Chapter 15

R

Example-15-1.R

library(AER);library(stargazer)
data(mroz, package='wooldridge')

# restrict to non-missing wage observations
oursample <- subset(mroz, !is.na(wage))

# OLS slope parameter manually
with(oursample, cov(log(wage),educ) / var(educ) )
# IV slope parameter manually
with(oursample, cov(log(wage),fatheduc) / cov(educ,fatheduc) )


# OLS automatically
reg.ols <-   lm(log(wage) ~ educ, data=oursample)

# IV automatically 
reg.iv <- ivreg(log(wage) ~ educ | fatheduc, data=oursample) 

# Pretty regression table
stargazer(reg.ols,reg.iv, type="text")

Example-15-10.R

library(plm)
data(jtrain, package='wooldridge')

# Define panel data (for 1987 and 1988 only)
jtrain.87.88 <- subset(jtrain,year<=1988)
jtrain.p<-pdata.frame(jtrain.87.88, index=c("fcode","year"))

# IV FD regression
summary( plm(log(scrap)~hrsemp|grant, model="fd",data=jtrain.p) )

Example-15-4.R

library(AER);library(stargazer)
data(card, package='wooldridge')

# Checking for relevance: reduced form
redf<-lm(educ ~ nearc4+exper+I(exper^2)+black+smsa+south+smsa66+reg662+
           reg663+reg664+reg665+reg666+reg667+reg668+reg669, data=card)
# OLS
ols<-lm(log(wage)~educ+exper+I(exper^2)+black+smsa+south+smsa66+reg662+
           reg663+reg664+reg665+reg666+reg667+reg668+reg669, data=card)
# IV estimation
iv <-ivreg(log(wage)~educ+exper+I(exper^2)+black+smsa+south+smsa66+
             reg662+reg663+reg664+reg665+reg666+reg667+reg668+reg669 
          | nearc4+exper+I(exper^2)+black+smsa+south+smsa66+
            reg662+reg663+reg664+reg665+reg666+reg667+reg668+reg669
          , data=card)

# Pretty regression table of selected coefficients
stargazer(redf,ols,iv,type="text",
          keep=c("ed","near","exp","bl"),keep.stat=c("n","rsq"))

Example-15-5.R

library(AER);library(stargazer)
data(mroz, package='wooldridge')

# restrict to non-missing wage observations
oursample <- subset(mroz, !is.na(wage))

# 1st stage: reduced form
stage1 <- lm(educ~exper+I(exper^2)+motheduc+fatheduc, data=oursample)

# 2nd stage
man.2SLS<-lm(log(wage)~fitted(stage1)+exper+I(exper^2), data=oursample)

# Automatic 2SLS estimation
aut.2SLS<-ivreg(log(wage)~educ+exper+I(exper^2) 
             | motheduc+fatheduc+exper+I(exper^2) , data=oursample)

# Pretty regression table
stargazer(stage1,man.2SLS,aut.2SLS,type="text",keep.stat=c("n","rsq"))

Example-15-7.R

library(AER);library(lmtest)
data(mroz, package='wooldridge')

# restrict to non-missing wage observations
oursample <- subset(mroz, !is.na(wage))

# 1st stage: reduced form
stage1<-lm(educ~exper+I(exper^2)+motheduc+fatheduc, data=oursample)

# 2nd stage
stage2<-lm(log(wage)~educ+exper+I(exper^2)+resid(stage1),data=oursample)

# results including t tests
coeftest(stage2)

Example-15-8.R

library(AER)
data(mroz, package='wooldridge')

# restrict to non-missing wage observations
oursample <- subset(mroz, !is.na(wage))

# IV regression
summary( res.2sls <- ivreg(log(wage) ~ educ+exper+I(exper^2)
                | exper+I(exper^2)+motheduc+fatheduc,data=oursample) )

# Auxiliary regression
res.aux <-  lm(resid(res.2sls) ~ exper+I(exper^2)+motheduc+fatheduc
                       , data=oursample) 

# Calculations for test
( r2 <- summary(res.aux)$r.squared )
( n <- nobs(res.aux) )
( teststat <- n*r2 )
( pval <- 1-pchisq(teststat,1) )

Python

Example-15-1.py

import wooldridge as woo
import numpy as np
import pandas as pd
import linearmodels.iv as iv
import statsmodels.formula.api as smf

mroz = woo.dataWoo('mroz')

# restrict to non-missing wage observations:
mroz = mroz.dropna(subset=['lwage'])

cov_yz = np.cov(mroz['lwage'], mroz['fatheduc'])[1, 0]
cov_xy = np.cov(mroz['educ'], mroz['lwage'])[1, 0]
cov_xz = np.cov(mroz['educ'], mroz['fatheduc'])[1, 0]
var_x = np.var(mroz['educ'], ddof=1)
x_bar = np.mean(mroz['educ'])
y_bar = np.mean(mroz['lwage'])

# OLS slope parameter manually:
b_ols_man = cov_xy / var_x
print(f'b_ols_man: {b_ols_man}\n')

# IV slope parameter manually:
b_iv_man = cov_yz / cov_xz
print(f'b_iv_man: {b_iv_man}\n')

# OLS automatically:
reg_ols = smf.ols(formula='np.log(wage) ~ educ', data=mroz)
results_ols = reg_ols.fit()

# print regression table:
table_ols = pd.DataFrame({'b': round(results_ols.params, 4),
                          'se': round(results_ols.bse, 4),
                          't': round(results_ols.tvalues, 4),
                          'pval': round(results_ols.pvalues, 4)})
print(f'table_ols: \n{table_ols}\n')

# IV automatically:
reg_iv = iv.IV2SLS.from_formula(formula='np.log(wage) ~ 1 + [educ ~ fatheduc]',
                                data=mroz)
results_iv = reg_iv.fit(cov_type='unadjusted', debiased=True)

# print regression table:
table_iv = pd.DataFrame({'b': round(results_iv.params, 4),
                         'se': round(results_iv.std_errors, 4),
                         't': round(results_iv.tstats, 4),
                         'pval': round(results_iv.pvalues, 4)})
print(f'table_iv: \n{table_iv}\n')

Example-15-10.py

import wooldridge as woo
import pandas as pd
import linearmodels.iv as iv

jtrain = woo.dataWoo('jtrain')

# define panel data (for 1987 and 1988 only):
jtrain_87_88 = jtrain.loc[(jtrain['year'] == 1987) | (jtrain['year'] == 1988), :]
jtrain_87_88 = jtrain_87_88.set_index(['fcode', 'year'])

# manual computation of deviations of entity means:
jtrain_87_88['lscrap_diff1'] = \
    jtrain_87_88.sort_values(['fcode', 'year']).groupby('fcode')['lscrap'].diff()
jtrain_87_88['hrsemp_diff1'] = \
    jtrain_87_88.sort_values(['fcode', 'year']).groupby('fcode')['hrsemp'].diff()
jtrain_87_88['grant_diff1'] = \
    jtrain_87_88.sort_values(['fcode', 'year']).groupby('fcode')['grant'].diff()

# IV regression:
reg_iv = iv.IV2SLS.from_formula(
    formula='lscrap_diff1 ~ 1 + [hrsemp_diff1 ~ grant_diff1]',
    data=jtrain_87_88)
results_iv = reg_iv.fit(cov_type='unadjusted', debiased=True)

# print regression table:
table_iv = pd.DataFrame({'b': round(results_iv.params, 4),
                         'se': round(results_iv.std_errors, 4),
                         't': round(results_iv.tstats, 4),
                         'pval': round(results_iv.pvalues, 4)})
print(f'table_iv: \n{table_iv}\n')

Example-15-4.py

import wooldridge as woo
import numpy as np
import pandas as pd
import linearmodels.iv as iv
import statsmodels.formula.api as smf

card = woo.dataWoo('card')

# checking for relevance with reduced form:
reg_redf = smf.ols(
    formula='educ ~ nearc4 + exper + I(exper**2) + black + smsa +'
    'south + smsa66 + reg662 + reg663 + reg664 + reg665 + reg666 +'
    'reg667 + reg668 + reg669', data=card)
results_redf = reg_redf.fit()

# print regression table:
table_redf = pd.DataFrame({'b': round(results_redf.params, 4),
                           'se': round(results_redf.bse, 4),
                           't': round(results_redf.tvalues, 4),
                           'pval': round(results_redf.pvalues, 4)})
print(f'table_redf: \n{table_redf}\n')

# OLS:
reg_ols = smf.ols(
    formula='np.log(wage) ~ educ + exper + I(exper**2) + black + smsa +'
    'south + smsa66 + reg662 + reg663 + reg664 + reg665 +'
    'reg666 + reg667 + reg668 + reg669', data=card)
results_ols = reg_ols.fit()

# print regression table:
table_ols = pd.DataFrame({'b': round(results_ols.params, 4),
                          'se': round(results_ols.bse, 4),
                          't': round(results_ols.tvalues, 4),
                          'pval': round(results_ols.pvalues, 4)})
print(f'table_ols: \n{table_ols}\n')

# IV automatically:
reg_iv = iv.IV2SLS.from_formula(
    formula='np.log(wage)~ 1 + exper + I(exper**2) + black + smsa + '
            'south + smsa66 + reg662 + reg663 + reg664 + reg665 +'
            'reg666 + reg667 + reg668 + reg669 + [educ ~ nearc4]',
    data=card)
results_iv = reg_iv.fit(cov_type='unadjusted', debiased=True)

# print regression table:
table_iv = pd.DataFrame({'b': round(results_iv.params, 4),
                         'se': round(results_iv.std_errors, 4),
                         't': round(results_iv.tstats, 4),
                         'pval': round(results_iv.pvalues, 4)})
print(f'table_iv: \n{table_iv}\n')

Example-15-5.py

import wooldridge as woo
import numpy as np
import pandas as pd
import linearmodels.iv as iv
import statsmodels.formula.api as smf

mroz = woo.dataWoo('mroz')

# restrict to non-missing wage observations:
mroz = mroz.dropna(subset=['lwage'])

# 1st stage (reduced form):
reg_redf = smf.ols(formula='educ ~ exper + I(exper**2) + motheduc + fatheduc',
                   data=mroz)
results_redf = reg_redf.fit()
mroz['educ_fitted'] = results_redf.fittedvalues

# print regression table:
table_redf = pd.DataFrame({'b': round(results_redf.params, 4),
                           'se': round(results_redf.bse, 4),
                           't': round(results_redf.tvalues, 4),
                           'pval': round(results_redf.pvalues, 4)})
print(f'table_redf: \n{table_redf}\n')

# 2nd stage:
reg_secstg = smf.ols(formula='np.log(wage) ~ educ_fitted + exper + I(exper**2)',
                     data=mroz)
results_secstg = reg_secstg.fit()

# print regression table:
table_secstg = pd.DataFrame({'b': round(results_secstg.params, 4),
                             'se': round(results_secstg.bse, 4),
                             't': round(results_secstg.tvalues, 4),
                             'pval': round(results_secstg.pvalues, 4)})
print(f'table_secstg: \n{table_secstg}\n')

# IV automatically:
reg_iv = iv.IV2SLS.from_formula(
    formula='np.log(wage) ~ 1 + exper + I(exper**2) +'
            '[educ  ~ motheduc + fatheduc]',
    data=mroz)
results_iv = reg_iv.fit(cov_type='unadjusted', debiased=True)

# print regression table:
table_iv = pd.DataFrame({'b': round(results_iv.params, 4),
                         'se': round(results_iv.std_errors, 4),
                         't': round(results_iv.tstats, 4),
                         'pval': round(results_iv.pvalues, 4)})
print(f'table_iv: \n{table_iv}\n')

Example-15-7.py

import wooldridge as woo
import numpy as np
import pandas as pd
import statsmodels.formula.api as smf

mroz = woo.dataWoo('mroz')

# restrict to non-missing wage observations:
mroz = mroz.dropna(subset=['lwage'])

# 1st stage (reduced form):
reg_redf = smf.ols(formula='educ ~ exper + I(exper**2) + motheduc + fatheduc',
                   data=mroz)
results_redf = reg_redf.fit()
mroz['resid'] = results_redf.resid

# 2nd stage:
reg_secstg = smf.ols(formula='np.log(wage)~ resid + educ + exper + I(exper**2)',
                     data=mroz)
results_secstg = reg_secstg.fit()

# print regression table:
table_secstg = pd.DataFrame({'b': round(results_secstg.params, 4),
                             'se': round(results_secstg.bse, 4),
                             't': round(results_secstg.tvalues, 4),
                             'pval': round(results_secstg.pvalues, 4)})
print(f'table_secstg: \n{table_secstg}\n')

Example-15-8.py

import wooldridge as woo
import numpy as np
import pandas as pd
import linearmodels.iv as iv
import statsmodels.formula.api as smf
import scipy.stats as stats

mroz = woo.dataWoo('mroz')

# restrict to non-missing wage observations:
mroz = mroz.dropna(subset=['lwage'])

# IV regression:
reg_iv = iv.IV2SLS.from_formula(formula='np.log(wage) ~ 1 + exper + I(exper**2) +'
                                        '[educ ~ motheduc + fatheduc]', data=mroz)
results_iv = reg_iv.fit(cov_type='unadjusted', debiased=True)

# print regression table:
table_iv = pd.DataFrame({'b': round(results_iv.params, 4),
                         'se': round(results_iv.std_errors, 4),
                         't': round(results_iv.tstats, 4),
                         'pval': round(results_iv.pvalues, 4)})
print(f'table_iv: \n{table_iv}\n')

# auxiliary regression:
mroz['resid_iv'] = results_iv.resids
reg_aux = smf.ols(formula='resid_iv ~ exper + I(exper**2) + motheduc + fatheduc',
                  data=mroz)
results_aux = reg_aux.fit()

# calculations for test:
r2 = results_aux.rsquared
n = results_aux.nobs
teststat = n * r2
pval = 1 - stats.chi2.cdf(teststat, 1)

print(f'r2: {r2}\n')
print(f'n: {n}\n')
print(f'teststat: {teststat}\n')
print(f'pval: {pval}\n')

Julia

Example-15-1.jl

using WooldridgeDatasets, GLM, DataFrames, Econometrics, Statistics

mroz_wm = DataFrame(wooldridge("mroz"))

# restrict to non-missing wage observations:
mroz = mroz_wm[.!ismissing.(mroz_wm.wage), :]

# OLS slope parameter manually:
cov_yz = cov(mroz.lwage, mroz.fatheduc)
cov_xy = cov(mroz.educ, mroz.lwage)
cov_xz = cov(mroz.educ, mroz.fatheduc)
var_x = var(mroz.educ)
x_bar = mean(mroz.educ)
y_bar = mean(mroz.lwage)
b_ols_man = cov_xy / var_x
println("b_ols_man = $b_ols_man\n")

# IV slope parameter manually:
b_iv_man = cov_yz / cov_xz
println("b_iv_man = $b_iv_man\n")

# OLS automatically:
reg_ols = lm(@formula(lwage ~ educ), mroz)
table_ols = coeftable(reg_ols)
println("table_ols: \n$table_ols\n")

# IV automatically:
reg_iv = fit(EconometricModel,
    @formula(lwage ~ (educ ~ fatheduc)), mroz)
table_iv = coeftable(reg_iv)
println("table_iv: \n$table_iv")

Example-15-10.jl

using WooldridgeDatasets, GLM, DataFrames, Econometrics

jtrain = DataFrame(wooldridge("jtrain"))

# define panel data (for 1987 and 1988 only) and sort:
jtrain_8788 = subset(jtrain, :year => ByRow(<=(1988)))
sort!(jtrain_8788, [:fcode, :year])

# manual computation of deviations of entity means:
grouped_df = groupby(jtrain_8788, :fcode)
diff_df = DataFrame(fcode=unique(jtrain_8788.fcode))
diff_df.lscrap_diff1 = combine(grouped_df, :lscrap => diff).lscrap_diff
diff_df.hrsemp_diff1 = combine(grouped_df, :hrsemp => diff).hrsemp_diff
diff_df.grant_diff1 = combine(grouped_df, :grant => diff).grant_diff

# IV regression:
reg_iv = fit(EconometricModel,
    @formula(lscrap_diff1 ~ (hrsemp_diff1 ~ grant_diff1)), diff_df)
table_iv = coeftable(reg_iv)
println("table_iv: \n$table_iv")

Example-15-4.jl

using WooldridgeDatasets, GLM, DataFrames, Econometrics

card = DataFrame(wooldridge("card"))

# checking for relevance with reduced form:
reg_redf = lm(@formula(educ ~ nearc4 + exper + (exper^2) + black +
                              smsa + south + smsa66 + reg662 +
                              reg663 + reg664 + reg665 + reg666 +
                              reg667 + reg668 + reg669), card)
table_redf = coeftable(reg_redf)
println("table_redf: \n$table_redf\n")

# OLS:
reg_ols = lm(@formula(log(wage) ~ educ + exper + (exper^2) + black +
                                  smsa + south + smsa66 + reg662 +
                                  reg663 + reg664 + reg665 + reg666 +
                                  reg667 + reg668 + reg669), card)
table_ols = coeftable(reg_ols)
println("table_ols: \n$table_ols\n")


# IV automatically:
reg_iv = fit(EconometricModel,
    @formula(log(wage) ~ exper + (exper^2) + black + smsa +
                         south + smsa66 + reg662 + reg663 +
                         reg664 + reg665 + reg666 + reg667 +
                         reg668 + reg669 + (educ ~ nearc4)), card)
table_iv = coeftable(reg_iv)
println("table_iv: \n$table_iv")

Example-15-5.jl

using WooldridgeDatasets, GLM, DataFrames, Econometrics

mroz_wm = DataFrame(wooldridge("mroz"))

# restrict to non-missing wage observations:
mroz = mroz_wm[.!ismissing.(mroz_wm.wage), :]

# 1st stage (reduced form):
reg_redf = lm(@formula(educ ~ exper + (exper^2) +
                              motheduc + fatheduc), mroz)
mroz.educ_fitted = predict(reg_redf)
table_redf = coeftable(reg_redf)
println("table_redf: \n$table_redf\n")

# 2nd stage:
reg_secstg = lm(@formula(log(wage) ~ educ_fitted + exper +
                                     (exper^2)), mroz)
table_reg_secstg = coeftable(reg_secstg)
println("table_reg_secstg: \n$table_reg_secstg\n")

# IV automatically:
reg_iv = fit(EconometricModel,
    @formula(log(wage) ~ exper + (exper^2) +
                         (educ ~ motheduc + fatheduc)), mroz)
table_iv = coeftable(reg_iv)
println("table_iv: \n$table_iv")

Example-15-7.jl

using WooldridgeDatasets, GLM, DataFrames

mroz_wm = DataFrame(wooldridge("mroz"))

# restrict to non-missing wage observations:
mroz = mroz_wm[.!ismissing.(mroz_wm.wage), :]

# 1st stage (reduced form):
reg_redf = lm(@formula(educ ~ exper + (exper^2) +
                              motheduc + fatheduc), mroz)
mroz.resid = residuals(reg_redf)

# 2nd stage:
reg_secstg = lm(@formula(log(wage) ~ resid + educ +
                                     exper + (exper^2)), mroz)
table_reg_secstg = coeftable(reg_secstg)
println("table_reg_secstg: \n$table_reg_secstg")

Example-15-8.jl

using WooldridgeDatasets, GLM, DataFrames, Econometrics, Distributions

mroz_wm = DataFrame(wooldridge("mroz"))

# restrict to non-missing wage observations:
mroz = mroz_wm[.!ismissing.(mroz_wm.wage), :]

# IV regression:
reg_iv = fit(EconometricModel,
    @formula(log(wage) ~ exper + (exper^2) +
                         (educ ~ motheduc + fatheduc)), mroz)
table_iv = coeftable(reg_iv)
println("table_iv: \n$table_iv\n")

# auxiliary regression:
mroz.resid_iv = residuals(reg_iv)
reg_aux = lm(@formula(resid_iv ~ exper + (exper^2) +
                                 motheduc + fatheduc), mroz)

# calculations for test:
R2 = r2(reg_aux)
n = nobs(reg_aux)
teststat = n * R2
pval = 1 - cdf(Chisq(1), teststat)

println("R2 = $R2\n")
println("n = $n\n")
println("teststat = $teststat\n")
println("pval = $pval")