ISSN (Print) 0473-453X

Discussion Paper No. 1147

ISSN (Online) 2435-0982

THE IMPACT OF ASSET PURCHASESIN AN EXPERIMENTAL MARKET
WITH CONSUMPTIONSMOOTHING MOTIVES
Jieyi Duan
Nobuyuki Hanaki

Revised September 2022
November 2021

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

The impact of asset purchases in anexperimental market with consumption
smoothing motives∗
Jieyi Duan†

Nobuyuki Hanaki‡

September 19, 2022
Abstract
We investigate the effect of preannounced market intervention on
an asset price as well as participants’ welfare in an experimental framework where participants have consumption smoothing motives to trade
the asset. The results show that, on one hand, the preannounced intervention results in significantly larger overpricing of the asset relative
to the rational expectations equilibrium level in periods prior to theintervention compared with the treatment without it. The participants’ welfare, measured by the discounted sum of the payoffs at the
beginning of the experiment, on the other hand, are not significantly
worsened by the intervention.

JEL Code: C90, D84
Keywords: Asset Pricing, Consumption Smoothing, Bounded Rationality,
Quantitative Easing∗

The experiments reported in this paper has been approved by IRB of the Instituteof Social and Economic Research, Osaka University. We gratefully acknowledge financial
support from grant-in-aid for scientific research (KAKENHI, grant number: 18K19954,
20H05631) from the Japan Society for the Promotion of Science (JSPS) as well as support
from the Joint Usage/Research Center at ISER, Osaka University. We thank Daiki Maeda
and participants at the international workshop on lab and field experiments (Osaka), 2021
ESA Global Online Meeting for comments and discussion.
†
Faculty of Economics and Management, Kyoto University of Advanced Science. Email: duan.jieyi@kuas.ac.jp‡
Institute of Social and Economic Research, Osaka University.
E-mail:nobuyuki.hanaki@iser.osaka-u.ac.jp1

1

Introduction

The biggest monetary policy experiment in recent years has been quantitativeeasing (QE). Between 2008 and 2017, seven central banks (Mexico, England,
Japan, Europe, US, Switzerland, and Sweden) have employed this policy(Committee on the Global Financial System, 2019). Furthermore, QE has
been extended in duration in many countries in response to the economic
downturn resulting from the spread of Covid-19. For example, since March
2020, the US Federal Reserve has implemented an unlimited QE policy.
However, from the perspective of the standard textbook model with complete markets without frictions and infinitely lived rational decision makers,
this policy should have no effects on any macroeconomic variables (Eggertsson and Woodford, 2003). Nevertheless, a number of empirical studies provide evidence that QE has indeed affected the market price of financial assets.
For instance, Corbet et al. (2019) find the Federal Open Market Committee announcement has significantly and substantially increased stock market
volatility, McLaren et al. (2014) and Grosse-Rueschkamp et al. (2019) indicate that the QE announcements from central banks has reduced bond yields,
implying there exists a QE announcement effect. In particular, D’Amico andKing (2013) and McLaren et al. (2014) observe a “local supply” effect, i.e.,
the yield curve within a particular maturity sector has responded more tochanges in the total value of outstanding bonds in that sector than to similar changes in the other sectors, indicating a segmentation or an imperfect2

substitution within the Treasury bond market.
Penalver et al. (2020) offer, based on an experimental analysis, a perspective based on the limited rationality of investors a la level-K (Nagel, 1995)
or the cognitive hierarchy (Camerer et al., 2004) model; namely, a possibilityof some market participants (maybe naively) believing that QE will raise theprices of bonds because QE is a commitment by the central bank, who is anunusual participant to the market, to buy a large amount of bonds. Sucha possibility would indeed result in QE raising the prices of bonds because
other, more sophisticated, participants optimally respond to the existence ofsuch naive participants.1
The experiment of Penalver et al. (2020) is similar to that of Bostian andHolt (2009) and extends the framework of Smith et al. (1988).2 In the Benchmark setting, participants trade a set of risk-free bonds using experimental
currency (cash) for a known finite number of periods. Bonds and cash, when
carried over to the next period, generate a dividend and an interest income,respectively. The bond matures at the end of the final trading period andis converted into cash. The interest on cash, the dividend, and the valueof the bond at maturity are set so that the fundamental value of the bondis constant, and equal to the value of the bond at maturity in all trading
1

Farhi and Werning (2019) analyze, theoretically, an implication of similar limited rationality on the effects of monetary policy in the New Keynesian setup. Namely, the authors
show that level-k thinking together with incomplete credits markets, idiosyncratic risks
that cannot be insured, and borrowing constraints that bind occasionally, can potentiallyexplain the “forward guidance puzzle”; i.e., monetary policy being too effective.
2
See, among others, Palan (2013) and Powell and Shestakova (2016), for surveys of thelarge literature on the experimental asset market pioneered by Smith et al. (1988).

3

periods. In the treatment with QE intervention, after a preannounced number of periods, the computer (acting as a QE operator) intervenes to buy
a prespecified quantity of bonds from participants through a discriminatory
auction. Penalver et al. (2020) find that such a market intervention not only
raises the postintervention prices of bonds, but also, after participants experience it once, significantly raises preintervention market prices when theexperiment is repeated.3
The effect of market intervention observed in the experiments by Penalver
et al. (2020) and Haruvy et al. (2014) are observed in an environment where
no trade is predicted under a risk neutral rational expectations equilibrium(REE, for short). As reported by Lei et al. (2001), in such an environment,
asset prices tend to deviate from their fundamental value more because themain rationale for participants to trade the asset is to speculate. The sameconclusion is also obtained by Crockett et al. (2019), who find the mispricing
of assets is significantly decreased when the speculate motivation is removed
by giving participants an incentive to trade, such as consumption smoothing
motive. Hence, the effect of intervention observed by Penalver et al. (2020)and Haruvy et al. (2014) may be exaggerated compared with situations whereparticipants have nonspeculative motives to trade the asset.
In this study, therefore, we reexamine the effect of preannounced mar3

Haruvy et al. (2014) also show, in a similar but a different experimental design, that assets being (re-)purchased by computer from market participants raises their prices. Haruvy
et al. (2014) did not investigate, however, how participants experiencing the effect of (repurchase) intervention once influences the preintervention price by repeating the experiment.

4ket intervention considered by Penalver et al. (2020) in a new experimental framework introduced by Asparouhova et al. (2016) and Crockett et al.
(2019), where participants trade assets to smooth their consumption acrossperiods. This new experimental framework is designed based on the Lucas asset pricing model (Lucas Jr, 1978)4 , and has the following characteristics: (1)there are an indefinite number of periods, instead of a known finite numberof periods; (2) participants receive incomes, which can be used to consume
or to trade the assets, that fluctuate across periods; and (3) participants arepaid based on their consumption at the end of periods, instead of the final
value of their portfolio at the end of the last period. In this setting, the asset
will be traded to smooth consumption in the REE.
We investigate, in this new framework, the effect of preannounced market
intervention (which we call QE operations below), as well as the effect of
the existence of an additional method of consumption smoothing; i.e., thepossibility to directly save cash. Compared with Penalver et al. (2020) andHaruvy et al. (2014), such a framework reduces the effect of the speculate
motivation which may exaggerate the impact of market intervention in the4

To our knowledge, only three experimental studies adopted this model for different
purposes besides our research. Asparouhova et al. (2016) is the first research to adopt theexperiment based on the Lucas model. This research aims to examine the model’s featuresin the laboratory. Compared with Asparouhova et al. (2016), Crockett et al. (2019) aims
to clarify the relationship between the existence of trading motivation and mispricing
through modifying the participants’ exchange function. Finally, the most recent research
is Carbone et al. (2021), which extends the framework of Crockett et al. (2019) from a
two-period cyclical world to a three-period cyclical world, aiming to test the robustness ofthe features of Lucas model and the results of Crockett et al. (2019). Appendix A showsa specific comparison of the experimental setting of these studies, including this research.

5

laboratory.
Our data show that the existence of QE operations significantly increase
the magnitude of overpricing of the asset (which we call bonds below) relative
to the REE level regardless of the existence of a saving possibility even before
participants having experienced the effect of the QE operation. However, theparticipants’ welfare, measured by the discounted sum of per period payoffs,
are not significantly worsened by the larger mispricing of assets caused by
the preannounced intervention.
The rest of the paper is organized as follows. Section 2 describes the modeland experimental design. Section 3 outlines the theoretical predictions andhypotheses. Section 4 provides an analysis of the data. Finally, Section 5offers some conclusions.

2

Experiments

2.1

Basic experimental design

Our experimental design in the Benchmark (B) treatment builds upon theprevious experiments by Crockett et al. (2019) and Asparouhova et al. (2016).
Appendix A compares experimental settings between ours and other studies
based on the Lucas asset pricing model. We consider an indefinite horizon
economy with a nonstorable consumption good and an indefinitely lived asset.
In the experiment, the nonstorable consumption good and the indefinitely
lived asset are represented by the experimental currency (francs) and the6bond, respectively. Time is discrete. At the beginning of the economy (t = 1),
each trader is endowed with some units of bond and some francs, which they
can use to trade among themselves. Subsequently, at the beginning of periodt ≥ 2, each trader receives yti francs of income as well as D = 2 francs per unitof bonds they hold as the dividend payment. While the aggregate income,P iii yt , is constant across periods, individual income, yt , fluctuates between
odd- and even-numbered periods. Let yoi and yei denote trader i’s income in
odd- and even-numbered periods, respectively.
Specifically, in the experiment, there are eight traders in an economy.
These eight traders are equally divided into two types of traders, Type 1 andType 2, who differ in their endowment and income streams. The endowments
are 92 francs and one unit of bonds for Type 1 traders and 32 francs andfour units of bonds for Type 2 traders, respectively. Incomes are set so that
yo1 = ye2 = 90 francs and ye1 = yo2 = 24 francs, where superscripts denotetrader’s type.
At the end of each period (t ≥ 1), each trader consumes the francs he/shehas. Consumption, c, is converted into JPY (Japanese Yen) according to thefollowing increasing and strictly concave function:uJP Y (c) = 3573.50 − 64872.01 × (c + 40.5)−0.7478 .

(1)

In the experiment, the “consumption” occurs as follows: each participant’s end-of-period franc balance is forcibly converted into JPY through7

the exchange function shown in Eq. 1.
Once consumption takes place, the economy continues to the next periodwith probability π = 5/6 or ends with probability 1 − π = 1/6. (Appendix B
gives a visual description of the timeline of each period for all treatments.)
Recall that while francs are nonstorable and cannot be carried over to thenext period, the bond is storable and can be carried over to the next period.
However, if the economy ends, all the bond holdings are lost without any
compensation. In the experiment, participants, who are acting as traders,are paid based on their final consumption before the economy ends according
to a prespecified conversion rate (Eq. 1). The risk neutral fundamental valueof a unit of bonds in period t is F Vt = Dπ/(1 − π) = 10 francs for all t.
Under this experimental setting, traders can obtain a higher expected
payoff by smoothing their consumption across periods. Note, however, tosmooth the consumption, traders need to trade bonds. Thus, unlike many experiments employing the framework of Smith et al. (1988) including Haruvy
et al. (2014) and Penalver et al. (2020), trade will take place in the current
experimental setup under the REE. Crockett et al. (2019) demonstrated thatsuch a consumption smoothing motive of trading reduces the price deviationfrom the fundamental value.

2.2

Trading mechanism

The experiment adopts an open-book continuous double-auction mechanism.
The trading period lasts 120 seconds. As noted above, at the beginning of8period t, before the market opens, trader i who hold Kti units of bonds
receives yti + 2Kti units of cash (francs) as his/her income and the dividend
payment.
Once trading begins, traders can submit a bid order (a buy order) and/or
an ask order (a sell order) for a unit of bonds in continuous time. Traders
can trade as many units of bonds as they wish during the 120 seconds within
their budget constraint. No borrowing of cash or short-selling of bonds ispermitted. Orders are sorted according to price and the time of the ordersubmission. A transaction takes place when the best bid and the best ask
cross, at the price determined by whichever is submitted earlier. Once atransaction takes place, cash and bond holdings are immediately updated
and all the outstanding orders submitted by the two traders who just traded
are automatically canceled.

2.3

Treatments

We use a two-by-two between-subjects design, in which we vary the existenceof QE operations (with v.s. without QE operations), and the existence ofan additional way of smoothing consumption (with v.s. without the possibility of saving francs). Table 1 summarizes these four treatments. And
Appendix B shows the differences in the experiment process in each periodamong treatments.
Regarding the QE operations, before the experiment begins, participants
are informed that, just before the trading in period 4 and after participants9

Table 1: Four treatments
Without saving With saving
without QE
BBSwith QE
QE
QES
receive their income and dividend, a maximum of six units of bonds will
be bought by the computer through a uniform price auction. During thisintervention, participants who want to sell their bonds to the computer,
place an order by specifying the minimum price at which they wish to sell
their bonds and the number of units they wish to sell.
Then, the computer buys up to six units of bonds from the lowest-pricedorders from the participants in each group. The transaction price of theintervention is the highest price among those accepted orders in the group.
In the treatments with saving (BS and QES), francs become storable.
Namely, just after the trading in each period, participants can determine
how much of their remaining francs to save and to carry over to the next
period. The saved francs generate an interest earning with a 20% interest
rate, which is paid at the beginning of the next period. If the economy ends,
however, just as the bond is lost, the saved francs are lost. Interest earnings
are rounded down to the nearest integer. We set the interest rate at 20% tomake it equal to the return of bonds at the rational expectations equilibrium.

10

2.4

Termination, timing, and payment

To secure sufficient data and to ensure that market intervention occurs in the
QE and QES treatments, we adopted the method of block random termination (BRT, Fréchette and Yuksel, 2017). Similarly to the standard random
termination, under BRT, the computer rolls a die at the end of each period
to determine whether an economy (called a round) ends or not. However,participants must at least experience the round for a fixed number of periods(one block). Whether the round has ended or not is disclosed only at the endof each block. If the round has ended during the current block, participants
are told in which period it has happened, and their corresponding payoffs
at that period. Recall that participants’ payoff (for the round) is computed
based on their consumption at the final period of the round. Otherwise, they
are told that the round has not ended yet, and they start a new block. In
this experiment, at the end of each period, the round ends with a probability
1/6, and each block consists of six periods. Appendix C summarizes thisprocedure.
At the end of a round, if fewer than 35 minutes have passed since thebeginning of the first round, a new round begins; otherwise, the experimentends. Therefore, each session of the experiment consists of at least one round.
Furthermore, each round consists of at least one block of six periods. At thestart of each round, the endowments of all participants are reset. After theexperiment ends, the computer randomly selects one round to calculate theparticipant’s earning. Participants are paid in cash based on their earnings
11

in the chosen round in addition to the 1000 JPY show-up fee.
To exclude the effect from variations in duration of rounds, and to control
the length of the experiment, we use a computer program to randomly determine the number of periods (thus, the number of the block) in each roundin advance.5 Then, we used this predetermined number of periods acrossrounds for all the sessions in our experiment. Therefore, each round has
the same number of periods (blocks) in all the sessions, and all the sessions
consist of at least two rounds in our experiment. In particular, all of therounds in the four treatments consist of one block of six periods, and eachsession of all the treatments except for B consists of two rounds, while eachsession of B consists of three rounds. We did not provide participants withthis information.6

3

Hypothesis

Let us derive the REE bond price under the representative agent framework.
At period 0, the agent faces the following maximization problem.

max{ct ,kt+1 }∞
t=0

[

∞
X

π t v(ct )]

(2)

t=0

5

Although there is so far no evidence showing that variations in duration of rounds
affect asset pricing in the macroeconomics experiment, some studies document that suchvariations indeed affect the experimental results. For instance, Bo and Fréchette (2011)and Engle-Warnick and Slonim (2006) report that such variations can affect the extent
of cooperative behavior in repeated prisoner’s dilemma game experiments and repeatedtrust game experiments.
6
Such a design is also adopted by Duffy and Puzzello (2014), Duffy and Puzzello (2020),
and Fréchette and Yuksel (2017).

12

subject to
yt + (D + Pt )kt = ct + Pt kt+1 ,(3)

where ct is the consumption of francs, Pt is the bond price, and kt is thenumber of the bonds that the agent owns at the beginning of period t. π ∈(0, 1) is the continuation probability. v(ct ) = (1 − π)uJP Y (ct ) + π0 = (1 −π)u(ct ) is the expected monetary reward in period t by “consuming” ct .
We define the Lagrangian as follows:

L=

∞
X


π t v(ct ) + λt (yt + (D + Pt )kt − ct − Pt kt+1 ) .

(4)

t=0

The first order condition with respect to ct is∂L= π t v 0 (ct ) − λt = 0 for all t.
∂ct

(5)

The first order condition with respect to kt+1 is∂L= −λt Pt + λt+1 (D + Pt+1 ) = 0 for all t.
∂kt+1

(6)

Combining Eq. 6 and Eq. 5 for ct and ct+1 gives us
π t v 0 (ct )Pt = π t+1 v 0 (ct+1 )(D + Pt+1 ).

Thus,
Pt∗ =

v 0 (ct+1 )π(Pt+1 + D),
v 0 (ct )13(7)

where Pt∗ is the equilibrium price of the bond at period t. By applying thelaw of iterated expectations, Eq. 7 can be rewritten as

Pt∗ =

∞
X
τ =1

πτ

v 0 (ct+τ )D,
v 0 (ct )(8)with v 0 (ct ) = (1 − π)u0JP Y (ct ) for all t. As uJP Y (ct ) is strictly concave, in
0

)
= 1.
treatment B, consumption satisfies c1 = c2 = ... = ct = .... Thus, v v(c0 (ct+τt)

Therefore,
Pt∗,B =∞Xτ =1

πτ D =πD= F V for all t.
1−π

(9)

We now consider the REE price of the QE treatment. In the experiment, theQE operation occurs at the beginning of period 4. Because up to six unitsof bonds are purchased during the QE operation, the dividend loss of thepurchased bonds leads to a decrease in consumption after period 4. Thus,

c4 > c1 = c2 = c3 > c5 = c6 = ...

(10)v 0 (ct|t≥5 ) > v 0 (ct|t≤3 ) > v 0 (c4 ).

(11)

and

Given that consumption will be constant, in the equilibrium, after period 5,
we have∗,QE
Pt|t≥5= F V.

14(12)

The equilibrium prices in period 4 are
P4∗,QE =v 0 (c5 )v 0 (c5 )
π(F
V
+
D)
=
F V,
v 0 (c4 )v 0 (c4 )(13)which depends on c4 ; i.e., the outcome of the QE operation. The equilibrium
price in period 3 isv 0 (c5 )v 0 (c4 )v 0 (c4 ) ∗,QE
(P4+ D) = π 0
FV + π 0D.
P3∗,QE = π 0v (c3 )v (c3 )v (c3 )

(14)

In period 4, if the agent responds to the QE operation, the expected payoff
must be no less than when the agent can expect from not doing so. Thismeans that the consumption stream must satisfy the following inequality∞Xπ τ [v(c3 ) − v(c∗∗ )] ≤ v(c4 ) − v(c3 ),

(15)

τ =1

where c∗∗ is the optimal per period consumption from period 5 on.
The left part of the above inequality is the discounted future loss frompermanently lower income (because of lost dividend income) when the agent
responds to the QE operation, and the right part is the short-term gain in
welfare from doing so. If the competition among agents drives the QE pricedown to the point of indifference, this impliesv(c3 ) − πv(c∗∗ )= v(c4 ).
1−π

15

(16)

This identifies the equilibrium QE intervention price. Although we could
not derive the relationship between P3∗,QE and F V under general conditions,
we can at least numerically derive the specific value of P3∗,QE for the specificparameter used in our experiment. Assuming, consistent with the representative agent assumption, that all the agents have the same level of consumption
in the REE, when the computer purchases six units of bonds in the QE operation, we ct|t≤3 = 62 and ct|t≥5 = 60.5. Moreover, substituting these values
in Eq. 16, we have c4 = 70.1216 under the representative agent assumption(so that each agent sells 6/8 units of bonds to the computer during the QE
operation), with the equilibrium intervention price being
6p∗,QE
inter = (70.1216 − 62)/ = 10.82.
8(17)With uJP Y (ct ) and P5∗,QE = F V = 10, we obtain
∗,QE
∗,B
Pt=3
= 10.00959 > F V = Pt=3.

(18)

Given Eq. 7, this means
∗,QE
∗,QE
∗,QE
> Pt=2> Pt=1
> 10;
Pt=3

(19)

∗,QE
∗,QE
= 10.0042. Thus, the announced QE
in particular, Pt=2
= 10.005, Pt=1

operation slightly raises the prices in preintervention periods under the REE.
In the BS and QES treatments, because participants can carry over their16francs into the next period by saving with an interest rate of 20%, a 10 francs
saving can perfectly substitute for holding one unit of bonds when the market
price is F V . Thus, there is no reason that participants buy or sell the bonds
at a market price higher or lower than F V under the REE. Furthermore, in
the QES treatment, for the same reason, the intervention price converges to
FV when the QE operation is fully competitive.
While the REE bond prices are (slightly) different across the four treatments, we hypothesize, based on the REE,
Hypothesis 1 The magnitudes of mispricing are the same across the four
treatments.
Alternatively, if, as proposed by Penalver et al. (2020), some participants
naively anticipating profits to be made during the QE operation causes prices
to deviate from the REE, the magnitude of mispricing would be larger in thetreatments with QE than those without, especially, in the periods prior to
the QE operation.
Furthermore, because of the competition during the QE operation, we
expect, based on the REE,
Hypothesis 2 The ex ante expected payoffs are the same across the four
treatments.
Alternatively, while QE operations may raise the consumption level inperiod 4 (and if saving is possible in the later periods) and thus make par-17

ticipants better off, speculative trades in periods prior to it may disturb consumption smoothing and thus may make participants worse off. The overall
effect is, however, not clear and the ex ante expected payoff may differ acrosstreatments.

4

Results and Discussions

The experiment was programmed using z-Tree (Fischbacher, 2007) and was
run at the experimental laboratory of the Institute of Social and Economic
Research at Osaka University from October 2020 to June 2021. All participants were students enrolled in the school and recruited by the ORSEE
recruiting system (Greiner, 2015).
In total, 304 students participated in the experiment across 13 sessions.
In all the sessions, the instruction movie was played to the participants. The
participants had a printed handout at hand. The participants’ understanding of the rules of the experiment, including how their payoffs are computed,
was checked with a quiz. To ensure that participants understood the rules,
the experiment started only after all the participants had answered all thequestions correctly. There are nine groups in Benchmark, QE, and BS treatments and 11 Groups in the QES treatment.7 The sessions lasted between
7
In the QES treatment, however, the computer failed to purchase the bonds in threegroups in one session because of a programming mistake. Subsequently, the error in the
program was corrected, and we excluded the data of these three groups from the analyses.
Thus, data from 35 groups (nine groups each in the Benchmark, QE, and BS treatments,and eight in the QES treatment) are used for subsequent analysis.

18

one and a half to two hours.8 The average payoff was 2456 JPY (≈ 22.99
USD, based on the exchange rate at the time experiments were conducted).

4.1

Price dynamics and mispricing

Did the intervention affect the bond transaction prices? Figures 1 and 2
show the dynamics of mispricing observed in each treatment in Rounds 1
and 2, respectively. The mispricing in period t of round r of group g is
P g,r g,r,n ∗,r ∗,r(Pt −pt )/pt , where Ntg,r is the number
calculated by M Ptg,r = N1g,r Nnt

of transactions in the group for period t of round r, Ptg,r,n is the realized priceof the n-th transaction in period t of round r for the group, and p∗,r
is thet
REE price in period t of round r for the treatment as derived in the previous
section.
Each solid line shows the dynamics of the within period median mispricing
of a group. The dashed lines correspond to the dynamics of the across-groupmedian for the treatments. As mentioned in Section 2.4, because all sessions
adopted the same sequence of predetermined dice numbers, the duration ofeach round is the same. Precisely, each round consists of one block (sixperiods).
Figure 1 reveals that, in Round 1, mispricing tends to be lower in B compared with QE, and in BS compared with QES. In particular, this tendency
is observed not only after the QE operation that takes place in period 4
8
We recruited participants for two hours, but our sessions all ended within two hours,
so as to avoid any possible end game effects.

19Figure 1: Dynamics of mispricing: Round 1
BS

5

5

4

4

3

3
Mis−pricing

Mis−pricing

B

2

2

1

1

0

0

−1

−1
1

2

3

4

5

6

1

2

3

Period

QE

5

6

4

5

6

QES

5

5

4

4

3

3
Mis−pricing

Mis−pricing

4
Period

2

2

1

1

0

0

−1

−1
1

2

3

4

5

6

1

Period2

3
PeriodNote: Each line represents the dynamics of the normalized median prices of a group. The dashedlines represent the dynamics of the median normalized prices for the treatment in the round.

20

Figure 2: Dynamics of mispricing: Round 2
BS

5

5

4

4

3

3
Mis−pricing

Mis−pricing

B

2

2

1

1

0

0

−1

−1
1

2

3

4

5

6

1

2

3

Period

QE

5

6

4

5

6

QES

5

5

4

4

3

3
Mis−pricing

Mis−pricing

4
Period

2

2

1

1

0

0

−1

−1
1

2

3

4

5

6

1

Period2

3
PeriodNote: Each line represents the dynamics of the normalized median prices of a group. The dashedlines represent the dynamics of the median normalized prices for the treatment in the round.

21

(periods 4–6), but also before it takes place (periods 1–3). Furthermore, themispricing in QES tends to be smaller than that in QE. Between B and BS, apart from the latter half of the round, the mispricings are similar. A similartendency is observed in Round 2, shown in Figure 2, except that mispricing
in BS tends to be smaller than the one in B.
To formally compare the degree of mispricing, we compute the geometricdeviation (GD) introduced by Powell (2016).9 For group g in round r, GDg,ris defined as

g,r

GDg,r = exp

N
1 X pg,rng,rN n=1 p∗n

!
− 1,

(20)

where N g,r is the number of transactions that occurred in round r, pg,rn is
the realized price of the n-th transaction, and p∗n are the REE prices in the
period when the n-th transaction occurred. As GD takes the direction ofprice deviation into account, the bonds are overpriced (underpriced) relative
to the REE prices if GD is significantly higher (lower) than 0.
We calculate the GDs for two subperiods separately: periods 1–3 denotethe preintervention periods, and periods 4–6 denote the postintervention periods. Table 2 summarizes the median GDs in Round 1 for each treatmentin the preintervention and postintervention periods (top panel), as well as
the p − values of the pairwise treatment comparisons based on the Wilcoxon
rank-sum test (bottom panel). These p-values are corrected for multiple
comparisons using the Bonferroni method.
Table 2 shows that, in Round 1, the preintervention GDs in the QE treat9

See Appendix D for results based on other measures of mispricing.

22

Table 2: Median GDs in Round 1
Median GDs
B
QE
BS
QES
Preintervention-0.052 0.467 -0.208 0.101
Postintervention
0.166 0.871 -0.054 0.252∗
p-values (H0 : Pre = Post) 0.004 0.074 0.910 0.547
Observations
99
98
p-values+ for treatment comparisons
Preintervention periods
Postintervention periods
B
QE
QES
B
QE
QES
QE
0.969
QE
0.047
QES 0.164 1.000
QES 1.000 0.833
0.113 0.011 1.000
BS
1.000 0.034 0.047 BS∗: p − values from the Wilcoxon signed-rank (WSR) test are reported.
+: p−values from the pairwise Mann–Whitney U (MW) test are reported. Bonferroni
method is used for correcting p-values for multiple comparisons.

ment are significantly higher than those in the B treatment (p = 0.047), andsimilarly, the preintervention GDs in the QES treatment are significantly
higher than in the BS treatment (p = 0.047). Thus, unlike the results reported in Penalver et al. (2020), the announced intervention raises the degreeof mispricing even before the intervention actually takes place, regardless ofthe existence of the saving possibility.
Observation 1 In Round 1, the announcement of the QE intervention results in significantly larger overpricing of the bond in the preintervention
periods than the treatments without the intervention.
Moreover, although the median postintervention periods GDs are higher
in the QE treatments than in the B treatments (and also in the QES treat23

ments than in the BS treatments), as reported in the bottom panel of Table 2,these differences are not statistically significant. Thus, unlike in Penalver
et al. (2020), the intervention does not significantly affect the magnitude ofmispricing in the postintervention periods compared with the cases withoutit.
Observation 2 In Round 1, the intervention does not result in a statisticallysignificant difference in the magnitude of mispricing in the postintervention
periods compared with the cases without the intervention.
A potential reason for the absence of the significant differences in thepostintervention GDs between the B and QE treatments is the significant
increase in the GDs in the postintervention periods compared with the preintervention periods observed in the B treatment. We have, however, no clear
explanation for the upward trend in the mispricing observed in this treatment.
Let us now turn to the outcomes of Round 2. Penalver et al. (2020) reportthat once the effect of intervention is experienced in Round 1, the bond issignificantly overpriced in the preintervention periods in the treatment withpreannounced intervention in Round 2.
Table 3 shows the median preintervention and postintervention GDs in
Round 2 for each treatment. While the median preintervention GD is higher
in the QE than in the B treatments (higher in the QES than in the BS
treatments) as shown in the top panel, there is no statistically significant

24

Table 3: Median GDs in Round 2
Median GDs
B
QE
BSPreintervention
0.275 0.860 -0.056
Postintervention
0.264 0.764 -0.331∗
p-values (H0 : Pre = Post) 0.654 0.027 0.129
Observations
9
9
9

QES
0.198
-0.0590.742
8p-values+ for treatment comparisons
Preintervention periods
Postintervention periods
B
QE
QES
B
QE
QES
QE
0.815
QE
0.969
QES 1.000 0.278
QES 1.000 1.000
0.011 0.005 1.000
BS
0.047 0.002 0.355 BS∗: p − values from the Wilcoxon signed-rank (WSR) test are reported.
+: p−values from the pairwise Mann–Whitney U (MW) test are reported. Bonferroni
method is used for correcting p-values for multiple comparisons.

difference in preintervention or postintervention GDs between the QE andthe B treatments (and in the QES treatments and BS treatments) in Round 2.
Thus, unlike the results of Penalver et al. (2020), the effect of intervention
does not persist when participants repeat the same experiment with the samegroup of participants under the same market conditions.
It should be noted that preintervention GDs are significantly higher inRound 2 than in Round 1 for the QE treatment (p = 0.008, WSR test)
suggesting that having experienced the high preintervention and postintervention market prices in Round 1, participants in the QE treatment traded
the bond at an even higher price before the intervention in Round 2 than inRound 1. However, as noted above, probably because of the upward price25

trend observed in the B treatment in Round 1, its preintervention GDs in
Round 2 are also significantly higher than those in Round 1 (p = 0.004,
WSR test).10 In Penalver et al. (2020), and many other experiments using
the Smith et al. (1988) paradigm, the magnitude of mispricing decreases as
participants gain experience in the baseline treatment. We believe that theincrease in the magnitude of mispricing in Round 2 under the B treatment is
the reason for the absence of the persistence of the QE intervention when thesaving possibility is absent. We also note that in Round 2, the GDs are significantly higher in the B treatment than in the BS treatments both for the
preintervention (p = 0.047, using the MW test) and for the postintervention(p = 0.011, using the MW test). Thus, in the absence of the intervention, thesaving possibility significantly reduces the magnitude of overpricing amongexperienced participants.11

4.2

Welfare and Consumption Smoothing

Note that in our experiment, the participants’ expected payoffs do not directly depend on the transaction price in each period but on their consumption paths across several periods. Here, we first compare participants’ welfare, measured by the discounted sum of the payoffs over six periods (for par10

There is no statistically significant difference in the preintervention GDs between
Round 1 and Round 2 for the BS and QES treatments (p = 0.496 in the BS treatment andp = 0.641 in the QES treatment, using the WSR test). Furthermore, there is no significant
difference (at the 5% significance level) in the postintervention GDs between Rounds 1
and 2 for all the treatments (p-values are 1.000, 0.570, 0.098, 0.461, for the B, QE, BS,
and QES treatments, respectively, using the WSR test.
11
See Appendix E for analyses on trading volumes.

26

ticipant i, it is defined as wi =

P6

t=1 π

t−1

uJP Y (cit )), across four treatments.12

We use the within-group mean of wi , W g , as an independent observation.
Table 4 shows the across-group median W g in the four treatments in two
rounds. In Round 1, the W g s are similar between the B and QE treatments(p = 1.000), but the W g in the BS treatment is significantly smaller thanthat in the QES treatment (p = 0.047). Thus, despite the significantly
larger preintervention mispricing observed in the QE and QES treatments
than in the B and BS treatments, the discounted payoffs are not significantly
worsened. On the contrary, in the presence of a saving possibility, the QE
intervention increased welfare.
Table 4 also shows that the W g s are significantly higher in Round 2 thanin Round 1 at the 5% significance level in all the treatments except for QES.
In Round 2, there is no longer significant differences in the W g s between the
BS and QES treatments.13
As noted above, the QE intervention may lower the payoffs in the preintervention period because of increased mispricing, while improving the postintervention payoffs because of the increased consumption induced by the cash
injection. However, as reported in Appendix G, the anticipated intervention
does not result in a significant change in (nondiscounted) mean payoffs either
12Here, we do not regard participant payment as welfare since it can’t well reflect participant performance throughout the experiment, such as the performance of consumption
smoothing.
13
In Appendix F, we separately analyze discounted payoffs for two types. The results
show that significant treatment differences in the discounted payoffs are mainly becauseof the variation in the discounted payoff of Type 2 players.

27

Table 4: Median W g
Median W g
B
QE
Round 15723.84 5747.33
Round 25851.31 5892.67∗
p-values (H0 : R1 = R2) 0.008
0.004
Observations
99BS
5507.735838.08
0.004
9

QES
5798.265955.090.055
8p-values+ for treatment comparisons
Round 1Round 2
B
QE
QES
B
QE
QES
QE
1.000
QE
1.000
QES 1.000 1.000
QES 0.560 1.000
1.000 1.000 0.560
BS
0.240 0.302 0.047 BS∗: p − values from the Wilcoxon signed-rank (WSR) test are reported.
+: p − values from the pairwise Mann–Whitney U (MW) test are reported. Bonferroni
method is used for correcting p-values for multiple comparisons.

in the preintervention or postintervention periods at the 5% significance levelin both rounds.
Observation 3 The intervention does not significantly affect welfare, measured by the discounted payoffs, in Round 2. It improves it in the presenceof a saving possibility in Round 1.
We also compute the Gini coefficient of wi for each group to investigate
whether the QE intervention has increased the within-group inequality inthe discounted payoffs. Table 5 shows the median Gini coefficient in eachtreatment. While there is no statistically significant difference between any
relevant pairs of treatments, we do observe significant reduction in the Gini
coefficient in Round 2 compared with Round 1 for the BS treatment. This re28

Table 5: Median Gini coefficient based on wiMedian Gini coefficientB
QE
Round 10.030 0.044
Round 20.030 0.041∗
p-values (H0 : R1 = R2) 0.91 0.652
Observations
9
9

BS
0.068
0.032
0.012
9

QES
0.050
0.037
0.641
8

p-values+ for treatment comparisons
Round 1Round 2
B
QE
QES
B
QE
QES
QE
1.000
QE
0.970
QES 1.000 1.000
QES 1.000 1.000
1.000 0.970 1.000
BS
0.110 0.460 1.000 BS∗: p − values from the Wilcoxon signed-rank (WSR) test are reported.
+: p − values from the pairwise Mann–Whitney U (MW) test are reported.
Bonferroni method is used for correcting p-values for multiple comparisons.

duction in the Gini coefficient in the BS treatment is because of the improvement in the discounted payoff of Type 2 participants in Round 2 comparedwith Round 1.14
Observation 4 The intervention does not significantly affect within-groupinequality in terms of their discounted payoffs.

4.3

Prices in the intervention

As reported in Section 4.1, the magnitudes of the overpricing in the preintervention periods are significantly larger in the presence of intervention than
14

In fact, while the mean discounted payoffs are significantly higher in Round 2 than inRound 1 for Type 2 players at the 5% significance level in all the treatments except for
QES, there is no significant increase for Type 1 participants. See Appendix F.

29

Table 6: Comparison of the mispricing during the intervention between QE
and QES treatments and rounds.
QE
QES
p − values∗∗∗∗∗∗
Round 1
1.032
0.850
0.726
∗∗∗
∗∗
0.525
Round 21.309
0.300
p − values
0.195
0.125
Observations
98
Note: The median mispricing of each treatment in each roundis reported. The fourth column reports the p-values of the differences between treatments from the Wilcoxon rank-sum test.
The third row reports the p-values of the differences between
rounds within treatments from the Wilcoxon signed-rank test.
**, and *** indicate a significant difference from 0 at the 5 and1% significance levels using the Wilcoxon rank-sum test.

in the absence of it. This indicates that participants expect the bonds tobe sold at high prices during the intervention, pushing the preintervention
prices up. Are their expectations fulfilled? Here we investigate the following
two questions: (1) do participants sell the bonds to the computer at a pricehigher than the competitive equilibrium intervention price? and (2) is theintervention price influenced by the possibility of saving?
Table 6 compares the magnitude of mispricing during the intervention
between the QE and QES treatments for Rounds 1 and 2. The mispricing
g,rg,ris computed as (Pinter− p∗inter )/p∗inter , where Pinteris the realized computerpurchasing price for group g in round r, and p∗inter is the competitive equilibrium price derived in Section 3. The fourth column reports the p-valuesof differences between treatments. The last row reports the p-values of differences between rounds within treatments. The “*”s indicate whether themispricing is significantly different from zero.

30

As shown in Table 6, the mispricings during the intervention are significantly higher than 0 in both treatments in both rounds. This result is
consistent with Penalver et al. (2020), who suggest that the price competition
was not strong enough during the QE operation.15
Observation 5 The intervention prices are significantly higher than thecompetitive equilibrium intervention prices, regardless of the existence of thesaving possibility.
Besides, Table 6 (the fourth column) shows that the magnitude of mispricing is not significantly different between the QE and QES treatments.
Thus, the saving condition does not influence the intervention prices. Table 6 (the last row) also fails to show any statistically significant difference
between Round 1 and Round 2 within both treatments, implying participants observing a high intervention in Round 1 do not promote the pricecompetition during the QE operation of Round 2.

5

Conclusions

In this study, we conducted an experiment to examine the effect of market
intervention in the presence of a consumption smoothing motive to trade.
Existing experimental studies that investigate the impact of market inter15
In Bertrand price competition experiments, for example, conducted by Dufwenberg
and Gneezy (2000) and Baye and Morgan (2004), overpricing is also observed. Dufwenberg
and Gneezy (2000) explain the reason for participants not competing aggressively enougha la the level-k model.

31

vention (Haruvy et al., 2014; Penalver et al., 2020) have employed variantsof the Smith et al. (1988) paradigm where no trade is expected under the risk
neutral rational expectations equilibrium, and a large mispricing has been observed. By employing the new experimental framework based on the Lucas
asset pricing model (Lucas Jr, 1978) proposed by Asparouhova et al. (2016)
and Crockett et al. (2019), we reexamine the effect of market intervention in
the framework where assets are traded to smooth consumption. In this newframework, Crockett et al. (2019) report that the magnitude of mispricing
tends to be smaller than those observed in the Smith et al. (1988) framework.
To the best of our knowledge, this study is the first study that examines theeffect of market intervention under the Lucas asset pricing model in a lab.
Furthermore, we investigated the effect of the market intervention under
the two conditions: with and without the possibility to save. Under a nosaving condition, participants need to smooth consumption only by trading
assets, and under the saving condition, they can smooth consumption not
only by trading assets, but also by saving.
The results show a significant effect of market intervention on overpricingof the asset before the intervention actually occurs, regardless of the existenceof the saving possibility. This result is consistent with that of Penalver
et al. (2020). However, contrary to Penalver et al. (2020), which showsthe effect becomes larger as participants repeat the same experiment, in
our experiment, the effect of market intervention on the mispricing becomes
statistically insignificant in the second round. Surprisingly to us, despite32the significant effect on the overpricing of the asset, the intervention did not
significantly worsen participants’ payoffs. On the contrary, in the presenceof a saving possibility, it improved it, although the effect was observed onlyin the first round.
However, there may exist some questions of external validity in this study.
In our experiment, following Penalver et al. (2020), the computer purchased
up to 30 percent of the bond from each market through the intervention.
In the real world, however, an intervention of such a scale may cause hyperinflation, and thus not a realistic scenario to be considered. Clarifying
the relationship between the scale of the intervention and its effects on themarket outcome is a fruitful future research.
Another question that we consider interesting is how an intervention on
one asset influences the pricing of other assets in a setting with multiple assets
being traded simultaneously. Because experimental analyses with multiple
assets markets are still scarce, and, apart from Asparouhova et al. (2016),
they use the Smith et al. (1988) framework (Charness and Neugebauer, 2019;
Duffy et al., 2021), we believe such an exercise will be very fruitful.

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38

A

Experimental setting comparison of the studies based on the Lucas model.
Table A.1: Experimental setting comparison (1)Study

Our study

PurposeThe number of Assets
participant permarketTo test the effect of 8participants A
nonstorable
asset
QE policy on the fi- per market(experimental
curnancial asset pricerency/cash/token)
anda risk-free infinitely lived
asset (bond)

Crockett et al.
(2019)

To investigate the re- 12 participants
lationship between the per market
existence of trading
motivation and mispricingA
nonstorable
asset(experimental
currency/cash/token)
anda risk-free infinitely lived
asset (asset)

Asparouhova
et al. (2016)

To examine the fea- 12 to 30 partictures of the Lucas ipants per marmodel in the labora- kettory.

A
nonstorable
asset(experimental
currency/cash/token),arisk-free infinitely lived
asset (bond), and a risky
asset (tree)

Carbone et al.
(2021)To test the robustnessof the features of Lucas model to a threeperiod cyclical world

A nonstorable asset (Experimental currency), a riskfree infinitely lived asset(asset), and a risk-free
short-lived asset (credit)39

12 participants
per market

Table A.2: Experimental setting comparison (2)Study
Our study

The features of the Termination
Exchange function
Concave
Random block termination. The market
continues with a probability of 5/6

Payment
Final payment is theearning of the final period of a round randomly selected+1,000
Japanese Yen

Crockett et al.
(2019)

Concave and linear

Random termination. Payoffs are earned
The market continues from every period ofwith a probability of every round
5/6

Asparouhova
et al. (2016)

LinearRandom termination.
The market continues
with a probability of
5/6

Carbone et al.
(2021)

Concave and step

Random termination. Payoffs are earned
The market continues from every period ofwith a probability of every round
5/6

40

Pay for 2 of the replications (round) randomly chosen after
conclusion of the experiment

B

The details on experiment timeline in eachperiod.
Figure B.1: The timeline of Period 1
Benchmark and QE

BS and QES

41

Figure B.2: The timeline of the period after period 1
Benchmark and QE

BS and QES

42

Figure B.3: The timeline of period 4 in QE and QES

QE

QES

43

C

The details of block random terminationand payment.

As described in Sub-session 2.4, to secure sufficient data and to ensure thatmarket intervention occurs in the QE and QES treatments, we adopted themethod of block random termination (BRT, Fréchette and Yuksel, 2017).
Figure C.1 reports the details of BRT in this experiment. Participants mustat least experience the round for a block consisting of six periods. At the endof each period, the computer rolls six-sided dice, whereas participants can’t
observe the results until the block ends. At the end of each block, whether
the round continues depends on the results of dice rolling of each period: theround continues to a new block if 6 did not appear in any of the six periodsin that block; otherwise, the round ends. At the end of a round, if less than
35 minutes have passed since the beginning of the first round, a new round
begins; otherwise, the experiment ends.
Then, a participant’s payoff is determined as follows. Once the experiment ends, participants are paid in cash based on their earnings in the
randomly chosen round in addition to the 1,000 JPY show-up fee. The earnings of each round of a participant equal the amount of Japanese Yen basedon his/her consumption at the end of the ”final period” of the round. Note
that, the ”final period” does not mean the final period of the final block but
the earliest period in which the roll of a dice resulted in six. For ease ofunderstanding, we give the following example in Figure C.2 to show how we
44Figure C.1: The experiment process of each round and the implementationof the random block termination.

45

determine a participant’s payment.
In Figure C.2, the numbers below the period numbers are the amount ofJapanese Yen based on the consumption of a participant, and the numbers
below the Japanese Yen are the results of dice rolling at the end of eachperiod.
In round 1, since the dice rolling resulted in 6 for the first time in period
3, this round ends when the first block ended. The ”final period” of thisround was period 3, and the earning of the participant in this round was 1,
524 JPY.
In round 2, since no dice rolling resulted in six in any of the six periods inthe first block, the round continued to the second block. In the second block,since the dice rolling resulted in six for the first time in period 9, this roundended when this block ended. Although the dice rolling resulted in six alsoin period 11, because the earliest period that dice rolling resulted in six wasperiod 9, this period was the ”final period” of round 2, and the participant
earning of this round was 1,701 JPY.
Suppose more than 35 minutes have passed since the beginning of thefirst round when round 2 ended. Then session ends when round 2 ends.
The computer will randomly select one round from round 1 and round 2 to
calculate this participant’s final payment. If round 1 is selected, the final
payment of this participant is 1,524 + 1,000 = 2,524 JPY; otherwise, ifround 2 is selected, the final payment of this participant is 1,701 + 1,000 =
2,701 JPY.
46

Figure C.2: The example of how we determine a participant’s earning of eachround.

47

D

Other measures of market outcomes
Table D.1: Definitions of the measures of mispricing.
PN pn −p∗t1
| p∗ |
Relative absolute deviation (RAD)NnPn=1
pn −p∗tN
1
Relative deviation (RD)n=1 p∗nN
P
pn
Geometric absolute deviation (GAD) exp( N1 N
n=1 |ln p∗n |) − 1Ppn
Geometric deviation (GD)
exp( N1 N
n=1 ln p∗ ) − 1nThis section presents the comparison results for mispricing among treatments based on the four measures proposed in the literature, including thegeometric deviation (GD) reported in the main text. Table D.1 summarizes the definition of each measure. Table D.2 displays the median valueof each measure of each treatment in each round and reports the results ofcomparisons between the treatments with and without intervention.
In Table D.2, consistent with the GD results, in the preintervention periods of the first round, we observe that there also exists a significant difference
in relative deviation (RD) between the B and QE treatments (p − value =0.047) and between the BS and QES treatments (p−value = 0.047) at the 5%
significance level. However, we do not find any difference in relative absolutedeviation (RAD) or geometric absolute deviation (GAD) in the preintervention periods. The reason is that RAD and GAD do not differentiate between
overpricing and underpricing. While in the preintervention periods, bonds
tend to be underpriced in the B and BS treatments, and they tend to be
overpriced in the QE and QES treatments.

48

49

a: p-values are based on the pairwise Wilcoxon rank-sum test among the four treatments

Table D.2: Median value (standard deviation) of each measure of bond mispricing.
B
QE
BS
QES
B = QEa BS = QESa
Round 1, Periods 1 - 3. Preintervention periods
RAD 0.180 (0.154) 0.631 (0.440) 0.261 (0.177) 0.197 (0.316) p = 0.375
p = 1.000
RD -0.046 (0.259) 0.546 (0.497) -0.200 (0.323) 0.117 (0.354) p = 0.033 p = 0.033
GAD 0.221 (0.237) 0.596 (0.426) 0.388 (0.319) 0.201 (0.303) p = 0.815
p = 1.000
GD -0.524 (0.243) 0.467 (0.493) -0.208 (0.318) 0.101 (0.328) p =0.047 p = 0.047
Round 1, Periods 4 - 6. Postintervention periods
RAD 0.233 (1.061) 0.920 (1.918) 0.164 (0.133) 0.479 (0.432) p = 0.815
p = 0.447
RD 0.170 (1.096) 0.875 (1.934) -0.050 (0.232) 0.285 (0.565) p = 0.969
p = 0.684
GAD 0.237 (1.051) 0.871 (1.401) 0.232 (0.243) 0.591 (0.494) p = 0.969
p = 0.684
GD 0.166 (1.091) 0.871 (1.433) -0.054 (0.233) 0.252 (0.596) p = 0.969
p = 1.000
Round 2, Periods 1 - 3. Preintervention periods
RAD 0.277 (1.024) 0.908 (0.778) 0.200 (0.138) 0.251 (0.420) p = 1.000
p = 1.000
RD 0.276 (1.041) 0.902 (0.778) -0.053 (0.227) 0.200 (0.482) p = 0.969
p = 0.355
GAD 0.276 (1.017) 0.860 (0.759) 0.248 (0.213) 0.272 (0.415) p = 1.000
p = 1.000
GD 0.276 (1.036) 0.860 (0.759) -0.055 (0.227) 0.198 (0.483) p = 0.969
p = 0.355
Round 2, Periods 4 - 6. Postintervention periods
RAD 0.333 (0.643) 0.786 (0.612) 0.392 (0.255) 0.507 (2.173) p = 1.000
p = 1.000
RD 0.268 (0.648) 0.775 (0.645) -0.240 (0.358) -0.048 (2.34)
p = 0.969
p = 1.000
GAD 0.331 (0.602) 0.764 (0.544) 0.686 (1.260) 0.702 (1.291) p = 1.000
p = 1.000
GD 0.264 (0.607) 0.764 (0.574) -0.331(0.376) -0.059 (1.314) p = 0.815
p = 1.000

E

Analysis of trading volume

Besides the mispricing and consumption, we also consider whether the intervention influences the trading volume. Intuitively, in the QES treatment,
if some participants expect to sell bonds to the computer at a high market
price during the QE operation, they have an incentive to trade the bonds.
That means the trading volume in the QES treatment may be higher thanthat in the BS treatment in the preintervention periods. Moreover, because
participants have to smooth consumption by trading in the B and QE treatments, the trading volume in the B and QE treatments should be higher
than in the BS treatment.
Table E.1 reports the median of Turnover in each treatment (top panel),as well as the results of comparisons among treatments (bottom panel).
Turnover of group g, T Og , is defined asT

1 X qt,TO =T t=1 OStg(E.1)

where qt is the trading volume at period t, and OSt is the total number of
the tradable bonds at period t.
Contrary to our intuition, from Table E.1, we observe that while Turnoveris higher in the B treatment than in the QE treatment, and also in the
B treatment than in the BS treatment, there is no statistically significant
difference in Turnover among treatments either in the preintervation or the
postintervention periods. This may be because the intervention may not only50

Table E.1: Median of Turnover in each treatment.
Preintervention periods
B
QE BS QES
Round 1 0.50 0.40 0.40 0.38
Round 2 0.43 0.38 0.37 0.30

Round 1Round 2

Postintervention periods
B
QE BS QES
0.42 0.40 0.38 0.35
0.40 0.48 0.33 0.48

The comparison across treatments.
Preintervention periods
Postintervention periods
B
QE
QES
Benchmark QE
QES
QE
1.000
QE
1.000
QES 0.600 1.000
QES
1.000
1.000
BS
0.250 1.000 1.000 BS
1.000
1.000 1.000
B
QE
QES
Benchmark QE
QES
QE
1.000
QE
0.790
QES
0.540
1.000
QES 0.550 1.000
BS
1.000 1.000 1.000 BS
1.000
0.150 0.180

Note: The p − values from the pairwise Wilcoxon rank-sum test are reported. Bonferroni method is used
for correcting p-values for multiple comparisons.

increase the participants’ incentive to buy the bonds, but also increase the
incentive to keep bonds, and neutralizes the variation of the trading volume.

51

F

Discounted payoffs of each typeIn this appendix, we compare discounted payoff, wi =

P6

t=1 π

t−1

uJP Y (cit )),for two types (1 and 2) separately across four treatments. Here, we use thegifor each type (∈ {1, 2}) , Wtype, as an independent
within-group mean of wtype

observation.
Table F.1 shows the across-group medians W1g and W2g in the four treatments for Rounds 1 and 2. It shows that W1g and W2g are significantly
different in the BS treatment in both rounds. Furthermore, it shows thatsignificant differences across treatments are observed only for Type 2 in bothrounds. Finally, a statistically significant increase in W2g in Round 2 compared with Round 1 is observed at the 5% significance level in all the treatments except for QES, but not for W1g .
The significantly lower discounted payoffs for Type 2 compared withType 1 in the BS treatment is because of the difficulty Type 2 players hadin trading the bond. When saving is possible, Type 1 players whose initialendowment consists of a larger amount and one unit of bonds can easily
carry their surplus cash to the next period without purchasing the bondfrom Type 2 players who are initially endowed with four units of bonds anda smaller amount of cash. As a result, Type 2 players’ consumption becomes
lower in early periods, and thus the lower discounted payoffs.

52

Table F.1: Median W1g and W2g
The median W1g and W2g in Round 1
B
QE
BS
Type 1 (W1g )5629.78 5727.28 5894.95
5833.97 5684.92 5235.36
Type 2 (W2g )gg∗p-values (H0 : W1 = W2 ) 0.359
0.496
0.039

QES
5783.585856.08
0.945

p-values+ for treatment comparisons for Round 1
Type 1
Type 2
B
QE
QES
B
QE
QES
QE
1.000
QE
1.000
QES 1.000 1.000
QES 1.000 0.684
0.034 0.024 0.033
BS
1.000 1.000 1.000 BSMedian W1g and W2g in Round 2
B
QE
BS
QES
g
Type 1(W1 )5687.36 5800.10 5996.34 5930.37
Type 2 (W2g )6036.74 5861.82 5679.81 6019.47
gg∗p-values (H0 : W1 = W2 ) 0.039
0.129
0.008
0.945
p-values+ for treatment comparisons for Round 2
Type 1
Type 2
B
QE
QES
B
QE
QES
QE
1.000
QE
1.000
QES 1.000 1.000
QES 0.091 0.556
BS
0.189 0.969 1.000 BS
0.001 0.085 0.047
p-values∗ comparing Round 1 and Round 2
B
QE
BS
QES
Type 1(R1=R2) 0.820 0.734 0.074 0.148
Type 2 (R1=R2) 0.020 0.004 0.004 0.055∗: p − values from the Wilcoxon signed-rank (WSR) test are reported.
+: p − values from the pairwise Mann–Whitney U (MW) test are reported. Bonferroni
method is used for correcting p-values for multiple comparisons.

53

G

Nondiscounted payoffs in preintervention
and postintervention periods

In this section, we investigate further the effect of intervention by separately
considering the preintervention and postintervention periods. Namely, wei=compare nondiscounted payoffs in preintervention (periods 1 to 3), w
epre
P3
P
1
i
i
epost
= 31 6t=4 uJP Y (cit ).
t=1 uJP Y (ct ), and in postintervention (periods 4 to 6), w
3

We use within-group means as an independent observation. Table G.1 reports these measures for the four treatments in Rounds 1 and 2.
iare not significantly different
Table G.1 shows that in Round 1, w
epre

(at the 5% significance level) between the B and QE treatments, as well asibetween the BS and QES treatments. The same is true for w
epost. Thus,the QE intervention does not significantly affect the nondiscounted payoffs.
ii
isis significantly lower (p = 0.034), while w
epost
Table G.1 also shows that w
epre

significantly higher (p = 0.003), in the BS treatment than in the B treatment.
Thus, the saving possibility, in the absence of QE intervention, results insignificantly lower payoffs in periods 1 to 3, while it results in significantly
higher payoffs in periods 4 to 6. In Round 2, contrary to Round 1, the saving
possibility does not significantly lower the payoffs in periods 1 to 3. However,it results in significantly higher payoffs in the postintervention periods both in
the presence (QE vs QES, p = 0.022) and in the absence (B vs BS, p < 0.001)
of the intervention.

54

i
i
and w
epost
Table G.1: Median w
epre
iiMedian w
epre
and w
epost
in Round 1
B
QE
BS
QES
i
Preintervention (wepre )
4358.03 4202.81 3880.03 4168.39
i4277.37 4326.12 4719.25 4869.29
Postintervention (wepost )
p-values∗ (H0 : Pre = Post) 0.734
0.004
0.004
0.008

p-values+ for treatment comparisons in Round 1
Preintervention periods
Postintervention periods
B
QE
QES
B
QE
QES
QE
0.462
QE
0.969
QES 0.022 0.216
QES 0.556 1.000
0.003 0.113 1.000
BS
0.034 0.011 0.091 BSiiMedian w
epre
and w
epost
in Round 2
B
QE
BS
QES
i
Preintervention (wepre)
4413.53 4402.24 4278.49 4347.75
i)4371.66 4461.73 4733.41 4756.16
Postintervention (wepost∗
p-values (H0 : Pre = Post) 0.652
0.359
0.004
0.008

p-values+ for treatment comparisons in Round 2
Preintervention periods
Postintervention periods
B
QE
QES
B
QE
QES
QE
1.000
QE
1.000
QES 1.000 1.000
QES <0.001 0.022
BS
0.064 0.302 1.000 BS<0.001 0.024 1.000∗: p − values from the Wilcoxon signed-rank (WSR) test are reported.
+: p−values from the pairwise Mann–Whitney U (MW) test are reported. Bonferroni method
is used for correcting p-values for multiple comparisons.

55