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Theory and Decision

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01-02-2014

Use of data on planned contributions and stated beliefs in the measurement of social preferences

Authors: Anna Conte, M. Vittoria Levati

Published in: Theory and Decision | Issue 2/2014

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Abstract

In a series of one-shot linear public goods game, we ask subjects to report their contributions, their contribution plans for the next period, and their first-order beliefs about their present and future partner. We estimate subjects’ preferences from plan data by a finite mixture approach and compare the results with those obtained from contribution data. Controlling for beliefs, which incorporate the information about the others’ decisions, we are able to show that plans convey accurate information about subjects’ preferences and, consequently, are good predictors of their future behavior.

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Survey questions are consequential if the “survey’s results are seen as potentially influencing an agency’s actions and the agent cares about the outcomes of those actions” (Carson and Groves 2007, p. 183).

We chose this protocol to minimize strategic effects from repeated play and to allow for revisions to beliefs only at the population level.

To simplify notation, we always refer to player $i$’s partner as $j$, although this is a different person in each period.

A similar procedure for incentivizing subjects to state a carefully considered, truthful plan has been applied by Barkan and Busemeyer (1999).

When convenient, we will equivalently use the notation $p_{\cdot ,t}^{t+1},\, t = 1, \ldots , 14$, to indicate contribution plans made in $t$ for $t+1$.

The instructions make clear that subjects have to predict the decisions of two different persons: the current-period partner ($\mathbf{b}_{i,t}^{t}$) and the next-period partner ($\mathbf{b}_{i,t}^{t+1}$).

To simplify presentation, players’ contributions in treatment $C$ will be sometimes referred to as “final” even though no distinction between final and planned contributions is made in $C$.

See Selten (1998) for an axiomatic characterization of the rule, and Offerman et al. (2009) for an experiment investigating its behavioral properties.

A similar rule has been used by, e.g., Offerman et al. (1996), Costa-Gomes and Weizsäcker (2008), and Rey-Biel (2009), although there exists no consensus among experimentalists about the optimal incentive mechanism for eliciting beliefs. Huck and Weizsäcker (2002) compare beliefs elicited via a quadratic scoring rule with beliefs elicited via a Becker-DeGroot-Marshak pricing rule, and find that the quadratic scoring rule yields more accurate beliefs.

The instructions are available from the authors upon request.

Because of our re-matching protocol, the numbers of statistically independent observations are 6 in $C$, 5 in $P_\mathrm{I}$, and 5 in $P_{\mathrm{{NI}}}$.

In particular, the one-period-ahead and final expected contributions are computed, respectively, as

$$\begin{aligned} E_{i,t-1}[c_{j,t}] = \frac{\sum \nolimits _{a=0}^{10} \left( a\times 10\right) \times b_{i,t-1}^{t}\left( a\right) }{100} \qquad \text{ and } \qquad E_{i,t}[c_{j,t}] = \frac{\sum _{a=0}^{10} \left( a\times 10\right) \times b_{i,t}^{t}\left( a\right) }{100}. \end{aligned}$$

To characterize the behavior of conditional cooperators, we could have used either a utility function à la Fehr and Smith (1999) or a different rule for $Y_{j,t}$ like, e.g., the final (one-period-ahead) expected contribution. We opted for our simple rule for three reasons: (a) finding the functional form that fits the data best is not one of the objectives of this article; (b) we wanted for the conditional cooperator type a behavioral rule as straightforward as the one used for the other two types; (c) finally, but most importantly, our data analysis suggests that about 50 % of the contributions, both final and planned, comply with such a rule.

Nevertheless, identification fails to achieve in the following cases: when one of the modes of $i$’s distribution of beliefs always corresponds to $a = 0$ and $i$ always chooses to contribute 0 (in this case, a conditional cooperator is indistinguishable from a selfish subject); when one of the modes of $i$’s distribution of beliefs always corresponds to the median of $i$’s contributions and $i$ always chooses to contribute exactly that amount (in that case, a conditional cooperator is indistinguishable from an altruist); when subjects change preferences over time.

See Moffatt and Peters (2001) and Loomes (2005).

To the best of our knowledge, this is the first time a tremble is estimated under such assumptions. We want the tremble probability to be individual-specific because this allows us to capture different kinds of behavior. There can be subjects who stick with their rule in all periods, subjects whose decisions are noisy at the beginning but not toward the end, and vice versa. Finally, there can be subjects whose decisions are extremely noisy throughout the entire game.

Details can be found in Train (2003).

In unreported analysis, we estimate the four models in Table 1 without time effects (i.e., constraining $b_{1}$ and $g_{1}$ to equal zero). Likelihood-ratio tests strongly reject the null hypothesis of no time effects (in all cases the $p$-values of the tests are $<$0.000). The regression results of these models are available from the authors upon request. We do not report the results here for two reasons: none of the conclusions concerning the main hypothesis under investigation changes when time effects are added to the mixture model; the models with time effects showed to be far superior on statistical grounds.

For this reason, we exclude six subjects from treatment $P_{\mathrm{{NI}}}$.

Similar inconsistencies, referred to as “instabilities of preferences,” are found and discussed in Wilcox (2007) and Conte and Hey (2013).

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Title: Use of data on planned contributions and stated beliefs in the measurement of social preferences
Authors: Anna Conte
M. Vittoria Levati
Publication date: 01-02-2014
Publisher: Springer US
Published in: Theory and Decision / Issue 2/2014
Print ISSN: 0040-5833
Electronic ISSN: 1573-7187
DOI: https://doi.org/10.1007/s11238-013-9365-4

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