hendrik/applied-econometrics-2024
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

question 2.8

Browse source
This commit is contained in:
Hendrik Tillemans 2024-12-30 23:58:35 +01:00
parent a8233a3075
commit d2900ea279
10 changed files with 239 additions and 64 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

BIN
figures/question_2_5.png Normal file
View file

Binary file not shown.
Side by side

After

Width:  |  Height:  |  Size: 24 KiB

BIN
figures/question_2_6.png Normal file
View file

Binary file not shown.
Side by side

After

Width:  |  Height:  |  Size: 32 KiB

122
report/Assignment.tex
View file

@ -257,44 +257,6 @@ Because $Var(x_1)$ changed from 36 in to 1, we expect the standard error to be $
If the standard deviation from $x_1$ changes to 0, $\beta_1$ cannot we calculated. As we have seen with the no multicollinearity assumption.
\section{examples}
Some greek letters:
$\alpha$
$\beta$
$\gamma$
$\theta$
$\varepsilon$
$\pi$
$\lambda$
$\tau$
$x=x+27$
x=x+27
$A \Longrightarrow B$
$\underbrace{abs}_{test}$
sub and superscript
$\beta_0$
$\sum_{i=1}^{n} i$
In an equation:
\begin{equation}
\sum_{j=1}{n} j^2 \beta
\end{equation}
Equation without number
\begin{equation*}
A \Rightarrow B
\end{equation*}
\section{Empirical Investigation}
@ -315,13 +277,13 @@ We retain 2510 observations.
\subsection{Question 2.2}
\begin{figure}
\begin{figure} [ht]
\includegraphics[width=0.6\paperwidth]{../figures/question_2_2_wage}
\caption{Histogram wage}
\label{fig::question_2_2_wage}
\end{figure}
\begin{figure}
\begin{figure} [ht]
\includegraphics[width=0.6\paperwidth]{../figures/question_2_2_lwage}
\caption{Histogram lwage}
\label{fig::question_2_2_lwage}
@ -331,6 +293,8 @@ The lwage histogram in fig \ref{fig::question_2_2_lwage} is nicely centered so t
\subsection{Question 2.3}
We are going to investigate the correlation between the variables wage, age, school, man, malay, chinese and indian.
\begin{table}[ht]
\centering
\input{table_2_3}
@ -338,10 +302,86 @@ The lwage histogram in fig \ref{fig::question_2_2_lwage} is nicely centered so t
\label{tab::table_2_3}
\end{table}
We can see that there is a positive correlation between wage and school. It means that people who go longer to school will get a higher wage. There is a negative correlation between age and school. The younger generation is higher educated than older generation. Chinese citizens are better payed than malay, indian citizens have a negative correlation with wage.
We can see in table \ref{tab::table_2_3} that there is a positive correlation between wage and school. It means that people who go longer to school will get a higher wage. There is a negative correlation between age and school. The younger generation is higher educated than older generation. Chinese citizens are better payed than malay, indian citizens have a negative correlation with wage.
\subsection{Question 2.4}
We estimate a regression for lwage using the variables chinese and indian. We can calculate malay influence from the results.
\begin{table}[ht]
\centering
\input{results_24}
\caption{Linear model lwage}
\label{tab::results_24}
\end{table}
$R^{2} = 00.0255$ this means that there is a very weak correlation found. If we look at the coefficients in table \ref{tab::results_24}. We see a negative value of 0.17 for indian and a positive value of 0.14 for chinese. This gives a slightly positive value for the malay of $0.14 - 0.17 + 0.03 = 0$
This results implicate that there is a wage gap based on ethnicity.
\subsection{Question 2.5}
We estimate a regression for lwage using the variables chinese, indian and school.
\begin{table}[ht]
\centering
\input{results_25}
\caption{Linear model lwage/school}
\label{tab::results_25}
\end{table}
$R^{2} = 0.224$ this means that there is a weak correlation found. If we look at the coefficients in table \ref{tab::results_25}. We see a negative value of 0.07 for indian and a positive value of 0.18 for chinese. This gives a negative value for the malay of $0.18 - 0.07 - 0.11 = 0$
To see if lwage vs years of schooling is not linear. We plot it:
\begin{figure} [ht]
\includegraphics[width=0.6\paperwidth]{../figures/question_2_5}
\caption{lwage vs school}
\label{fig::question_2_5}
\end{figure}
In figure \ref{fig::question_2_5} there is no obvious non-linearity.
\subsection{Question 2.6}
We estimate a regression for lwage using the variables chinese, indian and school.
\begin{table}[ht]
\centering
\input{results_26}
\caption{Linear model lwage/age}
\label{tab::results_26}
\end{table}
$R^{2} = 0.370$ this means that there is a weak correlation found. If we look at the coefficients in table \ref{tab::results_26}.
To see if lwage vs age of schooling is not linear. We plot it:
\begin{figure} [ht]
\includegraphics[width=0.6\paperwidth]{../figures/question_2_6}
\caption{lwage vs age}
\label{fig::question_2_6}
\end{figure}
In figure \ref{fig::question_2_6} there is a banana shaped model indicating an non-linear relationship with a peak earnings around 40.
We can use \textbf{agesq} to do a parabolic fit. If we run this model we get:
\begin{table}[ht]
\centering
\input{results_26b}
\caption{parabolic model lwage/age}
\label{tab::results_26b}
\end{table}
We find a $R^{2} = 0.429$ which is higher than without the agesq.
In table \ref{tab::results_26b} a negative coefficient for agesq wich explains the parabolic distribution with a maximum.
\subsection{Question 2.8}
\begin{table}[ht]
\centering
\input{results_28}
\caption{Linear model 2.8}
\label{tab::results_28}
\end{table}
From the table \ref{tab::results_28} we can conclude that age does not differ substantially between the tables. For school we see a little difference.
\end{document}

9
report/results_24.tex Normal file
View file

@ -0,0 +1,9 @@
\begin{tabular}{lrrrrrr}
\toprule
& Coef. & Std.Err. & t & P>|t| & [0.025 & 0.975] \\
\midrule
const & 0.793313 & 0.022022 & 36.023272 & 0.000000 & 0.750129 & 0.836496 \\
chinese & 0.138678 & 0.035496 & 3.906889 & 0.000096 & 0.069074 & 0.208282 \\
indian & -0.173653 & 0.034758 & -4.996017 & 0.000001 & -0.241812 & -0.105495 \\
\bottomrule
\end{tabular}

10
report/results_25.tex Normal file
View file

@ -0,0 +1,10 @@
\begin{tabular}{lrrrrrr}
\toprule
& Coef. & Std.Err. & t & P>|t| & [0.025 & 0.975] \\
\midrule
const & 0.039704 & 0.035695 & 1.112307 & 0.266113 & -0.030291 & 0.109699 \\
chinese & 0.189360 & 0.031751 & 5.963947 & 0.000000 & 0.127099 & 0.251620 \\
indian & -0.066426 & 0.031317 & -2.121045 & 0.034016 & -0.127836 & -0.005015 \\
school & 0.087562 & 0.003462 & 25.294557 & 0.000000 & 0.080774 & 0.094350 \\
\bottomrule
\end{tabular}

11
report/results_26.tex Normal file
View file

@ -0,0 +1,11 @@
\begin{tabular}{lrrrrrr}
\toprule
& Coef. & Std.Err. & t & P>|t| & [0.025 & 0.975] \\
\midrule
const & -1.128876 & 0.058122 & -19.422515 & 0.000000 & -1.242848 & -1.014904 \\
chinese & 0.203956 & 0.028611 & 7.128603 & 0.000000 & 0.147853 & 0.260060 \\
indian & -0.010308 & 0.028310 & -0.364116 & 0.715802 & -0.065821 & 0.045205 \\
school & 0.114892 & 0.003318 & 34.628243 & 0.000000 & 0.108386 & 0.121398 \\
age & 0.028072 & 0.001163 & 24.136639 & 0.000000 & 0.025791 & 0.030353 \\
\bottomrule
\end{tabular}

12
report/results_26b.tex Normal file
View file

@ -0,0 +1,12 @@
\begin{tabular}{lrrrrrr}
\toprule
& Coef. & Std.Err. & t & P>|t| & [0.025 & 0.975] \\
\midrule
const & -2.689961 & 0.111653 & -24.092167 & 0.000000 & -2.908903 & -2.471020 \\
chinese & 0.216072 & 0.027252 & 7.928647 & 0.000000 & 0.162633 & 0.269511 \\
indian & -0.004273 & 0.026958 & -0.158500 & 0.874076 & -0.057134 & 0.048589 \\
school & 0.106121 & 0.003206 & 33.103889 & 0.000000 & 0.099835 & 0.112408 \\
age & 0.126927 & 0.006240 & 20.341402 & 0.000000 & 0.114691 & 0.139163 \\
agesq & -0.135899 & 0.008442 & -16.098099 & 0.000000 & -0.152453 & -0.119345 \\
\bottomrule
\end{tabular}

12
report/results_28.tex Normal file
View file

@ -0,0 +1,12 @@
\begin{tabular}{lrrrrrr}
\toprule
& Coef. & Std.Err. & t & P>|t| & [0.025 & 0.975] \\
\midrule
const & -1.205128 & 0.057278 & -21.039804 & 0.000000 & -1.317446 & -1.092810 \\
age & 0.025987 & 0.001154 & 22.523092 & 0.000000 & 0.023724 & 0.028249 \\
school & 0.111415 & 0.003261 & 34.169989 & 0.000000 & 0.105021 & 0.117809 \\
chinese & 0.221610 & 0.028027 & 7.907069 & 0.000000 & 0.166652 & 0.276568 \\
indian & 0.013045 & 0.027769 & 0.469753 & 0.638572 & -0.041408 & 0.067498 \\
men & 0.258888 & 0.024088 & 10.747734 & 0.000000 & 0.211654 & 0.306122 \\
\bottomrule
\end{tabular}

25
report/table_2_3.tex
View file

@ -1,20 +1,13 @@
\begin{tabular}{lrrrrrrrr}
\begin{tabular}{lrrrrrrr}
\toprule
& count & mean & std & min & 25\% & 50\% & 75\% & max \\
& wage & age & school & men & malay & chinese & indian \\
\midrule
paidwork & 2510.000000 & 1.000000 & 0.000000 & 1.000000 & 1.000000 & 1.000000 & 1.000000 & 1.000000 \\
lwage & 2510.000000 & 0.780391 & 0.737255 & -3.336058 & 0.299333 & 0.766255 & 1.241741 & 4.208274 \\
men & 2510.000000 & 0.624303 & 0.484398 & 0.000000 & 0.000000 & 1.000000 & 1.000000 & 1.000000 \\
malay & 2510.000000 & 0.435458 & 0.495919 & 0.000000 & 0.000000 & 0.000000 & 1.000000 & 1.000000 \\
chinese & 2510.000000 & 0.272510 & 0.445334 & 0.000000 & 0.000000 & 0.000000 & 1.000000 & 1.000000 \\
indian & 2510.000000 & 0.292032 & 0.454793 & 0.000000 & 0.000000 & 0.000000 & 1.000000 & 1.000000 \\
age & 2510.000000 & 33.025101 & 10.699703 & 15.000000 & 25.000000 & 31.000000 & 39.000000 & 65.000000 \\
agesq & 2510.000000 & 12.050953 & 7.977792 & 2.250000 & 6.250000 & 9.610000 & 15.210000 & 42.250000 \\
gexpr & 2510.000000 & 18.933865 & 12.482897 & 0.000000 & 9.000000 & 16.000000 & 26.000000 & 59.000000 \\
gexprsq & 2510.000000 & 5.142518 & 6.277625 & 0.000000 & 0.810000 & 2.560000 & 6.760000 & 34.810001 \\
yprim & 2510.000000 & 5.277291 & 1.711691 & 0.000000 & 6.000000 & 6.000000 & 6.000000 & 6.000000 \\
ysec & 2510.000000 & 2.813944 & 2.704680 & 0.000000 & 0.000000 & 3.000000 & 5.000000 & 14.000000 \\
school & 2510.000000 & 8.091235 & 3.783405 & 0.000000 & 6.000000 & 9.000000 & 11.000000 & 20.000000 \\
wage & 2510.000000 & 2.903078 & 2.886990 & 0.035577 & 1.348958 & 2.151692 & 3.461635 & 67.240379 \\
wage & 1.000000 & 0.206329 & 0.406310 & 0.172137 & 0.014109 & 0.112021 & -0.125078 \\
age & 0.206329 & 1.000000 & -0.333795 & 0.144930 & 0.018370 & 0.015293 & -0.035007 \\
school & 0.406310 & -0.333795 & 1.000000 & 0.056334 & 0.119656 & -0.010267 & -0.120423 \\
men & 0.172137 & 0.144930 & 0.056334 & 1.000000 & 0.097288 & -0.027757 & -0.078907 \\
malay & 0.014109 & 0.018370 & 0.119656 & 0.097288 & 1.000000 & -0.537530 & -0.564071 \\
chinese & 0.112021 & 0.015293 & -0.010267 & -0.027757 & -0.537530 & 1.000000 & -0.393085 \\
indian & -0.125078 & -0.035007 & -0.120423 & -0.078907 & -0.564071 & -0.393085 & 1.000000 \\
\bottomrule
\end{tabular}

102
scripts/empirical.py
View file

@ -140,48 +140,136 @@ data_frame_to_latex_table_file(report_dir + 'table_2_3.tex',
print_question('Question 2.4: Estimate lwage model')
# explanatory variables for question 2.4
# x_vars_24 = data[['smcity', 'AA']] # TODO
x_vars_24 = data[['chinese', 'indian']]
# add a constant
# X_24 = sm.add_constant(x_vars_24) [uncomment]
X_24 = sm.add_constant(x_vars_24)
# set-up model
# model_24 = sm.OLS(,) #TODO
model_24 = sm.OLS(data['lwage'], X_24)
# estimate the model
# results_24 = model_24. #TODO
results_24 = model_24.fit()
# print the OLS output
# print(results_24.summary()) [uncomment]
print(results_24.summary())
# export the coefficients part of the summary to a table
# data_frame_to_latex_table_file(report_dir + 'results_24.tex',
# results_24.summary2().tables[1])
data_frame_to_latex_table_file(report_dir + 'results_24.tex',
results_24.summary2().tables[1])
# -----------------------------------------------------------------------------
# Question 2.5
# -----------------------------------------------------------------------------
print_question('Question 2.5: Adding school')
# explanatory variables for question 2.5
x_vars_25 = data[['chinese', 'indian', 'school']]
# add a constant
X_25 = sm.add_constant(x_vars_25)
# set-up model
model_25 = sm.OLS(data['lwage'], X_25)
# estimate the model
results_25 = model_25.fit()
# print the OLS output
print(results_25.summary())
# export the coefficients part of the summary to a table
data_frame_to_latex_table_file(report_dir + 'results_25.tex',
results_25.summary2().tables[1])
plt.scatter(data['school'], data['lwage'])
plt.savefig(figure_dir + "question_2_5.png")
plt.show()
# -----------------------------------------------------------------------------
# Question 2.6
# -----------------------------------------------------------------------------
print_question('Question 2.6: Adding age')
# explanatory variables for question 2.5
x_vars_26 = data[['chinese', 'indian', 'school', 'age']]
# add a constant
X_26 = sm.add_constant(x_vars_26)
# set-up model
model_26 = sm.OLS(data['lwage'], X_26)
# estimate the model
results_26 = model_26.fit()
# print the OLS output
print(results_26.summary())
# export the coefficients part of the summary to a table
data_frame_to_latex_table_file(report_dir + 'results_26.tex',
results_26.summary2().tables[1])
coef = results_26.summary2().tables[1]['Coef.']
lwage_26 = data['lwage'] - coef['chinese']*data['chinese'] - coef['indian']*data['indian'] - coef['school']*data['school']
lwage_26 = data['lwage'] - coef['school']*data['school']
plt.scatter(data['age'], data['lwage'])
plt.savefig(figure_dir + "question_2_6.png")
plt.show()
# explanatory variables for question 2.5
x_vars_26b = data[['chinese', 'indian', 'school', 'age', 'agesq']]
# add a constant
X_26b = sm.add_constant(x_vars_26b)
# set-up model
model_26b = sm.OLS(data['lwage'], X_26b)
# estimate the model
results_26b = model_26b.fit()
# print the OLS output
print(results_26b.summary())
# export the coefficients part of the summary to a table
data_frame_to_latex_table_file(report_dir + 'results_26b.tex',
results_26b.summary2().tables[1])
# -----------------------------------------------------------------------------
# Question 2.7
# -----------------------------------------------------------------------------
print_question('Question 2.7: Create the woman variable')
data['women'] = 1 - data['men']
# -----------------------------------------------------------------------------
# Question 2.8
# -----------------------------------------------------------------------------
print_question('Question 2.8: lwage model')
# explanatory variables for question 2.5
x_vars_28 = data[['age', 'school', 'chinese', 'indian', 'men']]
# add a constant
X_28 = sm.add_constant(x_vars_28)
# set-up model
model_28 = sm.OLS(data['lwage'], X_28)
# estimate the model
results_28 = model_28.fit()
# print the OLS output
print(results_28.summary())
# export the coefficients part of the summary to a table
data_frame_to_latex_table_file(report_dir + 'results_28.tex',
results_28.summary2().tables[1])
# -----------------------------------------------------------------------------
# Question 2.9
# -----------------------------------------------------------------------------