Experimental Design Details

In an online experiment, the participants reveal their risk preferences (decision 1), make decisions in three investment games (decisions 2 to 4), and answer a set of questions. The “investment into returns game” represents the conventional scenario where the probability of success of an investment project is exogenously given and people invest (part of) their endowment to get a tripled return. The success of their investment is determined by a roll of a fair die. Instead of {1,2,3,4,5,6} dots, our die has a star on three of its sides and the remaining three sides are blank. The participant has therefore 50% chance to roll a star, in which case he/she triples their investment, and a 50% chance to roll an empty side, in which case he/she receives 0.

In the “investment into probability game”, the return of the game is exogenously given but the participants choose the probability with which they would like to play the game. The amount of money the participants decide to invest determines the number of sides with a star on a die. If the participant rolls a star, he/she wins a fixed amount of money (270 CZK or 10.36 Eur), otherwise, the return equals 0. The participant can choose from five different dice which differ in the number of stars they have on their sides (ranging from 1 star, in which case there is a 16.7% chance of winning, up to 5 stars, in which case the chance is 83.3%). The reason for having such non-standard dice is to ensure that everyone understands which die has a higher chance of winning even if they cannot calculate the probability of winning themselves.

At the beginning of the experiment, the participants are endowed with 150 CZK (approximately 5.75 Eur) which they can use for investment decisions(note that the minimum wage per hour is 90.5 CZK which is approximately 3.47 Eur; the average wage per hour is 221.5 CZK or approximately 8.49 Eur). The order of these two games is randomly selected. In the first step, half of the sample is randomly offered to play the Probability game first while the rest play the Return game first. This between-subject design represents a clear distinction between investment decisions in the two games, free from potential order effect. Random allocation ensures that the two groups are in expectations comparable in terms of observable well as unobservable characteristics. Within-subject design based on pooled decisions from Steps 1 and 2 helps us understand changes in investment decisions between the two games for each participant. To understand the level of understanding of the game instructions, the participants answer a set of control questions before making each investment decision. The participants are financially incentivized to answer the questions correctly.

Our theoretical findings predict that if we implement policies in which investments increase the probability of success, we shall observe risk-averse people either to invest all they have or nothing. In that case, we should see a unimodal distribution of investment choices in the return game and a bimodal distribution in the probability game, especially for the risk-averse individuals. We elicit participants’ willingness to take a risk using a set of 11 choices between a lottery and a safe option (Dohmen et al., 2011). The participants decide whether they prefer a lottery in which they could win 1,300 CZK (approximately 49.8 Eur) or 0 CZK, each with a 50% chance, or a safe option which increases by increments of 100 CZK from 0 in the first row up to 1,000 in the 11th row. We do not ask the participants to make a decision for each row separately. Instead, we ask them to reveal in which row their preferences switch (i.e., from which row they start preferring Option B over Option A). Later in the experiment, we also ask the participants a general question to self-evaluate themselves in terms of their willingness to take a risk. With a 10% probability, this decision is selected towards the final payment. In that case, the computer selects randomly one of the 11 rows. If the subject chose a lottery in the selected row, he/she will roll a die to determine the outcome. If the subject selected a safe option, he/she will be paid the corresponding amount of CZK.

We also predict that risk-averse agents should select a lottery with a higher probability of winning, rather than a lottery with the same probability but higher return. In the final “step-by-step game”, the participants are informed that the first fraction (30 CZK) of their endowment was invested for them such that they have a 16.7% chance of getting 270 CZK (10.35 Eur) and they are asked to make four sequential investment decisions. In each of the decisions, they are asked to invest an additional fraction (30 CZK) to either increase the chance of winning while keeping the return fixed or to increase their return while keeping the probability of success fixed. The expected returns in each of the four decisions are equal. Different combinations of four decisions represent 16 possible “decision paths”. The decision paths allow us to check whether the second-order stochastic dominance holds. After the participants reveal their decision paths, they make their last payoff relevant investment decision and decide how much of 150 CZK they would like to invest assuming the probabilities and returns are taken from their decision path.

Once the participants make their final decision in the Step-by-step game and answer a set of questions, they roll their dice to see the outcomes in each of the four decisions they made separately. While decision 1 is selected with a 10% probability, decisions 2 to 4 are selected with a 30% probability each. Only one of the investment outcomes will be selected for payment which is decided in the final roll of a dice.