import numpy as np
import pandas as pd
import scipy as sp
import scipy.stats as ss
import statsmodels
import statsmodels.api as sm
import statsmodels.formula.api as smf
from statsmodels.iolib.summary2 import summary_col
from wooldridge import *
df = dataWoo("nyse")
print(smf.ols('df[("return")] ~ return_1 + 1', data=df).fit().summary())
OLS Regression Results
==============================================================================
Dep. Variable: df[("return")] R-squared: 0.003
Model: OLS Adj. R-squared: 0.002
Method: Least Squares F-statistic: 2.399
Date: Tue, 21 Apr 2020 Prob (F-statistic): 0.122
Time: 16:31:17 Log-Likelihood: -1491.2
No. Observations: 689 AIC: 2986.
Df Residuals: 687 BIC: 2996.
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept 0.1796 0.081 2.225 0.026 0.021 0.338
return_1 0.0589 0.038 1.549 0.122 -0.016 0.134
==============================================================================
Omnibus: 114.206 Durbin-Watson: 1.997
Prob(Omnibus): 0.000 Jarque-Bera (JB): 646.991
Skew: -0.598 Prob(JB): 3.22e-141
Kurtosis: 7.594 Cond. No. 2.14
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
df =dataWoo("nyse")
mrk_lag2 = smf.ols('df[("return")] ~ return_1 + df[("return")].shift(2)', data=df).fit()
print(mrk_lag2.summary())
OLS Regression Results
==============================================================================
Dep. Variable: df[("return")] R-squared: 0.005
Model: OLS Adj. R-squared: 0.002
Method: Least Squares F-statistic: 1.659
Date: Tue, 21 Apr 2020 Prob (F-statistic): 0.191
Time: 16:31:17 Log-Likelihood: -1489.0
No. Observations: 688 AIC: 2984.
Df Residuals: 685 BIC: 2998.
Df Model: 2
Covariance Type: nonrobust
===========================================================================================
coef std err t P>|t| [0.025 0.975]
-------------------------------------------------------------------------------------------
Intercept 0.1857 0.081 2.289 0.022 0.026 0.345
return_1 0.0603 0.038 1.580 0.115 -0.015 0.135
df[("return")].shift(2) -0.0381 0.038 -0.998 0.319 -0.113 0.037
==============================================================================
Omnibus: 117.320 Durbin-Watson: 1.998
Prob(Omnibus): 0.000 Jarque-Bera (JB): 652.237
Skew: -0.627 Prob(JB): 2.34e-142
Kurtosis: 7.602 Cond. No. 2.22
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
hypotheses = '(return_1 = df[("return")].shift(2) = 0)'
f_test = mrk_lag2.f_test(hypotheses)
print(f_test)
<F test: F=array([[1.65857123]]), p=0.19117456962590035, df_denom=685, df_num=2>
df = dataWoo("phillips")
print(smf.ols('cinf ~ unem + 1', data=df[(df['year']<1997)]).fit().summary())
OLS Regression Results
==============================================================================
Dep. Variable: cinf R-squared: 0.108
Model: OLS Adj. R-squared: 0.088
Method: Least Squares F-statistic: 5.558
Date: Tue, 21 Apr 2020 Prob (F-statistic): 0.0227
Time: 16:31:17 Log-Likelihood: -110.12
No. Observations: 48 AIC: 224.2
Df Residuals: 46 BIC: 228.0
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept 3.0306 1.377 2.201 0.033 0.259 5.802
unem -0.5426 0.230 -2.357 0.023 -1.006 -0.079
==============================================================================
Omnibus: 22.805 Durbin-Watson: 1.770
Prob(Omnibus): 0.000 Jarque-Bera (JB): 52.071
Skew: -1.239 Prob(JB): 4.93e-12
Kurtosis: 7.460 Cond. No. 23.9
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
df = dataWoo("fertil3")
fert_lag2 = smf.ols('cgfr ~ cpe + df[("cpe")].shift(1) + df[("cpe")].shift(2)', data = df).fit()
print(fert_lag2.summary())
OLS Regression Results
==============================================================================
Dep. Variable: cgfr R-squared: 0.232
Model: OLS Adj. R-squared: 0.197
Method: Least Squares F-statistic: 6.563
Date: Tue, 21 Apr 2020 Prob (F-statistic): 0.000605
Time: 16:31:17 Log-Likelihood: -189.03
No. Observations: 69 AIC: 386.1
Df Residuals: 65 BIC: 395.0
Df Model: 3
Covariance Type: nonrobust
========================================================================================
coef std err t P>|t| [0.025 0.975]
----------------------------------------------------------------------------------------
Intercept -0.9637 0.468 -2.060 0.043 -1.898 -0.029
cpe -0.0362 0.027 -1.352 0.181 -0.090 0.017
df[("cpe")].shift(1) -0.0140 0.028 -0.507 0.614 -0.069 0.041
df[("cpe")].shift(2) 0.1100 0.027 4.092 0.000 0.056 0.164
==============================================================================
Omnibus: 4.167 Durbin-Watson: 1.414
Prob(Omnibus): 0.124 Jarque-Bera (JB): 3.673
Skew: 0.323 Prob(JB): 0.159
Kurtosis: 3.928 Cond. No. 20.7
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
hypotheses = '(cpe = df[("cpe")].shift(1) = 0)'
f_test = fert_lag2.f_test(hypotheses)
print(f_test)
<F test: F=array([[1.28941437]]), p=0.2823824025023764, df_denom=65, df_num=2>
print(smf.ols('lhrwage ~ loutphr + t', data=dataWoo("earns")).fit().summary())
OLS Regression Results
==============================================================================
Dep. Variable: lhrwage R-squared: 0.971
Model: OLS Adj. R-squared: 0.970
Method: Least Squares F-statistic: 641.2
Date: Tue, 21 Apr 2020 Prob (F-statistic): 5.27e-30
Time: 16:31:17 Log-Likelihood: 89.196
No. Observations: 41 AIC: -172.4
Df Residuals: 38 BIC: -167.3
Df Model: 2
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept -5.3285 0.374 -14.230 0.000 -6.086 -4.570
loutphr 1.6396 0.093 17.565 0.000 1.451 1.829
t -0.0182 0.002 -10.428 0.000 -0.022 -0.015
==============================================================================
Omnibus: 1.119 Durbin-Watson: 0.567
Prob(Omnibus): 0.572 Jarque-Bera (JB): 0.913
Skew: -0.055 Prob(JB): 0.633
Kurtosis: 2.277 Cond. No. 2.12e+03
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 2.12e+03. This might indicate that there are
strong multicollinearity or other numerical problems.
print(smf.ols('ghrwage ~ goutphr', data=dataWoo("earns")).fit().summary())
OLS Regression Results
==============================================================================
Dep. Variable: ghrwage R-squared: 0.364
Model: OLS Adj. R-squared: 0.348
Method: Least Squares F-statistic: 21.77
Date: Tue, 21 Apr 2020 Prob (F-statistic): 3.75e-05
Time: 16:31:17 Log-Likelihood: 107.37
No. Observations: 40 AIC: -210.7
Df Residuals: 38 BIC: -207.4
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept -0.0037 0.004 -0.868 0.391 -0.012 0.005
goutphr 0.8093 0.173 4.666 0.000 0.458 1.160
==============================================================================
Omnibus: 2.405 Durbin-Watson: 1.526
Prob(Omnibus): 0.300 Jarque-Bera (JB): 1.340
Skew: 0.325 Prob(JB): 0.512
Kurtosis: 3.618 Cond. No. 64.7
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
df = dataWoo("fertil3")
fert_lags = smf.ols('cgfr ~ df[("cgfr")].shift(1) + cpe + df[("cpe")].shift(1) + df[("cpe")].shift(2)', data =df).fit()
print(fert_lags.summary())
OLS Regression Results
==============================================================================
Dep. Variable: cgfr R-squared: 0.318
Model: OLS Adj. R-squared: 0.275
Method: Least Squares F-statistic: 7.464
Date: Tue, 21 Apr 2020 Prob (F-statistic): 5.34e-05
Time: 16:31:17 Log-Likelihood: -184.95
No. Observations: 69 AIC: 379.9
Df Residuals: 64 BIC: 391.1
Df Model: 4
Covariance Type: nonrobust
=========================================================================================
coef std err t P>|t| [0.025 0.975]
-----------------------------------------------------------------------------------------
Intercept -0.7022 0.454 -1.547 0.127 -1.609 0.204
df[("cgfr")].shift(1) 0.3002 0.106 2.835 0.006 0.089 0.512
cpe -0.0455 0.026 -1.773 0.081 -0.097 0.006
df[("cpe")].shift(1) 0.0021 0.027 0.077 0.939 -0.051 0.056
df[("cpe")].shift(2) 0.1051 0.026 4.108 0.000 0.054 0.156
==============================================================================
Omnibus: 1.628 Durbin-Watson: 1.941
Prob(Omnibus): 0.443 Jarque-Bera (JB): 0.979
Skew: 0.051 Prob(JB): 0.613
Kurtosis: 3.575 Cond. No. 21.2
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
hypotheses = '(cpe = df[("cpe")].shift(1) = 0)'
f_test = fert_lags.f_test(hypotheses)
print(f_test)
<F test: F=array([[1.65577132]]), p=0.1990186450928186, df_denom=64, df_num=2>