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\title{\vspace{-1cm}
 Peer Advice on Financial Decisions: \\
 A case of the blind leading the blind?}

\author{Sandro Ambuehl,\; B. Douglas Bernheim,\; \\
 Fulya Ersoy,\; and Donna Harris\thanks{\protect\doublespacing\normalsize Ambuehl: Department of Economics and UBS Center for Economics in Society, University of Zurich, Bl\"uemlisalpstrasse 10, 8006 Z\"urich, Switzerland, sandro.ambuehl@econ.uzh.ch.
Bernheim: Department of Economics, Stanford
University, 579 Serra Mall, Stanford, CA 94305, USA, bernheim@stanford.edu. Ersoy: Department of Economics, Loyola Marymount University, 1 LMU Drive, Los Angeles, CA, 90045, fulya.ersoy@lmu.edu. Harris: Department of of Economics, University of Oxford, Manor Road Building, Manor Road, OX1 3UQ, United Kingdom,
donhatai.harris@economics.ox.ac.uk. We are especially grateful to
Michalis Drouvelis and the people at the Birmingham Experimental Economics
Laboratory for letting us perform our experimental sessions at their
facilities. We also thank James Choi, Florian Ederer, Glenn W. Harrison,
and the audiences at various seminars and conferences for helpful comments and discussions. David Zuckerman provided
excellent research assistance. This research has been approved by
the Stanford IRB in protocol 31364. We gratefully acknowledge funding
from the Alfred P. Sloan foundation (grant number G-2017-9017) and
from the Stanford Department of Economics.}
}

\maketitle
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\vspace{-1cm}

\begin{abstract}
\normalsize
We investigate the impact of peer interaction on the quality of financial decision making in a laboratory experiment. Face-to-face communication with a randomly assigned peer significantly improves the quality of subsequent private decisions even though simple mimicry would have the opposite effect. We present evidence that the mechanism involves general conceptual learning (because the benefits of communication extend to previously unseen tasks), and that the most effective learning relationships are horizontal rather than vertical (because people with weak skills benefit most when their partners also have weak skills). The benefits of demonstrably effective financial education do not propagate to peers.\\
\indent \emph{JEL codes: C91, D12, D69, G53} \\

\end{abstract}

\newpage{}

\doparttoc
\faketableofcontents


\section{Introduction}

\setcounter{page}{1}

When making financial decisions, people often seek advice from family and friends rather than from experts.\footnote{For example, \citet*{BenartziThaler.RetirementSavings} surveyed recently hired staff at the University of Southern California about decisions pertaining to their pension plans and found that most of them did not consult anyone other than their family members. See also \citet*{BernheimInMitchellSchieber,Lusardi2003,Lusardi2008,vanRooijetal.,LusardiMitchellReview}.}
This tendency is most prevalent among those with low levels of financial sophistication, due in part to their mistrust of other information sources and avoidance of professional advisors \citep{Collins2012, EBRI}. A large literature shows that these social interactions \emph{affect} personal financial choices, but there is little direct evidence about the extent to which they improve or degrade the quality of decision making \citep*[][also see Section \ref{lit}]{Hastingsetal.Review}.

Unfortunately, within any group of family and friends, even the most financially knowledgeable individual may have little or no actual expertise. In addition, the financially unsophisticated decision makers who turn to peers are typically ill-equipped to evaluate the advisor's qualifications, or to distinguish between good and bad advice. The practice of relying on peers for financial advice therefore raises the concern that people may receive and credit poor advice -- in other words, that the blind may (mis)lead the blind.

To complicate matters further, optimal financial decisions depend on preference characteristics that vary from one person to the next, such as patience and risk aversion. The problem of learning from peers becomes more challenging when preferences enter the mix \citep[see, e.g.][for a formal model]{GagnonBartsch.TasteProjection}. To the extent informal advice simply encourages mimicry, it can be highly suboptimal even when the advisor happens to make the right choice for themselves, because their preferences may differ from those of the advice-seeker. To benefit from peer-to-peer communication, people must be able to either (i) separate principles from preferences and apply the principles based on their own preferences, or (ii) recognize and mimic those with better information and similar preferences.


In this paper, we study the effect of peer advice on the quality of financial decision making in a laboratory experiment with face-to-face interaction. The choices we study require an understanding of some simple financial
principles, but they also implicate personal preferences. In contrast to our approach, previous studies that speak to the effects
of peer communication on the quality of financial decision making
typically employ tasks with dominant alternatives, which remove preferences
from the mix, thereby artificially simplifying the problem of social learning \citep*{HvideOstberg,Haliassosetal.}.


We use a laboratory experiment for three reasons. First, it allows us to measure decision quality cleanly in domains that implicate preferences.\footnote{We assess the quality of decision making using the notion of Deliberative Competence developed by \citet*{AmbuehlBernheimLusardi}, which accommodates differences in preferences (unlike dominance-based approaches). See Section \ref{TasksMeasures} for details. \citet*{BernheimTaubinsky} explain how this approach relates to and differs from other approaches.} Second, it offers opportunities for introducing controlled variation in conditions and for monitoring communication, both of which facilitate an examination of the mechanisms through which peer effects operate. Third, through the exogenous assignment of treatments and peers, we avoid well-known econometric challenges associated with the measurement of peer effects in observational data
\citep*{Manski.Reflection}. While one might worry that people would spend less time on decisions in the laboratory than in the real world, empirical evidence suggests otherwise. A survey of non-faculty staff at the University of Southern California, for instance, revealed that 58 percent of respondents spent less than one hour --- the duration of many economic experiments --- determining their contribution rates and asset allocations for their retirement savings plans \citep{BenartziThaler.RetirementSavings}.


In our experiment, subjects make decisions concerning investments that accrue compound
interest. Optimal choices depend on subjects' idiosyncratic time preferences.
We compare subjects in a \emph{Communication} treatment with others
in a \emph{Solitary} treatment. In both treatments, subjects start
by making decisions about investments in private. Next, those in the \emph{Communication}
condition take part in a face-to-face discussion with a randomly assigned peer about similar
investments, while those in the \emph{Solitary}
condition study the same investments on their own. Subjects then make additional decisions in private.
A third treatment, \emph{Indirect Education}, mirrors the \emph{Communication}
treatment, except that, before speaking with a randomly matched peer, half of the subjects view an educational
video about compound interest that demonstrably improves the
quality of their decisions. This
treatment allows us to assess whether the benefits of an effective educational
intervention propagate through social interactions.

Our analysis consists of four parts. We begin by asking whether peer interaction can improve the quality of individual decision making in a setting where optimal choices vary widely due to preference heterogeneity. We find that communication is, on average, beneficial, especially for those with relatively little financial sophistication, who are more likely to rely on family and friends in practice.
To be clear, we do not claim that peer interaction is \emph{always} beneficial. Indeed, the literature appears to offer counterexamples.\footnote{For example, \citet{KaustiaKnupfer.PeerPerformance} show that entry into stock market investing is greater following periods in which peers have higher returns, which suggests that peers may encourage return-chasing. Relatedly, \citet{EscobarPedraza} find that inexperienced students in classrooms undergoing a large-scale financial education initiative overestimate the value of active trading if they are exposed to peers with large returns on single trades. \citet{Heimer} shows that peers can amplify the disposition effect because people are unwilling to concede losses in front of others. Our experiment does not encompass distortions resulting from concern for social image because decisions and consequences are private.} Instead, our study shows that people can benefit from such interaction even under unfavorable circumstances (specifically, when objectives differ).

How do people manage to derive these benefits? The next two parts of our analysis investigate mechanisms. The second part asks whether these mechanisms involve specific learning or general learning. In this context, specific learning refers to the possibility that people emerge from peer interaction with solutions to the particular decision problems they discussed. In contrast, general learning refers to the possibility that, through peer interaction, people acquire a portable conceptual understanding of a class of decision problems that allows them to solve new problems more successfully. To answer this question, we structure our experiment so that subjects make a collection of decisions after discussing a subset of them. We find that the improvement in the quality of decision making due to peer communication is roughly the same for the decision problems subjects discussed, and for the ones they did not discuss. We conclude that the pertinent mechanisms involve general learning rather than specific learning.

The third part of our analysis asks whether the underlying mechanisms involve vertical or horizontal learning relationships between peers. In a perfectly vertical relationship, information flows from the informed to the uninformed: either one person teaches another (a teacher/pupil relationship) or one person serves as an exemplar for another (a role-model/follower relationship). In a perfectly horizontal relationship, peers work together as equals to solve problems or arrive at applicable principles.\footnote{A sizable experimental literature finds that when groups make \emph{collective} decisions, they often perform better than individuals (see \citet*{KerrTindale} and \citet*{CharnessSutter} for reviews). Whether the benefits translate to private decisions is unclear.} According  to  the vertical learning  hypothesis,  the  better  the  decision  quality  of  the discussion partner, the larger the beneficial effect of peer communication on a subject's own decision quality.
In contrast, according to the horizontal learning hypothesis, communication is more effective between people who appreciate each others' gaps in knowledge, reasons for confusion, and preferred pace; consequently, the benefits from communication may
be largest when peers are most similar, even when greater similarity
implies lower skill.\footnote{\citet*{HoxbyWeingarth}, \citet*{Booijetal.}, and \citet*{FeldZolitz} document effects consistent with this mechanism.}
Consistent with the horizontal learning hypothesis, we find that people in the
bottom half of the decision-skill distribution experience greater
improvements when interacting with others in the bottom half than
when interacting with others in the top half. Qualitative analysis of subjects'
discussions supports this interpretation, in that similarly skilled partners appear to discuss each problem in greater
depth.


The fourth part of our analysis asks whether peer-to-peer communication can
augment the effects of beneficial financial education interventions
that target limited numbers of consumers by propagating their effects
through the population. Based on the preceding discussion, two countervailing
mechanisms may be at work. On the one hand, consumers who received an \emph{effective} education intervention (treated consumers) acquire
new skills, which they may transmit to others. On the other hand, an effective treatment reduces the similarity between treated and
untreated individuals, potentially hindering the transmission process. Treated individuals may also have greater difficulty communicating recently acquired conceptual knowledge.

We use an education intervention that demonstrably improves the quality of decision making for treated subjects. Overall, communication with a treated peer is no more beneficial to untreated participants than communication with an untreated peer. However, there is an important qualification. Communication with a treated peer is more beneficial for decision problems the pair discussed, and less beneficial for decision problems the pair did not discuss. This finding suggests that the beneficial effects of communicating with a treated partner are mostly attributable to specific rather than general learning. An analysis of the content of conversations provides corroborating evidence that the intervention reduces the subjects' perceived similarity. It also shows that subjects spend more time discussing a decision heuristic highlighted in the education intervention (the Rule of 72) and less time discussing general conceptual principles (how compound interest works).


The remainder of this paper proceeds as follows. Section \ref{lit} reviews related research.  Section \ref{design}
explains the design of our experiment. Section \ref{data} describes
our data and performs preliminary analyses. Section \ref{mainAnalysis} addresses each of the four questions featured above and
presents our main results. Finally, Section \ref{Conclusion} explores
policy implications and concludes.

\section{Related literature} \label{lit}

This work relates to three strands of literature. The first concerns peer effects in financial decision making.\footnote{See \citet*{MobiusRosenblat} for a general review of social learning in economics.} Notable studies include \citet{
DufloSaezSocialInteraction,
Hongetal.2005,
KaustiaKnupfer.PeerPerformance,
Bursztynetal.PeerEffects,
Beshearsetal.PeerInfoSavings,
Caietal.Networks,
Frydman,
HvideOstberg,
Heimer,
McCartneyShah,
KoPirinsky,
EscobarPedraza,
OuimetTate}; and
\citet{Arrondel}.


Our contribution to that literature is fourfold. First, while much of the literature documents directional behavioral effects, we study the \emph{quality} of financial decision making, which we measure in a precise and theoretically rigorous way, within a domain that implicates preferences.  Second, we study peer effects in a controlled laboratory setting, thereby identifying causal influences and investigating associated mechanisms in greater detail and under weaker identifying assumptions than existing work.\footnote{Two studies offer related evidence concerning mechanisms.
\citet{Bursztynetal.PeerEffects} examine peer effects among Brazilian investors. They find that these investors both learn from each other and mimic each others' asset holdings. Similarly, \citet*{Arrondel} studies how social interactions affect stock market participation among a representative sample of French investors. Using survey data, they provide evidence of both mechanisms, but especially for the learning channel.} Third, we distinguish between a peer's baseline competence and recently acquired skills, showing that people have little ability to transmit the latter. Fourth, we provide causal evidence on the role of peers' characteristics.\footnote{Our laboratory findings have a few observational counterparts.  \citet*{OuimetTate} find that employees who are poorly (highly) informed about employee stock purchase plans for U.S. public firms are most influenced by others who are poorly (highly) informed. \citet*{KoPirinsky}
find that sociability within a county promoted more conservative demand
for housing and more stable real estate prices during the 2008 housing
bubble, particularly when the number of financially sophisticated
residents in an area was high.} Our paper is most closely related to \citet*{Haliassosetal.}, which finds that proxy measures of financial decision-making quality are higher among refugees in Sweden when neighbors have economics
or business education, but only when the head of the household is educated or male.
They infer that the underlying mechanism involves knowledge transfer
rather than mere imitation. Our use of a laboratory experiment permits us to deploy a more theoretically robust and quantitatively precise measure of decision-making quality, and to measure causal effects by creating the necessary exogenous variation in conditions.


The second related strand of literature concerns financial education;
see \citet*{Hastingsetal.Review} and \citet*{LusardiMitchellReview}
for reviews, and  \citet*{Fernandesetal.Meta} \citet*{Miller} and \citet*{Kaiseretal.FinEdReview}
for meta analyses. Some have argued for targeting interventions at
influencers and relying on social diffusion to leverage the effects
of financial education \citep[see, e.g.,][]{Haliassosetal.,OuimetTate}.
Because the indirect beneficial effects of education in our experiment
arise from mimicry rather than from improved conceptual understanding,
our experiment calls the effectiveness of many such diffusion strategies
into question. Beneficial diffusion may be limited to the transmission
of descriptive information and narratives; it appears that conceptual decision strategies are less
likely to propagate through social networks.\footnote{ \citet*{Haliassosetal.} conclude that a social multiplier amplifies the effects of education. However, they identify this effect based on whether peers happen
to be educated. Consequently, they cannot rule out the possibility that the multiplier effect pertains to characteristics that are correlated with education, rather than with education itself.}

Third, we contribute to an experimental literature on peer effects
in learning. Our paper is most closely related to \citet*{Kimbroughetal.PeerTeaching},
which finds that peer-teaching improves learning about Sudoku puzzles, but that ability-tracking
has a detrimental effect. In contrast, \citet*{BoudreauMcCubbins}
find that providing subjects taking a mathematics test with polls
of their peers' beliefs about the correct answers leads them to perform
less well.\footnote{As we focus on communication in pairs, our experiment differs from the literature on social learning \citep[e.g.][]{Bikhchandanietal., Banerjee.HerdBehavior, Weizsacker, Eysteretal.SocialMislearning} which considers (mis-)learning from others in larger networks.} One important difference from the current
study is that tasks involving puzzles and math problems do not implicate preferences.


\section{Design}

\label{design}


As shown in Table \ref{experimentStructure}, all subjects complete three stages of decision making, numbered 0, 1, and 2. Subjects experience two interventions, numbered 1 and 2, interleaved between the three decision stages. The first intervention involves either financial education or a placebo documentary. The second intervention involves either communication or solitary contemplation.

We randomly assign each subject to one of three experimental conditions. The first, \emph{Solitary}, provides a baseline: subjects view the placebo documentary between stages 0 and 1 and engage in solitary contemplation between stages 1 and 2. The second, \emph{Communication}, departs from the \emph{Solitary} condition by randomly pairing subjects and introducing communication between Stages 1 and 2. The communication focuses on specific decision tasks, labeled \emph{Discussed}. The third, \emph{Indirect Education}, is the same as the \emph{Communication} treatment, except that it replaces the placebo documentary with financial education for one member of each pair.

We also assign each subject to one of two roles, distinguished according to whether the \emph{Discussed} tasks appear in stage 1 or stage 2. We refer to those who performed the \emph{Discussed} tasks in stage 2, after any communication, as \emph{Receivers} (role $A$), and to those who performed them in stage 1, before any communication, as \emph{Senders} (role $B$).\footnote{We do not explicitly inform subjects of these roles.} Note, however, that communication can flow in either direction, or not at all. Also notice that, in the \emph{Solitary} treatment, all subjects are in role $A$. Our analysis focuses on role $A$ subjects.

We evaluate the effects of communication by comparing the change in outcomes from stage 1 to stage 2 for subjects assigned to the \emph{Communication} and \emph{Solitary} conditions. Because we focus on \emph{Receivers} (role $A$), we can distinguish between effects on choices in tasks that are familiar to their discussion partner (the \emph{Discussed} tasks), and choices in tasks that neither partner has previously seen. We evaluate the effects of education on the educated by comparing the change in outcomes from stage 0 to stage 1 for \emph{Senders} receiving education versus \emph{Senders} not receiving education. We evaluate the indirect effects of education on social contacts by comparing the change in outcomes from stage 1 to stage 2 for \emph{Receivers} (who never receive education) in the \emph{Indirect Education} condition versus those in the \emph{Communication} condition.

In the following subsections we provide details concerning the tasks, the interventions, and implementation.


\begin{sidewaystable}[p]
\caption{\label{experimentStructure} Experiment Design.}\begin{centering}
\begin{tabular}{lccccc}
\toprule
Role  & \multicolumn{3}{c}{$A$ (Receivers)} & \multicolumn{2}{c}{$B$ (Senders)}\\
\cmidrule(r){2-4} \cmidrule(r){5-6} \emph{Treatment label} & \emph{Solitary}  & \emph{Communication}  & \emph{Indirect Education}  & \emph{Communication}  & \emph{Indirect Education} \\
\midrule
Stage 0  & \multicolumn{3}{c}{Decision Problems} & \multicolumn{2}{c}{Decision Problems}\\
 & \multicolumn{3}{c}{\footnotesize(Tasks: \textit{Simple}, \textit{Anc}$_{0}$)} & \multicolumn{2}{c}{\footnotesize(Tasks: \textit{Simple}, \textit{Anc}$_{0}$)}\\
 && $\downarrow$ & & $\swarrow$ & $\searrow$ \\
 \textit{Intervention 1}  & \multicolumn{3}{c}{\textit{Documentary}} & \textit{Documentary}  & \textit{Education} \\
  && $\downarrow$ & & $\searrow$ & $\swarrow$
 \\
Stage 1  & \multicolumn{3}{c}{Decision Problems } & \multicolumn{2}{c}{Decision Problems}\\
 & \multicolumn{3}{c}{\footnotesize(Tasks: \textit{Simple}, \textit{Complex}$_{1}$, \textit{Anc}$_{1}$)} & \multicolumn{2}{c}{\footnotesize(Tasks: \textit{Simple}, \textit{Discussed}, \textit{Anc}$_{1}$)}\\
&$\swarrow$&$\downarrow$&$\searrow$&\multicolumn{2}{c}{$\downarrow$} \\
 \textit{Intervention 2}  & \textit{Contemplation}  & \textit{Communication}  & \textit{Communication}  & \multicolumn{2}{c}{\textit{Communication}}\\
 &   & \textit{w Uneducated}  & \textit{w Educated}  & \multicolumn{2}{c}{\textit{w Uneducated}}\\
 & $\searrow$ & $\downarrow$ & $\swarrow$  &\multicolumn{2}{c}{$\downarrow$}
 \\
 Stage 2  & \multicolumn{3}{c}{Decision Problems } & \multicolumn{2}{c}{Decision Problems}\\
 & \multicolumn{3}{c}{\footnotesize(Tasks: \textit{Simple}, \textit{Complex}$_{2}$, \textit{Discussed})} & \multicolumn{2}{c}{\footnotesize(Tasks: \textit{Simple}, \textit{Complex}$_{1}$, \textit{Complex}$_{2}$)}\\
\bottomrule
\end{tabular}
\par\end{centering}
\medskip
\textbf{\textit{Notes:}} All subjects proceed through the experiment in the order indicated by the arrows. Table \ref{decisionProblems} lists the parameters of the task sets \textit{Simple}, \textit{Complex}$_{1}$, \textit{Complex}$_{2}$.
\end{sidewaystable}


\subsection{Tasks and measures of decision quality}
\label{TasksMeasures}

Each round of decision making elicits valuations for a future reward. There are three different types of decisions. Decisions in the \emph{simple frame} require the subject to choose between a sure number of tokens $V$ paid the day of the experiment, and $x$ tokens received in $t$ days. Decisions in the \emph{complex frame} are similar, except that the future reward $x$ is framed as a compound-interest accruing investment: ``We will invest $y$ tokens in an account with $r$\% interest per day. Interest is compounded daily. We will pay you the proceeds in $t$ days.'' \emph{Ancillary} decisions are similar to complexly framed decisions, but subjects decide between the investment and a sure number of tokens paid in $t$ days. Accordingly, each ancillary decision has a single correct solution that is independent of the subject's preferences. In each case, the subject's valuation is the number of tokens $V$ that leaves her indifferent between the tokens and the future reward. We elicit the indifference point through once-iterated multiple decisions lists that vary the comparison amount, $V$.\footnote{The comparison amounts range from  0 to 109 tokens. The first list in each round has a resolution of 10 tokens;  the second list in each round has a resolution of 1 token. Appendix \ref{decision} presents screenshots of the decision screens.}

\paragraph{Measures of decision quality}

The simply and complexly framed valuations allow us to assess the quality of decision making using the \emph{Deliberative Competence} method of \citet*{AmbuehlBernheimLusardi}. Intuitively, someone who fully understands
the consequences of her decisions should make the same choice in substantively
equivalent decision problems even if they are framed differently. The absolute value of the difference in valuations across equivalent simply and complexly framed tasks therefore provides a natural measure of decision quality. \citet*{AmbuehlBernheimLusardi} show
that one can interpret this difference as the maximal welfare loss a
subject incurs by having to make a choice in the complex frame rather
than in the simple frame, as judged by the preferences she reveals
in the simple frame, for which the consequences of choices are transparent (the \emph{normative benchmark}).

A potential reservation concerning conventional methods of Behavioral Welfare Economics is that conclusions may be sensitive to other biases outside the scope of the analysis. In the present experiment, one might worry that biases such as time inconsistency or an excessive suspicion that the experimenter will renege on promised future payments corrupt choices in both frames. If so, then choices in the simple frame do not reveal ``true preferences.'' \citet{LipseyLancaster} reasoned that the right way to handle these types of issues is to analyze all distortions (here, biases affecting valuations) and all remedies for them simultaneously. Because of the practical challenges that approach presents, the overwhelming preference of economists, as revealed by research in this area, is to analyze policies one at a time. Indeed, the dominant strategy is to treat the decision making apparatus as flawless except with respect to the bias targeted by the policy one seeks to evaluate. But the data are not in fact generated by an otherwise faultless decision process. Hence, there is no reason to think that solutions derived in this manner are desirable, as \citet{LipseyLancaster} pointed out in a related setting with multiple distortions. Nor can one coherently paste together solutions for different biases derived in this way, because each solution implicitly assumes that the other solutions are unnecessary.

To address this difficulty, \citet*{AmbuehlBernheimLusardi} introduce \emph{idealized welfare analysis}. This approach requires the analyst to conduct welfare analysis pertaining to an intervention that seeks to address a particular bias under the assumption that other biases \emph{will be} (but have not yet been) addressed through other policies, such as financial incentives, nudges, and commitment devices. When adopting this perspective, the analyst acknowledges that other biases infect the observed data, but does not contemplate using the policy of interest to treat them, because that policy is just one component of a broader effort to diagnose and correct flaws in decision making. Idealized welfare analysis is useful because it provides a conceptually coherent framework for compartmentalizing policy analysis. It permits analysts to arrive at an overall solution to multiple interacting problems by solving them one at a time.


Implementation of idealized welfare analysis might appear challenging because the welfare concept pertains to behavior in the counterfactual scenario for which all other biases are removed, rather than to observed behavior, which other biases may infect. However, \citet*{AmbuehlBernheimLusardi} prove that, under reasonably general conditions, their measure of Deliberative Competence (the absolute difference in valuations across the simple and complex frames), which is based on observed choices (without the other biases removed), approximates the idealized welfare effect (with the other biases removed), up to an invariant multiplicative scalar. In this sense, welfare measures based on the Deliberative Competence method are robust with respect to certain types of biases, known and unknown, outside the scope of the analysis that may corrupt choices in the simple frame.


\begin{table}[p!]
\caption{\label{decisionProblems} Task parameters. }
\begin{centering}
\begin{tabular}{lcccc}
\toprule
Task set & \textit{Complex}$_{1}$  & \textit{Complex}$_{2}$  & \textit{Discussed} \\
\midrule
 & \multicolumn{4}{c}{Investment duration: 72 days}\\
\cmidrule(r){2-5} Daily interest rate  & 3\%  & 1\%  & 2\%\\
Principal & $\{3,7,11\}$   & $\{12,28,44\}$  & $\{6,14,22\}$  \\
\# of doublings  & 3  & 1  & 2 & \\
\\
 & \multicolumn{4}{c}{Investment duration: 48 days}\\
\cmidrule(r){2-5} Daily interest rate  & 3\%  & 4.5\%  & 1.5\%  \\
Principal & $\{6,14,22\}$   & $\{3,7,11\}$   & $\{12,28,44\}$ \\
\# of doublings  & 2  & 3  & 1  &\\
\bottomrule
\end{tabular}
\par\end{centering}
\end{table}


\paragraph{Task parameters}

Each complexly framed task specifies three parameters: investment duration, daily interest rate, and principal. As shown in Table \ref{decisionProblems}, our investigation involves three sets of these tasks, labelled \textit{Complex}$_{1}$, \textit{Complex}$_{2}$, and \textit{Discussed}. Each of these sets includes two subsets of three tasks. Each subset involves a single combination of the investment duration and the interest rate, which we present with three different principal amounts in order to increase statistical power. All payments are denominated in tokens, which are worth \pounds 0.20 each.

The Deliberative Competence method, which we use to measure decision quality, requires us to compare valuations in the complex frame to valuations in the simple frame. Because each investment in Table \ref{decisionProblems} compounds to approximately 24, 56, or 88 tokens over either 48 or 72 days, there are a total of 6 equivalent simply framed prospects. Subjects provide valuations for a similar set of 6 prospects in each stage (0, 1, and 2). To avoid showing subjects the same set of simply framed prospects three times, we vary the future rewards slightly from one stage to the next.\footnote{Specifically, future rewards with a 72-day delay are $(26,59,90),(25,58,92)$,
and $(24,57,91)$ in Stages 0, 1, and 2, respectively. The corresponding
rewards with a 48-day delay are $(24,58,89),(24,57,90)$, and $(25,58,91)$.} Each set of ancillary tasks, \textit{Anc}$_{0}$ and \textit{Anc}$_{1}$, includes elicitations for three prospects.\footnote{The parameters of problems in set \textit{Anc}$_{0}$ in the format (duration, interest rate, principal, future reward) are given by $(18,8,22,88),(36,4,6,24)$,
and $(54,4,7,56)$. For set \textit{Anc}$_{1}$, they are $(18,4,12,24),(36,6,7,56)$,
and $(54,2.67,22,88)$.}

\paragraph{Order of Decision Tasks}

In addition to depicting the experiment's overall structure (summarized above), Table \ref{experimentStructure} displays the order in which subjects in the various roles and treatments complete the sets of simply framed, complexly framed, and ancillary tasks.


The purpose of Stage 0 is to establish baselines for financial knowledge and valuations of simply framed rewards. Accordingly, all subjects perform the \textit{Anc}$_{0}$ and \textit{Simple} tasks.


The purpose of Stage 1 is to evaluate financial knowledge, valuations of simply framed tasks, and valuations of complexly framed tasks after the first intervention. Tasks include \textit{Anc}$_{1}$, \textit{Simple}, and a set of complexly framed tasks \textendash{} \textit{Complex}$_{1}$ for subjects in role $A$, and \textit{Discussed} for subjects in role $B$. We assess the effects
of the intervention on financial knowledge by comparing choices in \textit{Anc}$_{0}$ and \textit{Anc}$_{1}$.

The purpose of Stage 2 is to elicit valuations of simply framed tasks and complexly framed tasks
after communication or contemplation. Tasks include \textit{Simple}, \textit{Discussed}
and \textit{Complex}$_{2}$ for subjects in role $A$ and \textit{Simple}, \textit{Complex}$_{1}$ and
\textit{Complex}$_{2}$ for subjects in role $B$.
Comparisons between assessed Deliberative Competence (the discrepancies between simply and complexly framed choices) in Stages 1 and 2 allow us to determine
the extent to which the second intervention affects decision making
quality. For subjects in role $A$, we can separately evaluate the effects
on the quality of decision making for tasks they have discussed (\textit{Discussed})
and for tasks they have not previously seen (\textit{Complex}$_{2}$).

In all stages, we intermingle decisions in an individually randomized
order. Substantively equivalent simply framed and complexly framed decision tasks are never identified
as such.

\subsection{Interventions}


\paragraph{Communication}

Subjects in the non-solitary conditions physically move next to a randomly assigned partner to engage in private face-to-face communication. We ask them to discuss specific financial decisions. To facilitate these conversations, we distribute six sheets to each pair, each describing one of the complexly framed tasks in the \emph{Discussed} set.\footnote{The following is an example. ``Decision Task 10. We will invest 6 tokens at 2\% for 72 days, compounded daily. You will get whatever
is in the account after that time. How many tokens would we have to
give you today, so you would be just as happy with receiving those
tokens today as with receiving the proceeds in the account in 72 days?''
The problem described on every sheet shares this same structure.} Each subject in role $B$ has made decisions concerning the
investments on the decision sheets (in Stage 1) before conversing
with their partner. Subjects in role $A$ have not seen these tasks before the conversation.\footnote{The purpose of this design feature is to ensure that the advice given by those who have received financial education reflects prior efforts to apply the education to their own financial decisions. In practice, adult financial education generally occurs through the workplace, and companies typically provide it to assist with imminent financial decisions, such as those pertaining to retirement investments. Thus, those who have received this education typically have had a chance to apply it, and presumably speak to others from that experience.}
We recommend that subjects use 15 minutes for discussion, but they
are free to end the discussion whenever they like, and can continue
with the experiment once they are done. To help subjects break the
ice, we ask them to note two questions they plan to ask their partner,
and two pieces of advice they may want to give. We provide no explicit
incentives for engaging in discussion, but we remind subjects they
will complete 18 additional decision tasks in private, which may include
the ones we ask them to discuss; consequently, there is a substantial
chance that their payment will be determined by one of those decisions.
All decision problems are numbered so that subjects can check whether
they have seen a problem before. We unobtrusively record all communication,
and subjects are aware that we do so.

Subjects in the \emph{Solitary} treatment receive the same discussion sheets as all other subjects, but are asked to consider the investments in private. Nonetheless, at the outset of the experiment, we inform all subjects, including those in the Solitary treatment, that they will discuss the financial investments with a peer. Unbeknownst to the subjects, in the Solitary treatment that conversation occurs only after all decisions are completed. This design feature serves to hold constant the effort subjects expend on their decisions in anticipation of having to discuss them with someone else. Accordingly, our design isolates the effects of communication per se, and is unconfounded by the fact that the mere expectation of communication may cause some individuals to pay greater attention.\footnote{In a preliminary version of the \emph{Solitary} treatment, subjects did not anticipate that they would communicate with anyone. The quality of financial decision making was generally lower, presumably because these subjects lacked the social motivation for good decision making that was present in the other treatments. \citet*{IyengarSchotter}, \citet*{BlanesIVidalNossol}, and \citet*{KuhnenTymula} document related attempts to save face.}


\paragraph{Education intervention}

The education intervention we employ in the \emph{Indirect Education} condition consists of videos of narrated slide presentations and practice questions with personalized feedback. The slides and narration are based on the section concerning compound interest from a popular investment guide, \emph{The Elements of Investing: Easy Lessons for Every Investor},
by \citet*{MalkielEllis}. It focuses on the rule of 72, a simple method for approximating the
time it takes for an investment to double. The narration
is verbatim from the text (with a few minor adjustments), while the
slides summarize key points.\footnote{Experiment B of \citet*{AmbuehlBernheimLusardi} uses the same intervention. To maximize effectiveness, we tested several versions using a series of pilot experiments on Amazon Mechanical Turk.} See Appendix \ref{interventionDetails} for details.


\subsection{Implementation}


All instructions are displayed on screen and explained via an audio
recording to minimize experimenter effects.\footnote{The instructions are reproduced in Appendix \ref{instruction}.} Subjects proceed at their own pace. They begin with a short video
recording of one of the authors (Bernheim), vouching that we will
pay subjects exactly the amount and at precisely the time we promise them.


Because people typically have access to computational tools when making
financial decisions, we provide each subject with a calculator that
includes a function for exponentials.\footnote{Typically, people also have access to the internet. However, \citet*{LusardiMitchellOUP}
find that only about 20\% of a representative sample make use of these
tools for real financial decisions, and the web-based experiment in
\citet*{AmbuehlBernheimLusardi} finds that an equally small proportion
of experimental subjects use these tools for their experimental decisions.} Subjects know from the outset that, at the end of the experiment, we will select one of their decisions at random, and that the selected decision will determine their payment in Amazon gift cards.\footnote{We opted for payment in the form of Amazon gift cards because they simplify the disbursement of delayed payments.} Accordingly, subjects have  incentives to choose carefully in every decision.

Additional elements of the experiment include tasks that allow us to assess subjects' comprehension of the mechanics of multiple decision lists, as well as survey questions designed to elicit psychological characteristics, financial literacy, accounts of their decision-making processes, and views about their partners. See Appendix \ref{AdditionalElements} for details.


\section{Data Collection and Preliminary Analysis}

\label{data}

\paragraph{Data Collection}

Our subjects are undergraduate students at the University of Birmingham,
UK.\footnote{We chose the University
of Birmingham because the subject pool is large and diverse in terms
of mathematical skills. We are grateful to Michalis Drouvelis for facilitating our use of the Birmingham
Experimental Economics Laboratory.} University students comprise an important demographic group whose members  are just beginning to make important personal financial
decisions. However, many of them may be ill-equipped to do so: a mere
45\% of our sample correctly answer three standard financial literacy
questions \citep{Lusardi2008}.
Students are also a target demographic group for many financial education
interventions.\footnote{In the UK, financial literacy education for students aged 11-16 became
part of the National Curriculum in September 2014, as part of citizenship
requirements \citep*{UKfinEdPolicy}. Given their ages and the timing
of the study, the subjects in our sample were not
affected by this policy.}

We ran sessions from Fall 2015 to Spring 2016.\footnote{See Appendix \ref{sessionDetails} for details.} On average, sessions lasted 124 minutes, and subjects earned \pounds26.55,
including a \pounds12.5 participation fee. We restrict our analysis to subjects
who demonstrated comprehension of the experimental procedures ($87.12\%$,
or 460 of 528 subjects).\footnote{90.78\% of Senders and 85.67\% of Receivers passed the initial comprehension
check. We retain subjects who passed the check even if they were paired with subjects who did not, since the
quality of communication does not depend on understanding the experimental procedures. Despite our precautions, four subjects participated
twice. These subjects may have had multiple accounts in the participant
management system. We identify these subjects by their email addresses,
which they had to supply to receive payment via Amazon gift cards. For
these subjects, we retain only the data from their first session.} Among those subjects, 99 in the \emph{Communication} treatment, 89 in the \emph{Indirect Education} treatment, and 75 in the \emph{Solitary} treatment participated as Receivers (in Role $A$). Appendix \ref{summaryStats} presents summary statistics.


\paragraph{Temporal Discounting}

We first present summary statistics on choices in the simple and complex frames.  To compare behavior across rewards of different sizes, we normalize
valuations. Specifically, if the future reward associated with decision problem
$d$ is given by $x$, and if $V_{j,d}^{f}$ denotes individual $j$'s valuation
in decision problem $d$ with framing $f\in\{simple,complex\}$, we define subject $j$'s \emph{normalized valuation} as $\delta_{j,d}^{f}=\frac{V_{j,d}^{f}}{x}$.\footnote{Because we elicit valuations using multiple price lists, they are interval-coded. We use interval midpoints.}

Figure \ref{distributionDiscountRates} shows a histogram of  within-subject averages of normalized valuations among Receivers. Panel A displays within-subject averages for decisions in the simple frame, separately for Stage 1 and Stage 2. The vast majority of subjects display discount rates lower than 1. Pooling across stages, the average subject values \pounds1 at \pounds0.87 on average if it is paid with a delay of 48 days, and at \pounds0.85 if it is paid with a delay of 72 days (with a population-level standard deviation of \pounds0.25 in both cases).\footnote{The respective figures are 0.87 and 0.84 for Stage 1, and  0.89 and 0.86 for Stage 2. Analogous statistics for subjects in the role of Sender are similar.} These discount factors are comparable to those in the literature on discounting over similarly brief time frames \citep*{Fredericketal.Review}. Crucially, the Deliberative Competence approach we employ to measure decision quality yields valid measures of idealized welfare losses even if these choices reflect not only normatively valid discount rates, but also ancillary decision-making imperfections such as present bias or exaggerated concerns that the experimenter will not follow through on the promised delayed payment.


Panel B shows the distribution of valuations in complexly framed tasks, again averaged across all decisions in Stages 1 and 2, respectively. Valuations are significantly more dispersed than in the simple frame, with lower averages of \pounds 0.78 and \pounds 0.75 for the 48 and 72 day timeframes, respectively. The fact that mean valuations are lower in complexly framed tasks than in simply framed tasks is consistent with exponential growth bias, the well-established tendency to underestimate compound interest \citep{ StangoZinman}. Tellingly, complexly framed valuations in Stage 2 are higher and more tightly concentrated than in Stage 1, as one would expect if the intervening communication improved decision quality.


\begin{figure}[p]
\caption{Distributions of valuations and Deliberative Competence\label{distributionDiscountRates}  \label{distributionFinComp}}
\begin{center}
\begin{tabular}{cc}
\includegraphics[width = 0.49\textwidth]{Figures/distributionSimpleReceivers.pdf} &
\includegraphics[width = 0.49\textwidth]{Figures/distributionComplexReceivers.pdf} \\
(A) & (B) \\
\multicolumn{2}{c}{\includegraphics[width = 0.7\textwidth]{Figures/distributionFinCompReceivers.pdf}
} \vspace{-1.7cm}
\\
\multicolumn{2}{c}{(C)}\\
\end{tabular}
\end{center}
\textbf{\textit{Notes:}} \doublespacing
Panels A and B: Distribution of normalized valuations for tasks in the simple frame (Panel A) and the complex frame (Panel B), censored at 2 to increase resolution.  Panel C: Distribution of Deliberative Competence in Stage 1, censored at -1 to increase resolution. In all panels, we display within-subject averages across all relevant decisions for Receivers.
\end{figure}


\paragraph{Deliberative Competence}

We measure the quality of subjects' decision making by assessing their \emph{Deliberative Competence} \citep*{AmbuehlBernheimLusardi}. Given normalized valuations $\delta _{j,d}^{complex}$ and $\delta _{j, d}^{simple}$, we define Deliberative Competence as
$c _{j,d}=- \left| \delta _{j,d}^{complex} - \delta _{j, d}^{simple} \right|.
$
With this sign convention, a higher number indicates greater Deliberative Competence. To interpret the magnitude of $c_{j,d}$, suppose a subject is willing to
pay \pounds 0.8 for a complexly framed investment that she would value
at \pounds 1 if she properly understood her opportunity set. In that case,
$c_{j,d}=-0.2$. If we are willing to interpret the subjects' choices in the simple frame as normatively valid, we would conclude that she is vulnerable to a maximum welfare loss of \pounds 0.20 per dollar due to her deficient command of compound interest. If we are unwilling to accept choices in the simple frame as normatively valid due to suspicion that other biases are present, we can nevertheless adopt an idealized welfare perspective and conclude that, in a setting with effective remedies for other bias, the subject would be vulnerable to a maximal welfare loss equal to 20 percent of the dollar-equivalent value of the opportunity, as \citet{AmbuehlBernheimLusardi} show.


Panel C of Figure \ref{distributionFinComp} shows a histogram of Deliberative Competence
averaged over all decisions in Stage 1 for Receivers. The distribution is skewed, with a mean of $-0.26$ and a median
of $-0.18$. The first and third quartiles are $-0.42$ and $-0.04$, respectively. Deliberative Competence is virtually perfect (between $0$ and $-0.01$) for 10\% of subjects.


\section{Main Analysis}

\label{analysisCommunication} \label{prelimAnalysis} \label{mainAnalysis}

Our analysis proceeds in four parts. We first study the overall effect of
communication with a randomly assigned peer on the quality of financial
decision making (Section \ref{main}). We then examine mechanisms.
We investigate whether the beneficial effects of communication reflect
genuine learning, or are merely a consequence of subjects' ability
to identify high-competence peers and mimic their choices without
comprehending the underlying concepts (Section \ref{mechanism}).
We also study how the effectiveness of communication depends on the
relative financial sophistication of the subjects and their partners (Section
\ref{SecWhoBenefits}). Finally, we investigate whether the effects
of beneficial financial education propagate through peer-to-peer communication
(Section \ref{indirect}).
 In all regressions, we include controls for subject characteristics. Specifically, our controls consist of gender, age, age-squared, ethnicity indicators, an indicator for whether English is the subject's first language, an indicator for whether the subject is an international student, and indicator variables for whether the subject lives in a rural, suburban, or urban area. Appendix Sections \ref{mainResultsControls} and \ref{whoBenefitsWithControls} show that our results are robust with respect to the inclusion of additional control variables, and to the omission of controls.


\afterpage{
\thispagestyle{empty}
\begin{figure}[p]
\caption{Overview of results.\label{mainFig}}
\begin{center}
\vspace{-0.5cm}
\begin{tabular}{cc}
\multicolumn{2}{c}{A. Overall effect of communication.} \medskip\\
\multicolumn{2}{c}{\includegraphics[width=.5\textwidth]{./Figures/levelReceiversMainNoCIFull} } \\
B. Effect on discussed problems. &
C. Effect on new problems. \medskip\\
\includegraphics[width=0.5\textwidth]{./Figures/levelReceiversMainDiscOLSNoCIFullD} &
\includegraphics[width=0.5\textwidth]{./Figures/levelReceiversMainDiscOLSNoCIFullND} \\
D. Effect  on Receivers in top half &
E. Effect  on Receivers in bottom half \medskip\\
\includegraphics[width=0.5\textwidth]{./Figures/levelReceiversMainWhomNoCIFullReceiverBetter} &
\includegraphics[width=0.5\textwidth]{./Figures/levelReceiversMainWhomNoCIFullReceiverWorse} \\
\end{tabular}
\end{center}
\vspace{-0.5cm}
\doublespacing
\textbf{\textit{Notes:}} The panels depict average Deliberative Competence in Stage 1 and Stage 2 for different groups of Receivers, and for different types of questions. Estimates control for demographics; displayed levels pertain to the average subject. See Tables \ref{comOnImprovementSplit} and \ref{whoBenefits} for associated regression estimates.
\end{figure}
\clearpage
}


\afterpage{
\thispagestyle{empty}
\begin{table}[htbp!]
\begin{footnotesize}
\setstretch{1.2}
\setlength{\tabcolsep}{2pt}
\caption{{Effect of communication}.\label{comOnImprovementSplit} \label{comImprovementDiscNonDisc}  }
\begin{center}
\begin{tabular}{lcccccccccc}
\toprule
  &(1) & (2) & (3) & (4) & (5a)  & (5b)  & (6a)  & (6b)   \\
VARIABLES  & \multicolumn{8}{c}{Improvement in Receivers' Deliberative Competence}  \\& \multicolumn{8}{c}{before / after communication}\\
\midrule
Benchmark simply framed choices &Contemp. & Stage 0 & Contemp. & Stage 0 & \multicolumn{2}{c}{Contemporaneous} & \multicolumn{2}{c}{Stage 0}\\
\cmidrule(r){6-7}\cmidrule(r){8-9}
Set of decision problems \\
\quad \textit{Discussed}  & Yes  & Yes  & Yes  & Yes   & No  & Yes & No  & Yes  \\
\quad \textit{New}   & Yes  & Yes & No  & No   & Yes & No  & Yes & No \\
Counterfactual mimicry & No & No & Yes & Yes & No & No & No & No\\
 \cmidrule(r){6-7}  \cmidrule(r){8-9}
\textit{Improvement in {Solitary}}
	& 0.021 & 0.000 & 0.014  & -0.010  & 0.014 & 0.027 & -0.007 & 0.007 \\
	 & (0.018) & (0.019)& (0.026)  & (0.027) & (0.021) & (0.022) & (0.021) & (0.022) \\
\multicolumn{2}{l}{Row A: \emph{Communication}} &   \\
\quad\textit{Improvement} & 0.066** & 0.068**  & -0.107** & -0.070 & 0.065** & 0.068** & 0.067** & 0.069** \\
\quad\textit{(compared to \emph{Solitary})} & (0.028) & (0.028) & (0.049) & (0.048)& (0.028) & (0.029) & (0.028) & (0.030) \\
\multicolumn{2}{l}{Row B: \emph{Indirect Education}} & \\
\quad \textit{Improvement} & 0.073*** & 0.067** & 0.008 & 0.033& 0.047 & 0.099*** & 0.041 & 0.093*** \\
\quad\textit{(compared to \emph{Solitary})} & (0.028) & (0.028) & (0.047) & (0.048) & (0.029) & (0.030) & (0.029) & (0.031) \\
\textit{p-values} & \\
\quad Communication = Indir. Educ. & 0.788 & 0.972   & 0.039 & 0.050 & 0.263  & 0.519 & 0.396  & 0.341  \\
\cmidrule(r){6-7} \cmidrule(r){8-9}
\quad Discussed = Not-discussed  &&&&& \multicolumn{2}{c}{0.885} & \multicolumn{2}{c}{0.918} \\
\qquad if Sender uneducated  & \\
\quad Discussed = Not-discussed  &&&&& \multicolumn{2}{c}{0.006} & \multicolumn{2}{c}{0.006} \\
\qquad if Sender educated  &  \\
\quad Difference in differences  &&&&& \multicolumn{2}{c}{0.005} & \multicolumn{2}{c}{0.004} \\
 Observations& 3,156&3,156 &1,572 &1,572 & \multicolumn{2}{c}{526} & \multicolumn{2}{c}{526} \\
Subjects &263&263 & 262 & 262 & \multicolumn{2}{c}{263} & \multicolumn{2}{c}{263} \\
\bottomrule
\end{tabular}
\end{center}
\vspace{-0.4cm}
\textbf{\textit{Notes:}}
Improvement in Deliberative Competence from Stage 1 to Stage 2. Based on all subjects in the role of Receiver. Estimates
in the \textit{Improvement in Solitary} row indicate the average level of improvement for a Receiver in the \emph{Solitary} condition. Subsequent rows show the additional improvement from communication and indirect education. All regressions control for initial skills and demographic characteristics. See Appendix
\ref{mainResultsControls} for additional specifications.
The dependent variable in Columns (3) and (4) is the hypothetical improvement in Deliberative Competence we would observe if all Receivers blindly mimicked their matched Sender's choices in discussed complexly framed tasks. All other columns use actual improvements. Columns(1)-(4) present OLS regressions with standard errors clustered
by subject. Columns (5a) and (5b), as well as (6a) and (6b), each present estimates of a two-equation SUR regression. In the latter regressions, we average improvement within each task set to obtain a single pair of observations per subject. $^{*}p<0.1,^{**}p<0.05,^{***}p<0.01$.
\end{footnotesize}
\end{table}
\clearpage
}


\subsection{Overall Effect of Communication on Decision-Making Quality\label{main}}

We begin by studying whether communication about financial decisions is helpful, harmful, or haphazard (a case of the blind leading the
blind).

Panel A of Figure \ref{mainFig} displays the levels of Deliberative Competence across Stages 1 and 2 separately for the \emph{Solitary} and
\emph{Communication} treatments. While competence increases slightly
in the \emph{Solitary} treatment, the improvement in the \emph{Communication}
treatment is substantially larger.\footnote{The increase in Deliberative Competence within the \emph{Solitary} condition does not necessarily reflect
learning. An alternative explanation is that Stage 2 employs
a different set of decisions than Stage 1.} In our experiment, communication with a randomly selected peer has
a clear beneficial effect on the quality of decision making.


To formalize this result, we estimate regressions in which the dependent variable measures the extent to which a subject's Deliberative Competence \emph{changes} between Stage 1 (which precedes communication) and Stage 2 (which follows communication). We consider {changes}
rather than levels to difference out individual-level heterogeneity
in Deliberative Competence and thus obtain more precise estimates. Specifically,
we pair each complexly framed decision $d$ in Stage 2 with the unique
complexly framed decision $d'$ in Stage 1 that has the same time
frame and (approximately) the same future value, and we let $c_{j,d, 1}$ and $c_{j,d', 2}$ denote the measures of Deliberative Competence corresponding to these decisions. We then define $j$'s improvement on task $d$ as $\textit{Improvement}_{j,d} = c_{j,d, 2} - c_{j,d', 1}. $

This procedure yields 12 observations per subject, one for each complexly framed decision in Stage 2. We run an OLS regression of this outcome variable on treatment indicators, using data on Receivers, pooling across discussed decisions (the \textit{Discussed} set) and novel decisions (the \textit{Complex}$_{2}$ set):
\vspace{-0.4cm}
\begin{equation}
\label{equ: main}
Improvement_{j,d}=\beta_0+\beta_1Communication_{j}+\beta_2IndirectEducation_{j}+X_{j}\Gamma+\Phi_{d}+\epsilon_{j,d}
\end{equation}

\vspace{-0.3cm}
In addition to the subject characteristics listed at the beginning of this section, the vector of subject-specific controls $X_j$ includes Receivers' preexisting levels of financial skills (measured by their decisions in the \textit{Anc}$_{0}$ and \textit{Anc}$_{1}$ sets, which they made before the communication or contemplation intervention).\footnote{To be clear, this measure of initial financial skills does not involve the data we use to compute initial Deliberative Competence, which is a component of the dependent variable.}  The specifications therefore allow for the possibility that subjects who differ with respect to initial skills may improve to varying degrees over the course of the experiment, either due to differential learning or because of regression to the mean. If we did not control for initial skills, differences in starting points across the treatment groups could manifest as spurious treatment effects. We also include a vector of question fixed effects $\Phi_{d}$.

Column 1 of Table \ref{comOnImprovementSplit} displays the results. The improvement in the \emph{Solitary} treatment, 2.1 percentage points,
is statistically insignificant. The increase
in the Deliberative Competence of Receivers in the \emph{Communication} treatment is 6.6
percentage points larger than this baseline ($p<0.05$); see Row A. This size
of this effect is particularly impressive when compared to the average
level of Deliberative Competence among all Receivers in Stage 1 (26.1 percent). It bears emphasis that the quantitative interpretation -- a communication-induced reduction in the idealized welfare loss of 25.3\% (i.e., 6.6/26.1) compared to the initial level -- remains valid even if biases other than those pertaining to the evaluation of compound interest afflict choices in both the simple and complex frames \citep[see ][]{AmbuehlBernheimLusardi}.

Because Deliberative Competence is defined as the absolute difference
in valuations across simple and complex frames, changes in competence
could reflect behavioral changes in either frame. To demonstrate that
peer communication increases competence primarily through its effect
on behavior with complex framing, column 2 replicates column 1 using an alternative normative benchmark to calculate Deliberative Competence: we pair complexly framed choices in each stage with the corresponding simply framed choices made in Stage 0 rather than with those made contemporaneously. By construction, this alternative measure is unaffected by changes in simply framed choices that may result from communication. We find that the estimated treatment effects remain virtually unchanged. Hence, we conclude that communication improves measured Deliberative Competence primarily through its effect on choices in the complex frame.

Significantly, our subjects achieve the gains documented in this section despite the fact that, due to preference heterogeneity, indiscriminate mimicry would be harmful. We simulate mimicry by substituting the Sender's Stage 1 choices for the Receiver's Stage 2 choices in the set of \emph{Discussed} tasks. We then estimate model (\ref{equ: main}) using these counterfactual decisions for those tasks. As column (3) shows, indiscriminate mimicry would decrease Receivers' Deliberative Competence by more than 10 percentage points ($p<0.05$). When we use simply framed choices from Stage 0 as the normative benchmark, statistical significance vanishes, but the coefficient estimate remains negative (column 4).


\subsection{General versus Specific Learning}

\label{mechanism}

To understand the mechanisms underlying the beneficial effect of peer
communication, we study whether subjects learn something specific about the tasks they discuss, or something they can generalize to new tasks. Panels B and C of Figure \ref{mainFig} separate panel A into these two types of tasks (decision sets \textit{Discussed}
and \textit{Complex}$_{2}$, respectively).\footnote{We use the same Stage 1 decisions in both these panels.} Comparing discussed and new tasks, the improvement of subjects is essentially the same in the \emph{Communication} treatment, and is only slightly different in the \emph{Solitary} treatment. It follows that communication enhances improvements in decision-making quality to roughly the same degree for both types of tasks. This finding suggests that communication improves decision making through general learning,
and not merely through learning that is limited to the discussed tasks.

Formally, we measure these effects by estimating the following two-equation system using Seemingly Unrelated Regression (SUR):
\begin{equation}
\begin{split}
\label{equ: mechanism}
\begin{bmatrix}
\overline{Improvement}_{j,C} \\
\overline{Improvement}_{j,D}
\end{bmatrix}
=
\begin{bmatrix}
\beta_{0C}+\beta_{1C}Communication_{j}+\beta_{2C}IndirectEducation_{j}+X_{j}\Gamma+\epsilon_{j,C} \\
\beta_{0D}+\beta_{1D}Communication_{j}+\beta_{2D}IndirectEducation_{j}+X_{j}\Gamma+\epsilon_{j,D}
\end{bmatrix}
\end{split}
\end{equation}
where $\overline{Improvement}_{j,C}$ is the average improvement of Receiver $j$  across the six \textit{Complex}$_{2}$ decision tasks and $\overline{Improvement}_{j,D}$ is the average improvement of subject $j$  across the six \textit{Discussed} decision tasks. We average across the respective decisions to obtain a single pair of observations per subject.


Columns 5a and 5b of Table \ref{comImprovementDiscNonDisc} display the results.
Row A column 5a shows that a Receiver in the \emph{Communication} treatment
improves by an additional 6.5 percentage points for new questions
(the \textit{Complex}$_{2}$ set) compared to the \emph{Solitary} treatment.
The corresponding figure for discussed questions (the \textit{Discussed}
set) is 6.8 percentage points (row A column 5b). While both of these coefficient
estimates are statistically significant at the 5\% level, they are
not statistically distinguishable from each other ($p>0.8$). The results remain qualitatively unchanged when we isolate the portion
of these effects due to changes in behavior in the complex frame by
using the simply framed choices from Stage 0 as the normative benchmark
(columns 6a - 6b).


\subsection{Horizontal versus Vertical Learning Relationships}

\label{SecWhoBenefits}

The mechanisms underlying the effects of peer communication likely
depend on the characteristics of the subjects in each pairing. On the one hand, communication may facilitate
the transmission of financial decision-making skills
from those who have them to those who do not. Under this first hypothesis,
a subject's improvement should be larger the more competent her peer.
On the other hand, effective skill transmission may require an ability
to understand each others' sources of confusion and to address each
other's questions and concerns at the appropriate level, and at a
comprehensible pace. It may also require people to feel comfortable
asking questions without fear of embarrassing themselves \citep*{Edmondson}, and the act of explaining material to somebody else may improve one's own comprehension.
Under this second hypothesis, the benefits from communication may
be largest when peers are most similar, even when greater similarity
requires the peer to have less Deliberative Competence.

To determine which of these hypotheses more accurately accounts for our data, we classify each subject according to whether her Deliberative Competence falls into the top or bottom half of the distribution before she communicates with another subject. We then study how the effects of communication vary across the four possible combinations of Sender and Receiver types. We perform this classification using the tasks in \textit{Anc}$_{0}$
and \textit{Anc}$_{1}$, rather than the tasks we use to define our
primary outcome variables (i.e., the decisions in \textit{Complex}$_{1}$,
\textit{Complex}$_{2}$, \textit{Discussed}, and the corresponding simply framed choices).\footnote{For Senders, we also use decision set \textit{Discussed} for classification. Senders make these decisions before meeting their peer, and the inclusion of these decisions increases statistical power.} Accordingly, our measured changes in Deliberative Competence do not
simply reflect regression to the mean.\footnote{Our analysis is not confounded by regression to the mean as long as measurement error in tasks \textit{Anc}$_{0}$
and \textit{Anc}$_{1}$ is uncorrelated with measurement error in our primary outcome variables based on the decisions in \textit{Complex}$_{1}$,
\textit{Complex}$_{2}$, \textit{Discussed}, and the corresponding simply framed choices.} To increase statistical power,
we pool across the \emph{Communication} and \emph{Indirect Education} treatments.\footnote{Section \ref{indirect} shows that Receivers' choices are similar across these two treatments.}

Panels D and E of Figure \ref{mainFig} display the results. Panel D shows that there is little room for improvement among Receivers whose initial skills are above the median.  Hence, communication has little if any effect on their degree of improvement regardless of the peer's skills. In contrast, Receivers whose initial stills are below the median improve substantially
when they communicate, as shown in panel E. Significantly, the improvement
is \emph{smaller} for low-skill Receivers paired with
high-skill rather than low-skill Senders. Thus, peer-to-peer
communication transmits financial decision-making skills most effectively
when peers are equally uninformed, rather than when an informed decision
maker teaches an uninformed peer.\footnote{The following conversation between two of our subjects illustrates the importance of responding to the partner at the right level and pace:
\textit{Subject 1: But you already have one whole pie. I hope I'm making it
clear. So you've got a whole pie, right? This is day zero. You've
got to have a pie, but after day one, you gain a slice of that pie,
so you have more slices. And on day two, you get even more slices
of pie. Subject 2: Okay, that seems to make sense. Subject 1: Yeah, so that's why
you have to add one to it, because you already have this pie. This
is one, but this is 0.02. Subject 2: On top of that. Subject 1: Yeah. The pie is good
example? Subject 2: Yeah, that was much easier.} Later in the conversation:
\textit{Subject 2: You've just taught me more maths then I've ever learned,
ever.}}

We formalize these comparisons by estimating the following OLS regression using data on Receivers:
\vspace{-0.7cm}
\begin{eqnarray}
\label{equ: whoBenefits}
Improvement_{j,d}&=&\beta_0+\beta_1 \big(R\_bottom_j \times S\_bottom_{j}\big)+\beta_2 \big(R\_bottom_j \times S\_top_{j}\big)  \nonumber \\
&&+\beta_3 \big(R\_top_j \times S\_bottom_{j}\big) +\beta_4 \big(R\_top_j \times S\_top_{j}\big)  \\ \nonumber
&&+\beta_5 R\_top_{j}+X_{j}\Gamma+\Phi_{d}+\epsilon_{j,d}
\end{eqnarray}
\vspace{-1.3cm}

\noindent where $R\_bottom_j$ and $R\_top_j$ indicate whether Receiver $j$ is in the bottom or top half of the skill distribution, respectively, and $S\_bottom_j$ and $S\_top_j$ are defined similarly for the Sender paired with Receiver $j$. For Receivers in the Solitary treatment, we set $S\_bottom_j = S\_top_j=0$. We control for initial skills, decision problem fixed effects, and the demographic characteristics listed at the beginning of this section.\footnote{We obtain similar results for specifications with different sets of control variables; see Appendix \ref{whoBenefitsWithControls}.} We cluster standard errors at the subject level.


Results appear in column 1 of Table \ref{whoBenefits}. Communication produces the largest improvement in decision quality when a Receiver in the bottom half of the skill distribution interacts with a Sender in the bottom half of the skill distribution (16.4 percentage points over and above the gains in the \emph{Solitary} condition, $p<0.01$). While Receivers also benefit from communication
with Senders in the top half, the gain is only about half as large (8.3 percentage points, $p<0.1$). The difference between these estimates is significant at the 10\% level. Columns
2 and 3 perform this analysis separately for the sets of new and
discussed decision problems, respectively. The results are similar
to those in column 1. When Receivers in the bottom half of the skill distribution communicate with similarly skilled Senders, they achieve substantial gains both in the tasks they discussed and in new tasks. In contrast, when those Receivers communicate with more skilled Senders, their gains are considerably smaller, and mostly limited to the tasks they discussed. In contrast, communication does not appear to benefit Receivers in the top half of the skill distribution irrespective of the type of task or their partner's skill. As mentioned previously, this result may reflect the fact that this group's high level of Deliberative Competence limits the potential for gain.

We compare these results to the improvements we would observe if Receivers indiscriminately mimicked their matched Senders. Specifically, we reestimate model (\ref{equ: whoBenefits}) replacing the Receiver's Stage 2 choices with the Sender's Stage 1 choices for all discussed complexly framed tasks. Column 4 shows that indiscriminate mimicry would yield large gains for low-skill subjects who interact with high-skill subjects, but would not help low-skill subjects who interact with low-skill subjects. (It also shows that indiscriminate mimicry would be harmful for high-skill subjects.)  Thus, communication produces the greatest gains precisely when mimicry offers the smallest advantages.


To evaluate the extent to which our results capture the impact of communication on
complexly framed choices as opposed to simply framed choices, columns
5-8 replicate columns 1-4 using the simply framed choices from Stage
0 as the normative benchmark. This modification strengthens our conclusions:
the incremental improvement when a Receiver in the bottom half communicates
with a Sender in the bottom half rather than a Sender in the top half is now
statistically significant at the 1\% level.

\afterpage{
\thispagestyle{empty}
\begin{table}[p]
\begin{footnotesize}
\setlength{\tabcolsep}{1.5pt}
\caption{\label{whoBenefits} {Effect of communication by pair characteristics.}}
\begin{centering}
\begin{tabular}{lcccccccc}
\toprule
 & (1)  & (2)  & (3)  & (4)  & (5)  & (6) & (7)  & (8) \\
VARIABLES  & \multicolumn{8}{c}{Improvement in Receiver's Deliberative Competence}\\
Benchmark choices in simple frame  & \multicolumn{4}{c}{Contemporaneous} & \multicolumn{4}{c}{Stage 0}\\
\cmidrule(r){2-5} \cmidrule(r){6-9} Sets of decision problems  &  &  &  &  &  & \\
\hspace{0.2cm} \textit{Discussed} & Yes  &  & Yes  & Yes  & Yes  &  & Yes  & Yes \\
\hspace{0.2cm} \textit{Complex}$_{2}$ & Yes  & Yes  & & & Yes  & Yes  & & \\
Counterfactual mimicry & No & No & No & Yes & No & No & No & Yes \\
\emph{Improvement in Solitary condition}  & 0.031{*}  & 0.023  & 0.040{*}{*}  & 0.042  & 0.010  & 0.000  & 0.020 & 0.017\\
\quad{\emph{for bottom half Receiver}}  & (0.016)  & (0.016)  & (0.017) & (0.019) & (0.017)  & (0.017)  & (0.018) & (0.021) \\
\emph{Additional improvement from communication if}  &  &  &  &  &  & \\
\quad Receiver bottom half   &  &  &  &  &  & \\
\qquad {and} Sender bottom half ($\beta_1)$ & 0.164{*}{*}{*}  & 0.148{*}{*}{*}  & 0.179{*}{*}{*} &  -0.013  & 0.183{*}{*}{*}  & 0.158{*}{*}{*}  & 0.208{*}{*}{*} & 0.023  \\
 & (0.045)  & (0.049)  & (0.046) & (0.075) & (0.045)  & (0.049)  & (0.046) & (0.076) \\
\qquad {and} Sender top half  ($\beta_2$) & 0.083{*}  & 0.054  & 0.112{*}{*}& 0.184*** & 0.053  & 0.029  & 0.078 & 0.202***\\
 & (0.044)  & (0.044)  & (0.049) & (0.058)  & (0.044)  & (0.044)  & (0.050) & (0.056)\\
\quad Receiver top half  &  &  &  &  &  & \\
\qquad and Sender bottom half  ($\beta_3$ )& 0.005  & 0.008  & 0.002 & -0.391*** & 0.005  & 0.009  & 0.002 & -0.351*** \\
 & (0.019)  & (0.021)  & (0.020) & (0.064)  & (0.017)  & (0.018)  & (0.019) & (0.059)\\
\qquad and Sender top half ($\beta_4$) & -0.022  & -0.022  & -0.021 & -0.113*** & -0.013  & -0.006  & -0.019 & -0.077***  \\
 & (0.020)  & (0.022)  & (0.021) & (0.027) & (0.018)  & (0.020)  & (0.018) & (0.028) \\
\emph{p-values about effect on Receiver} &  &  &  &  &  & \\
\quad ($R$ bottom, $S$ bottom) = ($R$ bottom, $S$ top)  & 0.092  & 0.065  & 0.181  & 0.016 & 0.006  & 0.010  & 0.008 & 0.023 \\
\quad ($R$ bottom, $S$ bottom) = ($R$ top, $S$ bottom)  & 0.001  & 0.008  & 0.000  & 0.000  & 0.000  & 0.004  & 0.000  & 0.000  \\
\quad ($R$ bottom, $S$ top) = ($R$ top, $S$ top)  & 0.029  & 0.121  & 0.012   & 0.000 & 0.160  & 0.486  & 0.057  & 0.000 \\
\quad ($R$ top, $S$ bottom) = ($R$ top, $S$ top)  & 0.191  & 0.157  & 0.294  & 0.000  & 0.321  & 0.469  & 0.253  & 0.000 \\
\
 \quad Joint insignificance  & 0.004  & 0.022  & 0.002  & 0.000  & 0.001  & 0.019  & 0.000  & 0.000 \\
 Observations  & 3,156  & 1,578  & 1,578 & 1,572 & 3,156  & 1,578  & 1,578 & 1,572 \\
Subjects  & 263  & 263  & 263 &262 & 263  & 263  & 263 &262\\
\bottomrule
\end{tabular}
\par\end{centering}
\textbf{\textit{Notes:}}
Based on all subjects in the role of Receiver. Estimates in the \emph{Improvement in Solitary} row indicate the average level
of improvement for a bottom-half Receiver in the \emph{Solitary} condition. Subsequent rows show the additional improvement from communication. The dependent variable in columns 4 and 8 is the hypothetical improvement in Deliberative Competence we would observe if all Receivers blindly mimicked their matched Sender's choices in discussed, complexly framed tasks. All other columns use actual improvements. All  regressions  control  for  initial skills, top-half Receiver dummy, decision problem fixed effects, and demographic characteristics. See Appendix \ref{whoBenefitsWithControls} for additional specifications. Standard errors are clustered by subject. $^{*}p<0.1,^{**}p<0.05,^{***}p<0.01$.
\end{footnotesize}
\end{table}
\clearpage
}

Next, we check whether the foregoing inferences are consistent with the content of subjects' conversations. To make this content amenable to statistical analysis, we obtained two independent transcriptions of each audio recording using workers hired through Amazon Mechanical Turk. Most recordings were of sufficient quality to allow transcription, yielding qualitative data on the nature of communication for 175 out of 188 pairs in the \emph{Communication} and \emph{Indirect Education} treatments. Research assistants at Stanford University then reviewed these transcripts and coded qualitative information concerning each discussion regarding (i) whether subjects highlight similarities between each other, through statements such as ``I'm bad at this too, so let's see whether we can help each other out,'' (ii)  the number of decision problems discussed, (iii) the number of pre-specified small-talk topics that came up during the discussion,\footnote{Transcribers indicated which of three pre-specified small-talk topics subjects discussed: place of origin, field of degree, and years of study.}  (iv) whether one person explicitly claimed to know how to solve the decision tasks, and (v) whether subjects discussed the rule of 72, which is the focus of our education intervention.\footnote{Coders also recorded additional information, such as whether the subjects discussed market interest rates. Our research assistants used the summary information form shown in Appendix \ref{transcriberMask}.} In addition, each Receiver's survey interface automatically recorded the time that passed between the beginning of the discussion stage and the resumption of the survey.


For each of these variables, we estimate the following OLS regressions to determine how the composition of a Receiver-Sender pair with respecct to Deliberative Competence relates to the types of topics they discussed. Formally, letting $Y_i$ denote a generic communication outcome variable for pair $i$, we estimate:
\bmath
\label{equ: transcription}
Y_{i}=\alpha_1ComDifs_{i}+\alpha_2ComSame_{i}+\alpha_3IndEduDif_{i}+\alpha_4IndEduSame_{i}+\nu_i
\emath
where $ComDif_{i}=1$ if the pair members are in the \emph{Communication} treatment and in different halves of the skill distribution, $ComSame_{i}=1$ if the pair members are in the \emph{Communication} treatment and in the same half of the skill distribution, $IndEduDif_{i}=1$ if the pair members are in the \emph{Indirect Education} treatment and in different halves of the skill distribution, $IndEduSame_{i}=1$ if the pair members are in the \emph{Indirect Education} treatment and in the same half of the skill distribution.\footnote{We can match each of our audio recordings to a unique pair of subjects in our data, but we cannot reliably identify whether a speaker participated as a Sender or Receiver. Hence, all our analysis of discussion content is at the pair level.} We use data on subjects in the \emph{Communication} and \emph{Indirect Education} treatments.


The first two rows of Table \ref{transcriptionData} show the estimated coefficients for subjects in the \emph{Communication} treatment. Column 1 shows that partners were much more likely to highlight similarities when they fell into the same half of the skill distribution than when they fell into different halves (62.2\% vs. 34.1\%, $p<0.01$). Moreover, column 2 reveals that similar pairs spent roughly 25\% more time discussing tasks than heterogeneous pairs (10.15 minutes versus 8.26 minutes, $p<0.1$ for differences across pairs). This difference relates to the quality and focus of the conversation: while the number of tasks discussed does not differ across similar and heterogeneous pairs (column 3), the number of small-talk topics discussed is smaller when skills are similar (column 4, $p<0.1$). Appendix  \ref{sec:transcriptionDataFE} explores the robustness of these conclusions by adding transcriber fixed effects. The estimates and their statistical significance remain largely unaffected.


\begin{table}[p]
\begin{centering}
\small
\setlength{\tabcolsep}{1pt}
\caption{\label{transcriptionData} {Discussion content by treatment and pair characteristics.}}
\begin{tabular}{lccccccc}
\toprule
 & (1)  & (2)  & (3)  & (4)  & (5)  & (6)  & (7) \\
VARIABLES  & Highlight  & Minutes  & \# problems  & \#small  & One person  & Rule  & Compounding \\
 & similarities  & discussed  & discussed  & talk  & proclaims  & of 72  & formula \\
 &  &  &  & topics  & skills  & discussed  & discussed \\
\midrule
\multicolumn{2}{l}{Communication treatment} &  &  &  &  &  & \\
\quad Different skills $(\alpha_1)$ & 0.341 & 8.264 & 4.136 & 0.659 & 0.250 & 0.000 & 0.744 \\
 & (0.073) & (0.799) & (0.280) & (0.111) & (0.068) & (0.048) & (0.073) \\
\quad Similar skills $(\alpha_2)$  & 0.622 & 10.154 & 4.073 & 0.400 & 0.159 & 0.047 & 0.698 \\
 & (0.073) & (0.775) & (0.290) & (0.110) & (0.068) & (0.048) & (0.073) \\
\multicolumn{2}{l}{Indirect Education treatment} &  &  &  &  &  & \\
\quad Different skills $(\alpha_3)$  & 0.386 & 8.516 & 4.023 & 0.432 & 0.432 & 0.773 & 0.409 \\
 & (0.073) & (0.816) & (0.280) & (0.111) & (0.068) & (0.048) & (0.072) \\
\quad Similar skills $(\alpha_4)$  & 0.357 & 9.499 & 4.476 & 0.214 & 0.366 & 0.786 & 0.452 \\
 & (0.075) & (0.844) & (0.287) & (0.114) & (0.071) & (0.049) & (0.074) \\
\emph{p-Values}  &  &  &  &  &  &  & \\
\quad Effect of similarity  &  &  &  &  &  &  & \\
\qquad \textit{Comm. tr. }$(\alpha_1=\alpha_2)$  & 0.007 & 0.091 & 0.876 & 0.099 & 0.346 & 0.495 & 0.652 \\
\qquad \textit{Indirect Educ. tr. }$(\alpha_3=\alpha_4)$  & 0.781 & 0.403 & 0.260 & 0.172 & 0.502 & 0.849 & 0.675 \\
\quad Effect of indirect education  &  &  &  &  &  &  & \\
\qquad \textit{Similar skills} $(\alpha_2=\alpha_4)$  & 0.012 & 0.568 & 0.325 & 0.241 & 0.036 & 0.000 & 0.019 \\
\qquad \textit{Dissimilar skills} $(\alpha_1=\alpha_3)$  & 0.662 & 0.826 & 0.775 & 0.149 & 0.061 & 0.000 & 0.001\medskip
\\
\quad All four parameters equal  & 0.023 & 0.301 & 0.674 & 0.050 & 0.026 & 0.000 & 0.001 \\
\quad Diff-in-diff & 0.036 & 0.576 & 0.365 & 0.852 & 0.856 & 0.728 & 0.538 \\
Observations  & 175 & 188 & 171 & 175 & 173 & 172 & 172 \\
\bottomrule
\end{tabular}

\par\end{centering}
\begin{centering}
\par\end{centering}
\doublespacing
\textit{\textbf{Notes:}} Based on subjects in the \emph{Communication} and \emph{Indirect Education} treatments. Regressions for communication outcomes correspond to Equation (\ref{equ: transcription}).  The Qualtrics survey automatically provides the measure of \emph{Minutes discussed} for all 188 pairs. The other dependent variables are based on classifications of audio transcriptions for 175 pairs. Columns 3, 5, 6, and 7 exclude pairs for which the transcriber encoded the corresponding variable as `unclear.'
\end{table}

In the Appendix, we extend this analysis in two directions. First, in Appendix \ref{confidence}, we ask whether communication with peers enhances confidence in decision making. Our strategy is to estimate regressions similar to those in Table \ref{whoBenefits}, using a subjective measure of confidence as the dependent variable in place of Deliberative Competence.\footnote{At the end of the study, we asked subjects the following question: ``Do you feel you had a firm grasp of how to make good decisions in this study?"} We find that the confidence of low-skill subjects increases significantly when they interact with high-skill subjects. The effect is smaller and statistically insignificant when low-skill subjects interact with low-skill subjects.\footnote{For high-skill subjects, there is no evidence that communication meaningfully impacts confidence.} Thus, communication produces the greatest gains for low-skill subjects when its impact on confidence is smallest. This finding casts doubt on the possibility that communication with peers improves decision making by enhancing confidence.

Second, in Appendix \ref{perceivedCompetence}, we ask whether a subject's ability to detect financial competence in peers is related to their own competence. At the end of our experiment, subjects answered the following question (on a 7-point scale): ``Do you feel your partner had a firm grasp of how to make good decisions in this study?" We regress these responses on a measure of the Sender's actual Deliberative Competence, allowing the effect to differ according to the Receiver's Deliberative Competence. We find that, when partners are more competent, subjects generally recognize them as such. However, we do not detect a robust relationship between the ability to recognize competence in others and the Receiver's own competence. Thus we do not find support for the hypothesis that an inability to recognize competence among those with low competence contributes to their reliance on family and friends rather than those with greater expertise.


\subsection{Indirect Effects of Financial Education\label{indirect}}

The beneficial effects of peer communication raise the possibility
that social networks may propagate the influence of financial education
through the population, magnifying its benefits. Accordingly, in this
subsection we examine the indirect effects of financial education
on those who have not participated themselves. The preceding results
suggest two competing hypotheses. On the one hand, treated individuals
acquire new skills, which they may transmit to others. On the other
hand, an effective educational treatment reduces the similarity between
treated and untreated individuals, potentially stymying the transmission
process. Subjects may also have greater difficulty communicating
recently acquired conceptual knowledge.

Before investigating the indirect effects of education, we demonstrate that our intervention has a direct beneficial effect on
those who participate. We regress Senders' Deliberative Competence in
Stage 1 on an indicator for whether they participated in the education
intervention. We find that the direct effect of the intervention is to raise Senders' Deliberative Competence. The level of competence is $-0.192$ for Senders who undergo the intervention, compared with $-0.274$ for those who
do not. The difference of 8.2 percentage points is substantial, and
corresponds to roughly a one-third reduction in the idealized welfare loss. The estimated treatment effect is significant at the 10\% level. It increases and becomes significant at the 5\% level once we control for preexisting skills and demographics; see Appendix \ref{educationAnalysis}.\footnote{\citet{AmbuehlBernheimLusardi} use the same education intervention for a population of workers on Amazon Mechanical Turk and similarly find that it improves Deliberative Competence from $-0.256$ to $-0.186$. The difference of 7.1 percentage points in that study is highly statistically significant.}

Next we test whether peer communication is  more effective if the Sender has participated in the education intervention. The pertinent results appear in Row B of
Table \ref{comOnImprovementSplit}, which reports estimates based on equation (\ref{equ: main}). Column 1 shows that there are no detectable
indirect effects of education on a Receivers' degree of improvement beyond those arising from communication alone when we
pool discussed and new tasks ($p=0.788$). We obtain similar results when we use the simply framed choices made in Stage 0 as the normative benchmark (column 2).

Differences do emerge, however, once we distinguish between discussed
and new tasks. Focusing again on Row B of Table \ref{comImprovementDiscNonDisc}, columns 5a and 5b show that Receivers who are indirectly exposed to the education intervention
improve to a significantly greater degree in decision tasks they have
discussed than in new ones
($p<0.05$ in each specification).
The difference-in-differences estimates,
which compare improvements of Receivers in the \emph{Communication} and \emph{Indirect Education} treatments for the discussed versus new tasks,
are statistically significant ($p<0.05$). Once again, we obtain similar results when we use the simply framed choices made in Stage 0 as the normative benchmark (columns 6a-6b).\footnote{Our results are robust with respect to adding and omitting control variables; see Appendix  \ref{mainResultsControls}.} These results suggest that education helps people successfully transmit useful information concerning the specific decisions they discuss with others, but does not help them transmit generalized knowledge.

To what extent does the content of subjects' conversations reflect these differences? Column 1 of Table \ref{transcriptionData} shows that pairs consisting of members in the same half of the initial skill distribution become much less likely to highlight their similarities if the Sender has participated in the education intervention ($p<0.05$). At the same time, column 5 shows that one of the members becomes more likely to claim they have pertinent skills ($p<0.05$), and this result also holds for pairs whose members are in different halves of the initial skill distribution ($p<0.1$). This finding suggests that education may increase the likelihood that Senders rely on strategies akin to `proof by intimidation,' which might help Receivers perform better in the problems they discuss while diminishig the benefits of peer communication for new problems.


An additional possibility is that the contents of the education intervention crowd out other methods of decision making. Indeed, column 6 of Table \ref{transcriptionData} shows that, in the \emph{Indirect Education} treatment, more than three quarters of the pairs discussed the rule of 72 (the main substantive component of the education intervention) whereas
virtually no one did so in the \emph{Communication} treatment ($p<0.01$). Meanwhile, around 70\% of pairs discussed the exact compound interest formula, \textit{future\;value}$=$\textit{present\;value}$\cdot(1+r)^{t}$, if the Sender had not participated in the education intervention, while fewer than half did so in the \emph{Indirect Education} treatment (column 7). If the rule of 72 is an inferior substitute for the exact formula (either because the Sender fails to explain it intelligibly, or because the Receiver fails to apply it correctly), then such crowding out could reduce the effectiveness of peer communication.

\section{Conclusion}

\label{Conclusion}

We have presented an experiment in which communication about financial
decisions between randomly paired subjects leads to genuine improvements
in the quality of decision making, measured according to the \textit{Deliberative Competence} method of \citet*{AmbuehlBernheimLusardi}. We have shown that the improvements reflect conceptual learning
rather than mimicry of the choices of those who are better informed.
The beneficial effects of communication are especially pronounced
in interactions between people who are similarly unskilled, and who
seem to be more adept at addressing each others' questions and concerns
at the appropriate level and pace. Subjecting one member of each pair
to an effective financial education intervention, however, provides
no benefits beyond those arising from communication alone. The intervention
provides subjects with more skills to transmit, but decreases the
effectiveness of skill transmission by creating competence differentials
and by crowding out more effective forms of communication.

Some researchers argue for targeting interventions at influencers and relying
on social diffusion to leverage the effects of financial education. Because
the indirect beneficial effects of education in our experiment arise
from mimicry rather than from improved conceptual understanding, our
experiment calls the effectiveness of such diffusion strategies into
question. For the same reason, our results caution against promoting
rules of thumb that are appropriate for particular segments of the
population, but that may propagate to other segments for which they are less well-suited.\footnote{For instance, rules of thumb that encourage paying off or abstaining from debt may compound mistakes arising from debt aversion \citep{MartinezShi}.}

A natural extension of our research would involve the study of peer
effects in settings where  subjects interact with peers of their own
choosing. Another extension would examine interaction among larger
groups of individuals. In both settings, subjects' abilities to identify
those from whom they can benefit most, and to avoid those who set
bad examples, would play important roles in determining the effects
of social interaction. A third extension would investigate in greater detail the mechanisms that render communication beneficial. We have not attempted to determine whether communication is helpful because subjects learn from the knowledge of their peers, because they learn by teaching their peers \citep*{Cohen1982},\footnote{A related concept to learning by teaching is \emph{rubber ducking} in computer science. This method involves debugging code by explaining what it does line by line to an inanimate object such as a rubber duck.} or because interaction invites subjects to think in new ways \citep*{IyengarSchotter}. We leave these issues for further research.


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\newpage{}


\appendix
\global\long\def\thetable{\thesection.\arabic{table}}
 \global\long\def\thefigure{\thesection.\arabic{figure}}
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\begin{center}
\textbf{\Huge{}ONLINE APPENDIX}{\Huge{} }\\
{\Huge{} }{\Large{}{}\textbf{\Large{}Peer Advice on Financial Decisions:
}\\
\textbf{\Large{} A case of the blind leading the blind?}{\Large{}}
}\\
 \vspace{0.5cm}
 {\Large{}Sandro Ambuehl, B. Douglas Bernheim, Fulya Ersoy, Donna
Harris}
\par\end{center}

\setcounter{table}{0}
\setcounter{footnote}{0}
\addcontentsline{toc}{section}{Appendix}


\part{}

\vspace{-2cm}

\pagenumbering{gobble} \parttoc

\pagenumbering{arabic}


\setcounter{table}{0}
\setcounter{figure}{0}

\section{Experiment details}
\subsection{Contents of the education intervention}\label{interventionDetails}

The text begins with a simple explanation of compound interest illustrated through an iterative calculation. It then introduces a quantitative heuristic, the rule of 72. The rule of 72 is a method for approximating an investment's doubling period. It states that the percentage interest rate on an investment multiplied by the number of periods required for its value to double approximately equals 72. Along with the explanation of the rule of 72 and its applications, the text provides quotes regarding the power of compounding and various anecdotes concerning small investments that grew to impressive sums over long time periods.

To increase the effectiveness of the education intervention, we added practice questions with personalized feedback to the education module.\footnote{We pretest the effectiveness of practice questions with the population used in \citet{AmbuehlBernheimLusardi} and find that education intervention with this tweak is effective at improving the quality of decision making.} Practice questions are basic compound interest calculation problems and similar to the ones taught in the education intervention.\footnote{E.g. ``\$100 is invested at 9\% for 32 years, compounded yearly. How much will be in the account after these 32 years?"} We divide the education video to three similar length clips. After each clip, subjects are required to answer one or more multiple choice practice questions. After the first and second clips, they are asked one practice question. If they answer the question incorrectly in their first try, we provide them feedback based on their incorrect answer. For example, when they choose the answer that corresponds to the simple interest calculation instead of the compound interest calculation, we explain why the answer is wrong with an iterative example. If they answer the question incorrectly in their second try, we let them continue. After the third clip (at the end of the education module), they are asked two more practice questions. For the first question, we walk them through the three steps required to answer the question by using the rule of 72.\footnote{These steps are: 1. How long does it take for the money to double at a given interest rate? 2. How many times does it double in the given investment period?  3. How much will be in the account after it doubles that many times?} Subjects are required to correctly answer both questions to be able to continue with the experiment. \footnote{The three videos that belong to the education module can be found here: \url{https://youtu.be/EnFVLiM1dTs}, \url{https://youtu.be/3pjkVdOXMlk}, and \url{https://youtu.be/kjPYqcZNzPI}.}


\subsection{Design details}
\label{AdditionalElements}
\paragraph{Elicitation of valuations}

We elicit all valuations using once-iterated multiple price lists \citepappendix*{AndersenMPL} with comparison amounts ranging from 0 to 109 tokens.\footnote{The first  list for each task has a resolution of 10 tokens; the second list has a resolution of 1 token. Appendix \ref{decision} presents screenshots of the decision screens.} Subjects with well-defined valuations will choose the comparison amount $V$ if and only if $V$ is large enough. Any subject whose choices are inconsistent with well-defined valuations view an error message that prompts them to revisit their decisions. Subjects complete all lists at their own pace.

In each decision, the investment compounds to approximately 24, 58, or 88 tokens (with deviations of up to 2 tokens). These amounts are located near the top, middle, and bottom of the multiple decision lists, so that any tendency to choose switching points towards the middle of a list does not systematically influence our results.

\paragraph{Additional elements}

To assess subjects' comprehension of the mechanics
of multiple decision lists, we present them with an initial list that
asks them to decide, on each line, whether they prefer to receive
$x$ pence or \pounds1 for a range of values $x$. Since these are decisions
between larger and smaller amounts of money to be received at the
same point in time, any switching point other than 100 indicates deficient
understanding. In addition, subjects see a completed list, and are
required to indicate their payment in case the computer selects a
given line for implementation. Subjects proceed regardless of their
answers to these questions. These decisions are not incentivized.

Before participating in the main stages of the experiment, subjects complete a battery of unincentivized psychological questions. These include a 10-item version of the big-five personality
scale \citepappendix*{BigFiveShort}, the \citetappendix*{ConformityQuestionnaire}
conformity scale, and the three-item
Cognitive Reflection Test \citepappendix{CRT}.

Subjects also answer three standard financial literacy questions \citepappendix*{Lusardi2008}. We ask these questions at the beginning of the study
to prevent answers from being influenced by subjects' communication
partners. The financial literacy questions are:

\begin{itemize}
\item Suppose you had
\$100 in a savings account and the interest rate was 2\% per year.
After 5 years, how much do you think you would have in the account
if you left the money to grow? \textit{{[}More than \$102, Exactly
\$102, Less than \$102, Don't know{]}}
\item Imagine that the interest
rate on your savings account was 1\% per year and inflation was 2\%
per year. After 1 year, with the money in this account, would you
be able to buy \textit{{[}More than today, Exactly the same as today,
Less than today, Don't know{]}}?
\item Do you think the following statement
is true or false? Buying a single company stock usually provides a
safer return than a stock mutual fund. \textit{{[}True, False, Don't
know{]}}.
\end{itemize}

At the end of the experiment, subjects complete an unincentivized demographic
survey. They also answer questions about their decision-making processes
and about their partners.


\subsection{Sessions}\label{sessionDetails}

\begin{table}[htp!]
\begin{scriptsize}
\caption{Experimental sessions. \label{sessions}}
\begin{center}
\begin{tabular}{ l c r rr} \toprule
Session & Date  & Time & \# of Subjects & Type \\ \midrule
1 &	21 October 2015 & 10am & 20 & Communication and Indirect Education \\
2 &	21 October 2015 & 2pm & 20 & Communication and Indirect Education \\
3 &	22 October 2015 & 10am & 20 & Communication and Indirect Education\\
4 &	22 October 2015 & 2pm & 20 & Communication and Indirect Education\\
5 &	23 October 2015 & 10am & 16 & Communication and Indirect Education\\
6 &	23 October 2015 & 2pm & 20 & Communication and Indirect Education\\
7 &	28 October 2015 & 9am & 20 & Communication and Indirect Education\\
8 &	28 October 2015 & 12pm & 18 & Communication and Indirect Education\\
9 &	28 October 2015 & 3pm & 20 & Communication and Indirect Education\\
10 &	29 October 2015 & 9am & 12 & Communication and Indirect Education\\
11 &	29 October 2015 & 12pm & 12 & Communication and Indirect Education \\
12 &	29 October 2015 & 3pm & 20 & Communication and Indirect Education \\
13 &	30 October 2015 & 9am & 8 & Communication and Indirect Education\\
14 &	30 October 2015 & 12pm & 10 & Communication and Indirect Education\\
15 &	30 October 2015 & 3pm & 18 & Communication and Indirect Education\\
16 &	15 February 2016 & 10am & 20 & Communication and Indirect Education\\
17 &	15 February 2016 & 2pm & 20 & Communication and Indirect Education\\
18 &	16 February 2016 & 10am & 20 & Communication and Indirect Education\\
19 &	16 February 2016 & 2pm & 20 & Communication and Indirect Education\\
20 &	17 February 2016 & 10am & 20 & Communication and Indirect Education\\
21 &	17 February 2016 & 2pm & 20 & Communication and Indirect Education\\
22 &	18 February 2016 & 10am & 18 & Communication and Indirect Education\\
23 &	18 February 2016 & 2pm & 20 & Communication and Indirect Education\\
27 &	24 February 2016 & 10am & 6 & Communication and Indirect Education\\
28 &	24 February 2016 & 2pm & 18 & Communication and Indirect Education\\
29 &	6 May 2016 & 10am & 10 & Solitary\\
30 &	6 May 2016 & 2pm & 18 & Solitary\\
31 &	9 May 2016 & 10am & 10 & Solitary \\
32 &	9 May 2016 & 2pm & 14 & Solitary\\
33 &	10 May 2016 & 10am & 8 & Solitary \\
34 &	10 May 2016 & 2pm & 4 & Solitary\\
35 &	11 May 2016 & 10am & 6 & Solitary\\
36 &	11 May 2016 & 2pm & 6 & Solitary\\
37 &	12 May 2016 & 2pm & 16 & Solitary\\
\bottomrule
\end{tabular}
\end{center}
\end{scriptsize}
\end{table}

Table \ref{sessions} displays details about each session we conducted. In addition to the listed sessions, we ran three sessions of a preliminary Solitary treatment on February 23, 2016 with a total of 62 subjects. While subjects in the Solitary treatment know that they will discuss with another person, subjects in the preliminary Solitary treatment had no expectation of communication whatsoever, and exert a significantly lower amount of effort.


\flushleft
\subsection{Decision interface}\label{decision}
In each round, the first choice list ranges from 0 tokens to 100 tokens. After the subject has made a selection, the second decision list ranges from $x$ tokens to $x+9$ tokens in steps of 1, where $x$ is the largest number of tokens such that the subject still prefers the evaluation option. In the example in Figure \ref{decisionInterface}, $x = 30$.

\begin{figure}[htp]
\caption{Decision interface. \label{decisionInterface}}
\centering
\textbf{First decision list in a round} \medskip \\
\fbox{
\includegraphics[width=0.52\textwidth]{./screenshots/MPL1clicked.png}
}
\\ \medskip
\textbf{Second decision list in a round}\medskip \\
\fbox{
\includegraphics[width=0.52\textwidth]{./screenshots/MPL2.png}
}\\
\begin{flushleft}
\textbf{\textit{Notes:}} The range of evaluation options in the second decision list depends on the switching point in the first decision list, which is 30 in this example.
\end{flushleft}
\end{figure}

\flushleft


\includepdf[pages=1,pagecommand={\subsection{Mask for coding audio recordings}\label{transcriberMask}}, height = 0.9\textheight]{./screenshots/transcriptionsSurvey}
\includepdf[pages=2-,height = 0.9\textheight]{./screenshots/transcriptionsSurvey}


\setcounter{table}{0}
\section{Additional Analysis}
\setlength{\parindent}{2em}


\subsection{Summary statistics}\label{stats}\label{summaryStats}

Table \ref{demographics} reports the means of 36 subject-level variables across our three treatments (\emph{Solitary}, \emph{Indirect Education}, and \emph{Communication}) for Receivers. For each variable we report four $p$-values, three for each pairwise test of equality of means across treatments, and one for a joint test. Comparing across our three treatments (\emph{Communication}, \emph{Indirect Education}, and \emph{Solitary}), we reject joint equality at the 10\% level for four variables and at the 5\% level for an additional three variables, which slightly exceeds what is expected by chance. Significant differences appear for gender, age, and credit card ownership. Moreover, differences are present in some of the debriefing questions (e.g. whether subjects had previously talked about the study with others), which possibly reflects the fact that we ran the \emph{Solitary} treatment after the \emph{Communication} treatment.\footnote{We conducted the \emph{Solitary} treatment at a later time than the treatments involving communication, as our initial hypotheses focused on the comparison between the \emph{Communication} treatment and the \emph{Indirect Education} treatment alone.}  Indeed, most of these differences pertain to the \emph{Solitary} treatment; the sample is reasonably well-balanced between the \emph{Communication} and \emph{Indirect Education} treatments. Hence, sample imbalance does not impact our results concerning the mechanisms of skill transmission, which focus on comparisons within the \emph{Communication} treatment or across the \emph{Communication} and \emph{Indirect Education} treatments. Nonetheless, we statistically account for sample differences by including controls for subject characteristics in all regressions. In the main tables, we control for gender, age, age-squared, ethnicity indicators, an indicator for whether English is the subject's first language, an indicator for whether the subject is an international student, and indicator variables for whether the subject lives in a rural, suburban, or urban area. Appendix Sections \ref{mainResultsControls} and \ref{whoBenefitsWithControls} show that our results are robust to the exclusion of these controls and the inclusion of additional control variables.

\afterpage{
\thispagestyle{empty}
\begin{table}[htbp!]
\setlength{\tabcolsep}{2pt}
\caption{\label{demographics} {Characteristics of subjects in the role of Receiver.}}
\begin{center}
\begin{tiny}
\begin{tabular}{lcccccccccccc}
\toprule
			& \multicolumn{3}{c}{Means} &  \multicolumn{4}{c}{$p$-values} \\
			\cmidrule(r){2-4} \cmidrule(r){5 - 8}
			& Solitary 	& Indirect 		& Communication 	& Solitary			& Solitary		& Indir. Educ. 	& Joint 	\\
			&  		& Education  	&  				&  v. Indir. Educ.	&  v. Comm.	&  v. Comm.	&  		\\  \midrule

Pass MPL check	&	0.852	&	0.809	&	0.908	&	0.388 	&	0.265 	&	0.037**	&	0.111 		\\

\\
\multicolumn{8}{l}{\emph{\textbf{Demographic Variables}}}\\
 Male				&	0.330	&	0.473	&	0.468	&	0.043**	&	0.051*	&	0.942 	&	0.079*		\\
 Age					&	22.932	&	21.745	&	21.752	&	0.048**	&	0.049**	&	0.990 	&	0.082*		\\
 English native language		&	0.511	&	0.527	&	0.523	&	0.825 	&	0.872 	&	0.949 	&	0.975 \\

Ethnicity \\
\hspace{0.4cm} Black		&	0.080	&	0.073	&	0.119	&	0.869 	&	0.338 	&	0.234 	&	0.445 		\\
\hspace{0.4cm} Chinese		&	0.193	&	0.191	&	0.174	&	0.968 	&	0.736 	&	0.753 	&	0.930 		\\
\hspace{0.4cm} Other Asian	&	0.159	&	0.264	&	0.202	&	0.074*	&	0.466 	&	0.264 	&	0.193 		\\
\hspace{0.4cm} Mixed		&	0.068	&	0.045	&	0.028	&	0.448 	&	0.176 	&	0.526 	&	0.399 		\\
\hspace{0.4cm} Other 		&	0.011	&	0.027	&	0.018	&	0.424 	&	0.726 	&	0.635 	&	0.722 		\\

International student \\
\hspace{0.4cm} Yes			&	0.420	&	0.455	&	0.477	&	0.634 	&	0.430 	&	0.739 	&	0.731 		\\
\hspace{0.4cm} No response	&	0.045	&	0.036	&	0.009	&	0.707 	&	0.135 	&	0.234 	&	0.281 		\\

Living environment \\
\hspace{0.4cm} Suburban		&	0.295	&	0.255	&	0.339	&	0.532 	&	0.503 	&	0.171 	&	0.391 		\\
\hspace{0.4cm} Rural		&	0.102	&	0.100	&	0.128	&	0.960 	&	0.563 	&	0.505 	&	0.765 		\\

\\
\multicolumn{8}{l}{\emph{\textbf{Financial Variables}}}\\
Initial financial competence	&	0.474	&	0.348	&	0.365	&	0.038**	&	0.072*	&	0.767 	&	0.085*		\\
Log household income p.c. 	&	0.101	&	0.049	&	-0.087	&	0.648 	&	0.098*	&	0.203 	&	0.218 		\\
Full financial literacy score	&	0.500	&	0.464	&	0.486	&	0.613 	&	0.848 	&	0.739 	&	0.875 		\\

\# credit cards	&	0.466	&	0.336	&	0.312	&	0.060*	&	0.026**	&	0.706 	&	0.061*		\\
Used cash advance \\
\hspace{0.4cm} No	&	0.386	&	0.327	&	0.294	&	0.382 	&	0.171 	&	0.598 	&	0.388 		\\
\hspace{0.4cm} Not applicable	&	0.511	&	0.600	&	0.624	&	0.210 	&	0.113 	&	0.721 	&	0.256 		\\
Credit card debt rolled over\\
\hspace{0.4cm}\pounds1 - \pounds99	&	0.034	&	0.073	&	0.064	&	0.252 	&	0.373 	&	0.789 	&	0.495 		\\
\hspace{0.4cm}\pounds100 - \pounds499	&	0.080	&	0.009	&	0.046	&	0.015**	&	0.242 	&	0.175 	&	0.049**		\\
\hspace{0.4cm}\pounds500 - \pounds1000	&	0.023	&	0.018	&	0.018	&	0.819 	&	0.826 	&	0.993 	&	0.968 		\\

\hspace{0.4cm}\pounds 1000 - \pounds 2500&0.000	&	0.009	&	0.000	&	0.266	&	1.000	&	0.240	&	0.410 \\
\hspace{0.4cm}$>$ \pounds 2500	&	0.023	&	0.000	&	0.009	&	0.107 	&	0.337 	&	0.491 	&	0.272 		\\
\hspace{0.4cm}Not applicable		&	0.545	&	0.709	&	0.706	&	0.015**	&	0.017**	&	0.967 	&	0.025**		\\

\\
\multicolumn{8}{l}{\emph{\textbf{Psychological and Debriefing Variables}}}\\

Conformity scale	&	-6.841	&	-6.700	&	-4.817	&	0.925 	&	0.175 	&	0.181 	&	0.292 		\\

Big Five \\
\hspace{0.4cm}Conscientiousness	&	1.057	&	0.891	&	1.229	&	0.435 	&	0.418 	&	0.092*	&	0.242 	\\
\hspace{0.4cm}Agreeableness		&	1.250	&	1.364	&	1.211	&	0.606 	&	0.860 	&	0.463 	&	0.749 		\\
\hspace{0.4cm}Neuroticism		&	-0.466	&	-0.382	&	-0.128	&	0.744 	&	0.192 	&	0.298 	&	0.380 		\\
\hspace{0.4cm}Openness			&	1.159	&	1.173	&	1.037	&	0.953 	&	0.598 	&	0.534 	&	0.796 		\\
\hspace{0.4cm}Extraversion		&	0.648	&	0.645	&	0.633	&	0.993 	&	0.954 	&	0.959 	&	0.998 		\\

CRT score					&	1.284	&	1.364	&	1.596	&	0.629	&	0.059	&	0.135	&	0.133	 \\

Never heard about rule of 72 	&	0.852	&	0.855	&	0.862	&	0.964 	&	0.841 	&	0.869 	&	0.977 		\\
Heard others talk about study 	&	0.045	&	0.145	&	0.183	&	0.037**	&	0.004**	&	0.400 	&	0.014**		\\
Prepared for study			&	0.023	&	0.045	&	0.018	&	0.348 	&	0.857 	&	0.236 	&	0.452 		\\
Allow contact for followup 		&	0.761	&	0.845	&	0.872	&	0.117 	&	0.041**	&	0.606 	&	0.108 		\\
\bottomrule
\end{tabular}
\end{tiny}
\end{center}
\textbf{\textit{Notes:}} Reported values include subjects who failed the understanding check on multiple price lists (MPL check). Omitted categories are ``white" for \textit{ethnicity}, ``no" for \textit{international student}, ``urban" for \textit{living environment}, ``yes" for \textit{cash advance}, and ``\pounds 0" for \textit{Credit card debt rolled over}.
\end{table}
\clearpage
}

\newpage
\subsection{Table \ref{comOnImprovementSplit} with alternative control variables}\label{mainResultsControls}

In this section, we replicate our main results using alternative sets of control variables. On the one hand, we show that our results are robust to excluding demographic control variables (Appendix Table \ref{mainResultsNoControls}). Second, we show that they are also robust to including financial and psychological control variables in addition to the demographic variables (Appendix Table \ref{mainResultsAllControls}). Specifically, \emph{Financial variables} encompass
log household per capita income, dummies for credit card ownership,
having used a cash advance, having rolled over credit card debt, and
a dummy indicating whether the subject correctly answered all of the
three unincentivized financial literacy questions administered at
the beginning of the survey (46\% of Receivers answered all of
those questions correctly).\footnote{Similarly, 44.3\% of U.S. college graduates answered all three questions
correctly \citepappendix*{LusardiMitchellReview}. In our sample, 97.7\%,
88.2\%, and 50.6\% of Receivers answered the first, second, and third
questions correctly, respectively. To avoid priming the subjects, we did not directly elicit their initial
knowledge of the compound interest formula. Assuming subjects discussed
the formula if they knew it, however, we can assess the fraction who knew it
based on the fraction of pairs who discussed it. 37.4\% of pairs did not discuss
the formula. Because we paired subjects randomly, we estimate the likelihood
that any given subject was initially unfamiliar with the formula as
$0.374^{1/2}=61.2\%$. } \emph{Psychological and debriefing variables}
consist of subjects' performance on the Cognitive Reflection Test
\citepappendix*{CRT}, the five dimensions of the big five personality scale
\citepappendix*{BigFiveShort}, subjects' conformity score \citepappendix*{ConformityQuestionnaire},
and dummies indicating whether subjects had heard about the study
before participating, had talked to others about it, had prepared
for it, and wished to be contacted about any follow-up study.


\afterpage{
\thispagestyle{empty}
\begin{table}[htbp!]
\begin{footnotesize}
\setstretch{1.2}
\setlength{\tabcolsep}{2pt}
\caption{Replication of Table \ref{comOnImprovementSplit} without demographic control variables \label{mainResultsNoControls}}
\begin{center}
\begin{tabular}{lcccccccccc}
\toprule
  &(1) & (2) & (3) & (4) & (5a)  & (5b)  & (6a)  & (6b)   \\
VARIABLES  & \multicolumn{8}{c}{Improvement in Receivers' Deliberative Competence}  \\& \multicolumn{8}{c}{before / after communication}\\
\midrule
Benchmark simply framed choices &Contemp. & Stage 0 & Contemp. & Stage 0 & \multicolumn{2}{c}{Contemporaneous} & \multicolumn{2}{c}{Stage 0}\\
\cmidrule(r){6-7}\cmidrule(r){8-9}
Set of decision problems \\
\quad \textit{Discussed}  & Yes  & Yes  & Yes  & Yes   & No  & Yes & No  & Yes  \\
\quad \textit{New}   & Yes  & Yes & No  & No   & Yes & No  & Yes & No \\
Counterfactual mimicry & No & No & Yes & Yes & No & No & No & No\\
 \cmidrule(r){6-7}  \cmidrule(r){8-9}
\textit{Improvement in {Solitary}}
& 0.022 & 0.000 & 0.012 & -0.009 & 0.012 & 0.012 & -0.010 & -0.010 \\
	 & (0.018) & (0.020)& (0.023)  & (0.025) & (0.021) & (0.021) & (0.021) & (0.021) \\
\multicolumn{2}{l}{Row A: \emph{Communication}} &   \\
\quad\textit{Improvement} & 0.064** & 0.069** & -0.101** & -0.068 & 0.066** & 0.062** & 0.071** & 0.067** \\
\quad\textit{(compared to \emph{Solitary})}  & (0.027) & (0.028) & (0.047) & (0.045) & (0.028) & (0.029) & (0.028) & (0.030) \\
\multicolumn{2}{l}{Row B: \emph{Indirect Education}} & \\
\quad \textit{Improvement} & 0.073** & 0.067** & 0.008 & 0.030 & 0.054* & 0.092*** & 0.047 & 0.087*** \\
\quad\textit{(compared to \emph{Solitary})}  & (0.029) & (0.028) & (0.046) & (0.046) & (0.029) & (0.030) & (0.029) & (0.030) \\
\textit{p-values} & \\
\quad Communication = Indir. Educ.  & 0.748 & 0.955 & 0.046 & 0.062 & 0.648  & 0.290 & 0.376 & 0.459  \\
\cmidrule(r){6-7} \cmidrule(r){8-9}
\quad Discussed = Not-discussed  &&&&& \multicolumn{2}{c}{0.846} & \multicolumn{2}{c}{0.819} \\
\qquad if Sender uneducated  & \\
\quad Discussed = Not-discussed  &&&&& \multicolumn{2}{c}{0.043} & \multicolumn{2}{c}{0.033} \\
\qquad if Sender educated  &  \\
\quad Difference in differences   &&&&& \multicolumn{2}{c}{0.016} & \multicolumn{2}{c}{0.010} \\
 Observations& 3,156&3,156 &1,572 &1,572 & \multicolumn{2}{c}{526} & \multicolumn{2}{c}{526} \\
Subjects &263&263 & 262 & 262 & \multicolumn{2}{c}{263} & \multicolumn{2}{c}{263} \\
\bottomrule
\end{tabular}
\end{center}
\vspace{-0.4cm}
\textbf{\textit{Notes:}}
Improvement in Deliberative Competence from Stage 1 to Stage 2. Based on all subjects in the role of Receiver. Estimates
in the \textit{Improvement in Solitary} row indicate the average level of improvement for a Receiver in the \emph{Solitary} condition. Subsequent rows show the additional improvement from communication and indirect education. All regressions control for initial skills.
The dependent variable in Columns (3) and (4) is the hypothetical improvement in Deliberative Competence we would observe if all Receivers blindly mimicked their matched Sender's choices in discussed, complexly framed tasks. All other columns use actual improvements. Columns(1)-(4) present OLS regressions with standard errors clustered
by subject. Columns (5a) and (5b), as well as (6a) and (6b), each present estimates of a two-equation SUR regression. In the latter regressions, we average improvement within each task set to obtain a single pair of observations per subject. $^{*}p<0.1,^{**}p<0.05,^{***}p<0.01$.
\end{footnotesize}
\end{table}
\clearpage
}

\afterpage{
\thispagestyle{empty}
\begin{table}[htbp!]
\begin{footnotesize}
\setstretch{1.2}
\setlength{\tabcolsep}{2pt}
\caption{Replication of Table \ref{comOnImprovementSplit} with demographic, financial, and psychological control variables \label{mainResultsAllControls}  }
\begin{center}
\begin{tabular}{lcccccccccc}
\toprule
  &(1) & (2) & (3) & (4) & (5a)  & (5b)  & (6a)  & (6b)   \\
VARIABLES  & \multicolumn{8}{c}{Improvement in Receivers' Deliberative Competence}  \\& \multicolumn{8}{c}{before / after communication}\\
\midrule
Benchmark simply framed choices &Contemp. & Stage 0 & Contemp. & Stage 0 & \multicolumn{2}{c}{Contemporaneous} & \multicolumn{2}{c}{Stage 0}\\
\cmidrule(r){6-7}\cmidrule(r){8-9}
Set of decision problems \\
\quad \textit{Discussed}  & Yes  & Yes  & Yes  & Yes   & No  & Yes & No  & Yes  \\
\quad \textit{New}   & Yes  & Yes & No  & No   & Yes & No  & Yes & No \\
Counterfactual mimicry & No & No & Yes & Yes & No & No & No & No\\
 \cmidrule(r){6-7}  \cmidrule(r){8-9}
\textit{Improvement in {Solitary}}
& 0.016 & -0.004 & -0.002 & -0.037 & 0.009 & 0.009 & -0.011 & -0.011 \\
& (0.018) & (0.019)& (0.028)  & (0.031) & (0.021) & (0.021) & (0.021) & (0.021) \\
\multicolumn{2}{l}{Row A: \emph{Communication}} &   \\
\quad\textit{Improvement} & 0.072*** & 0.072*** & -0.096* & -0.041 & 0.071** & 0.073** & 0.072** & 0.071** \\
\quad\textit{(compared to \emph{Solitary})}   & (0.027) & (0.027) & (0.050) & (0.048) & (0.029) & (0.030) & (0.029) & (0.030) \\
\multicolumn{2}{l}{Row B: \emph{Indirect Education}} & \\
\quad \textit{Improvement} & 0.080*** & 0.076*** & 0.038 & 0.075 & 0.055* & 0.106*** & 0.048 & 0.103*** \\
\quad\textit{(compared to \emph{Solitary})}   & (0.028) & (0.028) & (0.047) & (0.050) & (0.029) & (0.030) & (0.029) & (0.031) \\
\textit{p-values} & \\
\quad Communication = Indir. Educ. & 0.747 & 0.871 & 0.020 & 0.030 & 0.541 & 0.241 &0.393  & 0.269  \\
\cmidrule(r){6-7} \cmidrule(r){8-9}
\quad Discussed = Not-discussed  &&&&& \multicolumn{2}{c}{0.917} & \multicolumn{2}{c}{0.977} \\
\qquad if Sender uneducated  & \\
\quad Discussed = Not-discussed  &&&&& \multicolumn{2}{c}{0.005} & \multicolumn{2}{c}{0.003} \\
\qquad if Sender educated  &  \\
\quad Difference in differences  &&&&& \multicolumn{2}{c}{0.004} & \multicolumn{2}{c}{0.001} \\

 Observations& 3,156&3,156 &1,572 &1,572 & \multicolumn{2}{c}{526} & \multicolumn{2}{c}{526} \\
Subjects &263&263 & 262 & 262 & \multicolumn{2}{c}{263} & \multicolumn{2}{c}{263} \\
\bottomrule
\end{tabular}
\end{center}
\vspace{-0.4cm}
\textbf{\textit{Notes:}}
Improvement in Deliberative Competence from Stage 1 to Stage 2. Based on all subjects in the role of Receiver. Estimates
in the \textit{Improvement in Solitary} row indicate the average level of improvement for a Receiver in the \emph{Solitary} condition. Subsequent rows show the additional improvement from communication and indirect education. All regressions control for initial skills, demographic, financial, and psychological control variables.
The dependent variable in Columns (3) and (4) is the hypothetical improvement in Deliberative Competence we would observe if all Receivers blindly mimicked their matched Sender's choices in discussed, complexly framed tasks. All other columns use actual improvements. Columns(1)-(4) present OLS regressions with standard errors clustered
by subject. Columns (5a) and (5b), as well as (6a) and (6b), each present estimates of a two-equation SUR regression. In the latter regressions, we average improvement within each task set to obtain a single pair of observations per subject. $^{*}p<0.1,^{**}p<0.05,^{***}p<0.01$.
\end{footnotesize}
\end{table}
\clearpage
}

\FloatBarrier
\newpage


\subsection{Table \ref{whoBenefits} with alternative control variables}\label{whoBenefitsWithControls}

For brevity, all estimations in Table  \ref{whoBenefits} include demographic control variables and initial skill levels. Here we replicate the analysis of Table \ref{whoBenefits} by excluding demographic variables (Appendix Table \ref{whoBenefitsNoControls}) and by including demographic, financial, and psychological variables as controls (Appendix Table \ref{whoBenefitsControls}). As the tables show, the alternative sets of control variables leave the coefficient estimates largely unchanged. The additional improvement a below-median Receiver enjoys when communicating with a below-median rather than with an above-median Sender remains highly statistically significant using stage-0 simply framed choices as a benchmark (columns 4 - 6), but $p$-values exceed 0.1 in some specifications with contemporaneous simply framed choices used as benchmark.


\afterpage{
\thispagestyle{empty}
\begin{table}[p]
\begin{footnotesize}
\setlength{\tabcolsep}{1.5pt}
\caption{Replication of Table \ref{whoBenefits} without demographic controls.\label{whoBenefitsNoControls} }
\begin{centering}
\begin{tabular}{lcccccccc}
\toprule
 & (1)  & (2)  & (3)  & (4)  & (5)  & (6) & (7)  & (8) \\
VARIABLES  & \multicolumn{8}{c}{Improvement in Receiver's Deliberative Competence}\\
Benchmark choices in simple frame  & \multicolumn{4}{c}{Contemporaneous} & \multicolumn{4}{c}{Stage 0}\\
\cmidrule(r){2-5} \cmidrule(r){6-9} Sets of decision problems  &  &  &  &  &  & \\
\hspace{0.2cm} \textit{Discussed} & Yes  &  & Yes  & Yes  & Yes  &  & Yes  & Yes \\
\hspace{0.2cm} \textit{Complex}$_{2}$ & Yes  & Yes  & & & Yes  & Yes  & & \\
Counterfactual mimicry & No & No & No & Yes & No & No & No & Yes \\
\emph{Improvement in Solitary condition}  & 0.032 & 0.020 & 0.043 & 0.043 & 0.009 & -0.004 & 0.021 & 0.016 \\
\quad{\emph{for bottom half Receiver}}
 & (0.015) & (0.017) & (0.016) & (0.016) & (0.017) & (0.019) & (0.018) & (0.019) \\
\emph{Additional improvement from communication if}  &  &  &  &  &  & \\
\quad Receiver bottom half   &  &  &  &  &  & \\
\qquad {and} Sender bottom half ($\beta_1)$ & 0.156*** & 0.144*** & 0.168*** & 0.065 & 0.180*** & 0.159*** & 0.200*** & 0.016 \\
 & (0.046) & (0.050) & (0.047) & (0.058) & (0.047) & (0.051) & (0.048) & (0.075) \\
\qquad {and} Sender top half  ($\beta_2$) & 0.090** & 0.066 & 0.114** & 0.207*** & 0.057 & 0.036 & 0.077 & 0.203*** \\
 & (0.045) & (0.046) & (0.051) & (0.053) & (0.045) & (0.046) & (0.051) & (0.055) \\
\quad Receiver top half  &  &  &  &  &  & \\
\qquad and Sender bottom half  ($\beta_3$ )& 0.001 & 0.010 & -0.007 & -0.291*** & 0.006 & 0.014 & -0.002 & -0.347*** \\
 & (0.016) & (0.018) & (0.017) & (0.046) & (0.015) & (0.016) & (0.017) & (0.058) \\
\qquad and Sender top half ($\beta_4$) & -0.020 & -0.018 & -0.023 & -0.089*** & -0.007 & 0.001 & -0.015 & -0.071*** \\
 & (0.015) & (0.018) & (0.014) & (0.020) & (0.015) & (0.017) & (0.015) & (0.021) \\
\emph{p-values about effect on Receiver} &  &  &  &  &  & \\
\quad ($R$ bottom, $S$ bottom) = ($R$ bottom, $S$ top) & 0.184 & 0.134 & 0.303 & 0.033 & 0.009 & 0.013 & 0.014 & 0.018 \\
\quad ($R$ bottom, $S$ bottom) = ($R$ top, $S$ bottom)  & 0.002 & 0.011 & 0.001  & 0.000 & 0.001 & 0.007 & 0.000 & 0.000 \\
\quad ($R$ bottom, $S$ top) = ($R$ top, $S$ top) & 0.020 & 0.087 & 0.009 & 0.000 & 0.180 & 0.467 & 0.079 & 0.000  \\
\quad ($R$ top, $S$ bottom) = ($R$ top, $S$ top) & 0.190 & 0.119 & 0.366 & 0.000 & 0.364 & 0.362 & 0.430 & 0.000 \\
\
 \quad Joint insignificance  & 0.007 & 0.029 & 0.003 & 0.000 & 0.004 & 0.022 & 0.001 & 0.000 \\

 Observations  & 3,156  & 1,578  & 1,578 & 1,572 & 3,156  & 1,578  & 1,578 & 1,572 \\
Subjects  & 263  & 263  & 263 &262 & 263  & 263  & 263 &262\\
\bottomrule
\end{tabular}
\par\end{centering}
\textbf{\textit{Notes:}}
Based on all subjects in the role of Receiver. Estimates in the \emph{Improvement in Solitary} row indicate the average level
of improvement for a bottom-half Receiver in the \emph{Solitary} condition. Subsequent rows show the additional improvement from communication. The dependent variable in columns (4) and (8) is the hypothetical improvement in Deliberative Competence we would observe if all Receivers blindly mimicked their matched Sender's choices in discussed, complexly framed tasks. All other columns use actual improvements. All  regressions  control  for  initial skills, top-half Receiver dummy, and decision problem fixed effects. Standard errors are clustered by subject. $^{*}p<0.1,^{**}p<0.05,^{***}p<0.01$.
\end{footnotesize}
\end{table}
\clearpage
}
\afterpage{
\thispagestyle{empty}
\begin{table}[p]
\begin{footnotesize}
\setlength{\tabcolsep}{1.5pt}
\caption{\label{whoBenefitsControls} \ Replication of Table \ref{whoBenefits} including demographic, financial and psychological controls.}
\begin{centering}
\begin{tabular}{lcccccccc}
\toprule
 & (1)  & (2)  & (3)  & (4)  & (5)  & (6) & (7)  & (8) \\
VARIABLES  & \multicolumn{8}{c}{Improvement in Receiver's Deliberative Competence}\\
Benchmark choices in simple frame  & \multicolumn{4}{c}{Contemporaneous} & \multicolumn{4}{c}{Stage 0}\\
\cmidrule(r){2-5} \cmidrule(r){6-9} Sets of decision problems  &  &  &  &  &  & \\
\hspace{0.2cm} \textit{Discussed} & Yes  &  & Yes  & Yes  & Yes  &  & Yes  & Yes \\
\hspace{0.2cm} \textit{Complex}$_{2}$ & Yes  & Yes  & & & Yes  & Yes  & & \\
Counterfactual mimicry & No & No & No & Yes & No & No & No & Yes \\
\emph{Improvement in Solitary condition}  & 0.028 & 0.020 & 0.036 & 0.036 & 0.008 & -0.002 & 0.017 &-0.005  \\
\quad{\emph{for bottom half Receiver}} & (0.016)  & (0.016)  & (0.017)  & (0.017)  & (0.017)  & (0.017) & (0.018) & (0.024) \\
\emph{Additional improvement from communication if}  &  &  &  &  &  & \\
\quad Receiver bottom half   &  &  &  &  &  & \\
\qquad {and} Sender bottom half ($\beta_1)$ & 0.158*** & 0.150*** & 0.167*** & 0.073 & 0.178*** & 0.158*** & 0.199*** & 0.058 \\
 & (0.044) & (0.048) & (0.045) & (0.055) & (0.045) & (0.048) & (0.046) & (0.076) \\
\qquad {and} Sender top half  ($\beta_2$) & 0.092** & 0.062 & 0.123** & 0.222*** & 0.062 & 0.035 & 0.088* & 0.242*** \\
 & (0.043) & (0.044) & (0.048) & (0.052) & (0.045) & (0.046) & (0.049) & (0.059) \\
\quad Receiver top half  &  &  &  &  &  & \\
\qquad and Sender bottom half  ($\beta_3$ )& 0.017 & 0.019 & 0.015 & -0.270*** & 0.013 & 0.016 & 0.009 & -0.322*** \\
 & (0.022) & (0.025) & (0.023) & (0.044) & (0.020) & (0.023) & (0.022) & (0.057) \\
\qquad and Sender top half ($\beta_4$) & -0.019 & -0.027 & -0.011 & -0.089** & -0.012 & -0.009 & -0.015 & -0.063 \\
 & (0.025) & (0.027) & (0.026) & (0.035) & (0.021) & (0.024) & (0.023) & (0.039) \\
\emph{p-values about effect on Receiver} &  &  &  &  &  & \\
\quad ($R$ bottom, $S$ bottom) = ($R$ bottom, $S$ top) & 0.177 & 0.089 & 0.393 & 0.018 & 0.017 & 0.018 & 0.029 & 0.020 \\
\quad ($R$ bottom, $S$ bottom) = ($R$ top, $S$ bottom)  & 0.005 & 0.017 & 0.003  & 0.000 & 0.001 & 0.009  & 0.000  & 0.000 \\
\quad ($R$ bottom, $S$ top) = ($R$ top, $S$ top)  & 0.027 & 0.091 & 0.013  & 0.000 & 0.137 & 0.400 & 0.050  & 0.000 \\
\quad ($R$ top, $S$ bottom) = ($R$ top, $S$ top) & 0.101 & 0.050 & 0.261  & 0.000 & 0.244 & 0.267 & 0.290  & 0.000 \\
\
 \quad Joint insignificance  & 0.003 & 0.007 & 0.003 & 0.000 & 0.002 & 0.014 & 0.000 & 0.000 \\
 Observations  & 3,156  & 1,578  & 1,578 & 1,572 & 3,156  & 1,578  & 1,578 & 1,572 \\
Subjects  & 263  & 263  & 263 &262 & 263  & 263  & 263 &262\\
\bottomrule
\end{tabular}
\par\end{centering}
\textbf{\textit{Notes:}}
Based on all subjects in the role of Receiver. Estimates in the \emph{Improvement in Solitary} row indicate the average level
of improvement for a bottom-half Receiver in the \emph{Solitary} condition. Subsequent rows show the additional improvement from communication. The dependent variable in Columns (4) and (8) is the hypothetical improvement in Deliberative Competence we would observe if all Receivers blindly mimicked their matched Sender's choices in discussed, complexly framed tasks. All other columns use actual improvements. All  regressions  control  for  initial skills, top-half Receiver dummy, decision problem fixed effects, and demographic, financial, and psychological controls. Standard errors are clustered by subject. $^{*}p<0.1,^{**}p<0.05,^{***}p<0.01$.
\end{footnotesize}
\end{table}
\clearpage
}


\newpage
\FloatBarrier

\subsection{Table \ref{transcriptionData} with transcriber fixed effects} \label{sec:transcriptionDataFE}
Here, we replicate Table \ref{transcriptionData} including the transcriber fixed effects. All the coefficients are similar to those in Table \ref{transcriptionData} and all the statistically significant results remain significant.

\begin{table}[H]
\caption{\label{transcriptionDataFE} Replication of Table \ref{transcriptionData} with transcriber fixed effects}
\begin{footnotesize}
\begin{centering}
\setlength{\tabcolsep}{1pt}
\begin{tabular}{lccccccc}
\toprule
 & (1)  & (2)  & (3)  & (4)  & (5)  & (6)  & (7) \\
VARIABLES  & highlight  & minutes  & \# problems  & \#small  & one person  & Rule  & Compounding \\
 & similarities  & discussed  & discussed  & talk  & proclaims  & of 72  & formula \\
 &  &  &  & topics  & skills  & discussed  & discussed \\
\midrule
\multicolumn{2}{l}{Panel A: \emph{Communication}} &  &  &  &  &  & \\
\hspace{0.4cm} Different skills $(\alpha_1)$  & 0.422 & 8.264 & 3.572 & 0.617 & 0.287 & -0.030 & 0.732 \\
 & (0.075) & (0.799) & (0.291) & (0.123) & (0.072) & (0.053) & (0.080) \\
\hspace{0.4cm} Similar skills $(\alpha_2)$ & 0.736 & 10.154 & 3.511 & 0.347 & 0.194 & 0.015 & 0.672 \\
 & (0.078) & (0.775) & (0.307) & (0.127) & (0.075) & (0.054) & (0.082) \\
\multicolumn{2}{l}{Panel B: \emph{Indirect Education}} &  &  &  &  &  & \\
\hspace{0.4cm} Different skills $(\alpha_3)$ & 0.480 & 8.516 & 3.477 & 0.391 & 0.463 & 0.744 & 0.391 \\
 & (0.075) & (0.816) & (0.291) & (0.123) & (0.072) & (0.052) & (0.079) \\
\hspace{0.4cm} Similar skills $(\alpha_4)$  & 0.480 & 9.499 & 3.811 & 0.159 & 0.395 & 0.754 & 0.422 \\
 & (0.080) & (0.844) & (0.311) & (0.131) & (0.078) & (0.056) & (0.085) \\
\emph{p-Values}  &  &  &  &  &  &  & \\
\hspace{0.4cm} Effect of similarity  &  &  &  &  &  &  & \\
\hspace{0.8cm} \textit{Communication tr.} $(\alpha_1=\alpha_2)$  & 0.001 & 0.091 & 0.873 & 0.088 & 0.320 & 0.505 & 0.562 \\
\hspace{0.8cm} \textit{Indirect Education tr.} $(\alpha_3=\alpha_4)$   & 0.997 & 0.403 & 0.380 & 0.150 & 0.472 & 0.887 & 0.762 \\
\hspace{0.4cm} Effect of indirect education  &  &  &  &  &  &  & \\
\hspace{0.8cm} \textit{Similar skills} $(\alpha_2=\alpha_4)$  & 0.009 & 0.568 & 0.437 & 0.239 & 0.036 & 0.000 & 0.017 \\
\hspace{0.8cm} \textit{Dissimilar skills} $(\alpha_1=\alpha_3)$  & 0.550 & 0.826 & 0.800 & 0.153 & 0.060 & 0.000 & 0.001\medskip\\
\hspace{0.4cm} All four parameters equal  & 0.006 & 0.301 & 0.817 & 0.044 & 0.024 & 0.000 & 0.001 \\
\hspace{0.4cm} Diff-in-diff  & 0.023 & 0.576 & 0.463 & 0.863 & 0.854 & 0.710 & 0.532 \\
Observations  & 175 & 188 & 171 & 175 & 173 & 172 & 172 \\
\bottomrule
\end{tabular}
\par\end{centering}
\end{footnotesize}
\begin{centering}
\par\end{centering}
\textit{\textbf{Notes:}} Hypothesis tests based on linear regressions
with coder fixed effects. Column 2 does not include coder fixed effects
because minutes discussed is measured directly. Levels are displayed for the coder who encoded the largest number (86 of 175) of the transcripts.
\end{table}

\FloatBarrier
\newpage


\subsection{Effects of Communication on Confidence\label{confidence}}
In this section, we consider the effect of communication on subjects' confidence about  their decision skills. We study whether the effect differs by pair characteristics. At the end of our experiment, subjects answered the following question: ``Do you feel you had a firm grasp of how to make good decisions in this study?" Answers ranged from ``No, not at all" to ``Yes, I'm very confident that I made good decisions" (on a seven point scale). We estimate the following model with OLS, using data on Receivers, pooling across \emph{Communication} and \emph{Indirect Education} treatments:
\vspace{-0.7cm}
\begin{eqnarray}
Confidence_{j}&=&\beta_0+\beta_1 \big(R\_bottom_j \times S\_bottom_{j}\big)+\beta_2 \big(R\_bottom_j \times S\_top_{j}\big)  \nonumber \\
&&+\beta_3 \big(R\_top_j \times S\_bottom_{j}\big) +\beta_4 \big(R\_top_j \times S\_top_{j}\big)  \\ \nonumber
&&+\beta_5 R\_top_{j}+X_{j}+\epsilon_{j}
\end{eqnarray}
\vspace{-1.3cm}

\noindent where $Confidence_{j}$ is the answer of Receiver $j$ to the confidence question, $R\_bottom_j$ and $R\_top_j$ indicate whether Receiver $j$ is in the bottom or top half of the skill distribution, respectively, $S\_bottom_j$ and $S\_top_j$ are defined similarly for the Sender paired with Receiver $j$, and where $X_j$ is a vector of controls that always includes Receivers' preexisting skills. For Receivers in the Solitary treatment, we set $S\_bottom_j = S\_top_j=0$.

Column 1 of Table \ref{tab: confidence} displays the results. We see that bottom Receivers' confidence increases significantly when communicating with top Senders compared to the solitary treatment $(p<0.05)$. While the effect on confidence is greater when talking with a top Sender than with a bottom Sender, the difference not statistically significant ($p>0.2$). These findings remain qualitatively unchanged when we add controls for demographics (column 2) and, additionally, for financial and psychological variables (column 3), though in the latter case the effect of matching bottom Receivers with top Senders declines slightly both in magnitude and in statistical significance.


\begin{table}[H]
\caption{Effect of communication on confidence by pair characteristics.}
\label{tab: confidence}
\begin{footnotesize}
\setlength{\tabcolsep}{15pt}
\begin{center}
\begin{tabular}{lccc}
\hline
 & (1) & (2) & (3) \\
VARIABLES  &\multicolumn{3}{c}{Receivers' Confidence in Their Decisions} \\
\hline
\emph{Confidence in Solitary condition}  & 4.945 & 5.033 & 5.109 \\
 \quad\emph{for bottom half Receiver}& (0.175) & (0.174) & (0.188) \\
\emph{Additional confidence from communication if}  & \\
\quad Receiver bottom half   &  \\
\qquad {and} Sender bottom half ($\beta_1)$ & 0.432 & 0.409 & 0.404 \\
 & (0.313) & (0.319) & (0.320) \\
\qquad {and} Sender top half  ($\beta_2$) & 0.802** & 0.822** & 0.599* \\
 & (0.348) & (0.355) & (0.339) \\
\quad Receiver top half  &  \\
\qquad and Sender bottom half  ($\beta_3$ )& 0.149 & -0.054 & -0.118 \\
 & (0.295) & (0.290) & (0.337) \\
\qquad and Sender top half ($\beta_4$) & 0.002 & -0.219 & -0.287 \\
 & (0.307) & (0.330) & (0.361) \\
\emph{p-values about effect on Receiver} &   \\
\quad ($R$ bottom, $S$ bottom) = ($R$ bottom, $S$ top)   & 0.238 & 0.185 & 0.524 \\
\quad ($R$ bottom, $S$ bottom) = ($R$ top, $S$ bottom)  & 0.512 & 0.275 & 0.249 \\
\quad ($R$ bottom, $S$ top) = ($R$ top, $S$ top) & 0.086 & 0.031 & 0.057 \\
\quad ($R$ top, $S$ bottom) = ($R$ top, $S$ top)  & 0.545 & 0.544 & 0.507 \\
 \quad Joint insignificance  & 0.219 & 0.206 & 0.360 \\
\emph{Controls} \\
\quad Demographics & No & Yes & Yes  \\
\quad Financial and psychological & No & No & Yes   \\
Subjects  & 243 & 243 & 243   \\
\hline
\end{tabular}
\end{center}
\end{footnotesize}
\textbf{\textit{Notes:}}
Based on all Receivers. Estimates in the \emph{Confidence in Solitary condition for bottom half Receiver} row indicates the average level of improvement for a bottom-half Receiver  in the \emph{Solitary} condition. Subsequent rows show the additional confidence from communication. All  regressions  control  for  initial  skills and top-half  Receiver  dummy. Additional controls are listed in Appendix \ref{summaryStats}. Robust standard errors are in parentheses. $^{*}p<0.1,^{**}p<0.05,^{***}p<0.01$.
\end{table}


\subsection{Actual Competence and Perceived Competence\label{perceivedCompetence}}
In this section, we analyze whether a subject's ability to detect Deliberative Competence in peers is related to their own competence. We first classify each subject according to whether her Deliberative Competence falls into the top or bottom half of the distribution before she communicates with another subject, as in Section \ref{SecWhoBenefits}. We measure the perceived competence of the partner using the following question, which we asked at the end of our experiment: ``Do you feel your partner had a firm grasp of how to make good decisions in this study?" Subjects answer using a seven point scale. We regress the responses to this question on a set of control variables and the following indicators: Receiver Bottom Half $\times$ Sender Top Half,  Receiver Top Half, Receiver Top Half $\times$ Sender Top Half. Receiver Bottom Half is the omitted category.

Table \ref{table: perceivedCompetence} displays the results. The constant term in Column 1, 5.02 (out of 7), is the average perception of Receivers in the bottom half about the competence of Senders in the bottom half. This perception increases by 0.851 points ($p<0.01$) for Senders in the top half, and by 0.599 points ($p<0.1$) if the Receiver making the assessment is herself in the top half. These findings suggest that Receivers tend to recognize more competent Senders, on average. While the effect of Sender competence on bottom Receivers' assessments is robust to adding controls (columns 2 and 3), the effect on top Receivers' assessments is not.

Greater Receiver competence is not, however, unambiguously associated with greater ability to recognize sender competence. The difference between the two interaction terms is not statistically significant in any specification. Moreover, a continuous specification yields the opposite effect, again without statistical significance.


\begin{table}[H]
\begin{small}
\caption{Correlations of Receivers' Competence, Senders' Competence and Perceived Competence of Senders.}
\setlength{\tabcolsep}{13pt}
\begin{center}
\begin{tabular}{lccc}
\toprule
 & (1) & (2) & (3) \\
VARIABLES  &\multicolumn{3}{c}{Perceived Competence of Sender} \\
\midrule
Receiver bottom half $\times$ Sender top half & 0.851*** & 0.857** & 0.823** \\
 & (0.312) & (0.330) & (0.353) \\
 Receiver top half & -0.294 & -0.247 & -0.251 \\
 & (0.335) & (0.381) & (0.426) \\
 Receiver top half $\times$ Sender top half & 0.599* & 0.513 & 0.465 \\
 & (0.328) & (0.330) & (0.344) \\
 Constant & 5.021*** & 3.409 & 1.007 \\
 & (0.241) & (4.938) & (5.356) \\
\emph{p-value} &   \\
\quad R bottom half $\times$ S top half  = R top half $\times$ S top half & 0.578 & 0.459 & 0.488 \\
\emph{Controls} \\
\quad Demographics & No & Yes & Yes  \\
\quad Financial \& Psychological & No & No & Yes   \\
Subjects  & 177 & 177 & 177  \\
\bottomrule
\end{tabular}
\end{center}
\textbf{\textit{Notes:}} Based on Receivers in the \emph{Communication} and \emph{Indirect Education} treatments. Classifications to Receiver (Sender) bottom or top half are based on a median split of Receivers' (Senders') Deliberative Competence calculated using their answers to the Stage 1 complexly and simply framed decision problems.  Omitted category is Receiver bottom half. Controls are listed in Appendix \ref{summaryStats}. Robust standard errors are in parentheses. $^{*}p<0.1,^{**}p<0.05,^{***}p<0.01$.
\label{table: perceivedCompetence}
\end{small}
\end{table}

\newpage
\subsection{Effect of the education intervention} \label{educationAnalysis}

We analyze the direct effect of the education intervention on those who participate. We regress Senders' financial competence in Stage 1 on an indicator of whether they have participated in the education intervention. Table \ref{education} displays the results. The estimates mentioned in the main text are from Column 1. Column 2 controls for subjects' initial skill levels using  decisions in tasks \textit{Anc}$_0$.\footnote{In contrast to the previous regressions, we control for preexisting
Deliberative Competence using only the \textit{Anc}$_{0}$ tasks and
not the \textit{Anc}$_{1}$ tasks, because the educational intervention
is administered between these two stages.} The treatment effect remains similar, showing that the effect does not merely arise because more skilled subjects happened to be assigned to the education treatment. Columns 3 and 4 further control for demographics, as well as financial and psychological characteristics, respectively. Controlling for these covariates slightly decreases the estimated effect size, but it is still substantial.

\begin{table}[htbp!]
\begin{center}
\caption{\label{education} Direct effect of the education intervention.}
\begin{tabular}{lcccc} \toprule
 & (1) & (2) & (3) & (4)  \\
VARIABLES & \multicolumn{4}{c}{Financial competence } \\
		 & \multicolumn{4}{c}{among Senders for problems \textit{Discussed}} \\ \midrule
 &  &  &    \\
\emph{Level of Competence} \\
\hspace{0.4cm} No education & -0.274*** & -0.283*** & -0.276*** & -0.270*** \\
& 0.0390 & 0.0360 & 0.0340 & 0.0330 \\
\hspace{0.4cm}  Education & -0.192*** & -0.181*** & -0.189*** & -0.196*** \\
 & 0.0290 & 0.0250 & 0.0250 & 0.0270 \\
Treatment effect & 0.082* & 0.103** & 0.087** & 0.074* \\
 & (0.049) & (0.045) & (0.041) & (0.045) \\
 &  &  &   & \\
\textit{Controls} \\
\hspace{0.4cm} Initial skills & - & Yes & Yes &Yes   \\
\hspace{0.4cm} Demographic & -  & - & Yes & Yes  \\
\hspace{0.4cm} Financial \& Psychological & - & - & -  & Yes \\
Observations  & 1,014 & 1,014 & 1,014 & 1,014  \\
Subjects & 169  & 169 & 169 & 169  \\ \bottomrule
\end{tabular}
\end{center}

\textit{\textbf{Notes:}} Financial competence in stage 1. Only Senders who pass the comprehension checks and whose partners pass the comprehension checks are included in the analysis. Initial skills are measured as the absolute deviation between a subject's valuation and the true future value in decision set $Anc_0$.  A full list of demographic, financial and psychological controls is given in Appendix Table \ref{demographics}. Standard errors clustered by subject. $^* p < 0.1, ^{**}p < 0.05, ^{***}p < 0.01$.
\end{table}
\newpage


\FloatBarrier
\newpage
\section{Instructions and Survey Questions}\label{instruction}


\textit{We add comments for the reader in italics.}
\includegraphics[width=\textwidth]{./screenshots/instructions1.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions2.png}\\
\textit{The University of Birmingham Economics Laboratory uses a procedure that requires all subjects to pick a random token from a bowl with tokens numbered 1 through $N$ where $N$ is the number of subjects in a session. Subjects are seated at computer terminals according to their token numbers. This process happens when all subjects are present or at the beginning of the session, whichever happens first. Subjects who arrive after token selection cannot participate in the experiment.}
\includegraphics[width=\textwidth]{./screenshots/instructions3.png}\\
\centering
\textit{The subject next watches a video in which B.D. Bernheim reads the following script.}\\
\includepdf[pages=-]{./screenshots/trustScript}
\includegraphics[width=\textwidth]{./screenshots/instructions4.png}\\
\centering
\textit{The subject watches a video in which B.D. Bernheim reads the following script.}\\
\includepdf[pages=-]{screenshots/instructions_0_PRELIMINARY}
\includegraphics[width=\textwidth]{./screenshots/instructions5.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions6.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions7.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions8.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions9.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions10.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions11.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions12.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions13.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions14.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions15.png}\\
\textit{The subject next watches a video in which B.D. Bernheim reads the following instructions, shown on screen.}
\includepdf[pages=-]{./screenshots/part1}
\includegraphics[width=\textwidth]{./screenshots/instructions16.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions17.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions18.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions19.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions20.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions21.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions22.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions23.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions24.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions25.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions26.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions27.png}\\
\textit{Subjects face eight more decision problems in Part 1. The decision problems presented in the same format. The decision problem shown here serves as an example, and it is not necessarily the first decision problem a subject would encounter due to the randomization.}
\newpage \textit{Part 2 is labeled as Stage 1 in the main text.}
\newline\textit{\textbf{Receivers in all treatment groups and Senders in the Communication treatment watch the documentary.}}
\includegraphics[width=\textwidth]{./screenshots/instructions28.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions29.png}\\
\textit{\textbf{Documentary: }}\url{https://www.dropbox.com/s/w6cb8dablyieidx/documentary.mp4}
\newpage\textit{\textbf{Senders in the Indirect Education treatment watch the Education Intervention.}}
\includegraphics[width=\textwidth]{./screenshots/instructions61.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions29.png}\\
\textit{\textbf{Education Intervention, part 1: }} \url{https://youtu.be/EnFVLiM1dTs}
\newline \textit{\textbf{Part 1 Practice Question}}
\includegraphics[width=\textwidth]{./screenshots/E2.png}\\
\textit{\textbf{If the answer is correct in the first trial:}}
\includegraphics[width=\textwidth]{./screenshots/E3b.png}\\
\textit{\textbf{If the answer is incorrect in the first trial:}}
\includegraphics[width=\textwidth]{./screenshots/E3a.png}\\
\textit{\textbf{If the answer is correct in the second time:}}
\includegraphics[width=\textwidth]{./screenshots/E4b.png}\\
\textit{\textbf{If the answer is incorrect  in the second trial:}}
\includegraphics[width=\textwidth]{./screenshots/E4a.png}\\
\includegraphics[width=\textwidth]{./screenshots/E5.png}\\
\textit{\textbf{Education Intervention, part 2: }}\url{https://youtu.be/3pjkVdOXMlk}
\newline \textit{\textbf{Part 2 Practice Question}}
\includegraphics[width=\textwidth]{./screenshots/E6.png}\\
\textit{\textbf{If the answer is correct in the first trial:}}
\includegraphics[width=\textwidth]{./screenshots/E7hE9a.png}\\
\newpage
\textit{\textbf{If the answer is incorrect in the first trial:}}
\newline \textit{Subjects see one of the following explanations depending on their previous answer and they re-attempt the question.}
\newline\textit{\textbf{If their previous answer was \$100:}}
\includegraphics[width=\textwidth]{./screenshots/E7a.png}\\
\textit{\textbf{If their previous answer was \$200:}}
\includegraphics[width=\textwidth]{./screenshots/E7b.png}\\
\textit{\textbf{If their previous answer was \$388:}}
\includegraphics[width=\textwidth]{./screenshots/E7c.png}\\
\textit{\textbf{If their previous answer was \$400:}}
\includegraphics[width=\textwidth]{./screenshots/E7d.png}\\
\textit{\textbf{If their previous answer was \$600:}}
\includegraphics[width=\textwidth]{./screenshots/E7e.png}\\
\textit{\textbf{If their previous answer was \$800:}}
\includegraphics[width=\textwidth]{./screenshots/E7f.png}\\
\textit{\textbf{If their previous answer was \$1200:}}
\includegraphics[width=\textwidth]{./screenshots/E7g.png}\\
\textit{\textbf{Re-attempt the question:}}
\includegraphics[width=\textwidth]{./screenshots/E8.png}\\
\textit{\textbf{If the answer is correct in the second time:}}
\includegraphics[width=\textwidth]{./screenshots/E7hE9a.png}\\
\textit{\textbf{If the answer is incorrect  in the second trial:}}
\includegraphics[width=\textwidth]{./screenshots/E9b.png}\\
\includegraphics[width=\textwidth]{./screenshots/E10.png}\\
\textit{\textbf{Education Intervention, part 3: }}\url{https://youtu.be/kjPYqcZNzPI}
\newline \textit{\textbf{Practice Questions at the end of the Intervention}}
\includegraphics[width=\textwidth]{./screenshots/E11.png}\\
\includegraphics[width=\textwidth]{./screenshots/E12.png}\\
\textit{\textbf{If the answer for part(a)  is incorrect in the first trial:}}
\includegraphics[width=\textwidth]{./screenshots/E13a.png}\\
\textit{\textbf{If the answer for part(a)  is incorrect in the second trial:}}
\includegraphics[width=\textwidth]{./screenshots/E14.png}\\
\textit{\textbf{If the answer for part(a) is correct in the first trial or later trials:}}
\includegraphics[width=\textwidth]{./screenshots/E13bE15}\\
\textit{\textbf{If the answer for part(b) is incorrect in the first trial:}}
\includegraphics[width=\textwidth]{./screenshots/E16a.png}\\
\textit{\textbf{If the answer for part(b) is correct in the first trial or later trials:}}
\includegraphics[width=\textwidth]{./screenshots/E16b.png}\\
\textit{\textbf{If the answer for part(c) is incorrect in the first trial:}}
\includegraphics[width=\textwidth]{./screenshots/E18.png}\\
\textit{\textbf{If the answer for part(c) is correct in the first trial or later trials:}}
\includegraphics[width=\textwidth]{./screenshots/E19.png}\\
\textit{\textbf{If the answer for Question 2 is incorrect in the first trial:}}
\includegraphics[width=\textwidth]{./screenshots/E20.png}\\
\textit{\textbf{If the answer for Question 2 is correct in the first trial or later trials:}}
\includegraphics[width=\textwidth]{./screenshots/E21.png}\\
\textit{\textbf{Post Education Intervention Question}}
\includegraphics[width=\textwidth]{./screenshots/E21.png}\\
\includegraphics[width=\textwidth]{./screenshots/E22.png}\\
\newpage \centering \textit{\textbf{All Subjects}}
\includegraphics[width=\textwidth]{./screenshots/instructions30.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions31.png}\\
\textit{Subjects face fourteen more decision problems in Part 2. The decision problems presented in the same format. The decision problem shown here serves as an example, and it is not necessarily the first decision problem a subject would encounter due to the randomization.}
\vspace{1cm}
\newline\centering{\textit{\textbf{Part 3 (labeled as Stage 2 in the main text)}}}
\includegraphics[width=\textwidth]{./screenshots/instructions35.png}\\
\textit{The subject next watches a video in which B.D. Bernheim reads the following instructions, displayed on screen.}\\
\includepdf[scale=0.85,pages=-]{screenshots/part3communication}
\textit{The subject next watches a video in which B.D. Bernheim reads the following instructions, displayed on screen.}\\
\includepdf[scale=0.85,pages=-]{screenshots/part3solitary}
\includegraphics[width=\textwidth]{./screenshots/instructions36.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions37.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions38.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions39.png}\\
\newpage\textit{\textbf{Solitary Treatment}}
\includegraphics[width=\textwidth]{./screenshots/instructions42.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions43.png}\\
\newpage\textit{\textbf{Communication and Indirect Education Treatments}}
\includegraphics[width=\textwidth]{./screenshots/instructions62.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions63.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions64.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions65.png}\\
 \newpage\textit{\textbf{All Subjects}}
\includegraphics[width=\textwidth]{./screenshots/instructions44.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions45.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions46.png}\\
\textit{Subjects face seventeen more decision problems in Part 3. The decision problems presented in the same format. The decision problem shown here serves as an example, and it is not necessarily the first decision problem a subject would encounter due to the randomization.}
\newpage\textit{\textbf{Solitary Treatment}}
\includegraphics[width=\textwidth]{./screenshots/instructions47.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions48.png}\\
\newpage\textit{\textbf{All Subjects}}
\includegraphics[width=\textwidth]{./screenshots/instructions49.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions50.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions51.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions52.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions53.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions54.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions55.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions66.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions57.png}\\
\newpage\textit{\textbf{Senders}}
\includegraphics[width=\textwidth]{./screenshots/instructions67.png}\\
\includegraphics[width=.8\textwidth]{./screenshots/instructions68.png}\\
\newpage\textit{\textbf{Receivers in the Communication and Indirect Education Treatments}}
\includegraphics[width=.7\textwidth]{./screenshots/instructions69.png}\\
\includegraphics[width=.7\textwidth]{./screenshots/instructions71.png}\\
\newpage\textit{\textbf{All Subjects}}
\includegraphics[width=\textwidth]{./screenshots/instructions58.png}\\
\textit{The numbers shown below serves as an example. Subjects' payoffs vary depending on the choices they have made during the experiment and the randomization.}
\includegraphics[width=\textwidth]{./screenshots/instructions59.png}\\
\includegraphics[width=\textwidth]{./screenshots/instructions60.png}\\


\flushleft


\phantomsection
\stepcounter{section}
\addcontentsline{toc}{section}{\protect\numberline{\thesection}References}


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\end{document}
