Gambling to leapfrog in status?

An Erratum to this article was published on 23 October 2015

This article has been updated

Abstract

This paper tests our theoretical prediction that households with positional concerns use gambling to attempt leapfrogging in the social hierarchy. We rely on household data that is representative for Germany and proxy the households’ positional concerns by their expenditures for conspicuous consumption. Our empirical results strongly indicate that households who care about status are not only more likely to participate in gambling but also to invest more in gambling.

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  • 23 October 2015

    An erratum to this article has been published.

Notes

  1. 1.

    For instance, Dohmen et al. (2011) provide evidence for the importance of relative income for subjective well-being using functional magnetic resonance imaging (fMRI). Further empirical evidence for the importance of relative income positions for individual happiness and actions can be found in Stutzer (2004) and Frey et al. (2008), for instance.

  2. 2.

    It is important to note that subjective status is relevant for privately optimal behavior, where this subjective position is partly determined by the individual when it determines the peer group, for example (e.g., Falk and Knell 2004). There is evidence that the respect and admiration one gets from interaction with face-to-face groups such as colleagues and friends are a major determinant of status concerns (see Anderson et al. 2012; Clark and Senik 2010; Friehe et al. 2014; Senik 2009). As a result, even subjects with an objectively high status may perceive to be disadvantaged in this regard.

  3. 3.

    For example, Haisley et al. (2008) report that people received only 53 cents in return for every dollar spent on lottery tickets over the years 1964–2003 in the US. Clotfelter and Cook (1990) state a similar ratio and assert on p. 109 that “this asset has no place in the portfolio of a prudent investor”.

  4. 4.

    Along these lines, Winkelmann (2012) establishes for Switzerland that the prevalence of luxury cars in one’s own municipality decreases income satisfaction, and Kuhn et al. (2011) find that neighbors of people who won a car in the lottery have significantly higher levels of car consumption than others.

  5. 5.

    The findings on the effect of gender on the strength of positional concerns hitherto are ambiguous (Alpizar et al. 2005; Corazzini et al. 2012; Dohmen et al. 2011; Friehe and Mechtel 2014; Pingle and Mitchell 2002).

  6. 6.

    For example, Haisley et al. (2008) report that the average expected value of a dollar spent on lottery tickets was −.47 dollars.

  7. 7.

    It is interesting to note that the externality created by a household who invests in gambling (i.e., an investment opportunity with a negative expected value) is positive when individual risks are uncorrelated. This is due to the fact that the household is in expectation lowering the level of average consumption \(\bar{x}\) that is used as the reference level by other households. On the comparison of private and social optimality, see Konrad and Lommerud (1993) for a more extensive discussion.

  8. 8.

    For further information on the EVS, see, for instance, Statistisches Bundesamt (2005a, b).

  9. 9.

    When studying the relative importance of conspicuous consumption, we consider the amount of expenditures for categories of goods that may be considered as having good signaling attributes. We do not observe how the expenditures in a specific category come about such that we cannot tell, for example, the make of the car bought in a given year.

  10. 10.

    Even though our information at the household level is very detailed and of high quality, we cannot control for all aspects that may have a bearing on the decisions we analyze. For example, the risk attitude and the time preference rates of the decision-makers are variables with a potential influence on gambling behavior that we cannot control for. We discuss omitted variable bias in Sect. 4.1.2.

  11. 11.

    For all variables measured in monetary units, we add 1 euro to the actually observed value in order to circumvent having ln(0).

  12. 12.

    In line with the results from other regression exercises (see, e.g., Beckert and Lutter 2013; Humphreys et al. 2010), we find that our empirical models for the participation and the level of the expenditure yield a relatively low level of Pseudo-R 2 and R 2. In view of the difficulty of explaining gambling behavior with a unitary theory (as described, for example, in Ariyabuddhiphongs 2011), this is not necessarily a concern.

  13. 13.

    As suggested by a referee, we additionally created a random basket of goods and included a household’s expenditures for these goods as alternative explanatory variable (instead of \(\ln ({\text {CC}}_i)\)) into the regressions. It turns out that this variable is negatively related to both the probability of participation and gambling expenditures in most estimations, while it is insignificant in others. Furthermore, we followed the suggestion to include a proxy for non-conspicuous consumption expenditures in our analysis. We used the difference between a household’s income and the sum of expenditures for conspicuous consumption and savings. In summary, in contrast to conspicuous consumption expenditures, there seems to be no systematic relationship between expenditures on less or non conspicuous goods and gambling activities.

  14. 14.

    The fact that our finding obtains for even the narrowest definition of conspicuous consumption discards potential objections about the result following from the identity of income equating total consumption and savings.

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Acknowledgments

We gratefully acknowledge the comments received from Laszlo Goerke, Florian Hett, Stephan Jank, Markus Pannenberg, and two anonymous reviewers on earlier versions of the paper.

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Correspondence to Mario Mechtel.

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An erratum to this article is available at https://doi.org/10.1007/s11150-015-9312-y.

Appendix: Details on the theoretical model

Appendix: Details on the theoretical model

The preferences of the representative household are represented by the function:

$$T=u(x)+v(y)+gw(S), $$
(9)

where x and y are the consumption levels of the positional and the non-positional good, and S is the relative standing. We assume \(u'>0>u''\), \(v'>0>v''\), and both \(\lim _{x\rightarrow 0}u'=\infty \) and \(\lim _{y\rightarrow 0}v'=\infty \). The scalar \(g\ge 0\) represents the relative importance given to status, where relative standing is determined by

$$S\equiv x-\bar{x}, $$
(10)

with \(\bar{x}\) as the average level of absolute consumption of the positional good.

The household with income I may participate in a lottery, paying Bl with probability 1 − p for an investment of l, where B > 1 (i.e., the investment influences only the payout of the lottery). Lotteries usually have a negative expected payoff, \(EV=(1-p)(Bl-l)-pl\), such that

$$EV_l=(1-p)(B-1)-p<0. $$
(11)

We distinguish the level of available income left for consumption depending on whether the winning state M or the no win state N materializes:

$$ I_M=I+Bl-l$$
(12)
$$ I_N=I-l. $$
(13)

The household seeks to

$$\begin{aligned} \max _{y_j,l} ET&=p[u(I_N-y_N)+v(y_N)+gw(I_N-y_N-\bar{x})]\nonumber \\&\quad+(1-p)[u(I_M-y_M)+v(y_M)+gw(I-y_M-\bar{x})], \end{aligned}$$
(14)

where \(x_j=I_j-y_j\), \(j=M,N\). We obtain

$$ ET_{y_N}=p\left[v'_N-u'_N-gw'_N\right]=0$$
(15)
$$ET_{y_M}=(1-p)\left[v'_M-u'_M-gw'_M\right]=0$$
(16)
$$ET_{l}=(1-p)(B-1)\left[u'_M+gw'_M\right]-p\left[u'_N+gw'_N\right]\le 0 $$
(17)
$$l\times ET_l=0 $$
(18)

where \(v'_j\) is a shorthand for \(v'(y_j)\) and so on.

We are interested in heterogeneity regarding the level of g. In this regard, we arrive at our first observation.

Lemma 1

Households with negligible positional concerns (i.e., households for which g → 0 holds) will not participate in a lottery with negative expected value.

This follows from the fact that the household spends more on x in state M than in state N, diminishing utility with respect to the good x, and (11). As a next step, we turn to households with a non-negligible weight g. When the household chooses to invest in the lottery, the condition \(ET_l=0\) together with (11) implies

$$\frac{(1-p)(B-1)}{p}=\frac{u'_N+gw'_N}{u'_M+gw'_M}<1, $$
(19)

such that

$$ 0<u'_N-u'_M<g\left[ w'_M-w'_N\right] . $$
(20)

This allows us to conclude:

Lemma 2

Households who invest in a lottery with negative expected value must have status utility w that is sufficiently strictly convex.

We summarize as follows.

Proposition 1

Households who attach more importance to relative standing are more likely to gamble.

Next, we present results from a comparative-statics analysis for subjects that do participate in the lottery. Our research question concerns how household investment in the lottery varies with their ambition for favorable status positions. In the following, we will disregard equilibrium effects on the level of comparison consumption \(\bar{x}\). The comparative-static properties of the model follow from

$$\left( \begin{array}{*{20}c} ET_{y_Ny_N} & 0 & ET_{y_Nl} \\ 0 & ET_{y_My_M} & ET_{y_Ml} \\ ET_{ly_N} & ET_{ly_M} & ET_{ll} \end{array}\right) \left( \begin{array}{c} dy_N \\ dy_M \\ dl \end{array}\right) = \left( \begin{array}{c} -ET_{y_Ng} \\ -ET_{y_Mg} \\ 0 \end{array}\right) dg. $$
(21)

The determinant of the 3 × 3 matrix on the left-hand side will be denoted H in our subsequent argumentation, and is supposed to be negative by the sufficient second-order conditions.

From the first-order conditions and the assumption that the sufficient second-order conditions are fulfilled, we obtain

$$ ET_{y_My_M}=(1-p)\left[ v''_M-u''_M-gw''_M\right] <0 $$
(22)
$$ET_{y_Ny_N}=p\left[ v''_N-u''_N-gw''_N\right] <0 $$
(23)
$$ET_{ll}=p\left[ u''_N+gw''_N\right] +(1-p)(B-1)^2\left[ u''_M+gw''_M\right] <0$$
(24)
$$ ET_{y_Nl}=p\left[ u''_N+gw''_N\right] $$
(25)
$$ET_{y_Ml}=-(1-p)(B-1)\left[ u''_M+gw''_M\right] $$
(26)
$$ ET_{y_Ng}=-pw'_N<0 $$
(27)
$$ ET_{y_Mg}=-(1-p)w'_M<0 . $$
(28)

We are interested in the expenditures for lotteries of status-oriented households, and therefore seek to interpret:

$$\begin{aligned} \frac{dl}{dg}= A\left\{ (1-p)(B-1)\left[ u''_M+gw''_M\right] \frac{v''_N-u''_N-gw''_N}{v''_M-u''_M-gw''_M}-p\left[ u''_N+gw''_N\right] \frac{w'_N}{w'_M}\right\} \end{aligned}$$
(29)

where \(A=\left\{ p(1-p)w'_M\left[ v''_M-u''_M-gw''_M\right] \right\} H^{-1}>0\).

An increase in the importance attached to relative standing implies that both the beneficial comparison in the winning state of the world and the disadvantageous comparison in the losing state of the world have a greater impact on well-being. The former comparison gets even more favorable as a consequence of a greater investment in the lottery, whereas the latter one becomes more unfavorable. We have concluded in Lemma 2 that households who invest in the lottery must have strictly convex status utility. This can be used for the interpretation of (29), because the first term in the parentheses will be positive (due to \(u''_M+gw''_M>0\)) and the second one will go to zero for w sufficiently convex. Our second prediction follows therefrom.

Proposition 2

Households who participate in the lottery will invest the more in the lottery, the more importance they attach to relative standing for w sufficiently convex.

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Friehe, T., Mechtel, M. Gambling to leapfrog in status?. Rev Econ Household 15, 1291–1319 (2017). https://doi.org/10.1007/s11150-015-9306-9

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Keywords

  • Conspicuous consumption
  • Status
  • Relative income
  • Gambling
  • Behavioral economics

JEL Classification

  • D12
  • D14
  • D62