Survey data show that subjects positively discount both gains and losses but discount gains more heavily than losses. This holds for monetary and non-monetary outcomes

D. Dragone

M. Casari

English

Research Papers in Economics

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 1 
On Negative Time Preference 
 
Marco Casari and Davide Dragone 
University of Bologna 
 
20 March 2010 
 
 
Abstract 
Survey data show that subjects positively discount both gains and losses but discount gains more 
heavily than losses. This holds for monetary and non-monetary outcomes. 
JEL classification:  C91, D90.  Keywords: discounting, sequences 
 
 
1.  Introduction 
Under positive discounting, a subject wants to anticipate a given reward and to postpone a given 
pain.  In  two  well-known  papers,  Loewenstein  (1987)  and  Loewenstein  and  Prelec  (1991) 
question the general validity of the assumption that people (positively) discount future outcomes 
(Koopmans, 1960).
1 They support this point by reporting intertemporal choices over hypothetical 
situations with monetary and non-monetary stimuli. While subjects positively discount money, 
they sometimes negatively discount non-monetary outcomes, such as a kiss from your favorite 
movie star or an electric shock (Loewenstein, 1987, L87 from now on). In addition,  subjects 
greatly dislike sequences of  dinners at restaurants that decline in value (Loewenstein and Prelec, 
1991, LP91 from now on). 
   We conducted a similar survey. Our data show differences between discounting of gains and 
losses and little support for negative time preferences.  
   The paper is structured as follows. Section 1 describes the setup. Section 2 reports the results. 
Section 3 discusses the results within the literature and concludes. 
 
                                                 
1  L87 has 223 citations and LP91 has 82 (18 March, 2010, Google Scholar, only published papers). 2 
2.  Design 
We  asked  to  190  undergraduates  hypothetical  questions  about  money  equivalents    and 
preferences over sequences.
2  
    We asked four questions about money equivalents: (1) “What is the highest amount of money 
you are willing to pay now to receive with certainty 100 euros in the specified date?” Each 
subject stated an amount for five dates: “I am willing to pay at most ______ euros now to receive 
100 euros in 1 year” or in 4 weeks, or in 2 weeks, or 3 days, or now.
3 The latter date was added 
as a control. The following questions had the same structure and concerned (2) “avoid losing 
with certainty 100 euros,” (3) “avoid receiving with certainty a short, non-lethal 220-volt electric 
shock,” (4) ”receive with certainty a kiss from your favourite movie star/singer.”  
    We asked  three questions about preferences over sequences:  
(5) “If we gave you a voucher for a dinner at the restaurant, which one of the following options 
would you prefer?” (N=186) 
·  A dinner in a fish restaurant  (131, 70.4%) 
·  A dinner in a pizzeria  (55, 29.6%) 
(6a) “If you answered that you would use the voucher in a fish restaurant,  
select your favourite option between the following ones:” 
·  A dinner in a fish restaurant on Saturday in one month (112, 85.5%) 
·  A dinner in a fish restaurant on Saturday in two months (19, 14.5%)  (…) 
(7a)     “select your favourite option between the following ones:” 
·  A dinner in a fish restaurant on Saturday in one month and a dinner in a pizzeria in 
two months (91, 69.5%) 
·  A dinner in a pizzeria in one month and a dinner in a fish restaurant on Saturday in 
two months (40, 30.5%) 
(6b) “If you answered that you would use the voucher in a pizzeria,  
       select your favourite option between the following ones:” 
·  A dinner in a pizzeria on Saturday in one month (46, 83.6%) 
·  A dinner in a pizzeria on Saturday in two months (9, 16.4%)  (…) 
                                                 
2 University of Bologna, Italy; session dates: April 1
st, May 13, 20, 22, 2009. 
3  Italics and bold in the original instructions. 3 
(7b)      “select our favourite option between the following ones:” 
·  A dinner in a pizzeria on Saturday in one month and a dinner in a fish restaurant in 
two months (48, 87.3%) 
·  A dinner in a fish restaurant in one month and a dinner in a pizzeria on Saturday in 
two months (7, 12.7%) 
 
Figure 1: Maximum payment to obtain/avoid outcomes at selected time 
Mean of the proportion of current value 4 
Notes: If on a single question a subject did not fill in all items, we dropped this observation. If on other questions the 
same subject filled in all items, we kept those observations. Hence, sample sizes may vary across questions. N=178 
for 100 euro gain, 180 for 100 euro loss, 138 for kiss, 163 for shock. 
 
 
2. Results 
We report the results about the money equivalents questions (1-4) and then about the preferences 
over sequences questions (5-7).  
   On the money equivalent questions we find that subjects positively discount both gains and 
losses but discount gains more heavily than losses. First, subjects positively and monotonically 
discount  future outcomes. Figures 1 illustrates the mean willingness to pay  for outcomes  at 
selected times, normalized by their current value (“nwtp”). By definition the lines originate at 1 
because they are expressed as proportion of the current value. When a nwtp value is below 1, it 
indicates positive discounting with respect to now. In Figure 1 all nwtp values, except loss of 100 
euros, are always below 1. To support the result of positive discounting, we carried out four 
Wilcoxon matched-pairs signed-ranks tests for each question, and found that all nwtp values, 
including loss of 100 euros, are significantly below 1 (p<0.01, N=138-180 depending on the 
question).  A  monotonic  line  in  Figure  1  indicates  monotonic  discounting.  All  lines  are 
monotonic, except the shock but this deviation is not significant. For each question we checked 
for significantly positive discounting in all pairs of nwtp values (3 days vs. 2 weeks, 3 days vs. 4 
weeks, etc.). We carried out six additional Wilcoxon matched-pairs signed-ranks tests for each 
question and found that more distant values are always significantly lower (p<0.01, N=138-180 
depending on the question). 
    Second, subjects’ intertemporal preferences are domain-specific. One can compare the nwtp 
values  of  different  lines  in  Figure  1  for  a  given  time  delay.  Sometimes,  subjects  discount 
differently  kiss,  shock,  and  monetary  outcomes.  For  each  time  delay,  we  carried  out  six 
Wilcoxon matched-pairs signed-ranks tests and found that subjects discount the kiss differently 
than the shock at all time delays. Moreover, they discount the kiss differently than the 100 euro 
loss and they discount the shock differently than the 100 euro gain.
5 
                                                 
5 p<0.05, N=123-174 depending on the question. The kiss is not discounted differently than the 100 euro loss at 1 
year delay (p=0.06) and the shock is not discounted differently than a 100 euro gain (p=0.06). 5 
    The crucial feature of the stimulus is not whether it is monetary or non-monetary. The above 
tests reveal similar discounting of a 100 euro loss and a shock, and similar discounting of a 100 
euro gain and a kiss.
6 The relevant characteristic of the stimulus is whether it is in the gain or 
loss domain. Within monetary stimuli, a 100 euro gain is discounted differently than a 100 euro 
loss. Within non-monetary stimuli, a kiss is discounted differently than a shock. This distinction 
was also mentioned in LP91 and has been reported in the literature review of Frederick et al. 
(2002, p. 362-363). 
   On the preferences over sequences questions we report, first, that an overwhelming majority of 
subjects  positively  discount  dinner  outcomes;  and,  second,  that  this  tendency  is  stronger  for 
individual items than for sequences. When comparing individual choices in questions 5 and 6, 
only 15.0% of subjects prefer to delay their best option, i.e. exhibit negative time preferences on 
single-outcome events (n=28). When comparing sequences of events, more subjects prefer to 
delay their best option. More precisely, 25.3% of individual choices in questions 5 and 7 reveal 
negative  time  preferences  (n=47).  Finally,  when  checking  for  consistency  in  choices  across 
questions 5, 6, and 7, about 69.9% always exhibit positive time preferences, and 10.2% always 
negative time preferences.  
 
3.  Discussion 
Some of our results are different from those in the literature. Figure 2 reports the results of L87, 
which are similar to ours for the monetary outcomes and different for the non-monetary items. In 
Figure 2 subjects sometimes negatively discount a kiss and a shock, which we did not find.   
                                                 
6 The 100 euro loss and shock are discounted differently at 2 weeks; the 100 euro gain and the kiss are discounted 
differently at 1 year (5% significance level). 6 
 
Figure 2: Maximum payment to obtain/avoid outcomes at selected time in Loewenstein 
(1987) 
Mean of the proportion of current value 
 
 
LP91 state that outcomes that decline in value are greatly disliked and report the supporting 
evidence that: “Of the 86 percent of subjects who preferred the fancy French dinner, 80 percent 
preferred a more immediate dinner over a more delayed dinner. However, when the French 
dinner was composed into a sequence with the Greek dinner, a slight majority (57 percent) 
preferred to have the better dinner come later. Even with single-outcome events there is some 
motivation to defer the French dinner -witness the 20 percent of subjects who opted for the 
longer delay. “ (p. 348).  7 
Based on questions 5-7 of this study, of the 70.4% of subjects who preferred the fish dinner,  
85.5% preferred a more immediate dinner  over a more delayed dinner. However, when the fish 
dinner was composed into a sequence with the pizza dinner, a minority (30.5%) preferred to have 
the better dinner come later. With single-outcome events there is some motivation to defer the 
fish dinner - as 14.5% of subjects opted for the longer delay.  To conclude, subjects compatible 
with negative time preferences exists but in our study are a smaller fraction of about 10-20% of 
the sample. 
   One  can  put  forward  various  conjectures  for  these  discrepancies.  One  is  that  hypothetical 
questions generally yield noisy responses. To take care of it, we increased sample size and also 
looked at median instead of mean answers. While L87 involved 30 US undergraduates and LP91 
involved 95 Harvard undergraduates, our sample size is 190. When checking results in Figure 1 
in terms of median, they confirm positive time discounting. Another conjecture may be subject 
pool differences. L87 and LP91 conducted their study in the US while this study was conducted 
in Italy. Finally, there were some procedural and wording differences. Some of the time delays 
for the money equivalent questions were different from L87: we dropped 3 hours, 24 hours, and 
10 years; we added 2 weeks and 4 weeks. L87 employed two money amounts ($4, $1000) while 
we employed just one (100€). Restaurant types were adjusted to fit the Italian culture. LP91 
dinners were at either a fancy French or a local Greek restaurant. Frederick and Loewenstein 
(2008) found that procedural issues influenced results. 
   L87 and LP91 employed a survey as an illustrative example for a model where utility can 
depend  not  only  on  the  consumption  of  a  good  (or  a  bad),  but  also  on  the  anticipation  of 
consumption.  This argument sounds intuitive and appealing and should not be discarded simply 
because our data do not find support for it. Yet, the role of the experimenter is to try to replicate 
these studies. In the about 20-years period between the original experiments and our study, we 
have not  found  a published replication of  this  important  result.  Our  results  suggest  that  the 
behavioral difference in discounting is less between monetary and non-monetary stimuli, and 
more between gains and losses. 
 
 
 8 
Bibliography 
 
Frederick,  S.  and  Loewenstein,  G.,  2008,  Conflicting  motives  in  evaluations  of  sequences, 
Journal of Risk and Uncertainty, 37, 221–235 
Frederick,  S.,  Loewenstein,  G.,  and  O' Donoghue,  T.,  2002,  Time  discounting  and  time 
preference: A Critical Review, Journal of Economic Literature, 40(2), 351-401 
Koopmans T. C., 1960, Stationary Ordinal Utility and Impatience, Econometrica, 28(2), 287-
309. 
Loewenstein,  G.,  1987,  Anticipation  and  the  Valuation  of  Delayed  Consumption,  Economic 
Journal, 97(387), 666-84. 
Lowenstein, G., and Prelec, D., 1991, Negative Time Preference, American Economic Review, 
81(2), 347-52. 
  

On Negative Time Preference

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