simulation code done
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22 changed files with 1638 additions and 27 deletions
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figures/quadratic_model_linear.png
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figures/quadratic_model_quadratic.png
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figures/quadratic_model_y.png
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report/Assignment.tex
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\documentclass[12pt]{article}
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\usepackage{natbib}
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\usepackage{url}
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\usepackage[utf8x]{inputenc}
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\usepackage{mathtools}%
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\usepackage{graphicx}
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\usepackage{parskip}
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\usepackage{xcolor}%
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\usepackage{fancyhdr}
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\usepackage{vmargin}
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\usepackage{booktabs}%
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\usepackage{sectsty}% for coloring sections
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\setmarginsrb{3 cm}{2.5 cm}{3 cm}{2.5 cm}{1 cm}{1.5 cm}{1 cm}{1.5 cm}
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% define your own custom colors
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% If you want to change the colors you would need to update the RGB code in the
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% last brackets. Better not change the name of the color as it is used elsewhere
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\definecolor{report_main}{HTML}{200045}
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\definecolor{report_second}{HTML}{F39912}
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\definecolor{report_third}{HTML}{8B0010}
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\title{\color{report_main}{Assignment Econometrics 2024}} % Title
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\author{Hendrik Marcel W Tillemans} % Author
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\date{\today} % Date
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\makeatletter
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\let\thetitle\@title
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\let\theauthor\@author
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\let\thedate\@date
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\makeatother
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\pagestyle{fancy}
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\fancyhf{}
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\rhead{\theauthor} % header on the right
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\lhead{\thetitle} % header on the left
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\cfoot{\thepage} % footer in the center
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\sectionfont{\color{report_main}}
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\subsectionfont{\color{report_third}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% This is where the actual document starts
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{document}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% This section details the group information
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{titlepage}
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\centering
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\vspace*{0.5 cm}
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\includegraphics[scale = 0.95]{../figures/vub.png}\\[1.0 cm] % University Logo
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\textsc{\LARGE \newline\newline Free University Brussels}\\[2.0 cm] % University Name
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\textsc{\Large \color{report_main}{Class: Econometrics}}\\[0.5 cm] % Course Code
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\rule{\linewidth}{0.2 mm} \\[0.4 cm]
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{ \huge \bfseries \thetitle}\\
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\rule{\linewidth}{0.2 mm} \\[1.5 cm]
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\begin{minipage}{0.5\textwidth}
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\begin{flushleft} \large
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\emph{Professor:}\\
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Jeroen Kerkhof\\
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Faculty of Economic Sciences\\
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\end{flushleft}
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\end{minipage}~
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\begin{minipage}{0.4\textwidth}
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\begin{flushright} \large
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\emph{Group:} \\
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Hendrik Marcel W Tillemans\\
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\end{flushright}
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\end{minipage}\\[2 cm]
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% takes the current date
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\thedate
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\end{titlepage}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% This details the inclusion (or not) of the table of contents
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% and list of figures and tables.
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% You can add/remove page breaks as you seem fit.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\tableofcontents
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\pagebreak
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\listoffigures
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\listoftables
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\pagebreak
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% This is the start of the actual document content
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% You can just write text in here as you would in any other word processor.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Question 1}
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This my answer to question 1.
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\subsection{Example}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\pagebreak
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creates a page break.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Simulation Study}
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\subsection{1.2: Linear Fit on Generated Data}
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\begin{table}[h]
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\input{table_1_2}
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\caption{Linear Fit on Generated Data}
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\label{tab::table_1_2}
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\end{table}
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\subsection{1.3: Linear Fit with 1 Variable}
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\begin{table}[h]
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\input{table_1_3}
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\caption{Linear Fit with 1 Variable}
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\label{tab::table_1_3}
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\end{table}
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\subsection{1.4: New Linear Fit on Generated Data}
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\begin{table}[h]
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\input{table_1_4}
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\caption{New Linear Fit on Generated Data}
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\label{tab::table_1_4}
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\end{table}
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\subsection{1.5: New Linear Fit with 1 Variable}
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\begin{table}[h]
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\input{table_1_5}
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\caption{Linear Fit with 1 Variable}
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\label{tab::table_1_5}
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\end{table}
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\subsection{1.6: Generate Data with Small Variance on x1}
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\begin{table}[h]
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\input{table_1_6}
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\caption{Generate Data with Small Variance on x1}
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\label{tab::table_1_6}
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\end{table}
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\section{examples}
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Some greek letters:
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$\alpha$
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$\beta$
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$\gamma$
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$\theta$
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$\varepsilon$
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$\pi$
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$\lambda$
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$\tau$
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$x=x+27$
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x=x+27
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$A \Longrightarrow B$
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$\underbrace{abs}_{test}$
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sub and superscript
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$\beta_0$
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$\sum_{i=1}^{n} i$
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In an equation:
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\begin{equation}
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\sum_{j=1}{n} j^2 \beta
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\end{equation}
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Equation without number
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\begin{equation*}
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A \Rightarrow B
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\end{equation*}
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\section{Empirical Investigation}
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Here is some example code to create tables and graphs from the
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Python script. In order for this to work you would first need
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to run the script non\_linear\_models\_example\_report.py. Running that
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file (using the recommended file structure) creates some figures
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in the figures folder and some tables in .tex files in the report folder.
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\subsection{Question 3}
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For instance, here the file df\_table.tex is used print the actual numbers
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in the table.
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\begin{table}[h]
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\input{df_table}
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\caption{This tables has the estimates for ...}
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\label{tab::estimation_results}
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\end{table}
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\subsection{Question 4: Some graphs}
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\begin{figure}
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\includegraphics[width=0.6\paperwidth]{../figures/quadratic_model_y}
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\caption{This is a Figure coming straight from Python.}
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\label{fig::example_data}
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\end{figure}
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In Figure \ref{fig::example_data} we see the data.
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\begin{figure}
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\includegraphics[width=0.6\paperwidth]{../figures/quadratic_model_linear}
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\caption{This is a linear fit on a quadratic model.}
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\label{fig::example_quadratic_linear}
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\end{figure}
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In Figure \ref{fig::example_quadratic_linear} we see a linear fit.
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\begin{figure}
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\includegraphics[width=0.6\paperwidth]{../figures/quadratic_model_quadratic}
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\caption{This is quadratic fit on a quadratic model.}
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\label{fig::example_quadratic_quadratic}
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\end{figure}
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In Figure \ref{fig::example_quadratic_quadratic} we see that
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\subsection{Question 5}
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Equation example with matrices:
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\begin{equation}\label{eq::wald_test}
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H_0: \beta_1 = - \beta_2; \beta_3=0; \beta_2 + 2\beta_4 = 2
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\quad H_1: \neg H_0
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\end{equation}
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can be written in matrix form as:
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\begin{equation}\label{eq::matrix_form}
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\begin{bmatrix}
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1 & 1 & 0 & 0 \\
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0 & 0 & 1 & 0 \\
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0 & 1 & 0 & 2
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\end{bmatrix}
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\begin{bmatrix}
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\beta_1 \\
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\beta_2 \\
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\beta_3 \\
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\beta_4
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\end{bmatrix} =
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\begin{bmatrix}
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0 \\
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0 \\
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2
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\end{bmatrix}
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\end{equation}
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In equation \eqref{eq::wald_test} we see that... and in equation \eqref{eq::matrix_form} we see that
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\subsection{Question 6}
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$\beta$
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\begin{table}
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\input{summary}
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\caption{This tables has the estimates summary}
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\label{tab::estimation_results_summary}
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\end{table}
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Table \ref{tab::estimation_results_summary} has the full summary.
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\begin{table}
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\input{results_coef}
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\caption{This tables has the estimates summary}
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\label{tab::estimation_results_coef}
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\end{table}
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Table \ref{tab::estimation_results_coef} has the only the coefficient
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results.
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\end{document}
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report/df_table.tex
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report/df_table.tex
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\begin{tabular}{lrrrrr}
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\toprule
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& coeff & tvals & pvals & conf\_lower & conf\_higher \\
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\midrule
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0 & 17.880000 & 1.730000 & 0.090000 & -2.800000 & 38.560000 \\
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1 & 0.390000 & 0.560000 & 0.580000 & -0.990000 & 1.770000 \\
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2 & -0.490000 & -18.290000 & 0.000000 & -0.550000 & -0.440000 \\
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\bottomrule
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\end{tabular}
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report/example_report_24.tex
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report/example_report_24.tex
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\documentclass[12pt]{article}
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\usepackage{natbib}
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\usepackage{url}
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\usepackage[utf8x]{inputenc}
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\usepackage{mathtools}%
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\usepackage{graphicx}
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\usepackage{parskip}
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\usepackage{xcolor}%
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\usepackage{fancyhdr}
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\usepackage{vmargin}
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\usepackage{booktabs}%
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\usepackage{sectsty}% for coloring sections
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\setmarginsrb{3 cm}{2.5 cm}{3 cm}{2.5 cm}{1 cm}{1.5 cm}{1 cm}{1.5 cm}
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% define your own custom colors
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||||||
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% If you want to change the colors you would need to update the RGB code in the
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% last brackets. Better not change the name of the color as it is used elsewhere
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\definecolor{report_main}{HTML}{200045}
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\definecolor{report_second}{HTML}{F39912}
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\definecolor{report_third}{HTML}{8B0010}
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\title{\color{report_main}{Assignment Econometrics 2024}} % Title
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\author{Hendrik Marcel W Tillemans} % Author
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\date{\today} % Date
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\makeatletter
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\let\thetitle\@title
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\let\theauthor\@author
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\let\thedate\@date
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\makeatother
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\pagestyle{fancy}
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\fancyhf{}
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\rhead{\theauthor} % header on the right
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\lhead{\thetitle} % header on the left
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\cfoot{\thepage} % footer in the center
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\sectionfont{\color{report_main}}
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\subsectionfont{\color{report_third}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% This is where the actual document starts
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{document}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% This section details the group information
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{titlepage}
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\centering
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\vspace*{0.5 cm}
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\includegraphics[scale = 0.95]{../figures/vub.png}\\[1.0 cm] % University Logo
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||||||
|
\textsc{\LARGE \newline\newline Free University Brussels}\\[2.0 cm] % University Name
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||||||
|
\textsc{\Large \color{report_main}{Class: Econometrics}}\\[0.5 cm] % Course Code
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||||||
|
\rule{\linewidth}{0.2 mm} \\[0.4 cm]
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{ \huge \bfseries \thetitle}\\
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||||||
|
\rule{\linewidth}{0.2 mm} \\[1.5 cm]
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||||||
|
|
||||||
|
\begin{minipage}{0.5\textwidth}
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||||||
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\begin{flushleft} \large
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\emph{Professor:}\\
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||||||
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Jeroen Kerkhof\\
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||||||
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Faculty of Economic Sciences\\
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||||||
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\end{flushleft}
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\end{minipage}~
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||||||
|
\begin{minipage}{0.4\textwidth}
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|
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||||||
|
\begin{flushright} \large
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||||||
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\emph{Group:} \\
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Hendrik Marcel W Tillemans
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\end{flushright}
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||||||
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\end{minipage}\\[2 cm]
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||||||
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||||||
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% takes the current date
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||||||
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\thedate
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||||||
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\end{titlepage}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
% This details the inclusion (or not) of the table of contents
|
||||||
|
% and list of figures and tables.
|
||||||
|
% You can add/remove page breaks as you seem fit.
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
|
||||||
|
\tableofcontents
|
||||||
|
|
||||||
|
\pagebreak
|
||||||
|
|
||||||
|
\listoffigures
|
||||||
|
|
||||||
|
\listoftables
|
||||||
|
|
||||||
|
\pagebreak
|
||||||
|
|
||||||
|
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
% This is the start of the actual document content
|
||||||
|
% You can just write text in here as you would in any other word processor.
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
|
||||||
|
\section{Question 1}
|
||||||
|
|
||||||
|
This my answer to question 1.
|
||||||
|
|
||||||
|
\subsection{Example}
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
|
||||||
|
\pagebreak
|
||||||
|
|
||||||
|
creates a page break.
|
||||||
|
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
|
||||||
|
|
||||||
|
\section{Simlulation Study}
|
||||||
|
|
||||||
|
Here
|
||||||
|
|
||||||
|
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}
|
||||||
|
|
||||||
|
Here is some example code to create tables and graphs from the
|
||||||
|
Python script. In order for this to work you would first need
|
||||||
|
to run the script non\_linear\_models\_example\_report.py. Running that
|
||||||
|
file (using the recommended file structure) creates some figures
|
||||||
|
in the figures folder and some tables in .tex files in the report folder.
|
||||||
|
|
||||||
|
|
||||||
|
\subsection{Question 3}
|
||||||
|
|
||||||
|
For instance, here the file df\_table.tex is used print the actual numbers
|
||||||
|
in the table.
|
||||||
|
|
||||||
|
\begin{table}[h]
|
||||||
|
\input{df_table}
|
||||||
|
\caption{This tables has the estimates for ...}
|
||||||
|
\label{tab::estimation_results}
|
||||||
|
\end{table}
|
||||||
|
|
||||||
|
\subsection{Question 4: Some graphs}
|
||||||
|
|
||||||
|
\begin{figure}
|
||||||
|
\includegraphics[width=0.6\paperwidth]{../figures/quadratic_model_y}
|
||||||
|
\caption{This is a Figure coming straight from Python.}
|
||||||
|
\label{fig::example_data}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
In Figure \ref{fig::example_data} we see the data.
|
||||||
|
|
||||||
|
\begin{figure}
|
||||||
|
\includegraphics[width=0.6\paperwidth]{../figures/quadratic_model_linear}
|
||||||
|
\caption{This is a linear fit on a quadratic model.}
|
||||||
|
\label{fig::example_quadratic_linear}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
In Figure \ref{fig::example_quadratic_linear} we see a linear fit.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}
|
||||||
|
\includegraphics[width=0.6\paperwidth]{../figures/quadratic_model_quadratic}
|
||||||
|
\caption{This is quadratic fit on a quadratic model.}
|
||||||
|
\label{fig::example_quadratic_quadratic}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
In Figure \ref{fig::example_quadratic_quadratic} we see that
|
||||||
|
|
||||||
|
\subsection{Question 5}
|
||||||
|
|
||||||
|
Equation example with matrices:
|
||||||
|
|
||||||
|
\begin{equation}\label{eq::wald_test}
|
||||||
|
H_0: \beta_1 = - \beta_2; \beta_3=0; \beta_2 + 2\beta_4 = 2
|
||||||
|
\quad H_1: \neg H_0
|
||||||
|
\end{equation}
|
||||||
|
|
||||||
|
can be written in matrix form as:
|
||||||
|
\begin{equation}\label{eq::matrix_form}
|
||||||
|
\begin{bmatrix}
|
||||||
|
1 & 1 & 0 & 0 \\
|
||||||
|
0 & 0 & 1 & 0 \\
|
||||||
|
0 & 1 & 0 & 2
|
||||||
|
\end{bmatrix}
|
||||||
|
\begin{bmatrix}
|
||||||
|
\beta_1 \\
|
||||||
|
\beta_2 \\
|
||||||
|
\beta_3 \\
|
||||||
|
\beta_4
|
||||||
|
\end{bmatrix} =
|
||||||
|
\begin{bmatrix}
|
||||||
|
0 \\
|
||||||
|
0 \\
|
||||||
|
2
|
||||||
|
\end{bmatrix}
|
||||||
|
\end{equation}
|
||||||
|
|
||||||
|
In equation \eqref{eq::wald_test} we see that... and in equation \eqref{eq::matrix_form} we see that
|
||||||
|
|
||||||
|
\subsection{Question 6}
|
||||||
|
|
||||||
|
|
||||||
|
$\beta$
|
||||||
|
|
||||||
|
\begin{table}
|
||||||
|
\input{summary}
|
||||||
|
\caption{This tables has the estimates summary}
|
||||||
|
\label{tab::estimation_results_summary}
|
||||||
|
\end{table}
|
||||||
|
|
||||||
|
Table \ref{tab::estimation_results_summary} has the full summary.
|
||||||
|
|
||||||
|
\begin{table}
|
||||||
|
\input{results_coef}
|
||||||
|
\caption{This tables has the estimates summary}
|
||||||
|
\label{tab::estimation_results_coef}
|
||||||
|
\end{table}
|
||||||
|
|
||||||
|
Table \ref{tab::estimation_results_coef} has the only the coefficient
|
||||||
|
results.
|
||||||
|
|
||||||
|
|
||||||
|
\end{document}
|
||||||
9
report/results_coef.tex
Normal file
9
report/results_coef.tex
Normal file
|
|
@ -0,0 +1,9 @@
|
||||||
|
\begin{tabular}{lrrrrrr}
|
||||||
|
\toprule
|
||||||
|
& Coef. & Std.Err. & t & P>|t| & [0.025 & 0.975] \\
|
||||||
|
\midrule
|
||||||
|
const & 17.880598 & 10.325727 & 1.731655 & 0.088744 & -2.796314 & 38.557509 \\
|
||||||
|
x1 & 0.387451 & 0.688193 & 0.562997 & 0.575645 & -0.990632 & 1.765533 \\
|
||||||
|
x2 & -0.494529 & 0.027036 & -18.291331 & 0.000000 & -0.548668 & -0.440390 \\
|
||||||
|
\bottomrule
|
||||||
|
\end{tabular}
|
||||||
34
report/summary.tex
Normal file
34
report/summary.tex
Normal file
|
|
@ -0,0 +1,34 @@
|
||||||
|
\begin{center}
|
||||||
|
\begin{tabular}{lclc}
|
||||||
|
\toprule
|
||||||
|
\textbf{Dep. Variable:} & y & \textbf{ R-squared: } & 0.936 \\
|
||||||
|
\textbf{Model:} & OLS & \textbf{ Adj. R-squared: } & 0.934 \\
|
||||||
|
\textbf{Method:} & Least Squares & \textbf{ F-statistic: } & 416.4 \\
|
||||||
|
\textbf{Date:} & Sun, 29 Dec 2024 & \textbf{ Prob (F-statistic):} & 9.69e-35 \\
|
||||||
|
\textbf{Time:} & 21:32:34 & \textbf{ Log-Likelihood: } & -327.30 \\
|
||||||
|
\textbf{No. Observations:} & 60 & \textbf{ AIC: } & 660.6 \\
|
||||||
|
\textbf{Df Residuals:} & 57 & \textbf{ BIC: } & 666.9 \\
|
||||||
|
\textbf{Df Model:} & 2 & \textbf{ } & \\
|
||||||
|
\textbf{Covariance Type:} & nonrobust & \textbf{ } & \\
|
||||||
|
\bottomrule
|
||||||
|
\end{tabular}
|
||||||
|
\begin{tabular}{lcccccc}
|
||||||
|
& \textbf{coef} & \textbf{std err} & \textbf{t} & \textbf{P$> |$t$|$} & \textbf{[0.025} & \textbf{0.975]} \\
|
||||||
|
\midrule
|
||||||
|
\textbf{const} & 17.8806 & 10.326 & 1.732 & 0.089 & -2.796 & 38.558 \\
|
||||||
|
\textbf{x1} & 0.3875 & 0.688 & 0.563 & 0.576 & -0.991 & 1.766 \\
|
||||||
|
\textbf{x2} & -0.4945 & 0.027 & -18.291 & 0.000 & -0.549 & -0.440 \\
|
||||||
|
\bottomrule
|
||||||
|
\end{tabular}
|
||||||
|
\begin{tabular}{lclc}
|
||||||
|
\textbf{Omnibus:} & 0.223 & \textbf{ Durbin-Watson: } & 2.169 \\
|
||||||
|
\textbf{Prob(Omnibus):} & 0.894 & \textbf{ Jarque-Bera (JB): } & 0.397 \\
|
||||||
|
\textbf{Skew:} & -0.106 & \textbf{ Prob(JB): } & 0.820 \\
|
||||||
|
\textbf{Kurtosis:} & 2.662 & \textbf{ Cond. No. } & 837. \\
|
||||||
|
\bottomrule
|
||||||
|
\end{tabular}
|
||||||
|
%\caption{OLS Regression Results}
|
||||||
|
\end{center}
|
||||||
|
|
||||||
|
Notes: \newline
|
||||||
|
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
|
||||||
9
report/table_1_2.tex
Normal file
9
report/table_1_2.tex
Normal file
|
|
@ -0,0 +1,9 @@
|
||||||
|
\begin{tabular}{lrrrr}
|
||||||
|
\toprule
|
||||||
|
& True & Estimated & Std Err & t-Stat \\
|
||||||
|
\midrule
|
||||||
|
0 & 3.000000 & 2.962797 & 0.117377 & 25.241713 \\
|
||||||
|
1 & -4.000000 & -4.018728 & 0.015964 & -251.729125 \\
|
||||||
|
2 & 2.000000 & 1.985917 & 0.020033 & 99.132074 \\
|
||||||
|
\bottomrule
|
||||||
|
\end{tabular}
|
||||||
8
report/table_1_3.tex
Normal file
8
report/table_1_3.tex
Normal file
|
|
@ -0,0 +1,8 @@
|
||||||
|
\begin{tabular}{lrrrr}
|
||||||
|
\toprule
|
||||||
|
& True & Estimated & Std Err & t-Stat \\
|
||||||
|
\midrule
|
||||||
|
0 & 3.000000 & 7.040489 & 0.362044 & 19.446476 \\
|
||||||
|
1 & -4.000000 & -3.986195 & 0.052565 & -75.833855 \\
|
||||||
|
\bottomrule
|
||||||
|
\end{tabular}
|
||||||
9
report/table_1_4.tex
Normal file
9
report/table_1_4.tex
Normal file
|
|
@ -0,0 +1,9 @@
|
||||||
|
\begin{tabular}{lrrrr}
|
||||||
|
\toprule
|
||||||
|
& True & Estimated & Std Err & t-Stat \\
|
||||||
|
\midrule
|
||||||
|
0 & 3.000000 & 3.062084 & 0.164930 & 18.565919 \\
|
||||||
|
1 & -4.000000 & -4.006083 & 0.020178 & -198.535392 \\
|
||||||
|
2 & 2.000000 & 1.974439 & 0.024519 & 80.526341 \\
|
||||||
|
\bottomrule
|
||||||
|
\end{tabular}
|
||||||
8
report/table_1_5.tex
Normal file
8
report/table_1_5.tex
Normal file
|
|
@ -0,0 +1,8 @@
|
||||||
|
\begin{tabular}{lrrrr}
|
||||||
|
\toprule
|
||||||
|
& True & Estimated & Std Err & t-Stat \\
|
||||||
|
\midrule
|
||||||
|
0 & 3.000000 & 12.965134 & 0.300905 & 43.087097 \\
|
||||||
|
1 & -4.000000 & -3.011484 & 0.043688 & -68.931429 \\
|
||||||
|
\bottomrule
|
||||||
|
\end{tabular}
|
||||||
9
report/table_1_6.tex
Normal file
9
report/table_1_6.tex
Normal file
|
|
@ -0,0 +1,9 @@
|
||||||
|
\begin{tabular}{lrrrr}
|
||||||
|
\toprule
|
||||||
|
& True & Estimated & Std Err & t-Stat \\
|
||||||
|
\midrule
|
||||||
|
0 & 3.000000 & 3.107269 & 0.320425 & 9.697336 \\
|
||||||
|
1 & -4.000000 & -4.067205 & 0.100288 & -40.555170 \\
|
||||||
|
2 & 2.000000 & 1.985469 & 0.020038 & 99.084266 \\
|
||||||
|
\bottomrule
|
||||||
|
\end{tabular}
|
||||||
207
scripts/assignment_empirical_jan_2025_starter (1).py
Normal file
207
scripts/assignment_empirical_jan_2025_starter (1).py
Normal file
|
|
@ -0,0 +1,207 @@
|
||||||
|
#!/usr/bin/env python3
|
||||||
|
# -*- coding: utf-8 -*-
|
||||||
|
"""
|
||||||
|
Empirical assignment 2024 - 2025
|
||||||
|
|
||||||
|
STARTER FILE
|
||||||
|
"""
|
||||||
|
|
||||||
|
import os
|
||||||
|
import numpy as np
|
||||||
|
import numpy.linalg as la
|
||||||
|
import matplotlib.pyplot as plt
|
||||||
|
import statsmodels.api as sm
|
||||||
|
import scipy.stats as stats
|
||||||
|
import pandas as pd
|
||||||
|
|
||||||
|
from helper import print_question, data_frame_to_latex_table_file
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Start of Script for Empirical assignment Econometrics
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Set the folders for output of graphs and tables
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
# for the figures
|
||||||
|
data_dir = '../data/'
|
||||||
|
if not os.path.exists(data_dir):
|
||||||
|
os.makedirs(data_dir)
|
||||||
|
# for the figures
|
||||||
|
figure_dir = '../figures/'
|
||||||
|
if not os.path.exists(figure_dir):
|
||||||
|
os.makedirs(figure_dir)
|
||||||
|
# for the latex document
|
||||||
|
report_dir = '../report/'
|
||||||
|
if not os.path.exists(report_dir):
|
||||||
|
os.makedirs(report_dir)
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Here we set the seed for our group to your group number
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
# first birthday
|
||||||
|
bd_1 = 3112
|
||||||
|
# second birthday
|
||||||
|
bd_2 = 3112
|
||||||
|
|
||||||
|
group_seed = bd_1 * bd_2
|
||||||
|
|
||||||
|
# set the seed
|
||||||
|
np.random.seed(group_seed)
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# set the random number generator and seed
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
# set the seed and the random number generator for reproducible results
|
||||||
|
rng = np.random.default_rng(group_seed)
|
||||||
|
|
||||||
|
# setting for output printing
|
||||||
|
print_line_length = 90
|
||||||
|
print_line_start = 5
|
||||||
|
|
||||||
|
# number of x points
|
||||||
|
num_points = 60
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Load data 2.1
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
data_full = pd.read_stata(data_dir + 'assignment2025.dta')
|
||||||
|
|
||||||
|
num_obs = int(0.75 * data_full.shape[0])
|
||||||
|
# select 75% observations randomly ( the rng uses your seed )
|
||||||
|
observations = rng.choice (len(data_full), num_obs , replace =False)
|
||||||
|
# select the observationsfor your group
|
||||||
|
data = data_full.iloc[observations , :].copy()
|
||||||
|
|
||||||
|
#data = data_full
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Descriptive statistics 2.1
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.1: Descriptive Statistics')
|
||||||
|
|
||||||
|
# compute the summary statistics
|
||||||
|
# data_summary = TODO
|
||||||
|
|
||||||
|
# print to screen
|
||||||
|
# print(data_summary.T) [uncomment]
|
||||||
|
|
||||||
|
# export the summary statistics to a file
|
||||||
|
# data_frame_to_latex_table_file(report_dir + 'summmary_stats.tex',
|
||||||
|
# data_summary.T) [uncomment]
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.2
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.2: Plot histogram wage / lwage')
|
||||||
|
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.3
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.3: Sample correlations')
|
||||||
|
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.4
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.4: Estimate lwage model')
|
||||||
|
|
||||||
|
# explanatory variables for question 2.4
|
||||||
|
# x_vars_24 = data[['smcity', 'AA']] # TODO
|
||||||
|
|
||||||
|
# add a constant
|
||||||
|
# X_24 = sm.add_constant(x_vars_24) [uncomment]
|
||||||
|
|
||||||
|
# set-up model
|
||||||
|
# model_24 = sm.OLS(,) #TODO
|
||||||
|
|
||||||
|
# estimate the model
|
||||||
|
# results_24 = model_24. #TODO
|
||||||
|
|
||||||
|
# print the OLS output
|
||||||
|
# print(results_24.summary()) [uncomment]
|
||||||
|
|
||||||
|
# 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])
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.5
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.5: Adding school')
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.6
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.6: Adding age')
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.7
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.7: Create the woman variable')
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.8
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.8: lwage model')
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.9
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.9: Test ethnicity')
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.10
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.10: Estimate models separately')
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.11
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.11: Predict lwage')
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.12
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.12: Estimate model with squared terms')
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.13
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.13: Squared terms')
|
||||||
|
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.14
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.14: Add interaction terms')
|
||||||
|
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.15
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.15: Find your favourite model')
|
||||||
|
|
||||||
93
scripts/assignment_simulation_jan_2025_starter.py
Normal file
93
scripts/assignment_simulation_jan_2025_starter.py
Normal file
|
|
@ -0,0 +1,93 @@
|
||||||
|
#!/usr/bin/env python3
|
||||||
|
# -*- coding: utf-8 -*-
|
||||||
|
"""
|
||||||
|
Simulation assignment 2024 - 2025
|
||||||
|
|
||||||
|
STARTER FILE
|
||||||
|
|
||||||
|
"""
|
||||||
|
|
||||||
|
import os
|
||||||
|
|
||||||
|
import matplotlib.pyplot as plt
|
||||||
|
import numpy as np
|
||||||
|
import numpy.linalg as la
|
||||||
|
import pandas as pd
|
||||||
|
import scipy.stats as stats
|
||||||
|
import statsmodels.api as sm
|
||||||
|
#import varplot as vpl
|
||||||
|
|
||||||
|
#plt.style.use("finthabo")
|
||||||
|
|
||||||
|
# this imports all functions from the helper file
|
||||||
|
from helper import data_frame_to_latex_table_file, print_question
|
||||||
|
|
||||||
|
#colors = vpl.color_list()
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Start of Script for Simulation assignment Econometrics
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Set the folders for output of graphs and tables
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
# for the figures
|
||||||
|
FIGURE_DIR = "../figures/"
|
||||||
|
if not os.path.exists(FIGURE_DIR):
|
||||||
|
os.makedirs(FIGURE_DIR)
|
||||||
|
# for the latex document
|
||||||
|
REPORT_DIR = "../report/"
|
||||||
|
if not os.path.exists(REPORT_DIR):
|
||||||
|
os.makedirs(REPORT_DIR)
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Here we set the seed for our group to your group number
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
# first birthday
|
||||||
|
bd_1 = 3112
|
||||||
|
# second birthday
|
||||||
|
bd_2 = 3112
|
||||||
|
|
||||||
|
group_seed = bd_1 * bd_2
|
||||||
|
|
||||||
|
# set the seed
|
||||||
|
np.random.seed(group_seed)
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# set the random number generator and seed
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
# setting for output printing
|
||||||
|
print_line_length = 90
|
||||||
|
print_line_start = 5
|
||||||
|
|
||||||
|
# the number of data sets that we will simulate
|
||||||
|
num_obs = 2**10
|
||||||
|
|
||||||
|
# set the seed and the random number generator for reproducible results
|
||||||
|
# this ensures that every time you run this code you get exactly the same random numbers.
|
||||||
|
# changing the seed would change the random numbers.
|
||||||
|
rng = np.random.default_rng(group_seed)
|
||||||
|
|
||||||
|
# the true value of the parameters.
|
||||||
|
# Known in your role as creator, unknown to the modeller.
|
||||||
|
beta = np.array([3.0, -4.0, 2.0])
|
||||||
|
|
||||||
|
# standard deviation of the error terms
|
||||||
|
u = rng.normal(0, 3, (num_obs,))
|
||||||
|
|
||||||
|
x1 = rng.normal(3, 6, (num_obs,))
|
||||||
|
x2 = rng.normal(2, 5, (num_obs,))
|
||||||
|
|
||||||
|
# y = TODO
|
||||||
|
|
||||||
|
# X = TODO
|
||||||
|
|
||||||
|
# m = TODO
|
||||||
|
# results = #TODO
|
||||||
|
|
||||||
207
scripts/empirical.py
Normal file
207
scripts/empirical.py
Normal file
|
|
@ -0,0 +1,207 @@
|
||||||
|
#!/usr/bin/env python3
|
||||||
|
# -*- coding: utf-8 -*-
|
||||||
|
"""
|
||||||
|
Empirical assignment 2024 - 2025
|
||||||
|
|
||||||
|
STARTER FILE
|
||||||
|
"""
|
||||||
|
|
||||||
|
import os
|
||||||
|
import numpy as np
|
||||||
|
import numpy.linalg as la
|
||||||
|
import matplotlib.pyplot as plt
|
||||||
|
import statsmodels.api as sm
|
||||||
|
import scipy.stats as stats
|
||||||
|
import pandas as pd
|
||||||
|
|
||||||
|
from helper import print_question, data_frame_to_latex_table_file
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Start of Script for Empirical assignment Econometrics
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Set the folders for output of graphs and tables
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
# for the figures
|
||||||
|
data_dir = '../data/'
|
||||||
|
if not os.path.exists(data_dir):
|
||||||
|
os.makedirs(data_dir)
|
||||||
|
# for the figures
|
||||||
|
figure_dir = '../figures/'
|
||||||
|
if not os.path.exists(figure_dir):
|
||||||
|
os.makedirs(figure_dir)
|
||||||
|
# for the latex document
|
||||||
|
report_dir = '../report/'
|
||||||
|
if not os.path.exists(report_dir):
|
||||||
|
os.makedirs(report_dir)
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Here we set the seed for our group to your group number
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
# first birthday
|
||||||
|
bd_1 = 3112
|
||||||
|
# second birthday
|
||||||
|
bd_2 = 3112
|
||||||
|
|
||||||
|
group_seed = bd_1 * bd_2
|
||||||
|
|
||||||
|
# set the seed
|
||||||
|
np.random.seed(group_seed)
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# set the random number generator and seed
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
# set the seed and the random number generator for reproducible results
|
||||||
|
rng = np.random.default_rng(group_seed)
|
||||||
|
|
||||||
|
# setting for output printing
|
||||||
|
print_line_length = 90
|
||||||
|
print_line_start = 5
|
||||||
|
|
||||||
|
# number of x points
|
||||||
|
num_points = 60
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Load data 2.1
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
data_full = pd.read_stata(data_dir + 'assignment2025.dta')
|
||||||
|
|
||||||
|
num_obs = int(0.75 * data_full.shape[0])
|
||||||
|
# select 75% observations randomly ( the rng uses your seed )
|
||||||
|
observations = rng.choice (len(data_full), num_obs , replace =False)
|
||||||
|
# select the observationsfor your group
|
||||||
|
data = data_full.iloc[observations , :].copy()
|
||||||
|
|
||||||
|
#data = data_full
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Descriptive statistics 2.1
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.1: Descriptive Statistics')
|
||||||
|
|
||||||
|
# compute the summary statistics
|
||||||
|
# data_summary = TODO
|
||||||
|
|
||||||
|
# print to screen
|
||||||
|
# print(data_summary.T) [uncomment]
|
||||||
|
|
||||||
|
# export the summary statistics to a file
|
||||||
|
# data_frame_to_latex_table_file(report_dir + 'summmary_stats.tex',
|
||||||
|
# data_summary.T) [uncomment]
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.2
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.2: Plot histogram wage / lwage')
|
||||||
|
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.3
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.3: Sample correlations')
|
||||||
|
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.4
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.4: Estimate lwage model')
|
||||||
|
|
||||||
|
# explanatory variables for question 2.4
|
||||||
|
# x_vars_24 = data[['smcity', 'AA']] # TODO
|
||||||
|
|
||||||
|
# add a constant
|
||||||
|
# X_24 = sm.add_constant(x_vars_24) [uncomment]
|
||||||
|
|
||||||
|
# set-up model
|
||||||
|
# model_24 = sm.OLS(,) #TODO
|
||||||
|
|
||||||
|
# estimate the model
|
||||||
|
# results_24 = model_24. #TODO
|
||||||
|
|
||||||
|
# print the OLS output
|
||||||
|
# print(results_24.summary()) [uncomment]
|
||||||
|
|
||||||
|
# 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])
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.5
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.5: Adding school')
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.6
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.6: Adding age')
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.7
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.7: Create the woman variable')
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.8
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.8: lwage model')
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.9
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.9: Test ethnicity')
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.10
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.10: Estimate models separately')
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.11
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.11: Predict lwage')
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.12
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.12: Estimate model with squared terms')
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.13
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.13: Squared terms')
|
||||||
|
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.14
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.14: Add interaction terms')
|
||||||
|
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Question 2.15
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
print_question('Question 2.15: Find your favourite model')
|
||||||
|
|
||||||
84
scripts/helper.py
Normal file
84
scripts/helper.py
Normal file
|
|
@ -0,0 +1,84 @@
|
||||||
|
#!/usr/bin/env python3
|
||||||
|
# -*- coding: utf-8 -*-
|
||||||
|
"""
|
||||||
|
Helper functions for assignment
|
||||||
|
"""
|
||||||
|
import os
|
||||||
|
import numpy as np
|
||||||
|
import pandas as pd
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# ALL FUNCTIONS ARE ON TOP
|
||||||
|
#
|
||||||
|
# THE SCRIPT IS BELOW THE FUNCTIONS
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Helper function to transform results summary into a dataFrame
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
def results_summary_to_dataframe(results, rounding=2):
|
||||||
|
'''take the result of an statsmodel results table
|
||||||
|
and transforms it into a dataframe'''
|
||||||
|
|
||||||
|
# get the values from results
|
||||||
|
# if you want, you can of course generalize this.
|
||||||
|
# e.g. if you don't have normal error terms
|
||||||
|
# you could change the pvalues and confidence bounds
|
||||||
|
# see exercise session 9?!
|
||||||
|
pvals = results.pvalues
|
||||||
|
tvals = results.tvalues
|
||||||
|
coeff = results.params
|
||||||
|
conf_lower = results.conf_int()[:, 0]
|
||||||
|
conf_higher = results.conf_int()[:, 1]
|
||||||
|
|
||||||
|
# create a pandas DataFrame from a dictionary
|
||||||
|
results_df = pd.DataFrame({"pvals": np.round(pvals, rounding),
|
||||||
|
"tvals": np.round(tvals, rounding),
|
||||||
|
"coeff": np.round(coeff, rounding),
|
||||||
|
"conf_lower": np.round(conf_lower, rounding),
|
||||||
|
"conf_higher": np.round(conf_higher, rounding)
|
||||||
|
})
|
||||||
|
# This is just to show you how to re-order if needed
|
||||||
|
# Typically you should put them in the order you like straigh away
|
||||||
|
#Reordering...
|
||||||
|
results_df = results_df[["coeff", "tvals", "pvals", "conf_lower",
|
||||||
|
"conf_higher"]]
|
||||||
|
|
||||||
|
return results_df
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
def data_frame_to_latex_table_file(file_name, df):
|
||||||
|
"""takes a DataFrame and creates file_name.tex with LaTeX table data. """
|
||||||
|
print(df.columns)
|
||||||
|
# create and open file
|
||||||
|
text_file = open(file_name, "w")
|
||||||
|
# data frame to LaTeX
|
||||||
|
df_latex = df.to_latex()
|
||||||
|
# Consider extensions (see later in class)
|
||||||
|
# write latex string to file
|
||||||
|
text_file.write(df_latex)
|
||||||
|
# close file
|
||||||
|
text_file.close()
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
def print_question(statement, print_line_start=5, print_line_length=90):
|
||||||
|
"""
|
||||||
|
Print question description.
|
||||||
|
|
||||||
|
Args:
|
||||||
|
statement (string): Question description.
|
||||||
|
print_line_start (int): column where statement starts
|
||||||
|
print_line_length (int): total columns.
|
||||||
|
|
||||||
|
Returns:
|
||||||
|
None.
|
||||||
|
|
||||||
|
"""
|
||||||
|
print(print_line_start * '#' + ' ' + statement + ' ' +
|
||||||
|
(print_line_length - len(statement) - print_line_start - 2) * '#')
|
||||||
|
|
||||||
198
scripts/non_linear_models_example_report.py
Normal file
198
scripts/non_linear_models_example_report.py
Normal file
|
|
@ -0,0 +1,198 @@
|
||||||
|
#!/usr/bin/env python3
|
||||||
|
# -*- coding: utf-8 -*-
|
||||||
|
"""
|
||||||
|
Examples of non-linear models
|
||||||
|
"""
|
||||||
|
|
||||||
|
import os
|
||||||
|
|
||||||
|
import matplotlib.pyplot as plt
|
||||||
|
import numpy as np
|
||||||
|
import numpy.linalg as la
|
||||||
|
import pandas as pd
|
||||||
|
import scipy.stats as stats
|
||||||
|
import statsmodels.api as sm
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# ALL FUNCTIONS ARE ON TOP
|
||||||
|
#
|
||||||
|
# THE SCRIPT IS BELOW THE FUNCTIONS
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Helper function to transform results summary into a dataFrame
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
def results_summary_to_dataframe(results, rounding=2):
|
||||||
|
"""take the result of an statsmodel results table
|
||||||
|
and transforms it into a dataframe"""
|
||||||
|
|
||||||
|
# get the values from results
|
||||||
|
# if you want, you can of course generalize this.
|
||||||
|
# e.g. if you don't have normal error terms
|
||||||
|
# you could change the pvalues and confidence bounds
|
||||||
|
# see exercise session 9?!
|
||||||
|
pvals = results.pvalues
|
||||||
|
tvals = results.tvalues
|
||||||
|
coeff = results.params
|
||||||
|
conf_lower = results.conf_int()[:, 0]
|
||||||
|
conf_higher = results.conf_int()[:, 1]
|
||||||
|
|
||||||
|
# create a pandas DataFrame from a dictionary
|
||||||
|
results_df = pd.DataFrame(
|
||||||
|
{
|
||||||
|
"pvals": np.round(pvals, rounding),
|
||||||
|
"tvals": np.round(tvals, rounding),
|
||||||
|
"coeff": np.round(coeff, rounding),
|
||||||
|
"conf\_lower": np.round(conf_lower, rounding),
|
||||||
|
"conf\_higher": np.round(conf_higher, rounding),
|
||||||
|
}
|
||||||
|
)
|
||||||
|
# This is just to show you how to re-order if needed
|
||||||
|
# Typically you should put them in the order you like straigh away
|
||||||
|
# Reordering...
|
||||||
|
results_df = results_df[["coeff", "tvals", "pvals", "conf\_lower", "conf\_higher"]]
|
||||||
|
|
||||||
|
return results_df
|
||||||
|
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
|
||||||
|
def data_frame_to_latex_table_file(file_name, df):
|
||||||
|
"""takes a DataFrame and creates file_name.tex with LaTeX table data."""
|
||||||
|
# create and open file
|
||||||
|
text_file = open(file_name, "w")
|
||||||
|
# data frame to LaTeX
|
||||||
|
df_latex = df.to_latex()
|
||||||
|
# Consider extensions (see later in class)
|
||||||
|
# write latex string to file
|
||||||
|
text_file.write(df_latex)
|
||||||
|
# close file
|
||||||
|
text_file.close()
|
||||||
|
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Set the folders for output of graphs and tables
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
# for the figures
|
||||||
|
FIGURE_DIR = "../figures/"
|
||||||
|
if not os.path.exists(FIGURE_DIR):
|
||||||
|
os.makedirs(FIGURE_DIR)
|
||||||
|
# for the latex document
|
||||||
|
REPORT_DIR = "../report/"
|
||||||
|
if not os.path.exists(REPORT_DIR):
|
||||||
|
os.makedirs(REPORT_DIR)
|
||||||
|
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Start of Script
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# set the random number generator and seed
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
# set the seed and the random number generator for reproducible results
|
||||||
|
seed = 425246524
|
||||||
|
rng = np.random.default_rng(seed)
|
||||||
|
|
||||||
|
# number of x points
|
||||||
|
num_points = 60
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Quadratic
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
# the true parameters of the Data Generating process (DGP)
|
||||||
|
beta = np.array([20, 0.5, -0.5])
|
||||||
|
|
||||||
|
# values for x
|
||||||
|
x = np.linspace(-20, 40, num_points)
|
||||||
|
|
||||||
|
# error term
|
||||||
|
sigma_eps = 59
|
||||||
|
# generate random numbers
|
||||||
|
eps = rng.normal(0, sigma_eps, (num_points,))
|
||||||
|
|
||||||
|
# create y values for the DGP
|
||||||
|
y = beta[0] + beta[1] * x + beta[2] * x**2 + eps
|
||||||
|
|
||||||
|
# estimate the model
|
||||||
|
results = sm.OLS(y, sm.add_constant(x)).fit()
|
||||||
|
|
||||||
|
# generate a figure and save it to disk
|
||||||
|
fig_num = 1
|
||||||
|
fig = plt.figure(num=fig_num)
|
||||||
|
ax = fig.add_subplot(111)
|
||||||
|
ax.grid(ls=":")
|
||||||
|
ax.plot(x, y, "o", color="tab:brown", label="$y$")
|
||||||
|
ax.legend(loc="best")
|
||||||
|
ax.set_title("Quadratic model")
|
||||||
|
plt.savefig(FIGURE_DIR + "quadratic_model_y.png")
|
||||||
|
plt.show()
|
||||||
|
fig_num += 1
|
||||||
|
|
||||||
|
|
||||||
|
fig = plt.figure(num=fig_num)
|
||||||
|
ax = fig.add_subplot(111)
|
||||||
|
ax.plot(x, results.fittedvalues, label=r"$\hat{y}$")
|
||||||
|
ax.grid(ls=":")
|
||||||
|
ax.plot(x, y, "o", color="tab:brown", label="$y$")
|
||||||
|
ax.legend(loc="best")
|
||||||
|
ax.set_title("Quadratic model")
|
||||||
|
plt.savefig(FIGURE_DIR + "quadratic_model_linear.png")
|
||||||
|
plt.show()
|
||||||
|
fig_num += 1
|
||||||
|
|
||||||
|
X = sm.add_constant(np.array([x, x**2]).T)
|
||||||
|
|
||||||
|
results = sm.OLS(y, X).fit()
|
||||||
|
|
||||||
|
fig = plt.figure(num=fig_num)
|
||||||
|
ax = fig.add_subplot(111)
|
||||||
|
ax.plot(x, results.fittedvalues, label=r"$\hat{y}$")
|
||||||
|
ax.grid(ls=":")
|
||||||
|
ax.plot(x, y, "o", color="tab:brown", label="$y$")
|
||||||
|
ax.legend(loc="best")
|
||||||
|
ax.set_title("Quadratic model")
|
||||||
|
plt.savefig(FIGURE_DIR + "quadratic_model_quadratic.png")
|
||||||
|
plt.show()
|
||||||
|
fig_num += 1
|
||||||
|
|
||||||
|
# print a summary
|
||||||
|
print(results.summary())
|
||||||
|
|
||||||
|
# The results can also be exported to LaTeX.
|
||||||
|
# do either
|
||||||
|
latex_summary = results.summary().as_latex()
|
||||||
|
|
||||||
|
# alternatively for each group separately
|
||||||
|
for table in results.summary().tables:
|
||||||
|
print(table.as_latex_tabular())
|
||||||
|
|
||||||
|
###############################################################################
|
||||||
|
# Generate LateX tables
|
||||||
|
###############################################################################
|
||||||
|
|
||||||
|
# write a string to a file
|
||||||
|
with open(REPORT_DIR + "summary.tex", "w") as f:
|
||||||
|
f.write(latex_summary)
|
||||||
|
|
||||||
|
# create a DataFrame for the results
|
||||||
|
estimation_results_df = results_summary_to_dataframe(results)
|
||||||
|
|
||||||
|
# give a name to the table
|
||||||
|
table_data_file = REPORT_DIR + "df_table.tex"
|
||||||
|
# create a latex file with the table information
|
||||||
|
data_frame_to_latex_table_file(table_data_file, estimation_results_df)
|
||||||
|
|
||||||
|
# an alternative to only send the coefficients part of the results
|
||||||
|
# to a LaTeX table
|
||||||
|
data_frame_to_latex_table_file(
|
||||||
|
REPORT_DIR + "results_coef.tex", results.summary2().tables[1]
|
||||||
|
)
|
||||||
|
|
@ -1,3 +0,0 @@
|
||||||
import util
|
|
||||||
|
|
||||||
print(util.group_seed())
|
|
||||||
188
scripts/simulation.py
Normal file
188
scripts/simulation.py
Normal file
|
|
@ -0,0 +1,188 @@
|
||||||
|
#!/usr/bin/env python3
|
||||||
|
# -*- coding: utf-8 -*-
|
||||||
|
"""
|
||||||
|
Simulation assignment 2024 - 2025
|
||||||
|
|
||||||
|
STARTER FILE
|
||||||
|
|
||||||
|
"""
|
||||||
|
|
||||||
|
import os
|
||||||
|
|
||||||
|
import matplotlib.pyplot as plt
|
||||||
|
import numpy as np
|
||||||
|
import numpy.linalg as la
|
||||||
|
import pandas as pd
|
||||||
|
import scipy.stats as stats
|
||||||
|
import statsmodels.api as sm
|
||||||
|
#import varplot as vpl
|
||||||
|
|
||||||
|
#plt.style.use("finthabo")
|
||||||
|
|
||||||
|
# this imports all functions from the helper file
|
||||||
|
from helper import data_frame_to_latex_table_file, print_question
|
||||||
|
|
||||||
|
#colors = vpl.color_list()
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Start of Script for Simulation assignment Econometrics
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Set the folders for output of graphs and tables
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
# for the figures
|
||||||
|
FIGURE_DIR = "../figures/"
|
||||||
|
if not os.path.exists(FIGURE_DIR):
|
||||||
|
os.makedirs(FIGURE_DIR)
|
||||||
|
# for the latex document
|
||||||
|
REPORT_DIR = "../report/"
|
||||||
|
if not os.path.exists(REPORT_DIR):
|
||||||
|
os.makedirs(REPORT_DIR)
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# Here we set the seed for our group to your group number
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
# first birthday
|
||||||
|
bd_1 = 303
|
||||||
|
# second birthday
|
||||||
|
bd_2 = 309
|
||||||
|
|
||||||
|
group_seed = bd_1 * bd_2
|
||||||
|
|
||||||
|
# set the seed
|
||||||
|
np.random.seed(group_seed)
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# set the random number generator and seed
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
# setting for output printing
|
||||||
|
print_line_length = 90
|
||||||
|
print_line_start = 5
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# 1.1
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
# the number of data sets that we will simulate
|
||||||
|
num_obs = 1000
|
||||||
|
|
||||||
|
# set the seed and the random number generator for reproducible results
|
||||||
|
# this ensures that every time you run this code you get exactly the same random numbers.
|
||||||
|
# changing the seed would change the random numbers.
|
||||||
|
rng = np.random.default_rng(group_seed)
|
||||||
|
|
||||||
|
# the true value of the parameters.
|
||||||
|
# Known in your role as creator, unknown to the modeller.
|
||||||
|
beta = np.array([3.0, -4.0, 2.0])
|
||||||
|
|
||||||
|
# standard deviation of the error terms
|
||||||
|
u = rng.normal(0, 3, (num_obs,))
|
||||||
|
|
||||||
|
x1 = rng.normal(3, 6, (num_obs,))
|
||||||
|
x2 = rng.normal(2, 5, (num_obs,))
|
||||||
|
|
||||||
|
# y
|
||||||
|
y = beta[0] + beta[1]*x1 + beta[2]*x2 + u
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# 1.2
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
# X
|
||||||
|
X = np.array([np.ones(num_obs), x1, x2]).T
|
||||||
|
|
||||||
|
# m
|
||||||
|
m = sm.OLS(y, X)
|
||||||
|
# results =
|
||||||
|
results = m.fit()
|
||||||
|
d = {'True': beta,
|
||||||
|
'Estimated': results.params,
|
||||||
|
'Std Err': results.bse,
|
||||||
|
't-Stat': results.tvalues}
|
||||||
|
df = pd.DataFrame(data = d)
|
||||||
|
data_frame_to_latex_table_file(REPORT_DIR + 'table_1_2.tex', df)
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# 1.3
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
# X
|
||||||
|
X = np.array([np.ones(num_obs), x1]).T
|
||||||
|
|
||||||
|
# m
|
||||||
|
m = sm.OLS(y, X)
|
||||||
|
# results =
|
||||||
|
results = m.fit()
|
||||||
|
d = {'True': beta[0:2],
|
||||||
|
'Estimated': results.params,
|
||||||
|
'Std Err': results.bse,
|
||||||
|
't-Stat': results.tvalues}
|
||||||
|
df = pd.DataFrame(data = d)
|
||||||
|
data_frame_to_latex_table_file(REPORT_DIR + 'table_1_3.tex', df)
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# 1.4
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
x2_new = 0.5*x1 + rng.normal(5,4,(num_obs,))
|
||||||
|
|
||||||
|
y_new = beta[0] + beta[1]*x1 + beta[2]*x2_new + u
|
||||||
|
|
||||||
|
# X
|
||||||
|
X = np.array([np.ones(num_obs), x1, x2_new]).T
|
||||||
|
|
||||||
|
# m
|
||||||
|
m = sm.OLS(y_new, X)
|
||||||
|
# results =
|
||||||
|
results = m.fit()
|
||||||
|
d = {'True': beta,
|
||||||
|
'Estimated': results.params,
|
||||||
|
'Std Err': results.bse,
|
||||||
|
't-Stat': results.tvalues}
|
||||||
|
df = pd.DataFrame(data = d)
|
||||||
|
data_frame_to_latex_table_file(REPORT_DIR + 'table_1_4.tex', df)
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# 1.5
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
# X
|
||||||
|
X = np.array([np.ones(num_obs), x1]).T
|
||||||
|
|
||||||
|
# m
|
||||||
|
m = sm.OLS(y_new, X)
|
||||||
|
# results =
|
||||||
|
results = m.fit()
|
||||||
|
d = {'True': beta[0:2],
|
||||||
|
'Estimated': results.params,
|
||||||
|
'Std Err': results.bse,
|
||||||
|
't-Stat': results.tvalues}
|
||||||
|
df = pd.DataFrame(data = d)
|
||||||
|
data_frame_to_latex_table_file(REPORT_DIR + 'table_1_5.tex', df)
|
||||||
|
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
# 1.6
|
||||||
|
# -----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
x1 = rng.normal(3, 1, (num_obs,))
|
||||||
|
y = beta[0] + beta[1]*x1 + beta[2]*x2 + u
|
||||||
|
|
||||||
|
# X
|
||||||
|
X = np.array([np.ones(num_obs), x1, x2]).T
|
||||||
|
|
||||||
|
# m
|
||||||
|
m = sm.OLS(y, X)
|
||||||
|
# results =
|
||||||
|
results = m.fit()
|
||||||
|
d = {'True': beta,
|
||||||
|
'Estimated': results.params,
|
||||||
|
'Std Err': results.bse,
|
||||||
|
't-Stat': results.tvalues}
|
||||||
|
df = pd.DataFrame(data = d)
|
||||||
|
data_frame_to_latex_table_file(REPORT_DIR + 'table_1_6.tex', df)
|
||||||
|
|
@ -1,24 +0,0 @@
|
||||||
import os
|
|
||||||
import numpy as np
|
|
||||||
|
|
||||||
|
|
||||||
def group_seed():
|
|
||||||
bd_env_var = os.getenv("BIRTHDAYS")
|
|
||||||
|
|
||||||
# If no birthdays are set, complain and exit
|
|
||||||
if not bd_env_var:
|
|
||||||
print("Environment variable BIRTHDAYS is missing")
|
|
||||||
exit(-1)
|
|
||||||
|
|
||||||
# convert birthdays to ints
|
|
||||||
birthdays = [int(bd) for bd in bd_env_var.split(",")]
|
|
||||||
|
|
||||||
# multiply them to get the group seed
|
|
||||||
seed = 1
|
|
||||||
for bd in birthdays:
|
|
||||||
seed *= bd
|
|
||||||
|
|
||||||
return seed
|
|
||||||
|
|
||||||
|
|
||||||
rng = np.random.default_rng(group_seed())
|
|
||||||
Loading…
Add table
Reference in a new issue