key: cord-1054435-0qp0s9il
authors: Penalver, Adrian; Hanaki, Nobuyuki; Akiyama, Eizo; Funaki, Yukihiko; Ishikawa, Ryuichiro
title: A quantitative easing experiment()
date: 2020-08-29
journal: J Econ Dyn Control
DOI: 10.1016/j.jedc.2020.103978
sha: df87eae5b63c6cca481468d7c094d96689faabb2
doc_id: 1054435
cord_uid: 0qp0s9il

We experimentally investigate the effect of a central bank buying bonds for cash in a quantitative easing (QE) operation. In our experiment, the bonds are perfect substitutes for cash and have a constant fundamental value which is not affected by QE in the rational expectations equilibrium. We find that QE raises bond prices above those in the benchmark treatment without QE. Subjects in the benchmark treatment learned to trade the bonds at their fundamental value but those in treatments with QE became more convinced after repeated exposure to the same treatment that QE boosts bond prices. This suggests the possibility of a behavioural channel for the observed effects of actual QE operations on bond yields.

Quantitative easing (QE) has been the biggest monetary policy experiment in modern times. Since 2008, seven major central banks have implemented large scale asset purchase programmes, buying on average assets equivalent to 15% of nominal GDP. 1 They have bought a wide range of assets, including corporate and covered bonds, and asset-backed securities but the core interventions have been in government bond markets. In this most basic form, QE is the purchase of government bonds in exchange for central bank reserves with the intention to retain them for a significant length of time. In an era in which interest is paid on reserves, this amounts to the exchange of one interestbearing liability of the state for another. In textbook models with frictionless and complete markets and fully rational and infinitely long-living agents, such a transaction can have no temporary or permanent effects on any macroeconomic variables in equilibrium (Eggertsson and Woodford, 2003) .

In particular, short-term and long-term interest rates will be unchanged and there will be no effect on output and inflation. 2 In these circumstances, QE would just be an irrelevant shortening of the average maturity of net public debt.

There is, however, strong evidence that QE programmes have moved bond prices and yields, although the scale and duration of such effects is still being debated (Krishnamurthy and Vissing-Jorgensen, 2011; Joyce et al., 2011; Arrata and Nguyen, 2017) . The literature has focused on two departures from the textbook model to explain these effects. One theory is that central bank money and government bonds are not perfect substitutes (Tobin, 1958) perhaps because markets are segmented due to investors' 'preferred habitat' (Vayanos and Vila, 2009) or investors do not like holding the interest rate risk associated with long-term bonds. If long-term government bonds and central bank reserves are not perfect substitutes, a fall in the volume of long-term bonds in private hands can raise the price and lower the yield relative to short-term rates. The alternative explanation is that QE is a means by which central banks can give credibility to forward guidance commitments to deviate from established monetary policy behaviour, such as a Taylor rule (Eggertsson and Woodford, 2003) . QE reinforces the signal that the short-term rate will remain low for longer than a timeconsistent policy rule would suggest. Lowering the expected path of short-term rates drags down long-term rates through the expectations hypothesis of the term structure. This paper considers a different explanation. As currently implemented, QE is a commitment to buy relatively quickly a fixed value of bonds at any price. Indeed, since the intermediate objective of the policy is to lower bond yields, the greater the rise in bond prices is, the more "successful" the instrument is. The central bank is thus an unusual participant in the bond market because it is not deterred from buying by a higher market price (at least up to some point). If there were only one seller of government bonds, he or she could offer to sell at a price at which the central bank was just indifferent between buying and reneging on its commitment at a reputational cost.

In other words, once the central bank has committed to buy, there is an exploitable opportunity for sellers collectively. However, in a completely competitive market with fully rational agents, common knowledge, no segmentation and no ability to buy enough of the market to become a monopoly seller, such an effect should not exist.

But what if some of these assumptions do not hold, for example, when people's behaviors are better characterized by a level-k type thinking (Nagel, 1995; Camerer et al., 2004) ? In such framework, if k = 0 players have an instinctive response that the presence of a large external buyer should raise the price, then this will influence the views of k = 1 players which together affect the expectations of k = 2 players and so on. As long as it is believed that there are enough low k players who believe prices will rise, even a very sophisticated player might be induced to make an offer above the fundamental price. This structure is similar to the guessing game of Ledoux made famous by Nagel (1995) . 3 Level-k models can account for many non-equilibrium behaviors observed in the laboratory experiments, including, various types of auctions (see, among others, Crawford and Iriberri, 2007; Crawford et al., 2013) , 4 Bertrand price competition (Dufwenberg and Gneezy, 2000; Baye and Morgan, 2004) , and the travelers' dilemma game (Capra et al., 1999) . 5 Recently, researchers have started to incorporate level-k thinking in analyses of monetary policies. Lovino and Sergeyev (2018) construct a model of level-k thinking applied to QE, and Farhi and Werning (2019) use it, together with incomplete credit market, in explaining the "forward guidance puzzle." We therefore anticipate that many participants will have an instinctive response that the presence of a 3 See, Buhren et al. (2012) for historical details. 4 It is well known in the experimental literature on single unit demand auctions that subjects tend to overbid compared with the risk-neutral theoretical predictions in both private and common value auctions of various formats. See, among others, Kagel (1995) and Kagel and Levin (2017) for surveys. The literature suggests several explanations for such observed deviations, including nonstandard preferences, such as 'spite' and the 'joy of winning' (see, for example Cooper and Fang, 2008) or inconsistent beliefs, such as the cursed equilibrium (Eyster and Rabin, 2005) or level-k reasoning (Crawford and Iriberri, 2007) . We also note that there are experimental studies pointing out that the level-k model, which relies on the best reply on the wrongly specified belief, cannot account for observed behavior in a private value auction (Kirchkamp and Reiβ, 2011) or in a common value auction (Ivanov et al., 2010) . 5 We thank an anonymous referee for pointing this out.

large external buyer should raise the price.

The main purposes of the experiment presented in this paper are (a) to investigate whether interventions indeed raise the price of bonds, and (b) to investigate whether the observed effect of the interventions disappears with repeated exposure to the same treatment.

The environment which we consider is very simple, and is set out in more detail in Section 2.

The experiment is designed to remove as many extraneous sources of uncertainty (such as stochastic dividend payments) and confusion (such as an inability to understand a declining fundamental value) as possible. At the start of the experiment, participants are given bonds and cash, which are essentially identical ways of transferring this endowment to the end of the experiment in the rational expectations equilibrium (REE). The REE -or fundamental -price is constant throughout the experiment. In the Benchmark treatment, participants can trade the bonds for cash among themselves over 11 periods. There is no reason to trade one asset for the other at this fundamental price and the volume of trade should be indeterminate.

In our first QE treatment (called Buy&Hold treatment), the central bank will buy a third of the bonds available in the market before periods four and five, using a discriminatory price auction.

This will be described as a QE operation. The central bank holds these bonds until the end of the experiment. However, as this operation changes neither the value of the bonds at maturity nor the equilibrium cash flows, the auctions are competitive and nobody can become a monopoly seller, the market price for bonds in the REE does not change.

In our second QE treatment (called Buy&Sell treatment), the central bank again buys a third of the bonds available in the market before periods four and five, but sells them back again in a reverse discriminatory auction before periods eight and nine. Thus, the participants are back where they started and again there is no change in the fundamental price.

Despite its simplicity, we find statistically significant evidence of mispricing in the Benchmark treatment and in the two QE treatments when participants are first exposed to the experiment.

And the degree of mispricing is higher in the two QE treatments in the periods after the first intervention takes place. 6 The participants then repeat the same treatment to which they were originally exposed twice more. By the third round, as shown in the literature following Smith et al. (1988) , participants in the Benchmark treatment have clearly realized that prices should not deviate from the fundamental price and the median price is essentially flat across the 11 periods 6 We also found this in our first set of experiment reported online supplementary appendix I.

of trading at this level (Palan, 2013, Obs.1) . 7 By contrast, we find that prices remain statistically significantly above the fundamental price in both the QE treatments. However, there is relatively little to distinguish between the two QE treatment effects except for the last few periods following the reverse intervention.

Throughout the experiment, we collect forecasts of future market prices from the current period onwards from each participant. Thus, we have a rich data set on the beliefs of the participants. We report a very tight link between median forecasts and market prices and between past prices and current forecasts. Forecast dispersion across participants in each group that trades together shrinks very rapidly and although the participants do not know this (others' price forecasts are not revealed to participants), these common priors condition the evolution of future prices.

An interesting feature of both QE treatments is that participants begin to anticipate higher prices from the start, particularly by the third round. Thus, it is not an inability to think forward that prevents the equilibrium price from emerging. Instead, everyone comes to expect that the bonds will be priced high in the auctions.

Our experiment is most similar in motivation to Haruvy et al. (2014) . That paper considered share buybacks and share issues in a setup in which the fundamental price of an individual share should be independent of the quantity of outstanding shares. Thus, in REE, the market price should not be affected by these treatment operations. Nevertheless, the authors found that share prices rise after a buyback and fall after an issuance of shares, as we do in our experiment. Haruvy et al. (2014) proposes two possible reasons for this result: (i) the downward sloping nature of the demand schedule for the bonds, and (ii) the change in the traders' beliefs about the intrinsic value of shares owing to the change in the quantity of shares. In our experiment, the market demand schedule is downward sloping by construction, thus the first reason certainly applies. For the traders' beliefs, although we cannot analyze their beliefs about "intrinsic value" of bonds, we do show that the higher the average price paid during the buy operation in Round 1, the higher the period 1 price expectation in Round 2. Thus, the interventions do affect participants expectations about market prices. The latter analysis was made possible through our multiple rounds experiment with forecast elicitation. 8 7 See, Palan (2013) , Powell and Shestakova (2016) , and Nuzzo and Morone (2017) for recent surveys of the literature. The mispricing can reappear, however, when the common experience is broken by a change in the market environment (Hussam et al., 2008) or by inflows of new and inexperienced traders (Dufwenberg et al., 2005; Akiyama et al., 2014; Kirchler et al., 2015) . 8 We thank an anonymous reviewer for pointing this out.

Furthermore, we depart from the approach of Haruvy et al. (2014) in several other ways. Our bonds, unlike their shares, have no intrinsic uncertainty in their payoffs so risk aversion plays no role in determining prices. In addition, we consider a setup in which the fundamental price of the bond should be constant and equal to its maturity value, so there is no risk in our experiment that participants are confused by the idea of an asset that should fall in value, as noted by Kirchler et al. (2012) and Stöckl et al. (2015) . Furthermore, in our experiment, market transactions are organized according to a call market, instead of a continuous double auction and, importantly, market interventions take place outside of the usual trading periods, according to an auction rule, with subjects being clearly informed about the exact manner in which interventions will take place.

Our experiment setting also focuses on the direct effect of the asset purchases on prices and price forecasts and their interrelationship. The similar effects of interventions observed both in Haruvy et al. (2014) and in our study, despite of all these differences in the experimental setups, suggest that the initial effects (i.e., before the repetition) of interventions are robust to these differences.

The remainder of the paper is organized as follows. Section 2 describes the experiment in more detail, section 3 presents the main results, and section 4 concludes.

We first describe the aspects of the experiment that are common to all treatments. Then, we describe each of our three treatments. See online supplementary material (OSM) VI for an English translation of the instructions.

We set up an experimental bond market very similar to Bostian and Holt (2009) . A market consists of N traders who hold a portfolio of riskless bonds and cash on deposit. At the start of the experiment, each trader is endowed with eight bonds and 800 ECU of cash. Each round of the experiment lasts for T = 11 periods. Each bond pays a dividend of 6 ECU per period and matures at the end of period 11 for 120 ECUs. Cash on deposit receives a 5% interest rate per period. In this setting, the fundamental value (F V t ) of bond at the beginning of period t is 120 ECU for all t = 1, ..., T in REE. 9

9 Consider the beginning of period T . If a trader buys a unit of bond at price P T , then he or she or she will receive 6+120 ECU at the end of period T . If the trader kept the same amount cash until the end, then it will become In each period, the participants have the opportunity (but are not obliged) to trade bonds and cash with each other in a call market, as in van Boening et al. (1993) , Haruvy et al. (2007) , and Akiyama et al. (2014 . In a call market, traders submit an order by specifying a price-quantity pair. In period t, for example, if trader i wishes to submit a buy order, i must specify the maximum price at which i is willing to buy a unit of bond (bid, b i t ) and how many units of bonds trader i wishes to purchase (d i t ). If trader i wishes to submit a sell order in period t, i must specify the minimum price at which i is willing to sell a unit of bond (ask, a i t ) and how many units of bonds i wishes to sell (s i t ). In each period, each trader can submit both a buy order and a sell order, just one of them, or no order. Neither short-selling nor borrowing of cash is allowed. Thus, in the case where i submits a sell order in period t, i must have at least s i t units of bonds in his or her portfolio.

Similarly, if i submits a buy order in period t, his or her cash holding has to be no less than b i t d i t .

Finally, in the case where i submits both buy and sell orders, we require that b i t ≤ a i t . 10 Once all the traders in the market submit their orders, the orders are aggregated and a market-clearing price is computed. Following the existing studies (Haruvy et al., 2007; Akiyama et al., 2014 , when there are multiple market-clearing prices, we choose the minimum among them.

We have employed a call market structure instead of a continuous double auction to facilitate the forecasting task performed by participants (which will be described in the next subsection). In the call market, because there is only one market-clearing price per period, the prices that participants need to forecast are clearly defined. In any case, the existing experimental results show that call markets and continuous double auctions generate similar price dynamics (Palan, 2013, Obs. 27) , although trading volumes can be different.

By eliciting traders' expectations regarding the current and future period prices at the beginning of each period, we aim to better understand the link between price expectations and market prices and how and why price expectations evolve over time.

At the beginning of each period, before traders submit their orders, we ask subjects to submit 1.05P T after the interest payment. As these two have to be the same in the equilibrium, we have 1.05F V T = 126, i.e., F V T = 120. Now, consider the beginning of period T − 1. If a trader buys a unit of bond at P T −1 , he or she will have 6 + F V T = 126 in fundamental terms at the end of the period. If the same amount of cash is held until the end of period, it will become 1.05P T −1 . As these two have to be equivalent, 1.05F V T −1 = 126, i.e., F V T −1 = 120. One can do the same thing for all the remaining periods to obtain F Vt = 120 for all t = 1, . . . , T . 10 There was an additional technical constraint in that we only allowed a i t and b i t to take integer values between 1 and 2,000. This was purely due to the way the experimental software was programmed. their forecasts of the bond price in the current period as well as in all the remaining periods. That is, at the beginning of period t, subject i submits his or her forecasts for bond prices in periods t, t + 1, ..., T . This elicitation method allows us to observe the dynamics of subjects' short-run and long-run forecasts, and it has been employed, for example, by Haruvy et al. (2007) and Akiyama et al. (2014 

We consider three treatments: (T1) Benchmark, (T2) Buy&Hold, and (T3) Buy&Sell. The Benchmark treatment has no central bank intervention and is conducted under the basic setting described above. In both the Buy&Hold and Buy&Sell treatments, participants are told before the experiment begins that the central bank will try to buy a third of the outstanding bonds (by volume) through a discriminatory auction before the beginning of periods 4 and 5 (we call this the buy operation).

In the Buy&Sell treatment, it is pre-announced that, before the beginning of periods 8 and 9, the central bank will sell the bonds it has to the market (we call this the sell operation), again using a discriminatory auction. 12

Many of these features were chosen to mimic the way QE has been implemented. As mentioned in the Introduction, central banks have bought very significant shares of the outstanding volume of bonds. The ECB has set a purchase limit of 1/3 of the outstanding stock of any specific bond and purchases in some jurisdictions have approached this limit. Central banks have also announced their intentions to purchase bonds well before they actually started buying. These announcements have tended to have more effect on bond prices than the actual purchases. To see whether this effect 11 Akiyama et al. (2014 introduced this incentive scheme for the forecasting performance to minimize the possibility of subjects attempting to improve their forecasting performance by engaging in unprofitable trading strategies simply to make the market prices closer to their forecasts. Recently, however, Hanaki et al. (2018) found that rewarding subjects for their forecasting performance this way can enlarge mispricing compared with the experiments where subjects only trade and no forecast is elicited. Although the setup considered by Hanaki et al. (2018) is slightly different from ours, it is possible that similar effects operate in the current experiment. However, it should be noted that, because subjects are rewarded for their forecasting performance in an identical way across all the treatments that we consider in this paper, any such effects will not influence our analyses based on treatment comparisons. 12 The experiment was framed in a neutral language. Subjects were told that "the computer will buy (or sell) the bond" instead of "the central bank will buy (or sell)." would be replicated in the lab, we had three periods of market trading before the central bank began purchasing. We also spread the purchases and sales (where applicable) over two periods to have an interim market price. One difference with the way QE was actually implement is that our central bank commits to buy a quantity of bonds rather than a target value of bonds but we do not think this difference is important.

Part of the motivation for choosing a discriminatory auction for the market intervention is the way that the Bank of England implemented its asset purchase scheme. 13

During the buy operations in T2 and T3, the central bank attempts to buy half of the stock of bonds planned (i.e., a sixth of the outstanding bonds) in both periods 4 and 5. If it fails to buy the bonds planned in period 4, the residual amount is added to its operation in period 5. If it fails to buy its revised target in period 5, the shortfall is ignored. 14 During each of these two buy operations, each trader can submit a sell order that specifies a price-quantity pair. Once all the orders are submitted, the central bank sorts the submitted offers in ascending order and buys up to the targeted amount, paying the specified price in each case. 15

In the Buy&Hold treatment, once the central bank completes its buy operation, it will hold the bonds it bought until the end of period T. In other words, the central bank permanently removes those bonds from the market. In the Buy&Sell treatment, the central bank sells the bonds it has to the market participants during its sell operation before periods 8 and 9.

The sell operation before periods 8 and 9 in the Buy&Sell treatment is conducted in a similar manner to the buy operation. The central bank attempts to sell back half of the targeted amount in period 8 and whatever amount remains in period 9. If it fails to sell back all the units of bonds during these two sell operations, it will simply keep them until the end of period T. During these sell operations, each trader can submit a buy order that specifies a price-quantity pair and the central bank sorts the bids in descending order, and sells up to the targeted amount, in each case receiving the specified price.

Since a primary motivation for our experiment is to see whether QE can work through an entirely 13 See The Bank of England's Asset Purchase Facility (2017) for an explanation of how the Bank of England conducted QE. It should be noted that not all governments use discriminatory auctions in auctioning off their securities, with many using uniform price auctions. As summarized by Marszalec (2017) , the literature, both theoretical and empirical, is inconclusive regarding which method of the two commonly used auction formats is superior in terms of the revenue-raising ability.

14 Except for two cases to be reported in footnote 21, the central bank always bought or sold its planned amount in each period. 15 In cases with multiple offers at the same marginal offer price, purchases are randomly allocated across those participants. The second element is that the auctions are competitive and so any price above the fundamental price cannot be a REE. Even if several participants were to corner the market, each would have an incentive to offer at less than the price of the other sellers until any alternative equilibrium price would unravel. 16 Furthermore, we can rule out the existence of mixed strategy equilibria a la Kaplan and Wettstein (2000) because there is an upper limit for the order price one can submit in our experiment.

In all three cases, the same group of participants repeats the treatment that they were originally assigned three times. We call each sequence of 11 periods a round. We are interested in how subjects learn and adjust their forecasts and trading behavior based on their experience in playing the same treatment. At the end of the final round of the game, one of the three rounds is chosen randomly for payment. Subjects are paid based on their final cash holding and the bonus for their forecast performance of this chosen round, in addition to their participation fee of 500 JPY. The exchange rate between ECU and JPY was 1 ECU = 1 JPY.

Computerized experiments (with z-Tree, Fischbacher, 2007) were conducted at Waseda University and the University of Tsukuba between January and July 2017. We conducted the whole exercise with two market sizes, N = 6 and N = 12. This was intended to test whether our earlier results 16 In our experiment, because prices must be an integer, in addition to everyone bidding FV, there is another equilibrium in which everyone bids 1 ECU above the fundamental value. This is because when everyone bids FV+1, each can expect to obtain 1/3 of ECU per bond, while bidding FV will result in zero profit. Thus, there is no incentive to unilaterally deviate and bid lower. This issue of multiple equilibria due to an integer constraint is also known in p-beauty contest games (López, 2001 based on N = 6 (Penalver et al., 2017) were robust to the degree of competition in each market.

Because the results were not statistically significantly different between two market sizes, as reported in OSM IV, we combined the two datasets and report pooled results. A total of 438 students were recruited from a variety of disciplines and none had ever participated in similar experiments before. including the participation fee. Figure 1 illustrates the dynamics of the median observed price in our experiments for the three rounds. 17 The Benchmark is shown in thin blue, the Buy&Hold is in thick red, and the Buy&Sell is in dashed black. The median price path for the Benchmark treatment is slightly above 120 throughout the first round. But in the second and particularly the third rounds, the median price is scarcely different from the fundamental price.

In the Buy&Hold treatment, the median price drifts up from period 4 on (after the first intervention) and it stays high until period 8. The median price starts to decline from period 9 on and as in the Benchmark treatment, it converges back to 120 by period 11. In Round 2 of the Buy&Hold treatment, the action occurs earlier. The median price starts above 120 in period 1, and stays high again until period 8. The median price begins to decline towards the fundamental price in period 17 The dynamics of observed prices in each market are shown in the OSM II.

Round 2 Round 3 9. By Round 3, in the Buy&Hold treatment, the median price again starts above the fundamental price but it peaks in period 3. The median price converges to the FV by period 9.

The Buy&Sell treatment shows a very similar pattern to the Buy&Hold treatment in Round 1 except for a noticeable drop in the median price for the Buy&Sell treatment when the central bank starts to sell in period 8. The action again begins earlier in Round 2 and the median peaks in period 4. By Round 3, the median price is high initially and then declines after period 3.

Now, we formally compare the magnitude of mispricing observed in the three treatments over three rounds. Following Powell (2016), we measure the degree of mispricing using the volume-adjusted geometric absolute deviation (vGAD) and the volume-adjusted geometric deviation (vGD). 18 vGAD m and vGD m for market m are defined as follows:

where v m t and P m t are the volume and the realized price observed in period t of market m. F V t = 120 Visually, it is clear that there is very little difference between the cumulative distributions in Round 1 and this is confirmed using the KW test. Pairwise, the degree of mispricing in the benchmark is less than in the Buy&Hold treatment, but this difference is only marginally significant under the vGAD measure and not significant under the vGD measure. The picture changes dramatically in Rounds 2 and 3. According to both measures, the level of mispricing in the Benchmark treatment is lower than in both the Buy&Hold and the Buy&Sell treatments with a high statistical significance, although there is no significant difference between the latter two treatments over the whole period.

Looking at mis-pricing over the full 11 periods, however, hides some important differences across the three treatments between different sub-periods. The first three periods of trading rounds (periods 1-3) take place before the first buy operation (in Buy&Hold as well as Buy&Sell treatments). So, if participants anticipate some effect of the buy operation, this should show up in these periods in these treatments compared to the benchmark. Trading in periods 5-7 occurs between the buy and the sell operation (in Buy&Sell treatment), thus, if anticipation of the sell operation is to have any effects, they should be visible in these periods in this treatment relative to the Buy&Hold treatment.

Finally, trading in the last three periods (periods 9-11) takes place after the sell operation, when traders are only anticipating the maturity of the bonds. Analyzing these three sub-periods separately give us insights into the effects of these interventions. Figure 3 : ECD of vGAD in three subperiods. vGAD 1 (periods 1-3). vGAD 2 (period 5-7). vGAD 3 (period 9-11) for three rounds. T1: Benchmark (blue), T2: Buy&Hold (red), and T3: Buy&Sell (dashed black). P-values from the KW test for multiple comparison as well as MW tests for pairwise comparisons are reported.

pairwise differences between the mispricing in the Benchmark and the two treatments fall below the 5% significance level. Furthermore, in Round 3, the vGAD in the first subperiod is significantly higher in the Buy&Hold and the Buy&Sell treatments than in the Benchmark.

In this subsection, to better understand the dynamics of prices across periods and rounds in the three treatments, we first summarize the results of the market interventions. Table 2 reports the average prices during the buy operations (p bo , panel (a)) as well as their differences from the average market prices in the preceding three periods (p bo − p 1−3 , panel (b) ) and sell operations (p so , panel (c)) and their differences from the average prices in the preceding three periods (p so − p 6−8 , panel (d)). It also reports the difference between the average transaction prices between the buy and the sell operations (panel (e)).

We observe that, on average, the central bank paid prices substantially above the fundamental value during its buy operations, which may be natural given that the market prices are also higher than the fundamental value. The prices the central bank paid are, however, even higher than the average market prices in the three preceding periods although the difference becomes smaller in later rounds. The prices paid during the buy operations of both the Buy&Hold and Buy&Sell treatments are very similar and do not display any significant differences across three rounds. 20 The sell operation only occurs in the Buy&Sell treatment. Panel (d) of Table 2 reports that the central bank sells for a price below the average market prices in the three periods before the operation, although the difference becomes slightly smaller, in magnitude, in later rounds.

The observed high prices during the buy operation of our experiment, which result from subjects not competing aggressively enough, is very similar to price dispersion observed in Bertrand price competition experiments (called the "Bertrand Paradox", see, Dufwenberg and Gneezy, 2000; Baye and Morgan, 2004) as well as deviation from Nash equilibrium in experiments for the travelers' dilemma game (Capra et al., 1999) . What is rather surprising in our data is the absence of significant differences across the three rounds. In Dufwenberg and Gneezy (2000) , for example, when number of players is 3 or more, participants quickly learned to compete more aggressively in Bertrand competition experiment. This is not just for the average prices the central bank paid, but even at 20 The estimated coefficients of the Rounds 2 and 3 dummies on the group fixed effect regressions that regress p bo on a constant and these two dummies are not statistically significantly different from zero for the two treatments. In a repeated multi-unit auction of Abbink et al. (2006) , it takes as many as 25 repetitions for the outcomes (revenue measured relative to the value of the item being auctioned off) to stabilize.

Although the slow learning observed in Abbink et al. (2006) may partly be a result of the value of the items being auctioned varying from one auction to another, it is possible that if the experiment had been repeated many more times, participants in our experiment would have learned to bid more competitively during the buy operation. However, the current experiment is not sufficient to study this question.

Panel (e), for convenience, displays the difference in the prices paid and received in the Buy&Sell treatment. The difference is not statistically significantly different from zero in Round 1 but becomes strongly statistically significant in Rounds 2 and 3. As a result, the central bank makes a very large loss and a substantial amount of cash (on average, 20% of the fundamental value of the bonds) was transferred from the central bank to the market participants through these two operations.

Such a large transfer of cash from the central bank to market participants substantially increases the cash-to-asset ratio. Existing studies (see, e.g., Kirchler et al., 2012; Deck et al., 2014) have found that prices can rise when the ratio of cash to assets increases. So one reason why the two buy operations might increase prices is simply the resulting higher cash to assets ratios. To check if the higher cash-to-asset ratio is indeed the main driver of higher mispricing, we conduct the following regression:

where p bo m is the average transaction price per unit of bonds during the buy operation for market m, ∆p m ≡ p 5−7 m − p 1−3 m is the difference in the average prices for the three periods immediately before and after the buy operation for market m (with p l−k m being the average price observed between period l and k for market m).

Regression (3) tests whether the differences in prices in the market before and after the buy operation are related to the average prices paid by the central banks. If the cash-to-asset ratio was an important driver for the price increase after the buy operation, there should be a statistically (3).

The result is reported in Table 3 . We do not observe any statistically significant, positive relationship between the change in the market prices before and after the buy operation and the average price paid by the central bank during its buy operation. In Round 3, it is even negative rather than positive. 21 Thus, the cash-in-the-market effect does not seem to be the main driver of our results.

More importantly, the cash-in-the-market effect cannot explain the higher mispricing observed in the three periods before the buy operations in the two treatments with intervention compared with the Benchmark in Rounds 2 and 3 that we have seen above (in Figure 3) . This is because, in these first three periods, the cash-to-asset ratios are the same in all the treatments.

Indeed, regressing vGD 1 (vGD for periods 1-3) 22 on treatment dummies and the outcome of the buy operations in the previous round (reported in Table 4 ) shows that the mispricing in the first three periods of the current round is positively and significantly related to the average price that the central bank paid during its buy operation in the previous round.

This suggests that the results of market interventions in a round influenced subjects' price expectations, which in turn influenced the market prices, in the following round. In the next subsection, we will investigate this channel through analyzing the dynamics of subjects' forecasts. 21 There were two cases in Round 1 (for the market with six traders) where the central bank failed to buy the targeted amount of bonds (instead of 16, it bought 14 or 15). For these two instances, the p bo is not a precise measure of the change in the cash-to-asset ratio caused by the buy operation. We ran the regression (shown in eq. (3)) dropping these two instances, but the result is qualitatively the same. In addition, we ran the regressions separately for the Buy&Hold and Buy&Sell treatments. The results are qualitatively the same as the those presented in the right panel of Table 3 for both treatments. 22 We use vGD 1 , instead of vGAD 1 here to take into account the direction of mis-pricing. 

0.668 0.215 * statistically significant at the 10% level * * statistically significant at the 5% level * * * statistically significant at the 1% level

To set the scene, we first provide a comprehensive description of the paths of forecasts and prices across the three rounds for one group. Figure 4 shows, for each period of Round 1 (top panel) and

Round 2 (middle panel), as well as the first four periods of Round 3 (bottom panel), the complete path of individual forecasts (thin lines), their medians (thick lines), and realized prices (dots) for one group of six subjects in the Buy&Hold treatment. There are many interesting features that we observe in this figure that illustrate results that we demonstrate more formally later.

First, the very first forecasts elicited in period 1 of Round 1, before the participants have any experience of trading, vary widely. 23 However, they vary less at the end than they do at the beginning, suggesting that most participants realized that prices should converge towards the maturity value by period 11. 24 The first realized price, represented by the dot in the first period, is close to the median first-period forecast and very close to the fundamental price. Forecast paths narrow dramatically in period 2 of Round 1 as participants update their beliefs in light of the first period's realized price. The distribution of price forecasts across horizons is now much flatter.

What the central bank pays in periods 4 and 5 (illustrated by the red diamond) is well above the previous market prices and above the subsequent market prices in those periods. There is no obvious 23 As we show in Appendix B, the initial set of forecasts do not vary across the three treatments. Thus, our inexperienced student subjects initially did not systematically anticipate that different price paths would result from the pre-announced market interventions. This is also reflected in the absence of significant differences in the mispricing observed in the first three periods of round 1 in the three treatments.

24 One participant with extremely high initial forecasts is excluded to maintain a common scale throughout. immediate impact on price forecasts, although the median is gradually rising in line with realized prices. For this group, prices continue to rise until period 8 and then decline. It is interesting to note that, in periods 8 and 9, two distinct forecast patterns emerge: some who think that prices will continue to rise and a majority who realize that prices ought to be close to the fundamental value by the end.

When the participants start again in period 1 of Round 2, initial forecasts are again relatively dispersed particularly for early periods but converge towards (although they are slightly above) the maturity price in period 11. Importantly, however, the distribution of forecasts has shifted up. Short-term forecasts again narrow dramatically in period 2, centered on the realized price of period 1, which is well above the fundamental value but very close to what the central bank paid in Round 1. What the central bank pays in Round 2 is now squarely in line with previous and future prices. Realized market prices in Round 2 fall fairly monotonically thereafter but are still slightly above the maturity value in period 11.

By the time the participants start again in period 1 of Round 3, initial forecasts are virtually indistinguishable. There is a near universal belief that prices will initially jump to the price expected to prevail in periods 4 and 5 (for which there is complete consensus that prices will be equal to what the central bank paid in Round 2). Then, prices almost exactly track the initial median path, which is scarcely updated over the first four rounds. (The remaining periods of Round 3 are uninteresting.) Below, we analyze formally the suggestive evidence of Figure 4 . We first show a close relationship between the median short-term forecasts (forecasts for the current period price) and realized prices.

We then link how median short-term forecasts in early periods are influenced by market prices and the central bank interventions from the previous round.

We focus on the median short-term forecasts because the short-term forecasts of participants in each market quickly converge around the median, as demonstrated in Figure 4 and more vividly in Figure 5 . Figure 5 shows the dynamics of the median within-market standard deviation of the short-term forecasts in the three rounds in each of the three treatments. As one can clearly observe, the variations of short-term forecasts within each market become very small after a few periods in Round 1, and remain small in Rounds 2 and 3, except for a small increase in the first period in Round 2. Thus, we focus on the median instead of individual forecasts, as little insight will be lost.

Furthermore, Carle et al. (2019) who re-investigated the data of Haruvy et al. (2007) , reported that although short-term forecasts are related to subjects' trading behavior in a statistically significant manner, their long-term forecasts (i.e., forecasts for prices in all the remaining periods of a market) are not. Thus, focusing on short-term forecasts will allow us to understand more clearly the link between the outcomes across rounds.

The first link in the chain is to demonstrate statistically that market prices are highly correlated with median price forecasts within each market. Table 5 reports the results of group random effect regressions regressing the current period price P t on the median short-term forecasts, Medf t,t , for the three treatments and three rounds. The three treatments are considered jointly in a single regression by including two treatment dummies (for T2 and T3) and their interactions with Medf t,t . The regressions show that actual prices follow closely, although not perfectly, the median short-term forecasts from Round 1, and increasingly more so in later rounds. In fact, the estimated coefficients of the Medf t,t in the two treatments with the central interventions (T2 and T3) are not statistically significantly different from 1.0 in Round 3. The estimated coefficients of the treatment dummies and the interaction terms themselves are not statistically significantly different across three treatments. Such a close link between median forecasts and realized market prices is also reported by Carle et al. (2019) .

Equipped with this result about a tight link between the realized prices and median short-term forecasts, we now proceed to analyze how median short-term forecasts made in the first period in Rounds 2 and 3 are influenced by outcomes in previous rounds for the same market. We regress the initial median forecast (Medf R 1,1 ) of Round R on the realized first-period price in the previous ), the median price paid by the central bank during the buy operation (Medp R−1 bo ), and a constant. Table 6 reports the results of separate ordinary least squares (OLS) regressions for each treatment.

It is worth noting immediately that the adjusted R 2 s for these regressions are very high, particularly for Round 3, implying that these three independent variables explain almost all the variation in median initial price forecasts across the various markets. For all the treatments, the realized price for the same (first) period in the previous round has a large and highly statistically significant effect on the median price forecast for the current round. 25

Let us turn our attention to those treatments with the interventions. For Round 2, in both Standard errors in parentheses * p < 0.10, * * p < 0.05, * * * p < 0.01 the T2 (Buy&Hold) and T3 (Buy&Sell) treatments, the median prices paid by the central bank during the buy operations in Round 1 are positively and significantly related to the initial period price forecast. 26 This is closely linked to the result we have seen Table 4 However, the importance of the initial realized price in Round 2 markedly increases.

Drawing these strands together, realized market prices are highly correlated with median expectations, so the forecast formation process is critical. Price forecasts depend strongly on previous experience, but in two distinct steps. In Round 2, price forecasts are strongly influenced by what the central bank paid in Round 1, as well as by what was realized in the same period of Round 1.

By Round 3, each market seems to settle on an historical price that coordinates both market prices and the price paid by the central bank. This strong coordination of expectations in the case of the market interventions seems to dominate any possibility that the participants learn that this is not the REE, which they do manage to achieve in the Benchmark case without intervention.

In this paper, we have asked whether a large-scale asset purchases by a central bank (a quantitative easing operation) which should be neutral under a rational expectations equilibrium has an impact, and whether such an impact, if exists, survives after participants gaining experience by repeatedly experiencing the same experiment.

It is clear from the repeated Benchmark treatment that participants in our experiment can learn, in line with the results of the literature, that prices should not deviate from the fundamental price in the absence of QE after a couple of repetitions.

In the Buy&Hold treatment, in which the QE operations permanently remove some bonds from the market, prices rise statistically significantly well above the fundamental price and stay there, even after the central bank has stopped buying. In most markets, repeated exposure only strengthens the belief that prices should rise. However, in a minority of cases, the intervention has a limited effect.

We find that the central bank considerably overpays relative to the fundamental price and the most recent market price in Round 1. Rather than learning to compete this effect away, participants come to expect it. Indeed, by Round 3, the price path in the earlier rounds significantly conditions their price expectations. In addition, it was notable that the peak price effect occurs earlier in the later rounds, as participants start to anticipate higher prices from the beginning.

Price dynamics in the Buy&Sell treatment are remarkably similar to those in the Buy&Hold treatment, particularly over periods 1 to 7. The main difference occurs thereafter, as prices tend to drop to the fundamental price as the central bank sells. Overall, the evidence from this paper seems to suggest that QE could work through a purely behavioural mechanism.

In order to accommodate repeating the experiment three times, we have opted for rather short market horizon of 11 periods. In order to better separate the effect of anticipation of the maturity of bonds and those of the sell interventions, an experiment involving a longer time horizon and thus put sell operation much earlier than bond maturity would be desirable. Indeed, there are papers (for example, Lahav, 2011; Hoshihata et al., 2017) that demonstrate quite different price dynamics in much longer horizon market (200 periods in the former and 100 periods in the latter) compared to short horizon market (of 15 or less periods). We leave this as an interesting avenue for future research.

Of course, the analysis in this paper involves caveats. Abbink et al. (2006) suggested that it may take several repetitions, certainly more than three, for subjects to learn to bid aggressively in a discriminatory multi-unit auction. 27 Thus, it is possible that if we repeat our experiment many more times, subjects will eventually learn to compete more aggressively during the interventions and thus, learn to trade the bond at its fundamental value from the beginning of the market round. Abbink et al. (2006) also showed that subjects learn to bid aggressively much more quickly under a uniform price multi-unit auction than under discriminatory one. Thus, it is possible that we may have observed different results if the intervention had been implemented with a uniform instead of a discriminatory price auction. However, we leave such comparisons to future research.

The experimental paradigm on which we have based our experiment is the one where no trade theorem applies just like many other asset market experiments that follow the paradigm of Smith et al. (1988) . It has been recently pointed out, however, that the observed mis-pricing tends to be larger in such an environment compared to those in which participants have intrinsic motives to trade, e.g., to smooth consumption across periods (Asparouhova et al., 2016; Crockett et al., 2019) because of, e.g., participants' desire to do something during the experiment ("active participation hypothesis," Lei et al., 2001) in the absence of alternative activities during the experiment. Thus, it is possible that the effect of market intervention we report in the current paper would be quite different in the environment similar to the one considered by Asparouhova et al. (2016) and Crockett et al. (2019) . We believe future research investigating this issue will be of high importance. 28

Furthermore, professional bond traders are likely to be more strategically sophisticated than undergraduate students exposed to bond trading for the first time and thus, the results reported in this paper may not apply to real bond markets. However, recent research shows that this may not be a serious concern. For example, Weitzel et al. (2019) demonstrated that experimental asset markets consisting of financial professionals result in mispricing, despite its magnitude being smaller than in the case of markets consisting of students. Of course, it would be fruitful to conduct experiments with professionals to check if the mis-pricing caused by a neutral intervention persists as well.

27 See Kwasnica and Sherstyuk (2013) , among others, for a survey of multi-unit auction experiments. 28 We thank an anonymous reviewer for pointing this out.

A Subperiods analyses Figure A shows the ECD of three subperiods, vGD 1 (left), vGD 2 (right), and vGD 3 (right) across the three rounds. the outcome when we include period 4 in the second subperiods and period 8 included in the third subperiods (shown with * ). As one can see, the results are qualitatively the same. 

Here we analyze the initial set of forecasts submitted by the subjects to investigate whether the announced large-scale intervention had any impact on the future price expectations of inexperienced subjects. The deviations of the mean and median paths from FV are presented in Figure B .1 (T1:

Benchmark (thin blue), T2: Buy&Hold (thick red), and T3: Buy&Sell (black dashed)). Both paths show a tendency to increase, although this is much more evident for the mean than for the median.

The median paths are very similar across the three treatments and quite close to the FV. Indeed it is interesting to note that the median forecast for the final period (when bonds mature at FV) is exactly equal to the FV for the three treatments. The means are all above the median, suggesting that there is an upward skew in the initial distribution across the participants. where f i 1,p is subject i's forecast for the period p price elicited at the beginning of period 1 and D i x s are dummy variables that take a value of one if i has participated in treatment x ∈ {T 1, T 2, T 3}.

The standard errors are corrected for a potential within-group clustering effect. We have chosen this test to control for possible correlation among subjects within a group. 29 Overall, we do not observe a significant effect of the announced differences in treatments on the initial forecasts.

To further check that the policy announcement did not influence subjects' initial forecasts, we measured the deviation of price forecasts from FVs using two measures proposed by Akiyama et al. (2014 , the relative absolute forecast deviations (RAFD) and the relative forecast deviation (RFD). For the set of forecasts submitted by subject i at the beginning of period t, RAF D i t and RF D i t are defined as:

where f i t,p is the forecast asset price in period p submitted by subject i at the beginning of period t. However, note that because this is the first set of forecasts submitted by the subjects without observing the past realized prices, the effect of such a correlation should be very limited. Not correcting for the clustering effect does not change the result qualitatively.

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The absence of treatment effects in RAF D 1 and RF D 1 confirms the earlier finding. The announcement of a large intervention does not influence the subjects' initial expectations

30 Just as we have done for the forecasts for the period p price, the test of equality among the three treatments is done by running OLS regressions (and correcting for the clustering effect)

Dx is a dummy variable that takes a value of one if the treatment is x.) and testing whether the estimated coefficients of the treatment dummies are equal

Furthermore, the nonparametric KW test provides the same conclusion: p=0.867 for RAFD and p=0.836 for RDF