We start our analysis by investigating the presence of procedural utility before the draw. Through linear regression, we related happiness to the type of lottery ticket people possessed (purchased, free or both) and to a series of control variables. To remove observed and unobserved time-invariant characteristics from the analysis, we used as dependent variable the change in happiness between survey 1 and survey 2, \(\varDelta H_{12,i}\). We assume the following relationship:

$$\begin{aligned} \varDelta H_{12,i} = \alpha _1 + \beta _1 F_{i}+ \beta _2 B_{i} + \beta _3 C_i + \beta _4 X_i + \beta _5 \varDelta S_{12,i} + \beta _6 \varDelta LS_i + \varepsilon _{12,i} \end{aligned}$$ (1)

where \(\alpha _1\) represents a vector of interview date fixed effects, i refers to an individual, F is a dummy variable for whether or not a free lottery ticket was received (but no lottery ticket was bought), B is a dummy variable with value 1 if no free lottery ticket was received but one was bought, C is a dummy variable with value 1 if the individual had received a free lottery ticket in addition to having bought one, and \(\varDelta\) indicates the first difference of a variable. Furthermore, X is a vector of personal and personality characteristics, S if a vector of survey characteristics and LS represents life satisfaction. Finally, \(\beta _1\) to \(\beta _6\) are our (vectors of) parameters and \(\varepsilon _{12}\) is an error term.

In case of procedural utility before the draw, we expect that the change in happiness between \(T_1\) and \(T_2\) is significantly larger for lottery participants than for non-lottery participants. Furthermore, we expect that the change in happiness between \(T_1\) and \(T_2\) is not significantly larger for lottery participants with a free ticket than for lottery participants with a purchased ticket. If there would be a difference, the increase in happiness could be related to a monetary transfer, i.e. receiving the lottery ticket for free.

Table 1 Parameter estimates change in happiness between \(T_1\) and \(T_2\) Full size table

Table 1 provides the OLS parameter estimates for the change in happiness between \(T_1\) and \(T_2\).Footnote 13 The first column shows the parameter estimates of the lottery ticket effect on the change in happiness without including control variables. On average, people with a lottery ticket report a significantly higher change in happiness score (Panel A), where there are no significant differences between players with only a free ticket, a free and purchased ticket, and only a purchased ticket (Panel B).Footnote 14 As shown in the second column, our results are robust to including several groups of control variables, i.e. personal characteristics, lottery behavior variables and survey characteristics. In the third column, we also control for the change in life satisfaction in the period between \(T_1\) and \(T_2\)—which can be considered a very conservative estimate of the lottery play effect. Even then, the effect of obtaining a lottery ticket on the change in happiness is positive and significant. All in all, we conclude that on a scale from 1 to 10, participating in a lottery increases happiness with 0.25–0.40.Footnote 15

One potential problem in our analysis is that in the group of free ticket holders there are individuals that intended to buy a ticket but a free one came along and the purchase never happened. In a sensitivity analysis represented in the fourth column of Table 1, we therefore distinguish between holders of free tickets who played the State lottery last year (and therefore have a higher chance to have the intention to buy a ticket) and holders of free tickets that did not play the State lottery in the last year. As shown, there is no difference in happiness gain between T1 and T2 between the two groups. In the group of people who participated in the State lottery last year, we made a further distinction between frequent and infrequent gamblers (at least monthly vs. less than one time per month). Again, we find no difference between the different groups.Footnote 16

Table 2 Additional parameter estimates change in happiness between \(T_1\) and \(T_2\) : thinking about the draw Full size table

It can be argued that it is difficult to gain procedural utility from a lottery draw if one never thinks about the lottery. Hence, we re-estimated our models, using information from the survey shortly before the lottery draw. More specifically, we investigated whether the intensity of thinking about the lottery affects the change in happiness before the lottery draw, i.e. between \(T_1\) and \(T_2\). Here, we distinguish between three groups of lottery players: players that never thought about the lottery (answer category 1; 15% of the lottery players), players that sometimes thought about the lottery (answer category 2–3; 69% of the lottery players), and players that frequently thought about the lottery (answer category 4 or higher; 16% ) using the following equation:

$$\begin{aligned} \varDelta H_{12,i} = \alpha _2 + \gamma _1 LT_{i} I_{1,i} + \gamma _2 LT_{i} I_{2,i} + \gamma _3 LT_i I_{3,i}+\gamma _4 X_i + \gamma _5 \varDelta S_{12,i} + \gamma _6 \varDelta LS_i + \epsilon _{12,i} \end{aligned}$$ (2)

where \(\alpha _2\) represents a vector of interview date fixed effects, LT is a dummy variable indicating whether or not an individual had a lottery ticket irrespective of whether this was bought or received because of the field experiment and \(I_1\)–\(I_3\) are dummy variables indicating whether the individual had no thoughts about the lottery, sometimes thought about the lottery or frequently thought about the lottery. And, \(\gamma _1\)–\(\gamma _6\) are (vectors of) parameters.

The first column of Table 2 shows that players who never thought about the lottery did not experience a significantly higher increase in happiness than non-players. At the same time, players who thought about the lottery experienced higher increases in happiness than non-players and players who never thought about the lottery. As shown in the second and third columns, the difference remains significant if we include control variables and also the change in life satisfaction. The fourth to sixth column of Table 2 show that our results hold if we account for the intensity of thinking about the lottery draw. The change in happiness between \(T_1\) and \(T_2\) after receiving a lottery ticket is present if the individual thought about the lottery, but it does not matter whether the individual thought about the lottery sometimes or frequently.

Along similar lines, it is difficult to gain procedural utility from a lottery draw if one does not have positive feelings when thinking about the lottery. Accordingly, we examined to what extent the procedural utility from a lottery draw is contingent on having overall positive emotions when thinking about the draw. In this regard, it is also interesting to note that participants thinking regularly about the draw experience higher levels of positive emotions and not higher levels of negative emotions compared to participants thinking never or only sometimes about the draw (see Fig. 1). We observe this across the whole range of positive emotions.Footnote 17 In our regression, we investigate whether having positive emotions about the draw affects the change in happiness before the draw (again between \(T_1\) and \(T_2\)), where we take the balance of positive to negative affect (PANA) score regarding the draw as main indicator for the positivity ratio when thinking about the draw. We use the following equation:

$$\begin{aligned} \varDelta H_{12,i} = \alpha _3 + \phi _1 LT_{i} + \phi _2 LT_{i} PN_{2,i} + \phi _3 X_i + \phi _4 \varDelta S_{12,i} + \phi _5 \varDelta LS_i +

u _{12,i} \end{aligned}$$ (3)

where \(\alpha _3\) represents again a vector of interview date fixed effects and LT is a dummy variable indicating whether or not an individual had a lottery ticket irrespective of whether this was bought or received because of the field experiment, PN is a mean-centered continuous variable indicating a respondents’ positivity ratio (PANA) regarding the draw. And, \(\phi _1\) to \(\phi _5\) are (vectors of) parameters. Our regression results are presented in Table 3. The first two columns show that players who had a higher positivity ratio regarding the draw experienced higher increases in happiness, where column 3–6 show that these results are primarily driven by the positive emotions. To exemplify, players that had no or hardly any positive emotions at all regarding the draw (maximum average score on the PA of 2 out of 7), did not experience an increase in happiness between \(T_1\) and \(T_2\) (\(p=0.086\)).

Fig. 1 Positive and negative emotions about participation in the State Lottery; experienced before the lottery draw by frequency of thinking about the draw Note: Only for respondents who possessed a lottery ticket for the lottery draw of May 10; average answers to questions on emotions on a scale from 1 (not at all) to 7 (completely) Full size image

Table 3 Additional parameter estimates change in happiness between \(T_1\) and \(T_2\) : emotions regarding the draw Full size table

Indirectly, the joy of lottery play could also be inferred from people’s willingness to pay for a lottery ticket. In the survey at \(T_1\), participants indicated their willingness to pay for a lottery ticket. In a hypothetical experiment, participants made a choice between receiving a small sum of money or a lottery ticket with a retail price of €15. Although this can also indicate that people overestimate the expected value of a lottery ticket, many people choose to get the lottery ticket when the amount of money they would have received was larger than the retail price of the lottery ticket. Most notably, 43% of the participants preferred the lottery ticket over receiving €17.50, while even 30% of the participants preferred the lottery ticket over receiving €25.Footnote 18