We compare the Becker-DeGroot-Marschak (BDM) mechanism to a discrete choice mechanism for revealing willingness to pay (WTP) in a lab experiment. Differences in WTP disappear when considering only engaged bidders with non-zero bids. Only WTP elicited with BDM are sensitive to the variation of quantity offered to participants.experimental economics, substitution

Jutta Roosen

Sandrine Blanchemanche

Stephan Marette

English

Research Papers in Economics

     
 
 
  
  
Volume 30, Issue 2 
  
Value Elicitation using BDM and a Discrete Choice Mechanism 
  
 
 
Jutta Roosen  
Technische Universitaet Muenchen 
Stephan Marette  
UMR ECONOMIE PUBLIQUE INRA AGROPARISTECH 
Sandrine Blanchemanche  
Met@risk, INRA-AgroParisTech
Abstract 
We compare the Becker-DeGroot-Marschak (BDM) mechanism to a discrete choice mechanism for revealing 
willingness to pay (WTP) in a lab experiment. Differences in WTP disappear when considering only engaged bidders 
with non-zero bids. Only WTP elicited with BDM are sensitive to the variation of quantity offered to participants.
 
Citation: Jutta Roosen and Stephan Marette and Sandrine Blanchemanche, (2010) ''Value Elicitation using BDM and a Discrete Choice 
Mechanism'', Economics Bulletin, Vol. 30 no.2 pp. 1554-1563. 
Submitted: May 16 2010.   Published: May 26, 2010. 
 
       1
1. Introduction 
Eliciting willingness to pay (WTP) for one good may be altered by the presence or the absence 
of available substitutes during a lab experiment. Substitution among products poses a difficulty 
in designing a lab experiment, as a lab experiment usually requires a reduced number of possible 
choices so as to control the process of price determination or information revelation. Such a 
reduction may introduce biases. In particular, consumers’ behavior in the lab differs from their 
behavior in their usual environment, in which they have to choose between numerous substitutes.  
In most of lab experiments, WTP for a specific product/quality is evaluated through the 
rate of substitution between a quality parameter and income for a given product. Auctions or 
BDM mechanisms (Becker-DeGroot-Marschak, 1964) abstract from substitutes. However, 
substitutes should be considered also in the lab, since Lusk and Fox (2003) and Marette et al. 
(2008) showed that field valuations were greater than lab valuation. 
Our paper tackles this issue and compares in the lab a classical BDM mechanism
1 with a 
mechanism detailed by Binswanger and Masters & Sanogo (BMS), namely a discrete choice 
mechanism that evaluates WTP by measuring the propensity of substitution between two goods 
(see Binswanger, 1980; Masters and Sanogo, 2002). Under the BDM mechanism, participants 
had to indicate WTP for an enriched yogurt with cholesterol-lowering properties. Under the 
BMS mechanism, participants had to choose between plain yogurt and enriched yogurt. It is 
shown that for a given quantity offered to consumers (i.e., a given number of cups), responses 
under both mechanisms are statistically indistinguishable after controlling for engaged bidders 
(those interested by the good with non-zero bids). 
While several papers have compared auction mechanisms and BDM (e.g., Lusk et al. 
2004), the comparison between BDM and alternative choice mechanisms has been overlooked.
2 
Frykblom and Shogren (2000) compared open ended and discrete (dichotomous) choice 
questions. Our paper differs from this last paper, since we compared an open ended mechanism 
(the BDM) and a choice mechanism (the BMS) based on the quantity substitution between two 
goods, without testing any anchoring effect linked to difference in posted prices.  
Our paper also contributes to the quantity variation in mechanisms for eliciting WTP. List 
and Lucking-Reiley (2000) show that, in a multiple unit auction, consumers lower their bids for 
an additional unit of a commodity. In our paper, we show that, when the quantity offered to 
participants increases, the per-unit values significantly decrease with the BDM procedure but not 
with the BMS procedure.  
Section 2 demonstrates the theoretical equivalence of WTP evaluated using BDM and 
BMS. Section 3 introduces the experimental design and section 4 discusses the results. 
Conclusions are drawn in section 5. 
 
 
 
                                                 
1 We chose the BDM for comparison, because it is deemed incentive compatible, and a relatively simple 
mechanism. It allowed a within group test of both mechanisms. A combination with an auction mechanism would 
have been to demanding. In addition, enforcement of BDM and BMS mechanisms does not depend on the degree of 
competition within the group..  
2 Auctions fit “scarcity” situations and not situations of mass consumption in supermarkets without quantity 
constraints. Auctions are tailored to scarce goods where the offered quantity is limited (fixed supply), while the 
BDM and the BMS are tailored to real situations where offered quantities may vary a lot (variable supply). The 
quantity offered under BDM and BMS may easily vary, which is not the case under auction mechanism (see List 
and Lucking-Reiley, 2000).   2
2. WTP in BDM and BMS 
WTP is defined as the maximum amount of money that a consumer is willing to forego in order 
to receive a good. The consumer with income Y consumes two goods (types of yoghurts) A and 
B in quantities  A q  and  B q  and an outside good Z with price normalized to unity. The per-unit 
price of good A announced during the experiment is denoted by  A p .The budget constraint results 
as  AA BB p qW T P qZ Y   , where  B WTP  is the unknown WTP for one unit of good B. 
In the BDM procedure the consumer indicates a WTP for a given bundle  B q  such that 
(s)he is indifferent between receiving or not the good.  With the utility function U(.),  B WTP  
solves  
   Z q U WTP q Z q q U A B B B A , 0 , , ,   .        ( 1 )  
The idea developed by Binswanger (1980) and Masters and Sanogo (2002) is to use 
respondents’ choices to infer their relative preference and WTP. The BMS mechanism relies on 
the monotonicity of preferences and identifies the switching point by offering several choice 
situations to consumers. The mechanism is incentive compatible by randomly selecting one 
choice situation that is enforced at the end of the experiment.The quantity of product B,  B q ~ , at 
which the consumer switches from a given quantity of product A,  A q , to the choice of product B 
can be interpreted as the point at which the consumer reveals indifference, so that  
      Z q U Z q U Z q U B A B , ~ , 0 , 0 , , 1 ~ , 0    .
3       ( 2 )  
From the budget constraint and the definition of WTP, it follows that for  B q  , the inequalities 
 A A B B q p q WTP  1 ~  and  A A B B q p q WTP  ~
  are satisfied. Rewriting, the per-unit WTP is 
approximated by  
B
A A
B q
q p
WTP ~  . 
4          ( 3 )  
Hence, while the BDM evaluates the compensating variation in income for an additional bundle 
of good B, BMS derives a monetary value by the propensity of substitution between two goods.  
 
 
3. The experimental design 
We conducted the experiment in Paris, France, in February 2008 using enriched yogurts reducing 
cholesterol. The sample consists of 101 adults regularly consuming dairy products. We selected a 
plain yogurt (Danone Nature) and a yogurt enriched with sterols for their cholesterol-lowering 
properties (Danacol by Danone). Products were chosen to be as similar as possible (same brand, 
same weight, same packaging and same flavour (plain)).  
The subjects were randomly assigned to two different groups. Subjects in the group 
“BDM first” (“BMS first”) indicated their choices before and after health information, according 
to a BDM (BMS) procedure, and ended the experiment with a choice procedure based on the 
BMS (BDM) procedure. The group consisted of 54 (47) subjects. 
                                                 
3 Between (1) and (2) results will differ by an income effect as in the BMS consumers are endowed with  A q  units of 
good A, which is not the case in the BDM. Given the small value of endowment, income effects should be 
negligible. 
4 The quality of approximation depends on the size of the initial endowment of good A.   3
In the BDM procedure, participants were asked to indicate the WTP for Q cups of 
yoghurt B (sterol enriched), knowing the retail price of Q cups of yoghurt A (plain). At the end 
of the experiment, if WTP is less (more) than the randomly drawn price, the participant could not 
(had to) purchase Q cups of yogurts B.
5  
In the BMS, participants were asked to choose between an endowment of Q cups of 
yoghurt A and a number of cups of yoghurts B (sterols enriched), varying from 1 to 2Q. The 2Q 
choice situations were presented on a single sheet of paper with 2Q lines to check off. For each 
line, they had to choose either  A q = Q cups of yogurt A or  B q  cups of yogurt B with  B q {1,..., 
2Q}.  Despite differences, the BDM offers Q cups and the BMS starts with an endowment 
equivalent in quantity of Q cups. The choice sheet with 12 lines for exchanging the 6 cups of 
yogurt A was similar to the following truncated example with 3 lines (for saving space): 
 
Situation 1  O  6 cups of Yogurt A      or  O  1 cup of Yogurt B 
Situation k   O  6 cups of Yogurt A      or  O  k cups of Yogurt B 
Situation 12  O  6 cups of Yogurt A      or  O  12 cups of Yogurt B 
 
The session started with a trial round explaining both choice mechanisms. Participants 
received €15 of indemnity. For both procedures (BDM or BMS), the retail price of 6 cups of 
yoghurt A was revealed to control for anchoring regarding prices. The choice #1 was conducted 
according to the initial choice procedure assigned to the group (BDM for group “BDM first” and 
BMS for group “BMS first”) for Q=6, where Q is the offered quantity (see the figure 1). 
Product names were announced and health information on Danacol was revealed. The 
information detailed benefits and potential risks of consuming yogurts with added plant sterols 
for reducing cholesterol. Then, choice #2 for Q=6 was conducted using the initial choice 
procedure in each group. Choice #3 (using the same initial mechanism in each group) was 
realized after changing the quantity offered in the BDM and the endowed quantity of yoghurt A 
in the BMS to Q=8. The retail price of 8 cups of yoghurt A was revealed in both groups. Choice 
#4 was conducted according to the alternative choice procedure assigned to the group (BMS for 
group “BDM first” and BDM for group “BMS first”) with Q=6. The retail price of 6 cups of 
yoghurt A was recalled before each round of choices. 
The experiment concluded by randomly selecting one out of the 4 choices and then 
determining the choice situation or the product price that would be used for enforcing the choice 
during the experiment. Each participant bought/received the number of yoghurts linked to their 
WTP/selection in the randomly drawn choice situation. 
 
4. Results 
While the BDM mechanism directly reveals WTP for  B q cups, WTP is deduced from the choice 
mechanism in the BMS according to equation (3). If during the experiment, every 
j
B q } 2 ,..., 1 { Q   
only satisfies  Q p q WTP A B B  ~  (only yogurt B were selected in all 2Q situations on the choice 
sheet linked to BMS), we arbitrarily determined a value  B q ~ =1. If during the experiment no 
B q ~  Q 2 ..., , 1   observed for a respondent, the value is set at  B q ~ =2Q+1.  
                                                 
5 The upper bounds of the price distribution were not announced for avoiding an anchoring effect on WTP (Bohm et 
al., 1997).    4
One important difference between the BMS and the BDM mechanism is that BMS 
provides (2Q+1) discrete possible WTP defined in equation (3) while BDM elicits potential 
WTP on a continuum. The possible WTP under BMS follows a hyperbolic function.  
Table 1 and Table 2 compare both mechanisms showing WTP for 6 cups.
6 Statistical test 
use the Wilcoxon signed-rank (Mann-Withney-U) test for within (across) sample comparison. 
The Wilcoxon test accounts for the correlation of paired observations within sample. The 
difference between tables 1 and 2 concerns the presence or the absence of unengaged bidders, 
who offered zero under BDM for product B or who never chose product B under BMS (Lusk and 
Fox, 2003). Their share ranges between 39% and 75% in the respective subsample. In other 
words, table 1 considers all participants, while table 2 only takes into account engaged bidders 
who are interested in product B. For the comparison across samples, we also evaluate bids under 
BDM (BMS) (choice #2) with bids under BMS (BDM) at the end (choice #4) in the group 
starting with BDM (BMS). 
Tables 1 and 2 exhibit minor differences across BDM and BMS mechanisms. Several 
WTP differences that are statistically significant in table 1 are not statistically significant in table 
2. This difference may come from a bias linked to the BMS mechanism for unengaged bidders 
never selecting products B (Danacol), with a value arbitrarily determined with  B q ~ =2Q+1, 
leading to a small but positive WTP of 0.484, while BDM indicates zero values. Note however, 
that in the BMS mechanism more participants tend to become unengaged in comparison to the 
BDM. 
Tables 3 and 4 show the quantity impact on mechanisms coming from the comparison of 
choices #2 and #3. As BDM mechanism directly reveals WTP for Q cups, we divided the 
revealed WTP by Q for having the WTP per cup. 
Results show that WTP is sensitive to a variation of the reference quantity Q in the BDM 
mechanism. Results are robust across tables 3 and 4 capturing different types of participants 
(engaged or not). By showing a WTP decrease when the quantity increases, the BDM 
mechanism is consistent with List and Lucking-Reiley’s (2000) result showing that, in a 
multiple-unit auction, consumers lower their bids for an additional unit of a commodity.  
For BMS, WTP does not significantly decrease with the increase of quantity Q. The 
insignificant shift in WTP under BMS is explained by the “minor” changes in participants’ 
choices. As Q increases, the additional lines for the choice situation appear on the choice sheet. 
The point  B q ~  at which the consumer reveals indifference (see equation 2) only increases slightly, 
but it does not significantly influence the WTP determined by (3). 
 
4. Conclusion 
These results give support to the BMS mechanism as an alternative mechanism to other methods 
for evaluating willingness to pay. More studies are necessary for understanding the differences 
between mechanisms taking into account substitutability and discreteness/continuity of WTP 
evaluations (see Lust and Schroeder, 2006). The BMS confirms that the BDM leads to 
realistic/robust results for WTP estimations despite the absence of substitutes that is observed in 
studies using this BDM in a single-good context.  
 
                                                 
6 Per-unit WTP from the BMS was multiplied by 6 to obtain WTP for the bundle.   5
References 
Becker, G. M., M. H. DeGroot, and J. Marschak (1964) “Measuring Utility by a Single-Response 
Sequential Method” Behavioural Science 9, 226-32. 
Binswanger, H. P. (1980) “Attitudes toward Risk: Experimental Measurement in Rural India” 
American Journal of Agricultural Economics 62, 395-407. 
Bohm, P., J. Linden, and J. Sonnegard (1997) “Eliciting Reservation Prices: Becker-DeGroot-
Marschak Mechanisms vs. Markets” Economic Journal 443, 1079-89. 
Frykblom P. and Shogren J.F (2000). “An Experimental Testing of Anchoring Effects in Discrete 
Choice Questions.” Environmental and Resource Economics 16, 329-341. 
List, J.A. and D. Lucking-Reiley (2000) “Demand Reduction in Multiunit Auctions: Evidence 
from a Sportscard Field Experiment” American Economic Review 90, 961-972.  
Lusk, J.L. and J.A. Fox (2003) “Value Elicitation in Retail and Laboratory Environments” 
Economics Letters 79, 27-34.   
Lusk, J.L., T. Feldkamp and T. C. Schroeder (2004) “Experimental Auction Procedure: Impact 
of Valuation of Quality Differentiated Goods.” American Journal of Agricultural 
Economics 86, 389-406. 
Lusk, J.L. and T. C. Schroeder (2006) “Auction Bids and Shopping Choices” Advances in 
Economic Analysis & Policy 6, Iss. 1, Article 4. 
Marette, S., J. Roosen, and S. Blanchemanche (2008) “Health Information and Substitution 
between Fish: Lessons from Laboratory and Field Experiments” Food Policy 33, 197-208. 
Masters, W.A. and D. Sanogo (2002) “Welfare Gains from Quality Certification of Infant Foods: 
Results from a Market Experiment in Mali” American Journal of Agricultural Economics 
84, 974-989.   6
Figure 1. Timeline of Experimental Procedures 
GROUP BDM FIRST
BDM 
Q=6 
BDM 
Q=6 
BDM 
Q=8 
BMS
Q=6 
BMS
Q=6 
BMS
Q=6 
BMS
Q=8
BDM
Q=6 
Naïve bid
Choice#1 
New endowment
Choice #3
New mechanism
Choice #4
Choice #2
GROUP BMS FIRST
Revelationof  
Information  
   7
Table 1. Comparison of 6 cups WTP (€) for BDM versus BMS (all subjects) with Q=6 
 Mean  (std.dev.)     
Within Sample Comparison (Wilcoxon test) 
  Last BDM  Last BMS  z-value  p-value 
Group Starting BMS 
Choices #4 and #2 
 
0.635 
(0.784) 
N=51 
0.998 
(1.172) 
N=49 
 
-2.798
* 
 
0.005 
Group Starting BDM 
Choices #2 and #4 
 
1.116 
(0.984) 
N=56 
1.015 
(0.918) 
N=54 
 
-1.113 
 
0.266 
 
Across Sample Comparison (Mann-Witney-U test) 
 Group 
starting 
BDM 
Group 
starting 
BMS 
 
z-value 
 
p-value 
Choice #1  0.736 
(0.691) 
N=56 
1.451 
(1.692) 
N=51 
 
-2.003
* 
 
0.045 
Choices #2   1.156 
(0.984) 
N=56 
0.998 
(1.172) 
N=49 
 
-1.800 
 
0.072 
Choices #4   1.015 
(0.918) 
N=54 
0.918 
(0.784) 
N=51 
 
-2.780
** 
 
0.005 
Note: N is the number of participants taken into account. Within (Across) sample comparison by Wilcoxon (Mann-
Whitney-U). H0 : frequencies for a group = frequencies for the other group. * denotes rejection of H0 at 5% 
significance level. **  denotes rejection of H0 at 1% significance level.  
   8
Table 2. Comparison of 6 cups WTP (€) for BDM versus BMS (engaged bidders)  
with Q = 6 
 Mean  (Std.  Dev.)     
Within Sample Comparison 
 Last  BDM  Last  BMS  z-value  p-value 
Group Starting BMS  
Choices #4 and #2 
1.372 
(0.621) 
N=20 
1.668 
(1.627) 
N=20 
 
-0.121 
 
0.904 
Group Starting BDM  
Choices #2 and #4 
 
1.610 
(0.909) 
N=30 
1.430 
(1.067) 
N=30 
 
-1.417 
 
0.157 
 
Across Sample Comparison 
 Group 
starting 
BDM 
Group 
starting  
BMS 
 
z-value 
 
p-value 
Choice #1  1.144 
(0.518) 
N=36 
1.816 
(1.864) 
N=37 
 
0.371 
 
0.711 
Choices #2   1.541 
(0.831) 
N=42 
1.491 
(1.493) 
N=25 
 
-0.468 
 
0.640 
Choices #4   1.380 
(1.050) 
N=32 
1.295 
(0.623) 
N=25 
 
-0.936 
 
0.349 
Note: The note in table 1 applies to table 2. 
 
    9
Table 3. Analysis of Scope, per-cup WTP (€), all subjects 
 Choice  #2 
6 cups 
Q=6 
Choice #3 
8 cups 
Q=8 
z-value p-value 
  Mean (Std. Dev.)   
BDM (N=56)  0.193 
(0.164) 
0.173 
(0.125) 
 
 
-3.304
** 
 
0.001 
BMS (N=47)  0.170 
(0.199) 
 
0.163 
(0.196) 
 
1.886 
 
0.059 
Note: The note in table 2 applied to table 3. 
 
 
Table 4. Analysis of Scope, per-cup WTP per cup (€), engaged bidders 
 Choice  #2 
6 cups 
Q=6 
Choice #3 
8 cups 
Q=8 
z-value p-value 
  Mean (Std. Dev.)   
BDM (N=42)  0.257 
(0.139) 
 
0.218 
(0.108) 
 
-4.808
** 
  
0.000 
BMS (N=23)  0.259 
(0.257) 
 
0.234 
(0.261) 
 
-0.152 
 
0.879 
Note: The note in table 2 applied to table 4. 
 
 
 

An Experimental Testing of Anchoring Effects

Attitudes toward Risk: Experimental Measurement in Rural India”

Demand Reduction in Multiunit Auctions: Evidence from a Sportscard Field Experiment”

Eliciting Reservation Prices: Becker-DeGrootMarschak Mechanisms vs.

Experimental Auction Procedure: Impact of

Measuring Utility by a Single-Response Sequential Method”

Welfare Gains from Quality Certification of Infant Foods: Results from a Market Experiment in

Value Elicitation using BDM and a Discrete Choice Mechanism

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Value Elicitation using BDM and a Discrete Choice Mechanism

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