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+\documentclass[MSNbibl,nameyear,dvips]{arxstspdf}
+\usepackage{tikz}
+\usepackage{graphicx}
+\usepackage{flushend}
+\usepackage{stfloats}
+
+
+\volume{29}
+\issue{3}
+\pubyear{2014}
+\firstpage{363}
+\lastpage{366}
+\doi{10.1214/14-STS485} \referstodoi{10.1214/14-STS480}\docsubty{FLA}
+
+\makeatletter
+
+
+\newcommand{\lleft}{\left}
+\newcommand{\rright}{\right}
+
+\newcommand{\ind}{\mbox{$\,\perp\kern-5.5pt \perp\,$}}
+
+
+\renewcommand{\citep}[1]{(\citeauthor{#1}, \citeyear{#1})}
+\newcommand{\citepp}[1]{\citeauthor{#1}, \citeyear{#1}}
+
+\makeatother
+
+\begin{document}
+\begin{frontmatter}
+
+\vspace*{12pt}\title{ACE Bounds; SEMs with Equilibrium Conditions}
+\runtitle{ACE Bounds; SEMS with Equilibrium Conditions}
+\begin{aug}
+\author[a]{\fnms{Thomas S.} \snm{Richardson}\ead[label=e1]{thomasr@uw.edu}}
+\and
+\author[b]{\fnms{James M.} \snm{Robins}\ead[label=e2]{robins@hsph.harvard.edu}}
+
+\runauthor{T. S. Richardson and J. M. Robins}
+
+\affiliation{University of Washington and Harvard School of Public Health}
+
+\address[a]{Thomas S. Richardson is Professor and Chair, Department of Statistics, University of Washington,
+Box 354322, Seattle, Washington 98195, USA \printead{e1}.}
+
+\address[b]{James M. Robins is Mitchell L. and Robin LaFoley Dong Professor,
+Department of Epidemiology, Harvard School of
+Public Health,
+677 Huntington Avenue, Boston, Massachusetts 02115, USA \printead{e2}.}
+\end{aug}
+
+
+\end{frontmatter}
+
+We congratulate the author on an enlightening account of
+the instrumental variable approach from the viewpoint of Econometrics.
+We first make some comments regarding the bounds on the ACE under the
+nonparametric IV model,
+and then discuss potential outcomes in the market equilibrium model.
+
+\section{ACE Bounds Under the IV Model}
+We consider the model in which $X$ and $Y$ are binary, taking values in
+$\{0,1\}$, while
+$Z$ takes $K$ states $\{1,\ldots,K\}$. We use the notation $X(z_i)$ to indicate
+$X(z = i)$, similarly $Y(x_j)$ for $Y(x = j)$. We consider four
+different sets of assumptions:
+\begin{longlist}[(iii)]
+\item[(i)] $Z \ind Y({x}_0),Y({x}_1), X({z}_1),\ldots,X({z}_{K})$;
+\item[(ii)] $Z \ind Y({x}_0),Y({x}_1)$;
+\item[(iii)] for $i \in\{1,\ldots,K\}$, $j \in\{0,1\}$, $Z \ind
+X(z_i),\linebreak[4] Y(x_j)$;
+\item[(iv)] there exists a $U$ such that $U \ind Z$ and for $j \in\{
+0,1\}$, $Y(x_j) \ind X,Z \mid U$.
+\end{longlist}
+Condition (i) is joint independence of $Z$ and all potential outcomes
+for $Y$ and $X$. (ii) does not assume independence (or existence)
+of counterfactuals for $X$.
+(iii)~is a subset of the independences in (i), none of which involve
+potential outcomes from different worlds.\footnote{In other words,
+they do not involve both $Y(x_0)$ and $Y(x_1)$, nor $X(z_i)$ and
+$X(z_j$) for $i\neq j$.}
+The counterfactual independencies (i), (ii), (iii) arise most naturally
+in the context
+where the instrument is randomized, as depicted by the DAG in Figure~\ref{figswig}(a).
+Assumption (iii) may be read (via d-separation) from the Single-World
+Intervention Graph (SWIG)\footnote{See \citet{richardsonrobins2013}
+for details.}
+$\mathcal{G}_1(z,x)$, depicted in Figure~\ref{figswig}(b), which
+represents the factorization of $P(Z,X(z),Y(x),U)$, implied by the IV model.
+
+Lastly (iv) consists of only three independence statements, but does
+assume the existence of an unobserved variable $U$ that
+is sufficient to control for confounding between $X$ and $Y$. No
+assumption is made concerning the existence of counterfactuals
+$X(z)$; confounding variables ($U^*$) between $Z$ and $X$ are permitted
+(so long as $U^* \ind U$). The DAG $\mathcal{G}_2$ and
+corresponding SWIG $\mathcal{G}_2(x)$ are shown in Figure~\ref{figswig}(c), (d). In \citet{richardsonrobins2014}, we prove the following.
+
+
+\begin{thm} Under any of the assumptions \textup{(i)}, \textup{(ii)}, \textup{(iii)}, \textup{(iv)}, the set of possible joint distributions
+$P(Y(x_0), Y(x_1))$ are characterized by
+the $8K$ inequalities:\vspace*{-2pt}
+\begin{eqnarray}
+\label{eqmarg}&&P\bigl(Y(x_i) = y\bigr) \nonumber\\[-1pt]
+&&\quad \leq P(Y = y, X = i | Z = z)\\[-1pt]
+&&\qquad {}+ P(X = 1-i |
+Z = z),\nonumber
+\\[4pt]
+\label{eqjoint}&&P\bigl(Y(x_0) = y, Y(x_1) = \tilde{y}\bigr) \nonumber\\[-1pt]
+&&\quad \leq P(Y
+= y, X = 0 | Z = z)\\[-1pt]
+&&\qquad {} + P(Y = \tilde{y}, X = 1 | Z = z).\nonumber
+\end{eqnarray}
+\end{thm}
+
+Thus a distribution $P(X,Y | Z)$ is compatible with the stated
+assumptions if and only if there exists a distribution
+$P(Y(x_0), Y(x_1))$ satisfying (\ref{eqmarg}) and (\ref{eqjoint}).
+
+\begin{thm} Under any of the assumptions \textup{(i)}, \textup{(ii)}, \textup{(iii)}, \textup{(iv)}
+for all $i,j \in\{0,1\}$, $P(Y(x_i) = j) \leq
+g(i,j)$, where\vspace*{-2pt}
+{\fontsize{10.9}{12.9}\selectfont{\begin{eqnarray*}
+g(i,j) &\equiv&\min \Bigl\{ \min_{z} \bigl[\vphantom{\hat{P}} P(X
+= i, Y = j | Z = z)\\
+&&\hphantom{\min \Bigl\{\min_{z} \bigl[}{} + P(X = 1-i | Z = z) \bigr],
+\\
+&&\hphantom{\min \Bigl\{} \min_{z, \tilde{z}: z \neq\tilde{z}} \bigl[ P(X = i, Y = j | Z
+= z) \\
+&&\hphantom{\min \Bigl\{\min_{z, \tilde{z}: z \neq\tilde{z}} \bigl[}{}+ P(X = 1-i, Y = 0 | Z = z)
+\nonumber
+\\
+&&\hphantom{\min \Bigl\{\min_{z, \tilde{z}: z \neq\tilde{z}} \bigl[}{}  +  P(X = i, Y = j | Z =
+\tilde{z}) \\
+&&\hphantom{\min \Bigl\{\min_{z, \tilde{z}: z \neq\tilde{z}} \bigl[}{}+ P(X = 1-i, Y = 1 | Z = \tilde {z}) \bigr] \Bigr\}.
+\nonumber
+\end{eqnarray*}}}
+Furthermore, $P(Y(x_0))$ and $P(Y(x_1))$ are variation independent.
+Consequently,
+\begin{eqnarray*}
+1-g(1,0)-g(0,1) &\leq& \operatorname{ACE}(X \rightarrow Y)\\
+& \leq& g(0,0)+g(1,1)-1.
+\end{eqnarray*}
+These bounds are sharp.
+\end{thm}
+
+
+\begin{figure}
+
+\includegraphics{485f01.eps}
+
+\caption{\textup{(a)} IV model with no confounding between $Z$ and $X$; \textup{(b)}
+SWIG representing $P(Z, X(z),Y(x),U)$;
+\textup{(c)} IV model with confounding between $Z$ and $X$; \textup{(d)} SWIG
+representing $P(Z, X,Y(x),U,U^*)$.}\label{figswig}
+\end{figure}
+
+
+Note that to evaluate $g(i,j)$ requires finding a minimum over $K^2$
+expressions. In the case
+where $K=2$, these bounds reduce to those given by \citet
+{BalkPearboun1997}, who assume (i).\footnote{\citet{dawid2003} working
+in a non-counterfactual framework also established the bounds for $K=2$
+under the DAG in Figure~\ref{figswig}(a); however,
+his proof also applies to Figure~\ref{figswig}(c). \citet
+{robinsgreenland1996} observed that the Balke--Pearl bounds
+were also sharp under (ii).} \citet{robins1989} and \citet{manski1990} derived what are called
+the ``natural bounds'' on the ACE under the weaker assumption that $Z
+\ind Y({x}_0)$ and $Z \ind Y({x}_1)$.
+As noted by Imbens, without further assumptions these bounds are not
+sharp. However, the natural bounds are sharp under (i) or (iii), if, in
+addition, we assume there are no Defiers (an assumption that has
+testable implications). \citet{chengsmall2006} considered bounds on
+the ACE when $K=3$ under additional assumptions.
+
+
+\section{Market Equilibrium and BiCausal Models}
+Imbens' clear description of the market equilibrium model is
+particularly informative.
+We also strongly endorse the author's contention that the RHS of
+systems of structural equations
+should be interpreted as describing potential outcomes for the
+LHS.\footnote{
+\citet{pearl2000}, \citet{laucausal}, \citet{lauritzen02} argue that these are not
+really ``equations''
+but are better viewed as ``assignments'' in computer languages, for example, $ y
+\leftarrow x +1$;
+see also \citet{strotzwoldrecursive1960}, page 420.}
+
+However, we note that this position has important implications both for
+interpretation and inference.
+Furthermore, it does not
+seem to be universally accepted within Economics. \citet{leroy2006}
+states that ``economic models use the equality symbol with its usual
+mathematical meaning,
+not with the meaning of the assignment operator'';
+an approach that is clearly incompatible with an interpretation in
+terms of potential outcomes. For example,
+it becomes permissible to renormalize structural equations to change
+which variable is on the LHS.
+
+It has also been argued that statistical analyses of such models should be
+invariant to the normalization; see \citet{hillier1990},
+\citet{basmanncausal1963}.\hskip.2pt\footnote{For example, \citet{greene2003}, page 401, states (in the
+context of the IV model):
+``one significant virtue of [the Limited Information Maximum Likelihood
+Estimator]
+is its invariance to normalization of the equations.''}
+Contrary to Imbens' remark,\footnote{Footnote 8, page 331.} this
+alternative view does not appear to be motivated by
+considerations of measurement error. \citet{leroy2006} makes clear
+that he does not believe
+that structural equations describe potential outcomes for endogenous
+variables and does not discuss issues relating to measurement.\footnote
+{For example,
+\citet{leroy2006}, page 23, states that ``The assumption that it makes
+sense to delete one or more of the structural equations
+and replace the value of the internal variable so determined by a
+constant without altering the other equations [\ldots] is virtually never satisfied
+in economic models since each external variable typically affects
+equilibrium values of more than one internal variable.''
+He goes on to assert ``In fact, it is difficult to think of nontrivial
+models in any area of research in which the [\ldots] assumption is satisfied.''}
+Rather, this appears to be a fundamental difference in interpretation.
+
+The market equilibrium model specifies potential outcomes for
+$Q^d_t(p)$, $Q^s_t(p)$:
+\begin{eqnarray}
+\label{eqqd}Q^d_t(p)&=& \alpha^d + \beta^d p
++ \varepsilon_t^d,
+\\
+\label{eqqs}Q^s_t(p)&=& \alpha^s + \beta^s p
++ \varepsilon_t^s,
+\end{eqnarray}
+and imposes the equilibrium condition:\footnote{To simplify notation,
+throughout we work directly in terms of $\log$ price and $\log$ quantity.}
+\begin{eqnarray}
+Q^d_t(p) = Q^s_t(p).\label{eqequ}
+\end{eqnarray}
+\citet{strotzwoldrecursive1960} described such systems as \textit
+{bicausal}.
+It should be observed that the model does not
+specify potential outcomes for price ($P_t(q_s,q_d)$), nor does it view
+price as externally determined (i.e., exogenous).
+Instead price is determined implicitly as a consequence of the
+equilibrium condition. In this regard, the
+model might be regarded as incomplete: Indeed \citet
+{haavelmowhat1958} is quite critical of this model for failing to
+offer any \emph{explanation} as to
+how the equilibrium price is determined. The model also falls outside
+the scope of non-parametric structural equation models (NPSEM) (see, e.g., \cite{pearl2000}), which require one equation for each
+endogenous variable;\footnote{Indeed \citet{leroy2006} argues against the interpretation of
+structural equations in terms of potential outcomes on the grounds that
+this interpretation, as advanced by Pearl, requires a one-to-one
+mapping between equations and endogenous variables that he argues, does not
+make sense for the market equilibrium model.}
+likewise the model
+defies standard graphical representation, though see Figure~\ref{figone}(a).
+\begin{figure}
+
+\includegraphics{485f02.eps}
+
+\caption{\textup{(a)} Attempt to depict the bicausal model; \textup{(b)} a schematic
+showing the deterministic system (\protect\ref{eqcon})--(\protect\ref{eqmer});
+the edge
+\protect\tikz\protect\path(0ex,0ex) edge[->] node[above=0pt, black]
+{$\scriptscriptstyle I$} (3ex,0ex);
+denotes that $P$ is the integral of $\Delta P$; see Iwasaki and Simon (\citeyear
+{iwasaki1994}).}\label{figone}
+\end{figure}
+
+A related question concerns whether there exist dynamic acyclic (i.e.,
+recursive)
+systems of structural equations
+that lead to the equilibrium distribution corresponding either to a
+cyclic system
+of structural equations or a bicausal system.\footnote{Analysis of this question was stimulated by a heated debate that arose between
+Wold, who advocated a recursive, regression-based approach to demand
+analysis, and Haavelmo
+and the Cowles Commission who advocated simultaneous equations. See
+\citet{haavelmostatistical1943}, \citet{woldbentzelstatistical1946},
+\citet{woldjureendemand1953}, \citet{bentzelhansenrecursiveness1954},
+\citet{strotzwoldrecursive1960}, \citet{basmanncausal1963}; historical overviews
+are given by \citet{morganstamping1991},
+\citet{epsteinhistory1987}.} \citet{fishcorr} provides just such a ``correspondence principle''
+under which the distribution implied by a cyclic linear SEM is obtained
+as a time average of a deterministic
+set of first order difference equations reaching a static equilibrium
+subject to stochastic boundary conditions.
+The correspondence assumes that the equilibration time is very fast
+relative to the interval between observations
+so the time averaged variables are in deterministic equilibrium.
+Fisher also derived conditions on the coefficient matrices of a cyclic
+SEM that are required in order for the system
+to reach equilibrium; in fact he further required that each subset of
+structural equations also have this property.
+
+However, Fisher's correspondence presumes a normalization under which
+each variable is associated with
+a single equation (as in an NPSEM), and hence would not apply to a
+bicausal system. \citet{richphd}, Chapter~2,
+described a system of finite difference equations that gives rise to
+the bicausal system~(\ref{eqqd})--(\ref{eqequ}):
+\begin{eqnarray}
+\label{eqcon}\mbox{Consumers:}&&\hspace*{4pt}   Q^d_{t+(k+1)\delta}(p_{t+k\delta})\nonumber \\[-8pt]\\[-8pt]
+&&\hspace*{4pt}\quad =
+\alpha^d+ \beta^d p_{t+k\delta} + \varepsilon_{t}^d,\nonumber
+\\
+\label{eqsup}\mbox{Suppliers:}&&\hspace*{4pt}  Q^s_{t+(k+1)\delta}(p_{t+k\delta}) \nonumber\\[-8pt]\\[-8pt]
+&&\hspace*{4pt}\quad =
+\alpha^s+ \beta^s p_{t+k\delta} + \varepsilon_{t}^s,\nonumber
+\\
+\label{eqmer}\mbox{Merchants:}&&\hspace*{4pt}  P_{t+(k+1)\delta}\bigl(q^d_{t+k\delta},
+q^s_{t+k\delta},p_{t+k\delta}\bigr) \nonumber\\[-8pt]\\[-8pt]
+&&\hspace*{4pt}\quad = p_{t+k\delta} +
+\lambda \bigl(q^d_{t+k\delta} - q^s_{t+k\delta}
+\bigr),\nonumber
+\end{eqnarray}
+for $k=\{0,\ldots, \delta^{-1}-1\}$. Note that the disturbances
+$(\varepsilon_{t}^d, \varepsilon_{t}^s)$ represent boundary
+conditions and hence
+remain fixed during the interval $[t,t+1)$.
+As in Fisher's correspondence, the observed variables correspond to
+limiting time-averages over a unit
+interval:
+\begin{eqnarray*}
+\overline{Q}^d_t &=& \lim_{\delta\rightarrow0} \delta
+\sum_{k=0}^{\delta^{-1}-1} {Q}^d_{t+k\delta},\quad
+\overline{Q}^s_t = \lim_{\delta\rightarrow0} \delta
+\sum_{k=0}^{\delta^{-1}-1} {Q}^s_{t+k\delta},\\
+ \overline{P}_t &=& \lim_{\delta\rightarrow0} \delta\sum
+_{k=0}^{\delta^{-1}-1} {P}_{t+k\delta}.
+\end{eqnarray*}
+Under suitable conditions on the coefficients, $(\overline{Q}^d_t,
+\overline{Q}^s_t,\allowbreak  \overline{P}_t)$ obey
+equations (\ref{eqqd})--(\ref{eqequ}). Note that Merchants'
+equation (\ref{eqmer}) which includes $P$, leads to the equilibrium
+condition (\ref{eqequ}) that does not.\footnote{In causal terms,
+this model is similar to one presented in \citet{wold1959}. Wold
+viewed his model as a formalization of Cournot's theories.}
+It might be objected to the proposed model that there is no disturbance
+term in equation (\ref{eqmer}).
+The explanation for this is that the disturbance terms in the
+nonrecursive model correspond to constant factors in the deterministic
+evolution.
+The equation for price gives the change in price during a small
+interval (length $\delta$) to the discrepancy between supply and demand.
+Adding a disturbance term would say that throughout the observation
+period (length $1$) the Merchants' reaction to change in price was off
+by a constant factor, so that even if quantities supplied and demanded
+were identical, the Merchants would change the price. Thus, if we add
+an error $\varepsilon^p_t$ the model will not, in general, arrive at
+equilibrium
+within the unit interval.\footnote{Having said this, the equations
+(\ref{eqcon}) and (\ref{eqsup}) still imply that producers and
+consumers make systematic errors in computing prices over a time-scale
+of length $\delta$.}
+
+\citet{iwasaki1994} represent equilibrating mechanisms via ``causal
+influence diagrams'' in which the derivatives of variables are included.
+Under this scheme, model (\ref{eqcon})--(\ref{eqmer}) is
+represented by the graph in Figure~\ref{figone}(b).
+This example serves to show that time averages of (deterministic)
+equilibrating systems need not have a structural equation for each variable.
+See also \citep{2001.dash.esqaru} for related work.
+
+
+\section*{Acknowledgments}
+This work was supported by the US National Institutes of Health Grant
+R01 AI032475; Richardson was also supported by the US National Science
+Foundation Grant CNS-0855230.
+
+
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+\blocation{Berlin}.
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+\bedition{5th} ed.
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+\blocation{Upper Saddle River, NJ}.
+\end{bbook}
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+\end{barticle}
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+(\byear{1958}).
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+\bnote{(in {N}orwegian). English translation published as: {W}hat can static equilibrium models tell us? \textit{Economic Inquiry} \textbf{12} (1974) 27--34}.
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+(\byear{1990}).
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+\bibitem[\protect\citeauthoryear{Iwasaki and Simon}{1994}]{iwasaki1994}
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+\bauthor{\bsnm{Simon},~\bfnm{Herbert~A.}\binits{H.~A.}}
+(\byear{1994}).
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+\end{barticle}
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+\bibitem[\protect\citeauthoryear{Lauritzen}{2001}]{laucausal}
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+\bauthor{\bsnm{Lauritzen},~\bfnm{Steffen~L.}\binits{S.~L.}}
+(\byear{2001}).
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+In \bbooktitle{Complex Stochastic Systems ({E}indhoven, 1999)}.
+\bseries{Monogr. Statist. Appl. Probab.}
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+\bpublisher{Chapman \& Hall/CRC},
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+\end{bincollection}
+\bptok{imsref}\endbibitem
+
+\bibitem[\protect\citeauthoryear{Lauritzen and Richardson}{2002}]{lauritzen02}
+\begin{barticle}[mr]
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+(\byear{2002}).
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+\bptnote{check related}\end{barticle}
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+\bibitem[\protect\citeauthoryear{{LeRoy}}{2006}]{leroy2006}
+\begin{btechreport}[author]
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+(\byear{2006}).
+\btitle{Causality in economics}.
+\btype{Technical report, Univ. California, Santa Barbara}.
+\end{btechreport}
+\bptok{imsref}\endbibitem
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+\bibitem[\protect\citeauthoryear{Manski}{1990}]{manski1990}
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+\end{barticle}
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+
+\bibitem[\protect\citeauthoryear{Morgan}{1991}]{morganstamping1991}
+\begin{bincollection}[author]
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+(\byear{1991}).
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+In \bbooktitle{Appraising Economic Theories}
+(\beditor{\bfnm{Neil}\binits{N.}~\bparticle{de}~\bsnm{Marchi}} \AND
+\beditor{\bfnm{Mark}\binits{M.}~\bsnm{Blaug}}, eds.)
+\bpages{237--272}.
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+\end{bincollection}
+\bptok{imsref}\endbibitem
+
+\bibitem[\protect\citeauthoryear{Pearl}{2000}]{pearl2000}
+\begin{bbook}[mr]
+\bauthor{\bsnm{Pearl},~\bfnm{Judea}\binits{J.}}
+(\byear{2000}).
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+\bpublisher{Cambridge Univ. Press},
+\blocation{Cambridge}.
+\bid{mr={1744773}}
+\end{bbook}
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+
+\bibitem[\protect\citeauthoryear{Richardson}{1996}]{richphd}
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+\bauthor{\bsnm{Richardson},~\bfnm{T.~S.}\binits{T.~S.}}
+(\byear{1996}).
+\btitle{Models of feedback: Interpretation and discovery}.
+\btype{Ph.D. thesis, Carnegie-Mellon Univ}.
+\end{bphdthesis}
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+\bibitem[\protect\citeauthoryear{Richardson and Robins}{2013}]{richardsonrobins2013}
+\begin{btechreport}[author]
+\bauthor{\bsnm{Richardson},~\bfnm{Thomas~S.}\binits{T.~S.}} \AND
+\bauthor{\bsnm{Robins},~\bfnm{James~M.}\binits{J.~M.}}
+(\byear{2013}).
+\btitle{{S}ingle {W}orld {I}ntervention {G}raphs {(SWIGs)}: A unification of the counterfactual and graphical approaches to
+causality}.
+\btype{Technical Report 128, Center for Statistics and the Social Sciences, Univ.
+Washington, Seattle, WA}.
+\end{btechreport}
+\bptok{imsref}\endbibitem
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+\bibitem[\protect\citeauthoryear{Richardson and Robins}{2014}]{richardsonrobins2014}
+\begin{bunpublished}[author]
+\bauthor{\bsnm{Richardson},~\bfnm{T.~S.}\binits{T.~S.}} \AND
+\bauthor{\bsnm{Robins},~\bfnm{J.~M.}\binits{J.~M.}}
+(\byear{2014}).
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+\end{bunpublished}
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+\bibitem[\protect\citeauthoryear{Robins}{1989}]{robins1989}
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+(\byear{1989}).
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+In \bbooktitle{Health Service Research Methodology: A Focus on {AIDS}}
+(\beditor{\bfnm{L.}\binits{L.}~\bsnm{Sechrest}},
+\beditor{\bfnm{H.}\binits{H.}~\bsnm{Freeman}} \AND
+\beditor{\bfnm{A.}\binits{A.}~\bsnm{Mulley}}, eds.).
+\bpublisher{U.S. Public Health Service},
+\blocation{Washington, DC}.
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+\bptok{imsref}\endbibitem
+
+\bibitem[\protect\citeauthoryear{Robins and Greenland}{1996}]{robinsgreenland1996}
+\begin{barticle}[author]
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+(\byear{1996}).
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+\end{barticle}
+\bptok{imsref}\endbibitem
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+\bibitem[\protect\citeauthoryear{Strotz and Wold}{1960}]{strotzwoldrecursive1960}
+\begin{barticle}[mr]
+\bauthor{\bsnm{Strotz},~\bfnm{Robert~H.}\binits{R.~H.}} \AND
+\bauthor{\bsnm{Wold},~\bfnm{H.~O.~A.}\binits{H.~O.~A.}}
+(\byear{1960}).
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+\bid{issn={0012-9682}, mr={0120034}}
+\end{barticle}
+\bptok{imsref}\endbibitem\vfill\eject
+
+\bibitem[\protect\citeauthoryear{Wold}{1959}]{wold1959}
+\begin{bincollection}[mr]
+\bauthor{\bsnm{Wold},~\bfnm{Herman~O.~A.}\binits{H.~O.~A.}}
+(\byear{1959}).
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+\bpublisher{Almqvist \& Wiksell},
+\blocation{Stockholm}.
+\bid{mr={0109088}}
+\end{bincollection}
+\bptok{imsref}\endbibitem
+
+\bibitem[\protect\citeauthoryear{Wold and Jur{\'e}en}{1953}]{woldjureendemand1953}
+\begin{bbook}[author]
+\bauthor{\bsnm{Wold},~\bfnm{H.~O.~A.}\binits{H.~O.~A.}} \AND
+\bauthor{\bsnm{Jur{\'e}en},~\bfnm{L.}\binits{L.}}
+(\byear{1953}).
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+\bpublisher{Wiley},
+\blocation{New York}.
+\end{bbook}
+\bptok{imsref}\endbibitem\vfill
+
+
+\end{thebibliography}
+\end{document}