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\subfile{titlepage}
\newpage
\section{Introduction}
\subfile{0_introduction}
\section{Identification results}
\subfile{1_identification}
\section{Test for detecting violations of LiM}
\subfile{2_lim_test}
\section{Estimation of the CC-ACR}
\subfile{3_estimation}
\section{Empirical applications}
\label{sec:results}
The proposed methodology is broadly applicable to various studies involving nonbinary, ordered treatments and multiple instruments, including studies like \cite{attanasio2013community}. My results further extend to studies using Mendelian randomization, which employs genetic variants as instruments and has found applications in social sciences and economics (see, for example, \cite{dixon2020mendelian, scholder2013child}). To provide another example, my results are relevant to applications that instrument for child BMI using the BMI of biological relatives (see, for example, \cite{cawley2004impact, lindeboom2010assessing, kline2008wages}).
To demonstrate the results of the preceding sections, I consider two empirical applications. First, I revisit \citeauthor{card1995geographic}'s (\citeyear{card1995geographic}) seminal study on the returns to education. Second, I apply the novel methodology to \citeauthor{angrist1996children}'s (\citeyear{angrist1996children}) data to study the effect of an additional child on female labor market outcomes.
\bigskip
\subsection{The causal effect of schooling on wage}
\label{sec:results_card}
\subfile{4_results_card}
\subsection{The causal effect of additional child on female labor market outcomes}
\label{sec:results_twins}
\subfile{4_results_twins}
\section{Conclusion}
\label{sec:discussion}
\subfile{6_discussion}
\bigskip
\bibliography{references}
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