Template to be used in assignments, problem sets, etc. by graduate students of the Food and Resource Economics department, IFAS, University of Florida.
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%% Problem Set/Assignment Template to be used by the
%% Food and Resource Economics Department - IFAS
%% University of Florida's graduates.
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%% Version 1.0 - November 2019
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%% Ariel Soto-Caro
%% - asotocaro@ufl.edu
%% - arielsotocaro@gmail.com
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentclass[12pt]{article}
\usepackage{design_ASC}
\setlength\parindent{0pt} %% Do not touch this
%% -----------------------------
%% TITLE
%% -----------------------------
\title{Problem Set \#1} %% Assignment Title
\author{John Nash\\ %% Student name
AEB6933 - Fantastic Econometric Course\\ %% Code and course name
\textsc{University of Florida}
}
\date{\today} %% Change "\today" by another date manually
%% -----------------------------
%% -----------------------------
%% %%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\setlength{\droptitle}{-5em}
%% %%%%%%%%%%%%%%%%%%%%%%%%%
\maketitle
% --------------------------
% Start here
% --------------------------
% %%%%%%%%%%%%%%%%%%%
\section*{Question 1}
% %%%%%%%%%%%%%%%%%%%
{\bfseries You can write the questions here \ldots}
And your answers here \ldots
% %%%%%%%%%%%%%%%%%%%
\subsection*{Question 1.a}
% %%%%%%%%%%%%%%%%%%%
{\bfseries Also, you can write your sub-questions into subsection levels.}
And again, your answers here \ldots
% %%%%%%%%%%%%%%%%%%%
\section*{Mathematical notation}
% %%%%%%%%%%%%%%%%%%%
This template offers a set of customized mathematical symbols commonly used in FRED courses.
\begin{multicols}{2}
You can invoke the following symbols:
\begin{Verbatim}[frame=single, fontsize=\footnotesize]
\E(\cdot) % Expectation
\V(\cdot) % Variance
\Var(\cdot) % Variance
\Cov(\cdot) % Covariance
\Corr(\cdot) % Correlation
\tr(\cdot) % Trace
\rank(\cdot) % Rank
\N(0,1) % Normal
\op(\cdot) % "little o" ope
\Op(\cdot) % "big o" operator
\R^+ % Real positive num
\La(y|\beta,\sigma^2) % Lagrange function
\end{Verbatim}
\footnotesize{
\begin{itemize} \setlength\itemsep{0em}
\item $\E(\cdot)$
\item $\V(\cdot)$
\item $\Var(\cdot)$
\item $\Cov(\cdot)$
\item $\Corr(\cdot)$
\item $\tr(\cdot)$
\item $\rank(\cdot)$
\item $\N(0,1)$
\item $\op(\cdot)$
\item $\Op(\cdot)$
\item $\R^{+}$
\item $\La(y|\beta,\sigma^2)$
\end{itemize}}
\end{multicols}
Remember, these symbols have to be implemented into equation environments, that means, with dollar symbols \$\ldots\$, or \texttt{equation}-environments.
\newpage
There is a set of different accents you may use:
\begin{Verbatim}[frame=single, fontsize=\footnotesize]
$\hat \beta$, $\widehat \beta$, $\tilde \alpha$, $\widetilde \alpha$, $\bar y$,
$\varepsilon \sim \chi^2_t$
\end{Verbatim}
Which reproduce the following: $\hat \beta$, $\widehat \beta$, $\tilde \alpha$, $\widetilde \alpha$, $\bar y$, $\varepsilon \sim \chi^2_t$.
These are a couple of examples:
\begin{equation}
\Avar (b) = \frac{\sigma^2}{n} Q^{-1} \plim \left( \frac{1}{n}X'QX \right)Q^{-1}
\end{equation}
\begin{equation}
\sqrt{n}(b-\beta) \stackrel{d}{\longrightarrow} \N \left[0,\frac{\sigma^2}{n} Q^{-1} \plim \left( \frac{1}{n}X'\Omega X\right)Q^{-1}\right]
\end{equation}
% %%%%%%%%%%%%%%%%%%%
\section*{Code and scripts}
% %%%%%%%%%%%%%%%%%%%
If you want to print the raw outcomes from any software, it is recommended the \texttt{Verbatim}-environment :
%% Verbatim -----------------
\begin{Verbatim}[frame = single, fontsize = \footnotesize]
Parameters Estimates Std. err. Est./s.e. Prob. Gradient
------------------------------------------------------------------
P01 -0.5553 0.1446 -3.840 0.0001 0.0002
P02 -0.2255 0.1106 -2.039 0.0414 -0.0004
P03 -0.8588 0.2378 -3.612 0.0003 -0.0003
\end{Verbatim}
%% Verbatim -----------------
The same environment can be used for print a chunk of code (this is GAUSS by the way):
%% Verbatim -----------------
\begin{Verbatim}[frame = single, fontsize = \footnotesize]
ev = ev1 ~ ev2;
ev1 = sumc(ev[.,nest1]');
ev2 = sumc(ev[.,nest2]');
num = (ev1 .^ (k[1]-1)).*sumc(depm[.,nest1]') + (ev2 .^ (k[2]-1)).*sumc(depm[.,nest2]');
p = sumc((ev .* depm)').* num ./ ((ev1.^k[1])+(ev2.^k[2]));
\end{Verbatim}
%% Verbatim -----------------
If you want to print Stata-code, you can use the environment \texttt{lstlisting}, setting the \texttt{style} in \texttt{stata-editor}. This will highlight the Stata commands like the following example:
%% Stata-code -----------------
\begin{lstlisting}[language = Stata, style = stata-editor]
clogit depvar var1 var2 var3, group(id)
\end{lstlisting}
%% Stata-code -----------------
The same \texttt{lstlisting}-package can be used to print \textbf{R}-code, setting the only argument (\texttt{language}) in \texttt{R}.
%% R-code -----------------
\begin{lstlisting}[language = R]
Quad.reg <- function(z) {
grad <- cbind(z[4]+z[11]*m[1]+z[15]*m[2]+z[25]*m[3]+z[19]*m[4]+z[20]*m[5]+z[21]*m[6],
z[5]+z[12]*m[1]+z[16]*m[2]+z[19]*m[3]+z[26]*m[4]+z[22]*m[5]+z[23]*m[6],
z[7]+z[14]*m[1]+z[18]*m[2]+z[21]*m[3]+z[23]*m[4]+z[22]*m[5]+z[28]*m[6])
test1 <- min(grad) # have to be >0
test2 <- max(eigen(hess)$values) # have to be < 0
if(Mode == 1) {
lst <- list(Grad = grad, Hess = hess, Test1 = test1, Test2 = test2)
return(lst)
} else {
return(cbind(test1,test2))
}
}
\end{lstlisting}
%% R-code -----------------
\end{document}