Rounding is a common phenomenon when subjects provide an answer to an open-ended question, both in experimental tasks and in survey responses. From a statistical perspective, rounding implies that the measured variable is a coarsened version of the underlying continuous target variable. Since the coarsening process is non-random, inference from rounded data is generally biased. Despite the potentially severe consequences of rounding, little is known about its causes. In this paper, we focus on subjects’ uncertainty about the target variable as one potential cause for rounding behavior. We present a novel experimental method that induces uncertainty in a controlled way, thus providing causal evidence for the effect of subjects’ uncertainty on the extent of rounding. Then, we specify and estimate a mixture model that relates uncertainty and rounding. The results suggest that an increase in the exogenous level of uncertainty translates into higher variance of the subjects’ beliefs, which in turn results in more rounding.

We use instrumental variables for estimating the causal effect of beliefs on contributions in repeated public good games. The effect is about half as large as suggested by ordinary least squares. Thus, we present evidence that beliefs have a causal effect on contributions, but also that beliefs are endogenous. We compare the causal, belief-based model of contributions to alternative models based on matching the previous contributions of others and responding to one’s deviation from the average in the previous round. The causal, belief-based model performs well, indicating that beliefs have a central role in determining contributions.

The Stochastic Becker-DeGroot-Marschak (SBDM) mechanism is a theoretically elegant way of eliciting incentive-compatible beliefs under a variety of risk preferences. However, the mechanism is complex and there is concern that some participants may misunderstand its incentive properties. We use a two-part design to evaluate the relationship between participants’ probabilistic reasoning skills, task complexity, and belief elicitation. We first identify participants whose decision-making is consistent and inconsistent with probabilistic reasoning using a task in which non-Bayesian modes of decision-making lead to violations of stochastic dominance. We then elicit participants’ beliefs in both easy and hard decision problems. Relative to Introspection, there is less variation in belief errors between easy and hard problems in the SBDM mechanism. However, there is a greater difference in belief errors between consistent and inconsistent participants. These results suggest that while the SBDM mechanism encourages individuals to think more carefully about beliefs, it is more sensitive to heterogeneity in probabilistic reasoning. In a follow-up experiment, we also identify participants with high and low fluid intelligence with a Raven task, and high and low proclivities for cognitive effort using an extended Cognitive Reflection Test. Although performance on these tasks strongly predict errors in both the SBDM mechanism and Introspection, there is no significant interaction effect between the elicitation mechanism and either ability or effort. Our results suggest that mechanism complexity is an important consideration when using elicitation mechanisms, and that participants’ probabilistic reasoning is an important consideration when interpreting elicited beliefs.

This paper reports an experiment designed to assess the influence of workplace arrangements on the reactions to (the absence of) control. We compare behavior in an Internet and a laboratory principal-agent game where the principal can control the agent by implementing a minimum effort requirement. Then the agent chooses an effort costly to her but beneficial to the principal. Our design captures meaningful differences between working from home and working at the office arrangements. Online subjects enjoy greater anonymity than lab subjects, they interact in a less constrained environment than the laboratory, and there is a larger physically-oriented social distance between them. Control is significantly more effective online than in the laboratory. Positive reactions to the principal’s choice not to control are observed in both treatments, but they are significantly weaker online than in the laboratory. Principals often choose the highest control level, which maximizes their earnings.

In many experiments, particularly individual choice experiments, experimenters ask many questions to the subjects and use the random lottery incentive mechanism to give an incentive to the subjects. That is, the experimenter, at the end of the experiment, picks just one of the questions, plays out that question, and pays the subject on the basis of this one question. The idea is that subjects should separate the various questions and reply to each as if it were a separate question—in isolation from all the other questions in the experiment. This procedure is methodologically sound if the subjects behave in accordance with Expected Utility (EU) theory, since this theory says that the best procedure for the subjects is to separate the various questions. However, if there is any doubt as to whether the subjects obey EU theory, and particularly if the experiment is designed to test whether the behaviour of the subjects is in accordance with EU, this incentive mechanism is open to criticism. Indeed many referees use this argument against the research. The response that the subjects may not respect EU, yet still separate the various questions, is obviously open to objection and generally it is not clear whether this response is valid or not. There have been two direct tests of this separation hypothesis (by Starmer and Sugden (1991) and by Cubitt et al. (1998), which suggest that it is valid, but further evidence is required. This paper provides a further, stronger, test of this hypothesis: we confront the two stories—(1) that the subjects answer the various questions separately, and (2) that the subjects respond to the experiment as a whole—using experimental data from an experiment in which the random lottery incentive mechanism was used. Our analysis shows that it would appear that subjects do answer as if they were separating the questions. This should be considered reassuring for those experimenters who use the random lottery incentive mechanism.

The paper performs an in-depth comparison of four incentivised risk elicitation tasks. We show by means of a simulation exercise that part of the often observed heterogeneity of estimates across tasks is due to task-specific measurement error induced by the mere mechanics of the tasks. We run a replication experiment in a homogeneous subject pool using a between subjects one-shot design. Results shows that the task estimates vary over and above what can be explained by the simulations. We investigate the possibility the tasks elicit different types of preferences, rather than simply provide a different measure of the same preferences. In particular, the availability of a riskless alternative plays a prominent role helping to explain part of the differences in the estimated preferences.

Strictly proper scoring rules are designed to truthfully elicit subjective probabilistic beliefs from risk neutral agents. Previous experimental studies have identified two problems with this method: (i) risk aversion causes agents to bias their reports toward the probability of $1/2$, and (ii) for moderate beliefs agents simply report $1/2$. Applying a prospect theory model of risk preferences, we show that loss aversion can explain both of these behavioral phenomena. Using the insights of this model, we develop a simple off-the-shelf probability assessment mechanism that encourages loss-averse agents to report true beliefs. In an experiment, we demonstrate the effectiveness of this modification in both eliminating uninformative reports and eliciting true probabilistic beliefs.

We report four repetitions of Falk and Kosfeld's (Am. Econ. Rev. 96(5):1611—1630, 2006) low and medium control treatments with 476 subjects. Each repetition employs a sample drawn from a standard subject pool of students and demographics vary across samples. We largely confirm the existence of hidden costs of control but, contrary to the original study, hidden costs of control are usually not substantial enough to significantly undermine the effectiveness of economic incentives. Our subjects were asked, at the end of the experimental session, to complete a questionnaire in which they had to state their work motivation in hypothetical scenarios. Our questionnaires are identical to the ones administered in Falk and Kosfeld's (Am. Econ. Rev. 96(5):1611—1630, 2006) questionnaire study. In contrast to the game play data, our questionnaire data are similar to those of the original questionnaire study. In an attempt to solve this puzzle, we report an extension with 228 subjects where performance-contingent earnings are absent i.e. both principals and agents are paid according to a flat participation fee. We observe that hidden costs significantly outweigh benefits of control under hypothetical incentives.

We show how bounds around preferences parameters can be estimated under various levels of assumptions concerning the beliefs of senders in the investment game. We contrast these bounds with point estimates of the preference parameters obtained using non-incentivized subjective belief data. Our point estimates suggest that expected responses and social preferences both play a significant role in determining investment in the game. Moreover, these point estimates fall within our most reasonable bounds. This suggests that credible inferences can be obtained using non-incentivized beliefs.

We replicate three tasks for which Gneezy, List and Wu (Q. J. Econ. 121(4):1283—1309, 2006) document the so-called uncertainty effect: People value a binary lottery over non-monetary outcomes less than other people value the lottery's worse outcome. While the authors implement verbal lottery descriptions, we use a physical lottery format and also provide subjects with complete information about the goods they are to value. We observe for all three pricing tasks that subjects’ willingness to pay for the lottery is significantly higher than other subjects’ willingness to pay for the lottery's worse outcome.

Much experimental effort has been expended in attempts to establish the relative superiority of Expected Utility theory and the many recently-developed alternatives as descriptions of the behaviour of subjects in risky choice decision problems. The cumulative evidence shows clearly that there is a great deal of noise in the experimental data, which makes it difficult to identify the ‘best’ description of such behaviour. This paper reports on an experiment which seeks to determine whether such noise is relatively transitory and decays with experience and repetition, and thus whether a clearly ‘best’ theory emerges as a result of such repetition. We find that for some subjects this does indeed appear to be the case, while for other subjects the noise remains high and the identification of the underlying preference function remains difficult.

This paper discusses aspects of recruiting subjects for economic laboratory experiments, and shows how the Online Recruitment System for Economic Experiments can help. The software package provides experimenters with a free, convenient, and very powerful tool to organize their experiments and sessions.

This paper empirically compares the use of straightforward verses more complex methods to estimate public goods game data. Five different estimation methods were compared holding the dependent and explanatory variables constant. The models were evaluated using a large out-of-sample cross-country public goods game data set. The ordered probit and tobit random-effects models yielded lower p values compared to more straightforward models: ordinary least squares, fixed and random effects. However, the more complex models also had a greater predictive bias. The straightforward models performed better than expected. Despite their limitations, they produced unbiased predictions for both the in-sample and out-of-sample data.

Studying the likelihood that individuals cheat requires a valid statistical measure of dishonesty. We develop an easy empirical method to measure and compare lying behavior within and across studies to correct for sampling errors. This method estimates the full distribution of lying when agents privately observe the outcome of a random process (e.g., die roll) and can misreport what they observed. It provides a precise estimate of the mean and confidence interval (offering lower and upper bounds on the proportion of people lying) over the full distribution, allowing for a vast range of statistical inferences not generally available with the existing methods.

Protocol analysis, in the form of concurrent verbal ‘thinking aloud’ reports, is a method of collecting and analyzing data about cognitive processes. This approach can help economists in evaluating competing theories of behavior and in categorizing heterogeneity of thinking patterns. As a proof of concept, I tested this method in the context of a guessing game. I found that concurrent think aloud protocols can inform us about individual’s thought processes without affecting decisions. The method allowed me to identify game theoretic thinking and heterogeneous approaches to unravelling the guessing game. The think aloud protocol is inexpensive and scalable, and it is a useful tool for identifying empirical regularities regarding decision processes.

Laboratory experiments have been often replaced by online experiments in the last decade. This trend has been reinforced when academic and research work based on physical interaction had to be suspended due to restrictions imposed to limit the spread of Covid-19. Therefore, data quality and results from web experiments have become an issue which is currently investigated. Are there significant differences between lab experiments and online findings? We contribute to this debate via an experiment aimed at comparing results from a novel online protocol with traditional laboratory settings, using the same pool of participants. We find that participants in our experiment behave in a similar way across settings and that there are at best weakly significant and quantitatively small differences in behavior observed using our online protocol and physical laboratory setting.

We provide evidence on the extent to which survey items in the Preference Survey Module and the resulting Global Preference Survey measuring social preferences—trust, altruism, positive and negative reciprocity—predict behavior in corresponding experimental games outside the original participant sample of Falk et al. (Manag Sci, 2022. https://doi.org/10.1287/mnsc.2022.4455). Our results, which are based on a replication study with university students in Tehran, Iran, are mixed. While quantitative items considering hypothetical versions of the experimental games correlate significantly and economically meaningfully with individual behavior, none of the qualitative items show significant correlations. The only exception is altruism where results correspond more closely to the original findings.

When making decisions, people tend to look back and forth between the alternatives until they eventually make a choice. Eye-tracking research has established that these shifts in attention are strongly linked to choice outcomes. A predominant framework for understanding the dynamics of the choice process, and thus the effects of attention, is sequential sampling of information. However, existing methods for estimating the attention parameters in these models are computationally costly and overly flexible, and yield estimates with unknown precision and bias. Here we propose an estimation method that relies on a link between sequential sampling models and random utility models (RUM). This method uses familiar econometric tools (i.e., logistic regression) and yields estimates that appear to be unbiased and relatively precise compared to existing methods, in a small fraction of the computation time. The RUM thus appears to be a useful tool for estimating the effects of attention on choice.

For simple prospects routinely used for certainty equivalent elicitation, random expected utility preferences imply a conditional expectation function that can mimic deterministic rank-dependent preferences. That is, a subject with random expected utility preferences can have expected certainty equivalents exactly like those predicted by rank-dependent probability weighting functions of the inverse-s shape discussed by Quiggin (J Econ Behav Organ 3:323–343, 1982) and advocated by Tversky and Kahneman (J Risk Uncertainty 5:297–323, 1992), Prelec (Econometrica 66:497–527, 1998) and other scholars. Certainty equivalents may not nonparametrically identify preferences: Their conditional expectation (and critically, their interpretation) depends on assumptions concerning the source of their variability.

Garbarino et al. (J Econ Sci Assoc. https://doi.org/10.1007/s40881-018-0055-4, 2018) describe a new method to calculate the probability distribution of the proportion of lies told in “coin flip” style experiments. I show that their estimates and confidence intervals are flawed. I demonstrate two better ways to estimate the probability distribution of what we really care about—the proportion of liars—and I provide R software to do this.