DEPARTMENT OF ECONOMICS DISCUSSION PAPER SERIES FOR LOVE OR REWARD? CHARACTERISING PREFERENCES FOR GIVING TO PARENTS IN AN EXPERIMENTAL SETTING

This paper examines the motivation for intergenerational transfers between adult children and their parents, and the nature of preferences for such giving behaviour, in an experimental setting. Participants in our experiment play a series of dictator games with parents and strangers, in which we vary endowments and prices for giving to each recipient. We find that preferences for giving are typically rational. When parents are recipients as opposed to strangers, participants display greater sensitivity to the price of giving, and a higher relative proclivity for giving. Our findings also provide evidence of reciprocal motivations for giving, as players give more to parents who have full information regarding the context in which giving occurs.


Introduction
Understanding the motivations behind intergenerational transfers is an important and active research area in economics. The existence and responsiveness of familial transfers has consequences for the design of intra-and intergenerational redistributive programmes, particularly as such programmes may crowd out private transfers amongst altruistic family members. Yet, despite theoretical and empirical advances in this area, signi…cant gaps in our knowledge remain. In this paper, we advance the current literature by shedding light on both the motivation for providing intergenerational transfers, and on the nature of preferences for such giving behaviour, by using experimental techniques and revealed preference methods.
In this paper, we are speci…cally concerned with transfers made by adult children to their parents. It is clear that parents may invest in their children because they love them, but also because of an expectation that their children will reciprocate to provide support for them in old age. However, there is no commitment mechanism available to parents to enforce that their children provide the care that they may expect. So why do adult children provide support and resources to their parents in old age? This question is particularly salient in countries where parents have lower incomes than their children and rely on their adult children for …nancial support. However, it is also important for understanding what motivates grown children to devote time and other resources to ensure that parents in ill health receive the required care and support. More broadly, what motivates individuals to share scarce resources with family members? Early work addressing these questions determined that even sel…sh children could be incentivized to behave in the interest of the family by an altruistic patriarch (Becker, 1974).
Determining the primary motivation for familial transfers, speci…cally whether they are altruistically or strategically motivated, has long been a central question in the literature (see, for example, Bernheim et al., 1985;Cox 1987) with consequences for a number of diverse areas in economics. For example, Ricardian equivalence is hard to obtain when children are altruistically motivated towards their parents (Bilbiie and Monacelli, 2013). However, it is di¢ cult to disentangle the various motivations for intergenerational transfers in survey data. For example, while private transfers may decline when a recipient's income increases, this does not necessarily mean that transfers are altruistically motivated because other motives such as co-insurance cannot be ruled out (Kotliko¤ and Spivak, 1981). Distinguishing between altruistic and strategic motives for giving is further complicated by the fact that there are many other reasons for why people give: an aversion to unfairness or inequality (Fehr and Schmidt 1999); the warm-glow of giving (Andreoni, 1989(Andreoni, , 1990; reciprocity -rewarding friendly actions or punishing hostile actions at a cost (Rabin, 1993;Camerer and Fehr, 2004); and reciprocal altruism -giving to generate or relieve an obligation (Camerer and Fehr, 2004;Cox et al., 2004;Leider et al., 2009;Ligon and Schechter, 2012).
Our main contribution to this broad literature is to uncover the characteristics of, and motivations for, giving between adult children and their parents, by using a carefully designed experiment. Subjects play a series of dictator games in the lab, once with parents and once with strangers as recipients, where the amount to divide and the relative price of giving vary across games. To our knowledge, Peters et al. (2004) is the only prior study to have examined behaviour between parents and children in the lab, although their study di¤ers signi…cantly from ours as they studied interactions between young children (aged 8 to 16) and their parents in a very di¤erent experimental setting.
Our experimental design enables us to explore the salience of reciprocal motivations for transfers between adult children and parents. The dictator game is generally used in experimental settings because reciprocation, either in the form of reward or punishment is not possible when the recipient is an anonymous stranger. However, we cannot maintain control of any subsequent interactions between subjects and parents outside the lab, and these interactions in ‡uence the behaviour we observe in the lab. Our experiments were designed with this in mind, and provide an example of how the line between "lab" and "…eld" can be blurred to gain some understanding of behaviour outside of the lab in a novel way.
To explore adult childrens'motivations for giving, we vary the amount of information that parents receive about the games their children play in the lab in order to vary the likelihood of parental reciprocity. We …nd evidence of reciprocal motivations for sharing with parents, which di¤ers from prior work using survey data that found evidence of altruistically linked family members (e.g. Altonji et al., 1997). In our experiments, when participants were told that their parents would be receiving information about their choices, they gave more to their parents than those who were told their parents would not be informed of how payments were determined. If subjects had given to parents for purely altruistic reasons, then this information treatment would not have in ‡uenced the amount shared with them.
This novel experimental design also contributes to a strand of literature in experimental economics, which has shown evidence of reciprocal behaviour on the part of dictators in several di¤erent contexts (Ho¤man et al., 1996;Bohnet and Frey, 1999;Ben-Ner et al., 2004;Cox et al., 2004). In experiments in which recipients are friends, dictators share more with those to whom they are more closely connected (Goeree et al., 2010). Similarly, dictators give more to close friends than to strangers, and these di¤erences are strongest when the giving is not anonymous (Leider et al., 2009). Our paper di¤ers from these two studies in three di¤erent dimensions.
First, in contrast to the latter two experimental studies, we show evidence for reciprocal motives for familial transfers without the confounding in ‡uence of selection e¤ects. These past experimental studies on prosocial behaviour in social networks have found strong homophilous tendencies in choosing friends (Leider et al., 2009;Goeree et al., 2010). For example, people's friends often exhibit similar levels of kindness, so that it is not possible to di¤erentiate between the selection e¤ect in choosing one's friends from the social interaction e¤ect (Leider et al., 2009). We purposely designed our experiments to ensure that such a selection e¤ect would not be possible. This is one reason why we required parents to be recipients, rather than a chosen family member. In order to ensure this, we asked participants to send payments to their mothers if both parents were alive but living separately from one another.
Second, these prior studies have not directly addressed the nature of preferences for giving within families, a setting in which further questions arise. In our paper, we address these wider intrahousehold-speci…c questions to help inform, for example, recent work on the consequences of relaxing the assumption of perfectly transferable utility for explanations of the formation and dissolution of families (Giuliano, 2007;Chiappori et al., 2012a, b).
Third, we conduct a more ambitious preference recovery exercise than Leider et al. (2009), which is in the spirit of Andreoni and Miller (2002), by collecting su¢ cient information on the choice behaviours of each subject.
Using revealed preference and structural techniques, we use our experimental data to examine the rationality of intergenerational transfers, to recover how preferences for giving vary depending on the recipient of a gift and to examine the motivation for transfers from adult children to their parents. We …nd that the vast majority of subjects have consistent and well-behaved preferences for giving to strangers and parents when these transfers are treated as separate goods. We identify a series of preference 'types' in our subject pool and estimate the parameters of a Constant Elasticity of Substitution utility function. This allows us to examine the nature of preferences for giving and to explore how they vary by the recipient of a gift in great detail.
In doing so, we contribute to a second strand of literature in experimental economics. Our …ndings support the results of prior lab experiments with a similar experimental design in several di¤erent contexts: among young children (Harbaugh et al., 2001;List and Millimet, 2008); among economics students and other adults (Sippel, 1997;Mattei, 2000;Andreoni and Miller, 2002); and with a broader set of budget constraints (Fisman et al., 2007). In a further application of revealed preference methods, we go on to …nd that preferences for giving are conditional upon the recipient of a transfer. We also …nd that when we pool the choices from the games with parents with those played with strangers, the choices of the majority of players violate axioms of revealed preferences. This indicates that most players view giving to parents and strangers as distinct goods, and they have di¤erent preferences for each one.
In summary, we …nd greater proclivity for giving and greater price sensitivity of transfers when parents rather than strangers are recipients of transfers. However, we uncover signi…cant heterogeneity in preferences for giving to parents, which, to our knowledge, has not been explored in any previous work. Further, this is the …rst paper to provide estimates of preference parameters for giving to parents on the part of adult children, and such parameter estimates might be used to calibrate future macroeconomic multi-generation models. Finally, we …nd that many adult children do not share resources with parents in order to maximize social e¢ ciency gains within the family. That is, a number of subjects do not exhibit preferences of perfect substitutes for giving to parents. For these subjects, the oft used assumption of transferable utility in modeling family behaviour may not be relevant.
The rest of this paper is structured as follows. In Section 2, we describe our experimental design. In Section 3, we assess the rationality of subjects' choices (to ensure that a consistent preference ordering can be found that rationalises their choices) and test whether giving to parents and giving to strangers can be treated as the same good in a subject's utility function. In Section 4, we formally characterise the nature of preferences for giving to parents and strangers. In Section 5, we examine our subjects'motives for giving to parents using the results of our controlled information experiment. Section 6 concludes.

Experimental Design
This section describes our sample selection criteria and the design of our modi…ed dictator games and information treatment.

Sample selection
In recruiting subjects for our experiments, we focused upon adults who largely live independently from their parents. Further, we chose to deliberately exclude undergraduate students and those with a university quali…cation in economics from our study. Though undergraduate students live apart from parents, they often visit them, typically consider the parents'address to be their permanent address, and they often rely on parents …nancially. Furthermore, student and non-student subjects, especially those with a background in economics, often show very di¤erent patterns of behaviour in lab experiments (Harrison and List, 2004).
As our experiments took place in Oxford, England, the majority of our sample resided in the southeast region of the UK. In comparing our sample to those in the British Household Panel Survey (BHPS) who reside in the southeast region of the UK, we over-sample women and those with a college degree. The extent to which our …ndings may be generalized to a wider population may re ‡ect the extent to which gender and education may in ‡uence behavior in this particular context, although our …ndings are robust to controlling for such characteristics. We refer the reader to the Online Appendix 2 for further details of our recruitment procedures and subject pool.

Modi…ed dictator game
We designed our experiment to test the rationality and characteristics of preferences for giving to parents and strangers. Each subject played a series of dictator games separately with a parent and with an unknown stranger, who was another subject chosen at random from those participating in the same session, and whose identity remained anonymous. Rather than give a single amount to the subject to be divided up between herself and the recipient (as is usual in dictator games), each subject was tasked with allocating "tokens" under a series of di¤erent budgets.
Decision problems di¤ered by the number of tokens to be divided and the amount of money that each token was worth. Tokens were worth 10, 20, or 30 pence. The total number of tokens varied between 40 and 100. Table 1 provides the details of the eleven budgets that the subjects faced. 1 The order of the decision problems was randomised across subjects, and they were told that the experimenter would randomly choose one of the decision problems and carry it out. Notes. *** denotes statistical signi…cance at the 1% level. Table 1 also details the average amount that our subjects chose to share from each of the budgets. In comparison to subjects in Andreoni and Miller (2002), our subjects were more sensitive to the relative price of giving, sharing 50% when the price of giving was less than one, 36% when the price was one, and 30% when the price was greater than one. When we distinguish between games played with parents and strangers, we see that this sensitivity to price only holds for games played with parents. In games with strangers, our subjects were slightly more generous than those in Andreoni and Miller's sample, giving 30% on average irrespective of price. However, in their games with parents, our subjects gave about 70% of their share to parents when the relative price of giving was less than one, 45% when the price was one, and 30% when the price was greater than one. These di¤erences are statistically signi…cant.

Information Experiment
As a further dimension to our experimental design, we randomised the amount of information parents received about the games played in the lab. This randomisation allows us to explore whether subjects are altruistically or strategically motivated to share with parents. Note that this randomisation occurred at the session level rather than the subject level to avoid confusion and potential spillovers. Subjects were not aware of these di¤erences across sessions. All subjects in a session were assigned to one of three treatment groups: 1. Subject's parent was noti…ed that her child participated in a study, but no additional information was provided.
2. Subject's parent was given full information regarding the dictator games that her child played with her, including complete instructions on the games, how the child played each game, and how much was allocated to the parent and to the child.
3. Same as (2) above, but the subject was also given an opportunity to write a note to the parent that was included with the letter and payment mailed to the parent.
The third treatment group was implemented to give participants an opportunity to send their parents a message in case they were deterred from, for example, exhibiting perfect substitutes preferences out of concern that their parents might view this as sel…sh behaviour. 2 If this were true, subjects could have been more likely to exhibit sel ‡ess or Leontief preferences in Treatments 2 or 3 because of concerns about their parents' reaction to a small payment amount and a concern for being perceived of as fair (Andreoni and Bernheim, 2009).
Of the 64 subjects in Treatment 3, 41 wrote their parents a message. However, only four explained perfect substitutes behaviour. Four other subjects explained that they had tried their best to divide tokens so that total payouts were split equally. One subject explained sel…sh behaviour. The majority of those who wrote notes (32 subjects) did not send any message explaining their decisions in the game. For example, messages included: "Hi!" and "Enjoy, Mum X." All notes can be found in Online Appendix 1. The majority of subjects did not use the opportunity to write a note to their parents to explain behaviour, and we …nd there is little di¤erence between Treatments 2 and 3 in a¤ecting the amount shared with parents.
We also randomised whether subjects played …rst with their parents or with stangers, and this randomisation was done across individual lab sessions. It is important to note that subjects were not provided with any details of the experiment in advance of their participation. Thus, if they played dictator games with strangers initially, they did not know that they would repeat the same games with parents. Likewise, if they played games with parents …rst, they did not know this would be followed by another set of games played with strangers. This has important implications for how subjects would play, particularly with parents, and how they could have been in ‡uenced by the information treatment, which is discussed below.
Our 190 subjects were evenly distributed across the three treatment groups, with 66 subjects in Treatment 1,60 in Treatment 2, and 64 in Treatment 3 (see Table 2). For those in Treatment 1, 37 subjects played with a stranger …rst and 29 played …rst with a parent. Of the 60 subjects in Treatment 2, 19 played with a stranger …rst, and of the 64 subjects in Treatment 3, 33 played with a stranger …rst. 3 Are preferences for giving rational?
We begin by examining whether choices are rational, that is whether there exists some well-behaved preference ordering consistent with each individual's choices in the lab. We do so by checking for violations of the Generalised Axiom of Revealed Preference, GARP (Varian, 1982). 3 We …nd that we can rationalise the behaviour of the overwhelming majority of our subjects using the standard utility maximisation model (see Table 3). 91% of our sample satisfy GARP when playing with parents, while 89% of subjects satisfy GARP when playing with strangers. This di¤erence is not statistically signi…cant. These high pass rates are not the product of a weak test of rationality, as indicated by the measure of 'predictive success', s 2 [ 1; 1] for our tests (Beatty and Crawford, 2011). This measure allows us to correct observed pass rates for the demandingness of a revealed preference test, which is measured by the so-called 'relative area' a. An s in the neighborhood of 1 indicates that the choice behaviour data satisfy strict restrictions (the ideal situation), whilst an s in the neighborhood of -1, denotes the opposite; choice behaviour violating very weak restrictions. 4 3 We here refer to Crawford and De Rock (2014) who provide a comprehensive review of the literature on revealed preference methods and how GARP can be tested empirically. 4 A Monte Carlo simulation was used to estimate the relative area numerically. Relative areas were calculated by randomly drawing 50,000 choices from each budget using a uniform distribution across the entire budget and testing for whether each random choice set satis…es GARP. a is the proportion of these random choices that satisfy rationality. We estimate a = 0:051 for our budget environment.

Notes. Standard errors in parentheses.
Age and education do not impact the likelihood of passing GARP. However, men are more likely than women to satisfy GARP, other things equal. Whereas 97% of men pass GARP in games with strangers, 87% of women do so.
Similarly, 94% of men pass GARP with parents, and 86% of women pass GARP in games with parents. We refer the reader to Online Appendix 2 for further details.
Are preferences for giving conditional on the recipient? To determine whether preferences for giving depend on the recipient, we pool an individual's choices from the games played with strangers with the games played with parents and check whether a well-behaved preference ordering exists that can rationalise this full choice set. 5 We …nd that giving to parents and strangers cannot be rationalised by the same preference ordering for 73% of subjects (66% of men and 77% of women). For these individuals, giving to parents and strangers cannot be treated as a single good and preferences for giving are conditional upon the recipient. The greater demandingness of the revealed preference test does not explain the signi…cantly lower pass rate on the pooled choice set, as the predictive success measure is 0.266.

How signi…cant are the deviations from rationality?
We compute the severity of the GARP violations to check whether behaviour is essentially rational and fails our test due to small random errors. We do so by computing the 'Money Pump Index'(MPI) proposed by Echenique et al. (2011) for each subject. The MPI can be interpreted as the monetary value of tokens that could be extracted from a subject who behaves inconsistently. The severity of a GARP violation is then measured by the amount of money that a 'devious arbitrager'could have extracted from our subject. Money pump cost violations are relatively small when giving to parents and strangers are treated as separate goods, suggesting that choices are e¤ectively rational (see Figure 1). However, when choice sets are pooled, GARP violations are much more severe, suggesting that preferences for giving are indeed conditional on the intended recipient. 6 We also examined the number of budgets that had to be dropped for GARP violators to attain rationality. For most, only one budget had to be dropped. We did not …nd any patterns concerning the particular budget, or timing of budget, that had to be dropped. Further details are in Online Appendix 2.

Estimating preferences for giving
In this section, we examine how preferences for giving di¤er by recipient. We do so by estimating preference parameters for giving to parents and strangers for those who satisfy GARP.

Preference types
To characterise preferences for giving to parents and strangers, let s represent payment to one's self and o represent the payment amount to the recipient, so that one's utility is u( s ; o ). We group subjects into preference types depending on the similarity of their revealed preferences to four "extreme" preference classes: i Perfectly Sel…sh, u( s ; o ) = u( s ); ii Perfect Substitutes or Utilitarian, u( s ; o ) = s + o ; iii Leontief or Rawlsian, u( s ; o ) = minf s ; o g; iv Perfectly Sel ‡ess, u( s ; o ) = u( o ).
Many subjects'choice behaviour can be perfectly rationalised by one of these 'pure'preference types: 59% with regard to their preferences over giving to strangers and 73% for parents. The distribution of preference types is signi…cantly di¤erent across recipients ( 2 = 83:42) and displayed in Figure 2. Unsurprisingly, many more subjects played sel…shly with strangers than with parents and pure sel ‡essness occurred only with parents. In games with parents, the majority of subjects with strongly de…ned preferences exhibited a preference type of perfect substitutes, and thus acted to maximise joint payo¤s. This …nding of a higher proportion of perfect substitute types when giving to parents (which is statistically signi…cant at the 1% level with a t-stat of 16.8) also implies that giving to parents is more price sensitive than giving to strangers among those with strongly de…ned preferences. It is also interesting to note that an assumption of transferable utility between parents and children may be reasonable for those who play perfect substitutes with parents. However, as roughly half our sample, and over 30% of those with strong preferences, did not play perfect substitutes with their parents, our results cast some doubt on whether transferable utility is a valid assumption in general.

Fig. 2. Distribution of Strong Preference Types
There are 85 subjects whose preferences for both giving to parents and strangers are perfectly rationalised by one of the four preference categories. Table 4 gives the number of subjects with strong preferences that fall into each 'parent -stranger preference' cell. The three largest groups are: (i) Maximise family payo¤s -32 subjects played sel…shly with strangers but revealed perfect substitute preferences when playing with parents; (ii) Equality in dictator-recipient payo¤s -15 subjects split endowments equally, unconditional of recipient; (iii) Maximise social payo¤s -16 subjects revealed perfect substitute preferences irrespective of the identity of the recipient. All subjects who played perfect substitutes with strangers, also did so with their parents, and thus comprise the latter. There are an additional 8 subjects who played perfect substitutes with parents and Leontief with strangers, and this group may have similar preferences to those who play Leontief with both recipients. The di¤erences in games with parents may arise from di¤erences in the extent to which players believe they can "undo" the unequal shares in subsequent interactions with parents. 7

Estimating Preferences
We classi…ed subjects whose choices could not be perfectly rationalised by one of the four preference types into "weak" versions of these preference classes by assigning subjects the preference type that was "closest" to their revealed preference. Speci…cally, we placed subjects into the preference type with the minimal Euclidean distance between their actual choices and the choices dictated by the pure preference type. 8 To get a more detailed picture of preferences within these weak types, we estimate preference parameters for a Constant Elasticity of Substitution (CES) utility function within each weak preference type (with the exception of the "weakly sel ‡ess" category due to limited observations). 9 The functional form of the CES utility function is: The parameters have clear interpretations: a gives the weight on "own" consumption, indicating the degree of sel…shness (a = 1 when perfectly sel…sh and a = 0 when perfectly sel ‡ess), while determines the elasticity of 7 A limitation of this study is that we do not observe behaviour outside the lab. We did not follow up with subjects in order to ensure them that their decisions were made privately and would remain anonymous. For complete details on experimental procedures, see Online Appendix 2.
8 Results were not sensitive to other distance measures, for example, squared deviation and absolute deviation. 9 Additional analysis in Online Appendix 2 suggests that the assumption of homothetic or Gorman Polar Form preferences cannot be rejected for the majority of these subjects, which provides good grounds for our choice of CES utility function. substitution, = 1= (   1), between one's own payo¤ and that of the recipient. As approaches -1, preferences are Leontief. When = 1 , preferences are perfect substitutes. With the budget constraint s + p o = m, the CES demand function is: (1 ) and r = =( 1): A and r are estimated using a two-limit nonlinear tobit by maximum-likelihood to take into account the fact that subjects'choices are censored at both ends of the budget constraint. To remove heteroskedasticity in the error term in levels, demands are estimated as budget shares with an i.i.d error term. The estimated demand function is then: where "~N (0; 2 ). Table 5 gives our results. We …nd a greater proclivity to give to parents and some evidence that giving to parents is more price responsive. a is highest amongst those with weakly sel…sh preferences and, as we might expect, a is higher when strangers as opposed to parents are recipients. 10 There is considerable variation in estimated within our sample. For those with weakly Leontief preferences, the estimated is statistically signi…cant, negative, and relatively high in magnitude (in line with what we would expect). For those in the weakly perfect substitutes category, we …nd that the marginal rate of substitution between own and recipient payo¤ is greater when playing with parents, and that this di¤erence is statistically signi…cant, suggesting greater price responsiveness when giving to parents for this group.  Notes.
In this section, we explore the motivations for transfers to parents. We di¤erentiate between whether subjects give to parents because of altruism -either pure altruism or altruistic reciprocity (reciprocating kindness shown previously by their parents), or because of some reciprocal or strategic motive. If adult children are altruistically motivated, their preferences over payments to parents relative to payments to themselves should not di¤er by treatment group.
But if adult children are strategically motivated to share with parents, then they would value giving to parents quite di¤erently depending on the degree to which parents are informed of their decisions in the lab. Parents who receive full information may be inclined to either reward generosity and perhaps sharing the winnings of the experiment, or to punish a child's sel…shness and perhaps reduce subsequent transfers to the grown child.
An alternative to the latter explanation of strategic motives for giving is that parents may derive a 'signal value' from a child's gift, which is stronger when they have more information. For example, parents may feel more loved if they see that their grown child has sacri…ced tokens in order to share more with them. However, we do not believe that signalling is a compelling interpretation of our results. Subjects in Treatment 3 had an opportunity to write a note to their parents in which they could have provided some signal of love and explained that any possible zero payments were due to the fact that they maximised joint payo¤s. Yet, a very small number of subjects indicated the latter, and none provided a signal of love. Rather, those who played perfect substitutes indicated the possibility of undoing the experiment later on. In addition, we …nd no di¤erences in preferences or payments between Treatments 2 and 3. We also observe interesting di¤erences in behaviour by treatment group depending on whether a subject played …rst with strangers or …rst with parents that is di¢ cult to nest within a signalling narrative. 11 Finally, we note that we assume that it would have been prohibitively costly for participants in Treatment 1 to fully and credibly explain the details of the study to parents given that the study is relatively complicated to explain and would have required a long conversation with a parent. We made no contact with subjects or parents after the experiment to determine if this was the case. This was to assure participants'privacy in their decisions in the lab. 12

How information to parents a¤ects preference type
We …nd that the information treatment a¤ects preferences towards giving to parents depending on one's preferences towards giving to strangers. Table 6 records the di¤erences between the 'full information' and 'no information' treatment groups in the proportion who have strong preferences of type j when giving to strangers, who then have 1 1 Further, we believe it unlikely that giving a positive amount in such lab experiments to parents would be a desirable way to signal love to one's parents. In fact, past research on gift giving has generally found that "familial gift giving is more like primitive premarket exchange. . . where gifts provide social insurance-than like signaling during courtship, so the ine¢ ciencies that are important for signaling purposes need not be present in gift giving in the family" (Camerer, 1988). 1 2 For details on the experimental procedure, see Online Appendix 2.
strong preferences of type i when giving to parents. This change is calculated as follows: where n ij is the number of subjects with preferences to parents in category i and preferences to strangers in category j.
Players who are perfectly sel…sh towards strangers are signi…cantly less likely to behave sel…shly towards parents who are informed about details of the game, and they are more likely to share payo¤s equally with them. This is strong evidence that players with generally sel…sh preferences for giving may be strategically motivated when giving to parents. It is only when parents are informed about the game that they may want to appear equitable to parents who may reciprocate after the game. Notes. * indicates statistical signi…cance at the 10% level.
Interestingly, among those who reveal a preference for equity with strangers, subjects in the information treatment are less likely to play Leontief with parents and more likely to play perfect substitutes. Thus, subjects with a preference for sharing equally are more likely to maximise payo¤s when parents are more likely to share their winnings post-game. However, this di¤erence is not statistically signi…cant, perhaps due to the small sample size.

The e¤ect of information to parents on CES parameters and gift amounts
For those with weakly categorised preferences, we estimate the parameters of a CES utility function as previously.
However, due to sample size limitations, we estimate parameters within each treatment cell, pooling the observations of subjects with weakly categorised preferences within these groups. We …nd the weight on own consumption is statistically signi…cantly lower amongst those in the full information treatment group, which is again suggestive of strategic motives for giving to parents amongst those with weak preferences. Notes. *** indicates statistical signi…cance at the 1% level.
We use regression analysis to examine the marginal e¤ect of the information treatment on payments to parents, where the dependent variable is the payment amount to the recipient in each game, and the unit of observation is the game rather than the subject. Standard errors are clustered by respondent. Table 8 summarises the results. We …nd that subjects exposed to Treatments 2 and 3 give larger payments to parents, all else equal. These coe¢ cient estimates indicate an average increase in giving to parents of about 50%, as the average value of tokens passed to parents was 5 GBP. 13 In addition, the relative price of giving is a signi…cant factor in determining payment amounts to both recipients, and gifts to both recipients are normal goods. 14 These results are also robust to controlling for individual characteristics: gender; age; education; student status; number of children of one's own; number of biological children; and parents'living arrangements, to control for whether the payment recipient is both parents, father only, or mother only. 1 3 Results are very similar to those presented here when Treatments 2 and 3 are included separately in the regressions. 1 4 We also ran the same regressions on payment amounts to strangers, and the information treatment had no e¤ect on this outcome. Though there were similar income and price e¤ects, they were not as strong as in games with parents. Notes. *** p<0.01, ** p<0.05, * p<0.1 Robust standard errors in parentheses, clustered by respondent.
The unit of observation is the particular dictator game. The sample is restricted to respondents with weak preferences. The dependent variable is the amount given to parents in each game (pounds sterling). These results are robust to controlling for player characteristics (gender, age, education, student status, marital status, whether player has children), and identity of parent recipient.
Interestingly, when we separate the sample by those who played with strangers …rst and those who played with parents …rst, the treatment e¤ect only holds for the sample of players who initially played with strangers. Note that subjects did not know any details of the experiments in advance. Thus, when playing with strangers initially, subjects did not know they would then play the same games with parents and vice versa. In addition, when subjects in the full information treatment had played with strangers …rst, a large proportion of their endowment of tokens was given to parents; in 89% of budgets played with parents after playing with strangers, subjects gave away at least 75% of their tokens to parents; and for 17% of such budgets, subjects gave everything to their parents. However, among subjects who played the dictator games with parents …rst, there was no di¤erence across information treatments in the likelihood to give all, or nearly all, of one's endowment to one's parents at any particular budget (see Figure 3).

Theoretical rationalisation of the e¤ect of recipient order
The above results are suggestive of strategic motives for transfers between adult children and their parents. However, we have found that the e¤ect of the information treatment is much stronger when subjects with weak preferences have played with a stranger before playing with one's parent. 15 One might think that the di¤erences found in playing with strangers initially might be explained by a learning e¤ect. However, if there was a learning e¤ect, then we would see a similar pattern for those who play with strangers …rst, regardless of the information treatment. Yet, subjects give more to parents only in the case of full information to parents and when playing with strangers …rst.
Alternatively, one might consider that games with strangers provide a reference point for subsequent games with parents, the idea being that if a player plays with strangers before playing with parents, then that player may give more to parents than the amount given to strangers, where the latter would serve as a reference point in games with parents. However, again, if such di¤erences were to in ‡uence subsequent games with parents in the latter case, then we would not observe such large di¤erences across information treatments.
Rather, we explain this empirical …nding as an income e¤ect in the presence of strategic motives. When a subject …rst plays with strangers, they come to the round of dictator games with parents with some extra amount of lumpsum income from their winnings in the …rst set of games. 16 We would expect this additional income to boost gifts to parents given that our regression results indicate that gifts to parents are a normal good for those with weak preferences (see Table 8).
We could have avoided this income e¤ect if we had chosen to pay subjects for one decision from all 22 budgets, rather than paying them for one in each of the 11 decisions with the di¤erent recipients. We chose to pay subjects as we did because we did not want subjects to be aware of the second game when playing the …rst game. Subjects received no advance information regarding the experiment, so that those who played with parents or strangers …rst had no reason to expect that they would subsequently play the same set of games with strangers or parents. If we had not done this, we would not have had a clean way to determine how the two games impacted each other. Future work might explore the impact of alternative payment mechanisms.
We hypothesise that the positive income e¤ect combined with the presence of strategic motives for giving to parents provides a compelling explanation for our results. The CES estimates suggest that subjects in the full information group place higher weight on their parents' payo¤, which is what we would expect from those with strategic motives for giving to their parents. The additional payo¤s from games with strangers then act to magnify the impact of this variation in preferences.
To illustrate this argument, consider Figure 4 that depicts a hypothetical dictator game with parents. When a subject plays initially with parents rather than with strangers, she faces budget constraint SP . A subject playing with parents can keep all of the tokens, earning a payo¤ of S, can give all of the tokens to parents, earning them a payo¤ of P , or can choose any allocation along the budget constraint SP . As those in the full information group place greater weight on parents'payments than those in the no information group, the latter will choose allocation A, whereas the former will choose allocation B. Since our participants did not play sel ‡essly with strangers, subjects who initially played with strangers played subsequent games with parents with some positive amount expected from these prior rounds. This causes a parallel outward shift of this budget constraint by some positive amount X. 17 A subject would then be faced with budget constraint S 0 P 0 . However, not all points on this budget constraint are possible; any allocation along the budget constraint S 0 P 0 that is above P (e.g., C ) is not directly available as the subject does not have a mechanism by which she can trade-o¤ her additional payment X for increased payment to parents in the experimental setting (this region is indicated by a dashed line). For simplicity, imagine that subjects are endowed with homothetic preferences (in line with our choice of CES utility function). We can see that those in the full information group, who place higher weight on their parents' consumption, will choose a point B 0 over A 0 , sharing very generously with parents. The monetary divergence in payo¤s between treatment groups is also larger between A 0 and B 0 than between A and B. In addition, subjects who play strangers …rst and are in the full information group are more likely to be rationed over the total amount of tokens that they can pass to their parents (choosing C 0 as C is unavailable). Allocations B 0 and C 0 would explain the bunching of very large transfers to parents shown in Figure 3.

Conclusion
In this paper, we have made use of a novel experimental design to recover the characteristics of, and motivations for, giving to parents by adult children. We have found that when parents rather than strangers are recipients of transfers, respondents have a greater proclivity for giving and greater price sensitivity for transfers. The latter would suggest that there may be social e¢ ciency gains when reducing the transaction costs of giving to parents. However, it is important to note that we uncover signi…cant heterogeneity in preferences for giving to parents, which, to our knowledge, has not been explored in any previous work. Such heterogeneity in preference parameters for sharing resources across generations may need to be considered in multi-generational models of consumption and investment, which typically assume either perfectly altruistic or perfectly sel…sh overlapping generations.
Further, we have found evidence of adult children being strategically motivated to share with parents. For those with strongly de…ned preferences, those who played sel…shly with strangers also did so with parents who had no information, but they shared equally with fully informed parents. In addition, for those with weakly de…ned preferences, we estimated a lower weight on own payo¤ and a greater likelihood of sharing a large proportion of one's budget when parents received information about the experiment. This evidence suggests that our subjects are strategically motivated when sharing with parents, as they share more with parents who are more likely to reciprocate in subsequent interactions. However, it is the subjects who initially play dictator games with strangers who are particularly a¤ected by this change in information to parents. We hypothesise that this is because of an income e¤ect in ‡uencing those who initially play with strangers.
These …ndings provide an important contribution to the literature on intergenerational transfer motives, as it is the …rst experimental study to examine motives for giving between parents and adult children. By having adult children play dictator games with a designated family member, we show evidence of reciprocal behaviour that is not due to a selection e¤ect. We also show that while our subjects pass GARP, many of them do not behave in a way that would be consistent with the assumption of transferable utility that is often critical to many household models.
It would be interesting to use these methods to explore such motivations in developing countries, where elderly parents rely more on children than on public transfers for …nancial support, and where …nancial transfers generally ‡ow from adult children to parents (whereas in the UK and other industrialised countries, …nancial transfers ‡ow from parents to children, and elderly parents rely on own savings or public support). China may be one particularly interesting and relevant case, as the one child policy has meant that many adults are responsible for supporting four parents without any siblings to help them. There has been some evidence of crowding out of public transfers in developing countries (e.g., Cox et al., 2004), but by less than what would be predicted under a model of altruism (Cox and Jimenez, 1992). Experimental work with migrants has found that remittances may be strategically motivated (Ambler, 2012), though the majority of recipients in this study were not close family members (spouses, parents, children), and it would be interesting to examine whether migrants behave similarly in this case.
Future work using a combination of laboratory experiments and survey data may shed more light on these areas.
While the lab is restricted to monetary exchange, preferences for giving to parents can also be exhibited in other ways outside the lab. For example, adult children may provide time rather than money to parents . Future studies using these methods might also employ additional variations within subjects. For example, giving to parents could be compared to giving to charities. Finally, as there is a great degree of heterogeneity in sharing in the lab, it would be interesting to explore what individual characteristics or factors outside the lab (e.g., number of siblings, gender, frequency of contact with parents) might in ‡uence such variation.
9 Online Appendix 2 {FOR ONLINE PUBLICATION}

Recruitment Process and Study Sample
During the recruitment process, subjects had been told that this was a research study about adults' relationships with their parents; they were not told that this experiment was being conducted by economists. Throughout our recruitment process, we indicated that eligible participants required a non-coresiding biological parent living in the U.K. 19 Participants were informed in advance of their sessions that all payments would be mailed in the form of gift cards to Sainsbury's, a popular supermarket chain in the UK, and that their parents would also potentially receive a gift card to Sainsbury's. At the end of the experiment, each subject also received 4 GBP in cash as a show-up fee.
Subjects were initially recruited from the pool of experiment volunteers compiled by the Nu¢ eld College Centre for Experimental Social Sciences (CESS). The centre's database included information on student status, concentrations of study, and experience in past experiments. The database allowed us to exclude undergraduate students and economics majors from our sample.
We chose to depart from the usual subject pool of economics majors and undergraduate students, as we were interested in capturing aspects of relationships between adult children and their parents. Economics students may be familiar with the dictator game, and undergraduate students generally rely on their parents for …nancial support.
We wanted to ensure that there were subjects in our sample who were …nancially independent of their parents.
In order to recruit additional participants, we employed a number of other methods: ‡iers were handed out in front of Sainsbury's in central Oxford and Headington, with follow-up emails sent out to interested participants; ‡iers were posted in co¤ee shops, colleges, and Sainsbury's sta¤ lounges throughout Oxford; advertisements were posted in local and online listings; and emails were sent to sta¤ in all departments and colleges at the University of Oxford and Oxford Brookes University. Any participants recruited through these methods registered with CESS, which facilitated scheduling sessions and ensured that participants did not participate in our experiments more than once.
As our experiments took place in Oxford, England, the majority of our study sample resides in the southeast region of the UK (94%). We compare our study sample to the subsample of respondents in the British Household Panel Survey (BHPS), a nationally representative survey in the UK, who reside in the southeast region of the UK.
These descriptive statistics are summarized in Appendix Table A1. While the average age for this subsample is 30, the average age of our sample is slightly higher at 33. Approximately two-thirds of our sample are women. Finally, individuals in our study sample have higher education levels than those in the comparison sample of the BHPS.
While 16% of the BHPS sample have a graduate or higher degree, 36% of our study sample have a graduate degree. extent to which our …ndings may be generalized to a wider population may re ‡ect the extent to which gender and education may in ‡uence behavior in this particular context. Note that our …ndings are robust to controlling for gender, education, and age.
Appendix However, we do …nd that men are more likely to pass GARP than women, and this di¤erence is statistically signi…cant. Other individual characteristics do not predict the likelihood of passing GARP. These regression results are summarized below in Appendix Table A2. Appendix

Experimental Procedures
The …rst experimental session was a paper and pencil pilot, which was held in May 2011. All subsequent sessions were played on the computer. There were 19 sessions in all, which were held through October 2011. All but one session were held at 5:30 pm in order to facilitate participation of those working full-time. Due to multiple requests on the part of potential participants, one session was held on a Friday afternoon. As this session time proved inconvenient for too many potential subjects, all remaining sessions were held in the evening.
Prior studies have found that subjects' decisions may be in ‡uenced by a lack of anonymity and con…dentiality in their choices, particularly towards what might be considered pro-social behaviour (Ho¤man et al., 1994;. 20 We designed our experiment in order to ensure that subjects'anonymity and con…dentiality was maintained to the greatest extent possible, so that the experimenter would not be aware of any speci…c decisions, and so that subjects would not be in ‡uenced by any expectations on the part of the experimenter. 21 When a subject arrived in the lab at the Nu¢ eld College Centre for Experimental Social Sciences (CESS), he was asked to address a brown envelope to himself and a white envelope to his parents. If his parents lived at separate addresses, he was instructed to address the parent envelope to his mother. Subjects held onto these envelopes throughout the session.
Before entering the lab, the experimenter examined both envelopes to ensure that the brown envelope was addressed to the respondent to a local address, that the white envelope was addressed to a di¤erent parent address, and that both addresses were in the UK (gift cards were only valid in the UK). Each subject then picked up a claim ticket from those laid out on a table facing downward by the entrance to the lab. On the other side of the square was a number, and subjects were instructed to sit at the computer station with this number. They were instructed not to speak to one another and to await further instructions from the experimenter.
Subjects were informed that all allocation decisions would be kept strictly con…dential. The person who conducted the experiment was not involved in doling out payments, and subjects were told this at the start of the experiment.
In addition, the experimenter asked for one subject to volunteer to accompany the experimenter at the conclusion of the session to verify that all payments were being mailed out that day. This was done in order to assure the participants that the transfers would indeed be made, as any doubts regarding this would also potentially in ‡uence behaviour (Bolton et al., 1998). Payment allocations were recorded by each respondent's claim ticket number. In a room separate from the lab, research assistants inputted payment amounts onto gift cards and placed them in numbered payment envelopes corresponding to each ticket number. Brown numbered payment envelopes included cards to subjects and white numbered payment envelopes included cards to parents. Letters and any additional information being sent to parents were also included in these white envelopes. The contents of these envelopes did not include the subject's name or ticket number, and subjects were informed of this in order to assure them that their parents would not have any information that we could later use to match to their responses. At the end of the experiment, subjects were called individually by their claim ticket number. A research assistant gave the subject his brown payment envelope, and asked that he examine the gift card and then place it in the brown envelope he addressed to himself. A second research assistant gave the subject the white payment envelope, and asked the subject to examine the contents and place them in the white envelope he addressed to his parents. If the subject was also given an opportunity to write a note, the subject placed the top copy of his note, which indicated his claim ticket number, in a large envelope marked "NOTES,"and the bottom copy which did not have a claim ticket number, was to be placed in the white envelope addressed to the parent. The subject was asked to seal both envelopes and place them in a larger envelope marked "MAIL."All of these measures were taken to assure the subject of his anonymity.

Deviations from Rationality
In this section, we compute the signi…cance of rationality violations in our sample to check for patterns in violations that may be linked to our experimental design. For example, did violations occur for "early" budgets if people were confused about the game or for "late" budgets due to fatigue?
1. Afriat e¢ ciency Firstly, we compute the "Afriat E¢ ciency Index", e, for individuals who fail GARP, which returns the extent to which we would have to relax each budget constraint for the restrictions associated with GARP to be satis…ed. 22 Thus, e 2 (0; 1], with e further from 1 indicative of more signi…cant violations of rationality (Afriat, 1967).
Appendix  Table A4 shows that e re ‡ects the di¤erences in pass rates between the two recipients, and the low pass rate for the test of the recipients pooled together. The set of games in which parents are the recipients achieves the highest pass rate of 90.5%, with e = 0:945. When strangers are the recipients, the pass rate and e are slightly lower, 88.4% and e = 0:917. Our subjects treat giving to the two recipients as distinct goods. When we pool all dictator games together, only 26.8% of subjects pass GARP and e = 0:835: This is a relatively low Afriat E¢ ciency Index, so that the low GARP pass rates when all games are pooled is not simply a re ‡ection of a more di¢ cult test; rather, preferences for giving to parents and strangers are distinctly di¤erent for most subjects.
2. Size of largest rational choice set Calculating the largest number of choices over which GARP is satis…ed is an alternative way to assess the severity of deviations from rationality. Behaviour can be thought of as "more 2 2 On power indices for revealed preference tests, see Bronars (1986) and Andreoni and Harbaugh (2006).
rational" the fewer the number of choices that must be dropped for the remaining set to satisfy GARP. However, there are some subtle complications to contend with when calculating this metric. The set of choices that must be dropped for the remaining set to satisfy GARP is not necessarily unique. We adapt the partitioning algorithm de…ned in  to calculate the largest number of choices over which GARP is satis…ed when considering giving to parents and strangers as di¤erent goods.
Appendix We also examined whether subjects were more likely to make "mistakes" in the budgets they saw early on when they were learning the game, or perhaps later on when they got tired. In games with strangers, people were more likely to make "mistakes" in the …rst or last three budgets seen. For 17 subjects, one of the …rst three budgets seen caused them to fail GARP and for 14 subjects, one of the last three budgets seen did so, whereas one of the middle three budgets caused an issue for 8 subjects. But in games with parents, 11 subjects made errors in the last three budgets seen, whereas 8 subjects made errors in both the …rst three budgets and middle three budgets. Note the order of the budgets was randomised across subjects, so that these di¤erences are not due to any particular budget.
But each subject saw the budgets in the same order in both sets of games. So di¤erences between games with parents and strangers cannot be explained by any particular budgets.

Testing HARP and Gorman Polar Form
In Footnote 9, we note that tests of the Homothetic Axiom of Revealed Preference and Gorman Polar Form preferences suggest that the majority of subjects with weak preferences can have their choices rationalised by preferences with linear Engel curves. We here note the tests that we performed and also how we computed the necessary optimisation error to rationalise the behaviour of those failing both tests. To establish whether a subject's choices satisfy HARP, we check for the existence of a non-empty feasible set, fu i g i=1;:::;T , to the following linear programme: The existence of a solution to this programme is necessary and su¢ cient for choices to be rationalised by a homothetic utility function (see Varian, 1983).