Violations of Present-Value Maximization in Income Choice

GARY GIGLIOTTI AND BARRY SOPHER

VIOLATIONS OF PRESENT-VALUE MAXIMIZATION ININCOME CHOICE

ABSTRACT. We report results of an experiment testing for present-value maxi-mization in intertemporal income choice. Two-thirds of subjects did not maximizepresent value. Through a series of experimental manipulations that impose costson non-present value maximizers, we are able to reduce the level of violationssubstantially. We find, however, that a sizeable proportion of subjects continueto systematically violate present-value principles. Our interpretation is that thesesubjects either cannot or choose not to distinguish between income and expendi-ture in making their choices. Self-management, bounded rationality, and sequencepreference are suggested as possible explanations for such behavior.

KEY WORDS: Intertemporal choice, present value, self management, boundedrationality, sequence preference.

1. INTRODUCTION

A very powerful prediction of the economic theory of intertemporalchoice is that, all else equal, in a choice between alternative streamsof certain payments, the stream offering the higher present valueshould always be chosen. Nonetheless, there are many observableexamples of behavior that violate this principle of present-valuemaximization. Over-withholding of Federal income taxes and par-ticipation in Christmas Club savings plans are just two.1 Similarly,some individuals pay bills long before they are due. All three of theseexamples may involve non-trivial amounts of money and are typicalof the behavior of many individuals in our society. Experimentalstudies, such as those by Ben-Zion, Rapoport, and Yagil (1989),Ainslie (1975), Loewenstein and Sicherman (1991), Thaler (1981),and many of the contributions in Loewenstein and Elster (1992)illustrate behavior that is inconsistent with present value maximiza-tion.

There have been a number of recent attempts to explain theseinconsistencies with present value maximization. Many investigatorshave examined a prospect theory analogue for intertemporal choice:

Theory and Decision 43: 45–69, 1997.c 1997 Kluwer Academic Publishers. Printed in the Netherlands.

46 GARY GIGLIOTTI AND BARRY SOPHER

Loewenstein (1987), Loewenstein (1988), Loewenstein and Prelec(1992), Shelley (1994), Keren and Roelofsma (1995), Ahlbrechtand Weber (1996). Others have investigated dynamic consistency inchoice over time more generally, such as Strotz (1956), Elster (1979),Grout (1982), Schelling (1984), and Ainslie (1986). Machina (1989)presented a comprehensive discussion and noted that individualswith non-separable preferences may be still consistent in their deci-sions over time, but not in the same way as someone with separablepreferences.

But regardless of one’s intertemporal preference structure, sepa-rable or not, most economists would argue that rational individualswould like the largest choice set possible. They would not be influ-enced by the sequence of payments, but by the total expenditurethose payments could support over the time span of the problem. Itwould be surprising, or at any rate of more fundamental importancefor economic theory, if people systematically choose income streamsthat do not allow the optimal choice of consumption, whatever one’sspecific preferences might be. Such choice behavior suggests that nodistinction is being made between income, which is only the meansfor consumption, and expenditure, which is the act of acquiringconsumption goods. To shed some light on the behavior of individ-uals making decisions over time, we have constructed some simpleexperiments. In these experiments, subjects are always given choic-es between income streams in which there is a clear present-valuedominance relationship. Moreover, this dominance relationship doesnot require the existence of a capital market, not do we have tomake strong assumptions on the nature of subjects’ intertemporalconsumption preferences. We are concerned with three basic ques-tions:

1. When presented with easy-to-understand payment streams, dosubjects choose the streams with the highest present value?

2. If they do not, is their observed behavior systematically differentfrom present value maximization?

3. If so, can this systematic behavior be altered or rationalized byadditional experiments, i.e., do individuals respond in a wayconsistent with the basic premise that higher present value isbetter than lower present value?

VIOLATIONS OF PRESENT-VALUE MAXIMIZATION IN INCOME CHOICE 47

Below we report in detail the results of a series of experimentsthat were designed to answer the questions listed above. Our resultscan be briefly stated as follows. In Experiment 1, approximately70% of subjects failed to maximize present value. About 50% ofsubjects prefer streams of constant payments over time, even whena higher present-value stream is available. In Experiments 2 and 3we were able to increase the proportion of choices consistent withpresent value maximization by implicitly penalizing subjects fornon-present-value-maximizing choices. We conclude that presentvalue considerations do enter into subjects’ preferences over incomestreams, but that there are many other powerful considerations aboutincome streams that the present value model does not account for.

Experiment 4 uncovers a very strong context effect in incomechoice. Subjects asked to choose amongst hypothetical wage pay-ment streams are much more likely to violate present value principlesthan subjects asked to choose amongst hypothetical payment streamsfrom an inheritance. This suggests that, in addition to the system-atic departures from present value maximization in the relativelycontext-free environment of Experiments 1, 2 and 3, intertempo-ral choice decisions made within a specific real-world context areeven more likely to violate present value principles. We find frompost-experiment discussions with subjects that they bring all sortsof information, irrelevant to present value principles, and often fal-lacious, into the decision problem to rationalize non-present valuechoices. Explanations mentioned by subjects include a concern thatpay on their next job would be affected by their choice (ruled outin the instructions), a hedge against inflation (fallacious), and theunpleasantness of having one’s salary decline each year (a form ofintertemporally nonseparable preferences).

The remainder of the paper is organized as follows. Section 2 con-tains a general description of the experimental design and proceduresfor Experiments 1, 2 and 3. Section 3 contains analysis and discussionof the results of Experiment 1, which was designed to address Ques-tions 1 and 2 above. Section 4 contains the analysis and discussionof results for Experiments 2 and 3, which address Questions 1, 2, and3. Section 5 summarizes the results of Experiments 1 to 3. Section6 presents the results of a fourth experiment, which involved onlyhypothetical payoffs, which further delineates the systematic nature


of departures from present-value maximization. Section 7 concludesthe paper. An Appendix contains the complete set of instructions andquestions used in the experiments.

2. EXPERIMENTAL DESIGN

Each of the first three experiments consist of a questionnaire onwhich a subject is presented with three groups of three paymentstreams each: A group with decreasing payments over time, a groupwith constant payments over time, and a group with increasing pay-ments over time. Subjects are asked, in pairwise fashion, to choosebetween payment streams within each group, and they are asked, inpairwise fashion, to choose between their most-preferred paymentstreams from each group. Subjects in each experiment were told that10 of them would be chosen at random at the end of the experimentto be paid. For each of the 10 subjects chosen, one of the questionswould be selected at random, and their chosen payment stream forthis question would be paid to them in cash.

The purpose of this design is to present subjects with clear andsimple choices among income streams in which present value dif-ferences among the streams are apparent. Each payment stream wasto be paid out over a period of 6 weeks or less. Payments were tobe made ‘today’, ‘2 weeks from today’, ‘4 weeks from today’, or ‘6weeks from today’. The different payment streams in each group forExperiments 1 to 3 are shown in Table I. 2

There are eight possible patterns of pairwise choice for the intra-group questions, ignoring statements of indifference. There are 27different possible configurations of ‘most-preferred’ choices fromthese groups, ignoring statements of indifference and assuming nointransitive cycles of choice in any of the intra-group set of questions(which would make selection of a most-preferred option for a groupimpossible). Given a ‘most-preferred’ stream from each group, thereare eight possible patterns of pairwise choice for the inter-groupquestions. Assuming only a positive discount rate, our design makesone thing clear: failures to maximize present value always take theform of opting for more spread-out streams of income within a groupof questions.


TABLE IDefinition of payment streams.

Experiment 1 Decreasing Constant IncreasingPayment Received: Ad Bd Cd Ac Bc Cc Ai Bi Ci

Today $20 $15 $12 $15 $10 $7.50 $10 $5 $3In 2 Weeks $10 $10 $9 $15 $10 $7.50 $20 $10 $6In 4 Weeks — $5 $6 — $10 $7.50 — $15 $9In 6 Weeks — — $3 — — $7.50 — — $12

Experiment 2 Decreasing Constant IncreasingPayment Received: Ad Bd Cd Ac Bc Cc Ai Bi Ci

Today $19 $14 $11 $14 $9 $6.50 $9 $4 $2In 2 Weeks $9 $9 $8 $14 $9 $6.50 $19 $9 $6In 4 Weeks — $4 $5 — $9 $6.50 — $14 $8In 6 Weeks — — $2 — — $6.50 — — $11

Experiment 3� Decreasing Constant IncreasingPayment Received: Ad Bd Cd Ac Bc Cc Ai Bi Ci

Today $19 $14 $11 $13.50 $8.50 $6 $9 $4 $2In 2 Weeks $9 $9 $8 $13.50 $8.50 $6 $19 $9 $5In 4 Weeks — $4 $5 — $8.50 $6 — $14 $8In 6 Weeks — — $2 — — $6 — — $11

� Payments for form B shown. Payments for Form A are identical to those inExperiment 2.

The experiments were conducted in introductory economics class-es at Rutgers University in the Spring of 1993 (Experiment 1) andthe Spring of 1994 (Experiments 2 and 3), each in a different class. Itwas explained that the payments would be made in class (on the daythe experiment was done, and at successive two week intervals). Ineach case, the latest possible payment occurred before the end of thesemester. We do not believe that doubts about whether the promisedpayments would be made were a factor in the experiment.


TABLE IIIntra-group choice patterns, Experiment 1.

Decreasing Constant Increasing Preference PatternStreams (d) Streams (c) Streams (i)

Pattern Freq. (%) Freq. (%) Freq. (%) k = d; c; i for decreasing,Number constant, or increasing

1 133 (53.57) 109 (43.25) 132 (52.17) Ak�Bk; Bk�Ck; Ak�Ck

maximize present value2 1 (0.40) 0 (0.00) 1 (0.40) Ak�Bk; Bk�Ck; Ck�Ak

intransitive3 0 (0.00) 1 (0.40) 2 (0.79) Ak�Bk; Ck�Bk; Ak�Ck

extreme-preferring4 5 (1.98) 3 (1.19) 3 (1.19) Ak�Bk; Ck�Bk; Ck�Ak

extreme-preferring5 42 (16.60) 50 (19.84) 43 (17.00) Bk�Ak; Bk�Ck; Ak�Ck

middle-preferring6 29 (11.46) 34 (13.49) 28 (11.07) Bk�Ak; Bk�Ck; Ck�Ak

middle-preferring7 2 (0.79) 3 (1.19) 2 (0.79) Bk�Ak; Ck�Bk; Ak�Ck

intransitive8 41 (16.21) 52 (20.63) 42 (16.60) Bk�Ak; Ck�Bk; Ck�Ak

minimize present value

Totals 253 252� 253

� One observation deleted due to missing data on one question.

3. RESULTS OF EXPERIMENT 1

3.1. Intra-Group Choice Patterns

The results of Experiment 1 are presented in Tables II and III. TableII illustrates, for each group of three payment streams, the distribu-tion of choice patterns implied by subjects’ answers to three pair-wise choice questions. The payment streams are referred to by letter(Ak; Bk, and Ck, k = d; c; i) in the table, and are defined in TableI. In each group, a plurality, and usually a majority, always choosethe highest present-value payment stream.3 The second most com-mon type of choice pattern is (combining patterns 5 and 6) the‘middle-preferring’ pattern, in which the payment stream that is inthe middle, in present-value, is preferred to the other two. Between


TABLE IIIInter-group choice patterns, Experiment 1.

Pattern Freq. (%) Preference PatternNumber (most-preferred stream)

1 79 (35.11) Dec�Con, Con� Inc, Dec� Inc(decreasing)

2 1 (0.44) Dec�Con, Con� Inc, Inc�Dec(intransitive)

3 6 (2.67) Dec�Con, Inc�Con, Dec� Inc(decreasing)

4 4 (1.78) Dec�Con, Inc�Con, Inc�Dec(increasing)

5 54 (24.00) Con�Dec, Con� Inc, Inc�Dec(constant)

6 57 (25.33) Con�Dec, Con� Inc, Inc�Dec(constant)

7 1 (0.44) Con�Dec, Inc�Con, Dec� Inc(intransitive)

8 23 (10.22) Con�Dec, Inc�Con, Inc�Dec(increasing)

Totals 225�

� 28 Observations deleted due to missing data (failure to statemost-preferred stream for one or more groups explicitly) orinconsistent answers (stated most-preferred stream for oneor more groups inconsistent with answers to pairwise choicequestions within group).

one-fourth and one-third of choice patterns are middle-preferring.Finally, choice of the lowest present-value stream in each pair-wise choice is third most common. Other patterns are negligible.The only difference between the three groups is a lower propor-tion of present-value maximizing types, and correspondingly highermiddle-preferring and minimum present-value types, within the con-stant payment streams group.

3.2. Inter-Group Choice Patterns

Table III shows the distribution of observed inter-group choice pat-terns for Experiment 1. Since the payment streams are distinct in


each group – decreasing, constant, or increasing – one can state,for each possible inter-group choice pattern, which type of paymentstream is most-preferred overall. The right-most column of TableIII states the type of payment stream that is most preferred for eachpossible pattern of choice.

The most striking pattern in Table III is the prominence of a con-stant payment stream as the most-preferred overall (patterns 5 and6). About half of the subjects fall in this category. Even among indi-viduals who always chose the highest present value payment streamin each group, there is some tendency to prefer, overall, a constantpayment stream (18%). This ‘constant-preferring’ tendency is evenstronger among those subjects whose initial most-preferred choicesacross groups are inconsistent with present-value maximization.

3.3. Discussion

In answer to Questions 1 and 2 posed above, we find strong andsystematic deviations from present value maximization in paymentchoice in Experiment 1. While we did not expect to see 100% present-value maximization neither did we expect to see half of all subjectschoosing in a specific way (‘constant-preferring’) that violates thepresent value maximization.

The time periods in this experiment are short. In each paymentstream in each group in Experiment 1, the total amount paid out overa 6-week period is the same: $30. Subjects with a zero discount ratewould be indifferent between all of the payment streams in the exper-iment. Subjects might still choose systematically on other grounds.For example, they might value a constant stream of payments overtime. Experiment 2 and Experiment 3 were designed to make cer-tain that even subjects with zero discount rates would have a cleardominance ranking of payment streams within each group.

4. DESIGN AND RESULTS FOR EXPERIMENTS 2 AND 3

4.1. Experiment 2

The income streams used in Experiment 2 are a slight variation onthose used in Experiment 1, as noted in Table I. The payment streamswere derived by subtracting $1 from each payment in each incomestream in Experiment 1. In this way, the total amount paid out by


TABLE IVIntra-group choice patterns, Experiment 2.

Decreasing Constant Increasing Preference PatternStreams Streams Streams


1 203 (66.34) 199 (65.25) 197 (63.96) Ak�Bk; Bk�Ck; Ak�Ck

maximize present value2 4 (1.31) 1 (0.33) 5 (1.62) Ak�Bk; Bk�Ck; Ck�Ak

intransitive3 11 (3.59) 12 (3.93) 10 (3.25) Ak�Bk; Ck�Bk; Ak�Ck

extreme-preferring4 7 (2.29) 7 (2.30) 5 (1.62) Ak�Bk; Ck�Bk; Ck�Ak

extreme-preferring5 24 (7.84) 26 (8.52) 29 (9.42) Bk�Ak; Bk�Ck; Ak�Ck

middle-preferring6 19 (6.21) 19 (6.23) 26 (8.44) Bk�Ak; Bk�Ck; Ck�Ak

middle-preferring7 3 (0.98) 6 (1.97) 2 (0.65) Bk�Ak; Ck�Bk; Ak�Ck

intransitive8 35 (11.44) 35 (11.48) 42 (16.60) Bk�Ak; Ck�Bk; Ck�Ak

minimize present value

Totals 306� 305�� 308

� Two observations deleted due to missing data on one question. �� Three obser-vations deleted due to missing data on one question.

each payment stream in a group declines as the payments becomespread over a longer period. The most ‘front-loaded’ streams,Ad,Ac

andAi, total $28 and are fully paid out in two weeks. The streamsBd,Bc and Bi total $27, and are paid out over three periods. The mostspread-out streams, Cd, Cc and Ci, total $26. Therefore, someonewith a zero discount rate who chooses the payment stream withthe maximum present value should rank Ad best in the decreasinggroup, Ac best in the constant group, and Ai best in the increasinggroup. Even if the time periods are ‘too short’ for discounting tobe a significant factor, there is still a present value ordering for thestreams in each group.


Table IV displays the results for the intra-group choices in Experi-ment 2. The fraction of subjects that maximized present value withineach group is larger than in Experiment 1: nearly 2/3 of the subjectsin each case. As in Experiment 1, the ‘middle-preferring’ patternsof choice, Patterns 5 and 6 taken together, make up the next largestcluster of observed choices, but the percentage of observed choice inthis category is reduced by about half from the level in Experiment1, from about 30% to about 16%, on average.

In effect, we raised the cost of choosing a more spread-out pay-ment stream in Experiment 2 by lowering the total amount paid outin the more extended payment streams. This led to more observedbehavior consistent with the maximization of present value in Exper-iment 2 than in Experiment 1, but the general pattern of choices isthe same as in Experiment 1, with a majority choosing the paymentstream with the highest present value in each group, and a signifi-cant minority choosing the ‘middle-preferring’ patterns. Though thesystematic behavior found in Experiment 1 has been mitigated, ithas not been eliminated. As with Experiment 1, Experiment 2 showsthat subjects do not all maximize present value, and their departurefrom this behavior is systematic.

The inter-group choice patterns, shown in Table V for Experiment2, are much closer to those observed for Experiment 1 than the intra-group patterns. Nearly half of our subjects chose a constant stream astheir most preferred payment stream overall, lending more supportto the idea that some individuals have preferences over the patternof payments they receive. That is, even though more subjects inExperiment 2 than in Experiment 1 chose the highest present-valuepayment stream within the constant group, roughly the same propor-tion of subjects still chose their most-preferred constant stream overtheir most-preferred decreasing stream in both Experiments 1 and 2.

4.2. Experiment 3

By reducing the payments in the more spread-out stream in Experi-ment 2 we were able to increase the proportion of subjects choosingPattern 1 within each group. However, the inter-group choice pat-tern observed in Experiment 1 still persists. We think this is becausethe typical subject in Experiment 2 did not face an obvious penal-ty in the inter-group choice questions. That is, streams Ad, Ac and


TABLE VInter-group choice patterns, Experiment 2.


1 86 (28.96) Dec�Con, Con� Inc, Dec� Inc(decreasing)

2 13 (4.38) Dec�Con, Con� Inc, Inc�Dec(intransitive)

3 10 (3.37) Dec�Con, Inc�Con, Dec� Inc(decreasing)

4 7 (2.36) Dec�Con, Inc�Con, Inc�Dec(increasing)

5 74 (24.92) Con�Dec, Con� Inc, Dec� Inc(constant)

6 64 (21.55) Con�Dec, Inc�Con, Inc�Dec(constant)

7 12 (4.04) Con�Dec, Inc�Con, Dec� Inc(intransitive)

8 31 (10.44) Con�Dec, Inc�Con, Inc�Dec(increasing)

Totals 297�

� 11 Observations deleted due to missing data (failure to statemost-preferred stream for one or more groups explicitly) orinconsistent answers (stated most-preferred stream for oneor more groups inconsistent with answers to pairwise choicequestions within group).

Ai (the modal ‘most-preferred’ choices) all have the same total pay-ment. Experiment 3 was designed to penalize a particular inter-groupchoice pattern (constant-preferring), in an attempt to shift the dis-tribution of choices towards patterns consistent with present valuemaximization. Form A is identical to that used in Experiment 2, andwas included as a benchmark of comparison. Form B is identical toExperiment 2, except that each payment in the constant group hasbeen reduced by $0.50.

Since the present-value rankings within groups has not beenaltered, there should be no difference in the intra-group choice pat-terns. Since the constant streams have all been reduced, however, the


TABLE VIIntra-group choice patterns, Experiment 3.

Decreasing Constant Increasing Preference PatternStreams Streams Streams


1a 39 (72.22) 38 (70.37) 42 (77.77) Ak�Bk; Bk�Ck; Ak�Ck

1b 45 (81.82) 41 (73.21) 45 (80.36) maximize present value2a 0 (0.00) 1 (1.85) 0 (0.00) Ak�Bk; Bk�Ck; Ck�Ak

2b 0 (0.00) 1 (1.85) 0 (0.00) intransitive3a 1 (1.85) 1 (1.85) 0 (0.00) Ak�Bk; Ck�Bk; Ak�Ck

3b 0 (0.00) 3 (5.36) 3 (5.36) extreme-preferring4a 3 (5.56) 0 (0.00) 1 (1.85) Ak�Bk; Ck�Bk; Ck�Ak

4b 3 (5.45) 1 (1.79) 0 (1.62) extreme-preferring5a 4 (7.41) 2 (3.70) 2 (3.70) Bk�Ak; Bk�Ck; Ak�Ck

5b 3 (5.45) 3 (5.36) 3 (5.36) middle-preferring6a 0 (0.00) 4 (7.41) 4 (7.41) Bk�Ak; Bk�Ck; Ck�Ak

6b 4 (7.27) 3 (5.36) 3 (5.36) middle-preferring7a 0 (0.00) 0 (0.00) 0 (0.00) Bk�Ak; Ck�Bk; Ak�Ck

7b 0 (0.00) 2 (3.57) 0 (0.00) intransitive8a 7 (12.96) 8 (14.81) 5 (9.26) Bk�Ak; Ck�Bk; Ck�Ak

8b 0 (0.00) 3 (5.36) 2 (3.71) minimize present value

Totals a 54 54 54b 55� 56 56

� One observation deleted due to missing data on one question.

proportion of subjects choosing their best outcome from the constantgroup as best overall, should be reduced.

Tables VI and VII show the results for Experiment 3. The intra-group results for Form A in Table VI are similar to those for Exper-iment 2 with the expected qualification (see note 2) that there isa higher percentage of choices that maximize present value withineach group than in Experiment 2, about 75%. The inter-group choic-es, shown in Table VII, are also quite similar to those in Experiment2. The majority of subjects chose their best choice from the constantgroup as best overall, even though about 75% of all subjects pickedthe payment stream with the maximum present value within eachgroup.


TABLE VIIInter-group choice patterns, Experiment 1.


1a 17 (32.07) Dec�Con, Con� Inc, Dec� Inc1b 13 (23.31) (decreasing)2a 0 (0.00) Dec�Con, Con� Inc, Inc�Dec2b 0 (0.00) (intransitive)3a 0 (0.00) Dec�Con, Inc�Con, Dec� Inc3b 24 (42.86) (decreasing)4a 2 (3.77) Dec�Con, Inc�Con, Inc�Dec4b 6 (10.71) (increasing)5a 16 (30.19) Con�Dec, Con� Inc, Dec� Inc5b 6 (10.71) (constant)6a 15 (28.30) Con�Dec, Con� Inc, Inc�Dec6b 3 (5.36) (constant)7a 0 (0.00) Con�Dec, Inc�Con, Dec� Inc7b 0 (0.00) (intransitive)8a 3 (5.66) Con�Dec, Inc�Con, Inc�Dec8b 4 (7.14) (increasing)

Totals a 53�

b 56

The intra-group choice patterns for Form B in Table VI are likethose for FormA, but the inter-group choice patterns, shown in TableVII are quite different. The ‘middle-preferring’ responses, Patterns5 and 6, make up only 16% of the total for Form B, compared to58% for Form A. The compensating increase in the percentage ofresponses is in Pattern 3. There were no Pattern 3 responses for FormA, but 43% of the responses for Form B are in Pattern 3. Someonewho chose Ad, Ac, and Ai (the vast majority of subjects answeringFormB did just this) would follow Pattern 3 in Table VII if he or shechose Ad over Ac, Ai over Ac, and Ad over Ai. Reference to TableI shows that Ad and Ai both pay $28 in 2 weeks, but that Ac paysonly $27 in the same period. In this case, for appropriate rates ofdiscount, Pattern 3 is consistent with maximization of present valuein the choice of payment streams.


TABLE VIIIPayment streams, Experiment 4.

FORM A FORM BPayment Received: Dec Con Inc Dec Con Inc

At Start of Year 1 $27 000 $25 000 $23 000 $27 000 $24 900 $23 000At end of Year 1 $26 200 $25 000 $23 800 $26 200 $24 900 $23 800At end of Year 2 $25 400 $25 000 $24 600 $25 400 $24 900 $24 600At end of Year 3 $24 600 $25 000 $25 400 $24 600 $24 900 $25 400At end of Year 4 $23 800 $25 000 $26 200 $23 800 $24 900 $26 200At end of Year 5 $23 000 $25 000 $27 000 $23 000 $24 900 $27 000

5. SUMMARY OF EXPERIMENTS 1 TO 3

In answer to the three questions posed in Section 1, the results of ourexperiments show that:

1. When presented with easy-to-understand payment streams, amajority of subjects do not typically choose the payment streamswith the higher present values.

2. The inconsistency with present value maximization is systemat-ic: a large minority, in some cases a majority, of subjects preferpayment streams that are more evenly spread-out in time to thosethat are ‘front-loaded’.

3. This systematic behavior can be altered by raising the cost tothe subject of choosing a more spread-out payment stream. Bylowering the total dollar payout of such streams we were ableto reduce the frequency of ‘constant-preferring’ patterns, bothintra-group and inter-group. Nonetheless, a significant numberof subjects, 16% in Table VIII for Form B of Experiment 3,still exhibit a preference for the more spread-out streams ofpayments.

The tendency towards ‘constant-preferring’ streams of payments thatwe observed first in Experiment 1 has not completely disappearedin the face of the alterations we made in the payment streams inExperiments 2 and 3. These results imply that our subjects respondto changes in the value of income streams in ways quite familiarto economist; they substitute away from streams that have fallen invalue relative to the other income streams available. Though they do


Figure 1.

seem to realize that ‘more is better’, these subjects do not maximizepresent value when choosing an income stream. A suitably concavevalue function of monetary payoffs, and a reasonable positive interestrate, can rationalize these choices, both intra-group and inter-group.This rationalization can be interpreted as a discounted utility model,or more generally, a variation of a prospect theory model, with a valuefunction weighted by a subjectively determined discount factor.

Figure 1 illustrates three value functions which can be used torationalize the major shifts in patterns of choice across Experiment 1–3 for three representative individuals. Using the three value functionsbelow and a discount rate of 0.5%, and applying them to the incomestreams in Experiments 1–3, generates the following patterns ofchoice:


Value Function VD(x) = x for x � 15; VD(x) = x0:9975 for x > 15:For Experiment 1 and 2: Pattern 1 intra-group and Pattern 5 inter-groupFor Experiment 3b: Pattern 1 intra-group and Pattern 3 inter-group

Value function VC(x) = x for x � 13:5; VC(x) = x0:9900 for x > 13:5:For Experiment 1: Pattern 5 intra-group and Pattern 5 inter-groupFor Experiment 2: Pattern 1 intra-group and Pattern 5 inter-groupFor Experiment 3b: Pattern 1 intra-group and Pattern 3 inter-group

Value function VI (x) = x for x � 8:5; VI(x) = x0:9825 for x > 8:5:For Experiment 1: Pattern 8 intra-group and Pattern 5 inter-groupFor Experiment 2: Pattern 1 intra-group and Pattern 5 inter-groupFor Experiment 3b: Pattern 1 intra-group and Pattern 3 inter-group

Thus, a discounted utility or prospect theory approach, using zeropayments as the reference point, can rationalize many of the observedresponses not rationalized by present value theory.

As mentioned in Section 1, standard intertemporal choice theoryanalyzes decisions in the following way: individuals face a bud-get constraint. We can interpret the discounted utility or prospecttheory-style model discussed above as a situation in which the deci-sion maker fails to distinguish between income and expenditure, ortreats each period’s pay-off as a good, instead of a means to purchasegoods. A discounted utility interpretation would still imply that pref-erences are separable, i.e., utility from a payoff in a given period isindependent of the utility from a payoff in a different period.

Other non-separable preference interpretations are also possible.For example, as in prospect theory, individuals may compare eachpayoff to a status quo or reference point. Or some individuals mayrestrict their range of choice because they do not trust themselves toact in their own self-interest over an extended time period. Such indi-viduals may opt for a ‘self-management’ solution that will bind theirfuture behavior in some way to limit their ability to adversely affecttheir multi-period utility. Distrusting his or her ability to execute theoptimal consumption plan after choosing the highest present valueincome stream, he or she chooses a lower present value stream, withmore level payoffs, to limit his or her spending power per period.

Another possible explanation is that individual rationality is bound-ed. In this case, an individual may forego a pure present value max-imum because the time and trouble to calculate it is not worth theeffort. For example, if a constant stream of income is adequate to


cover one’s most urgent needs, with something left over, one mayopt for that and be done with it. Or some individuals may prefer fre-quent payments to less frequent ones, getting a psychological boostfrom the receipt of the payment, and not just the payment itself. Suchindividuals may make decisions with little concern for maximizingpresent value or the discounted utility of payoffs.

6. DO WORKERS REALLY PREFER INCREASING STREAMS OFINCOME? A SURVEY WITH HYPOTHETICAL PAYMENTS

Loewenstein and Sicherman (1991) conducted an experiment inwhich subjects were presented with choices among alternative pay-ment streams, described by one or two scenarios. In one scenario,subjects were asked to imagine that they were about to begin a jobthat was to last for five years, and that they had a choice of sevendifferent ways of receiving their wages. In the second scenario, thesubjects were asked to imagine that the payment streams representeda flow of rents from a property that they owned. The subjects werepaid a small fixed fee for answering the questions, but the paymentstreams themselves were hypothetical. The seven payment streamsincluded one decreasing, one constant and five increasing streams.These payment streams were presented graphically, and all totalledto the same amount in six payments over five years: $150,000. Thedecreasing stream had the highest present value, the constant streamhad the next highest, and so on through the increasing streams,assuming a positive rate of discount. When subjects were asked torank the payment streams, Loewenstein and Sicherman found thaton average subjects tended to prefer a payment stream in the middleof the five increasing streams over any other, including the decreas-ing stream, which had the highest present value. This tendency toprefer increasing payment streams was weaker in the rental incomescenario than in the wage income scenario, but the modal choice wasstill an increasing stream of payments.

In light of our results in Experiments 1 through 3, we investigateda problem similar to that of Loewenstein and Sicherman using theour basic design, i.e., analyzing patterns of pairwise choice amonga single increasing payment stream, a constant payment stream, anda decreasing payment stream. The differences reported by Loewen-


stein and Sicherman in responses to the wage and rental scenariossuggest that the context of the questions may be important. We pre-sented two scenarios, a wage scenario using the same wording asLoewenstein and Sicherman, and an inheritance scenario, in whichsubjects are asked to imagine that they are to inherit some moneyand must choose among different ways of receiving it.

Anticipating that the modal choice might be a ‘constant-preferring’pattern, as in Experiments 1 through 3, we used two forms for eachscenario, as in Experiment 3. On Form A all payment streams added-up to the same total. On Form B the payments in the constant streamwere reduced by a small amount. Thus, there were four differentforms in the experiment.

6.1. Design and Results for Experiment 4

The hypothetical payments for Experiment 4 are shown at the top ofTable VIII. Note that all payment options add up to the same totalon Form A, but that $100 was subtracted from each payment in theconstant payment stream on Form B. The forms were distributedin two introductory economics classes and two intermediate leveleconomics classes at Rutgers University.

As Table IX shows, the results for both Form A and Form B ofthe wage scenario questions replicate the findings of Loewensteinand Sicherman. Only 12% to 18% of the subjects follow Pattern1, picking the outcome with the maximum present value for eachbinary choice. About half of the subjects follow Pattern 8, choosingthe increasing payment stream as their most preferred overall. Thetwo ‘constant-preferring’ patterns, Patterns 5 and 6, taken together,account for more responses than Pattern 1. We notice little change inresponses within the wage scenario from Form A to Form B. For theinheritance scenario we again notice little change in responses fromForm A to Form B, but there are significant differences between thetwo scenarios. Within the inheritance scenario, on both Form A andForm B, about 1/3 of the subjects always maximize present value,following Pattern 1, a significant difference from what is observed inthe wage scenario. Another third choose Pattern 8, and the other thirdchoose something else, typically a ‘constant-preferring’ pattern.

These results are quite different from our inter-group results forExperiments 1–3, at first glance. First, the reduction in payments in


TABLE IXChoice patterns, Experiment 4.

Pattern Wage Inheritance Preference PatternsNumber Scenario Scenario

Freq. (%) Freq. (%) (most preferred stream)

1a 21 (18.26) 23 (34.33) Dec�Con, Con� Inc, Dec� Inc1b 14 (12.28) 24 (34.29) (decreasing)2a 0 (0.00) 0 (0.00) Dec�Con, Con� Inc, Inc�Dec2b 0 (0.00) 0 (0.00) (intransitive)3a 2 (1.74) 3 (4.48) Dec�Con, Inc�Con, Dec� Inc3b 9 (7.89) 3 (4.29) (decreasing)4a 3 (2.61) 1 (1.49) Dec�Con, Inc�Con, Inc�Dec4b 10 (8.77) 3 (4.29) (increasing)5a 5 (4.35) 7 (10.45) Con�Dec, Con� Inc, Dec� Inc5b 11 (9.65) 6 (8.57) (constant)6a 22 (19.13) 13 (19.40) Con�Dec, Con� Inc, Inc�Dec6b 14 (12.28) 10 (14.29) (constant)7a 2 (1.74) 0 (0.00) Con�Dec, Inc�Con, Dec� Inc7b 1 (0.88) 1 (1.43) (intransitive)8a 60 (52.17) 20 (29.85) Con�Dec, Inc�Con, Inc�Dec8b 55 (48.25) 23 (32.86) (increasing)

Totals a 115 67b 114 70

the constant stream on Form B did not have a large effect withineither scenario. Second, relatively few subjects followed Patterns 5and 6 on FormA in the first place. How can we explain the differencesbetween the results for Experiments 1–3, and Experiment 4? We nowsuggest possible explanations for these two differences.

Difference No. 1: Lowering of payments for constant stream had noeffect in Experiment 4. There seems to be one clear explanation: inExperiment 3, lowering the total payments for the constant streamslead to a noticeable effect; subjects shifted from choosing constantstreams as most preferred (Patterns 5 and 6) to choosing Pattern3, where the decreasing stream was most preferred. This did notoccur appreciably in Experiment 4. In Experiment 3, the declinein the per-period payments for the constant stream was about 6%.


In Experiment 4, the decline in the per-period payments for theconstant stream was $100, or 0.4%. Since the decline in paymentswas so small in Experiment 4, it is not surprising that little effect wasnoticed. We suspect that if Experiment 4 was performed again, with areduction in payments per period for the constant stream comparableto the percentage reduction in Experiment 3, about $1500 per period,a result very similar to that of Experiment 3 would occur.

Difference No. 2: The Modal response in Experiment 4 was to choosethe increasing stream, rather than a decreasing or constant stream.There are several possible explanations:

a. The relative slopes of increasing, decreasing and constantstreams are less steep in Experiment 4 than for the intergroup choicesin Experiments 1–3. For example, examine the two-period streamsin Experiment 1, Ad = 20 today, 10 in two weeks, Ac = 15 today,15 in two weeks, and Ai = 10 today, 20 in two weeks. Notice thatthe payment today for the increasing stream is 1/3 larger than thefirst period payment for the constant stream, and double the pay-ment today for the decreasing stream. For Experiment 4, the initialpayment for the increasing stream is only 8% larger than the initialpayment for the constant stream, and 17% larger than the initialpayment in the decreasing stream. Therefore, the income streams inExperiment 4 are much more similar than the streams in Experiment1, and for Experiments 2 and 3, too. An individual opting for theincreasing stream in Experiment 4 is pays a much smaller price inpresent value terms than would an individual choosing Ai in Exper-iment 1. It is not unusual, then, to find many more subjects choosingan increasing stream in Experiment 4 than in Experiment 1.

b. Experiment 4 was rich in context, while Experiments 1–3 werestripped of any obvious context. One could argue that the paymentstreams in Experiments 1–3 would be viewed as a windfall or gift bythe typical subject. But, in Experiment 4, a specific wage or inheri-tance scenario was presented to the subjects. It is likely that subjectschose increasing streams in the wage scenario to indicate the increas-ing value of their worth in the labor market (See Loewenstein andSicherman, 1991). It seems that no such obvious ‘normal’ paymentpattern is suggested by the inheritance scenario. Indeed, responses


Figure 2.

in the inheritance scenario were almost equally distributed betweenincreasing, decreasing and constant payment patterns.

c. Individuals may have used one of the income streams in Exper-iment 4 as a point of reference, and evaluated the gains and lossesin such a way that gains had a smaller marginal effect than losses,such as in prospect theory. As mentioned earlier, the lack of contextin Experiments 1–3, and the relatively small payments and shorttime periods involved, could lead subjects to treat the payments asa windfall or a gift, using their status quo at the beginning of theexperiment as their reference point. But the structure of the questionin Experiment 4 could lead subjects to choose one of the incomestreams themselves as the reference point.

A prospect theory-style approach would be the following. Thesubject would subtract the payment stream used as a point of refer-ence from the other streams and evaluate the differences. Using a


typical prospect theory type of value function over gains and losses(see Figure 2), with the distinguishing feature of being steeper forlosses than for gains, the subject could choose the increasing streamif the function was sufficiently steep for losses and the discountrate were sufficiently large. For example, a discount rate of 10%,the increasing stream as a reference point, and the value functionlabelled Vi in Figure 24 would lead to a choice of Pattern 8. Similar-ly, the value functions labelled Vd and Vc in Figure 2, combined withthe constant or increasing streams, respectively, as reference points,would lead to choices of Pattern 1 or Pattern 5.

d. Individuals may have negative discount rates. If individualshave negative discount rates, then they would choose increasingpayment streams over constant or decreasing streams in our experi-ments. Negative discounting would then explain the results observedin Experiment 4. But we do not find negative discounting to be con-vincing in this context since we observed that so few subjects chooseincreasing streams in Experiments 1–3. We suspect that the follow-ing experiment would refute the negative discounting explanation:given a choice between $150,000 today and $150,000 five yearsfrom now, how many subjects would choose the later? We expectthat few, if any, would do so.

7. CONCLUSIONS

Our experiments investigated whether or not our subjects choseincome streams with the highest present value. There was a clearpresent value ranking of the available income streams that did notdepend on the existence of an explicit capital market; our subjectsalways had the option of holding earlier payments until a later time.

In the standard theory of intertemporal consumer choice, rationalagents maximize their utility of expenditure on bundles of goodsacross two or more periods of time subject to a budget constraint.The budget constrain is constructed as the tradeoff between thepresent and future value of the agent’s income stream. The agentis assumed to be able to shift income from one period to anotheraccording to a given rate of interest.

We can interpret our experiments as investigating whether or notour subjects chose the constraint in their own intertemporal maxi-


mization problem with the highest present value. We did not inves-tigate their choices of expenditure per period on goods, nor whethertheir utility functions over these expenditures were separable or non-separable.

In a series of simple experiments a large percentage of the subjectsdid not choose streams of income that maximized present value. Asignificant proportion of our subjects chose streams of income withpayments more evenly spread out in time over front-loaded paymentstreams. We found that when differences in present value betweenstreams was made larger, subjects moved away from the streams thatfell in present value towards the higher present value streams. Butmany subjects did not choose the stream with the maximum presentvalue in spite of our experimental treatments.

The best explanation for this behavior seems to be that some sub-jects have strongly held preferences about how they receive theirincome. Though individuals may not maximize present value inincome choice, this need not imply that they are irrational. It doessuggest, however, that many people cannot or do not make the dis-tinction, required by the theory, between income and expenditure.Perhaps, as in prospect theory, they choose a reference point fromwhich to evaluate alternative income streams.

Our conjecture is that some subjects do not view income as mere-ly a means to an end. The pattern of payments matters to them.For example, they chose a constant stream rather than a decreasingstream, even though the constant stream had a lower present value.As we showed in our fourth experiment, context also matters. Sub-jects treated the choice of income streams differently when thosestreams were presented as flows of earnings rather than as flowsfrom an inheritance.

It is possible that due to concerns about their ability to managetheir expenditures properly, some subjects opted for a constant pay-ments stream as a second-best alternative. More likely, we think,some of our subjects did not make a direct connection betweenthe present value of the income streams and the expenditures thosestreams would make possible. That is, they did not understand thata lower present value income stream would create a smaller choiceset over expenditure on goods than would a larger present valuestream. Although we endeavored to make clear to subjects the trade-


off between present value and the pattern of payments with ourpairwise choice format, some subjects, we suspect, were influencedby various psychological factors having to do with the pattern ofpayments or the context of the questions.

These issues merit further investigation, both experimentally andtheoretically. Our subjects seem to be asking, can one separate pref-erences over income and preferences over consumption? Economictheory says one should do so. We have not addressed this questionwith our experiments. The best test of this question would seem tobe whether people would want to change their choices if shown thatthey could be ‘better off’ with a different income stream.5

ACKNOWLEDGEMENT

Financial support of the Rutgers Research Council is acknowledged.We thank Greg Clare for his help in collecting the survey data forExperiment 4.

NOTES

1 See Schelling (1984, p. 58).2 There were two versions of the forms in Experiments 1 and 2, one with

payment streams in the same order as shown in Figures 1 and 2, the other with theorder reversed (so that stream Ad¸is in the position of Ci, Bd¸is in the positionof Bi, etc.). There were no statistical differences in the distribution of patterns ofchoice between the two forms, so all analysis in the next section is of the pooleddata for each experiment. Experiments 1 and 2 were administered in IntroductoryEconomics classes with university-wide enrollment, while Experiment 3 wasadministered in a special Introductory Economics course for engineering students.Form A in Experiment 3 was identical to that used in Experiment 2, to serve asa baseline of comparison for Form B, which contained the new income streams,shown in Figure 3. There was only one order of presentation of income streamsin Experiment 3.

3 Under the maintained hypothesis that there is a positive discount rate, themost front-loaded income stream is also the highest present-value income stream.

4 VI is piecewise linear with a slope of 1 for gains and a slope of 1.5 for losses.VC has a slope of 1.45 for losses, while VD has a slope of 1 for losses.

5 Loewenstein and Sicherman (1991) explained the idea that income is a meansto expenditure to their subjects and found no stronger tendency towards present-value maximizing choices, suggesting that it is not enough to simply tell peoplethat something is good for them for them to believe that it is good for them.


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Rutgers University,Department of Economics,116 College Avenue,NJ 08903, U.S.A.

Violations of Present-Value Maximization in Income Choice

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