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    {\Large \textbf{\textsc{\@title}}} \par
    {\small \textsc{Paul Schrimpf}} \par
    {\small \textsc{\@date}} \par
    {\small \textsc{University of British Columbia}} \par
    {\small \textsc{Economics 628: Topics in econometrics}} \par
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\title{Homework 4}
\date{Due: Friday, November 4th}

\begin{document}

\maketitle

This assignment asks you to recreate some of the analysis of
\cite{chv2010b}\footnote{The 2009 version of this paper is listed on
  the syllabus, but there is a newer 2010 version.}. We will be using
slightly different data and slightly different estimators, but we will
estimate some of the same things.  

The dataset for this assignment is
\href{http://faculty.arts.ubc.ca/pschrimpf/628/hw4-nlsy.csv}{hw4-nlsy.csv}. 
It is an extract from the NLSY79. It consists of white men who are not 
missing any of the variables that will be used in our analysis. The
variables are:
\begin{enumerate}
\item \texttt{yob}: year of birth
\item \texttt{mhgc\_mi}: mother's highest grade of schooling completed
\item \texttt{numsibs}: number of siblings
\item \texttt{urban14}: whether lived in an urban area at age 14
\item \texttt{tuit4}: tuition at nearest four year college 
\item \texttt{locCol}: whether there is a college in the county of
  residence at age 14
\item \texttt{afqt}: armed forces qualifying test score, adjusted for
  education at time of test and standardized
\item \texttt{college}: whether ever attended college
\item \texttt{avgEarn89\_00}: average earnings from 1989-2000 in year
  2000 dollars
\end{enumerate}
This data is not exactly the same as in \cite{chv2010b}. The earnings
measure is different, and the local college variable also seems to be
messed up. It also included a local tuition measure, which we will use
as an instrument. There is some code to get you started with the first
few parts of the assignment on the course web page. 

\begin{mpart}\label{p1}
  Estimate the return to college using OLS and IV. Regress log
  earnings on college. Include AFQT as a control, and use tuition as
  an instrument. Report the coefficient on college and the standard
  error. Divide by four to make it a return per year of college, since
  that's what people usually report.
\end{mpart}

\begin{mpart}
  Flexibly estimate the propensity score, the probability of college
  as a function of $x$ and $z$. As in part \ref{p1} just use AFQT as
  $x$ and tuition as $z$. You may use either series or kernel
  regression.  Plot you estimate of the propensity score as a function
  of $x$ and $z$. Also plot the support of the estimated propensity
  score as a function of $x$. Vary the number of series terms or
  bandwidth, and report how the results change.
\end{mpart} 

\begin{mpart}
  Flexibly estimate the marginal treatment effect conditional on
  AFQT. Plot the estimated marginal treatment effect as a function of
  $u$ and AFQT.  Also plot the marginal treatment effect as a function
  of $u$ at the average AFQT. Again, investigate the sensitivity of
  the results to the number of series terms or bandwidth. 
\end{mpart}

\begin{mpart}
  Compute uniform confidence bands for your plot of the marginal
  treatment effect as a function of $u$ at the average AFQT. Draw the
  plot with the uniform confidence bands included. 
\end{mpart}

\begin{mpart}
  Specify an alternate policy and estimate the policy relevant
  treatment effect. The policy could be something like reduce tuition
  by some percent, or it could be something more artificial like increase
  $\pi(z,x)$ in some way. Compute the standard error of your estimate.
\end{mpart}

\bibliographystyle{econometrica}
\bibliography{../628}

\end{document}

 