of 61
Intertemporal Choice Experiments and Large-Stakes
Behavior
Diego Aycinena
Facultad de Econom ́ıa
Universidad del Rosario
diego.aycinena@urosario.edu.co
Szabolcs Blazsek
Escuela de Negocios
Universidad Francisco Marroqu ́ın
sblazsek@ufm.edu
Lucas Rentschler
Department of Economics and Finance
Utah State University
lucas.rentschler@usu.edu
Charles Sprenger
Department of Economics and Rady School of Management
University of California, San Diego
csprenger@ucsd.edu
December 8, 2019
Abstract
Intertemporal choice experiments are frequently implemented to make inference about
time preferences, yet little is known about the predictive power of resulting measures.
This project links standard experimental choices to a decision on the desire to smooth a
large-stakes payment — around 10% of annual income — through time. In a sample of
around 400 Guatemalan Conditional Cash Transfer recipients, we find that preferences
over large-stakes payment plans are closely predicted by experimental measures of patience
and diminishing marginal utility. These represent the first findings in the literature on
the predictive content of experimentally elicited intertemporal preferences for large-stakes
decisions.
JEL classification:
D1, D3, D90
Keywords
: Structural estimation, Out-of-sample prediction, Discounting, Convex Time Budget
We thank Michaela Pagel for helpful comments. Diego Aycinena grateful for the financial support provided by Fundaci ́on
Capital and the program “Inclusi ́on productiva y social: programas y pol ́ıticas para la promoci ́on de una econom ́ıa formal”, code
60185, which conforms the
Alianza EFI - Econom ́ıa Formal Inclusiva
,undertheContingentRecoveryContractNo.FP44842-220-
2018. We are grateful to Pablo Pastor, Alvaro Garcia and the field implementation team; Raul Zurita, Arturo Melville and Amy
Ben ́ıtez. Betzy Sandoval provided excellent research assistance, including field supervision, data handling and support in the project
logistics and design implementation.
1 Introduction
Intertemporal choice is prevalent in economic decision making. Explicit characterization of
structural discounting models has led to widely appreciated theoretical developments (
Samuel-
son
,
1937
;
Koopmans
,
1960
;
Laibson
,
1997
;
O’Donoghue and Rabin
,
2001
). Measurement of
the broad forces of these models and corresponding utility parameters has received deserved
empirical attention as well, with notable contributions in both laboratory and field settings.
1
A prominent discussion related to the measurement of intertemporal preferences has devel-
oped in the last decade.
Frederick, Loewenstein and O’Donoghue
(
2002
)noteacriticalissue: the
confounding e
ects of diminishing marginal utility for making inference on patience. A decision
maker who is indi
erent between $45 today and $50 in one month can be arbitrarily impatient
depending on changes in utility over this range.
2
Diminishing marginal utility confounds both
quantitative and qualitative predictions of measured discounting models. Erroneous inference
on the level of discounting will lead to poor quantitative out-of-sample prediction; while at-
tributing to discounting a behavior that is truly driven by diminishing marginal utility may
lead even qualitative predictions to be incorrect.
Recognizing this confounding e
ect, recent work has developed experimental methodology
to identify diminishing marginal utility alongside discounting parameters (
Andersen, Harrison,
Lau and Rutstrom
,
2008
;
Andreoni and Sprenger
,
2012
).
3
Although this work shows that
estimates of discounting are indeed influenced by the shape of utility, it is unknown whether
the corresponding parameters meaningfully predict large-stakes behavior. Given that out-of-
1
Examples include
Hausman
(
1979
);
Lawrance
(
1991
);
Warner and Pleeter
(
2001
);
Harrison, Lau and
Williams
(
2002
);
Cagetti
(
2003
);
DellaVigna and Malmendier
(
2006
);
Laibson, Repetto and Tobacman
(
2007
);
Andersen, Harrison, Lau and Rutstrom
(
2008
);
Mahajan and Tarozzi
(
2011
);
Andreoni and Sprenger
(
2012
);
Fang and Wang
(
2015
).
2
An individual indi
erent between $45 received now and $50 received in one month under exponential
discounting reveals
u
(45)
/u
(50) =
. Let
k
=
u
(50)
u
(45) represent the change in utility between $45 and $50,
such that
k/u
(50) = 1
. Normalizing
u
(0) = 0, values of
k
2
(0
,u
(50)) are consistent with strict monotonicity
of
u
(
·
). As
k
!
0,
!
1 and as
k
!
u
(50),
!
0.
3
The methodologies of
Andersen, Harrison, Lau and Rutstrom
(
2008
) and
Andreoni and Sprenger
(
2012
)
share a common objective, but reach starkly di
erent conclusions with respect to marginal utility, perhaps due
to the source of information used to identify marginal utility. Appendix
A
contains a detailed discussion of this
topic.
2
sample prediction is a central use for structural estimates, this gap in the literature is potentially
important. If experimental choices are reflective of time preferences and diminishing marginal
utility, they should predict relevant large-stakes decision-making outside of the experiment. If
not, then the growing body of literature making inference on preferences from these designs is
missing a critical piece of foundation.
4
Our project seeks to fill this gap in the literature by linking experimental choices and
corresponding preference estimates to a large-stakes decision to smooth intertemporal payments,
valuing around 10% of annual income. Our data come from a low-income, low-literacy and
low-numeracy sample of 490 participants in Guatemala’s “Mi Bono Seguro” Conditional Cash
Transfer (CCT) program.
5
In a first task, all subjects completed the modified Convex Time
Budget (CTB) tasks of
Andreoni, Kuhn and Sprenger
(
2015
). Subjects allocate an experimental
budget over two payment dates, one sooner and one later. Choosing interior allocations with
smooth payments over the two dates is interpreted as evidence of diminishing marginal utility,
while allocating more funds to the sooner date is interpreted as reflecting greater impatience.
6
Then, in a second task, subjects were entered into a draw with a one-in-thirty chance of re-
ceiving GTQ1,200 (around $164). This amount represents at least sixty percent of the monthly
household income for most (87%) of our subjects, and more than one month’s household income
for the median subject. Each subject was asked to choose one of six structured payment plans,
which would be implemented if they won the draw. The first payment plan was a single lump-
4
Other works have examined correlations between experimental measures of discounting and measures such
as self-reported smoking, diet and exercise, credit card borrowing and default, short-term e
ort decisions, small-
stakes monetary tradeo
s, take up of savings commitment devices, and tax-filing behavior (
Chabris, Laibson,
Morris, Schuldt and Taubinsky
,
2008b
;
Meier and Sprenger
,
2010
,
2012
;
Andreoni, Callen, Khan, Ja
ar and
Sprenger
,
2018b
;
Ashraf, Karlan and Yin
,
2006
;
Martinez, Meier and Sprenger
,
2017
;
Andreoni, Kuhn and
Sprenger
,
2015
). Although those works point helpfully towards the predictive content of experimental measures
for low-to-moderate stakes with single and repeated decisions, they do not investigate behavior under large
stakes, with the exception of
Andreoni, Kuhn and Sprenger
(
2015
);
Andreoni, Callen, Khan, Ja
ar and Sprenger
(
2018b
), and do not utilize methods designed to simultaneously elicit curvature and discounting.
5
Relative to most laboratory samples, we view these subjects as potentially more likely to be confused by
arguably complex experimental designs. Critiques about comprehensibility noted below support the hypothesis
that experimental choices are reflective of confusion rather than preferences, which should lead to limited
predictive power.
6
The stakes of the CTB decisions were GTQ100 Guatemalan Quetzales (around USD12.8 at the time of the
experiment). These stakes themselves are not insubstantial, representing two-thirds of the monthly transfer for
eligible recipients from the “Mi Bono Seguro” program.
3
sum payment of GTQ1,200 received on a fixed date after the experiment. The other payment
plans featured multiple smaller payments with equal total value, such as two GTQ600 payments
received three months apart. Diminishing marginal utility and patience should jointly inform
plan values. A more patient individual with more rapidly diminishing marginal utility should
express a greater desire for multiple payment plans rather than the single payment plan.
We document several results related to diminishing marginal utility, patience and payment
plan preferences. First, relative to laboratory samples with college students, our sample shows
amuchgreaterdesiretosmooththeirCTBallocationsovertime. Forty-sixpercentofCTB
choices are interior allocations and only 8.4% of subjects exhibit zero interior choices. For
comparison, with a sample of University of California San Diego (UCSD) undergraduates,
Andreoni, Kuhn and Sprenger
(
2015
)findonly12%interiorallocationsandthat60%ofsubjects
exhibit zero interior choices. Corresponding structural estimates of preferences demonstrate
marginal utility decreasing substantially over the CTB payment values, reflecting the preference
for smooth intertemporal payments.
7
Subjects are estimated to discount the future at around
1.73% per month, or 23.20% per year. Given these estimates of marginal utility and patience,
multiple payment plans should be around 20% more valuable on average than the single payment
plan. Echoing this aggregate prediction, 78% of subjects actually chose one of these smooth
payment plans.
Second, preferences over payment plans are closely in accordance with CTB behavior and
estimated preferences. In reduced form, subjects who chose the single payment plan made
significantly more impatient and significantly fewer interior CTB allocations than those who
chose smooth payment plans. Correspondingly, subjects who chose the single payment plan
have estimated discounted utility functions that are significantly less concave and less patient
than subjects who chose smooth payment plans. These di
erential estimates generate starkly
di
erent estimated plan values. Subjects who chose the single payment plan are estimated to
value the single payment plan around 10% more than the average smooth payment plan. Sub-
7
Although diminishing marginal utility is estimated to be substantial, it is still very far from estimates
informed by risky choice experiments (
Andersen, Harrison, Lau and Rutstrom
,
2008
).
4
jects who chose smooth payment plans are estimated to value the average smooth payment plan
around 35% more than the single payment plan. Individual preference estimates corroborate
these findings with sharp di
erences in estimated preferences and plan values across single and
smooth payment choice.
To the best of our knowledge, our findings are the first to examine the predictive content of
experimentally elicited measures of discounting and marginal utility for large-stakes decisions.
Our specific application yields several additional contributions and implications. First, a liter-
ature has recently evolved that questions the use of monetary payments in the measurement of
time preferences. When liquidity constraints are absent, monetary discounting choices should
reveal nothing about individual consumption preferences, only the interval of borrowing and
lending rates (for discussion, see
Cubitt and Read
,
2007
;
Chabris, Laibson and Schuldt
,
2008a
;
Andreoni and Sprenger
,
2012
). Further, in CTB designs these arbitrage arguments imply that
only corner solutions, consistent with maximizing present value at the market interest rate,
should be observed. Indeed,
Augenblick, Niederle and Sprenger
(
2015
);
Sprenger
(
2015
)inter-
pret the preponderance of corner solutions in monetary choice for college samples as potential
evidence of arbitrage. However, our subjects are particularly likely to be liquidity constrained,
as they are uniformly of low income, with 92.2% having no savings in any financial institution
and 86.6% reporting never having used a credit card. Indeed, these subjects seem to use both
the CTB experiment and the structured payment plans to smooth consumption over time. In
the discussion of the use of monetary payments to elicit discounting, it may be particularly
valuable to explicitly measure liquidity constraints and examine the proportion of CTB in-
terior solutions to evaluate the plausibility of arbitrage, and hence the plausibility that true
intertemporal preferences are being captured in experimental response.
Second, our results examine the link between experimental responses and payment plan
choice through both reduced-form and structural lenses. Our structural exercise goes beyond
simple correlation of preference estimates with subsequent behavior.
8
Structural estimates are
8
Examples of such correlational work include
Chabris, Laibson, Morris, Schuldt and Taubinsky
(
2008b
);
Meier and Sprenger
(
2010
,
2012
);
Ashraf, Karlan and Yin
(
2006
);
Martinez, Meier and Sprenger
(
2017
).
5
6
used to predict plan values and whether smooth or single payment plans will be preferred.
We demonstrate consistency between predicted values and actual plan choice at the aggregate
and individual levels. Providing out-of-sample predictions is one of the major values of struc-
tural exercises beyond counterfactual construction and welfare exercises (
Card, DellaVigna and
Malmendier
,
2011
). Our project joins a small literature that aims to test the out-of-sample
point
predictions made from experimental estimates of time preferences (
Andreoni, Kuhn and
Sprenger
,
2015
;
Andreoni, Callen, Khan, Ja
ar and Sprenger
,
2018b
).
Third, contracts such as our structured payment plans are a frequent form of contract choice
(examples include lottery payment, lawsuit payment, annuity buyouts, leases, and rent-to-own
agreements). Our analysis shows that predicting these temporal contract choices is greatly
aided by the measurement of diminishing marginal utility. We make this point concretely in
our analysis by demonstrating a sharp drop in predictive value when ignoring di
erences in
marginal utility across subjects.
The paper proceeds as follows: Section
2
describes our study environment and implementa-
tion. Section
3
presents results for reduced form analysis, structural estimation and large stake
choice predictions and robustness tests. Section
4
concludes.
2 Experimental Design and Structural Estimation
2.1 Environment and Sample
The data that are used in this paper are from an artefactual field experiment conducted in
Guatemala in 2013. Our sample consists of 490 participants in Guatemala’s “Mi Bono Seguro”
CCT program. “Mi Bono Seguro” is a targeted CCT program overseen by Guatemala’s Ministry
of Social Development. Program participants can receive transfers of GTQ150 (approximately
USD19.2) per month for health, education, or both, provided all household members comply
with the conditions.
Panel A of Table
1
provides demographic characteristics for our sample of subjects. Due
7
to program requirements, our sample is not representative of the Guatemalan population. Our
subjects are primarily married women between the ages of 18 and 76 years (mean 36 years,
median 35 years), with children.
9
Our sample is comprised of impoverished households. Panel
BofTable
1
shows that roughly sixty percent of our sample reports monthly household earnings
of less than GTQ1,000 (USD128).
Panel C of Table
1
documents the levels of financial assets and access among our sample.
Around two-thirds of the study participants have never had a savings account, while nearly
eighty percent have never had a checking account and almost ninety percent have never used
a credit card. This suggests quite limited access to liquidity for our sample. Panel D of
Table
1
also provides information on liquidity and recent changes in liquidity. More than 90%
of subjects have no formal or informal savings. This suggests limited savings to draw on to
smooth consumption. On the day of the study, subjects had received income on average around
10.9 days prior to the study and were expecting income to arrive in another 10.1 days. This
indicates that our experiment was not, on average, conducted at a time of particularly extreme
liquidity conditions.
10
2.2 Measuring Time Preferences
We elicit time preferences using the modified CTB design introduced by
Andreoni, Kuhn and
Sprenger
(
2015
). In each experimental decision, subjects made an allocation to a sooner pay-
ment,
x
t
,andalaterpayment,
x
t
+
k
,atagivenmarginalrateoftransformation. Specifically,
each allocation is required to satisfy the future value budget constraint
Px
t
+
x
t
+
k
=
M,
(1)
9
As with most CCT programs, funds are usually disbursed to adult women within a recipient household.
Exceptions are only made when there is no adult woman present. For instance, if a mother is not yet eighteen
years old or has passed away, then funds are disbursed to an adult male in the household.
10
In subsection 3.3.3, we relate cross-sectional variation in liquidity to experimental behavior.
8
Table 1: Socio-Demographic Characteristics
Full Sample
Analysis sample
Characteristic
#Obs Mean [Median] #Obs Mean [Median]
(s.e)
(s.e)
Panel A: Socio-Demographics Information
Female
490
0.99
408
0.99
Age
470
36.02 [35.04]
390
35.98 [35.22]
(0.42)
(0.45)
Married or with Partner
490
0.72
408
0.71
Household Size
490
5.84 [5]
408
5.86 [5]
(0.10)
(0.11)
Number of Children
490
3.04 [3]
408
3.07 [3]
(0.07)
(0.08)
Head of Household
490
0.39
408
0.37
Panel B: Monthly Household Income
<
GTQ500 (USD64)
490
0.22
408
0.21
GTQ501 - GTQ1,000 (USD64-USD128)
490
0.39
408
0.39
GTQ1,001 - GTQ2,000 (USD128-USD256) 490
0.26
408
0.26
GTQ2,001 - GTQ3,000 (USD256-USD384) 490
0.07
408
0.07
>
Q3,001 (USD384)
490
0.01
408
0.01
Panel C: Financial Access Information
Never Had Savings Account
490
0.66
408
0.66
Never Had Checking Account
490
0.77
408
0.78
Never Used Credit Card
490
0.86
408
0.88
Never Applied for a Loan
490
0.63
408
0.63
Panel D: Liquidity and Changes to Liquidity
Any Formal Savings
485
0.08
405
0.09
Formal Savings
>
GTQ500 (USD64)
490
0.07
408
0.08
Any Informal Savings
487
0.07
406
0.08
Informal Savings
>
GTQ500 (USD64)
490
0.07
408
0.08
Any Savings Plan
490
0.06
408
0.06
Days Since Last Income (Self)
490
10.87 [5]
408
10.98 [5]
Days Since Last Income (Household)
490
9.31 [5]
408
9.17 [5]
Days Until Next Income (Self)
490
10.11 [5]
408
10.37 [5]
Days Until Next Income (Household)
490
8.71 [5]
408
8.88 [5]
Notes
: Demographic characteristics measured from self-reports in end-of-experiment survey. Our Analysis Sample
excludes 29 individuals who showed no variation in all 24 choices, 45 individuals who showed more than 4 non-
monotonic choices that di
ered by more than one category, and 8 individuals who chose custom payment plans.
9
where
M
is the total budget to be allocated, and
P
captures the rate at which money delayed
from the sooner,
t
,tothelaterpaymentdate,
t
+
k
,istransformed. Thecentraldi
erence
between the modified CTB design and the original CTB is that subjects’ allocation options
were restricted to a subset of six points along the budget rather than having a continuum of
available options. Participants were instructed to choose their most preferred option. Figure
1
contains a sample question, as it was presented to participants, with
P
=1
.
25. Each option
specified the amount at time
t
,theamountattime
t
+
k
,andthetotalamount. Sincemany
participants had low levels of literacy and numeracy, we presented all choices in the CTB using
both numbers, and pictures of the associated quantities of money. The CTB followed the
procedure used in
Andreoni, Kuhn and Sprenger
(
2015
), for which amounts were denominated
in local currency (GTQ) and scaled up by a multiple of 5.
11
Following
Andreoni, Kuhn and
Sprenger
(
2015
), we consider
t
2
{
0
,
35
}
,and
k
2
{
36
,
63
}
,foratotaloffourcombinationsof
t
and
t
+
k
.Foreachofthesecombinationsthereweresixbudgets,eachwithadi
erentvalue
of
P
.TheseparametersaresummarizedinTable
B.1
of Appendix
B
.
As described in
Andreoni, Kuhn and Sprenger
(
2015
), the inclusion of interior options,
in which a participant can receive a positive amount at both time
t
and time
t
+
k
,per-
mits identification of diminishing marginal utility from variation in
P
.Apersonwithmore
rapidly diminishing marginal utility will exhibit less sensitivity to price, a smaller elasticity of
intertemporal substitution. Variation in delay length,
k
,permitsidentificationofdiscounting,
and comparing behavior in cases where the sooner amount is delayed (i.e.,
t
=35)withcases
where it is not (i.e.,
t
=0)identifiespresentbias.
12
11
The average market exchange rate from February to March 2013 was GTQ7.82 per USD. According to
the World Development Indicators, 2013 international dollars at purchasing power parity (PPP$), using the
conversion factor for private consumption was GTQ4.05 per PPP$.
12
To explore robustness, we also introduced three between-session variations in the CTB. First, for a given
combination of
t
and
t
+
k
, we varied the order in which participants saw the six budgets. In a given session,
the value of
P
was either monotonically increasing or decreasing across the six budgets associated with a given
t
and
t
+
k
. Second, the options within a given budget were ordered such that the sooner amount was either
monotonically increasing or decreasing. Finally, the GTQ25 participation payment which was added to both
payments at time
t
and time
t
+
k
was explicitly shown in all CTB options in some sessions. This treatment
simply varies the salience of the participation fee, as this information was also given to all participants prior to
completing the tasks. The e
ects of these design features are quite limited and we discuss them primarily in
Appendix
C.5
on robustness.
10
Figure 1: Sample question, as it was presented to participants, with
P
=1
.
25.
In total, subjects made allocations in 24 CTB tasks. One task for each subject was chosen
at the end of the experiment. Participants additionally earned GTQ50 (about USD6.4) for par-
ticipation in the experiment. Following
Andreoni and Sprenger
(
2012
), half of this participation
fee was added to the sooner payment and half was added to the later payment of the randomly
selected budget from the CTB. This was intended to help equalize transaction costs between
options. Even if a participant was to allocate GTQ0 to a given date, she would still incur any
11
transaction costs associated with receiving this minimum payment at that date. Participants
received two checks, each with the date that they could cash it, implied by
t
and
t
+
k
for the
randomly selected allocation.
13
2.2.1 Identifying and Estimating Time Preferences
Andreoni, Kuhn and Sprenger
(
2015
)discussanumberofmethodologiesforstructurallyesti-
mating time preferences from CTB data. The method that they implement in their subsequent
prediction exercise for small-stakes laboratory and hypothetical decisions is based on simple
regression analysis.
Preferences over bundles (
x
t
,x
t
+
k
)aredescribedbyatime-separable,quasi-hyperbolically
discounted constant relative risk averse utility function,
U
(
x
t
,x
t
+
k
)=
8
>
>
<
>
>
:
x
t
+
k
x
t
+
k
if
t
=0
x
t
+
k
x
t
+
k
if
t>
0
.
(2)
The parameter
is the exponential discount factor between periods, and
is the present-
bias parameter, which is applied to the later payment in the case that the earlier payment is
realized in the present. The parameter,
,capturesthedegreeofutilitycurvature,andhence,
determines diminishing marginal utility, and the preference for smoothness in intertemporal
payments.
Maximization of (2) under constraint (1) implies
x
1
t
t
0
k
x
1
t
+
k
=
P,
where
t
0
is an indicator for whether
t
=0. Takinglogsandrearranging,onearrivesatthe
13
For a few subjects, cashing bank checks did not follow the experimental protocol. Specifically, we have check
cashing data for 360 of the 408 subjects in our sample, and find that for 16.4% of participants, CTB checks
were cashed prior to their specified payment date. Such early cashing may be problematic if subjects forecasted
the ability to do so. Evidence suggests this is not the case as someone who forecasts this ability should simply
choose the maximal later payment value in each choice. There is no correlation between the amount allocated
to the later date in the CTB and early cashing (
=0
.
0124
,p
=0
.
814)
.
12
linear form,
ln
x
t
x
t
+
k
=
ln(
)
1
t
0
+
ln(
)
1
k
+
1
1
ln(
P
)
.
(3)
Equation (3) makes clear the mapping from the variation of experimental parameters to struc-
tural parameter estimates alluded to above. Variation in
P
identifies the marginal utility
parameter,
1. For a fixed
P
,variationindelaylength,
k
,identifiesthediscountfactor,
,
and variation in
t
0
identifies the present bias parameter,
.
Identifying
from the sensitivity of allocations to variation in prices highlights the connec-
tion between diminishing marginal utility and preferences for smoothness in consumption. A
person with rapidly diminishing marginal utility will be relatively insensitive to price changes,
and prefer smoother interior allocations to budget corners.
Estimation based on equation (3) requires formulation of an error structure. CTB applica-
tions generally impose an additive error structure, leaving equation (3) estimable with standard
techniques such as ordinary least squares (OLS). Note, however, such an estimation strategy
ignores the discretized nature of the modified CTB data where (
x
t
,x
t
+
k
)takesoneofsixval-
ues for each allocation.
Andreoni, Kuhn and Sprenger
(
2015
)provideanumberofadditional
estimation strategies accounting for this discreteness, documenting broadly similar estimated
parameter values. We follow their approach, basing our predictions primarily on the simple
least squares estimator, and we evaluate alternative estimation strategies in Appendix
C.3
.
Note that the log allocation ratio, ln(
x
t
x
t
+
k
), is not defined for corner solutions where
x
t
=0
or
x
t
+
k
=0. Weadopttheconventionof
Andreoni, Kuhn and Sprenger
(
2015
)andsetthese
corner solution values to GTQ0.001 for the purposes of estimation.
An additional issue related to the estimation of time preferences from experimental data is
background consumption.
Andersen, Harrison, Lau and Rutstrom
(
2008
)and
Andreoni and
Sprenger
(
2012
) provide estimates of time preferences and marginal utility under assumptions
of fixed background consumption.
Andreoni and Sprenger
(
2012
)alsodemonstrateapotential
sensitivity of curvature estimates with respect to varying assumptions of background consump-
tion. If, for example, the background consumption is GTQ1,000 in equation (3), then the value
13
ln(
x
t
+1000
x
t
+
k
+1000
)willberelativelyinsensitivetovariationinln(
P
), and
will be estimated close
to zero regardless of choice. Following equation (3), background consumption also influences
estimates of
and
, with higher assumed background consumption leading to increases in both
and
.Forourcoreanalysis,wefollowtheconvention(asmuchoftheliteraturehasdone)
and assume zero background consumption.
14
In Appendix
C.3
,weevaluatethesensitivityof
our results to changes in background consumption.
For behavior in our monetary discounting tasks to be informative of consumption prefer-
ences, subjects must have limited access to liquidity. An agent who can borrow (or save) at a
better rate than that implied by
P
should allocate her entire budget to the later (or sooner)
date. Behaviorally, one should observe only corner solutions and identify only the interval of
borrowing and lending rates, rather than any information about preferences. This point broadly
calls into question the use of monetary discounting tasks to identify consumption preferences
(
Cubitt and Read
,
2007
;
Chabris, Laibson and Schuldt
,
2008a
;
Andreoni and Sprenger
,
2012
).
15
Table
1
demonstrates that our sample is likely to be liquidity constrained, being both poor and
with limited access to formal financial instruments. As such, one might expect our sample’s
behavior to be more reflective of their consumption preferences than college subject pools.
Car-
valho, Meier and Wang
(
2016
)showplausiblerelationshipsbetweenobjectivefinancialsituation
and behavior in CTB tasks. In subsection 3.3.3 we link liquidity and financial access variables
to experimental behavior and find qualitatively similar results for groups where these potential
motives are more or less prevalent.
2.3 Large-Stakes Intertemporal Choice
Our experimental methodology identifies time preferences and marginal utility from CTB
choices with a future value of GTQ100. These stakes are substantial for our sample; they are
14
A background consumption parameter of zero is consistent with the literature on mental accounting, specif-
ically related to narrow bracketing (
Read, Loewenstein, Rabin, Keren and Laibson
,
1999
;
Thaler
,
1999
).
15
On the other hand,
Andreoni, Gravert, Kuhn, Saccardo and Yang
(
2018a
) presents evidence that even under
favorable conditions (i.e., college students with access to instant bank transfers) choices in the CTB task are
far from the perfect arbitrage prediction.
14
about two thirds of a monthly “Mi Bono Seguro” transfer. Our high-stakes decisions involve
twelve times that amount. Each participant was assigned a one-in-thirty chance of winning
GTQ1,200. This sum amounts to more than a month of household income for around 60% of
individuals in our sample.
After completing the CTB tasks, each participant was asked to specify how they would like
to receive these GTQ1,200 over a six month period, supposing that they won the draw. Six
payment plan choices were available to subjects, varying the timing of payments. All options
had the same date for the first payment, 7 to 20 days after the date of the experiment.
16
Depending on the option chosen, subsequent payments would take place at fixed intervals after
the first payment. One payment plan option was to receive a single payment of GTQ1,200
on the 22nd or 8th of the month. The remaining payment plans provided opportunities to
smooth intertemporal payments with multiple payment options. Subjects could select two tri-
monthly payments of GTQ600, three bi-monthly payments of GTQ400, six monthly payments
of GTQ200, 12 bi-weekly payments of GTQ100, or customize a monthly payment schedule.
Figure
2
provides an example of the paradigm.
17
Subjects did not know the outcome of the randomization for their CTB choices prior to
making payment plan decisions, and they were not informed of the upcoming plan decisions
when making CTB choices, limiting potential pollution across tasks. Furthermore, when pay-
ment plan options were being presented, subjects were informed that upon winning, they would
have to choose between receiving the payment from the CTB allocation (GTQ100) or from the
payment plan (GTQ1,200). This ensures that potential CTB payment dates would not a
ect
choices over payment plan options as subjects knew they would only be paid for one of the two.
16
The first payment date was set to either the 22nd or 8th of the current or next month, depending on the
date of the session, so as to leave at least one week and no more than three weeks between the session and the
first payment date.
17
In order to evaluate robustness of decisions to framing e
ects, in around half of the sessions, we varied
the order in which these options were presented (either increasing or decreasing the number of payments).
Behavioral di
erences are evaluated in Appendix
C.5
.
15
0
0
1
1
1
HO
J
A
D
E
R
E
S
P
US
T
AS
P
AR
TE 2
D
E
CISI
Ó
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1
4
5
6
7
1. Sesión
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
2. Participante #
1
2
3
4
5
6
7
8
9
10
3. Encuestador
2.1b
Opción 1
Opción 2
Opción 3
Opción 4
Opción 5
Opción 6
¿
Cuán
t
o?
¿
Cuán
t
o?
¿
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t
o?
¿
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t
o?
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¿
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t
o?
¿
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t
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TOT
A
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:
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,
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TOT
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:
Q
1
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:
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TOT
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1
,
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TOT
A
L
:
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1
,
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TOT
A
L
:
Q
1
,
200
Figure 2: Example of a question about large-stakes intertemporal choice
2.4 Session Protocols
As participants arrived, they were asked to provide (oral) informed consent and were registered
before the start of the session. Each session was conducted by a session leader who had a team
of assistants. After welcoming the participants, the session leader gave a presentation of the
instructions, which was projected in the room. The text of these instructions, translated from
the original Spanish, can be found in Appendix
D
.
Due to participants’ low levels of formal education and literacy, we provided individual sup-
16
port to each participant throughout the session. In particular, assistants asked each participant
the questions for each experimental task individually, resolved any questions as they arose, and
recorded the participants’ decisions. In addition, we presented each choice in the experimental
tasks with visual aids and the presentation was intended to increase understanding.
Once participants had finished all the experimental tasks, they completed, again with the
help of an assistant, a socio-demographic survey. Their answers in this survey were not incen-
tivized. While the surveys were administered, participants received a snack, and something to
drink.
Each session lasted between three and four hours. A total of 23 sessions were run. In each
of these sessions, between 15 and 24 participants were present. Sessions were conducted during
February and March of 2013, and were run in 12 municipalities across 4 counties.
All 490 subjects who were initially selected for the experiment completed both the CTB
tasks and their large-stakes payment plan choice. Among the CTB decisions, twenty-nine (5.9%)
subjects exhibited no variation in experimental response across all 24 tasks. Additionally 45
subjects (9.8%) exhibited substantial non-monotonicities in demand, increasing their allocation
to the sooner payment date by more than one position as
P
increased 4 or more times in 20
opportunities.
18
These subjects are all removed from the analysis. Among the large-stakes
payment plan choice, 8 (1.74%) chose to customize their payment plan. For ease of explication,
we ignore this small sub-sample as well. Our final sample of subjects for analysis is 408 subjects.
Table
1
shows separate demographic characteristics for the full sample and the analysis sample
showing limited demographic di
erences.
18
A more extreme measure that may be more familiar to readers, is switching from allocating the entire
budget to the later payment to allocating the entire budget to the sooner payment, as
P
increases. Sixty-seven
subjects (14.5%) exhibited such extreme non-monotonicity, at least once. This figure compares favorably to the
similar behavior of multiple switching in standard price list experiments (see, e.g.,
Holt and Laury
,
2002
;
Meier
and Sprenger
,
2010
). In Figure
B.1
of Appendix
B
, we present histograms from the frequency of monotonicity
violations across subjects, demonstrating that most of our analysis sample respects monotonicity at high rates.
17
3 Results
We present the results in three broad sections. In the first subsection, we analyze the reduced-
form relationship between choice over structured payment plans and experimental responses.
In the second subsection, we present structural analysis linking intertemporal preference pa-
rameters to plan choice at both the aggregate and individual levels. In the third subsection,
we present robustness tests and additional analyses.
3.1 Reduced-Form Results
Table
2
presents plan choices for the 408 subjects in our analysis sample. Ninety subjects
(22%) opted for the single payment plan of GTQ1,200 and 318 subjects (78%) chose one of the
smooth payment plans. Among smooth payment plans, a similar proportion of subjects chose
two, three, and six payment plans, with only a small minority of subjects opting for twelve
bi-weekly payments of GTQ100. Table
2
also provides summaries of experimental choices in
the CTB design. We calculate the proportion of allocations that are impatient (the entire
budget is allocated to the sooner date), patient (the entire budget is allocated to the later
date), and interior. Forty-six percent of allocations are interior allocations, and only 34 of 408
subjects (8.4%) made zero interior allocations in 24 opportunities. These choice patterns di
er
qualitatively from CTB experiments in college subject pools. For example, with UCSD under-
graduates
Andreoni, Kuhn and Sprenger
(
2015
)report12%interiorallocationswith60%of
subjects making zero interior allocations in 24 opportunities.
19
With non-diminishing marginal
utility, one would expect only corner solutions in our CTBs, where the entire budget is allo-
cated to either the sooner or later payment depending on the rate of interest. Similarly, with
non-diminishing marginal utility, one would expect a preference for the single payment plan
among the payment plan options. Observed choices in both settings suggest an important role
for diminishing marginal utility; a preference for smoothing intertemporal payments is observed
19
In developing country sample, interior allocations appear more frequent.
Kramer, Janssens and Swart
(
2013
)
and
Gin ́e, Goldberg, Silverman and Yang
(
2012
) document in the range of 45% and 69% interior allocations.
18
in both CTB and payment plan choice.
Table 2: Payment Plan Choice and CTB Response
CTB Choice
Payment Plan Choice
# Observations (% of Total) Impatient Interior Patient
Chose Single Payment Plan (GTQ1,200)
90 (22%)
0.22
0.41
0.37
Chose Any Smooth Payment Plan
318 (78%)
0.13
0.47
0.39
Two Payments (GTQ600)
111 (27%)
0.13
0.38
0.48
Three Payments (GTQ400)
84 (21%)
0.14
0.48
0.37
Six Payments (GTQ200)
87 (21%)
0.11
0.56
0.33
Twelve Payments (GTQ100)
36 (9%)
0.14
0.52
0.33
Total
408 (100%)
0.15
0.46
0.39
Notes
: plan choice for 408 participants and Convex Time Budget (CTB) Choice. Impatient (Patient) choice reflects subject
allocating entire budget to sooner (later) payment.
Table
2
provides separate calculations for the proportion of impatient, interior, and patient
CTB behavior for each subgroup of payment plan choice. Interestingly, raw behavior seems
to di
er by plan choice. Subjects who chose the single payment option make around 9%-age
points (70%) more impatient choices and 6%-age points (13%) fewer interior allocations than
subjects who chose smooth payment plans.
20
These patterns carry a natural intuition. Greater
patience and more rapidly diminishing marginal utility, as conveyed by more interior and more
patient allocations, are linked to choosing smooth payment plans.
Figure
3
and Table
3
analyze the relationship between plan choice and experimental behavior
20
Among subjects choosing smooth payment plans further di
erences are observed, with a high number of
payments correlating with a greater proportion of interior choices and a lesser proportion of patience choices.
Among smooth payment plan subjects, the raw correlation between the number of interior and impatient choices
a subject made (out of 24) and the number of payments in the structured payment plan is
=0
.
16 (
p<
0
.
01)
and
=
0
.
15 (
p<
0
.
01), respectively. We provide further discussion of this variation across groups in Appendix
C.2
.
19

















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Figure 3: Allocation to the sooner payment date; proportion of impatient and interior choices.
20
Table 3: Plan Choice and Experimental Behavior
Dependent Variable:
Sooner Allocation
Impatient Choice
Interior Choice
(1)
(2)
(3)
(4)
(5)
(6)
Chose Smooth Payment Plan -6.198*** -17.903*** -0.089*** -0.200*** 0.068**
0.076
(2.197)
(4.904)
(0.025)
(0.061)
(0.034)
(0.076)
Rate of Transformation:
P
-33.492*** -42.215*** -0.176*** -0.291*** -0.059*** 0.024
(1.096)
(2.484)
(0.013)
(0.031)
(0.014)
(0.031)
Delay Length:
k
0.317*** 0.395*** 0.003*** 0.004***
0.001
-0.001
(0.027)
(0.068)
(0.000)
(0.001)
(0.000)
(0.001)
Immediate Choice:
t
0
-3.575*** -5.913***
-0.015
-0.022 -0.047*** -0.095***
(0.806)
(1.998)
(0.009)
(0.025)
(0.013)
(0.029)
Chose Smooth
P
11.189***
0.147***
-0.107***
(2.751)
(0.034)
(0.034)
Chose Smooth
k
-0.100
-0.002**
0.002*
(0.074)
(0.001)
(0.001)
Chose Smooth
t
0
2.998
0.009
0.061*
(2.177)
(0.027)
(0.033)
Constant
65.286*** 74.412*** 0.341*** 0.427*** 0.480*** 0.474***
(2.684)
(4.276)
(0.031)
(0.057)
(0.040)
(0.068)
R-Squared
0.152
0.155
0.048
0.052
0.007
0.009
#Observations
9789
9789
9789
9789
9789
9789
#Clusters
408
408
408
408
408
408
Notes
: Ordinary least squares (OLS) regressions with standard errors clustered on individual level. Standard errors are
reported in parentheses.
,
⇤⇤
and
⇤⇤⇤
indicate significance at the 10%, 5% and 1% levels, respectively.
in closer detail. In Panel A of Figure
3
,wepresenttheaverageallocationtothesooner
payment date for each value of
P
for the two delay lengths,
k
=35and
k
=63days.
21
At each interest rate, subjects opting for smooth payment plans allocate less money to the
sooner payment. Additionally, subjects opting for smooth payment plans are less sensitive to
variation in
P
.Columns(1)and(2)ofTable
3
provide corresponding statistics. Controlling for
the experimental parameters,
P
,
k
and
t
0
, subjects who chose smooth payment plans allocate
around GTQ6 less to the sooner payment and are around 20% less sensitive to variation in
P
than those who chose single payment plans. Panel B of Figure
3
and columns (3) through
(6) of Table
3
provide detail on the proportion of impatient and interior choices. Controlling
for experimental parameters, subjects who chose smooth payment plans make significantly
21
For the purposes of the graphic, data from observations with
t
0
equal to one and equal to zero are averaged
together.