# Introductory Econometrics - Jeffrey M. Wooldridge: Como replicar os exemplos do Capítulo 5 usando python?

+2 votos
390 visitas
perguntada Fev 18, 2016 em Economia

## 1 Resposta

0 votos
respondida Fev 18, 2016 por (5,486 pontos)

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

$(\hat \beta -\beta)/se(\hat \beta) \sim N(0,1)$

$(\hat \beta -\beta)/se(\hat \beta) \sim t_{n-k-1}.$

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.columns=['prate','mrate','totpart','totelg','age','totemp','sole','ltotemp']

prateData=df.as_matrix(columns=['prate'])

fig = plt.figure()
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.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.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)


                           OLS Regression Results
==============================================================================
Dep. Variable:                 narr86   R-squared:                       0.043
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
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)