Does a promise script work to reduce the hypothetical bias? Evidence from an induced value experiment

This paper explores whether a truth-telling promise can work to reduce the hypothetical bias in preference elicitation. Using an induced value experiment in China with a random nth-price auction, the author finds: 1) Hypothetical bias exists in a random nth-price auction with induced values and making a truth-telling promise can reduce the hypothetical bias. 2) All treatments are demand-revealing except for the hypothetical baseline. JEL C90 D44 Q51


Introduction
Cost and benefit analysis is important in policy decision making. However, there is no direct market for environmental goods. Economists rely on the contingent valuation methods (CVM) to measure the environmental benefits to the public.However, many literature find there is a hypothetical bias -the gap between subjects' stated willingness to pay and their real willingness to pay (Bohm [1972]; List and Gallet [2001]; Murphy et al. [2005];Ehmke et al. [2008]).The gap leads to critics about the reliability of the CVM method (Hausman [2012]). To eliminate the hypothesis bias, many methods such as CVM-X, cheap talk, and consequentiality are proposed with mixed success (Fox et al. [1998];Cummings and Taylor [1999];Carson and Groves [2007]) 1 .
Contemporary guidance for CVM studies is compiled by renowned environmental economists to promote the best practice of CVM and to increase its reliability (Johnston et al. [2017]). A recent attempt to eliminate the hypothetical bias is proposed by Jacquemet et al. [2013]. They use a solemn oath script and find it leads to truth-telling in an induced value experiment. In the homegrown valuation experiment, the oath also reduces the hypothetical 1 Cummings and Taylor [1999] introduce a cheap talk script by informing subjects there is a tendency for them to overestimate the willingness to pay. They find that cheap talk can reduce the hypothetical bias and perform equally as well as real monetary incentives in referendums of public goods. They also find that the effect of a cheap talk script depends on its length. Lengthy scripts work better than short scripts. They find that cheap talk can eliminate hypothetical bias for non-dealers but not for dealers who have more experience dealing with sports cards. Therefore, the effect of cheap talk depends on the length of the script and the type of respondent. Aadland and Caplan [2006] use a short and neutral cheap talk script in a 4,000-household phone contingent valuation survey and find that the cheap talk script exacerbates the hypothetical bias. They suggest caution in using cheap talk to control the hypothetical bias ex-ante.
bias. The effect of the oath is tested by later studies which are summarized in table 1 with success.
Although oaths work well in reducing the hypothetical bias, it might be too strong a mechanism. Oaths are rare and typically used only in serious situations such as the court, marriage, or joining a political party. Overuse of the oath may weaken its power. I step back and use a weaker version of the oath: a promise. Asking subjects to promise to tell the truth is a more natural way to commit in the Chinese context. Chinese are usually asked to read out a promise script in which they promise to carry out their jobs dutifully. The promise script is not unfamiliar to Chinese. For example, Carlsson et al. [2013] used a state preference survey with a promise script in both China and Sweden. They found that the promise affected people's willingness to pay differently in the two countries. In China, a promise to tell the truth significantly reduces the subjects' willingness to pay. In Sweden, however, a promise increases subjects' willingness to pay.
Herein I step back and explore whether a more common promise works as well as the rare oath to create a commitment to truth-telling in a random nth-price auction (see Shogren et al. [2001b]). I find that hypothetical bias exists and making a promise did improve subjects' sincere bidding.
To the best of my knowledge, my paper is the first directly test the effect of a promise script in reducing the hypothetical bias in an induced value (IV) experiment. The IV experiment allows me to know the real private values and to calculate the hypothetical bias. My paper differs from Carlsson et al. [2013], which use a promise script in the field with a contingent valuation study in both China and Sweden. My paper also differs from Jacquemet et al.
[2013] which tests the effect of an oath in France with a Vickrey auction. I use a random nth-price auction and run it in China. The random nth-price auction has some improvements over the Vickrey auction as it is incentivecompatible and can engage both on-margin bidders and off-margin bidders (Shogren et al. [2001b]).

Experimental Design
The goal of commitment theory is to create a nonmarket mechanism to correct the hypothetical bias ex-ante. This experiment follows Jacquemet et al.
[2013], but I start by using the weaker promise as a commitment device to see whether subjects bid sincerely in a random nth-price auction. This is an ex-ante approach to correct both the hypothetical bias in a hypothetical survey and the downward bias in a real economic commitment auction. The Design of the IV experiment. I use a random nth-price auction as the elicitation mechanism. In a random nth-price auction, the market price will be determined by a random draw from the bids. If a random draw is the nth highest bid, the n − 1 highest bidders will win the auction and pay the nth highest bid (Shogren et al. [2001b]). The random nth-price auction mechanism works similarly to the classic second-price auction except for the market-clearing price 2 . After all the bids are ranked, a random number will 2 Vickrey [1961] second-price auction has been a popular tool in the lab to elicit subjects' preferences for private goods. The Vickrey second-price auction works as follows: each subject submits their bid for a private good, and the bids are ranked from highest to lowest.
The highest bidder wins the good and pays the second-highest price. This mechanism is incentive compatible in theory as it separates what you pay from what you say. If a subject be drawn from 2 − N (the number of total participants). Assuming that n is the randomly drawn number, the n − 1 highest bidders will win the auction and pay the nth highest price. The merits of this mechanism are that it separates what you pay from what you say like the Vickrey auction and it also has more than one winner like the BDM. This mechanism is incentive compatible and also has an endogenously determined market-clearing price.
Shogren et al. [2001b] show that this mechanism is demand revealing in aggregate like the Vickrey auction and that it can engage both the on-margin I run the experiment in China. Chinese are more experienced with promises than with oath taking (Carlsson et al. [2013]). Subjects are recruited from Xi'an Jiaotong University, Xi'an. I place a notice on a campus bulletin board to recruit participants. Subjects are students from different majors. The experiments are carried out in a classroom. My instructions and questionnaires are translated into Chinese from Jacquemet et al. [2013]. bids more than his value for the good, he will risk winning and paying more than his true value. If a subject bids less than his true value, he will risk losing the chance to win the good. The weakly dominant strategy for a subject in this mechanism is to bid truthfully.
Another merit of this mechanism is that the market price is endogenously determined (Shogren et al. [2001b]). Several studies find that Vickrey's second-price auction can only engage on-margin bidders, but not off-margin bidders (see e.g., Kagel [1995];Shogren et al. [2001a]). The bidders who have higher values (on-margin bidders) bid truthfully as they have a higher chance to win. Bidders with lower values (off-margin bidders) will not bid truthfully as their chances of winning are low. I make some changes to fit the random nth-price auction. Subjects are not informed that their dominant strategy is to bid their resale values.
Each round has 9 steps.
Step 1. The experimenter assigns each bidder a resale value on his or her record sheet. The resale value is the price at which the bidder can sell the good back to the monitor after the experiment. Each bidder knows nothing about the other bidders' resale value. The resale value is drawn from a uniform distribution. The demand curve is 84; 76; 71; 68; 65; 63; 53; 38; 24 (It is similar to Jacquemet et al. [2013]). Each bidder is endowed with each value once during the experiment.
Step 2. Each bidder then submits a bid to buy one unit of the good.
Step 3. The experimenter ranks the bids from highest to lowest. In the event of ties, the ranking is drawn randomly.
Step 4. A random number will be drawn to determine how many participants will win the good. The random number will be somewhere between 2 and the total number of participants. Call this random number N .
Step 5. The N − 1 highest bidders will win the auction, and all winning bidders will pay the amount of the Nth highest bid for the exchange. For example, if the random number 5 is selected and the 5th highest bid is 40, the 4 highest bidders will win the auction and pay 40 for the good.
Step 6. The winning bidders then sell the unit back to the monitor. The price of this transaction is the resale value given to the subject on his/her record sheet in step 1. The profit that winning bidders earn for that round is the difference between the resale value and the market price: profit = resale value -market price (the Nth highest) Subjects are informed that they can have a negative profit if the market price is higher than their resale values.
Step 7. All bidders at or below the market price buy nothing; they make zero profit for that round.
Step 8. End of the round. The profit in that round appears on the subjects' record sheets.
Step 9. Go to the next round by going back to step 1. A new resale value for this new round will show up on the subjects' record sheets.
Each treatment is composed of two sessions. Each session has 9 bidders participating in 9 rounds. In all sessions, subjects are told that they will get a participation payment of RMB 30 yuan. In both the hypothetical and the promise treatments, subjects are clearly told that they will get a fixed payment of RMB 30 yuan. In the monetary incentive treatment, subjects are told that their payments depend on their decisions. All payments will be made after the experiment. Before the actual auction phase, a nonnumerical example is developed covering all the instructions. However, subjects are not told that bidding one's resale value is the dominant strategy. Subjects are also asked to complete a short questionnaire about the important features of the game before the experiment starts. Subjects' sociodemographic data are The promise script. Figure 1 shows the promise script. The promise 3 Fischbacher et al. [2001] argue a high stake level can make subjects take experiments more seriously. Studies such as Slonim and Roth [1998] find that stakes matter in ultimatum games.
treatment is identical to the baseline treatment except for the promise script.
In the promise treatment, each subject is asked to freely make a promise before entering the lab. Subjects are not informed about the nature of the experiment. Table 3 provides raw data on observed bids by treatment and round. We see that the subjects in the baseline treatment significantly inflated their bids.

Results
The average demand revelation is 137%. In the promise, monetary incentives, and promise + monetary incentive treatments, subjects inflate their bids and the average demand revelations are 118%, 110%, and 110%. I do not find that any treatment is perfectly demand-revealing just by inspecting the summary data.
At the individual bid level, experimental evidence shows that a random nth-price auction can engage both on-margin bidders and off-margin bidders (Shogren et al. [2001b]). This is contrary to the second-price auction, which typically only engages on-margin bidders, that is, those whose private value is at the higher end of the distribution (Parkhurst et al. Jacquemet et al. [2013]). Table 3 shows that a random nth-price auction can engage off-margin bidders (e.g., IV=24, 38, 53). On-margin bidders usually inflate their bids (e.g., IV=76, 84). In all four treatments, demand revelations are larger than 100% for both the lowest resale value and the highest resale value (except for the promise + monetary incentive treatment). Table 5 shows the frequency of actual bids relative to private values. I find that in all four treatments, most subjects inflate their bids. In the baseline, promise, monetary incentives, and monetary + promise treatments, 61.7%, 51.8%, 56.2%, and 53.1% of bids are higher than the induced value, respectively. I also find that the promise, monetary incentives, and monetary + promise treatments perform relatively well: 57.4%, 55.6%, and 58.6% of bids are within 10% of the induced value, respectively. I now state my first result.
Result 1: Hypothetical bias exists in the random nth-price auction with induced values (IV). Making a truth-telling promise can reduce IV hypothetical bias. Support: Hypothetical bias is the difference between the hypothetical bidding and the real money bidding (Jacquemet et al. [2013]). To test whether a difference exists between bidding behavior under the hypothetical and the real money treatments, I use the Wilcoxon rank-sum test to test the null hypothesis that the two treatments' bids are equally distributed. I reject the null hypothesis at the 5% significance level as the test statistics z = 2.19 and p = 0.029. Also, a median test resulted in a Pearson χ 2 test statistic of 3.1648 (p = 0.075); I reject at the 10% significance level the null hypothesis that the two treatments are drawn from populations that have identical medians. Subjects bid more in the hypothetical treatment than in real money treatment. Hypothetical bias exists. Result 2: All treatments are demand-revealing except for the hypothetical baseline. Support: To test the hypothesis of perfect demand revelation, I assume that the true bidding function is linear in the induced value (Shogren et al.
where b it is the bid of subject i in round t, v it is subject i's induced value at round t, φ t are rounding effects, α i are subject-specific characteristics, and it is bidding error. Assuming individual random effects, I also controlled for round fixed effects in the regression. Table 7 presents the estimation results.
I test the following hypothesis for each treatment: The null hypothesis for the baseline treatment is that the IV baseline treatment is demand revealing H 0 :(β = 1 and α = 0). The alternative hypothesis is that the IV baseline treatment is not demand revealing H 1 :

Conclusion
After fifty years of nonmarket valuation work, hypothetical bias is still observed in stated preference studies. In response, Jacquemet et al. [2013] introduced the oath as an ex-ante nonmarket commitment device to get people to commit to telling the truth about their preferences. They found that the oath leads to more sincere bidding in hypothetical induced value and homegrown value experiments in a second-price auction (Jacquemet et al. [2013]).
Herein I step back and explore the promise as a commitment device because oaths could be perceived as too powerful and too special to be commonly used in nonmarket valuation work. I focus on the performance of a promise script in a random nth-price auction in both induced value and homegrown valuation experiments in China. I find that in the induced value experiment, hypothetical bias exists and a promise of truth-telling helps: bidders are more like to bid sincerely.
Although I find some support for the use of a promise script to reduce the hypothetical bias, I recognize my sample size is relatively small. Future research can use a larger and more diversified sample to test the hypothesis.

A Appendix
The instructions and questionnaires are based on Jacquemet et al. [2013].
We make some changes to fit the random nth price auction. The random nth price auction instruction is based on Lusk and Shogren [2007].

A.1 Instructions
Part 1 Thank you for agreeing to participate in today's session. As you entered the room, you should have been assigned an ID number, which is located on the upper right hand corner of the instruction. You will use this ID number to identify yourself during this research session. We use random numbers in order to ensure confidentiality.
Before we begin, I want to emphasize that your participation in this session is completely voluntary. If you do not wish to participate in the experiment, please say so at any time. Non-participants will not be penalized in any way. I want to assure you that the information you provide will be kept strictly confidential and used only for the purposes of this research.
For obvious scientific reasons, it is mandatory not to speak during the experiment. Unfortunately, we will have to ask any participant not complying with this rule to leave the room without any opportunity to take potential earnings.
It is very important you understand the procedure of the experiment.
If you have any questions, please raise your hand, someone will come and answer you. Thank you for following these rules.

PAYMENT OF YOUR EARNINGS
Your earning during the experiment will be expressed in ECU (Experimental Currency Unit). These earnings are converted into RMB according to the rate: 3 ECU=1RMB. A fixed fee equal to 30 yuan is added to this payoff. You will be paid privately the corresponding monetary payoff in cash at the end of the experiment.

Instructions
At the beginning of this part, there are () participants.
Overview. You will be participating in an auction in which you are a buyer. You have to offer, at each round, a price in ECU to buy a good.
The experiment monitor will re-acquire this good from you. There will be several rounds of bidding. The outcome of each auction in each round has no influence on how much you will get paid at the end of the experiment ( Monetary incentives: The outcome of each auction in each round has directly influence on how much you will get paid at the end of the experiment).

PROCEDURE FOR EACH ROUND
Each round has 8 steps.
Step 1. Each bidder looks at his or her resale value on his or her recording sheet. We term resale value the price in ECU the monitor will pay to buy back a unit of the good that is purchased in the auction. The resale values of different participants can be different.
Step 2. Each bidder then submits a bid in ECU to buy one unit of the good. A monitor will come and collect all the bids.
Step 3. The monitor ranks the bids from highest to lowest. Step 4. A random number will be drawn to determine how many participants will win the good. The random number will be somewhere between 2 and the total number of participants. Call this random number N .
Step 5. The N − 1 highest bidders will win the auction and all winning bidders will pay the Nth highest bid amount for the exchange. In the above example, there were ten participants that submitted bids and the number 4 was randomly drawn by the monitor (i.e. N = 4). In this case, the 3 (N − 1) highest bidders will win the auction and each will pay the 4th highest bid ($d.dd) amount for the good.
Step 6. The winning bidders then sell the unit back to the monitor. The price of this transaction is the resale value listed for that round on his/her recording sheet. The profit in ECU winning bidders earn for that round is the difference between the resale value and the market price: profit = Resale value -market price (the Nth highest) Suppose your resale value is 6.50 ECU, the Nth highest price is 5.00 ECU, and you are one of the (N −1) highest bidders. This implies you buy one unit of the good at the Nth highest price 5.00 ECU and sell it to the monitor at your resale value 6.50 ECU. Your profit is positive, 1.50 ECU (=6.50-5.00).
Important note. You can have negative profits: if you buy a unit of the good and the resale value is less than the market price, your profits will be negative. Example: If your resale value was 4.50 ECU and the market price was 5.00 ECU, your profit is negative, -0.50 ECU (=4.50-5.00).
Step 7. All bidders at or below the market price (buyers #4 to #10) buy nothing, they make zero profit for that round.
Step 8. End of the round. Your profit in ECU in that round is calculated on the recording sheet.
Step 8. The next round starts and the monitor assigns a new resale value for each participant on his/her recording sheet.

EARNINGS FOR THIS PART
Your payoff in ECU for this part is 0 whatever your earnings at each period. [Monetary incentives: Your payoff in ecu for this part is set equal to the sum of your earnings at each period.] A.2 Pre-experiment questionnaire 1. Groups are reformed in each round.

YES NO
2. Each group is composed of ( ) participants.
3. At the beginning of each round, all participants belonging to my group are attributed the same resale value.

YES NO
4. When I make a bid, I can bid any amount I wish.
YES NO 5. The market price is set by the bid of the highest bidder in my group.

YES NO
6. If my bid is the 3rd highest bid and is equal to RR.U and the random number drawn is 4. The 4th highest bid is GG.K. Then I buy the unit of the good.

YES NO
If yes, I pay: ( ) for the good.
7. If I purchase a unit of the good and my resale value is greater than the market price, I will make positive profits.

YES NO
8. The monetary payoff I will get at the end of the experiment depends on the amount I earned in the auction.

YES NO
If you are surprised by some answers, please ask questions.