O Capítulo 5 do Wooldridge explora as propriedades assintóticas quando a amostra de interesse cresce muito. Ele discute que usando o teorema Central do Limite pode-se concluir que
\[(\hat \beta -\beta)/se(\hat \beta) \sim N(0,1)\]
ou, aproximadamente
\[(\hat \beta -\beta)/se(\hat \beta) \sim t_{n-k-1}.\]
Logo, existem poucos exemplos computacionais nesse capítulo.
Histogram of prate using the data in 401K.RAW (Figure 5.2)
import numpy as np
import statsmodels.api as sm
import matplotlib.pyplot as plt
import pandas as pd
import patsy as ps
if __name__ == '__main__':
df = pd.read_csv('/home/daniel/Documents/Projetos/Prorum/Python For Econometrics/DataSets/Txt/401K.raw',delim_whitespace=True,header=None)
df.columns=['prate','mrate','totpart','totelg','age','totemp','sole','ltotemp']
prateData=df.as_matrix(columns=['prate'])
fig = plt.figure()
ax = fig.add_subplot(111)
ax.hist(prateData,bins=10,normed=1)
ax.set_xlabel('Participation Rate (prate)')
ax.set_ylabel('Proportion in Cell')
plt.axis([0, 100, 0, 0.07])
Exemplo 5.2:
import numpy as np
import statsmodels.api as sm
import matplotlib as plt
import pandas as pd
import patsy as ps
# Ex. 5.2
if __name__ == '__main__':
df = pd.read_csv('/home/daniel/Documents/Projetos/Prorum/Python For Econometrics/DataSets/Txt/BWGHT.raw',delim_whitespace=True,header=None,na_values=".")
df.columns=['faminc','cigtax','cigprice','bwght','fatheduc','motheduc','parity','male','white','cigs','lbwght','bwghtlbs','packs','lfaminc']
dfHalf=df[:694]
ps.NAAction(on_NA='drop', NA_types=['None', 'NaN'])
y,X = ps.dmatrices('bwght ~ cigs + lfaminc',data=dfHalf, return_type='dataframe')
model = sm.OLS(y,X) # Describe Model
results = model.fit() # Fit model
print results.summary()
se1=results.bse['cigs']
ps.NAAction(on_NA='drop', NA_types=['None', 'NaN'])
y,X = ps.dmatrices('bwght ~ cigs + lfaminc',data=df, return_type='dataframe')
model = sm.OLS(y,X) # Describe Model
results = model.fit() # Fit model
print results.summary()
se2=results.bse['cigs']
print se2/se1
Exemplo 5.3:
import numpy as np
import statsmodels.api as sm
import matplotlib.pyplot as plt
import pandas as pd
import patsy as ps
# Example 5.3
if __name__ == '__main__':
df = pd.read_csv('/home/daniel/Documents/Projetos/Prorum/Python For Econometrics/DataSets/Txt/CRIME1.raw',delim_whitespace=True,header=None)
df.columns=['narr86','nfarr86','nparr86','pcnv','avgsen','tottime','ptime86','qemp86','inc86','durat','black','hispan','born60','pcnvsq','pt86sq','inc86sq']
# Model
y,X = ps.dmatrices('narr86 ~ pcnv + avgsen + tottime + ptime86 + qemp86',data=df, return_type='dataframe')
model = sm.OLS(y,X) # Describe Model
results = model.fit() # Fit model
print results.summary()
# Model
y,X = ps.dmatrices('narr86 ~ pcnv + ptime86 + qemp86',data=df, return_type='dataframe')
restModel = sm.OLS(y,X) # Describe Model
restResults = restModel.fit() # Fit model
print restResults.summary()
print "(LM,pValue,difference between the degree of freedom) = ", results.compare_lm_test(restResults)
Resultados:
OLS Regression Results
==============================================================================
Dep. Variable: narr86 R-squared: 0.043
Model: OLS Adj. R-squared: 0.041
Method: Least Squares F-statistic: 24.29
Date: Thu, 18 Feb 2016 Prob (F-statistic): 5.43e-24
Time: 10:52:32 Log-Likelihood: -3392.7
No. Observations: 2725 AIC: 6797.
Df Residuals: 2719 BIC: 6833.
Df Model: 5
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [95.0% Conf. Int.]
------------------------------------------------------------------------------
Intercept 0.7061 0.033 21.297 0.000 0.641 0.771
pcnv -0.1512 0.041 -3.701 0.000 -0.231 -0.071
avgsen -0.0070 0.012 -0.568 0.570 -0.031 0.017
tottime 0.0121 0.010 1.263 0.207 -0.007 0.031
ptime86 -0.0393 0.009 -4.403 0.000 -0.057 -0.022
qemp86 -0.1031 0.010 -9.915 0.000 -0.123 -0.083
==============================================================================
Omnibus: 2395.326 Durbin-Watson: 1.837
Prob(Omnibus): 0.000 Jarque-Bera (JB): 106869.684
Skew: 4.001 Prob(JB): 0.00
Kurtosis: 32.618 Cond. No. 16.3
==============================================================================
OLS Regression Results
==============================================================================
Dep. Variable: narr86 R-squared: 0.041
Model: OLS Adj. R-squared: 0.040
Method: Least Squares F-statistic: 39.10
Date: Thu, 18 Feb 2016 Prob (F-statistic): 9.91e-25
Time: 10:52:32 Log-Likelihood: -3394.7
No. Observations: 2725 AIC: 6797.
Df Residuals: 2721 BIC: 6821.
Df Model: 3
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [95.0% Conf. Int.]
------------------------------------------------------------------------------
Intercept 0.7118 0.033 21.565 0.000 0.647 0.776
pcnv -0.1499 0.041 -3.669 0.000 -0.230 -0.070
ptime86 -0.0344 0.009 -4.007 0.000 -0.051 -0.018
qemp86 -0.1041 0.010 -10.023 0.000 -0.124 -0.084
==============================================================================
Omnibus: 2394.860 Durbin-Watson: 1.836
Prob(Omnibus): 0.000 Jarque-Bera (JB): 106169.154
Skew: 4.002 Prob(JB): 0.00
Kurtosis: 32.513 Cond. No. 8.27
==============================================================================
(LM,pValue,difference between the degree of freedom) = (4.0707297062815408, 0.13063281201643845, 2.0)