-Watson: 2.143
# Prob(Omnibus): 0.000 Jarque-Bera (JB): 16984.817
# Skew: -0.215 Prob(JB): 0.00
# Kurtosis: 8.679 Cond. No. 1.00
# ==============================================================================
model = Regpyhdfe(df, "ln_wage", "hours_log", ["idcode", "year"])
results = model.fit()
print("ln_wage ~ hours_log, absorb(idcode, year)")
print(results.summary())
Clustering:
Very similar to standard regression, simply add a clustering_ids parameter to the parameter list passed to Regpyhdfe.
from regpyhdfe import Regpyhdfe
import pandas as pd
import numpy as np
df = pd.read_stata('data/cleaned_nlswork.dta')
df['hours_log'] = np.log(df['hours'])
regpyhdfe = Regpyhdfe(df=df,
target='ttl_exp',
predictors=['wks_ue', 'tenure'],
ids=['idcode'],
cluster_ids=['year', 'idcode'])
# (dropped 884 singleton observations)
# (MWFE estimator converged in 1 iterations)
#
# HDFE Linear regression Number of obs = 12,568
# Absorbing 1 HDFE group F( 2, 11) = 114.58
# Statistics robust to heteroskedasticity Prob > F = 0.0000
# R-squared = 0.6708
# Adj R-squared = 0.5628
# Number of clusters (year) = 12 Within R-sq. = 0.4536
# Number of clusters (idcode) = 3,102 Root MSE = 2.8836
#
# (Std. Err. adjusted for 12 clusters in year idcode)
# ------------------------------------------------------------------------------
# | Robust
# ttl_exp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
# -------------+----------------------------------------------------------------
# wks_ue | .0306653 .0155436 1.97 0.074 -.0035459 .0648765
# tenure | .8513953 .0663892 12.82 0.000 .7052737 .9975169
# _cons | 3.784107 .4974451 7.61 0.000 2.689238 4.878976
# ------------------------------------------------------------------------------
#
# Absorbed degrees of freedom:
# -----------------------------------------------------+
# Absorbed FE | Categories - Redundant = Num. Coefs |
# -------------+---------------------------------------|
# idcode | 3102 3102 0 *|
# -----------------------------------------------------+
# * = FE nested within cluster; treated as redundant for DoF computation
# OLS Regression Results
# =======================================================================================
# Dep. Variable: ttl_exp R-squared (uncentered): 0.454
# Model: OLS Adj. R-squared (uncentered): -623.342
# Method: Least Squares F-statistic: 114.8
# Date: Mon, 11 Jan 2021 Prob (F-statistic): 4.28e-08
# Time: 21:35:07 Log-Likelihood: -29361.
# No. Observations: 12568 AIC: 5.873e+04
# Df Residuals: 11 BIC: 5.874e+04
# Df Model: 2
# Covariance Type: cluster
# ==============================================================================
# coef std err z P>|z| [0.025 0.975]
# ------------------------------------------------------------------------------
# wks_ue 0.0307 0.016 1.975 0.048 0.000 0.061
# tenure 0.8514 0.066 12.831 0.000 0.721 0.981
# ==============================================================================
# Omnibus: 2467.595 Durbin-Watson: 1.819
# Prob(Omnibus): 0.000 Jarque-Bera (JB): 8034.980
# Skew: 0.993 Prob(JB): 0.00
# Kurtosis: 6.376 Cond. No. 2.06
# ==============================================================================
results = regpyhdfe.fit()
print(results.summary())