Five Facts about MPCs: Evidence from a Randomized Experiment∗
Johannes Boehm

Etienne Fize

Xavier Jaravel

Sciences Po & CEPR
johannes.boehm@sciencespo.fr

PSE & IPP
etienne.fize@ipp.eu

LSE & CEPR
x.jaravel@lse.ac.uk

June 1, 2024
Abstract
We present five facts from an experiment on the marginal propensity to consume (MPC) out of transitorytransfers: (1) the one-month MPC on a cash-like transfer is 23%; (2) it is substantially higher (61%) on atransfer administered via a card where the remaining funds expire after three weeks, inconsistent with money
fungibility; (3) the consumption response is concentrated in the first three weeks; (4) MPCs vary with household
characteristics, but are high even for the liquid-wealthy; (5) the unconditional MPC distribution exhibits large
variation. Our findings inform the design of stimulus policies and pose challenges to existing macroeconomic
models.
Keywords: Marginal Propensity to Consume, Randomized Controlled Trial, Helicopter Money.
JEL: D12, E21, C93, D91.

∗

For helpful comments, we thank Adrien Auclert, Florin Bilbiie, Corina Boar, Michael Boutros, Peter Ganong, Joe Hazell, Chen Lian,
Philippe Martin, Ben Moll, Sarah Mouabbi, Emi Nakamura, Alan Olivi, Jonathan Parker, Valerie Ramey, Xavier Ragot, Ricardo Reis,
Jesse Shapiro, Johannes Spinnewijn, Ludwig Straub, Gianluca Violante, Christian Wolf, as well as seminar and conference participantsat the Bank of England, the Bank of France, the Bank of Israel, the Center for Economic Studies at the U.S. Census Bureau, the CEPR
public economics symposium, the Federal Reserve Board, George Washington University, HEC, the Hebrew University of Jerusalem, theInstitute for Fiscal Studies, the London School of Economics, the Paris School of Economics, the SITE conference, Stockholm School of
Economics, UCL and the University of Munich. We are grateful to Emmanuel Giguel, Julien Fournel and the teams at Euro-Information
and Crédit Mutuel Alliance Fédérale for their work on the implementation of the experiment. Boehm gratefully acknowledges financial
support from the Agence Nationale de la Recherche under grant agreement ANR-20-CE26-0006 and from the Banque de France/Sciences
Po partnership. Jaravel gratefully acknowledges financial support from UKRI under grant agreement EP/X016056/1. We are indebted
to Antoine Ding and Tyler Woodbury for excellent research assistance. We dedicate this paper to the memory of Philippe Martin,
without whom this project would not have been possible. AEA preregistration: https://doi.org/10.1257/rct.9296-1.0.

1Introduction

The marginal propensity of households to consume out of a transitory income shock (MPC) plays acentral role in both macroeconomic models and stimulus policies. It determines the partial equilibrium
response to such shocks and has broader implications for general equilibrium responses, notably for how
monetary and fiscal authorities can boost demand through direct stimulus transfers (e.g., Kaplan et al.,2018, Auclert et al., 2023b). Despite extensive research, estimates of MPC out of transfers that are
relevant for fiscal policy remain debated due to limitations arising from the source of variation used forcausal identification (e.g., Parker et al., 2013, Orchard et al., 2023b, Borusyak et al., 2023). Furthermore,
the recent pandemic-induced downturn has seen an increased variety of large-scale stimulus policies, using
prepaid cards or time-limited consumption vouchers (including California, Milan, and Seoul in 2020, Hong
Kong and Northern Ireland in 2021, and Thailand in 2023), raising questions about whether the way a
stimulus payment is administered might affect economic outcomes. Finding scalable ways of raising MPCs
can be an important policy objective given recent estimates of low MPCs out of standard tax rebates in
the United States.1
In this paper, we estimate MPCs by running a randomized experiment, allocating transfers at random
across households. We use high-frequency bank data to measure households’ overall consumption response
and its heterogeneity across households.2 Going beyond standard estimation of MPCs, we examine
whether transfers with time limits or negative interest rates may yield larger MPCs, in order to inform
policymakers about the role of stimulus design in determining the consumption response to transfers.
Our experiment is designed with scalability and generalizability in mind. We randomly provide stimulus transfers to a sample of about 1,000 French individuals who are representative of the adult French
population, and for whom we observe detailed financial transactions and consumption expenditure data
through bank records. The experiment was launched in May 2022, at a time when interest rates were stillat zero in the euro zone. Our baseline treatment evaluates the consumption response to a simple one-offmoney transfer in the form of a debit card with a balance of 300 Euros. We compare the total consumption spending of treated households, on both the prepaid cards and their regular bank accounts, withthose of a large sample of about 90,000 untreated households. In further treatment groups, we investigate
two potential ways of increasing the households’ overall consumption response by assigning a negativeinterest rate on the transferred wealth: either by making the card expire after three weeks – at which
point any remaining balance is lost to the household – or with a weekly deduction of an amount close to
10 percent of the remaining balance on the card. While households in all treatment groups are free tospend the transfer however they want, we make the interest payments potentially binding by preventing
cash withdrawals from the cards. We also assign an additional framing treatment where participants are
asked to “spend soon, on French products, and on things [they] would have otherwise not purchased”.
Using this experimental setup, we establish five facts about MPCs. We then discuss why these facts are
informative for macroeconomic models and for the design of stimulus policies.
1

See Parker et al. (2022b) and Parker et al. (2022a) for MPCs out of the 2020 stimulus payment, Borusyak et al. (2023)
and Orchard et al. (2023b) for the 2008 stimulus payments, and Orchard et al. (2023a) for the 2001 stimulus.
2
A vast literature has examined MPCs out of various shocks, including typical income shocks (Ganong et al., 2020),
lottery winnings (Fagereng et al., 2021, Golosov et al., 2024), and recurring lump-sum payments (Kueng, 2018). Instead, westudy one-time transfers comparable to those deployed to simulate the economy during an economic downturn.

1

We start by estimating MPCs depending on the card type, establishing our first two key facts. We
find that participants in the baseline treatment group (without an expiry date or negative interest rate)increase their total consumption expenditure after receiving the card, with an average marginal propensity
to consume of 23 percent over one month (Fact #1). We then establish the main finding of the paper,
showing that implementation design matters: the MPC is substantially higher for treatment groups where
any remaining balance becomes unusable after three weeks, at 61% (or 70%, when conditioning on takeup), or where remaining balances are subject to the 10% negative interest rate every week, at 35% (Fact#2). In contrast, we do not find any significant effect of the additional “framing” treatment paragraphin the letter, suggesting that our results are unlikely to be driven by experimenter demand effects.
We examine the possibility that the faster spending for cards with an expiry date or negative interest
rates could induce detrimental consequences for these households due to behavioral internalities. We findno such evidence: these households do not incur more volatile nondurable consumption in later periods,
and they are not more likely to make purchases that could entail adverse health consequences, such as
tobacco or gambling.
We next analyze the dynamics of the consumption response – the path of intertemporal MPCs, or
iMPCs (Auclert et al., 2023b, Angeletos et al., 2023) –, yielding our third key fact. We find that,for all treatment cards, the additional spending occurs immediately after the onset of the experiment.
Specifically, the increase in consumption is much larger early on, in the first weeks following the transfer(Fact #3). We observe that the consumption response is concentrated early on even for non-durables.
To understand the spending behavior of the participants upon receiving the treatment, we administera survey among participants and we analyze the bank data to assess potential changes in the compositionof expenditures. Recipients are well aware that they spend less on their main account (thereby having
an MPC below one), and they mention precautionary saving as a key motive. They use the card theyreceive primarily to cover running expenses, but some also report purchasing a “treat”, or making a large
expenditure earlier. Treated households have similar expenditure shares on most consumption categories
as control households, but purchase relatively more clothing and household equipment. Treated households
also spend slightly more on durables and on imported goods.
We then turn to MPC heterogeneity, establishing our fourth and fifth key facts. We find that there issignificant MPC heterogeneity by observed household characteristics, including for liquid wealth, current
income, proxies for permanent income, gender, and age (Fact #4). The most important source of heterogeneity we document is about gender: the average MPC of men is about twice as high as for women.
We also find that households with lower income and households with lower average pre-treatment consumption levels (our proxy for permanent income) have higher MPCs. Liquid wealth does play a role inexplaining MPC heterogeneity, albeit a limited one, and MPCs remain high even for households whose
liquid wealth exceeds twice their monthly income. Finally, we find that MPCs appear to increase withage, although differences across age groups are relatively noisy. A set of LASSO regressions confirms thatthe most important predictors of MPC heterogeneity are treatment group memberships and demographic
characteristics like gender.
Going beyond heterogeneity that is associated with observed characteristics, we estimate the fullunconditional distribution of MPCs across households. Due to our experimental setting, we know thatthe distribution of error terms is identical in the treatment and control groups. Under the assumption that2the treatment effect is independent from the error term,3 this fact allows us to use statistical deconvolution
techniques to estimate the full unconditional distribution of treatment effects. Applying this methodology,
we find large unconditional heterogeneity in consumption responses following the transfer (Fact #5). In
the baseline treatment group where households receive a cash-like transfer, a quarter of households increase
their consumption expenditure over a 4-week horizon by less than 13 percent of the transfer, and a quarter
increase their consumption by more than 48 percent. In contrast, in the treatment group where cards
expire after three weeks, three quarters of recipients increase their 4-week consumption by more than 52
percent of the transfer amount. These results again highlight the power of implementation design choices
to shift MPCs.
Finally, we discuss the implications of these five facts about MPCs for macroeconomic models and forpolicy. While our MPC estimates do not speak to general equilibrium effects, they are informative about
key building blocks of modern macroeconomic models. Our findings contrast with the predictions of thecanonical implementation of the benchmark two-asset Heterogeneous-Agents New Keynesian (HANK)
model in three ways. First, the magnitude and dynamics of the MPC are difficult to reconcile with
HANK models. In all our treatment groups the entire spending response is concentrated in the firstweeks (up to three weeks), while the MPC response is much more long-lived according to HANK (Kaplan
and Violante, 2014, Kaplan et al., 2018, Auclert et al., 2023b). For example, in Kaplan et al. (2018), theMPC out of a $300 transfer is 17% over a quarter and increases to about 32% over a year. Instead, withour baseline treatment (without an expiry date or negative rates), we obtain a larger MPC in the firstmonth, at 23%, but no further increases in spending in later periods.4 Laibson et al. (2022) note thatdurables require special treatment when analyzing the dynamic reponse of spending, since the effective
consumption derived from durables occurs over a long period rather than at the time of purchase. However,the concentrated spending response we estimate is not driven by durables. Second, in HANK the MPC
is strongly correlated with the level of liquid assets that agents hold; while we do find some heterogeneityof MPCs for groups with different levels of liquid asset holdings, we find that average MPCs are also highfor households that have moderate or high levels of liquid asset holdings. Third, our estimates of theunconditional distributions of MPCs reveal that MPCs are high for a large majority of the population, in
contrast to standard calibrations of the HANK model, where high MPCs are concentrated among a subset
of agents who have low liquid wealth and hit their borrowing constraints. Assessing whether alternative
calibrations or extensions of the HANK model can match our five MPC facts is an important direction
for future research.
We also show that our results are difficult to reconcile with agents being rational and treating money
as fungible. A rational agent that treats money as fungible should first “use up” the treatment card to
avoid potentially losing money (through the negative interest rate or expiry) before using their normal
debit or credit card. The transferred amount of 300 euros is well below the normal 3-week consumption
expenditure of most households, suggesting that the expiry date in group 2 should in principle not bind(and therefore not affect behavior) for most households. Moreover, we observe that households in thetreatment groups with an expiry date or a negative interest rate frequently make payments with other3

We provide empirical support for this assumption through auxiliary tests in Section 4.
Our finding is consistent with quasi-experimental evidence on MPCs using the 2008 U.S. tax rebates. Using scanner
data to document high-frequency spending responses to tax rebates, Borusyak et al. (2023) show that they are concentrated
in the first month after the rebate.
43

means before exhausting the transfer card. Our results thus echo a literature documenting the nonfungibility of money (Hastings and Shapiro, 2013, 2018, Baugh et al., 2021, Geng et al., 2022, Gelman
and Roussanov, 2023), and deliver three lessons for behavioral models. First, models of consumption that
rely on present bias in preferences (e.g. Laibson, 1997, Maxted, 2020, Laibson et al., 2021) are able toexplain why the consumption response to the transfer is concentrated early on, but cannot explain the
difference in the magnitude of responses between the treatment groups. Indeed, under such preferences,consumers in all three groups should be present-biased but the negative interest rate and the expiry datewould remain non-binding constraints, given that it should be costless for agents to substitute current
account spending for prepaid card spending. Second, while implementations of “spender-saver” models(Campbell and Mankiw, 1989) can be made to feature consumption responses that are concentrated very
early on, they would also imply strongly bi-modal distributions of MPCs, which we do not find. Third,
our finding that households consume more when presented with an urgent spending need (in the formof the negative interest rate or expiry date) is consistent with theories where the salience of treatments
affects economic choices by drawing attention away from other considerations (Bordalo et al., 2012, 2013,
Ilut and Valchev, 2023). We note that other empirical studies of consumption behavior following income
shocks are consistent with theories of salience (Kueng, 2018, Baugh et al., 2021).
Our new facts have two implications for policy. First, the large difference in MPCs across treatmentgroups shows that changing the design of transfers can be a powerful way to increase the MPC. The
treatment we find to have the highest MPC takes a particularly simple form: a debit card that features
an expiry date, a feature that consumers know from gift vouchers. Second, our estimates of MPC heterogeneity have implications for the targeting of transfers by observable household characteristics.5 We findthat it is possible, based on simple observable characteristics like income, to find household populations
with significantly higher MPCs than average. However, the change in MPC obtained by targeting issmaller than when using a card with an expiry date. We conclude that implementation design choices area more powerful tool, compared with targeting, to increase the recipients’ average MPC.
Related literature. A unique feature of our setting is to use an experiment to analyze how the marginal
propensity to consume varies with implementation design choices, comparing the effects of standardtransfers to transfers featuring an expiry date or a negative interest rate. More broadly, our results
contribute to a vast literature that seeks to estimate marginal propensities to consume.
While there is a very large literature on MPCs (see, e.g., Jappelli and Pistaferri, 2010 for a survey),
only a relatively small subset of papers analyzes MPCs out of unanticipated and transitory transfers,
which are most informative for stimulus policies and macroeconomic models. The literature has taken
two types of approaches. First, a range of studies analyze the staggered disbursement of tax rebates.
The seminal papers analyzing staggered tax rebates in the United States (Johnson et al., 2006, Parker
et al., 2013, Broda and Parker, 2014) found large MPCs, of 50% to 90% over a quarter, which arecommonly used to discipline macro models. However, the staggered difference-in-differences design raises
an identification challenge: a recent literature finds that using difference-in-differences estimators that arerobust to treatment effect heterogeneity yields much smaller MPCs of about 25% over a quarter (Borusyak
5

Aguiar et al. (2023) discuss the targeting of individuals in a model where differences in MPCs originate from preference
heterogeneity. Gelman (2021) highlights the importance of discount factor heterogeneity in explaining MPC heterogeneity.

4

et al., 2023, Orchard et al., 2023b). The staggered disbursement leveraged in these studies means thateven control households were expecting to receive the rebates at some point. In contrast, our stimulustransfers are entirely unanticipated, and we compare the consumption response of treated households toconsumption of households that were entirely untreated. Second, the literature has studied the impact oflottery wins (Fagereng et al., 2021, Golosov et al., 2024), inferring the consumption response from income
and wealth data rather than using direct consumption measures like we do.6 While these studies benefit
from much larger samples than ours, a limitation is that they cannot analyze the consumption responseby expenditure type (e.g., durables vs. non-durables).
A much broader literature measures the spending responses to anticipated shocks (e.g., Gelman et al.,2014, Kueng, 2018, Olafsson and Pagel, 2018, McDowall, 2020, Gelman, 2022, Baugh et al., 2021), typicalincome shocks with a persistent component (Ganong et al., 2020), and unanticipated permanent shocks(Gelman et al., 2023). Relative to these papers, we focus on unanticipated transitory transfers that are
similar to standard stimulus transfers.
Four other strands of the literature provide MPC estimates. First, a growing literature seeks toestimate the distribution of MPCs (Misra and Surico, 2014, Lewis et al., 2019). A key advantage of ourexperimental setup is that we can use deconvolution methods to estimate the distribution of treatment
effects. Second, another strand of the literature uses theory-informed moment conditions to identify MPCs
(Blundell et al., 2008, Commault, 2022a). Third, a number of papers have elicited MPCs from surveys
where respondents are asked how they would respond to a hypothetical transfer (Shapiro and Slemrod,
2003, 2009, Jappelli and Pistaferri, 2014, Bunn et al., 2018, Parker and Souleles, 2019, Fuster et al., 2021,
Commault, 2022b). Fourth, a small literature estimates the spending response to consumption vouchers(Hsieh et al., 2010, Kan et al., 2017, Xing et al., 2023, Geng et al., 2022, Ding et al., 2023, Chan andKan, 2024). Appendix A describes large-scale policies using time-limited consumption vouchers that were
deployed in the wake of the Covid pandemic.
The advantages and drawbacks of randomized experiments have been discussed at length in the development literature, see e.g. Banerjee and Duflo (2009), Banerjee et al. (2016), Deaton (2010), and Deaton
and Cartwright (2018). The advantages of experiments are at the core of our contributions: we can evaluate the role of several different stimulus policy designs in the exact same setting, thereby cleanly isolating
the role of stimulus design (Fact 2); moreover, the assumptions required to identify the distribution oftreatment effects (Fact 5) are much more likely to be satisfied than in observational settings. However,as any experiment, our analysis is subject to several potential limitations. First, estimates obtained in
randomized experiments may suffer from experimenter demand effects, or Hawthorne effects. The findingthat our framing treatment does not lead to a significantly different response suggests that experimenter
demand effects are not driving our results (De Quidt et al., 2018). Second, empirical estimates obtained ina specific setting may not be externally valid. While this concern affects experimental and observational
studies alike, the fact that our experimental MPC estimates are close to the observational estimates of
Borusyak et al. (2023) and Orchard et al. (2023b), which were obtained in a completely different timeand setting, helps to alleviate such concerns. Third, due to the limited size of our experimental sample,
the standard errors of our estimates are larger than in some quasi-experimental studies (e.g., Ganong et
6
To impute consumption, Fagereng et al. (2021) use observed changes in assets and liabilities, while Golosov et al. (2024)
leverage estimates of capital gains.

5al., 2020), while they are more precise than in others (e.g., Parker et al., 2013). One advantage of ourexperimental settings for inference is that we can use Fisher’s exact test to assess the statistical significance of our estimates — which we use to probe the robustness of our main finding, Fact 2. Finally, ourexperimental estimates are only informative about a limited number of data moments (e.g., we did not
randomize stimulus size); they should therefore be viewed as complementing the existing literature only
along specific dimensions.
More broadly, this paper demonstrates the possibility of evaluating and improving the design ofmacroeconomic policy tools through experimental means.7 Our experimental stimulus transfers are designed with scalability and real-world implementability in mind. Moreover, our causal estimates help todistinguish between classes of macroeconomic models (Nakamura and Steinsson, 2018).
Outline.

The remainder of the paper is organized as follows: Section 2 presents the data and experi-mental design; Section 3 presents our main MPC estimates, establishing our first three key facts; Section
4 documents MPC heterogeneity, leading to our fourth and fifth key facts; Section 5 uses our five facts
to draw lessons for macroeconomic models and stimulus policies.

2

Data and Experimental Design

In this section, we describe our dataset, our main variables, as well as the experimental design.

2.1

DatasetOur analysis is made possible by running an experiment on a panel of households for which we have accessto comprehensive, detailed financial transactions data.8 This panel of households has been constructed tobe representative of the overall French population. For ethical and operational reasons we restricted thissample before randomly drawing treatment assignments. We describe both the larger and the restricted
samples in turn, as well as the content of the data.
The bank data and the experimental sample. Our data comes from the French banking groupCrédit Mutuel Alliance Fédérale.9 We start with a panel of households that were drawn by the bankin June 2020 and that are representative of the French population in terms of location, age, and socioeconomic characteristics, as shown by Bounie et al. (2020) and Bonnet et al. (2023), who compare thebank sample to official statistics (see Appendix B.1). The data provide socioeconomic information about
the individuals in the household, transaction-level information for transaction accounts, transaction-level
information for all payment cards linked to the accounts, debt and balances on non-transaction accounts
at the monthly frequency, as well as information about real estate assets at a much lower frequency. Card7

For an experimental study of the consumption response to credit expansions, see Aydin (2022).
See Baker and Kueng (2022) for a survey of recent research that uses financial transactions data.
9Crédit Mutuel Alliance Fédérale made de-identified data available to us on a secure server, protecting customer privacy.
The bank aims to contribute to the public good and policy debates by facilitating economics research. This is part of CréditMutuel Alliance Fédérale’s mission as an “entreprise à mission”, a French legal framework in which businesses pursue certain
societal goals. The total cost of the experiment, including the transfers and a fee to cover the operational cost, was financedby the researchers through a grant from the French national agency for research (“Agence nationale de la recherche”).
8

6

Table I Summary Statistics
N

Mean

S.D.

Age of eligible household member

85,700.00

47.03

12.92

Number of eligible household members

85,700.00

1.15

0.36

Avg. monthly incoming transfers, 6 months prior

85,685.00

2,654.04

1,439.56

Avg. monthly incoming salaries, social allowance, pensions, benefits, 6 months prior

80,034.00

2,109.55

4,968.86

Dummy: has received unemployment benefits within the last 6 months

85,685.00

0.14

0.35
19,976.04

Avg. current account balance, 6 months prior

85,698.00

4,448.51

Avg. liquid savings, 6 months prior

85,698.00

16,896.51

34,466.19

Avg. value of life insurance assets, 6 months prior

85,698.00

5,867.43

32,466.19

Avg. net illiquid wealth, 6 months prior

85,700.00

64,746.97

185,159.99

Avg. net liquid wealth, 1 month prior

85,700.00

19,265.55

46,067.00.
55,007.44

Avg. total debt, 6 months prior

85,698.00

33,300.8

Avg. consumer debt, 6 months prior

85,698.00

2,388.27

5,194.01

Avg. mortgage debt, 6 months prior

85,698.00

30,872.90

54,286.18

Number of adult members in the household

85,698.00

1.53

0.50

Number of children in the household

85,698.00

0.61

0.96

Avg. monthly consumption expenditures (cash, card payments), 1 year prior

85,698.00

1,205.52

658.29Avg. monthly direct debits, debt payments, subscriptions, 1 year prior

85,698.00

631.291,154.20

Avg. monthly outgoing transfers, 1 year prior

85,698.00

316.24639.88
1,736.50

Avg. total monthly consumption (broad measure)

85,698.00

2,153.05

Weekly consumption expenditure (cash and cards), total

2,571,000.00

417.66435.02

Weekly consumption expenditure (broad measure), excl. treatment cards

2,571,000.00

727.63

1,992.72

Notes: This table reports summary statistics for our main analysis sample. The broad measure of consumption includes thetotal of cash withdrawals, card spending, automatic debits, and wire transfers.

transactions include information on the Merchant Category Code (MCC) of the vendor, which we describe
in Appendix B.2, along with additional information on the data.
We use a subset of the full household panel for our experiment, based on eligibility criteria defined at
the individual level. To be eligible, individuals must be between 25 and 75 years of age, have a known
residential address, and should not be deemed by the bank to be financially fragile.10 In order to obtaina population where we are able to measure spending well, we retain only individuals who are part ofa household that, according to the bank’s records, do not hold accounts with another bank.11 We also
exclude those individuals that have been using their debit card infrequently in the months prior to theirexperiment, suggesting that they may predominantly use cash. After applying all conditions, we obtaina balanced sample of 85,700 unique households who have at least one or at most two eligible persons in
the household. We also drop 40 households that were treated in a pilot of the experiment. Purchasetransactions and assets/liabilities are available at the level of the household. Some specifications will
investigate response heterogeneity by characteristics of the individual that has been drawn to receive thetransfer.
10

About 1% of households are deemed financially fragile by the bank.
Note that it is relatively rare for households to use multiple banks in France. According to the 2017 French Wealth
Survey, 55% of French households only have one bank (i.e., no household member uses a different bank). Furthermore, 75%
of French household have checking accounts at a single bank. Finally, on average 81% of households’ total assets are held in
their main bank.
11

7

Variable definitions. Our main outcome variables is weekly consumption expenditure of the household,defined as the sum of all (credit and debit) card purchases and cash withdrawals of the household between
Tuesday and the subsequent Monday at midnight.12 We winsorize weekly consumption spending using
the non-treatment cards at the 99th percentile of the distribution, which is 1940 euros, before adding
treatment card expenditures to arrive at total weekly consumption expenditure. The results are notsensitive to this winsorization step, as described below. Furthermore, wire transfers and direct debit are
not included in our baseline consumption measure, but we analyze an expanded consumption measureincluding these outflows in robustness checks. Appendix B.3 provides more detail on variable definitions.
Our estimated consumption responses are thus marginal propensities to spend (see Laibson et al.,2022 on the difference between marginal propensities to spend and notional MPCs). For the purposeof studying heterogeneity in consumption responses with respect to observable characteristics, we define
time-invariant household characteristics as the average of the corresponding end-of-month characteristic
in the 6 months prior to the treatment (November 2021 to April 2022), per capita.
Summary statistics.

Table I shows summary statistics of the main variables. The table illustrates therichness of the bank data and the large heterogeneity in observable characteristics. Appendix Tables D1
and D2 provide additional summary statistics.

2.2

Experimental Design

Treatment arms.

From the set of eligible individuals, we randomly draw 915 participants over threetreatment groups.
Treatment Group 1 (G1, N = 379) participants receive a MasterCard debit card linked to a newtransactions account with an initial balance of 300 Euros. The card expires and becomes unusable fivemonths after it has been sent, after which the participants receive any unspent balance wired to theirmain transactions account. Prior to this date, the participants are unable to transfer funds from or to the
newly created transactions account, except by means of making purchases with the associated debit card.
Notably, participants are unable to withdraw cash from those accounts. Otherwise, the participants arefree to spend the account balance wherever MasterCard is accepted (i.e. in stores or online). Participants
can monitor the remaining balance through their mobile phone bank app, where the account appears
alongside their other bank accounts. Note that for purchases made in stores, merchants may be willing to
split transactions into several payments, thus allowing participant to purchase an item above 300 Euros
by combining the balance available on the treatment card with funds from their regular bank account.
Treatment Group 2 (G2, N = 268) participants receive the same type of account and card as G1
participants, except that the card expires after three weeks; any remaining balance on the account after
three weeks is not wired to their main checking account, but is deducted from the account and lost to theparticipants.
Treatment Group 3 (G3, N = 268) participants receive the same type of account and card as G1
participants, except that an “interest” payment is deducted at a weekly frequency. We approximate a
12
We choose this interval to line up with the negative interest payments of Group 3, which take place on Mondays at
midnight. One exception to the construction of weekly aggregates is that we assign Monday 2 May (the first day whenparticipants use the card) to the subsequent week. The first post-treatment week is therefore comprised of eight days; thisfeature does not create any challenge for the estimation of MPCs as we use week fixed effects, as described below.

810% negative interest rate by decreasing the remaining balance on the account (i) by 30 euros if theremaining euro balance is in the interval (200, 300], (ii) by 20 euros if the remaining euro balance is in
the interval [100, 200], and (iii) by 10 euro if the remaining balance is below 100 euros. If the remainingbalance is below 10 euros, the entire remaining balance is deducted. The card and account remain active
until the balance has reached zero. The deduction rule that we apply has the advantage of being quite
similar to a weekly negative rate of 10 percent, while still remaining easy to explain and understand.
Orthogonal to the treatment group status, half of the all treated participants (stratified across treatment groups) were additionally treated with a framing treatment, where they were encouraged to spend
the money quickly, on local goods or services, and “on items they would not have purchased otherwise, sothat the overall increase of [their] spending and its impact on the French economy is maximized” (transl.,
for the original see Appendix C.1).
Dividing the recipient households into these three treatment arms allows us to estimate the extent towhich transfer design choices might shift the MPC out of one-time transitory transfers. In particular, we
can learn about the role of negative interest rates with the cards in group 3 (close to 10% a week) andgroup 2 (as the expiry amounts to a 100% negative rate). While our experiment directly estimates theimpact of transfer design choices on the MPC, it is not meant to capture how households would consume
in a setting where they face a negative interest rate on their main bank account.
Timeline.

Our experiment took place between May and October 2022. On Wednesday April 27th thecards (which from now on we will call “treatment cards” or “prepaid cards” to distinguish them fromthe households’ other means of payment) and accompanying instructions and explanations (see Appendix
C.1), as well as pin codes are sent by post to the residential addresses of the selected individuals,13 withexpected arrival on or around Monday May 2nd. In the meantime, the bank advisers of the treatmentgroup individuals contact their clients by phone as well as through a banking app, explaining that they
have been selected to participate in an academic study, and explaining the terms of the cards according
to the treatment arm. Participants are informed that they can opt out from the study (in which casethey would be unable to use the money they are set to receive), although nobody expressed a desire
to do so. The fact that the bank advisors contacted the clients helps alleviate potential concern about
participants’ mistrust. Another letter with instructions, serving as a reminder, is sent to all participantson Wednesday, May 11.
On Monday May 9, Treatment Group 3 participants experience the first weekly deduction, for any
remaining balance. The second deduction for this group occurs on Monday May 16th, and so on every
week from then onward. For Treatment Group 2 participants, the card expires on Tuesday May 24th.
An online survey is sent to all participants in the middle of June, which we use to better understand thespending behavior of the participants. Finally, Treatment Group 1 cards expire on October 3rd, and theremaining balances are transferred to the participants’ main bank accounts.
Take-up.

Participants started using the card from May 2nd onward. Among the 915 treated households,

830 used the treatment card at least once before 6 October. 85 participants chose not to use the card,
possibly for economic reasons (e.g., Group 1 participants can save by not using the card and getting
13

The pin codes for the treatment cards are set by the bank to be the same as each participant’s main debit card.

9the remaining balance transferred to their account) or for operational reasons (e.g., in Group 2 someparticipants may have missed the deadline). We do not exclude these households from the sample inour main results, but investigate in robustness checks how MPC estimates change when conditioning on
take-up.14 The fact that participants receive a reminder and are informed about the remaining balancethrough their phone app reduces the likelihood that they forget that they have available funds on thetreatment card.
Randomization tests.

We implement statistical tests to assess the validity of the randomization pro-

tocol. Since the randomization was done at the level of the individual, but spending is observed at thelevel of the household, households with multiple eligible members will be over-represented in the treatment. We therefore conduct all our analysis within bins of households that have the same number of
eligible members E (which we will refer to as “household size”), always comparing households with one
treated member (we do not have households with multiple treated individuals) to households of the same
size with no treated individuals. For the sake of brevity, we will refer to households with one treatedindividual as “treated households”, and those without as “control households”.
Appendix Figure D1 shows the results of randomization tests, where we regress a treatment dummy ona set of standardized household characteristics and a set of dummies for the number of eligible individuals
within the household. The coefficients on the household characteristics are all small and not statisticallysignificant, indicating that the means of these characteristics are similar across treated and untreatedhouseholds (within bins for the number of eligible individuals). These result confirm the validity of theexperimental design.

3

Main MPC Estimates: Facts #1, #2 & #3

In this section, we report our main MPC estimates. We first consider all treatment cards at once (Subsection 3.1). We then report estimates by card types (Subsection 3.2), establishing our first three key
facts about MPCs in this subsection. We also describe the participants’ spending behavior by analyzing
the composition of expenditure as well as auxiliary survey data (Subsection 3.3). Finally, we report MPC
estimates by framing group (Subsection 3.4).

3.1

Pooled MPC Estimates

We first present MPC estimates for all treatment cards, first presenting evidence from the raw data andthen turning to a regression framework.
3.1.1

MPC Estimates from Raw Data

Panels A and B of Figure 1 presents the MPC estimates from raw data. Panel A first documents thetiming of purchases that treated households make using the treatment card alone. The figure shows that
average spending increases rapidly and reaches about 250 euros after two months, i.e. participants spend
14

Two participants filed a complaint stating that they did not receive a working card in time (they were issued a replacement
several weeks later); we exclude them from the analysis.

1084% of the transfer within two months. However, this direct spending response may be offset by reduced
spending in the households’ main bank accounts.
To assess the magnitude of potential substitution effects, we plot the level of spending in each week inthe treatment and control groups. Given that treatment was assigned at the level of eligible individuals,
we implement one adjustment to the raw data, reweighing participants by the propensity score, i.e. sothat the number of eligible individuals within households is the same across the control and treatmentgroups. Panel B of Figure 1 shows clear graphical evidence that treated households spend more uponreceipt of the transfer, but the extra spending is short-lived, lasting about three to four weeks. A monthafter the start of the experiment, there is no evidence for any difference in spending patterns between
treated and control households. Thus, the response is concentrated in the very short run, with little
intertemporal substitution. This panel also shows that spending displays significant seasonality, which
the control group allows us to address along with any other time variation in consumption.
Next, we move to a regression framework to provide more precise estimates of MPCs.
3.1.2

MPC Estimates from Regression Specification

Specification.

Our baseline econometric specification to estimate consumption responses is a standard

two-way fixed effect linear model:

Yit =

T̃
X

βτ 1(τ weeks since i treated)it + αi + αtE + εit

(1)

τ =0

where Yit is the outcome variable, usually consumption spending of household i in week t, the dummy1(τ weeks since i treated)it is one if and only if i contains a treated individual and week t is τ weeks after
the first treatment week (the week of May 2), αi are household fixed effects, and αtE are fixed effects
for “week by number of eligible individuals within the household.” Given that treatment is assigned at
random across eligible individuals, we only need to control for αtE to achieve identification,15 but we also
include household fixed effects to reduce noise. Standard errors are clustered at the household level.
Given that a control group of untreated households is available, our two-way specification is not
subject to the “negative weights” issue analyzed in recent work on difference-in-differences design (e.g.,
De Chaisemartin and Haultfoeuille, 2020, Borusyak et al., 2023).
Results.

The results are reported in Panels C.i and C.ii of 1. Panel C.i report the estimates for theβτ coefficients at a weekly frequency after treatment. The panel shows that, on average, participants’spending increases by 75 euros in the first week, 25 euros in the second week, and 20 euros in the third
week. The estimates are close to zero in the following weeks, indicating that the spending burst isconcentrated in the short run.16
Panel C.ii shows the point estimates and standard errors of the cumulative sum since the start oftreatment. The point estimate for the cumulative average effect after four weeks is 113 euros, corresponding to a marginal propensity to consume of 113/300 = 38 percent. As in other papers that compare15

In practice, the estimates remain similar when we do not include this control.
Consumption appears to fall in the first week of June, raising the possibility of intertemporal substitution. We discuss
cumulative MPC estimates below, finding little evidence of intertemporal substitution with our preferred FGLS estimates.
16

11

Figure 1 Pooled MPC Estimates
A. Cumulative Spending on Prepaid Card
Cumulative spending on prepaid card, in %

100%

75%

50%

25%

0%
May

Jun

Jul
Statusall

B. Average Total Spending in the Raw Data, Weekly
550

Control
Treated

Weekly expenditure, in euros

525
500
475
450
425
400
375
350
January

February

March

April

May

June

July

AugustC. Pooled MPCs
C.ii. Cumulative MPC since treatment onset

C.i. Weekly MPC
30%

40%

Cumulative MPC, in %Weekly MPC, in %

20%

10%

0%

20%

0%

−10%
−20%
May

Jun

Jul
Status

May

all

Jun

Jul
Statusall

Notes: Panels A and B report the treatment effects in the raw data, plotting cumulative spending on the prepaid
card in panel A for treated households, and average weekly spending for control and treated households in panel
B. The 95% confidence intervals for mean weekly spending are reported as shaded regions in panel B. Panel C
reports the regression-based MPC estimates. Panel C.i reports the weekly estimates, while panel C.ii depicts the
cumulative effects. 95% confidence intervals are reported, clustering the data at the household level.

12

recipients of transfers with non-recipients to estimate MPCs, estimates over longer horizons are becoming
increasingly less precise, as the variance of cumulative consumption increases for both treatment andcontrol groups over time due to the presence of idiosyncratic shocks. We find that the decrease in point
estimates over longer horizons in Panel C.ii of Figure 1 results from a small number of positive outliers
in weekly pre-period consumption expenditures, which push up the household fixed effects and makesubsequent expenditures appear small in comparison. Appendix Figure D2 shows FGLS estimates that
downweigh household groups with higher pre-period consumption volatility, and these estimates are flatover the corresponding horizon.
To investigate the dynamics of the cumulative MPC over longer horizons, we estimate a specification
analogous to (1), except that to increase parsimony we use a seventh-order polynomial to model the weekly
MPC response after treatment. Figure 2 plots the results over two quarters, showing that the cumulative
MPC increases very fast in the first few weeks and remains stable from the first month onward. The point
estimates are statistically significant at the 95% level for the first five months. If spending increased at thesame rate as during the first three weeks, the cumulative MPC would reach 300 euros around mid-June,
which we reject in Figure 2. This analysis thus confirms that the increase in spending is concentrated in
the short run.17
Figure 2 Long-term MPC estimates

500

Cumulative MPC, in euros

400

300

200

100

0

−100

−200
May

Jun

Jul

Aug

Sep

Confidence interval:

Oct

95%

Nov

Dec

Jan

Feb

68%

Notes: In this figure, we run a specification analogous to (1), except that to reduce noise we use a seventh-order
P8
polynomial to model the weekly MPC response after treatment: Yit = k=1 βτk−1 · τitk−1 + αi + αtE + εit . We stillview this specification as non-parametric estimation of the MPC, given the flexibility of the 7th-order polynomial.
To reduce noise further, we use the same feasible generalized least square (FGLS) procedure as in Figure D2. The
figure reports the cumulative MPC and both the 95% and 68% confidence intervals, clustered at the household
level.

Finally, it is worth noting that we of course lack the statistical power to detect long-term changes
in consumption of a few euros per month. For instance, a permanent income consumer would consume
17

Accordingly, in much of the analysis that follows, we choose the 1-month MPC as our main focus.

13the annuity value of the 300 euro transfer: with a 2% interest rate, this corresponds to an increase in
consumption of about 6 euros per year, or 0.50 cents per month, which we cannot detect in the data.
Our empirical results are therefore not inconsistent with theoretical reasoning based on an intertemporalbudget constraint and a transversality condition implying a long-term MPC of one.
Additional robustness results are reported in Online Appendix E.1, analyzing observed savings at thebank, alternative specifications, take-up, alternative consumption measures, reweighting, winsorization,and showing bootstrapped confidence intervals.

3.2

MPC Estimates By Card Type

Next, we analyze MPC by card type and establish the key result of the paper: the marginal propensity
to consume is larger when treatment cards have negative interest rates.
The estimates are reported in Figure 3 separately for the three treatment groups. Panel A shows
estimates of the βτ for households in Group 1, with no restrictions. Card 1 leads household to increase
their weekly consumption spending in the two weeks after treatment by about 40 euros; the point estimates
thereafter are close to zero and not significant. Panel B shows that households in Group 2—who receive
a card that expires after three weeks—increase their weekly consumption significantly for the first three
weeks after treatment, by about 65 euros in the first week, and by about 50 euros in the second andthird weeks. There is no sign of intertemporal substitution, as estimates hover around zero after the third
week. Finally, panel C shows the response for households in Group 3 – with the negative interest rates–, who increase their spending immediately in the first week of the experiment, by about 130 euros, but
not thereafter.18
Panels A and B of Figure 4 reports the cumulative spending response. The figure shows that the
cumulative MPC for group 1 is much lower than for groups 2 and 3. After 4 weeks, the cumulative MPC
for group 1 is 70 euros (23%), compared with 183 euros (61%) for group 2 and 106 euros (35%) for group
3. Panel B of Figure 4 shows MPC estimates conditional on using the card (at some point in the entire
sample) to make purchases. The point estimate for the average 4-week MPC of group 2 participants isabout 10 percentage points higher, at 70%. In both figures the consumption response to the stimulustransfer is substantially higher for group 2 compared to group 1, indicating that stimulus design choices
can affect the MPC.
Since the confidence intervals in Panels A and B of Figure 4 overlap, it is important to assess formallywhether there is a statistically significant difference by card type. Focusing on the cumulative MPC after
four weeks, Panels C and D report a significant difference between Card 2 and Card 1, which we view as
the key result of this paper. Both conventional t-tests and exact randomization tests show a significant
difference at the 5% confidence level. Appendix Figure D3 report the results for Cards 1 and 3, for which
we do not find statistically significant differences after four weeks. Note however, that heterogeneity inthe iMPCs is present: an F -test of the hypothesis of same path of MPC across all treatment groups for
18
The time pattern for this group suggest that most households understood correctly the terms of the card, as they
tried to spend it down before the date of the first negative interest rate. The terms were explained in simple language in
the instruction letter, including simple examples and explicitly stating that if the household spent the full amount of 300
EUR before the date of first deduction, no money would be lost. We cannot however know for certain that all households
understood the terms correctly, especially among those who did not spend down the card.

14

Figure 3 MPC by Card Type, Weekly

Weekly consumption spending, in euros

A. Group 1, no restrictions on treatment card

40

0

−40

May

Jun

Jul

StatusCard 1

B. Group 2, expiration after three weeks
Weekly consumption spending, in euros

100

50

0

−50
May

Jun

Jul

StatusCard 2
Dashed line: Card 2 expired dateWeekly consumption spending, in euros

C. Group 3, negative rates every week

100

0

May

Jun

Jul

StatusCard 3
Dashed line: 1st week negative interest rate

Notes: This figure reports MPC estimates depending on the card type. Panel A reports the weekly estimates forGroup 1, panel B for Group 2, and panel C for Group 3. Card 1 has no restrictions, while Card 2 expires three
weeks after the onset of the experiment, and Card 3 applies a negative interest rate on the remaining balance every
Monday at 11:59pm. 95% confidence intervals are reported, clustering the standard errors at the household level.

15Figure 4 MPC Estimates by Treatment GroupA. Unconditional estimates

B. Conditional on take-up
100%

75%

Cumulative MPC, in %Cumulative MPC, in %

75%

50%

25%

50%

25%

0%

0%
09−May16−MayCard Type

123−May209−May316−MayCard Type

C. 4-week MPC Difference
between Cards 2 and 1: t-test

1

23−May2

3

D. 4-week MPC Difference
between Cards 2 and 1: Fisher exact test

75%

Observed MPC Difference

2.0

Two sided p−value: 4.3%
1.5

50%

38.1%
Density

Cumulative 4−Week MPC Difference

100%

1.0

25%
0.5

0%
0.0
−30%

0%

30%

60%

4−Week Cumulative MPC Difference

Notes: Panels A and B of this figure reports cumulative MPC estimates depending on the card type. Card 1 has
no restrictions, while Card 2 expires three weeks after the onset of the experiment, and Card 3 applies a negativeinterest rate on the remaining balance every Monday at 11:59pm. Panel A includes treated households that do not
use the card in the treatment groups; panel B does not. 95% confidence intervals are reported, clustering the dataat the household level. Panels C and D report statistical tests to estimate the difference in cumulative MPCs after
four weeks for Cards 1 and 2. We estimate specification (1) with OLS and compare the sum of the coefficients forthe first four weeks for Cards 1 and 2. Panel C reports the point estimate and 95% confidence interval, while Panel
D reports the result obtained with randomization statistical inference (Fisher’s exact test). The distribution shownin Panel D is the distribution of estimated MPC differences where placebo treated households are drawn from the
population of untreated households.

16the first twelve weeks is rejected with a p-value of 2.5%. 19
Appendix Table D3 reports the differences in cumulative MPCs by card type after four, eight andtwelve weeks, using both OLS and FGLS. Comparing Card 2 and Card 1, we find that the differencein point estimates grows larger after two and three months but is no longer statistically significant atconventional levels, with p-values around 0.11-0.15. Furthermore, we do not find statistically significant
differences between Cards 1 and 3 or Cards 2 and 3 at any horizon, although the difference in point
estimates grows larger with time. Thus, an important direction for future research would be to scale up
sample sizes to more precisely estimate differences by card types, especially at long horizons.
Additional results are reported in Online Appendix E.2, analyzing long-term MPC dynamics, spendingon the prepaid card, predictors of take-up or lost funds, and showing bootstrapped confidence intervals.
Taking stock.

We can now summarize our first three key facts, about the magnitude of the MPC bycard type – including our main result, Fact 2 – and its time profile:Fact 1: The average one-month MPC on a cash-like transfer is 23%.
Fact 2: The design of the stimulus transfer can substantially affect the MPC: the average one-month
MPC out of a prepaid card whose remaining balance expires after three weeks is 61%.
Fact 3: The increase in consumption is much larger early on, in the first two to three weeks.

3.3

Understanding the Spending Response

To better understand the participants’ spending behaviors, we combine two approaches: survey questions
to the treatment group,20 and an analysis of the spending categories for treatment cards and linked bankaccounts. We first analyze the patterns for all cards, and then study the three types of cards in turn.
All cards. The results for all cards are presented in Figure 5. Our analysis delivers three takeaways.
First, survey responses show that participants are well aware that they spend less on their main accountand use the treatment card to substitute for regular spending. They mention precautionary savings as
key motive for the money they saved out of the transfer (panel A of Figure 5), and they report that they
use the treatment card primarily to cover running expenses (panel B).
Second, we use the treatment card and the bank data to analyze the composition of expenditures. For
each transaction, our data contains the 4-digit merchant category code (MCC) that is associated withthe vendor. Panel C of Figure 5 shows that treated households spend more on clothing and household
equipment (furniture, consumer electronics, etc.). Panel D breaks down the purchases on the treatment
cards by category, confirming the importance of spending on clothing and electronics.
Next, we examine whether there are significant differences in terms of spending on durables.21 Extending the product classification from Ganong and Noel (2019), we classify MCC codes into one of
19

There is a statistically significant difference between Card 1 and Card 2 despite the overlap in the 95% confidence
interval in Figure 4 because of the covariance between estimators. Specifically, estimating equation (1) by OLS, we findthat the correlation between the cumulative 4-week MPCs of Card 2 and Card 1 is 0.62. Intuitively, given the skewness of
consumption expenditures, large purchases in the control group during the treatment period can have a sizable impact on
the point estimates for all treatment cards.
20
The survey was administered via the implementation partner’s web platform. The survey response rate is 46%..
21
Of course, at a high frequency (e.g., weekly) it is difficult to draw distinctions between durables and nondurables – to acertain extent, all products can be viewed as durables.

17

Figure 5 Understanding Participants’ Spending Behavior, All Groups
A. How will you use the money you saved?

B. What did you buy with the treatment card?
0.5

0.5

0.4
0.4

0.3
Fraction

Fraction

0.3

0.2

0.2

0.1

0.1

0.0

0.0

Answers

Save for a rainy day

Save to buy something expensive

Investment

Other

Pay off debt

Answers

C. Total spending share by broad category, all cards

Running expenses

Small treat

Gifts

Other

Made larger expenditure earlier

D. Spending shares on the treatment card

Transport
TobaccoTransport

Recreation, culture

TobaccoMiscellaneous
Recreation, culture

Housing, energy

Miscellaneous

Hotels

Housing, energy

HealthHotelsHousehold Equipment

HealthFood away from home

Household equipment

Food at home

Food away from home
Food at home

Education

Education

Communications

Communications

Clothing
Clothing

Alcohol

Alcohol

05Status10
Percentage

15

TreatedControl

20

0Expenditure-weighted import content, in %Spending share on durables, in %

9.5

10
9
8
7
6
5
March

April

Date

May

30

June

July

Treated

F. Spending share on imported products
Control
Treated11

February

20
Percentage

StatusE. Spending share on durables

January

10

AugustControl
Treated

9.0
8.5
8.0
7.5
7.0
6.5
6.0
January

February

March

April

Date

May

June

July

AugustNotes: Panels A and B of this figure report the answers of participants to survey questions. The other panels use
the bank data to document the expenditure patterns of the treatment and control groups across product categories.
Panel C shows expenditure shares in the total expenditure basket, panel D shows expenditure shares using thetreatment cards only. Panel E shows the weekly average expenditure share on durables (as defined in the PCEclassification) for treatment and control groups; panel F shows the import content of households’ expenditurebaskets. The import content for each household’s consumption basket is the expenditure-weighted industry-level
import content. The industry-level import content has been constructed using INSEE’s input-output tables forFrance.

18

four spending categories used by the French National Statistical Institute (INSEE): nondurables (including food and drink, fuel, and items that depreciate quickly), semi-durables (including, notably, apparel,
footwear, and other textiles), durables (furniture, electronics, and durable household equipment, as wellas leisure items and cars), and services. Appendix Table D4 provides examples of products belonging toeach of these categories. We also build a crosswalk to the French input-output table to assess the importcontent of households’ consumption baskets. We find that the spending share on durables increases to 10
percent upon treatment, relative to about 7 percent in the control group, as reported in panel E of Figure
5. Appendix Figure D4 reports the cumulative MPC response separately for durables and nondurables,
showing a more sustained increase in spending on nondurables over time.
Finally, we analyze the propensity to spend on imports. We measure imports by mapping the MCC
codes to the French input-output tables, which provide import penetration rates across categories. We
find that treated households make purchases that have on average a higher import content, resulting in
an increase in the weighted average import share from 7% in the control group to 9% in the treatmentgroup (panel F). While these differences are statistically significant, they are modest from an economic
perspective.
By card type. We repeat the analysis by card type in Appendix Figure D5. We first rely on thesurvey results and find that households in Groups 2 and 3 report that they are less likely to cover running
expenses and more likely to make large purchases earlier, consistent with the higher MPC estimates inthe data.
Second, we decompose the consumption expenditure increase by durability. Table II shows the estimated fraction of the expenditure increase on each of the four durability categories by dividing the
4-week cumulative point estimate of a regression of consumption expenditure in the row category ontime-since-treatment dummies (and fixed effects as in the baseline specification) by the corresponding
4-week cumulative point estimate in a regression of all consumption expenditures (the baseline specification).
The results show that households that receive treatment Card 2 channel a substantial fraction of theadditional expenditure into personal services, whereas Card 3 households see a disproportionate increasein durables purchases. Comparing the three types of prepaid cards, Table II shows that the short-run
spending response is not driven by spending on durables, as Card 3 alone features a substantial increaseon this category. Additional results on the composition of spending by card type are reportd in Appendix
E.2, analyzing the response of durables over a longer horizon and using an alternative classification of
products into durables and nondurables.

19

Table II Decomposition of 4-week MPC and Expenditure Shares by Type of Expenditure

Nondurables
Semi-durables
DurablesServices
Not categorized

Decomposition of 4-week MPC

Expenditure shares over 4 weeks

Card 1(1)

Card 2(2)

Card 3(3)

Treatment group(4)

Control group
(5)

18.8%
49.0%
24.1%
13.6%
-5.6%

9.2%
30.9%
19.1%
54.2%
-13.5%

26.6%
28.6%
49.8%
11.6%
-16.9%

29.5%
19.8%
9.6%
36.6%
4.5%

30.5%
17.9%
7.8%
38.9%
4.7%

Notes: This table reports the average 4-week MPC on the row category divided by the total 4-week MPC (anyconsumption expenditure), for treatment groups 1, 2, and 3. Columns (4) and (5) report expenditure shares for thetreatment and control groups over the 4 weeks following treatment. The last row refers to expenditures that cannot
be classified into the four main product categories, for example cash. Columns do not sum up exactly to 100%
because of rounding. When computing the estimates for this table, we do not winsorize consumption expenditures
so that we can decompose the total consumption response across product categories.

A potential concern is that the higher overall spending response with Cards 2 and 3 might come at theexpense of the “quality” of spending. For example, a recent study by Jaroszewicz et al. (2022) finds that
unconditional cash transfer taking place during Covid-19 sometimes had detrimental effects on recipients’
self-reported measures of well-being in a sample of about 5,200 US households living in poverty. Other
papers have documented that consumption opportunities may lead to a “consumption binge”, with thepotential to reduce welfare in the long run (Garber et al., 2022). We study survey and spending outcomesto understand whether our transfers could have caused harm to some participants.
We first examine whether the spending share on goods that can be deemed to have “negative externalities” (drinking, tobacco, better, and lottery products) differs across treatment arm. Appendix Figure
D5 shows that there is no significant difference across treatment groups. Second, we analyze whether
participants of Groups 2 and 3 experience a fall in nondurable consumption, or higher volatility, which
could be caused by an initial “consumption binge”. We reject this hypothesis: participants in Groups 2
and 3 spend more on nondurables in the short run, and experience no fall in the longer-run (see AppendixE.2). Finally, we use the survey to elicit the subjective impact of the transfer. In response to the question:“Has the transfer of the 300 euro card increased your happiness?”, only eight out of 391 respondents (or2%) report that the transfer has not at all increased their happiness. 92% of respondents respond thatthe transfer has either “very strongly” or “somewhat” increased their happiness. We therefore conclude
that it is very unlikely that our implementation design choices have caused harm, while they led to a large
increase in MPCs.

3.4

MPC Estimates By Framing Group and Experimenter Demand Effects

Finally, we evaluate whether households have different average MPCs depending on the framing of theintervention. This framing treatment may be of susbtantive interest insofar as policymakers can framehousehold transfers through public discourse or in official letters to households. The results are also
informative about experimenter demand effects, or Hawthorne effects. Indeed, a potential concern about
20

our experiment is that some households may feel compelled to act according to what they perceive tobe the goal of the experiment. However, our framing treatment makes it possible to assess whether
Hawthorne effects are likely to drive our results, since only the participant in the framing group are
explicitly told that they are expected to spend fast and increase their total spending, instead of coveringrunning expenses.22
We find that households that received the additional framing treatment, with a paragraph encouraging
them to spend the money quickly on local goods or services, have very similar average consumption
expenditures overall (difference in MPC < 10pp, and not statistically significant) as households that did
not receive the framing treatment (Appendix Figure D6). We also examine whether the compositionof expenditures varies across groups, finding no difference. For example, spending on imports is similar
across the two framing groups (Appendix Figure D7).
Thus, we conclude that implementation design choices are powerful tools to increase the MPC, while
written framing treatments are unlikely to have large effects. These results also show that Hawthorne
effects are unlikely to drive our results.

4

MPC Heterogeneity across Households: Facts #4 & #5

We now turn to the analysis of MPC heterogeneity across households. Estimating MPC heterogeneity is
key both for policy – as policymakers may wish to target certain households to maximize the aggregate
MPC – and for macroeconomics models – as MPC heterogeneity is a useful moment to assess the accuracyof the predictions and potential falsify certain models. We first document MPC heterogeneity by observable household characteristics (Subsection 4.1), establishing our fourth key fact about MPCs. Finally,
we present estimates of the unconditional distribution of MPC across households with a deconvolution
approach (Subsection 4.2), our fifth key fact about MPCs. We discuss the implications of our findings in
Section 5.

4.1

Heterogeneity By Observable Household Characteristics

To examine the importance of various observable household characteristics in predicting treatment effectheterogeneity, we first use a simple OLS specification, and then turn to a machine learning (LASSO)
analysis.
22

See the translation of the letter in Appendix C.1. All participants are told that: “The objective of this initiative is to
study, within the framework of a policy aimed at promoting economic recovery, people’s spending behaviors when a sum ofmoney is distributed to them for free.” Participants in the framing group are also told the following: “Although you are free
to use the amount of 300 euros as you wish, we invite you to: spend the money as quickly as possible; buy products madein France and services that support local employment, as the objective of this transfer is to stimulate the French economy
by encouraging the consumption of products made in France; purchase products or services that you wouldn’t normally buy(other than your regular expenses) to increase your total spending and thereby contribute to the economic recovery, rather
than covering expenses that were already planned.”

21

OLS analysis.

We first estimate differences in the marginal propensity to consume for households withdifferent characteristics. Specifically, we estimate specifications of the form:

Yit =

4 X
T̃
X

+ εit
βτq 1(τ weeks since i treated)it 1(Xi ∈ QXq )i + αi + αtEQXq(2)

q=1 τ =0X
where QX
1 to Q4 are the quartiles of the distribution of the time-invariant household characteristic X.

We consider six characteristics: net liquid wealth, net illiquid wealth, average pre-treatment consumption (as a proxy for permanent income), income, age, and gender. The first four variables are motivatedby macroeconomic models, which make predictions about heterogeneity in the MPC by net wealth (e.g.,
Kaplan and Violante, 2014) and by current or permanent income (e.g., Straub, 2019); we further discuss
the relationship between our findings and these models in Section 5. In addition, we consider age andgender, as these characteristics are easily observed and could in principle be used to target transfers
toward certain populations.
The variables are built as follows. Net liquid wealth correspond to the sum of household-level current
account and liquid saving deposits net of short-term debt (for instance consumer debt) at the bank. We
measure this variable at the onset of the experiment, on the first day of May, to capture the liquid funds
actually available to households. Net illiquid wealth captures the sum of illiquid savings, asset level andmortgage debt for the household at the bank level. Average pre-treatment consumption is measured as
the average monthly consumption expenditure in the year prior to treatment, at the household level.
Lastly, we define income at the household level as the sum of all incoming transfers.23 Except for net
liquid wealth, which is measured at the beginning of the experiment, and average pre-period consumption,
which is computed as an average over a year, these variables are averages over the monthly levels in thesix months prior to the experiment. Regarding age and gender, the characteristics pertain to the eligible
household member.24
Figure 6 reports the results, plotting cumulative MPCs across household groups. We first consider
the role of liquid and illiquid wealth, in Panels A and B. Panel A shows that MPCs fall with the level ofnet liquid wealth. Although the standard errors are sizable, there appears to be a negative relationshipbetween the level of liquid wealth and the MPC. We obtain similar results when liquid wealth is measured
as an average over six months prior to the experiment, rather than at the beginning of the experiment.
Panel B turns to illiquid wealth, depicting a negative relationship between MPCs and illiquid wealth quartiles. Despite these negative relationships, Appendix Figure D8 shows that the MPC remains high evenfor households who have substantial liquid wealth, a fact we will use later on when drawing implicationsof our findings for consumption models. Figure D8 also shows that the results are similar when using
current account funds alone as the measure of liquid wealth.
Next, we turn to income, in Panels C and D. We first consider our proxy for permanent income,average consumption prior to the experiment. Panel C shows that MPCs tend to be lower for householdswith higher levels of consumption prior to the experiment. Similarly, Panel D reports that MPCs fallwith household income.
23

Inflows above 15 000 euros are trimmed out at the household level.
When there are multiple eligible household members in the control group, we pick one of the eligible members at random
and use their characteristics. For treated households, age and gender are taken from the selected individual.
24

22

Finally, Panels E and F consider in turn age and gender. Panel E shows that older households appear
to have larger MPCs. Turning to gender, Panel F show that women have a much lower MPC than men.
After a month, the cumulative MPC is close to 50% for men and only about half as large for women.
In sum, income and gender constitute the strongest sources of observable MPC heterogeneity among
the predictors we consider. Appendix E.3 reports additional results on liquidity and gender, FGLS
specifications, and the statistical precision of the estimates.
LASSO analysis.

We now turn to a set of regressions that attempts to uncover which household

characteristics are most relevant for explaining MPC heterogeneity after four weeks. We implement
specification (2) with all six variables (divided into quartiles when relevant) included jointly, as well assome additional variables (unemployment, local area characteristics, household size). In order to avoid
over-fitting, we estimate the coefficients using a LASSO estimator, for varying levels of the regularization
parameter. Although these results do not isolate causal links, they reveal which variables are the mostimportant predictors of MPC heterogeneity.
Figure 7 shows the results of our estimates on the entire sample of treatment and control group
participants. We find that the most important variables to predict treatment effect heterogeneity are
demographic characteristics – specifically, gender, high-age dummies, household size, and the location
characteristic (urban vs. rural; the omitted category is semi-urban) – as well as the dummy that captures
the top quartile of average past consumption (our proxy for permanent income), and the third quartileof liquid wealth. Conditional on these variables, others characteristics contribute little to predicting
treatment effect heterogeneity. Perhaps surprisingly, income and wealth (whether liquid or illiquid) havelittle predictive power to explaining MPC heterogeneity. The results also clearly show how the variables
that capture variation in the treatment design – the treatment group dummies – stand out in explaining
treatment effect heterogeneity.
Appendix E.3 reports complementary results, repeating the LASSO analysis with treatment group 1
alone as well as at a longer horizon.
While leading macroeconomic model highlight the role of liquid and illiquid wealth as key predictorsof treatment effect heterogeneity, our LASSO analysis show that other predictors are more powerful. We
further discuss the implications of these results for household targeting in Section 5.2.
Takeaways.

The OLS and LASSO results together establish our fourth key fact:

Fact 4: MPCs varywith observed household characteristics, notably by gender and proxies for permanent income, and are high even for the liquid-wealthy.

4.2

Unconditional Distributions of MPCs

We now proceed to estimating the unconditional distributions of MPCs across households, regardless ofobservable household characteristics. In an experimental setting like ours, the entire distribution of theoutcome variable is different from that of the control group only because of the treatment effect. Whenthe treatment effect is independent from the error term, we can therefore recover the full distribution of
the treatment effect using statistical deconvolution techniques.

23

Figure 6 MPC Heterogeneity by Observable Household Characteristics
A. By Net Liquid Assets Quartile

B. By Illiquid Wealth Quartile
75%

50%

50%

Cumulative MPC, in %Cumulative MPC, in %

75%

25%

25%

0%
0%

−25%
09−May16−MayNet liquid wealth quartile last month1223−May09−May3

Average illiquid wealth quartiles

4

C. By Average Consumption Quartile

16−May23−May1

2

3

4

D. By Income Quartile
80%

60%

Cumulative MPC, in %Cumulative MPC, in %

60%

30%

40%

20%

0%

0%

−30%
09−May16−MayConsumption Level Quartiles

23−May12309−May416−MayRevenue Quartiles

E. By Age Quartile

1

23−May2

3

4

F. By Gender

80%

60%

Cumulative MPC, in %Cumulative MPC, in %

60%

40%

20%

40%

20%

0%
0%
09−May16−MayAge Quartile1

2

23−May309−May416−MayGenderF

23−MayM

Notes: This figure reports MPC estimates depending on observable household characteristics. We document heterogeneity in turn by net liquid wealth, illiquid wealth, average consumption prior to the experiment (as a proxyfor permanent income), income, age, and gender. 95% confidence intervals, with standard errors clustered at thehousehold level, are reported in all panels.

24

Figure 7 LASSO Estimates of 4-Week MPC Heterogeneity

Notes: The figure shows LASSO estimates of coefficients of interactions of the respective characteristic with atreatment dummy in specification (2), for varying regularization parameters (horizontal axis). We predict the
cumulative MPC after four weeks. The dashed vertical line shows the regularization parameter chosen by 5-foldcross validation.

Setting, identification, and estimation.

Yit =

T̃
X

We consider the modelβτ 1(τ weeks since i treated)it + αi + αtE + εitτ =0where now, in contrast to the previously studied model, we assume that the βτ are stochastic, withβτ ∼ Fτ . We further assume that the βτ are independent from εit ; we discuss and test this key assumption
at the end of this section. As before, the treatment dummies are independent from the errors εit , as wellP
as from the βτ , due to the experimental design. We seek to recover the distribution of T̃τ =0 βτ , whichcorrespond to the T̃ -period marginal propensities to consume. Under the assumptions stated above,the distributions Fτ and therefore the distribution of the T̃ -period marginal propensity to consume isidentified under no parametric assumption.
The model thus takes the same form as a classic measurement error model (see Schennach, 2016
for a survey), and the distribution of the βτ can be estimated using a deconvolution method: we firstestimate the distribution of εit from the population of untreated households, and we then deconvolvethat distribution from the distribution of the dependent variable of the treated at time of treatment.
Intuitively, apart from the fixed effects αi , αtE , the distribution of outcome variables for treated anduntreated households differ only because of the presence of the treatment effect terms βτ . Under theassumption that the βτ are independent from εit , we can recover the distribution Fτ . Note that theassumption that the treatment and control groups have identical distributions of error terms εit would
be difficult to defend in a non-experimental setting. To avoid confounding treatment effects with thepotentially different tails of households of different size, we conduct the exercises in this subsection on
25

households with one eligible member only.
We implement this approach in a two-step procedure. In the first step, we estimate αi and αtE fromthe set of observations (i, t) where either i is not in the treatment group, or i is in the treatment groupbut has not been treated yet, in the spirit of Borusyak et al. (2023).25 In the second step, we construct
cumulatives of de-meaned weekly consumption expenditure:
CitT̃ =T̃X

(Yit − α̂i − α̂tE ).

τ =0

We estimate the distributions ofPT̃τ =0 βτthrough deconvolution, constraining the distribution of theestimand to have only positive support. This constraint is motivated by the fact that we find no evidence
for a fall in consumption anywhere in the distribution, as shown in Appendix Figure D9, which reports
the quantile treatment effects, i.e. the differences in the quantiles of the distributions of CitT̃ for treatedand untreated households, over 4-week, 8-week, and 12-week horizons. The figure shows that the left tailof the distributions of cumulative de-meaned consumption is the same for treated and control, implyingthat the treatment effect distributions do not have mass on the negative part of the real line.26
We use the flexible quadratic-programming-based estimation procedure proposed by Yang et al. (2020),
which, compared to standard Fourier-based methods, has the advantage that it also allows the density
to be restricted to be non-negative on its support and to integrate to one, restrictions that we also
impose. Since deconvolution estimates often suffer from from oscillating densities in the tails, Yang et al.
(2020) recommend regularizing the density estimates through a penalty term. We follow this suggestionand penalize oscillations by adding a weighted finite-difference estimate of the second derivative of thedensity, with a small penalty weight (λ = 10−5 ). Since deconvolution estimators tend to be sensitive
to noise in the tails of outcome distributions, we winsorize weekly consumption expenditure at the 90th
percentile. We obtain standard errors for the estimated quantiles of the treatment effect distribution
through a bootstrap of the entire two-step procedure.
Results.

Figure 8 shows estimates for the distribution of 4-week MPCs by treatment group. The median

MPCs are close to but slightly higher than the ATE estimates we obtained in Section 3.2 for each card
type, at 28%, 81%, and 53% for groups 1, 2, and 3, respectively. The estimates show a substantial
heterogeneity in the propensity to consume out of the transfer, with the bottom quartile having a 4-week
MPC of less than 13% (card 1), 52% (card 2), and 30% (card 3), while the top quartile has MPCs above
48% (card 1), 103% (card 2), and 77% (card 3). The distribution of estimated treatment effects for group
2 first-order stochastically dominates the distribution of group 1.
These results establish our fifth key fact:
Fact 5: There is substantial heterogeneity in the unconditional marginal propensity to consume outof a windfall transfer, and a large fraction of households has a high MPC.
25

We first estimate household effects αi from all pre-treatment observations; then, conditional on these estimates, weestimate αtE from control group observations. We choose this sequential procedure to avoid asymmetries across treatment
and control groups in the precision of α̂i , i.e. we ensure that we have the same number of observations to estimate households
fixed effects in treatment and control groups.
26
We emphasize however that this nonnegativity constraint is not necessary to successfully apply the deconvolution procedure, and that our results are very similar when not applying this constraint, as discussed below.

26

Figure 8 Household-level Quantiles of the 4-week MPC Distribution
140%
119 %

120%
103 %

96 %

100%

MPC

81 %

77 %

80%

67 %

60%

53 %

52 %

48 %

40%
30 %

20%

19 %
13 %

28 %

13 %

4%

0%
0%

10%

25%

50%

75%

90%

100%

Quantile
Treatment group

Card 1

Card 2

Card 3
Bootstraps : 150

Notes: This figure reports the quantiles of the distribution of 4-week treatment effects by treatment group. Shaded
regions are delineated by the 10th and 90th percent quantile of the bootstrapped simulated distribution of thecorresponding moment.

Fact 5 relates to existing papers that estimate the distribution of MPCs. Misra and Surico (2014)
compare spending distributions of US households around the 2001 and 2008 tax rebates using quantile
regressions and data from the Consumer Expenditure Survey. In contrast to our results, they find thatsignificant shares of households experience negative treatment effects. The fact that the left tails of the
spending distributions of treated vs untreated households are very similar (Appendix Figure D9) is difficult to reconcile with negative MPCs in our data. Lewis et al. (2019) use clustering-based Gaussian
Mixture linear models to estimate MPC heterogeneity following the 2008 tax rebates. In their modelthe distribution of MPCs is parameterized to be discrete: MPCs are fixed but vary across groups; groupmemberships and MPCs for each group are identified through parametric assumptions on the error terms.
In contrast to their approach, our treatment effect distribution is identified and estimated entirely nonparametrically. Similarly to us, they find that MPCs are ranging from close to zero to above one hundred
percent, and that most of the variation in MPCs is unexplained by observed characteristics. Our results
do not, however, indicate the presence of discrete mass points in the distribution of unconditional MPCs.
We report additional results in Online Appendix E.4, analyzing a model linear in log-consumption,
dropping non-negativity constraints, pooling treatment cards 2 and 3, and estimating quantile treatment
effects.
Robustness.

The key assumption for identification of the treatment effect distribution is that theerror term is independent from the treatment effect distribution. We now assess the plausibility of this27

assumption with several robustness checks.
First, the independence assumption may be violated if, for example, certain subgroups of the population (say, poorer households) that have a higher average treatment effect also happen to have systematically different errors terms εit shortly after the experiment was conducted (for example, because ofcalendar events such as bank holidays, which are common in May in France, where poorer households may
increase spending less than others). While we can also not directly test the independence assumption,
since both the treatment effect and the error terms are unobserved, we can perform a falsification test.
We conduct an exercise where, in the first step of the estimation procedure, we project consumption on
household fixed effects and week fixed effects interacted with (a, i, c, l, g) fixed effects, where a, i, c, andl are age, income, consumption, and liquid assets quartile bins, and g is a gender dummy (instead of
projecting it on just household and week fixed effects). The resulting estimates of the treatment effectdistribution, shown in Appendix Figure D10, remain virtually unchanged. Therefore, for our results tobe biased, unobservable predictors of MPC heterogeneity should be much more strongly correlated withunobserved shocks εit than observable predictors. This sensitivity test, in the spirit of Altonji et al. (2005)
and Oster (2019), lends support to our baseline estimates.
Second, another possible scenario that would violate the assumption of independence of treatment
effect and error term is that some households may have more volatile consumption than others and may
also have a systematically different MPC. For example, during bank holidays the volatility of consumption
may be higher for high-income households, who may have lower MPCs. In order to investigate thispotential concern, we split households into two groups, depending on whether they are above or below themedian variance of weekly consumption expenditure, measured in the pre-treatment period. We performthe deconvolution exercise separately by treatment group on each of those samples. The estimates, shownin Appendix Figure D11, are very similar across high- and low-variance groups for each card, indicatingthat MPC distributions are unlikely to be very different for groups of households with different higher
moments of the error term.

5

Implications

We now discuss the implication of our five facts about MPCs, for both macroeconomic models and stimulus
policies.

5.1

Implications for Models

Our experiment is not designed to test any particular model of consumption, but to instead robustly
estimate moments of consumption responses to transfers that are scalable and therefore relevant forpolicy. Nonetheless, it is worth discussing which models of consumption can be reconciled with ourfindings.
5.1.1

Benchmark Rational Models

We first compare our findings with the predictions of canonical “rational” models. In the HeterogeneousAgent New Keynesian (HANK) model of Kaplan et al. (2018), high average MPCs arise because of
precautionary savings in the presence of borrowing constraints. In their baseline calibration, matching28

moments of the liquid and illiquid wealth distributions and income processes, the simulated consumption
response to a one-off lump-sum transfer is long-lived (see Figure 2 in Kaplan et al. (2018)): the estimated
MPC is about 17% over a quarter (for a $300 transfer), about 25% over two quarters, and 32% over one
year; furthermore, the high MPCs are driven by households with low levels of liquid wealth. The MPC islong-lived in the benchmark HANK model because agents (rationally) increase spending whenever they
hit their borrowing constraints, which happens gradually over time as some agents experience negative
idiosyncratic income shocks. Over the first two quarters, the increase in the aggregate cumulative MPC
is driven by constrained households, who deplete the rebate in full at this horizon. Afterwards, theaggregate MPC increases more slowly due to the population of unconstrained agents, who consume theannuity value of the transfer.27
Our findings stand in contrast with the predictions of the canonical implementation of the benchmark
HANK model in three ways. First, even in our treatment group 1 – the group that receives a transfer
that is most similar to a cash transfer –, the entire spending response we find is concentrated in thefirst two weeks after the transfer (panel A of Figure 3).28 In contrast, as previously mentioned the MPC
response is much more long-lived in HANK and in canonical buffer-stock saving models (Kaplan et al.,2018, Auclert et al., 2023b). While spending on durables could in principle explain a short-run spending
burst in a standard model (Laibson et al., 2022), we find that the response is also concentrated in the
short run for non-durables. We compare our MPC estimates to the standard calibration of the HANK
model more formally in Appendix Figure D12, documenting that the rate of decay of MPCs we estimate
is one order of magnitude higher than in HANK.
Second, in HANK the simulated MPC is strongly correlated with the level of liquid assets that agents
hold. While we do find some heterogeneity of MPCs for groups with different levels of liquid asset holdings,
we find that average MPCs are also high for households that have moderate or high levels of liquid asset
holdings (Figure 6). In Appendix Figure D8, we show that the MPC remains high even for households
that hold liquid wealth above twice their monthly income. These findings echo results from the literaturethat finds high MPCs even for agents with high liquid wealth, including Kueng (2018) in response to
anticipated payouts from the Alaska Permanent Fund, Olafsson and Pagel (2018) in response to regularand irregular income transfers in Iceland, Fagereng et al. (2021) among lottery winners in Norway, andBaugh et al. (2021) in response to expected tax refunds in the United States.29
Third, our estimates of the unconditional distributions of MPCs reveal that MPCs are high for a large
majority of the population (Figure 8). For Group 1 participants, our estimates indicate that half of the27

See Achdou et al. (2022) for a characterization of how cumulative MPCs vary with the time horizon in the Aiyagari–
Bewley–Huggett model.
28
Consistent with our experimental finding, Borusyak et al. (2023) document that the consumption response to tax rebates
is concentrated in the first two to three weeks after the tax rebate. Likewise, Baugh et al. (2021) find that households spend asignificant part of the tax refunds they receive on consumption in the month after receiving the refund. In contrast, analyzing
lottery winnings in Norway worth $9,200 on average, Fagereng et al. (2021) estimate a more long-lived MPC response: there
is a large consumption response in the first year followed by gradually declining MPCs over several years. This finding could
stem from the fact that the lottery winnings are on average larger than tax rebates or tax refunds. The size of the shockmatters for the dynamics of the consumption response: for example, Boutros (2023) studies a structural behavioral modelin which the planning horizon of the households depends endogenously on the amount of the transitory income shock, suchthat a larger shock is endogenously smoothed over a longer time horizon.
29
Stephens and Unayama (2011), Parker (2017), Ganong and Noel (2019), and McDowall (2020) also find that highly liquidhouseholds still have elevated MPCs. In contrast, studying the consumption response to typical month-to-month fluctuations
in labor income, Ganong et al. (2020) find an MPC close to zero for households with high liquid wealth.

29

population has a one-month MPC above 28%, and three quarters have an MPC above 13%. The fractionof households with a high MPC is thus higher than in benchmark HANK models.30
Furthermore, our finding that MPCs are higher for households with lower average past consumption(our proxy for permanent income) stands in contrast with standard macroeconomic models featuringhomothetic preferences, where the MPC is independent of permanent income. Straub (2019) extends the
canonical precautionary savings model to include non-homothetic preferences, allowing for MPCs thatvary with permanent income, consistent with our findings.
Finally, it is instructive to compare our estimates to those used in standard calibrations of HANK
models. In Table III, we summarize the estimates of the consumption response to the 2008 tax rebatesin the United States, and we contrast them with our estimates. Following Laibson et al. (2022), we
now draw a distinction between the observed marginal propensity to spend (denoted MPX) and themodel-consistent, or “notional,” marginal propensity to consume that should be used as a target for
macroeconomic models.31 Columns (1) and (2) summarize the results of Parker et al. (2013) and Broda
and Parker (2014), which are the typical targeted moments in fiscal policy models. For example, Kaplan
and Violante (2014), Kaplan et al. (2018) and Auclert et al. (2023a) calibrate their heterogeneous agent
models to match an MPC of 25 percent on the nondurables component of consumption expenditures.
Columns (3) and (4) report the estimates of Borusyak et al. (2023) and Orchard et al. (2023b). Applying
event study estimators that are robust to treatment effect heterogeneity in the same samples as Broda andParker (2014) and Parker et al. (2013), they obtain smaller MPC estimates. Our experimental estimates
for treatment group 1, reported in column (5), are close to the bottom of the range of estimates from
Borusyak et al. (2023) and Orchard et al. (2023b). The last row of Table III reports the notional MPC
that should be used as a target for macroeconomic models, following the methodology of Laibson et al.
(2022). In sum, when studying standard fiscal transfers, macro models should target the notional MPCs
reported in columns (3) to (5), which are about half as large as in the commonly-used estimates from theseminal studies summarized in columns (1) and (2).
Assessing whether suitable calibrations or modifications of the HANK model can match the facts
summarized above is an important direction for future research.32 A potential avenue is to augment
standard consumption models with certain behavioral frictions. For example, in recent work Boutros(2023) and Lian (2021) develop structural behavioral models in which high-liquidity households have large
MPCs because of behavioral biases. Consistent with this line of work, some results of our experiment are
difficult to reconcile with agents being rational and treating money as fungible, which we discuss next.
30
For example, in Kaplan and Violante (2022)’s calibrated two-asset model, the 40% of households with the highest MPCs
(the hand-to-mouth) have an average MPC of 28% (see their Figure 4). In our Figure 8, 50% of households have an MPC
above 28%.
31
The notional MPC accounts for the fact that spending on durables corresponds to a consumption flow over several
periods, which can be consistent with consumption smoothing even though expenditures are front-loaded. Before Laibson etal. (2022) showed that the notional MPC is the relevant target, state-of-the-art macroeconomic models targeted nondurable
MPX estimates.
32
See Wolf (2023) for a characterization of the shape that intertemporal MPCs in HANK models can take, and the extent
to which they can be well approximation by simple models with occasionally binding borrowing constraints (as in, e.g., Farhi
and Werning, 2019).

30

Table III First-quarter MPX and MPC Estimates for Calibration of Macroeconomic Models
This paper,
Parker et al. (2013)

Broda and Parker (2014)

Borusyak et al. (2023)

Orchard et al. (2023b)

treatment group 1

(1)

(2)

(3)

(4)

(5)

Total MPX

52.3% to 91.1%

50.8% to 74.8%

24.8% to 36.6%

28%

23%

Nondurable MPX

12.8% to 30.8%

14.1% to 20.8%

6.9% to 10.2%

0%

6.6%

Notional MPC

16.3% to 28.5%

15.9% to 23.4%

7.8% to 11.4%

8.8%

7.2%

Notes: This table reports the first-quarter MPX and MPC in studies of the 2008 tax rebates in the United states (columns(1) through (4)) and for treatment Card 1 participants in our experiment (column (5)). The first row reports the marginal
propensity to spend on all goods and services, while the second row focuses on nondurables alone. The third row follows themethodology of Laibson et al. (2022) and reports the model-consistent (“notional”) MPC that can be used as a target for
macroeconomic models, equal to the total MPX divided by 3.2. The range of estimates in column (1) corresponds to different
household samples (see Tables 2 and 3 of Parker et al. (2013)). The range of estimates in columns (2) and (3) corresponds
to the lowest and highest values among the three rescaling methods used by Broda and Parker (2014) and Borusyak et al.
(2023) to extrapolate the spending response they observe for consumer packaged goods to broader samples. The estimatesin the first two rows of column (4) are taken from Tables 3 and 5 of Orchard et al. (2023b). We compare our estimates to alarger set of papers in Appendix Figure D13.

5.1.2

Behavioral Models

Our motivation to turn to behavioral models is that the difference in MPCs between households assigned
to Group 1 or Groups 2-3 rejects standard rational models where agents treat money as fungible. Indeed,
when we consider only transactions below 300 euros (which can be made with the treatment card), we
find that 88% of households in Group 2 spent at least 300 euros on the main bank account in the three
weeks before the expiry date of Card 2. This indicates that it should be costless for a vast majority ofhousehold to substitute current account spending for prepaid card spending. In other words, under therational benchmark, we expect that the 3-week expiry date for most households in treatment group 2
should not be a binding constraint, i.e., their MPC should be similar to households in treatment group
1, in contrast with our findings.
Appendix Figure D14 shows, for each day, the fraction of households in treatment groups 2 and 3
that would have had a high enough balance on the treatment card to cover the day’s expenditures (asmeasured by their spending on non-treatment cards) but for some reason did not use the card. A nonnegligible share of households in groups 2 and 3 have a high enough remaining balance on the treatment
card to cover the day’s expenditures but choose to use their regular debit or credit card instead to makepurchases. In the first few days of the experiment this ratio may be high because some households had
not opened their mail and therefore not started to use the card. But even after more than a week into theexperiment, the ratio remains above 15%. Appendix Figure D15 shows that the patterns are the same ina restricted sample of households with a single adult and no children, ruling out the possibility that thisphenomenon is driven by multi-person households of whom only one has access to the treatment card.33
33

Households may need to incur some (e.g., time) costs to use new means of payment for some transactions, for example
automatic payments like utility bills. A model where households face small costs to adjust their means of payment couldin principle generate the pattern in Appendix Figure D14, as households might wait to pay the switching cost. However,in France most automatic payments are made through wire transfers or direct debit, which are not included in our baseline
consumption measure: these transactions do not drive the patterns in Appendix Figure D14. Furthermore, a model withsmall costs cannot explain why the MPC in groups 2 and 3 is larger. Indeed, cards with an expiry date or negative rates
may spur households to pay the small adjustment costs faster and cover their automatic payments with the prepaid cards,
but this would result in a lower MPC for these groups, since these expenses were already planned. Alternatively, a model

31

These facts are hard to reconcile with rational households that treat money as fungible. Indeed, arational agent that treats money as fungible should first “use up” the treatment card to avoid potentiallylosing money (through the negative interest rate or expiry) before using their normal debit or credit
card. Thus, our results echo a literature in economics (Hastings and Shapiro, 2013, 2018, Gelman andRoussanov, 2023, Chan and Kan, 2024) and in sociology (e.g. Zelizer, 1989) that emphasizes the nonfungibility of money.34
With these patterns in mind, our findings deliver three lessons for behavioral models. First, modelsof consumption that rely on present bias in preferences (e.g. Laibson, 1997, Maxted, 2020, Laibson et al.,2021, Gelman, 2022) are able to explain why the consumption response to the transfer is concentrated
early on, but cannot explain the difference in the magnitude of responses between the treatment groups.
Indeed, under such preferences, consumers in all three groups should be present-biased but the negativeinterest rate and the expiry date would remain non-binding constraints, given that it should be costless
for agents to substitute current account spending for prepaid card spending. Thus, present bias does notappear to be the key friction explaining our findings.35
Second, another class of behavioral models that has been used for macro policy analysis is models
that feature two sets of agents, “savers” and “spenders”, who have low and, respectively, high MPCs
(Campbell and Mankiw, 1989, and the Two-Agent New Keynesian models (TANK), see the review inGalı́, 2018). While implementations of such models can be made to feature consumption responses thatare concentrated very early on, they would also imply strongly bi-modal distributions of MPCs, which we
do not find (Figure 8). Furthermore, like other models of present bias, this type of model cannot accountfor the difference in spending patterns by card type.
Third, our results are consistent with models of salience, where small but highly prominent featuresof the choice set distract the attention of decision makers and distort their choices (Bordalo et al., 2012,2013). In particular, salience can lead households to engage in “mental accounting” (e.g., Shefrin andThaler, 1988, Thaler, 1990, McDowall, 2020, Baugh et al., 2021, Boutros, 2023). In Appendix F, weformalize a stylized model of mental accounting that could explain the key empirical patterns we observe
for the three treatment groups. In this model, the agent faces a tradeoff when spending the prepaid cardon unplanned “windfall consumption” (e.g., going to a fancy restaurant, going out more frequently thanusual, purchasing a treat, etc.). On the one hand, the agent incurs a cognitive dissonance cost if they
spend the prepaid card on (planned) regular consumption rather than on an unplanned treat, because ofa mental account mechanism: the prepaid card is perceived by the agent to be “special money” meant tobe spent on extra consumption, like in the sociology literature (Zelizer, 1989, 2021). On the other hand,purchasing treats requires incurring search costs, while using the prepaid card to cover running expenses
does not. Resolving this tradeoff in the model, we show that the spending response is concentrated in thewhere people might forget about using the card, or might be distracted by certain life events, could generate the patterns inAppendix Figure D14. Forgetfulness may be plausible given that the amount (300 euros) is a small fraction of households’
lifetime income.
34
In contrast to work that has found that the labeling of cash transfers has an impact on spending patterns (Beatty et al.,2014, Benhassine et al., 2015), in Section 3.4 we detected no significant effect of framing on the magnitude and compositionof expenditures.
35
Loss aversion is another bias that has been widely studied (e.g., Tversky and Kahneman, 1992). While households
might exhibit loss aversion, it does not appear to be the key friction in our setting because loss aversion does not imply thatparticipants would not treat money as fungible: they could easily avoid any loss – from the expiry date or negative interest
rates – by using the prepaid card to cover running expenses.

32

short run for all cards and is largest for Group 2, followed by Group 3 and finally Group 1. Intuitively,
prepaid cards with an expiry date or a negative interest rate spur the agent to incur the search costs
faster, as long as these costs are not too large. This need to take action in the short run is salient andcan lead to Groups 2 and 3 having higher MPCs than Group 1. When the search costs are higher (e.g.,when a decision must be made within a week to avoid a negative interest rate, as in Group 3), the agent
is more likely to cover regular consumption than to purchase unplanned windfall consumption goods andservices, implying a lower MPC than with a longer expiry date (as in Group 2).36
Another potential mechanism through which the difference in MPCs between Groups 2 and 3 could
be explained is dual reasoning (Ilut and Valchev, 2023). Agents are confronted with different decision
problems and can make decisions either rapidly and intuitively by projecting on past deliberations (“system 1 thinking”), or by carefully considering their choices, which leads to better outcomes but which isalso cognitively costly (“system 2 thinking”). Situations where people receive a means of payment thatthey have a certain time frame to spend, such as in Group 2, are familiar to many from gift vouchers andgift cards, and may lead recipients to behave similarly to how they behaved in such situations (through“system 1 thinking”). In contrast, the situation where the participant receives a means of payment that
rapidly loses value is unfamiliar to most, resulting in careful deliberations (activating “system 2 thinking”)
to avoid the loss of value and, more often than not, the purchase of goods that they would have purchased
anyway, implying a lower marginal propensity to consume in Group 3 than in Group 2. Note that we
observe that Group 3 participants, triggered by the salience of the one-week ultimatum before they losemoney, on average spend more using the treatment card than Group 2 on each day of the first week.37

5.2

Implications for Macroeconomic Stabilization Policies

Our results have two immediate implications for policy. First, the difference in MPCs across treatmentgroups 1 and 2 (23% vs. 61%) shows that the design of stimulus transfers can help increase MPCs. Notethat because some money ends up being returned in treatment designs 2 and 3, the average consumption
stimulus per euro actually spent is larger than the MPC estimates reported above. In Appendix Figure
D16 we plot the MPC for Groups 2 and 3 corrected by the fraction of the money that is being returnedin the form of interest payments (Group 3) or remaining balance upon card expiry (Group 2), which isabout 16 percent for both groups. The resulting effective stimulus at the 4-week horizon is about 75 centper euro of net transfer for Group 2, and about 40 cent per euro for Group 3.
36

Analyzing the consumption response to tax refunds and tax payments, Baugh et al. (2021) highlight that the estimatesin their study are most consistent with a mental accounting life-cycle model following Shefrin and Thaler (1988). They findthat households increase spending when they receive an anticipated tax refund, and that these same households completely
smooth consumption when making anticipated tax payments, implying that they have the liquidity to smooth consumption
through refunds. Thus, households spend out of tax refunds by choice rather than due to liquidity constraints, consistent
with mental accounting. Anticipated tax refunds are part of the “future income” mental account and are not smoothed,
while tax payments are part of the “current income” mental account, which leads to consumption smoothing.
37
An alternative potential mechanism, suggested by an anonymous referee, is the presence of small “real” frictions combinedwith potentially small benefits from fully rational consumption smoothing behavior. In the presence of “real” frictions (e.g.,
the hassle cost of using a new card), setting an expiry deadline or a negative interest rate can endogenously lead households tospend down their prepaid cards faster. If these households are fully rational, they should treat money as fungible and smoothconsumption perfectly by reducing spending on their main account as they spend down the prepaid card, i.e. they should
not have a higher overall MPC. However, there may be settings in which households are willing not to smooth consumption(e.g., because the amount on the card is small relative to lifetime consumption, i.e. the utility loss from not smoothing issmall). In such cases, the real frictions could lead to higher spending and explain why Cards 2 and 3 induce higher MPCs
than Card 1.

33

The external validity of our experimental estimates, and its broad applicability to high-income countries, appears plausible given that (i) we used a representative sample of the French population, and (ii)our estimates for Group 1 are very similar to those obtained when studying the 2008 tax rebate response in
the United States with robust estimators (Borusyak et al., 2023, Orchard et al., 2023b). Our intervention
was deliberately designed to be scalable to the macro level, and we note that there are several examples oflarge-scale stimulus policies using prepaid cards or time-limited consumption vouchers, including Japan
in 1999, Taiwan in 2009, California, Milan, and Seoul in 2020, and Hong Kong in 2021. Finding ways ofraising MPCs is of particular importance given recent estimates of the MPCs out of standard tax rebatesin the United States, which are relatively low, as found by Parker et al. (2022b) and Parker et al. (2022a)
for the 2020 stimulus payment, and by Borusyak et al. (2023) and Orchard et al. (2023b) for the 2008
stimulus payments. Using prepaid card with negative rates or expiration dates to raise MPCs is therefore
a promising avenue for stimulus policies going forward, which could potentially be implemented by central
banks using central bank digital currencies.38 It is also worth noting that short-term interest rates wereclose to zero at the time when our experiment was implemented (see Appendix Figure D17), indicating
the possible potency of particular types of stimulus policies even in a liquidity trap.39
Second, our estimates of MPC heterogeneity have implications for the targeting of transfers by observable household characteristics. We documented in Section 4.1 that many household characteristics
can be used to predict heterogeneity in MPCs. Thus, transfers could be targeted to the householdswith the highest MPC. While liquidity is difficult to observe, other predictors are readily accessible topolicymakers. To assess the extent to which the average MPC of transfer recipients could be increasedby targeting, we conduct a simple exercise: we use the specification from Section 4.1 with two sets ofcharacteristics that policymakers might be able to observe as regressors, and estimate the distribution of
MPCs. We estimate the parameters using LASSO to avoid overfitting, in a sample consisting of control
group households and households receiving treatment card 1. By plotting the estimated distribution oftreatment effects we can thus assess the extent to which household targeting can help increase the MPC
for a standard transfer, without negative rates or an expiry date.
Figure 9 plots the distribution of predicted MPCs. In the first exercise, reported in panel A, werun LASSO with age quartiles, income quartiles, and unemployment status. This panel shows that byusing these observables it is possible to identify households with substantially above-average MPCs. For
example, 10% of households are predicted to have an MPC above 43%. In the second exercise, shown inpanel B, we predict the MPC distribution using gender, local area revenue tercile, and retirement status.
The top ten percent of households have an MPC of 61%. Targeting can therefore be a relatively powerfultool to increase the average MPC of recipients, although it is not as potent as changing the design ofthe treatment card. For example, treatment card 2, with an expiry date, yields an average MPC acrossall participants of 61%. Thus, our estimates highlight that implementation design choices are a more
38

If transfers with expiry dates were used repeatedly, one could worry that households may start viewing these transfers
as more fungible with their main bank account, and thus have a lower MPC. However, existing evidence suggest that mental
accounting continues to operate even for repeated transitory shocks, as found by Baugh et al. (2021) for tax rebates, byHastings and Shapiro (2013) for gasoline purchases, and by Hastings and Shapiro (2018) for food stamps.
39
Other types of stimulus policies at the ZLB potentially include VAT rate cuts, see e.g. Correia et al. (2013). Note that
our experiment cannot be used to learn about the impact of broader changes in interest rates on consumption behavior or
about the intertemporal elasticity of substitution for two reasons: (i) the “negative interest rates” are only applied to thetreatment card, i.e. to a very small fraction of househods’ assets; (ii) if households treated money as fungible, the negative
rates on the treatment cards would not affect their budget sets.

34

powerful tool, compared to targeting, to increase the recipients’ average MPC.40 In addition, targeting
may raise political economy or fairness considerations that are avoided by providing a treatment cardwith an expiry date to all.
Figure 9 Predicted MPC Heterogeneity
A. Using age quartiles, income quartiles
and unemployment status

B. Using gender, local area revenue tercile,and retirement status
Retirement, department revenue tercile, gender

150%

100%
100%

32 %
9%
0%

0%

48 %

50%

43 %

Predicted MPC

Predicted MPC

61 %

50%

0%

18 %
0%

0%
−13 %

−50%
−50%
−100%

−100%
0

10

25

50

75

90

100

0

Quantile

10

25

50

75

90

100

Quantile
Bootstraps : 200

Bootstraps : 200

Notes: This figure shows the distributions of the predicted MPC heterogeneity, using different sets of characteristics
as predictors of the treatment effect in a LASSO specification. Panel A uses age quartiles, income quartiles andunemployment status as features in the LASSO specification, while Panel B uses gender, local area revenue tercile,and retirement status as features. The sample is restricted to treatment card 1. The 95% confidence intervals are
obtained by bootstrap and shown as shaded regions.

6

Conclusion

In this paper we presented five facts about MPCs obtained from a randomized experiment where we
provide money transfers to a representative set of French households. These results inform the academic
debate on models of consumption, but are also directly relevant for the design of effective stimulus policies.
First, we found that the one-month MPC is 23% with a standard treatment card, without negativeinterest rates. Second, we established our main result: the design of the transfer matters. The one-month
MPC is higher when treatment cards feature a negative interest rate, at 61% when the remaining balanceis reduced to zero after three weeks, and 35% when the remaining balance is reduced by approximately
10 percent every week. Third, the increase in consumption is much larger early on, in the first two to
three weeks after receiving the transfer. Fourth, heterogeneity in the MPCs that is explained by observed
households characteristics is substantial, including by variables distinct from liquid wealth such as current
income, proxies for permanent income, and gender. Fifth, the unconditional heterogeneity in MPCs isvery large and a large fraction of households have high MPCs.
These five facts are hard to reconcile with standard two-asset models of consumption. They point
to the importance of behavioral features (e.g., salience) for macroeconomic model of the consumption
40
Of course the policymaker may have other goals than increasing the short-term MPC, for example to change the composition of spending, or to smooth consumption over a longer timeframe.

35

response to transfers, such that agents do no treat stimulus transfers as fungible with standard income
sources. The “five facts about prices” of Nakamura and Steinsson (2008) called for a reevaluation of menu
cost models; much in the same spirit, our five facts about MPCs provide moments that can help discipline
consumption and macro models.41
From a policy perspective, our findings indicate that implementation design, and to a lesser extent
household targeting, are key tools to manipulate MPCs and increase the effectiveness of stimulus. Prepaid
cards with negative interest rates or an expiry date deliver much larger MPC than standard fiscal stimulus,
and constitute a powerful tool to stimulate demand even when interest rates are low.
An important avenue for future research is to scale up sample sizes to obtain more precise estimatesof MPCs at longer horizons, and of the heterogeneity by observable household characteristics and treatment designs. Indeed, while our empirical results are supportive of little intertemporal substitution, theprecision of our estimates is not high enough to rule it out. To guide the design of future experiments,
Appendix G presents power calculations informed by our data.
Another important direction for future work is to quantify the welfare effects of administering stimulus
programs with cards featuring time limits or negative interest rates. Specifically, a fruitful task would be
to compare the household-level welfare losses when using such cards (as agents receiving these cards do
not smooth consumption as much)42 to the welfare gains from the aggregate demand externalities thatarise in general equilibrium.43 We leave these and other extensions for future work.

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,, and Johannes Wieland, “Micro MPCs and macro counterfactuals: the case of the 2008 rebates,”

Working Paper, 2023. 1, 5.1.1, 5.1.1, 5.2, 41, 43, F
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and Nicholas S Souleles, “Reported effects versus revealed-preference estimates: Evidence from thepropensity to spend tax rebates,” American Economic Review: Insights, 2019, 1 (3), 273–90. 1, 41, Jake Schild, Laura Erhard, and David Johnson, “Economic Impact Payments and Household
Spending During the Pandemic,” Brookings Papers on Economic Activity, 2022. 1, 5.2
,

,

, and

, “Household spending responses to the economic impact payments of 2020: Evidence

from the consumer expenditure survey,” NBER Working Paper, 2022. 1, 5.2, Nicholas S Souleles, David S Johnson, and Robert McClelland, “Consumer spending andthe economic stimulus payments of 2008,” American Economic Review, 2013, 103 (6), 2530–2553. 1,
5.1.1, 5.1.1
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Economics, 2016, 8, 341–377. 4.2
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Wolf, Christian K, “Interest rate cuts vs. stimulus payments: An equivalence result,” Working Paper,2023. 32
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43

For Online Publication
Appendix to “Five Facts about MPCs”
Johannes Boehm, Sciences Po & CEPR
Etienne Fize, PSE & IPP
Xavier Jaravel, LSE & CEPR
May 2024

Contents
A A Primer On Recent Time-Limited Consumption Vouchers Policies

A1

B Data Appendix

A1

B.1 Sampling and Representativeness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A1

B.2 Data Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A3

B.3 Variable Definitions

A4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

C Experimental Design Appendix

A6

C.1 Letter Sent to the Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A6

C.2 Survey Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A9D Main Additional Figures and Tables

A11

E Other Robustness Checks

A27

E.1 Robustness Checks for Pooled MPC Estimates . . . . . . . . . . . . . . . . . . . . . . . . A27
E.2 Robustness Checks for MPC Estimates by Card Type . . . . . . . . . . . . . . . . . . . . A31
E.3 Robustness Checks for the Estimates of Heterogeneity in MPCs by Observables . . . . . . A38
E.4 Robustness Checks for the Estimates of the Unconditional Heterogeneity in MPCs . . . . A44
F A Stylized Model

A48

G Power Calculations based on Estimated Effect Sizes

A53

G.1 Power for Detecting Differences in Average MPCs across Treatment Groups . . . . . . . . A53
G.2 Statistical Precision for Average MPCs Out of Standard Money Transfers . . . . . . . . . A55

A0A

A Primer On Recent Time-Limited Consumption Vouchers Policies

In recent years, in the wake of the Covid pandemic, several countries both in Europe and in Asia have
implemented time-limited consumption vouchers policies.
In Europe, the British Isle of Jersey implemented a program that delivered a £100 prepaid credit
card to all of its citizens which could be used in all national retail stores. The cards were issued in the
beginning of September 2020 and expired on October 31st of the same year. In total, 105,964 prepaid
cards were distributed, for a total cost of around 11.7 million pounds. 97.5% of cards were delivered
and activated. 98 % of the amount of all activated cards was spent. The spending was concentrated in
the first weeks as the majority of spending was achieved in the first month. Building on this experience,
Northern Ireland implemented a very similar scheme in 2021. The government of Northern Ireland also
distributed £100 prepaid cards to all its adult population (1.4 million residents). The card was limited
to physical purchases, excluding online transactions. The first cards were sent on October 3rd 2021, andthe deadline was December 19th. The take-up was very high: 99.6% card were activated and on average
97.94 pounds were spent(see Statistics and Branch (2022)). In Italy, the city of Milan also experimented
with time-limited pre-paid credit cards, which were sent to vulnerable citizens in 2020.
In Asia, similar policies were implemented. The city of Seoul, for instance, offered to households
below median income either a consumption voucher (“coupon”) or a prepaid card, both with a 5-month
expiry date. Household were free to choose either form of transfer: 80 % opted for the coupons, which had
geographic retrictions but carried a 10 % higher value than the cards. The take up rate for this program
was also very high, at 99 %. Woo et al. (2021) and Kim and Lee (2021) find a significant effect on directspending but are not able to compute MPCs with the available data. Studyign the same policy change,
Ku et al. (2023) estimate an MPC of at least 59%. Baek et al. (2023) look at a similar policy in Gyeonggi,
another Korean province, and find MPCs ranging from 36 to 58%.
China implemented a digital coupon program where the government would subsidize additional consumption for targeted categories and a very limited time period. The coupon works in the following way:
if a least X Yen were spent, Y Yen would be subsidized, where X and Y differ across product categories(for instance buy at least 24 Yen and get 8 free). Recents studies (Ding et al. (2024); Xing et al. (2023);
Liu et al. (2021); Wu et al. (2020)) analyzed this policy and documented large and persistent response of
consumption. According to these studies, for every 1 Yen of subsidiy, around 3 additional Yens are spent.

B

Data Appendix

In this appendix, we discuss the representativeness of the data, the data structure, and the exact definitionof our variables for replication purposes.

B.1

Sampling and RepresentativenessWe build on a sample of households that the bank drew in June 2020, using the following steps. First, inorder to be eligible for inclusion in the sample, the bank had to be the main bank used by the households
A1

(i.e., households could be using multiple banks but must have located their main assets, credits andincome at the bank). Second, households had to be client of the bank in January 2019. Third, Frenchoverseas territory and employees of the bank were excluded of the sampling process. Finally, the sampling
procedure drew clients from cells at the local area (“département”) × age bin level. Specifically, 94 differentdépartements and six age bins were used: 18-25, 26-35, 36-45, 46-55, 56-65 and 66+ years. For the largest
31 départements 1,000 households per cell were selected, then 500 for the next 26 départements and finally
100 for the least populated département. The initial sample size was around 300,000 households. The
sample was never renewed and, because of attrition, the sample size decreased over time. We received
remote access to anonymized versions of the data that start in January 2019.
This dataset is by design representative of the population of clients at the bank. Bounie et al. (2020)
and Bonnet et al. (2023) find that the sample is also broadly representative of the French population along
several characteristics, with some slight differences. Specifically, compared to the French population, thebank sample is younger, with fewer retired people, features a higher share of individuals out of the labor
force,1 and a higher share of single households. The distribution of spending (and the ratio of spending
over income) by income deciles in the bank sample are in line with the French consumption survey(“Budget des Familles”). The trends in card spending and liquid bank account balances also match
macro aggregates from the French national accounts (see Bounie et al., 2020 and Bonnet et al., 2021).
Bonnet et al. (2023) also show, using the 2017 French Wealth Survey, that the customer base of the bankis representative of the French population in terms of financial wealth and disposable income. This survey
shows that 75% of households in France have a checking account in one bank only. Moreover, more than
80% of all financial assets of French household is held in their main or only bank. Finally, Bonnet et al.
(2023) document that the distribution of monthly fuel spending with respect to income in the bank data
looks close to the one obtained from the French consumption survey (“Budget des Familles”).
Our paper focuses on a sub-sample of this panel. In order for an individual to be eligible in our
experimental draw, a number of conditions have to be satisfied:
1. Age above 26 and below 75 years at the time of draw, and be in legal capacity, i.e. not having alegal guardian (“majeur non protégé”)
2. Resident at the address registered with the bank
3. Account is a personal account, not a professional account. According to the records of the bank,the household is either entirely or mostly banking with them.
4. The checking account is active and the account holder is in good standing with the bank (“compte
courant ouvert et sain”), and there were movements on the checking account within the last 10
days.
5. At least one transfer received every month over the course of the last six months; at least 10 transfers
received in 2020, and at least 10 transfers received in 2019.
6. At least one payment made every month in the last six months, in 2020, and in 2019.
7. Has an active bank card that it has used at least once within the prior 20 days.
1

The “inactive” category includes students, the unemployed, and any other person with no professional activity.

A2

8. Is using internet/distance banking (“détenteur d’un contrat banque à distance”) with at least one
connection within the prior 20 days. Has an email address registered on file.
Constraints 1, 2, and 8 are imposed for operational and ethical reasons. Constraints 3, 4, 5, 6, and 7
are imposed to exclude people whose consumption expenditure patterns are poorly captured through thedata available to us.

B.2

Data Structure

The data is divided in six different tables:• The first table is at the individual×month level, it contains socio-demographic information for all
individuals in the household at month t.
• The second table is at the household×month level. It contains information on the balance of all
different bank accounts of the household (current account, liquid savings account, life insurance
and illiquid savings). The table also provides information on household debt (total debt, andby subcategories such as mortgage debt or consumption debt), and on the sum of incoming andoutgoing banking movement for some categories of banking operations (checks, cash withdrawal,
card purchases). Finally, it includes information on payment or other financial difficulties faced by
the household, such as overdraft.
• The third table is at the household×operation level. This dataset provides information (time,amount) on all banking operations, i.e. all inflows and outflows. These flows cover a vast rangeof transactions, including card purchases, wire transfers, checks, and direct debit. The bank also
provides information on incoming wire transfers. The bank classifies the incoming wire transfers
into distinct categories: pensions, unemployment insurance, government subsidies, and salaries.
• The fourth table is at the household×operation level. This dataset gives information on all cardtransactions.2 Compared to the previous table, this table gives more information for the cardtransactions (e.g., the Merchant Category Code (MCC) for the purchase). Moreover, while theprevious table records the date at which there is a banking movement, this table records the date
at which the transaction occurs (i.e., when the card is actually used). The two dates may differ forseveral reasons. For instance, some household choose to have a deferred debit, where the banking
movements comes at the end of each month for all card transactions. The difference can also comesfrom delays from either the bank (in case the purchase is made on a bank holiday, or on a Sunday)
or from the merchant (for instance, for fuel and gas purchases).
• The fifth table is at the household×operation level and provide provides a classification of all direct
debit operations (phone bill, water bill...).
• The sixth table is at the household×period level. This table is a snapshot of all real estate wealthowned by the household, according to the bank’s records. The information was collected twice, in
September of 2020 and in November of 2021.
2

Our dataset covers both debit and credit cards. About 2% of households have a credit card. French households use
credit cards primarily as a way to access a line of credit: contrary to the United States, credit card history is not used tobuild credit scores and there are rarely features such as cash back, reward points, or frequent-flyer miles.

A3

All of these tables can be joined thanks to an anonymized household identifier.

B.3

Variable Definitions

Our main variables are defined as follows:• Consumption expenditure, per week: sum of card purchases and cash withdrawals of the household within the week (according to the third table described in Appendix B.2). We construct our
winsorized weekly consumption spending by winsorizing regular client transactions at the 99th percentile (1940 euros in a week) and add up treatment card expenses in a week at the household
level.
• Consumption expenditure on non-durable / durable / semi-durable goods or services: sum of card
purchases and cash withdrawals of the household within the week linked to Merchant Category
Codes classification to include only expenditure on specific categories of consumption expenditure(following the classification of Ganong and Noel (2019)).
• Treatment card expenditure: sum of household treatment card purchases within a week. Treatedhousehold who have effectively used the treatment card will have at least one week with positive
value during the treatment period. Control group households have a value of zero for this variable.
• Regular card expenditure: sum of card purchases and cash withdrawals of the household within theweek (according to the third table described in Appendix B.2) that are not identified as treatment
card expenditure for treated households.
• Withdrawals: sum of cash withdrawals of the household within the week (according to the third
table described in Appendix B.2).
• Weekly consumption expenditure, broad measure: sum of card purchases and cash withdrawals of
the household within the week (according the third table described in Appendix B.2) plus all otheroutflows (direct debits, wire transfers, etc).
• Take-up dummy: Time-invariant dummy variable, equal to one for treated households who haveused the treatment card at some point during the treatment period.
• Number of eligible individuals in the household: number of individuals in the household that would
have been eligible to receive the treatment, at the time of randomization.
• Unemployed: time-invariant dummy, equal to one for households that receive at least one transferfrom the unemployment benefits agency (“Pôle emploi”) within the 6 months prior to treatment.
• Aggregation of individual characteristics to the household level: We aggregate individual characteristics to the household level by using the characteristic of the eligible household member. For control
group households composed of two eligible people, we randomly choose one person’s characteristic
to represent the entire household. For treatment group households with two eligible members, we
use the characteristic of the individual that has been chosen (at random) as treated. The relevant
individual characteristics are as follows:A4

– Age: time invariant variable that corresponds to the age of the individual.
– Location: capture the département where the household lives.
– Location type: this variable measures whether the household lives in rural, periphery or urban
areas.
– Occupation: this variable measures whether the individual works in one of the following occupations: farmers, artisans, executives, intermediate professions, employee, worker, retired,unemployed/students.
• Number of household members: this variable is used to correct time invariant characteristics likeincome and wealth. We account for the presence of children to compute a unit of consumption (UC)for each household. Following the OECD scale, we attribute 1 UC to a first adult in a household,
0.5 UC to the following one and 0.3 UC for every child below 14 years old.
• Variables for time-invariant heterogeneity analysis: all of these variables are divided by the sum of
the unit of consumption in the household (see above):– Household monthly mean expenditure: average of monthly card expenditures in a week for 1
year before treatment.
– Household monthly income: average monthly inflows to the household’s bank account within
the six months prior to treatment.

Individual transactions value above 15,000 euros aretrimmed.
– Household wealth: we build two versions of the variables listed below over different time
horizons, taking averages over either one month or six months prior to treatment.
∗ Household bank current account: current account balance prior to treatment. This variable
captures the bank account funds that the household can use at any point in time.
∗ Household liquid saving accounts: liquid saving balance prior to treatment. This variable
capture the funds available on liquid, tax-free savings accounts with instant access: Livret
A, Livret d’épargne populaire, Livret Jeune, and philanthropic savings accounts, etc.
∗ Household life insurance accounts: life insurance balance prior to treatment.
∗ Household illiquid savings: illiquid saving accounts balance prior to treatment, including
the “share savings plan” (Plan d’épargne en action).
∗ Net liquid wealth: sum of the balances of the household’s current account and liquid saving
accounts at the end of the month, net of consumer debt.
∗ Net illiquid wealth: sum of the balances of the household’s illiquid saving accounts, sharedealing accounts, and brokerage accounts at the end of the month, net of mortgage debt.
∗ Household real estate wealth: real estate wealth reported by the household during a survey
conducted in November 2021.

A5

C

Experimental Design Appendix

In this appendix, we describe the letter sent to the participants, as well as the survey administered inJune 2022.

C.1

Letter Sent to the Participants

The letter sent to participants is printed on the bank’s letterhead and is personally addressedto the selected participant:Vous avez été sélectionné pour participer à une étude* et ainsi bénéficier d’une enveloppe d’unmontant de 300 EUR, qui vous est offerte.
En effet, afin de contribuer au débat économique, le CIC participe à une étude scientifiquemenée par le Conseil d’Analyse Economique (CAE) et financée par l’Agence Nationale de laRecherche (ANR). L’objectif de cette initiative est d’étudier, dans le cadre d’une politiquedestinée à favoriser la relance économique, les comportements de dépenses des personnes
lorsqu’une somme d’argent leur est distribuée gratuitement.
Le CIC veille à la protection des données de ses clients. Toutes les analyses réalisées dans lecadre de cette étude seront effectuées sur des données strictement anonymisées sur les seuls
systèmes d’information sécurisés du CIC. Il s’agit des mouvements bancaires, de la situation
financière et de données socio-économiques.
Ce montant de 300 EUR sera utilisable au moyen d’une carte de paiement spécifique. Cette
carte vous sera adressée gratuitement par courrier postal dans les prochains jours.
• Le code confidentiel de cette carte est identique à celui de la carte que vous possédez déjà.
Vous pouvez le retrouver dans votre espace personnel en ligne, sur l’application mobile ou
le site internet www.cic.fr.
• Cette carte peut être utilisée auprès des établissements affichant les logos CB ou Mastercard, ainsi que pour des achats en ligne, dans la limite du solde disponible.
• Il n’est pas possible de retirer des espèces, ni d’effectuer des dépôts.
• Le suivi des opérations et le solde disponible sur cette carte sont consultables dans votre
espace personnel en ligne, sur l’application mobile ou sur le site internet www.cic.fr.
• Les conditions générales d’utilisation qui régissent votre carte actuelle, s’appliquent égalementà cette carte (CG.03.20).
Translation:
You have been selected to participate in a study* and, as a result, benefit from an amount of
300 EUR, which is offered to you.
Indeed, in order to contribute to the economic debate, CIC is participating in a scientific study
conducted by the Council of Economic Analysis (CAE) and funded by the National Research
Agency (ANR). The objective of this initiative is to study, within the framework of a policy
A6aimed at promoting economic recovery, people’s spending behaviors when a sum of money is
distributed to them for free.
CIC ensures the protection of its clients’ data. All analyses carried out as part of this study
will be performed on strictly anonymized data on CIC’s secure information systems. This
includes banking transactions, financial situation, and socio-economic data.
This amount of 300 EUR will be available for use through a specific payment card. This card
will be sent to you free of charge by postal mail in the coming days.
• The confidential code for this card is the same as the one for the card you already possess.
You can find it in your personal online space, on the mobile application, or on the website
www.cic.fr.
• This card can be used at establishments displaying the CB or Mastercard logos, as well
as for online purchases, up to the available balance.
• It is not possible to withdraw cash or make deposits. The operations and available balanceon this card can be checked in your personal online space, on the mobile application, oron the website www.cic.fr.
• The general terms of use that govern your current card also apply to this card (CG.03.20).
The next paragraph contains information that is specific to the treatment group.
For treatment group 1:
La carte fonctionne jusqu’au 03/10/2022. Si vous ne dépensez pas l’intégralité du montant de
300 EUR avant cette date, le solde restant sera automatiquement transféré sur votre compte
courant habituel du CIC.
Transl.: The card is valid until 10/03/2022. If you do not spend the entire amount of 300
EUR before this date, the remaining balance will be automatically transferred to your regularcurrent account at CIC.
For treatment group 2:
L’objectif de cette expérience est d’encourager une hausse de la consommation à court terme,dans le cadre d’une politique économique de relance. Pour cette raison, la carte fonctionne
jusqu’au 23/05/2022 à 23 heures 59. Il ne sera plus possible d’utiliser les fonds après cettedate limite; les fonds inutilisés seront perdus.
Transl.: The objective of this experiment is to encourage an increase in short-term consumption, as part of an economic policy for recovery. For this reason, the card is valid until
05/23/2022 at 11:59 PM. It will no longer be possible to use the funds after this deadline, andany unused funds will be lost.
For treatment group 3:

A7

L’objectif de cette expérience est d’encourager une hausse de la consommation à court terme,dans le cadre d’une politique économique de relance. Pour cette raison, le montant disponible
de la carte est débité automatiquement d’un certain montant chaque lundi à 23 heures 59(à partir du lundi 09/05/2022). Le montant débité dépend du solde restant à ce moment,
avec un montant débité plus élevé lorsque le solde restant est plus élevé afin d’encourager une
consommation rapide. Ainsi, le solde disponible sera diminué :• de 30 EUR si le solde restant est supérieur à 200 EUR ;• de 20 EUR si le solde restant est entre 100 EUR et 200 EUR ;• de 10 EUR si le solde est inférieur à 100 EUR (le débit correspond au solde restant si
celui-ci est inférieur à 10 EUR).
Par exemple, si vous dépensez le montant de 300 EUR avant le lundi 09/05/2022 à 23 heures
59, le solde restant est nul et aucun montant ne sera débité. Si vous dépensez seulement 50
EUR avant le lundi 09/05/2022 à 23 heures 59, le solde disponible sera diminué de 30 EUR
et le solde disponible le mardi 10/05/2022 à 00h00 sera de 220 EUR (= 300 – 50 – 30).
Transl.: The goal of this experiment is to promote an increase in short-term consumption aspart of an economic policy for recovery. For this reason, the available amount on the card isautomatically debited by a certain amount every Monday at 11:59 PM (starting from Monday,
05/09/2022). The debited amount depends on the remaining balance at that moment, with ahigher amount debited when the remaining balance is higher, to encourage rapid consumption.
As a result, the available balance will be reduced as follows:• by 30 EUR if the remaining balance is above 200 EUR;
• by 20 EUR if the remaining balance is between 100 EUR and 200 EUR;
• by 10 EUR if the remaining balance is below 100 EUR (the debit amount will be equal to
the remaining balance if it is below 10 EUR). For example, if you spend the full amount of
300 EUR before Monday, 05/09/2022, at 11:59 PM, the remaining balance will be zero,and no amount will be debited. If you only spend 50 EUR before Monday, 05/09/2022,
at 11:59 PM, the available balance will be reduced by 30 EUR, and the available balanceon Tuesday, 05/10/2022, at 12:00 AM will be 220 EUR (= 300 – 50 – 30).
Next, a paragraph that depends on whether the partipant is part of a framing group.
Participants that are not in the framing group receive the following message:
Vous êtes totalement libre d’utiliser le montant de 300 EUR comme vous le souhaitez.
Transl.: You are completely free to use the amount of 300 EUR as you wish.
Participants that are in the framing group receive instead:
Bien que vous soyez libre d’utiliser le montant de 300 euros comme vous le souhaitez, nous
vous invitons à:• dépenser l’argent aussi rapidement que possible;
A8• acheter des produits fabriqués en France et des services qui soutiennent l’emploi local,
car l’objectif de ce transfert est la relance de l’économie française, en encourageant laconsommation de produits made in France;• acheter des produits ou services que vous n’achèteriez pas habituellement (autres que vosdépenses courantes) afin d’augmenter vos dépenses totales, et ainsi de contribuer à larelance économique, plutôt que de couvrir des dépenses déjà prévues.
Transl.: Although you are free to use the amount of 300 euros as you wish, we invite you to:• spend the money as quickly as possible;• buy products made in France and services that support local employment, as the objectiveof this transfer is to stimulate the French economy by encouraging the consumption of"made in France" products;• purchase products or services that you wouldn’t normally buy (other than your regularexpenses) to increase your total spending and thereby contribute to the economic recovery,
rather than covering expenses that were already planned.
All groups conclude with the following:
L’utilisation de cette carte n’entraine aucun frais pour vous. Si vous ne souhaitez pas participerà cette étude, n’utilisez pas la carte et détruisez la. En utilisant la carte, vous acceptez departiciper à l’étude. En vous remerciant pour votre confiance, votre conseiller CIC se tient à
disposition pour répondre à toutes vos questions.
Transl.: The use of this card does not incur any fees for you. If you do not wish to participate
in this study, do not use the card and destroy it. By using the card, you agree to participate
in the study. Thank you for your trust; your CIC advisor is available to answer any questions
you may have.
The footnote is as follows:* L’étude est menée et a été définie par une équipe scientifique du CAE et financée par l’Agence
Nationale de la Recherche. Les critères de sélection des participants, l‘utilisation des cartes,les données étudiées et la durée de l’étude qui s’étend du 01/10/2021 au 03/10/2022 ont étédéfinis par le CAE. Les 1 000 participants qui bénéficient de la somme de 300 EUR ont ététirés au sort sous contrôle d’huissier.
Transl.: The study is conducted and has been defined by a scientific team from the CAE andfunded by the National Research Agency. The criteria for selecting participants, the use of
the cards, the data studied, and the duration of the study, which extends from 10/01/2021 to
10/03/2022, have been determined by the CAE. The 1,000 participants who are receiving thesum of 300 EUR have been randomly selected under the supervision of a bailiff.

C.2

Survey Questions

Participants were contacted by email with the following message:
A9

Bonjour,
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A10

D

Main Additional Figures and Tables
Figure D1 Randomization Tests

Single male
Consumption
Overdraft
Illiquid wealth
Liquid wealth
Revenue
Age
Number children
Number adults
Unemployed

Regression coefficients, %

Male

0.15

0.10

0.05

0.00

0.05

0.10

Notes: This figure reports the randomization tests for participation in the experiment, regressing a dummy forparticipation status on several household characteristics. We control for the number of eligible members in thehouseholds. The probability of being treated in the sample is 1%.

Figure D2 FGLS estimates of the MPC
A. For all cards

B. By treatment group

60%

Cumulative MPC, in %Cumulative MPC, in %

100%

40%

20%

50%

0%

0%
May

Jun

Jul
Status FGLS

May

all

Jun
Card FGLS

Jul
1

2

3

Notes: This figure shows the estimated MPC using a feasible generalized least square (FGLS) procedure, where
standard errors of each household’s error term are parameterized to be able to vary with each bin of time-invariant
characteristics calculated from pre-period data (10 age bins, 10 income bins, gender dummy, 10 liquid wealthbins, 10 average consumption expenditure bins, 95 local area dummies), i.e. in each iteration we calculate weightsfrom 1/σ̂i2 , where σ̂i is the predicted standard error from a regression of the household-level standard error in theprevious iteration on characteristic bin dummies. While Panel A considers all cards, Panel B presents the estimatesby treatment group. Both panels report 95% confidence intervals, clustered at the household level.

A11

Figure D3 4-week MPC Differences between Card Types

Cumulative 4−Week MPC Difference

75%

50%

25%

0%

−25%
Card 2 − Card 1

Card 2 − Card 3

Card 3 − Card 1

Notes: This figure reports the 4-week MPC difference between card types, with 95% confidence intervals.

Figure D4 Long-term MPC Estimates for Durables and Nondurables
A. Non durable MPC

B. Durable MPC
40

Cumulative MPC for Durable

Cumulative MPC for Non durable

150

100

50

0

20

0

−50
May

Jun

Jul

Aug

Sep

Confidence interval:

Oct

95%

Nov

Dec

Jan

Feb

May

68%

Jun

Jul

Aug

Sep

Confidence interval:
7th order

Oct

95%

Nov

Dec

Jan

Feb

68%
7th order

Notes: This figure reports the cumulative MPC estimates for nondurables and durables, considering all cards
together.
P8 To reduce noise we use a seventh-order polynomial to model the weekly outcome response after treatment:
Yit = k=1 βτk−1 · τitk−1 + αi + αtE + εit , which we estimate with the same FGLS procedure as in Figure D2. The
figure reports the cumulative change in the outcome and the 95% confidence intervals, clustered at the household
level.

A12

Figure D5 Understanding Participants’ Spending Behavior by Card Type
A. What did you buy with the prepaid card?

B. Were the purchases on the card already planned?
0.5

0.4

Fraction

Fraction

0.4
0.3

0.2

0.2

0.1

0.0

0.0
Card 1
Answers

Card 2
Running Expenses

Small Treat

Gifts

Other

Card 3

Card 1

Made Larger Expenditure Earlier

Answers

Card 2 and 3
Bought something extra

Bought earlier

No change

C. Spending share on goods with “negative externalities”
4%

Spending share

3%

2%

1%

0%
Control

Card 1

Card 2

Card 3

Notes: Drinking places, tobacco, betting, lottery, beer, wine, liquor are included in these shares

Notes: Panels A and B of this figure report the answers of participants to survey questions. The other panels use
the bank data to document the expenditure patterns of the treatment and control groups depending on the prepaid
card type. Panel C reports the spending share on treatment cards for the treatment groups, considering productsthat may have negative externalities (drinking, tobacco, betting, lottery).

A13

Figure D6 MPC Estimates by Framing GroupA. Cumulative spending on prepaid card

B. Total spending response

100%

75%
Cumulative MPC, in %Cumulative spending on prepaid card, in %

60%

50%

40%

20%

25%

0%
0%
02−May09−May16−MayFraming23−MayStandard

30−May06−Jun02−May09−MayWith additional paragraph

16−MayFraming23−MayStandard

30−May06−JunWith additional paragraphNotes: This figure reports MPC estimates depending on the framing of the intervention. We compare the consumption behavior of participants in who received the standard letter to those of participants who received a letter withan additional paragraph encouraging them to spend the money quickly and on local goods or services. Panel A
reports spending patterns on the prepaid card, while panel B report the overall MPC. In panel B, 95% confidence
intervals are reported, clustering the data at the household level.

Figure D7 Spending on Imports, by Framing Group
Framing 1
Framing 2
Control

14
13

Percentage

12
11
10
9
8
7
January

February

March

April

Date

May

June

July

AugustNotes: This figure shows the average expenditure share on imports for households in the two framing groups andthe control group. Imports are calculated as the fraction of each product category that is directly imported fromabroad, using the Input-Output table provided by the French statistical institute INSEE, and linked to MCC codes
using our crosswalk.

A14

Figure D8 Total spending response, weekly, for households with high liquid wealth
A. Liquid wealth > 2 × monthly income

B. By quartile of current account wealth

Cumulative consumption spending, in euros

Cumulative consumption spending, in euros

200

100

0

−100
May

Jun
Liquid wealth over Income

Jul
Others

200

0

−200

May

Jun

Ratio last month at least 2

Jul

Current account quartile last month

1

2

3

4

Notes: The panels of this figure shows the results of estimating equation 1 in a subsample of households whose
liquid wealth is larger than twice their monthly income, and by quartiles of current account wealth. The figure
plots the estimates for the cumulative MPC at different time horizons.

Figure D9 Quantile treatment effects: de-meaned cumulative consumption, treated vs. control
A. 4-week horizon

B. 8-week horizon
1.2

Quantile Treatment Effect

Quantile Treatment Effect

0.75

0.50

0.8

0.4

0.25

0.0
0.00
0.1

0.3

0.5

0.7

0.9

0.1

0.3

tau

0.5

0.7

0.9

tau

C. 12-week horizon
1.5

Quantile Treatment Effect

1.0

0.5

0.0

0.1

0.3

0.5

0.7

0.9

tau

Notes: This figure shows quantile treatment effects—the difference between the quantiles of the distribution oftreated and control groups—for cumulative de-meaned consumption expenditures. Standard errors are estimatedusing the bootstrap.

A15

Figure D10 Household-level Quantiles of the 4-week MPC Distribution: Robustness to inclusion ofobserved characteristics bins
140%

117 %

120%
99 %

MPC

100%

91 %

80%

74 %

74 %
64 %

60%

54 %
47 %

44 %

40%

33 %
29 %

20%

18 %
17

13 %

5%

0%
0%

10%

25%

50%

75%

90%

100%

Quantile
Treatment group

Card 1

Card 2

Card 3
Bootstraps : 150

Notes: This figure reports the quantiles of the distribution of 4-week treatment effects by treatment group in a
two-stage procedure with controls. In the first stage of our estimation procedure we project weekly consumption
expenditures on household and week fixed effects interacted with (a, i, c, l, g) fixed effects, where a, i, c, and l are age,income, consumption, and liquid assets quartile bins, and g is a gender dummy. In the second state we deconvolve,
as before, the outcome distribution for the treated by the empirical distribution of the error term of the control
group. Constraints on the estimated distribution (mass on positive part of real line, and penalization) are as in thespecification of the benchmark estimate. The figure shows the resulting treatment distribution estimates, which aresimilar to those reported using the baseline procedure. Shaded regions are delineated by the 10th and 90th percent
quantile of the bootstrapped simulated distribution of the corresponding moment.

A16

Figure D11 Unconditional MPC distribution estimates, high-variance vs low-variance households
A. Group 1

B. Group 2

140%

140%

120%

120%

134 %

118 %
105 %
102 %

100%

100%

MPC

MPC

82 %

80%
67
66 %
%

60%

80%

72 %

56 %

60%
50 %

42 %

41 %

40%

40%

31 %
22 %

20%
6%
3%

0%
0%

20%

15 %
9%

10%

25%

50%

75%

24 %
19 %

0%
0%

90%

10%

25%

50%

Quantile
Card 1Low variance

75%

90%

QuantileHigh variance

Card 2
Bootstraps : 150

Low varianceHigh variance
Bootstraps : 150

C. Group 3
140%

120%

111 %

100%

MPC

90 %
76 %
70 %

80%

58 %

60%
40 %

39 %

40%
25 %
17 %

20%
6%

0%
0%

10%

25%

50%

75%

90%

Quantile
Card 3Low varianceHigh variance
Bootstraps : 150

Notes: The panels of this figure show estimates of the 4-week MPC distribution for each treatment group, where thesample is split into households that have a below-median variance of pre-period weekly consumption expenditures(green) and above-median variance of pre-period weekly consumption expenditures (purple). For each treatment
card, the estimated distributions for both variance groups are very similar (indeed, no quantile is significantly
different from each other), giving support to the view that treatment effect distributions are similar even forhouseholds that have different higher moments of consumption. Shaded regions are delineated by the 10th and 90th
percent quantile of the bootstrapped simulated distribution of the corresponding moment.

A17

Figure D12 Comparison of Dynamic MPC Estimates to Standard HANK Model
A. Comparison to Card 1 MPC Estimates
80

HANK / Exponential Model: y = C0e−at

Coefficient (Euros)

40

Model
Baseline
Exponential
a=0.87 (0.63)

0

HANK
a=0.06

−40

0

2

4

6

8

10

12

Weeks Since Treatment

B. Comparison to Pooled MPC Estimates
100

HANK / Exponential Model: y = C0e−at

Coefficient (Euros)

50

Model
Baseline
Exponential
a=1.08 (0.34)
HANK
a=0.06
0

0

2

4

6

8

10

12

Weeks Since Treatment

Notes: This figures compare the dynamics of the spending response in our experiment and in the calibrated HANK
model of Kaplan et al. (2018). Panel A draws this comparison using Group 1 participants. The red line reports ourbaseline weekly MPC estimates for Card 1. The green line reports the estimates obtained by fitting an exponential
model such that the MPC t weeks after treatment is given by C0 · e−a·t . Finally, the blue line reports the path of
MPCs according to the calibrated HANK model of Kaplan et al. (2018); while their model is quarterly, we fit by
nonlinear least squares an exponential model of weekly MPCs to match the calibrated quarterly MPCs reported in
Figure 2 of Kaplan et al. (2018), which gives a cumulative MPC out of a $300 transfer of 17%, 25%, and 36% at
13, 26 and 52 weeks respectively. Panel A shows that the estimated decay parameter a is one order of magnitudelarger in our data than in HANK. We reject that the baseline weekly MPC model with Card 1 is the same as the
MPC path from HANK with a p-value of 0.038. In contrast, when comparing our baseline weekly MPC estimatesto our estimated exponential model, we cannot reject the exponential model (p-value = 0.63). Panel B repeats
the analysis using all treatment groups, rather than Group 1 alone. We estimate an even larger decay parameterand reject the HANK model with a p-value close to zero (p-value = 5 · 10−11 ). In contrast, we cannot reject ourestimated exponential model (p-value = 0.38).

A18

Figure D13 Summary of MPCs estimates
Ganong et al. (2020)
Gelman (2020)

Month

Borusyak et al. (2022)
This Paper − All Cards
This Paper − Card 1
This Paper − Card 2
This Paper − Card 3
Kan et al. (2017)

Quarter

Kueng (2018)
Parker et al. (2006)
Parker et al. (2013)

Six
MonthsOrchard et al. (2022)
Fagereng et al (2019)Year

Golosov et al (2021)
−0.1

0.0

0.1

All

Durables

0.2

0.3

0.4
MPC

0.5

0.6

0.7

0.8

0.9

1.0

Product Scope
Strictly non−durables

Strictly non−durables + Semi−durables

Notes: This figure reports the estimates of MPCs in the literature (typically from their baseline specifications),
coded by time horizon and expenditure categories; 95% confidence intervals are also reported.

A19

P(Not use prepaid card & enough money left on prepaid card)

Figure D14 A Simple Test of the Fungibility of Money
Card Group
2
3

0.5

0.4

0.3

0.2

0.1

0.02022-05-02

2022-05-09

2022-05-16
Date

2022-05-23

2022-05-30

Notes: This figure shows the fraction of households that should have used the treatment card but did not, by day
and card type. Specifically, the figure shows the fraction of households that satisfy the following conditions (i) at
the start of the day, they have a higher remaining balance on the treatment card than the realized consumption
expenditure on other cards during the day; (ii) they do not use the treatment card during that day; (iii) they havea nontrivial amount of money left on the treatment card (more than 20 euros); (iv) they have positive consumption
expenditures on that day (that are not auto-pay transactions); (v) they use the treatment card at some point during
the experiment. The results are reported separately for Card 2, which expires after three weeks, and Card 3, which
implements a negative interest rate of approximately 10% on the remaining balance on the treatment card every
Monday at 11:59pm.

A20

P(Not use prepaid card & enough money left on prepaid card)

Figure D15 Fraction of households that should have used the treatment card but did not: narrow
sampleCard Group
2
3

0.5

0.4

0.3

0.2

0.1

0.02022-05-02

2022-05-09

2022-05-16
Date

2022-05-23

2022-05-30

Notes: This figure shows the same result as Figure D14 – the fraction of households that should have used thetreatment card but did not – but only among the population of households that consist of a single adult and nochildren, and conditioning on making consumption expenditures on that day in physical stores only (i.e. not online
or via phone). This is to rule out the possibility that this phenomenon is driven by multi-person households ofwhom only one has access to the treatment card, or by households that are not aware that they could use the card
online.

A21

Consumption increase per euro of stimulus

Figure D16 Effective stimulus, for cards where not all money is spent

100%

50%

0%

−50%
May

Jun

Jul
Cards

2

3

Notes: This figure shows the MPC estimates for cards 2 and 3 (panel A of Figure 4) divided by the fraction of the
300 euro treatment card value that is spent by the average treated household in that group (i.e. that is not returned
through the weekly interest payments in group 3, or that is returned upon expiry in group 2). The resulting number
shows the average consumption stimulus per euro spent by the transferer.

Figure D17 Yield Curve for French bonds, May 2022

Annualized yield, in %

2

1

0

1 month

3 months 6 months 9 months

1 yearTime

2 years

5 years

10 years

30 years

May 2022

Notes: This figure shows the yield curve for French Treasury bonds at the start of our experiment, i.e. in May 2022(source: Bank of France).

A22

Table D1 Summary statistics, weekly consumption spending
N

Mean

SD

p10

p25

p50

p75

p90

Weekly cons. expend. (cash and cards), total

2,571,000

417.66435.0267.30

163.25315.95542.63848.64

Direct debits, debt payments, Subscriptions

2,571,000

198.551718.03

0.00

11.00

81.89

224.30452.71

Outgoing transfers

2,571,000

111.50845.94

0.00

0.00

0.00

0.00

100

Weekly cons. expend. (broad measure), excl. treatment cards

2,571,000

727.63

1992.72133.55269.78498.72848.24

1,337.29

Weekly cons. expend. (cash and cards), excl. treatment cards

2,571,000

417.57434.9967.25

163.19315.88542.53848.50Weekly cash withdrawals

2,571,000

23.74

83.71

0.00

0.00

0.00

0.00

70.00

Notes: The table shows summary statistics on different consumption categories by week. The sample consists ofall household-weeks since January 2022. The broad measure of consumption includes the total of cash withdrawals,
card spending, automatic debits, and wire transfers.

A23

A24
2,153.05

316.24631.291,205.52

0.61

1.53

-30,872.90-2,388.27-33,300.8

64,746.97

5,867.43

16,896.51

4,448.41

19,265.55

0.14

80.18

98.06

300.72

1,630.59

2,109.55

2,654.04

1.15

47.03

Mean

1,736.50

639.881,154.20

658.290.96

0.50

54,288.18

5,194.01

55,007.44

185,159.99

32,466.19

34,466.19

19,976.04

46,067.40

0.35

284.12199.81

691.855,003.78

4,968.86

1,439.56

0.36

12.92

SD

1,001.33

0.00

181.44545.840.00

1.00-96,402.39-7,590.37-99,130.28-43,194.32

0.00

17.30

63.50

121.38

0.00

0.00

0.00

0.00

0.00

493.06

1,317.69

1.00

30.00

p10

1,359.67

4.44

290.02794.550.00

1.00-50,413.24-2,979.42-52,931.94

0

0.00

617.74424.17

1,506.66

0.00

0.00

0.00

0.00

95.65

1,049.91

1,796.14

1.00

36.00

p25

1,823.69

83.33

451.201,102.82

0.00

2.00

0.00

0.00

-5,641.02

1,285.04

0.00

5,462.02

1,006.25

7,599.54

0.00

0.00

0.00

0.00

1,171.51

1,667.95

2,381.15

1.00

46.00

p50

2,484.41

368.72708.47

1,480.65

1.00

2.00

0.00

0.00

0.00

93,451.46

372.91

19,253.96

2,487.53

23,854.85

0.00

0.00

110.9320.00

2,077.47

2,348.71

3,159.71

1.00

58.00

p75

3,446.92

868.071,080.92

1,940.18

2.00

2.00

0.00

0.00

0.00

211,111.53

8,924.360

44,896.89

7,563.32

55,256.41

1.00

242.28298.32

1,464.42

3,053.53

3,259.71

4,217.33

2.00

65.00

p90

Notes: This table report the distributions of the household charactersitics used in our analysis. The variable “Avg. monthly outgoing transfers” includes
direct debits, debt payments, and subscriptions. The variable “Avg. total monthly consumption (broad measure)” includes the sum of cash withdrawals,
card spending, automatic debits, and wire transfers.

85,698.00

Avg. total monthly consumption (broad measure)

85,698.00

Avg. monthly consumption expenditures (cash, card payments), 1 year prior

85,698.00

85,698.00

Number of children in the household

85,698.00

85,698.00

Number of adult members in the household

Avg. monthly outgoing transfers, 1 year prior

85,698.00

Avg. mortgage debt, 6m prior

Avg. monthly direct debits, debt payments, subscriptions, 1year prior

85,698.00
85,698.00

Avg. consumer debt, 6m prior

85,700.00

Avg. net illiquid wealth , 6m prior

Avg. total debt, 6m prior

85,698.00

Avg. value of life insurance assets, 6m prior

Avg. current account balance, 6m prior
85,698.00

85,700.00
85,698.00

Avg. net liquid wealth, 1m prior

Avg. liquid savings, 6m prior

80,034.00
85,685.00

Dummy: has received unemployment benefits within 6m prior

80,034.00

Avg. monthly incoming social allowances, 6m prior

Avg. monthly incoming unemployment benefits, 6m prior

80,034.00

80,034.00

Avg. monthly salaries, social allowance, pensions, benefits, 6m prior

80,034.00

85,685.00

Avg. monthly incoming transfers, 6m prior

Avg. monthly incoming pension payments, 6m prior

85,700.00

Number of eligible household members

Avg. monthly incoming salaries, 6m prior

85,700.00

Age of eligible household member

N

Table D2 Summary statistics, household characteristics

Table D3 Cumulative MPC Differences by Card Type at Longer Horizons
Comparison

Horizon

OLS

FGLS

Difference (euros)(1)

p-value(2)

Difference (euros)(3)

p-value(4)

Card 2 - Card 1

4 weeks
8 weeks
12 weeks

114.92113.50188.22

0.045
0.145
0.158

109.30114.18185.73

0.026
0.142
0.114

Card 2 - Card 3

4 weeks
8 weeks
12 weeks

81.99
98.73
99.81

0.159
0.294
0.477

60.01
56.13
97.90

0.230
0.501
0.423

Card 3 - Card 1

4 weeks
8 weeks
12 weeks

32.92
34.76
88.42

0.538
0.687
0.494

49.30
58.05
87.83

0.279
0.436
0.405

Notes: This table report the differences in cumulative MPCs by card type after one, two and three months. We
report the point estimate and p-values using eithr OLS, in columns (1) and (2), or FGLS, in columns (3) and (4).

A25

Table D4 Examples of MCCs Classified across Product Categories
Description of MCC Product Category
Veterinary Services
Agricultural Co-operatives
Horticultural Services, Landscaping Services
General Contractors-Residential and Commercial
Air Conditioning Contractors , Sales and Installation, etc.
Electrical Contractors
Insulation , Contractors, Masonry, Stonework Contractors, etc.
Carpentry Contractors
Roofing , Contractors, Sheet Metal Work, etc.
Motor vehicle supplies and new parts
Office and Commercial Furniture
Construction Materials, Not Elsewhere Classified
Office, Photographic, Photocopy, and Microfilm Equipment
Computers, Computer Peripheral Equipment, Software
Men’s Women’s and Children’s Uniforms and Commercial Clothing
Commercial Footwear
Home Supply Warehouse Stores
Variety Stores
Misc. General Merchandise
Grocery Stores, Supermarkets
Meat Provisioners , Freezer and Locker
Candy, Nut, and Confectionery Stores
Dairy Products Stores
Bakeries
Misc. Food Stores , Convenience Stores and Specialty Markets

Product Type
S
S
S
S
S
S
S
S
S
D
D
D
D
D
SD
SD
SD
SD
SD
ND
ND
ND
ND
ND
ND

Notes: This table illustrates the classification of product categories, defined by their Merchant Category Code
(MCC), into four groups: services (S), durables (D), semi-durables (SD), and nondurables (ND). This table only
focuses on a subset of products, out of the total of 933 MCC categories in our data.

A26

E

Other Robustness Checks

In this section, we discuss additional empirical results, assessing the robustness of our main results.

E.1

Robustness Checks for Pooled MPC Estimates

We conduct several robustness checks for the pooled MPC estimates.
First, we estimate specification (1) with a different outcome, adding to our consumption measures
the observed savings at the bank in checking accounts and liquid or illiquid savings accounts. Appendix
Figure E1 shows that the cumulative sum of consumption and savings increases by 300 euros immediately
at the start of the experiment and hovers around this value for the following quarters, confirming that wecorrectly measure all flows. Appendix Figure E2 documents the increase in savings in liquid accounts fortreated households, with a cumulative increase of about 100 euros after a month.
Figure E1 The Response of Consumption and Savings

Total flows

750

500

250

0

May

Jun

Jul

Aug

Sep

Confidence interval:

Oct

95%

Nov

Dec

Jan

68%

Notes: In this figure, we run a specification analogous to (1), except that the outcome is the sum of consumption
flows and savings into the checking account and liquid or illiquid savings accounts at the bank. Furthermore, toreduce noise we use a seventh-order polynomial to model the weekly outcome response after treatment: Yit =P
8k−1· τitk−1 + αi + αtE + εit , which we estimate with the same FGLS procedure as in Figure D2. The figure
k=1 βτ
reports the cumulative change in the outcome and both the 95% and 68% confidence intervals, clustered at thehousehold level.

A27

Figure E2 Savings into liquid savings accounts

Cumulative active saving, in euros

200

100

0

May

Jun

Jul

StatusAll Treated
Bootstrap: 200

Notes: This figure analyzes the resposne of savings into liquid savings accounts at the bank (e..g, “Livret A”) for
the treated participants. The figure reports the cumulative net flows of savings after the start of the experiment.

Second, Appendix Figure E3 shows that the results are similar when leads are included in specification(1), with no sign of pre-trends. Third, Appendix Figure E4 documents the characteristics of the households
who chose not to use the treatment card. Fourth, we obtain similar results with alternative consumption
measures including direct debit transactions and wire transfers (Appendix Figure E5).
Figure E3 Total Spending Response, Weekly, with Treatment Leads

Weekly consumption spending, in euros

120

80

40

0

−40
Jan

Feb

Mar

Apr

May

Status

All

Jun

Jul

Aug

Notes: This figure shows the results of a regression estimating a specification analogous to equation 1, but including
pre-treatment leads.

A28

Figure E4 Observable Predictors of Non-Take-Up

Notes: This figure reports the predictors of non-take-up of the treatment card, using the full sample of treatedhouseholds. We use a range of characteristics to predict whether the household never used the prepaid card during
the six months following the experiment. We find that households who do not use the treatment card tend to be
younger, with fewer children, higher liquid wealth, and lower illiquid wealth. Card type does not affect take-up.

Cumulative consumption spending, in euros

Figure E5 Cumulative MPC Estimates with Broader Consumption Measure

200

100

0

−100

May

Jun
StatusJul

Cash & card

Card & cash & transfer & debit

Notes: This figure reports the results from specification (1), with a broader measure of consumption including all
direct debit transactions as well as wire transfers.

Fifth, Appendix Figure E6 shows that the estimates remain very similar with a reweighing scheme toensure that the sample is representative of the French population by local area, income, gender, age, andfamily structure. Note that this analysis also helps address attrition in our sample. Attrition occurs in our
sample because some households do not survive, all household members leave the bank, or because theyno longer use their checking account at the bank. Starting from the households included in the panel inJune 2020, attrition amounts to 5.7% of households by March 2023. Predicting attrition using observablecharacteristics, we find that the most significant predictors are age, household size, and income. Our
A29reweighting analysis in Figure E6 accounts for these compositional changes, leaving the estimated MPC
unchanged in practice.
Sixth, Appendix Figure E7 reports the results without winsorizing consumption expenditures, which
again yields very similar estimates. Finally, Appendix Figure E8 shows that the confidence intervals are
virtually identical when obtained via bootstrapping.
Figure E6 MPC Estimates for Reweighted Sample
A. Weekly MPC

B. Cumulative MPC since treatment onset
200
Cumulative consumption spending, in euros

Weekly consumption spending, in euros

100

50

0

150

100

50

0

−50

−50
May

Jun
Status

Our sample

Jul

May

French population reweighting

Jun
Status

Our sample

Jul
French population reweighting

Notes: This figure reports the results from specification (1) in a weighted OLS regression such that our sample isrepresentative of the French population by local area (“”), income decile, age, gender and family structure. The
population weights are obtained from the French statistical institute INSEE.

Figure E7 MPC Estimates without Winsorization
A. Weekly MPC

B. Cumulative MPC since treatment onset
Cumulative consumption spending, in euros

Weekly consumption spending, in euros

100

50

0

100

0

−50
May

June
StatusJuly

May

99th percentile
No winsorization

June
StatusJuly
99th percentile
No winsorization

Notes: This figure reports the results from specification (1), comparing the results in our main sample (winsorizing
consumption expenditures at the 99th percentile) and without winsorization.

A30

Figure E8 Bootstrapped confidence intervals for pooled MPC estimates
A. Weekly MPC

B. Cumulative MPC since treatment onset

40%

Weekly MPC, in %Cumulative MPC, in %

20%

0%

20%

0%

−20%
Jun

Jul
StatusJun

Jul
Statusall

all

Notes: This figure reports our main MPC estimates, with confidence intervals estimated by a bootstrap with 300
draws. Panel A reports the weekly estimates, while panel B depicts the cumulative effects.

E.2

Robustness Checks for MPC Estimates by Card TypeWe now conduct robustness check for MPC estimates by card type.
Appendix Figure E9 reports long-term MPC dynamics by card type over three quarters. We find thatthe cumulative MPC remains higher at longer horizons for Cards 2 and 3, compared to Card 1. Next,
Appendix Figure E10 reports cumulative spending on prepaid cards. In the short run, participants inGroups 2 and 3 spend down the prepaid card much faster than those in Group 1. But after three months,
the total cumulative spending is approximately the same across the three card types. Thus, Group 1
participants do not have a lower overall MPC simply because they do not spend down the prepaid card.
Rather, the substitution patterns differ depending on the card: Group 1 participants spend down about
85% of the prepaid card after three months but primarily cover expenses that they would have incurred
otherwise as well.

A31

Figure E9 Long-term MPC Estimates by Card Type

Cumulative MPC

A. Group 1, no restrictions on treatment card
1400
1300
1200
1100
1000
900
800
700
600
500
400
300
200
100
0
−100
−200
−300
−400
−500
−600
−700
May

Jun

Jul

Aug

Sep

Oct

Confidence interval card 1 :

Nov

95%

Dec

Jan

Feb

68%

Cumulative MPC

B. Group 2, expiration after three weeks
1400
1300
1200
1100
1000
900
800
700
600
500
400
300
200
100
0
−100
−200
−300
−400
−500
−600
−700
May

Jun

Jul

Aug

Sep

Oct

Confidence interval card 2 :

Nov

95%

Dec

Jan

Feb

68%

Cumulative MPC

C. Group 3, negative rates every week
1400
1300
1200
1100
1000
900
800
700
600
500
400
300
200
100
0
−100
−200
−300
−400
−500
−600
−700
May

Jun

Jul

Aug

Sep

Oct

Confidence interval card 3 :

Nov

95%

Dec

Jan

Feb

68%

Notes: This figure plots the cumulative MPC by card type over a long horizon. P
To reduce noise we use a seventh8
order polynomial to model the weekly outcome response after treatment: Yit = k=1 βτk−1 · τitk−1 + αi + αtE + εit ,which we estimate with the same FGLS procedure as in Figure D2. The figure reports the cumulative change inthe outcome and both the 95% and 68% confidence intervals, clustered at the household level.

A32

Figure E10 Cumulative Spending on the Prepaid Card by Card Type

Cumulative spending on prepaid card, in %

100%

75%

50%

25%

0%
May

Jun

Jul

Card Type1

2

3

Notes: This figure reports average cumulative spending on the preaid card for the three types of card. The figure
shows that households in Groups 2 and 3 lost 49.25 euros on average by not spending down the available funds by
the deadlines. 8.75% of households in these groups did not take up the card, accounting for a loss of 26.25 euros.
Conditional on using the card at least once, the median participant in Groups 2 and 3 lost only 3 euros. However, asmall number of households used the card very little before the deadlines: 5% of households lost at least 126 euros.
On average, conditional on using the cards participants lost 23 euros (7.67% of the total amount). Thus, the losses
on Cards 2 and 3 were not driven by widespread card usage frictions (which could have made it difficult for mosthouseholds to spend down the cards before the deadlines), but rather by a limited set of households who decided
not to use the cards at all or to use them very little.

Appendix Figure E11 documents that socio-demographic characteristics are not significant predictors
to identify the subset of households from Group 1 who did not use the card by July 1st, nor the subsetof households from Groups 2 and 3 who lost significant funds. Finally, Appendix Figures E12 and E13
show that the confidence intervals are very similar when obtained via bootstrapping.

A33

Figure E11 Characteristics of Households with Low Take-Up by Card Type
A. Group 1, no restrictions on treatment card
Unemployed

Revenue

Overdraft

Male

Liquid Wealth

Illiquid Wealth

Consumption

Age# Eligible# Children# Adult
−10

−5

0

5

Regresion Coefficients, %B. Group 2, expiration after three weeks
Unemployed

Revenue

Overdraft

Male

Liquid Wealth

Illiquid Wealth

Consumption

Age# Eligible# Children# Adult
−10

−5

0

5

10

Regresion Coefficients, %C. Group 3, negative rates every week
Unemployed

Revenue

Overdraft

Male

Liquid Wealth

Illiquid Wealth

Consumption

Age# Eligible# Children# Adult
−10

−5

0

5

10

Regresion Coefficients, %Notes: This figures analyzes the socio-demographic characteristics of Group 1 participants who did not use the cardby July 1st (panel A), and those of Group 2 and 3 participants who lost at least 50 Euros (panels B and C).

A34

Figure E12 Bootstrapped confidence intervals for MPC by Card Type, Weekly
A. Group 1, no restrictions on treatment card

B. Group 2, expiration after three weeks

80

Weekly consumption spending, in euros

Weekly consumption spending, in euros

100

40

0

50

0

−40

−50
Jun

Jul
StatusJun

Jul
StatusCard 1

Card 2

Weekly consumption spending, in euros

C. Group 3, negative rates every week

100

0

Jun

Jul
StatusCard 3

Notes: This figure reports MPC estimates depending on the card type. Panel A reports the weekly estimates forGroup 1, panel B for Group 2, and panel C for Group 3. Card 1 has no restrictions, while Card 2 expires three
weeks after the onset of the experiment, and Card 3 applies a negative interest rate on the remaining balance every
Monday at 11:59pm. 95% confidence intervals are reported, obtained from a bootstrap with 300 draws.

A35

Figure E13 Bootstrapped confidence intervals for Cumulative MPC Estimates by Treatment GroupA. Unconditional estimates

B. Conditional on take-up
100%

80%

60%

Cumulative MPC, in %Cumulative MPC, in %

80%

40%

60%

40%

20%
20%

0%

0%
09−May16−May23−MayCard Type1230−May09−May16−May23−MayCard Type31

230−May3Notes: This figure reports cumulative MPC estimates depending on the card type. Card 1 has no restrictions, while
Card 2 expires three weeks after the onset of the experiment, and Card 3 applies a negative interest rate on theremaining balance every Monday at 11:59pm. Panel A includes treated households that do not use the card in thetreatment groups; panel B does not. 95% confidence intervals are reported, obtained from a bootstrap with 300
draws.

We also present additional results regarding the composition of spending by card type. Appendix
Figure E14 shows the MPCs on these categories in the months following treatment. Appendix Figure
E15 shows the response of durables over a longer time horizon for each card type, highlighting that thehigher spending on durables for Card 3 is sustained in the following quarters.

A36

Figure E14 MPC by Spending Category
A. MPC on durables

B. MPC on semi-durables
Cumulative consumption spending, in euros

Cumulative consumption spending, in euros

150
100

50

0

100

50

0

−50

−50
May

Jun
Card Type

Jul
1

2

May

3

Card Type

50

0

Jun
Card Type

Jul
1

2

Jul
1

2

3

D. MPC on services
Cumulative consumption spending, in euros

Cumulative consumption spending, in euros

C. MPC on non-durables

May

Jun

100

0

−100

May

3

Jun
Card Type

Jul
1

2

3

Notes: This figure reports MPCs by spending category and card type.

As complementary evidence on the role played by various types of expenditure, we build an alternativeclassification of products allocating the semi-durables and services categories either into durables or
nondurables. The results are reported in Appendix Figure E15 for all products and Appendix Figure
E16 by card type. We find a sustained increase in spending for both types of products, for the threetreatment cards. Thus, the differences in the estimated marginal spending increase across groups do notarise merely from differences in durables purchasing behavior.

A37

Figure E15 MPC Estimates for Durables and Non-durables, Alternative Classification
A. Durables

B. Non-durables
30%

Cumulative MPC, in %Cumulative MPC, in %

40%

20%

20%

10%

0%
0%
Jun

Jul

Confidence interval:

95%

Jun

68%

Jul

Confidence interval:

95%

68%

Notes: This figure reports the cumulative MPC estimates for spending on durables (panel A) and non-durables(panel B), considering all cards together. In this figure, we classify all types of spending into either durable ornondurable purchases, instead of retaining the distinction between services, durable goods, nondurable goods, andsemi-durable goods as in Table II.
P8To reduce noise we use a seventh-order polynomial to model the weekly outcome
response after treatment: Yit = k=1 βτk−1 ·τitk−1 +αi +αtE +εit , which we estimate with the same FGLS procedure
as in Figure D2. The figure reports the cumulative change in the outcome and the 95% confidence intervals, clusteredat the household level.

Figure E16 MPC Estimates for Durables and Non-durables, Alternative Classification
A. Durables

B. Non-durables
60%

75%

Cumulative MPC, in %Cumulative MPC, in %

40%

50%

25%

20%

0%

−20%
0%
May

Jun
Cards FGLS

Jul
1

2

May

3

Jun
Cards FGLS

Jul
1

2

3

Notes: This figure reports the cumulative MPC estimates for spending on durables (panel A) and non-durables(panel B), by card type. In this figure, we classify all types of spending into either durable or nondurable purchases,
instead of retaining the distinction between services, durable goods, nondurable goods, and semi-durable goods
as in Table II. To reduce noise, we estimate the specification separately for each card type with the same FGLS
procedure as in Figure D2. The figure reports the cumulative change in the outcome and the 95% confidence
intervals, clustered at the household level.

E.3

Robustness Checks for the Estimates of Heterogeneity in MPCs by Observables

We now report complementary analyses of the heterogeneity in MPCs by observable characteristics.
First, we consider an alternative definition of liquidity. In Appendix Figure E17, we take as ourmeasure of a household’s liquid wealth the minimum level of liquidity attained on any day in April 2022
(for a vast majority of households, this occurs within the last five days of the month, i.e. likely rightA38

before payday). With this measure, a household is considered to live “hand to mouth” if they ran down
their account to low levels of liquidity at any point in April 2022. Repeating the heterogeneity analysis
with this alternative measure, we obtain results similar to our baseline estimates for quartiles 2, 3, and 4.
However, the 4-week cumulative MPC is now lowest for the bottom liquidity quartile, rather than highest
as in our baseline specification. This result confirms that high average MPCs do no appear to be driven
by a group of low-liquidity households.
Second, we provide complementary results for MPC differences by gender. Appendix Figure E18 showsthat the higher MPC for women is also observed in the subsample of households with a single member,rejecting the hypothesis that the allocation of shopping duties in the households could be the main driverof the MPC differences by gender. Appendix Figure E19 reports differences in spending composition bygender, suggesting than women spend more on food at home and clothing after receiving the prepaid
card – however, these differences are not statistically significant and are too small to drive the differencein overall MPCs by gender. Developing and testing a theory of MPC differences by gender would be a
fruitful direction for future research.
Third, Appendix Figure E20 shows that the results for each of the six dimensions of heterogeneity
we study remain similar when using a FGLS estimator to reduce noise, reporting the results over longer
horizons.
Fourth, we analyze the statistical significance of the difference in 4-week cumulative MPCs by observables. For each of observable predictors, using quartiles as in the main text, we test the null of equalityof the 4-week cumulative MPCs. The p-values of the F-tests are reported in Column (1) Table 4.1. The
table shows that these differences are noisy, with p-values ranging from 0.124 for gender to 0.453 for liquid assets. To reduce noise, we regress consumption on a linear function of the quartiles. The regression
coefficients are reported in Column (2) of Table 4.1, with the p-values in Colunm (3). Illiquid assets andpast consumption (our proxy for permanent income) are significant at the 10% level.
Finally, we conduct complementary analyses for the LASSO estimates. In Appendix Figure E21, we
document that results are similar when including only treatment group 1 and the control group. In Appendix Figure E22, we repeat the analysis at a 12-week horizon to assess policymakers’ ability to target
households with high long-term MPCs based on observable characteristics. With the optimal regularization parameter set by cross-validation, only gender is selected as a significant predictor of long-term MPC
heterogeneity. Applying the same LASSO methodology by interacting household characteristics with thetype of prepaid card, we examined whether the differences in consumption response between Card 1 andCard 2 were driven by a specific subset of households; we did not find significant differences by household
characteristics.

A39

Figure E17 Heterogeneity Analysis with Alternative Definition of Liquid Wealth80%

Cumulative MPC, in %

60%

40%

20%

0%

09−May16−MayLowest liquidity level before treatment

23−May1234Notes: This figure reports MPC estimates depending on households’ liquid wealth. Quartiles of household’s liquid
wealth are defined using the minimum level of liquidity attained on any day in April 2022. The figure plots theestimates for the cumulative MPC at different time horizons.

Figure E18 Heterogeneity by Gender for Single-Member Households

Cumulative MPC, in %

75%

50%

25%

0%
09−May16−MayGenderF

23−MayM

Notes: This figure shows the cumulative MPC by gender, using regressions where treatment and control households
are restricted to the subset of households with one adult member and no children.

A40

Figure E19 Spending Composition by Gender
Panel A: Prepaid card alone, spending shares
Transport
TobaccoRecreation, culture
Miscellaneous
Housing, energy
Household Equipment

GenderHotelsFemaleHealthMale

Food away from home
Food at home
Education
Communications
Clothing
Alcohol
0%

10%

20%

30%

Percentage

Panel B: Bank account spending and prepaid card, differences relative to the control group
Transport
TobaccoRecreation, culture
Miscellaneous
Housing, energy
Household Equipment

GenderHotelsFemaleHealthMale

Food away from home
Food at home
Education
Communications
Clothing
Alcohol
−10%

0%

10%

Percentage

Notes: Panel A shows the spending shares by gender for the prepaid card alone. Panel B shows differences inspending shares by gender for the treated households compared to control households when considering both the
prepaid card and the household’s bank account

A41

Figure E20 MPC Heterogeneity by Observable Household Characteristics
A. By Net Liquid Assets Quartile

B. By Illiquid Wealth Quartile
Cumulative consumption spending, in euros

Cumulative consumption spending, in euros

400

200

0

−200

400

200

0

−200
May

Jun

Jul

Net liquid wealth quartile last month FGLS

1

May

2

3

4

Jun

Jul

Average illiquid wealth quartiles FGLS

C. By Average Consumption Quartile

1

2

3

4

D. By Income Quartile
Cumulative consumption spending, in euros

Cumulative consumption spending, in euros

400

250

0

−250

200

0

−200

May

Jun

Jul

Consumption Level Quartiles FGLS

1

2

May
3

4

Jun
Revenue Quartiles FGLS

E. By Age Quartile

Jul
1

2

3

4

F. By Gender
Cumulative consumption spending, in euros

Cumulative consumption spending, in euros

300
300

200

100

0

−100

May

Jun
Age Quartile FGLS

Jul
1

2

3

200

100

0

May

4

Jun
Gender FGLS

Jul
F

M

Notes: This figure reports MPC estimates depending on observable household characteristics using a feasible
generalized least square (FGLS) procedure, where standard errors of each household’s error term are parameterized
to be able to vary with each bin of time-invariant characteristics calculated from pre-period data (10 age bins,
10 income bins, gender dummy, 10 liquid wealth bins, 10 average consumption expenditure bins, 95 departement
dummies), i.e. in each iteration we calculate weights from 1/σ̂i2 , where σ̂i is the predicted standard error froma regression of the household-level standard error in the previous iteration on characteristic bin dummies. We
document heterogeneity in turn by net liquid wealth, illiquid wealth, average consumption prior to the experiment(as a proxy for permanent income), income, age, and gender and marital status. 95% confidence intervals, withstandard errors clustered at the household level, are reported in all panels.

A42

Figure E22 LASSO Estimates of 12-week MPC Heterogeneity

Notes: The figure shows LASSO estimates of coefficients of interactions of the respective characteristic with atreatment dummy in specification (2), for varying regularization parameters (horizontal axis). We predict the
cumulative MPC after twelve weeks. The dashed vertical line shows the regularization parameter chosen by 5-foldcross validation.

Figure E21 LASSO estimates of treatment effect heterogeneity coefficients, group 1 and control group

Notes: This figure shows estimates of specification (2) on the set of observations pertaining to treatment group 1and control observations, for varying levels of the regularization parameter.

A43

Table E1 Statistical Significance Tests of Differences in 4-Week Cumulative MPCs by Observables
p-value of F-test for

Liquid Assets
Illiquid Asset
Consumption
IncomeAge
GenderLinear Specification in Quartiles

4-week Cumulative MPC

OLS coeff.

p-value

(1)

(2)

(3)

0.453
0.244
0.322
0.39
0.62
0.124

-26.99-32.43-38.89-31.66
19.02

0.209
0.09
0.082
0.148
0.349
N/A

Notes: This table report tests to assess whether there is a statistically significant difference in 4-week cumulative
MPCs. We the null of equality of the 4-week cumulative MPCs in Column (1), reporting the p-values of the F-tests.
We also run a regression using a linear function of the quartiles as predictor, reporting the OLS coefficient in Column(2) and the p-value in Column (3).

E.4

Robustness Checks for the Estimates of the Unconditional Heterogeneity in
MPCs

We carry our several robustness checks to assess the sensitivity of our estimates of the unconditional
heterogeneity in MPCs.
First, we estimate a model that is linear in log consumption. A disadvantage of such a model isthat the treatment effect distribution estimates cannot be directly interpreted as MPCs, but instead as
cumulative percentage deviations from the household’s average level of consumption. The results arereported in Appendix Figure E23 and lead to a shape of treatment effect distributions similar to ourbaseline analysis.
Second, Appendix Figure E24 shows results for specifications where we drop non-negativity constraints
and regularization, yielding similar findings. Third, Appendix Figure E25 reports the results of thedeconvolution by pooling together treatment cards 2 and 3, obtaining more precise estimates that confirm
that the cards with negative rates yield MPCs that are higher than those associated with treatment
card 1. Finally, consistent with the large MPC heterogeneity uncovered by our deconvolution approach,Appendix Figure E26 plots the quantiles of spending on the treatment card and shows that there is a lotof heterogeneity in the speed at which households spend these funds.

A44

Figure E23 Quantiles of the 4-week cumulative percentage deviation from mean household consumption
expenditure
140%

120%
99 %

100%

82 %

79 %

80%

60%

57 %

55 %

50 %

40%

20%

14 %

17 %

13 %
6%

3%
0%

0%
0%

32 %

32 %

32 %

10%

25%

50%

75%

90%

Quantile
Treatment group

Card 1

Card 2

Card 3
Bootstraps : 150

Notes: This figure reports the quantiles of the distribution of 4-week treatment effects by treatment group. In
contrast to the model from the baseline specification, the log of weekly consumption expenditure is here linear intreatment effects and fixed effects. Specifically, we estimate a specification in log weekly average consumption:log Yit =T̃Xβτ 1(τ weeks since i treated)it + αi + αtE + εit

τ =0

T̃
Cit
=

T̃
X

(log Yit − α̂i − α̂tE ).

τ =0

We estimate the distribution of treatment effects in this model using the same deconvolution approach as in themain text. Since the dependent variable, log consumption expenditure, is much less skewed than in the baselinemodel from Section 4.2, we winsorize it only at the 99th percentile. Note that here the treatment effect is not a
marginal propensity to consume, but a cumulative percentage deviation from the household’s mean consumption
expenditure level (on average 417 euros). The estimates from this model show similar economic effects to thebenchmark specification. Shaded regions are delineated by the 10th and 90th percent quantile of the bootstrapped
simulated distribution of the corresponding moment.

A45

Figure E24 Estimated distribution of MPCs without constraint to have no mass on negative values
140%
118 %

120%
103 %

96 %

100%
83 %
78 %

MPC

80%

71 %
60 %

60%

55 %

40%

33 %

31 %

20%

14
12 %
%

0%

−7 %

−20%
0%

53 %

12 %

10%

25%

50%

75%

90%

100%

Quantile
Treatment group

Card 1

Card 2

Card 3
Bootstraps : 150

Notes: The figure shows the estimated distributions of 4-week MPCs using the flexible deconvolution procedure of
Yang et al. (2020) when the support of the density of the distribution is not constrained to lie on the positive partof the real line.

Figure E25 MPC Distribution, Group 1 vs Groups 2 and 3 combined
140%

120%
110 %

MPC

100%

92 %

80%
67 %

66 %

60%
48 %
37 %

40%

28 %

20%

15 %

13 %

4%

0%
0%

10%

25%

50%

75%

90%

100%

Quantile
Treatment group

Card 1

Card 2 & 3
Bootstraps : 150

Notes: The figure shows the quantiles of the estimated distribution of MPCs, when the estimation is performed
separately for treatment group 1 and for treatment groups 2 and 3 (jointly). Standard errors are estimated using
a bootstrap with 150 draws.

A46

Figure E26 Distribution of cumulative spending on treatment card, across households

Cumulative gift card spending, in euros

300

250

200

150

100

50

0
May

Jun
Percentiles:

Jul
25th

50th

75th

Notes: The figure shows moments of the distribution of cumulative expenditures on the treatment card, for each
week.

A47

F

A Stylized ModelIn this appendix, we present a simple model to make predictions that qualitatively match our main
empirical results.
Overview.

The model relies on three key ingredients: (i) mental accounts; (ii) search costs; (iii) memory(i.e., certain agents can make purchases without incurring search costs). In our model, spending the
prepaid card on “windfall consumption” involves a key tradeoff: (1) it delivers a utility boost λ becauseof mental accounts; but (2) it requires incurring search costs to find suitable windfall purchases, except
for some agents who remember “windfall purchase opportunities”.
We summarize below the three key results we obtain in the model, thanks to the three key ingredients:• For Group 1 participants, the spending response is concentrated in the short run.
– Key channel: for Group 1 participants who remember suitable “windfall purchase opportunities”, it is optimal to purchase immediately.
• For Group 2 participants, the spending response is larger than for Group 1.
– Key channel: while Group 1 participants smooth search costs across a large number of periods,
Group 2 participants search for and buy more windfall consumption goods and services inperiod 0 using the prepaid card, in order spend it down before it expires in period 1.
• For Group 3 participants, the spending response lies in between Group 1 and Group 2.
– Key channel: the search costs are higher for Group 3 participants, leading them to prefer tospend relatively more on regular consumption (compared to Group 2) rather than incurring
very high search costs for windfall consumption goods and services in period 0.
Note that the model below produces these results with a common “mental account” parameter for all threegroups – rather than assuming different types of mental accounts for each card, which would be mechanical.
Although the simple model below makes predictions that qualitatively match the main patterns in ourdata, it is not meant to provide a quantitative match of the estimated marginal propensities to consume.
Setting.

Agents in the model receive a prepaid card and optimize consumption at an infinite horizon.

There are three treatment groups, motivated by our experiment. Group 1 participants have access to theremaining balance on the prepaid card for T + 1 periods. In contrast, Groups 2 and 3 both lose access to
the remaining balance on the card after the initial period.3
Preferences. The agent optimizes consumption over an infinite horizon with two goods, general consumption ct and “windfall consumption” gt . The utility function is:U=∞X

β t [λt · v(gt , st ) + u(ct ) − ψ(st )] ,t=03
In our experiment, Group 3 has a high negative interest rate, which we could model as well. However, for simplicity wecan model Group 3 by varying the search cost parameter, as discussed below.

A48

where st denotes search costs that help increase the marginal utility of windfall consumption, while λt is amarginal utility shifter for windfall consumption. st captures the idea that agents must incur calculation
costs to find windfall consumption goods and services that suit their tastes (in the spirit of Evans andRamey (1992) and Orchard et al. (2023b)); the convexity of costs is akin to Ellison and Wolitzky (2012).
The parameter λt captures the idea that utility for specific windfall goods and services may shift
because of mental accounting (in the spirit of Shefrin and Thaler (1988), Thaler (1990), and Baugh etal. (2021)). Specifically, we assume that the households who receive a prepaid card in our experimentperceive it as a windfall, akin to a gift, and that they incur a utility boost if they spend this windfall on
unplanned “windfall consumption” (e.g., going to a fancy restaurant, going out more frequently than usual,purchasing a durable good earlier than they otherwise would have, purchasing a treat, etc.) rather than on
regular consumption.4 To capture the idea that the marginal utility of spending on windfall consumption
goods and services is larger when spending from the prepaid card, we use a simple functional form:
λ0 = λ · 1{pg g0 =G0 −G1 >0} ,with λ > 0, i.e. marginal utility is positive when the agent buys a positive amount of treats using the
prepaid card, while it is null otherwise. Gt denotes the amount available on the prepaid card at timet, equal to 300 euros in our experiment. Note that in the functional form for λ0 , the budget constraint
is intertwined with the utility function. This approach is standard in models of mental accounts, goingback to Shefrin and Thaler (1988). In this way, the utility derived from a purchase differs depending on
the income source used to make the purchase, which is the very idea of a “mental account.” Our chosen
functional form simply means that the marginal utility of purchasing windfall consumption goods andservices is positive only when spending down the prepaid card to purchase these products.
For subsequent periods, the functional form is the same for Group 1, i.e. λt = λ1{pg gt =Gt −Gt+1 >0} .
We set λt = 0 for t ≥ 1 for Groups 2 and 3, because these participants lose the remaining balance on the
prepaid card after the initial period.
We make additional simple parametric assumptions to obtain closed-form solutions:ψ(st ) =κ η
s , η > 1,ηu(c) = log(c),v(gt , st ) = min(gt , st + eit ),where eit denotes an individual-specific “endowment” of ideas about which windfall consumption goods
and services to purchase. The functional form for v(gt , st ) captures the idea that to enjoy windfall
consumption the agent needs to purchase gt units of windfall consumption but also to incur search costs
st , or leverage their search endowment eit . We set ei0 = e0 > 0 for a fraction of agents, i.e. theseagents know which windfall consumption goods and services to purchase – as if they remembered past
4

This assumption is a line with the economics and sociology literature on the non-fungibility of money. To illustrate
our assumption, consider a different context: our assumption means that a households receiving money for Christmas or abirthday will disproportionately spend them on windfall consumption goods and services (rather than regular consumption,e.g. laundry supplies).

A49

opportunities to consume such goods and services. These agents can purchase up to e0 < G units ofwindfall consumption without the need to incur search costs. The endowment is set to zero for otheragents.5
Furthermore, we assume that search costs are larger for Group 3, which we will study below withcomparative statics on κ. This is motivated by the fact that, in our experiment, Group 3 participants
faced a large negative interest rate after a week only: search costs can be seen as particularly costly forthis group given the limited time available.
Thus, spending the prepaid card on windfall consumption involves a key tradeoff in the model: (i)it delivers a utility boost λ; but (ii) it requires incurring search costs. To obtain simple closed-form
solutions, we study the case of quadratic search costs, i.e. η = 2.
Budget constraint. The household faces a stream of per-period income z growing at rate g. The
amount available on the prepaid card is denoted G. The budget constraint is:

∞ 
X
1+g t
t=0

1+r

z+G=

∞
X

∞
X
1
c
+
pg · gt ,t(1 + r)tt=0
t=0using the price of general consumption as the numeraire and denoting the interest rate by r.6 Note thatthe interest rate does not apply to future period windfall consumption, because in equilibrium the agent
purchases treats with the prepaid card, where interests do not accrue.
1and g < r so that the equilibrium is well-behaved.
We make the standard assumptions β = 1+r

Equilibrium.

To solve the consumption problem, we first consider the standard problem without aprepaid card, setting G = 0. In this case, utility maximization yields the standard result that it is
optimal to equate consumption in each period:c∗t = r ·

z
∀t,
r−g

i.e. the agent consumes the annuity value of their total income stream in each period.
Group 1 participants. We now consider participants with a prepaid card expiring after T + 1 periods.
We first discuss some parameter restrictions so that we can focus on an equilibrium in which the agent
finds it optimal to spend the entire balance available on the prepaid card, G, on windfall consumption
across the T + 1 periods, and nothing on regular consumption. This equilibrium is sustained if, in eachperiod until T , the marginal utility of spending on windfall consumption – net of search costs and scaledby the price of windfall consumption – is above the marginal utility of regular consumption in that period,
equal to u′ (c∗t ) = 1/c∗t . Algebra yields that this is satisfied if
λ − κs∗0
r−g
>
,
pG
r·z
5

(A1)

In equilibrium, the endowment is depleted in the initial period as we discuss below, i.e. eit = 0 for all i and t ≥ 1.
Note that, in principle, agents in Groups 2 and 3 could lose some of the prepaid card balance G due to the expiration date.
However, in our model, by utility maximization agents never lose money and always spend it either on windfall consumption
or regular consumption.
6

A50

where s∗0 is defined below in terms of exogenous parameters. We assume that this condition holds, whichis guaranteed when λ is large enough.
Next, we consider an interior solution for search costs, i.e. the agent will decide to spend the entire
prepaid card balance on windfall consumption but will not do it at once in order to smooth the searchcosts across all T + 1 periods. For Group 1 participants endowed with e0 > 0, it is optimal to buy at least
g0 units of windfall consumption at no search cost: it would be suboptimal to wait until later periods
to spend the endowment, since later periods are discounted at rate β and the prepaid card yields nointerest rate. In addition, the agent exerts some search effort to buy additional windfall consumption.
Considering an interior solution for search effort and windfall consumption spending in all periods up to
T , the first-order conditions yield:β(λ − κst+1 ) = λ − κst ∀t < T − 1.
Since the agents purchase windfall consumption with the prepaid card only, we have the budget constraint:
TX
G− e0 =stpG
t=0

From this we obtain:
1 − 1/β
G
− e0
+ν
pG
1 − 1/β T +1
λ (1 − β)1∀t ∈ [1, T ]s∗t+1 = s∗t −
β
κ β
s∗0 =

T

T +1

2

T

1−1/β
(1−1/β)(T /β)−1/β (1−1/β )with ν = λκ (1−β).
β T 1−1/β T +1 + β(1−1/β T +1 )(1−1/β)This yields the optimal allocations:g0∗ = ei0 + s∗0 ,gt∗ = s∗t ∀t ∈ [1, T ],Note that g0∗ > gt∗ ∀t ∈ [1, T ], especially for households endowed with e0 > 0. This establishes our
first key result: for Group 1 participant, the extra spending is concentrated in the short run. Intuitively,
households who remember “windfall purchase opportunities” buy them immediately, at no search cost.
They then smooth the search costs over time.7
Group 2 participants. For Group 2 participants, the problem is the same as above except that λt =0 ∀t > 0. The agent now exerts optimal search effort s∗0 in period 0 to take advantage of the factthat the marginal utility of spending on windfall goods and services is larger, through λ, in this periodalone. The agent thus buys ei0 + s∗0 windfall consumption goods and services at price pg and spends
the remainder on regular consumption, with perfect consumption smoothing over time (i.e., consuming
7
Note that in this tractable version of the model, with parameter restrictions such that the card is entirely spent on
windfall consumption, the marginal propensity to consume out of the prepaid card is 100 % over T periods. To be in linewith our empirical findings of a modest MPC concentrated in the short run for Group 1 participants, we can set T → ∞ toobtain a small cumulative MPC over time, with a burst of spending in the initial period.

A51

r
∗
1+r · [G − pg (ei0 + s0 )] every period). We assume that the optimum satisfies an interior solution, i.e. theagents exerts search effort up to the point where the marginal utility of getting more windfall consumption
equates the marginal utility of spending on regular consumption in the initial period:
λ − κs∗0= u′ (c∗0 )
pg
=

(A2)
1

z
r
r · r−g+ 1+r· [G − pg (ei0 + s∗0 )]This characterizes the optimal choice of search effort s0 , and thus of windfall purchases g0 ; optimal
8
choices can be found by solving the quadratic formula: A + Bs∗0 + Cs∗2
0 = 0.

To compare the consumption response of Group 2 to Group 1, note that when G is small relative tozlifetime income r−g, as in the data, the right-hand side of equation (A2) remains essentially unchanged

regardless of the choice of s∗0 . Group 2 now equates the marginal utility of spending on windfall consumption (net of search costs) to the marginal utility of regular consumption, while in the case of Group 1 themarginal utility of spending on windfall goods and services remains larger, per equation (A1). Indeed,Group 1 agents are able to smooth the search costs over many periods. Instead, Group 2 agents searchmore and buy more windfall consumption in the initial period. We thus obtain our second key result:Group 2 participants have a larger increase in spending than Group 1 participants in the short run.
Group 3 participants. For Group 3 participants, the optimal allocation is also given by the equation(A2), but with the higher value of κ that characterizes Group 3. We can directly infer from equation (A2)that the equilibrium levels of search and spending on windfall goods and services fall with higher searchz
costs κ (again noting that G is small relative to lifetime income r−gon the right-hand side). Per thecomparison of equation (A2) to equation (A1), the spending of Group 3 remains larger than the spendingof Group 1 in the initial period. This establishes our third key result: the extra spending of Group 3 falls
between that of Group 1 and Group 2.
Additional prediction. The model above highlights that Group 1 participants who spend early on after
receiving the prepaid card should have a large MPC. In the model, these agents are endowed with e0 > 0
and are able to buy windfall consumption immediately at no search cost, while other agents smoothsearch costs over time and experience no spending burst upon receiving the card. Taking this prediction
to the data, we analyze the sub-sample of Group 1 participants who spent the prepaid card within thefirst three weeks. Consistent with the prediction, we estimate a large MPC in this sub-sample of Group
1 participants: their MPC is close to that of Group 2 participants, as reported in Appendix Figure F1.
This finding provides additional evidence about the channel whereby the expiry date can act as a spur tomake purchases for Group 2 participants, which in our model requires incurring higher search costs thatGroup 1 participants prefer to avoid.
8

The parameters are as follows:


λ
z
r
r·
+
(G − pg ei,0 ) − 1,
pg
r−g
1+r


r
κ
z
r
B = −λ−r·+(G − pg e0 ) ,
1+r
pg
r−g
1+r
r
C=
κ.
1+r
A=

A52

Figure F1 Testing an Auxiliary Prediction of the Simple Model

Cumulative consumption spending, in euros

300

200

100

0

May−05May−12
StatusMay−19Card 1, value spent on prepaid > 275 within 3 weeks
Card 1, value spent on prepaid <= 275 within 3 weeks

May−26
Card 2

Notes: Motivated by the auxiliary prediction of the simple model in Appendix F, this figure reports the cumulative
MPC for three groups of participants: all participants in Group 2, participants in Group 1 who used the prepaid
card to make purchases of a total value of more than 275 euros in the first three weeks of the experiment, and otherGroup 1 participants who did not spend down the prepaid card as quickly.

Extension: time-varying salience. Note that the salience effects above are only tied to the prepaid
card. An alternative modeling approach could assume that λt falls over time, i.e. the reference point forsalience is not just the card but also the time of receipt. This assumption would also yield a spending
response concentrated in the short run, without the need for the assumption that agents have a “search
endowment”.

G

Power Calculations based on Estimated Effect Sizes

To guide the design of future experiments, we conduct power calculations that we calibrate with effectsizes obtained from the point estimates in our experiment. The first set of simulations estimates thenumber of observations required to find, with a certain probability, statistically significant differences
between treatment groups average MPCs. A second set of simulations shows the distribution of standard
errors that one can expect on average MPCs.

G.1

Power for Detecting Differences in Average MPCs across Treatment Groups

We first investigate the statistical power to detect differences in average MPCs across treatment groups.
We draw D = 5, 000 times repeated samples of N households from the empirical distribution of households

A53

Figure G1 Power Curves for Detecting Differences in Average MPCs across Treatment Groups
A. 4-week horizon (OLS)

B. 4-week horizon (FGLS)
100%

Rejection share (p−values <.05)

Rejection share (p−values <.05)

100%

75%

50%

25%

0%

50

100

250

Treatment group difference

500
1000
Sample size (N)Card 2 vs 1

Card 3 vs 1

2500

75%

50%

25%

0%

5000

50

Card 2 vs 3

100

250

Treatment group difference

500
1000
Sample size (N)Card 2 vs 1

Card 3 vs 1

4 weeks Draws (D): 5000

Card 2 vs 3

D. 6-month horizon (FGLS)
100%

Rejection share (p−values <.05)

100%

Rejection share (p−values <.05)

5000

FGLS 4 weeks Draws (D): 5000

C. 3-month horizon (FGLS)

75%

50%

25%

0%

2500

50

100

250

Treatment group difference

500
1000
Sample size (N)Card 2 vs 1

Card 3 vs 1

2500

75%

50%

25%

0%

5000

Card 2 vs 3

50

100

250

Treatment group difference

FGLS 12 weeks Draws (D): 5000

500
1000
Sample size (N)Card 2 vs 1

Card 3 vs 1

2500

5000

Card 2 vs 3
FGLS 26 weeks Draws (D): 5000

Notes: This figure reports power curves for rejecting H0 : M P Cgi = M P Cgj versus H1 : M P Cgi ̸= M P Cgj using
a two-sided t-test with 95% size. N is the size of each treatment group; the size of the control group is constant at
10,000 households. Estimates are obtained using a bootstrap with 5,000 draws.

in each treatment group, as well as 10, 000 households from the control group.9 We then estimate thebaseline specification (i.e. the same as for Figure 4) to estimate average MPCs for each group. In eachdraw, we conduct a t-test to test whether the null hypothesis of same T -week average MPCs is rejected
or not at 95% test size, for T equal to 4, 12, or 26 weeks.
Figure G1 shows an estimate of the power curve, i.e. the fraction of the 5, 000 draws where the nullis rejected as a function of treated sample size N . We report calculations for OLS estimates in the shortrun (4 week horizon, panel A) and for FGLS estimates at longer horizons (up to 6 months, see panels B,
C, and D).10
The estimates show that, with the sample size of 300 households per treatment group, at a 4-weekhorizon the rejection share when comparing Cards 1 and 2 is around 50%, compared to about 30% or
9We restrict the control group to 10,000 households for computational reasons but discuss at the end of this section thatthe estimates are not sensitive to the size of the control group10
As explained in the main text, for longer horizons FGLS estimates are more reliable.

A54

Figure G2 4-week Power curve, Robustness

Rejection share (p−values <.05)

100%

75%

50%

25%

0%

50

100

250

Treatment group difference

500
1000
Sample size (N)Card 2 vs 1

Card 3 vs 1

2500

5000

Card 2 vs 3
4 weeks Draws (D): 10000

Notes: This figure reports power curves for rejecting H0 : M P Cgi = M P Cgj versus H1 : M P Cgi ̸= M P Cgj using
a two-sided t-test with 95% size. N is the size of each treatment group. Estimates are done using a bootstrap with
10,000 draws and using control groups of 85,000 households drawn from the population of untreated households.

Cards 2 and 3, and only 12% for Cards 1 and 3. For Cards 1 and 2, a sample size of 1,000 participants
per treatment group gives power above 80% at any horizon. For Cards 2 and 3, a sample size of 2,500
participants is required to achieve 80% power. Because our point estimate for the difference between Cards
1 and 3 is much lower, the statistical power for detecting differences between groups 1 and 3 remains loweven for larger treatment group sizes.
We find that the estimates remain very similar when using a larger control group, and when doing morebootstrap draws: see Figure G2, which reports 4-week estimates for a control group of 85,000 households,
and twice as many bootstrap draws. We focus on the estimates with fewer bootstrap draws for the control
groups for tractability, as the FGLS specification take a significantly longer time to run.
Overall, these simulation results suggest that a sample size of about 1,000 to 2,500 participants pertreatment group would allow future experiments to achieve good power. With transfers of 300 euros per
participant, the implied cost of about 900,000 to 2,250,000 euros, instead of about 300,000 euros in our
experiment. While substantial, these costs are not larger than the costs of the typical RCT in fields suchas development economics. We hope that future RCTs can use the simulations above to mobilize sufficient
resources to obtain precise and appropriately powered estimates. Doing so is an important task for future
work.

G.2

Statistical Precision for Average MPCs Out of Standard Money Transfers

We now conduct simulations to understand the precision of the estimates of average MPCs of standard
money transfers like in our treatment group 1. Figure G3 shows the distribution of standard errors on the
4-week, 3-month, and 6-month MPCs for treatment groups 1, 2, and 3, depending on the treatment groupsizes. These distributions are estimated using the bootstrap with 5,000 draws, by each time drawing
a sample of the given size for each treatment group, and a control group of 10,000 households, fromthe respective empirical distributions. We report the distribution of standard errors of the average MPC,
using the same specification as the baseline event study regressions, with household and time fixed effects.

A55

Figure G3 Distribution of Standard Errors for Average MPC out of Card 1
A. 4-week horizon (OLS)

B. 4-week horizon (FGLS)

50%
Standard error of the average 4−week MPC

Standard error of the average 4−week MPC

50%

25%

0%

50

100

250
500
Sample size (N)Treatment group

Card 1

1000

Card 2

2500

25%

0%

5000

50

Card 3

100

250
500
Sample size (N)Treatment group

Card 1

1000

Card 2

2500

5000

Card 34 weeks draws: 5000

4 weeks draws: FGLS 5000

C. 3-month horizon (FGLS)

D. 6-month horizon (FGLS)
375%
Standard error of the average 26−week MPC

Standard error of the average 12−week MPC

150%

125%

100%

75%

50%

25%

350%
325%
300%
275%
250%
225%
200%
175%
150%
125%
100%
75%
50%
25%

0%

50

100

250
500
Sample size (N)Treatment group

Card 1

Card 2

1000

2500

0%

5000

Card 3

50

100

250
500
Sample size (N)Treatment group
12 weeks draws: FGLS 5000

Card 1

Card 2

1000

2500

5000

Card 326 weeks draws: FGLS 5000

Notes: This figure reports box plots of the simulated distribution of standard errors for the estimate of the T -week
average MPC in our baseline specification, when the control group consists of 10,000 households and each treatmentgroup consists of N households receiving Card 1. Estimates are obtained using a bootstrap with 5,000 repetitions.

Panels A and B shows that, at a 4-week horizon, obtain a standard error of 5% requires a sample sizeof about 2,500 households. This sample size would yield a standard error of about 12.5% at a 3-monthhorizon (Panel C), and of about 20% at a 6-month horizon (Panel D). With 5,000 households, the standard
error at a 6-month horizon is around 10%. Thus, obtaining precise estimates of MPCs at long horizons
would require a large sample size of about 5,000 households.

A56