% Options for packages loaded elsewhere
% Options for packages loaded elsewhere
\PassOptionsToPackage{unicode}{hyperref}
\PassOptionsToPackage{hyphens}{url}
\PassOptionsToPackage{dvipsnames,svgnames,x11names}{xcolor}
%
\documentclass[
  letterpaper,
  DIV=11,
  numbers=noendperiod]{scrartcl}
\usepackage{xcolor}
\usepackage{amsmath,amssymb}
\setcounter{secnumdepth}{-\maxdimen} % remove section numbering
\usepackage{iftex}
\ifPDFTeX
  \usepackage[T1]{fontenc}
  \usepackage[utf8]{inputenc}
  \usepackage{textcomp} % provide euro and other symbols
\else % if luatex or xetex
  \usepackage{unicode-math} % this also loads fontspec
  \defaultfontfeatures{Scale=MatchLowercase}
  \defaultfontfeatures[\rmfamily]{Ligatures=TeX,Scale=1}
\fi
\usepackage{lmodern}
\ifPDFTeX\else
  % xetex/luatex font selection
\fi
% Use upquote if available, for straight quotes in verbatim environments
\IfFileExists{upquote.sty}{\usepackage{upquote}}{}
\IfFileExists{microtype.sty}{% use microtype if available
  \usepackage[]{microtype}
  \UseMicrotypeSet[protrusion]{basicmath} % disable protrusion for tt fonts
}{}
\makeatletter
\@ifundefined{KOMAClassName}{% if non-KOMA class
  \IfFileExists{parskip.sty}{%
    \usepackage{parskip}
  }{% else
    \setlength{\parindent}{0pt}
    \setlength{\parskip}{6pt plus 2pt minus 1pt}}
}{% if KOMA class
  \KOMAoptions{parskip=half}}
\makeatother
% Make \paragraph and \subparagraph free-standing
\makeatletter
\ifx\paragraph\undefined\else
  \let\oldparagraph\paragraph
  \renewcommand{\paragraph}{
    \@ifstar
      \xxxParagraphStar
      \xxxParagraphNoStar
  }
  \newcommand{\xxxParagraphStar}[1]{\oldparagraph*{#1}\mbox{}}
  \newcommand{\xxxParagraphNoStar}[1]{\oldparagraph{#1}\mbox{}}
\fi
\ifx\subparagraph\undefined\else
  \let\oldsubparagraph\subparagraph
  \renewcommand{\subparagraph}{
    \@ifstar
      \xxxSubParagraphStar
      \xxxSubParagraphNoStar
  }
  \newcommand{\xxxSubParagraphStar}[1]{\oldsubparagraph*{#1}\mbox{}}
  \newcommand{\xxxSubParagraphNoStar}[1]{\oldsubparagraph{#1}\mbox{}}
\fi
\makeatother


\usepackage{longtable,booktabs,array}
\newcounter{none} % for unnumbered tables
\usepackage{calc} % for calculating minipage widths
% Correct order of tables after \paragraph or \subparagraph
\usepackage{etoolbox}
\makeatletter
\patchcmd\longtable{\par}{\if@noskipsec\mbox{}\fi\par}{}{}
\makeatother
% Allow footnotes in longtable head/foot
\IfFileExists{footnotehyper.sty}{\usepackage{footnotehyper}}{\usepackage{footnote}}
\makesavenoteenv{longtable}
\usepackage{graphicx}
\makeatletter
\newsavebox\pandoc@box
\newcommand*\pandocbounded[1]{% scales image to fit in text height/width
  \sbox\pandoc@box{#1}%
  \Gscale@div\@tempa{\textheight}{\dimexpr\ht\pandoc@box+\dp\pandoc@box\relax}%
  \Gscale@div\@tempb{\linewidth}{\wd\pandoc@box}%
  \ifdim\@tempb\p@<\@tempa\p@\let\@tempa\@tempb\fi% select the smaller of both
  \ifdim\@tempa\p@<\p@\scalebox{\@tempa}{\usebox\pandoc@box}%
  \else\usebox{\pandoc@box}%
  \fi%
}
% Set default figure placement to htbp
\def\fps@figure{htbp}
\makeatother





\setlength{\emergencystretch}{3em} % prevent overfull lines

\providecommand{\tightlist}{%
  \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}



 


\KOMAoption{captions}{tableheading}
\makeatletter
\@ifpackageloaded{caption}{}{\usepackage{caption}}
\AtBeginDocument{%
\ifdefined\contentsname
  \renewcommand*\contentsname{Table of contents}
\else
  \newcommand\contentsname{Table of contents}
\fi
\ifdefined\listfigurename
  \renewcommand*\listfigurename{List of Figures}
\else
  \newcommand\listfigurename{List of Figures}
\fi
\ifdefined\listtablename
  \renewcommand*\listtablename{List of Tables}
\else
  \newcommand\listtablename{List of Tables}
\fi
\ifdefined\figurename
  \renewcommand*\figurename{Figure}
\else
  \newcommand\figurename{Figure}
\fi
\ifdefined\tablename
  \renewcommand*\tablename{Table}
\else
  \newcommand\tablename{Table}
\fi
}
\@ifpackageloaded{float}{}{\usepackage{float}}
\floatstyle{ruled}
\@ifundefined{c@chapter}{\newfloat{codelisting}{h}{lop}}{\newfloat{codelisting}{h}{lop}[chapter]}
\floatname{codelisting}{Listing}
\newcommand*\listoflistings{\listof{codelisting}{List of Listings}}
\makeatother
\makeatletter
\makeatother
\makeatletter
\@ifpackageloaded{caption}{}{\usepackage{caption}}
\@ifpackageloaded{subcaption}{}{\usepackage{subcaption}}
\makeatother
\usepackage{bookmark}
\IfFileExists{xurl.sty}{\usepackage{xurl}}{} % add URL line breaks if available
\urlstyle{same}
\hypersetup{
  pdftitle={Problem Set 6},
  colorlinks=true,
  linkcolor={blue},
  filecolor={Maroon},
  citecolor={Blue},
  urlcolor={Blue},
  pdfcreator={LaTeX via pandoc}}


\title{Problem Set 6}
\author{}
\date{}
\begin{document}
\maketitle


\begin{enumerate}
\def\labelenumi{\arabic{enumi}.}
\item
  \textbf{Under pressure: Interference} (from G \& G Ch. 8): In their
  study of spillover effects, Sinclair, McConnell, and Green\footnote{Sinclair,
    McConnell, and Green (2012). \emph{``Detecting Spillover Effects:
    Design and Analysis of Multilevel Experiments''} in \emph{American
    Journal of Political Science}.} sent mailings to randomly selected
  households in Chicago encouraging them to vote in an upcoming special
  election on April 7th 2009 (Figure~\ref{fig-postcard}). The mailings
  used a form of social pressure, disclosing whether the targeted
  individual had voted in previous elections. Because this type of mail
  had proven to increase turnout by approximately 4-5 percentage points
  in previous experiments, the authors used it to study whether the
  treatment effects are transmitted across households.

  Employing a multilevel design, they randomly assigned all, half, or
  none of the members of each nine-digit zip code to receive mail. For
  purposes of this example, we focus only on households with one
  registered voter. The outcome variable is voter turnout as measured by
  the registrar of voters. The results are as follows. Among registered
  voters in untreated zip codes, 1,201 of 6,217 cast ballots. Among
  untreated voters in zip codes where half of the households received
  mail, 526 of 3,316 registered voters cast ballots. Among treated
  voters in zip codes where half of the households received mail, 620 of
  2,949 voted. Finally, among treated voters in zip codes where every
  household received mail, turnout was 1,316 of 6,377.

  \begin{enumerate}
  \def\labelenumii{\alph{enumii}.}
  \item
    Identify the response variable, the units (measurement and
    experimental), and the experiental factor(s) and their levels.
  \item
    Using potential outcomes, define the direct treatment effects
    (parameters) of receiving mail addressed to subject \(i\).
  \item
    Define the spillover treatment effects (also parameters) of being in
    a zip code where varying fractions of households are treated.
  \item
    Propose an estimator for estimating the firsthand (direct) and
    secondhand (spillover) treatment effects. Show that the estimator is
    unbiased, explaining the assumptions required to reach this
    conclusion.
  \item
    Based on these data, what are your estimates of the magnitude of the
    mailing's direct and spillover effects? What did we learn here
    scientifically?
  \end{enumerate}

  \begin{figure}

  \centering{

  \includegraphics[width=3.125in,height=\textheight,keepaspectratio]{../31-interference-1/images/postcard.png}

  }

  \caption{\label{fig-postcard}Example of postcard mailed to registered
  voters.}

  \end{figure}%
\end{enumerate}

\newpage{}

\begin{enumerate}
\def\labelenumi{\arabic{enumi}.}
\setcounter{enumi}{1}
\tightlist
\item
  \textbf{Bring Out Your Bins: Non-compliance} Cotterill et al.~report
  the results of an experiment conducted in an area of the United
  Kingdom where only half of the local residents recycle their
  trash\footnote{Cotteril el al (2009). \emph{``Mobilizing Citizen
    Effort to Enhance Environmental Outcomes: A Randomized Controlled
    Trail of a Door-to-Door Recycling Campaign.''} in \emph{Journal of
    Environmental Management}.}. Canvassers visited homes and encouraged
  residents to recycle. Outcomes were measured by whether the home put
  out a recycling bin on at least one occasion during the following
  three weeks. We restrict our attention here to homes that did not
  recycle trash during a pre-experimental period of observation. When
  implementing the intervention, researchers encountered one-side
  noncompliance: 1,105 of the 1,849 homes assigned to the treatment
  group were successfully canvassed; none of the 1,430 homes assigned to
  the control group were canvassed. These researchers found that 591
  homes in the treatment group recycled, as opposed to 377 in the
  control group. The researchers also observed that 429 of 1,105 homes
  that were successfully canvassed recycled, as opposed to 539 of the
  2,264 homes that were not canvassed.
\end{enumerate}

\begin{enumerate}
\def\labelenumi{\alph{enumi}.}
\item
  Estimate the \(ITT_Y\) and interpret what that statistic captures in
  the context of this study.
\item
  Estimate the \(ITT_D\) and interpret what that statistic captures.
\item
  Estimate the \(CACE\) and interpret what that statistic captures.
\item
  Explain why comparing the recycling rates of the treated and untreated
  subjects tends to produce misleading estimates of the \(CACE\) and the
  \(ATE\).
\end{enumerate}

More questions coming soon!




\end{document}
