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\begin{document}

\title{{\it Appendix to} \\ On the Transportability of Laboratory Results}
\subtitle{}


\author[ \hspace{-1ex}]{Felix Bader}
\author[ \hspace{-1ex}]{Bastian Baumeister}
\author[ \hspace{-1ex}]{Roger Berger}
\author[*]{Marc Keuschnigg}
\affil[*]{Corresponding author: \href{mailto:marc.keuschnigg@liu.se}{marc.keuschnigg@liu.se}}
\renewcommand\Authands{, and }

\date{\it Sociological Methods \& Research}
\maketitle



%\thispagestyle{empty} % no page number on title page
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\subsection*{A1 Socio-demographics across Samples and Control Variables}

\noindent Table A1 summarizes the different socio-demographic backgrounds of our participants as well as relevant control variables capturing properties of our design potentially affecting elicited behavior. We include these characteristics in our calculations of conditional means (see Appendix A2 for the full models). We indicate binary measures with (0,1); all other measures are continuous. We test, further, for significant differences in sample composition, focusing on the seven pairwise comparisons that are crucial to our main analysis. 

\begin{description}
\item \textit{Gender}. Women are broadly overrepresented in both student pools in Leipzig and Munich. The nationwide sample, in which gender is one of the criteria for stratified sampling, has a balanced sex ratio. Women, however, make up only a third of the MTurk sample. 

\item \textit{Age}. On average, student participants are 22 years old, the broader population 45, and crowdworkers 33. Because age often correlates non-linearly with elicited behavior in the lab (see, for an overview, Fr\'echette 2016), we categorize age into intervals 18--22, 23--29, 30--45, and $\geq$46 for inclusion in our regressions (see Appendix A2). 

\item \textit{Education}. Participants in our student pools differ with respect to study fields. Among Leipzig students, most pursue a major in humanities (e.g., cultural studies, literature, pedagogy). In Munich, most major in other programs such as social sciences, law, or STEM fields. We particularly differentiate between students of economics and of the humanities. Prior studies have shown that the former behave more selfishly in incentivized games (Etzioni 2015). We use all other study fields as our reference category. In the nationwide sample, 60\% have at least a high-school diploma and 9\% are currently enrolled in a study program. Among crowdworkers, 90\% have at least secondary education and 12\% are currently students. 

\item \textit{Employment}. For student subjects, we code 1 if they have a side job (50\% in Leipzig and 63\% in Munich). In the non-student samples, we code 1 for the fully-employed. This is true for 58\% in the nationwide sample and for 69\% of crowdworkers. 

\item \textit{Income}. We measure monthly disposable income using the PPP\$-adjusted household income divided by the square root of household size. On average, students are significantly more affluent in Munich (PPP\$1,282) than in Leipzig (PPP\$870). Both groups have substantially less income at their disposal than the average German (PPP\$2,727). MTurk participants take a middle position with an average income of PPP\$1,562. In our regressions, we include a log transformation of this variable. 
 
\item \textit{Parenthood}. A number of observational studies find that parents differ in prosocial behavior compared to individuals without children (see Wiepking and Bekkers 2012 for an overview). Parenthood is rare among students (1--2\%). In the nationwide sample, 57\% have at least one child. This rate is 43\% for crowdworkers. 

\item \textit{Experience}. Prior experience with laboratory games varies considerably across studies. Both student subjects and members of the broader population on average had only taken 1--3 social experiments prior to participation. For MTurk workers, this number amounts to 66 on average.

\item \textit{Understanding}. For each game, participants had to answer two control questions following their decisions (see Appendix A6 for examples). Monitoring the understanding of instructions we allowed for repeated submissions, each time informing participants whether their entries were correct or incorrect. Our binary indicator of misunderstanding takes the value 1 for each subject providing more than three incorrect entries in either the Dictator Game (DG) or the Trust Game (TG). 85\% of those coded 1 struggled with questions on TG. The fraction of participants scoring 1 is lowest among students (15\%), but relatively high in both the broader population (43\%) and the MTurk sample (34\%). 

\item \textit{Surroundings during online participation}. We collected self-reported data on the physical and social surrounding during online participation. Most online subjects participated from their home, although this rate is significantly smaller for the two student samples (62\%) than for either the broader population (85\%) or the MTurk sample (87\%). Only a few reported that others were observing them while making their decisions: Rates are 9\% for both students and crowdworkers, and 6\% for the broader population. 

\item \textit{Decision sequence}. To account for sequence effects, we include in our regressions a binary variable indicating whether the current decision was not the focal subject's first. Note that we randomized participants to specific sequences of games and first- and second-mover roles. 
\end{description}

The tabulation finally demonstrates effective randomization of student participants to modes of data collection (see columns ``a vs c'' and ``b vs d''). With the exception of age ($p=$.026 for the Munich pool), differences in socio-demographics between lab and online participants are non-significant.


% TABLE A1 ##################################################
\begin{landscape}
\begin{table}[h]
\begin{center}
{{\bf Table A1.} Socio-demographics across samples.}\\
\vspace{0.4cm}
\begin{footnotesize}
\begin{tabular}{llrrrrrrrr}
\toprule
 & & \multicolumn{2}{c}{Study 1} & & \multicolumn{2}{c}{Study 2} & & & \\
 & & \multicolumn{2}{c}{Lab} & & \multicolumn{2}{c}{Online} & & & \\
  \cmidrule(r){3-4} \cmidrule(r){6-7}   
 & & \multicolumn{1}{c}{(a)} & \multicolumn{1}{c}{(b)} & \multicolumn{1}{c}{a vs b} & \multicolumn{1}{c}{(c)} & \multicolumn{1}{c}{(d)} & \multicolumn{1}{c}{c vs d} & \multicolumn{1}{c}{a vs c} & \multicolumn{1}{c}{b vs d} \\
Variable  &  Measure   & \multicolumn{1}{c}{Leipzig} & \multicolumn{1}{c}{Munich} & $p$  & \multicolumn{1}{c}{Leipzig} & \multicolumn{1}{c}{Munich} & $p$ & $p$ &  $p$ \\
\midrule
Gender & Female (0,1) & 0.70 & 0.66 & .279 & 0.68 & 0.70 & .690 & .746 & .353 \\
Age & Years since birth & 22.34 & 22.21 & .553 & 22.31 & 21.53 & .037 & .920 & .026 \\
Students' major & Economics (0,1) & 0.12 & 0.15 & .209 & 0.10 & 0.12 & .568 & .524 & .419 \\
& Humanities (0,1) & 0.47 & 0.37 & .006 & 0.53 & 0.43 & .132 & .250 & .227 \\
& Other (0,1) & 0.41 & 0.48 & .061 & 0.37 & 0.44 & .244 & .433 & .513 \\
Employment & Side job (0,1) & 0.51 & 0.63 & .001 & 0.48 & 0.64 & .009 & .498 & .789 \\
Income & Monthly disposable income & 879.85 & 1290.88 & <.001 & 841.25 & 1253.13 & <.001 & .177 & .268 \\
Parenthood & $\geq$1 Child (0,1) & 0.02 & 0.01 & .432 & 0.01 & 0.01 & .967 & .218 & .606 \\
Experience & Number of prior lab experiments & 0.52 & 2.61 & <.001 & 0.34 & 1.64 & .002 & .286 & .062 \\
Control questions & $>$3 Mistakes in DG or TG (0,1) & 0.13 & 0.17 & .082 & 0.12 & 0.16 & .459 & .905 & .663 \\
Online participation & At home (0,1) &  &  &  & 0.67 & 0.57 & .120 &  &  \\
& Observed by others (0,1) &  &  &  & 0.06 & 0.13 & .056 &  &  \\
Decision sequence & DG not first decision (0,1) &0.68 & 0.64 & .278 & 0.66 & 0.68 & .714 & .632 & .464 \\
& TG trustor not first decision (0,1) &0.83 & 0.83 & .775 & 0.86 & 0.86 & .996 & .477 & .366 \\
$N$        &                          & 362 & 351 & & 122 & 115 & & &  \\
\midrule
 & & \multicolumn{1}{c}{Study 3} & & \multicolumn{1}{c}{Study 4} & & & \\
 & & \multicolumn{1}{c}{Nationwide} & & \multicolumn{1}{c}{MTurk} & & & \\
  \cmidrule(r){3-3} \cmidrule(r){5-5}   
 & & \multicolumn{1}{c}{(e)} & \multicolumn{1}{c}{c+d vs e} & \multicolumn{1}{c}{(f)} & \multicolumn{1}{c}{c+d vs f} & \multicolumn{1}{c}{e vs f} & \\
Variable  &  Measure   & & $p$ & & $p$ & $p$ & &  \\
\midrule
Gender & Female (0,1) & 0.49 & <.001 & 0.35 & <.001 & <.001 \\
Age & Years since birth & 44.61 & <.001 & 32.98 & <.001 & <.001 \\
Education & $\geq$High-school diploma (0,1) & 0.60 &  & 0.90 &  & <.001 \\
& Currently student (0,1) & 0.09 &  & 0.12 &  & .035 \\
Employment & Fully employed (0,1) & 0.58 & .534 & 0.69 & <.001 & <.001 \\
Income & Monthly disposable income & 2727.03 & <.001 & 1561.55 & <.001 & <.001 \\
Parenthood & $\geq$1 Child (0,1) & 0.57 & <.001 & 0.43 & <.001 & <.001 \\
Experience & Number of prior lab experiments & 1.18 & .410 & 65.52 & .005 & .005 \\
Control questions & $>$3 Mistakes in DG or TG (0,1) & 0.43 & <.001 & 0.34 & <.001 & <.001 \\
Online participation & At home (0,1) & 0.85 & <.001 & 0.87 & <.001 & .321 \\
& Observed by others (0,1) & 0.06 & .128 & 0.09 & .970 & .034 \\
Decision sequence & DG not first decision (0,1) &0.66 & .955 & 0.50 & <.001 & <.001 \\
& TG trustor not first decision (0,1) &0.67 & <.001 & 0.50 & <.001 & <.001 \\
$N$        &                          & 1,223 & & 491 & & & & &  \\
\bottomrule
\end{tabular}
\end{footnotesize}
\end{center}
\begin{tablenotes}[flushleft] \footnotesize
\vspace{-.2cm}
\item \hspace{.3cm} \textit{Note:} We report means and $p$-values from $t$-tests for between-sample differences.
\end{tablenotes}
\end{table}
\end{landscape}
 


\subsection*{A2 Correlates of Elicited Behavior}

\noindent The conditional means reported in the main text are predicted values ($\hat Y$) for each Study obtained from pooled OLS regressions. Table A2 displays these models. The dependent variable is first-mover behavior in either the DG or TG. We allowed individual transfers in each game to be multiples of 10\% of the endowment (including 0\%). Hence, $Y\in[0,100]$. Because our dependent variables are both left and right censored we also ran tobit regressions, which yield comparable results. We repeat the predicted values mentioned in the text at the top of the table. The lower part shows how elicited behavior correlates with socio-demographic characteristics and how properties of our design affect subjects' choices. The reported coefficients rest on non-experimental variation and remain descriptive, even when controlling for all known confounders.  

First, there are apparent differences between games regarding the potential influence of individual characteristics: Dictator behavior appears amenable to socio-demographic influence. TG, on the other hand, remains less affected by individual characteristics. Differences in model determination ($R^2$) reflect this fact.


% TABLE A2 ################################################## 
\begin{table}[t!]
\begin{center}
{{\bf Table A2.} Correlates of elicited behavior}\\
\vspace{0.4cm}
\begin{footnotesize}
\begin{tabular}{l l D{.}{.}{4} D{.}{.}{4} c D{.}{.}{4} D{.}{.}{4} }
\toprule
& & \multicolumn{2}{c}{DG} && \multicolumn{2}{c}{TG} \\
\cmidrule(r){3-4}   \cmidrule(r){6-7}
Predicted means & & \multicolumn{2}{c}{$\hat Y$} & & \multicolumn{2}{c}{$\hat Y$} \\
\midrule
Study 1         & Leipzig (lab)    & \multicolumn{2}{c}{42.296} && \multicolumn{2}{c}{52.379} \\
                & Munich (lab)     & \multicolumn{2}{c}{36.377} && \multicolumn{2}{c}{48.607} \\
Study 2         & Leipzig (online) & \multicolumn{2}{c}{42.938} && \multicolumn{2}{c}{48.261} \\
                & Munich (online)  & \multicolumn{2}{c}{35.814} && \multicolumn{2}{c}{48.554} \\
Study 3         & Nationwide       & \multicolumn{2}{c}{47.691} && \multicolumn{2}{c}{58.808} \\
Study 4         & MTurk            & \multicolumn{2}{c}{33.721} && \multicolumn{2}{c}{42.371} \\
\midrule
& & \multicolumn{1}{c}{$\beta$} & \multicolumn{1}{c}{$t$} && \multicolumn{1}{c}{$\beta$} & \multicolumn{1}{c}{$t$} \\
\cmidrule(r){3-4}   \cmidrule(r){6-7}
Gender          & Female           & 0.583 & .77 && -5.674$$^{***}$$ & 5.01 \\
Age             & 18--22 (reference) & & && & \\
                & 23--29            & -4.445$$^{***}$$ & 4.13 && -1.639 & .99 \\
                & 30--45            & -4.136$$^{*}$$ & 2.41 && -4.387 & 1.80 \\
                & $\geq$46          & -3.982$$^{*}$$ & 2.25 && -6.585$$^{*}$$ & 2.54 \\
Students' major & Other (reference) & & && & \\
                & Economics        & -10.890$$^{***}$$ & 5.23 && -8.325$$^{*}$$ & 2.57 \\
                & Humanities       & 2.695$$^{*}$$ & 2.37 && -1.790 & .95 \\
Education       & $\geq$High-school diploma & 0.263 & 0.27 && -0.398 & .28 \\
                & Currently student& -2.721 & 1.31 && 1.482 & .56 \\
Income          & log(Monthly disposable income) & -2.018$$^{*}$$ & 2.50 && -0.714 & .76 \\
Employment      & Fully employed   & -0.540 & .69 && -1.966 & 1.70 \\
Parenthood      & $\geq$1 Child    & 1.811 & 1.68 && 0.329 & 1.22 \\
Experience      & Number of prior lab experiments                 & -0.005$$^{***}$$ & 6.34 && -0.003 & 1.25 \\
Control questions & >3 Mistakes in DG or TG  & 4.350$$^{***}$$ & 5.30 && -0.473 & .42 \\
Online participation & At home     & -1.429 & 1.34 && -0.500 & .31 \\
                & Observed by others & 4.248$$^{*}$$ & 2.26 && 4.413$$^{*}$$ & 2.00 \\
Decision sequence & Current decision not first & -1.575$$^{*}$$ & 2.12 && -4.504$$^{***}$$ & 3.88 \\
\midrule
$N$ &  &  \multicolumn{2}{c}{2,664}  && \multicolumn{2}{c}{2,664}  \\
\(R^{2}\) &  &  \multicolumn{2}{c}{0.139}  && \multicolumn{2}{c}{0.059}  \\
\bottomrule
\end{tabular}
\end{footnotesize}
\end{center}
\begin{tablenotes}[flushleft] \footnotesize 
\item \hspace{.5cm} \textit{Note:} OLS regressions on first-mover behavior in the Dictator Game (DG) and the Trust Game (TG), 
\item \hspace{.5cm} respectively. We report unstandardized coefficients and $t$-values calculated from robust standard  
\item \hspace{.5cm} errors. $^{***}$ $p$<.001, $^{**}$ $p$<.01, $^{*}$ $p$<.05.
\end{tablenotes}
\end{table}
%###############################################################


Second, we find noteworthy results for single variables. Women, although behaving similarly to men in DG, are significantly less trusting in TG ($p$<.001). Compared to subjects aged 18--22, older participants share considerably less in both DG and TG. For the latter game, this difference is only significant for those aged 46 and older ($p$=.011). With respect to students' study field, our results are consistent with prior evidence (Etzioni 2015), indicating that economics majors behave more selfishly in incentivized games: Compared to majors in other areas, they give almost 11.0 percentage points less of their endowment in DG ($p$<.001) and transfer 8.3 percentage points less in TG ($p$=.010). Students of the humanities, in contrast, give 2.7 percentage points more in DG ($p$=.018) than their counterparts from other disciplines. Affluent participants, in turn, are less giving: A 10\% higher disposable income associates with 0.2 percentage points lower dictator allocations ($p$=.013). Again, there is no such association in TG. Experimental experience, finally, correlates negatively with dictator allocations ($p$<.001). This finding is in line with prior results suggesting that frequent participation in social experiments provides the opportunity to calibrate one's responses and to arrive at behavior more consistent with the standard economic theory (Levitt and List 2007; Rand et al. 2014). In our data, however, this association is extremely weak (with each prior participation average allocation decreases by 0.005 percentage points) and absent for prosocial behavior as measured in TG. 

Third, we show how specific properties of our design correlate with  participants' choices. Subjects having difficulties in understanding the instructions exhibit considerably more prosocial behavior in DG ($p$<.001) but not in TG ($p$=.676). We address the crucial issue of comprehension in Appendix A3. Here, we stress the importance of controlling for differences in understanding to attain conditional means unaffected by some participants' faulty responses. Online subjects being observed by others during participation feature higher rates of prosocial behavior than those making their decisions in isolation ($p$=.024 in DG, $p$=.046 in TG). Finally, our analyses control for the sequence of games and roles (note that this variable is a randomized treatment). Not making the focal decision at first has a significant negative effect on prosocial behavior in both DG ($p$=.034) and TG ($p$<.001). This effect is most pronounced for placing trust, where having had previous decisions reduces sharing by 4.5 percentage points on average.   


\subsection*{A3 Comprehension}

\noindent In our studies, we place participants into decision situations in which making mistakes and showing prosocial behavior are, on average, confounded (Andreoni 1995; Recalde, Riedl, and Vesterlund 2018): Ambiguous individual responses in the middle of the choice set indicate sharing rates of 50\% of the endowment. The same holds for the average over many random responses on a 0--100\% continuum. Hence, ``mistakes and non-standard preferences move in the same direction (away from predictions for perfectly optimizing and selfish agents)'' (Fr\'echette 2016:472).

To test whether difficulties in understanding drive prosocial choices in our nationwide sample, we randomized participants in Study 3 into a time-limit treatment. Under \textit{time pressure}, we asked 50\% of our participants, after they had read their instructions, to take their decisions within 10 seconds in DG and within 15 seconds in TG, adjusting time pressure for the complexity of the decision situation. 17.6\% of exposed subjects did not comply with our time limit; to avoid selection bias (cf., Tingh\"og et al. 2013), we allowed entries outside the time frame and include non-compliers in our analysis. The other half faced \textit{time delay}, under which they could only take each decision after a waiting time of 20 seconds.

% Figure A1 Comprehension ############################################
\begin{figure}[t!]
\begin{center}
\caption*{Figure A1: Treatment effects of time pressure}
\includegraphics[scale=.5]{figA1}
\end{center}
\begin{tablenotes}[flushleft] \footnotesize 
\item \textit{Note:} Blank bars show unconditional means of first-mover transfers under time delay in the Dictator Game (DG) and the Trust Game (TG), respectively. Shaded bars represent unconditional means under time pressure. We include 95\% confidence intervals and two pairwise comparisons ($t$-tests). n.s.=nonsignificant.
\end{tablenotes}
\end{figure}

If differences in comprehension explain prosocial behavior in our broader population sample, behavior should map students' behavior more closely under the time-delay condition, permitting active deliberation and reconsideration of instructions. Under time pressure, one can plausibly assume that participants will deliberate less and make more mistakes. The latter should evoke random responses and thus move sample averages toward the middle of the choice set.

We find no statistically significant effect of the time-pressure treatment in either DG or TG (Figure A1), suggesting that differences in comprehension do not explain higher rates of prosocial behavior among the broader population. 


\newpage

\subsection*{A4 Replication: Proportions of Nonzero Transfers}

\noindent Differences between our samples' mean transfers in DG and TG partly stem from the proportions of nonzero transfers. In contrast to the standard economic theory, which predicts zero transfers in both decision situations (e.g., Engel 2011, Johnson and Mislin 2011), 90.5\% of our subjects shared positive amounts in DG and 92.8\% invested in TG. Confirming our results, we find behavioral differences similar to our main findings when, alternatively, focusing on proportions of nonzero transfers (Figure A2). We report $p$-values of two-sided $z$-tests. 


% Figure A2 Nonzero ############################################
\begin{figure}[h!]
\begin{center}
\caption*{Figure A2: Proportions of Nonzero Transfers}
\begin{minipage}[b]{0.5\textwidth}
\centering
\includegraphics[scale=.5]{figA2a}
\end{minipage}%
\begin{minipage}[b]{0.5\textwidth}
\centering
\includegraphics[scale=.5]{figA2b}
\end{minipage}%
\end{center}
\begin{tablenotes}[flushleft] \footnotesize 
\item \textit{Note:} Shaded bars show unconditional proportions of nonzero first-mover transfers in the Dictator Game (DG) and the Trust Game (TG), respectively. Blank bars represent conditional proportions obtained from logistic regressions keeping underlying socio-demographics constant. We include 95\% confidence intervals and seven pairwise comparisons ($z$-tests). $^{***}$ $p$<.001, $^{**}$ $p$<.01, $^{*}$ $p$<.05, n.s.=nonsignificant.
\end{tablenotes}
\end{figure}


Among the Leipzig students who participated in lab sessions, 94.5\% shared positive amounts in DG; this rate is 84.3\% in Munich. This difference between student pools remains when controlling for socio-demographics ($z$=3.23, $p$=.001). In TG, the difference is smaller (95.6\% in Leipzig and 89.7\% in Munich transferred positive amounts), but---in contrast to the results on mean transfers---the difference remains significant under conditioning on socio-demographics ($z$=2.10, $p$=.036). Corroborating our finding for mean transfers, pool differences in the rates of nonzero transfers are larger in DG.

Again, we find no mode effect. Within locations, rates of nonzero transfers in online sessions are similar to and not significantly different from those in the laboratory (DG in Leipzig $z$=0.14, $p$=.891 and in Munich $z$=0.24, $p$=.810; TG in Leipzig $z$=0.09, $p$=.925 and in Munich $z$=0.24, $p$=.814). 

The broader population sample, again, shows the highest rates of prosocial behavior in both decision situations---even when holding socio-demographics constant: 97.4\% transfer a positive amount in DG (compared to students online 88.6\%; $z$=3.48, $p$<.001) and 98.2\% in TG ($z$=3.68, $p$<.001). Like before, our implementation at MTurk returns the lowest rates of prosocial behavior in both decision situations: Adjusted for differences in socio-demographics, only 78.2\% transfer a positive amount in DG and 81.8\% in TG. In DG, these rates are significantly lower than those obtained in both the broader population ($z$=9.48, $p$<.001) and the pooled online student sample ($z$=2.18, $p$=.029). In TG, only the difference to the broader population sample is significant ($z$=9.45, $p$<.001). 



\subsection*{A5 Replication: Trustees and Ultimatum Game}

\noindent We can further substantiate our findings using second-mover behavior in TG. After receiving a monetary transfer (partly from a trustor and partly from the experimenter), a trustee can decide how much of the pie (0--100\%) she passes back to the trustor. To elicit back-transfers in the TG, we employed the strategy method (Rauhut and Winter 2010), asking trustees to respond to all possible transfers. We refrained from using the standard measure of trustee behavior (second player's response to actual transfer) in order not to censor the response variable. 

In Studies 1 and 2, we further ran the Ultimatum Game (UG) as a third decision situation. We dropped UG in our non-student Studies 3 and 4 to sustain online participants' attentiveness and to cap processing times to ranges typical for the respective panel or platform. In UG, a proposer receives a stake and can decide how much of the pie (0--100\%) she offers to a responder. The responder can then accept (and both receive their share) or decline the offer (and both receive nothing). In contrast to DG, UG introduces fear of sanction into first movers' decision situation. Proposers need to take into account responders' option of rejecting offers that fall short of a ``fair'' split. Responders' acceptance or rejection of offers, in turn, measures willingness to pay for the punishment of proposers' unfair behavior. Again, we measured response behavior in UG using the strategy method: Here, we asked second movers to accept or reject each feasible offer, allowing us to determine responders' minimal acceptable offer (MAO). 


% Figure A3 TG2, UG ############################################
\begin{figure}[t!]
\begin{center}
\caption*{Figure A3: Quantitative results from additional decision situations.}
\begin{minipage}[b]{0.5\textwidth}
\centering
\includegraphics[scale=.5]{figA3a}
\end{minipage}%
\begin{minipage}[b]{0.5\textwidth}
\centering
\includegraphics[scale=.5]{figA3b}
\end{minipage}%
\end{center}
\begin{tablenotes}[flushleft] \footnotesize 
\item \textit{Note:} Shaded bars show unconditional means of second-mover transfers in the Trust Game (TG) and first-mover and second-mover behavior in the Ultimatum Game (UG). Blank bars represent conditional means keeping underlying socio-demographics constant. We include 95\% confidence intervals and seven pairwise comparisons ($t$-tests).  $^{***}$ $p$<.001, $^{**}$ $p$<.01, $^{*}$ $p$<.05, n.s.=nonsignificant.
\end{tablenotes}
\end{figure}


Figure A3 summarizes our findings for second movers in TG and for both roles in UG. Pooled across Studies 1--4, trustees return on average 43.2\% of their received transfers. In his compendium on experimental games, Camerer (2003:86-88) reports trustees as typically returning about 100\% of trustors' unmultiplied investment. This, depending on the multiplication factor, amounts to 33--50\% of responders' actual received transfer. Pooled across Studies 1 and 2, mean offer in UG is 45.9\% of the individual endowment. Responders' MAO on average amounts to 27.4\%. A meta-analysis of 75 UG-results reports mean offers of 40.4\% (Oosterbeek, Sloof, and van de Kuilen 2004), with responders typically rejecting offers below 20\% about half of the time (Camerer 2003:49). 

Most important for our study is that the transportability of quantitative results fails for another laboratory measure of prosocial behavior: For trustees' back-transfers, four out of seven pairwise comparisons reveal significant differences. On the other hand, for the decision situations faced by both UG proposers and responders, not a single pairwise comparison is significant. 

In our two student pools (Studies 1 and 2), we find significantly different rates of trustees' back-transfers ($t$=2.60, $p$=.009). In contrast, \textit{pool generalizability} holds for the UG: Both proposers' offers ($t$=1.13, $p$=.258) and responders' MAOs ($t$=0.11, $p$=.911) are not significantly different between locations. The cross-location gap we were able to replicate for second movers in TG is absent for UG irrespective of whether we control for socio-demographic differences across students pools.  

With respect to \textit{sample generalizability}, trustees reproduce our earlier finding on the limited transportability of quantitative results: Back-transfers in the nationwide sample differ significantly from the student-online benchmark ($t$=2.98, $p$=.003). Similarly, comparing the student-online benchmark to participants at MTurk, we found \textit{context generalizability} violated ($t$=2.33, $p$=.020). These results further call into question the transportability of quantitative results in social science lab research. 

Corroborating our favorable result on \textit{mode generalizability}, we find no measurement effects of lab vs. online data collection (Study 2). At both locations, data collected from trustees ($t$=1.65, $p$=.100 in Leipzig; $t$=0.59, $p$=.557 in Munich), proposers ($t$=0.48, $p$=.630 in Leipzig; $t$=0.45, $p$=.653 in Munich), and responders ($t$=0.04, $p$=.969 in Leipzig; $t$=0.10, $p$=.918 in Munich) do not differ, on average, between lab and online sessions. 



\newpage

\subsection*{A6 Instructions}

\begin{figure}[h!]
\begin{center}
\caption*{Dictator Game Instructions}
\includegraphics[scale=.65]{A6a}
\end{center}
\end{figure}

\begin{figure}[h!]
\begin{center}
\caption*{Dictator Game Animation}
\includegraphics[scale=.65]{A6b}
\end{center}
\end{figure}

\begin{figure}[h!]
\begin{center}
\caption*{Dictator Game Decision}
\includegraphics[scale=.65]{A6c}
\end{center}
\end{figure}

\vspace{2cm}
\begin{figure}[h!]
\begin{center}
\caption*{Dictator Game Control Questions}
\includegraphics[scale=.65]{A6d}
\end{center}
\end{figure}


\newpage

\begin{figure}[h!]
\begin{center}
\caption*{Trust Game Instructions}
\includegraphics[scale=.65]{A6e}
\end{center}
\end{figure}

\begin{figure}[h!]
\begin{center}
\caption*{Trust Game Animation}
\includegraphics[scale=.65]{A6f}
\end{center}
\end{figure}

\begin{figure}[h!]
\begin{center}
\caption*{Trustor Decision}
\includegraphics[scale=.65]{A6g}
\end{center}
\end{figure}

\begin{figure}[h!]
\begin{center}
\caption*{Trustee Decision}
\includegraphics[scale=.55]{A6h}
\end{center}
\end{figure}

%\begin{figure}[h!]
%\begin{center}
%\caption*{Trust Game Control Questions}
%\includegraphics[scale=.5]{TG_control}
%\end{center}
%\end{figure}

\newpage


\subsection*{A7 Anonymization procedures in the two laboratories}
% Figure Anonymity ########################################################
\begin{figure}[h!]
\begin{center}
\begin{minipage}[b]{0.5\textwidth}
\centering
Leipzig 
\includegraphics[angle=270, scale=.25]{A7a}
\end{minipage}%
\begin{minipage}[b]{0.5\textwidth}
\centering
Munich 
\includegraphics[angle=270, scale=.25]{A7b}
\end{minipage}%

\begin{minipage}[b]{0.5\textwidth}
\centering
\includegraphics[angle=270, scale=.25]{A7c}
\end{minipage}%
\begin{minipage}[b]{0.5\textwidth}
\centering
\includegraphics[angle=270, scale=.25]{A7d}
\end{minipage}%

\begin{minipage}[b]{0.5\textwidth}
\centering
\includegraphics[scale=.25]{A7e}
\end{minipage}%
\begin{minipage}[b]{0.5\textwidth}
\centering
\includegraphics[scale=.25]{A7f}
\end{minipage}%

\end{center}
\begin{tablenotes}[flushleft] \footnotesize 
\item \textit{Note:} The top row shows the low-anonymity condition (no blinds, payoff at the experimenter's desk). The middle row shows the blinds used to create anonymity toward other participants (standard anonymity). The bottom row shows our payment setup to create anonymity toward the experimenter (high anonymity). 
\end{tablenotes}
\end{figure}

\newpage
	
	
\singlespacing

\section*{References}
\begin{description}
\begin{footnotesize}     
\setlength{\itemsep}{-2.3pt}                                                                                         


\item Andreoni, James 1995. ``Cooperation in Public-goods Experiments: Kindness or Confusion?'' \textit{American Economic Review} 85(4):891-904.

\item Camerer, Colin F. 2003. \textit{Behavioral Game Theory: Experiments in Strategic Interaction}. New York: Sage.

\item Engel, Christoph 2011. ``Dictator Games: A Meta Study.'' \textit{Experimental Economics} 14(4):583-610.

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\item Fr\'echette, Guillaume R. 2016. ``Experimental Economics Across Subject Populations.'' Pp. 435-80 in \textit{The Handbook of Experimental Economics, Vol. 2.}, edited by J. Kagel and A. Roth. Princeton, NJ: Princeton University Press.

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\item Recalde, Maria P., Arno Riedl, and Lise Vesterlund 2018. ``Error Prone Inference from Response Time: The Case of Intuitive Generosity in Public-good Games.'' \textit{Journal of Public Economics} 160:132-47.

\item  Tingh\"og, Gustav, David Andersson, Caroline Bonn, Harald B\"ottiger, Camilla Josephson, Gustaf Lundgren, Daniel V\"astfj\"all, Michael Kirchler, and Magnus Johannesson 2013. ``Intuition and Cooperation Reconsidered.'' \textit{Nature} 498:E1-E2.

\item Wiepking, Pamala and Ren\'e Bekkers 2012. ``Who Gives? A Literature Review of Predictors of Charitable Giving. Part Two: Gender, Family Composition and Income.'' \textit{Voluntary Sector Review} 3(2):217-45.

\end{footnotesize}
\end{description}


\end{document}
