ivreg-20221207.Rtex

% Brief workshop on instrumental variable regression in R
% (c) 2022 Malcolm Gillies <malcolm.gillies@unsw.edu.au>
% https://github.com/mbg-unsw/ivreg
%
% This work is licensed under a
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% International Licence
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\title{Intro to instrumental variable regression in R}
\author{Malcolm Gillies}
\date{7 December 2022}
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\begin{frame}{Acknowledgement}

The material in this presentation was adapted from:

\medskip

\textbf{Introduction to Econometrics with R}

\emph{Christoph Hanck, Martin Arnold, Alexander Gerber, and Martin Schmelzer}

2021-10-06

\url{https://www.econometrics-with-r.org/}

\medskip

Especially Chapter 12 / Section 12.1

\end{frame}

\begin{frame}{Note on terminology}
	\begin{itemize}
		\item Econometrics and (bio)statistics use different words for things
		\item A glossary can help, e.g. \cite{gunasekara_2008}
		\item \emph{Endogenous regressor} $\sim$ Confounded independent variable
	\end{itemize}
\end{frame}

\begin{frame}{IV assumptions}
	\begin{enumerate}
		\item Strongly related to the independent variable
		\item Uncorrelated with confounders and only related to
			outcome via the independent variable
	\end{enumerate}
\end{frame}

\begin{frame}{Notation}
	\begin{itemize}
		\item $X_i$ independent variable
		\item $Z_i$ instrumental variable
		\item $Y_i$ outcome variable
	\end{itemize}
\end{frame}

\begin{frame}{Two-stage least-squares regression}
First stage: regress independent variable on IV and
predict ``good part'' of independent variable
\begin{gather}
X_i = \underbrace{\pi_0 + \pi_1 Z_i}_\text{good} + \underbrace{\nu_i}_\text{bad} \\
\hat{X}_i = \hat{\pi}_0 + \hat{\pi}_1 Z_i
\end{gather}

Second stage: regress outcome on predictions to yield effect $\beta_1$

\begin{equation}
Y_i = \beta_0 + \beta_1 \hat{X}_i + \epsilon_i
\end{equation}
\end{frame}

\begin{frame}{Example: how do cigarette sales vary with price?}
\begin{itemize}
	\item Does increasing the price of cigarettes cause a decrease in sales?
		\begin{itemize}
			\item \emph{Elasticity of demand}
		\end{itemize}
	\item Not confounding per se
		\begin{itemize}
			\item \emph{Simultaneous causality} (two-way causality) in supply and demand
		\end{itemize}
	\item Instrumental variable analysis can remove bias
\end{itemize}
\end{frame}

\begin{frame}[fragile]{Setup}
%% begin.rcode vars, warning=FALSE, message=FALSE
%#### load the data set and get an overview
%library(AER)
%data("CigarettesSW")
%
%#### compute real per capita prices
%CigarettesSW$rprice <- with(CigarettesSW, price / cpi)
%
%####  compute the sales tax
%CigarettesSW$salestax <- with(CigarettesSW, (taxs - tax) / cpi)
% 
%#### generate a subset for the year 1995
%c1995 <- subset(CigarettesSW, year == "1995")
%
%% end.rcode
\end{frame}

\begin{frame}[fragile]{Scatterplot}
%% begin.rcode scatter, fig.height=1.7, fig.width=3.4
%library(ggplot2)
%ggplot(data=c1995, aes(x=log(rprice), y=log(packs))) +
%    geom_smooth(method='lm', formula= y~x) + geom_point()
%
%% end.rcode
\end{frame}

\begin{frame}[fragile]{Naive estimate}
%% begin.rcode lm
%summary(lm(log(packs)~log(rprice), data=c1995))$coefficients
%
%% end.rcode
\end{frame}

\begin{frame}[fragile]{Scatterplot (instrumental variable)}
%% begin.rcode scatter2, fig.height=1.7, fig.width=3.4
%library(ggplot2)
%ggplot(data=c1995, aes(x=salestax, y=log(rprice))) +
%    geom_smooth(method='lm', formula= y~x) + geom_point()
%
%% end.rcode
\end{frame}

\begin{frame}[fragile]{First stage regression (1)}
%% begin.rcode fs1
%cig_s1 <- lm(log(rprice) ~ salestax, data = c1995)
%
%coeftest(cig_s1, vcov = vcovHC, type = "HC1")
%
%% end.rcode
\end{frame}

\begin{frame}[fragile]{First stage regression (2)}
%% begin.rcode fs2
%#### inspect the R^2 of the first stage regression
%summary(cig_s1)$r.squared
%
%#### store the predicted values
%lcigp_pred <- cig_s1$fitted.values
%
%% end.rcode
\end{frame}

\begin{frame}[fragile]{Second stage regression}
%% begin.rcode ss
%cig_s2 <- lm(log(c1995$packs) ~ lcigp_pred)
%coeftest(cig_s2, vcov = vcovHC)
%
%% end.rcode
\end{frame}

\begin{frame}[fragile]{Automated TSLS using \texttt{ivreg()}}
%% begin.rcode ivreg
%cig_ivreg <- ivreg(log(packs) ~ log(rprice) | salestax, data = c1995)
%coeftest(cig_ivreg, vcov = vcovHC, type = "HC1")
%
%% end.rcode
\end{frame}

\begin{frame}[fragile]{Check strength of instrument using $F$ test}
%% begin.rcode ftest, size='scriptsize'
%linearHypothesis(cig_s1, "salestax=0", vcov = vcovHC, type = "HC1")
%
%% end.rcode
\end{frame}

\begin{frame}{Additional worked examples}
	\begin{itemize}
		\item \emph{Causal Inference in Education}
		\item \url{https://bookdown.org/aschmi11/causal_inf/instrumental-variables-estimation.html}
		\item A tutorial on the use of instrumental variables in pharamcoepidemiology \cite{ertefaie_2017}
	\end{itemize}
\end{frame}

\begin{frame}{References}
        \tiny\bibliography{ivreg.bib}
        \bibliographystyle{abbrvnat}
\end{frame}

\end{document}