Waldfogel%20The%20Deadweight%20Loss%20of%20Christmas

Waldfogel%20The%20Deadweight%20Loss%20of%20Christmas - The...

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Unformatted text preview: The Deadweight Loss of Christmas By JOEL WALDFOG EL* When economists comment on holiday gift-giving, it is usually to condone the healthy effect of spending on the macro- economy. However. an important feature of gift-giving is that consumption choices are made by someone other than the final eon- sumer. A potentially important microeco- nomic aspect of gift-giving is that gifts may be mismatched with the recipients‘ prefer- ences. In the standard microeconomic framework of consumer choice. the best a gift-giver can do with, say. $10 is to dupli- cate the choice that the recipient would have made. While it is possible for a giver to choose a gift which the recipient ultimately values above its price—for example, if the recipient is not perfectly informed—it is more likely that the gift will leave the recip- ient worse off than if she had made her own consumption choice with an equal amount of cash. In short, gift-giving is a potential source of deadweight loss. This paper gives estimates of the dead- weight loss of holiday gift-giving based on surveys given to Yale undergraduates.‘ I find that holiday gift-giving destroys be- tween 10 percent and a third of the value of gifts. While these recipients may be unrep— *Department of Economics, Yale University. New Haven, CT 06520. I am grateful to my colleagues at Yale for lunchtime conversation which refined this idea. 'Much existing research examines the theoretical desirability of cash, as opposed to in»kind transfers (cg, Maria Schmundt et al . 1975, Ronald A Dye and Rick Antle. I986; Charles Blackorby and DaVId Don» aldson, I‘J88). I am aware of no empirical research on reCipient valuation of transfers, except Eugene Smolensky ct al. (1977), which presents estimates of the value of government iii-kind transfer piograms to benefits rectpients Their results are compared With mine below resentative of the US. population, their gifts are not necessarily unrepresentative. Holi- day expenditures average $40 billion per year, implying that a conservative estimate of the deadweight loss of Christmas2 is a tenth as large as estimates of the dead— weight loss of income taxation. I also ex— plore how deadweight loss and the tendency to give cash gifts vary with the relationship and age difference between giver and recipi— ent. I find that gifts from friends and “sig- nificant others” are most efficient, while noncash gifts from members of the ex— tended family are least efficient and destroy a third of their value. I develop a simple expected-utility model to explain the deci— sion to give cash. as opposed to in-kind gifts. The data are consistent with the model: cash gifts are most common from the sorts of givers whose noncash gifts have the low- est expected value to recipients (given their cost) and high variability in recipient valua- tion. 1. Theory A. The Consequences of Gift-Giving Students are customarily taught in eco— nomics courses that unfettered consumer choice leads the consumer to higher utility than constrained choice. Thus. for example, government grants—in-kind are inefficient, unless the consumer would have chosen to consume at least the amount of the good granted, had the grant been cash. One can analyze the possible inefficiency of gift-giving from the recipient standpoint 2References to the deadweight loss of Christmas should be understood to apply equally to Hanukkah and other holidays with gift-giving rituals 1328 Copyright © 2001 All Rights Reserved VOL. 83 N0 5 WALDFOGEL' TH]. DI;4I)WEIGHTL()SS ()F ('HRIS‘TleS Gift Good (G) Flotiizi‘ it (in l-(lIVINt. ANI) Di «om l(il|l L()\‘\ Notes: The amount of the gift good ((1‘) is on the horizontal axis The vertical aXIs measures all other goods. in dollars Point 1 on budget line (111' describes the reCipient's holdings of the gift good and all other goods prior to receipt of the gilt. when her utility is U” When she receives u’t' units of the gift good. bet holding.“ the represented by point Ill on budget line lzb’ At this point her utility l\ l s Had she received a cash gift of equal cost to the giver. she could have thoseri any point on budget line bb’, and she would have chosen point ll. With utilitv (is. Because the utility of the bundle chosen freely by the recipient exceeds utility of an equal-cost bundle that includes the gift‘ there Is a deadwcight loss. In dollars. this deadweight loss is 1329 distance ob on the vertical aids in an indifference-curve diagram.1 (‘onsider Figure 1, with the gift good (G) on the horizontal axis and all other goods (A. with PA = 1) on the vertical axis. Point 1 depicts the gift recipient‘s position prior to receiv- ing this year’s gift. Suppose that the giver is planning to spend $x. If the gift comes in the form of cash, the recipient moves to 3Giving may confer utility on the giver. The present note is concerned only With the recrpient liven if the sum of giver and recipient valuations of gifts exceed their price, deadweight loss is present if the recipient values the gift below her valuation of a gift ot equal cost that the giver finds equally enjoyable to give budget constraint bb’. on which she may choose any point. Given this unconstrained choice, she chooses point ll. In this case the gift is completely efficient: fix is the mini— mum expenditure necessary to increase util- ity from UU to 1/1. ll, instead of cash, the gift consists of only the gift good. then the recipient receives (tr/P“) units of gift and arrives at point 111, also on budget constraint bii’. The resultant recipient utility is U:- This gift is inefficient because the recipient could have reached this level of utility with a cash gift smaller than $x. The dashed budget constraint shows the minimum additional expenditure necessary to achieve U3: it is distance ac. Copyright © 2001 All Rights Reserved 1330 THEAMERICAN ECONOMIC REVIEW which is less than the cost of the gift, dis- tance ab. Hence, distance cb is the dead- weight loss associated with the gift.4 The size of the deadweight loss depends on both the giver’s acquaintance with the recipient’s preferences and the recipient‘s knowledge of her own preferences. If the recipient is perfectly informed about gift items, then the giver can do no better than to give cash; and the better the giver knows the recipient’s preferences, the closer the giver can come to reproducing the recipient’s choice. However, if recipients are imperfectly informed, the giver may be able to choose a gift that the recipient would not have chosen but which makes the recipient better 0H than a cash amount equal to the cost of the gift. In this case, it is possible for a gift to create, rather than destroy. value. The better the giver knows the recipient’s preferences—«including, possibly, prefer- ences the recipient is unaware of——the more likely it is that the giver will choose a gift that the recipient values above its cost and will thereby create value through giving. B. Cash Gifts and the Goals of Gifl~Girers Givers sometimes give cash and some- times give gifts in kind. This section de- scribes a simple expected-utility model to explain the observed pattern of cash-giving. As far as the giver is concerned, the value that the recipient will attach to a noncash gift is a random variable g. Givers perceive that recipients evaluate their gifts according to the utility function U(g). If the giver has decided to spend an amount g” 0n a gift, the giver’s problem is to decide whether to give cash. which confers utility of U(g0) on the recipient, or a noncash gift, which has expected utility of ff(g)U(g)dg, where f( -) is the density function of recipient valua- tions. This density function has interesting interpretations. If the recipient is perfectly 4The fact that gifts may typically be exchanged eliminates this problem only in princrple, Because of transaction costs and perhaps gutlt, many ineflieicnt gifts are not exchanged. See the results in Sections ll and 11]. DECEMBER 1993 informed and the giver has exactly the re- cipient’s knowledge, f(-) is a spike at go. For a person who knows the recipient “bet— ter than she knows herself,” whose gift cost- ing g0 may have value to the recipient above g”. f(') includes probability density for g > go. The density of recipient valua- tions of gifts from a giver ignorant of the recipient’s preferences has a low mean and a high variance. Giver maximization of recipient utility implies that the giver gives cash if the giver’s perception of the recipient’s utility of gU in cash exceeds the givcr's expected recipient utility of a gift costing the giver g0. Givers whose gifts share the same distribution of recipient valuations may differ according to the degree of risk aversion they attribute to recipients. Hence, some givers of a type give cash while others give iii-kind gifts. (Some grandparent gifts are cash, and some are noncash, even if all grandparents" gifts share the same distribution of recipient valua- tions.) The observable implication of this model is that cash gifts are more likely from givers aware that their noncash gifts have lower expected utility. Hence, cash gifts are more likely from givers who give low-value non- cash gifts. relative to their costs. If givers perceive recipients to be risk-averse, then givers whose noncash gifts have higher vari— ance in value will also be more likely to give cash, all else constant. II. Data In the first of the two surveys, completed voluntarily by 86 intermediate microeco- nomics students in January 1993, gift recipi» ents were asked to estimate the total amounts paid (by the givers) for all of the holiday gifts the respondents received in 1992. Students were asked their gender and whether they exchanged any of their gifts. Finally, students were asked to place a value on their gifts, based on their willingness to pay for the gifts. The question was worded as follows: Ifyou made no exchanges, think of the gifts you received directly. Copyright © 2001 All Rights Reserved VOL 83 NO 5 If you made exchanges, think of the gifts you did not exchange as well as the things you obtained in exchange for gifts you received directly. Apart from any sentimental value of the items, if you did not have them, how much would you be willing to pay to obtain them? The second survey, given in March 1993, gathered data on each respondent’s individ- ual gifts. Fifty-eight respondents gave us- able information on 278 gifts.5 The survey asked respondents to describe each of their gifts, identify the givers’ ages and relation- ships to the recipient (parent, aunt or uncle, sibling, grandparent, friend, or “significant other”), estimate the prices that the givers paid for the gifts, and indicate whether the gifts were exchanged. The gift description allows gifts to be divided into three cate— gories: cash, gift certificates, and gifts. The respondents were asked to estimate the value of the gifts as the ...amount of cash such that you are indifferent between the gift and the cash, not counting the sentimental value of the gift. If you exchanged the original gift, assess the value of the object you got in exchange for the original gift. If you exchanged the orig- inal gift for cash, put the cash amount you received here. The survey also asked gender, age, family income, and the amount the recipient spent on holiday gifts for others in 1992. Note that valuations from both surveys take ex- changes into account. The difference between the two surveys’ valuation methods may be described as fol— lows: the first survey asks for the maximum the respondent would pay for her gifts, while the second survey asks for the minimum the respondent would accept in lieu of the gifts. As Jack L. Knetsch and J. A. Sinden (1984) 5An observation is usable if it includes valid infor- mation on price, value, relationship and age of giver. age of rec1pient, whether the gift was cash, and whether the gift was exchanged. WALDFOGEL. THE DhADWEIGHT LOSS OF CHRISTMAS 1331 TABLE l—AVERAGE AMOUNTS PAID AND VALUES or- Gir'rs, BY RECIPIENT Variable Survey 1 Survey 2 Amount paid ($) 438 2 508.9 Value ($)“ 313 4 462.1 Percentage ratio of average value 71 5 90.8 to average price patdh Average percentage yieldL (it) 1 87.1 (3.3) (3.2) Number of moments 86 58 Jln survey 1. respondents valued their gifts by their Willingness to pay for them. In survey 2, respondents valued their gifts as the money they would accept in lieu of the gifts (see text) h . . Ratio of average value to average price paid. ‘Average of (value, /price,). The standard error of average yield is given in parentheses. demonstrate, experimental subjects require more in return than they are willing to pay for similar objects. Hence, we expect valua- tions to be higher—and deadweight losses to be lower—in the second survey. The true amount of deadweight loss lies in between. 111. Empirical Analysis A. How Large is the Deadweight Loss? The responses of the 86 students taking the first survey and the 58 students taking the second survey, are reported in Table I.“ In survey 1, respondents estimate that friends and family paid an average $438 for the recipients’ total gifts, but respondents express a willingness to pay only $313, on average, for the same gifts. Because losses are approximately proportionate to receipts across receipt sizes, the ratio of average value to the average price (71.5 percent) is close to the average ratio of value to price, or average “yield,“ of 66.1 percent. A re- gression of log value on log price across recipients’ total gift receipts confirms that the relationship between value and price is f’Table 1 reports data averaged across reCipients. The remaining tables report averages across gifts. W “MN ,m ” «WW Ma.mawm-~mmw,wmww .a. ,v Copyright © 2001 All Rights Reserved I332 THE AMERICAN ECONOMIC REVIEW essentially proportional: log(va1ue,)= —0.314 + 0.964log(priee,) (0.44) (0.08) with standard errors in parentheses and an R2 of 65.6 percent. Forming a deadweight- loss measure from average yield indicates that gift-giving destroys a third of gift value. Note that the cash component of a recipi- ent’s gifts are included in both the price and value estimates in survey 1. Hence, the av- erage yield on noncash gifts is below 66.1 percent, and the deadweight loss among noncash gifts actually exceeds one—third. Putting aside the inclusion of cash, the valu- ation by willingness to pay in survey 1 makes one-third an upper—bound estimate of the deadweight-loss fraction. The 58 respondents to the second survey estimate that $509 was paid for their gifts, but they value these gifts at only $462. The average yield across these recipients (87.1 percent) is quite similar to the ratio of the average value to the average price (90.8 percent). A regression of the log value of receipts on log prices across recipients again confirms that value is nearly proportional to price: log(value,)=—0.618 + 1.()7510g(price,) (0.23) (0.04) with standard errors in parentheses and an R2 of 93.2 percent. As expected, the implied deadweight loss is less than the results of the first survey would suggest. For compara— bility with total receipt figures in survey 1, cash is not excluded, so that the deadweight loss among noncash gifts is higher. Aver— aged across gifts, rather than recipients, the average yield on noncash gifts is 83.9 per- cent, suggesting a deadweight-loss fraction of 16.1 percent (see Table 2). This is a lower bound because of the survey—2 valuation method. While the survey respondents’ total gift receipts (averaging $400~ 500) and family incomes (averaging $143,000 for the 43 stu— dents reporting family income) are unrepre— sentative of the US. population. the frac— tion of the gifts” value destroyed through DECEMBER 1993 TABLE 2—AVFRAUF. YiELD av PRir‘F. or GIFT (Ex( 1 UDING Cvst GiF’rs) Percentage Standard PrlCC average error range yield (percent) N $07$25 85.8 5.6 102 $264$50 74.4 3 4 82 $51~$100 89.8 4.2 47 Over $100 88 5 4.3 47 Overall: 83.9 2.8 246 Note Overall figures are based only on observations With valid information about giver. inefficient exchange need not be unrepre- sentative.7 First, among survey recipients the yield ratio does not vary with family income. Thus, while the general population has lower average income than the survey recipients, yield rates for survey recipients with income nearer to the population aver- age do not differ from the survey average. Second. deadweight losses are large and significant for gifts in all price ranges, thus including price ranges typical for gift recipi— ents generally. Table 2 reports the average yield for noncash gifts in various price ranges. Over a third of the gifts in the survey are estimated to cost less than $25, a range with an average yield of 85.8 percent (with a standard error [SE] of 5.6 percent). Nearly an additional third of gifts are esti- mated to cost between $26 and $50; these gifts have an average yield of 74.4 percent (SE: 3.4 percent). Average yield is some— what higher for larger gifts, about 89 per- cent for gifts estimated to cost over $50. The fraction of gift price that is wasted reaches a maximum of a quarter for gifts costing between $25 and $50 and is other- wise approximately constant at 10—15 per- cent. Recall that these figures are based on the conservative valuation method of survey 2. Whatever the average size of gifts in the general population. if their yields are simi- lar to the yields on similar-sized gifts in this 7The average holiday gift expenditure per US. fam- ily was $400 in 1092 (see Bureau of National Affairs. 1992). Copyright © 2001 All Rights Reserved VOL. 83 N0 5 WALDFOGEL THE DI‘A[)WEIGHT LOSS OF CHRISTMAS 1333 TABLE 3—GiFr YIFU) AND TFNIM NCY To Givi CAsii, HY Int \Tlfl or GIVER Aunt, uncle Sibling Parents Significaniother Grandparent Friend All Variable A. Yield of Noncash Gifts Number of observations 24 4*) 113 Value ($)8 40.5 23.5 133.3 Price (s)h 64 a 38.3 135.6 Percent yieldC 64.4 86.2 (7.0) (5 2) Yield standard error 34.1 36.1 Percentage exchangedd 20 8 6 1 B. Tendency T0 Gil e Cash: Number of observations 28 52 125 Agec 44 20 Percentage cash1 14.3 5.8 "Estimated value of gift to reCipient. {’Recipient’s estimate of price giver paid for the gift. 86.5 33.9 8 15 31 246 24.1 56.1 23 l 77 6 25.4 75.9 25.3 84.0 91.7 62 9 98.8 83.9 (3.2) (8.3) (103) (14.7) (2.8) 23 6 40.0 82.0 43.9 0.0 13.3 6.5 9.8 8 26 33 278 23 73 37 41 l).() 42 3 6 1 11.5 LAverage of ratio (value, /price,): standard errors of average yield in parentheses. G‘lFraction of noncash gifts exchanged. ‘Age of giver (recipients are all aged ”922). 1Percentage of gifts that are cash or gift certificates. sample, then the deadweight loss Will be at least 10 percent of the price of gifts. B. Determinants of Gift Yield and Cash-Giving This section examines gift yields and the tendency to give cash, by type of giver, to answer the following questions, First, how does the deadweight loss vary with familiar- ity of the giver with the recipient’s prefer- ences? We expect the deadweight loss to increase with the social distance between giver and recipient. as measured by the na- ture of the relationship (aunt or uncle, sib- ling, parent, significant other. grandparent. and friend) and the age difference between giver and recipient. Second. when do givers give cash? Are cash gifts more likely when the expected utility of noncash gifts is likely to be low? The top panel of Table 3 reports the fraction of gifts exchanged. as well as the average value, price, and yield of gifts, by identity of the giver. The table also reports the standard error of gift yield. The table clearly indicates that gifts from givers hear- ing different relationships to the recipients vary significantly in their suitability to recip- ient preferences. Excluding cash gifts. the fraction of gifts exchanged gives a rough measure of how well the gifts match the recipients’ preferences. Aunt/uncle and grandparent gifts are most likely to be ex~ changed, a...
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