Buyer Uncertainty WTP
 

Due to the importance of willingness-to-pay (WTP) in the area of pricing, many different methods have been proposed on measuring WTP. However, significant discrepancies are obvious among these elicitation methods when the estimates are compared. Attempts to reconcile these inconsistencies suggest that certain biases may be inherent of many measurement methods, e.g. hypothetical bias and strategic bias.

In this paper, we propose that besides the two known biases, inconsistencies of WTP estimates may be a result of overlooking buyer uncertainties (e.g. information uncertainty and preference uncertainty.) When the level of buyer uncertainty is high, not only will it generate large discrepancy among estimates of extant methods, using these estimates of WTP for pricing purpose can also be highly misleading. Therefore, a practical guidance on dealing with buyer uncertainty when measuring WTP is warranted.

In this paper, we first review the extant definitions and provide a synthesis when buyer uncertainty is presented. Then we review the extant methods of measuring WTP on their pros and cons in practice. We then provide empirical evidences with two experiments that WTP estimates can be significantly biased when buyer uncertainty is overlooked.
 

Review of Extant Definitions and Synthesis with Buyer Uncertainty

The economics literature interprets WTP as the combined economic value to a consumer of all the benefits that would accrue from the product (Ryan and Miguel 2000). It is noteworthy that extant definitions either assume buyer uncertainty does not exist or it can be solved by consumers when a price is presented to him/her.

In other words, a single price point exists across which buy/not buy decision is clearly defined. The researchers may not be able to observe this price threshold accurately. If the estimates of WTP are not in line with the actual behavior, the usual suspect is measurement errors instead of buyer’s uncertainty.

According to Wang, Venkatesh and Chatterjee (2007), the inconsistencies in the definitions emerge when they clarify how a consumer would behave if the seller’s price is set at the threshold representing the WTP. Since buyer uncertainty is best represented as purchase probability, all the extant definitions differ remarkably in the implied level of purchase probability.

The lack of consensus goes beyond the economics studies. We classify in Table 1 a number of studies on WTP and highlight how they differ in their definitions and their implicit purchase probability when buyer uncertainty is presented.

As proposed by Wang, Venkatesh and Chatterjee (2007), the meaning of convergence would be that the transition in purchase probability from 100% to 0% occurs at a particular point, as shown in Figure 1A.

Figure 1B schematically represents the alternative argument of Wang, Venkatesh and Chatterjee (2007) – that of the WTP as a range of thresholds. (The specific shape of the curve is obviously individual specific.) Their range conceptualization seems able to unify the various definitions of WTP and has the single point representation as a special case. When buyer uncertainty does not exist, all these definitions converge to a single point.#p#分頁標題#e#
 

An Assessment of Extant Approaches for WTP Measurement under Buyer Uncertainty

Given our primary interest in WTP at the individual level, we will review related methods only. The six prominent methods that we consider are direct self-explication, Vickrey auction, BDM’s point-of-purchase procedure, ICERANGE, conjoint analysis and choice experiment. The first four are methods for direct elicitation of WTP whereas the last two involve indirect estimation.

Remarkably, when buyer uncertainty is overlooked, the estimates from the alternative methods diverge in systematic ways. For example, the estimates of WTP from the BDM are found to be lower than those from direct self-explication and choice experiment (Wertenbroch and Skiera 2002). The estimates from conjoint analysis based methods are all found to be higher than those from direct self-explication (Chung and Rao 2003, Jedidi and Zhang 2002).

The biases that the alternative methods ignore or overcome are arguably a key source of the observed differences. Two important types of biases examined in the WTP literature are incentive compatibility bias and strategic response behavior bias (Wang, Venkatesh and Chatterjee 2007). We proposed another bias from overlooking buyer uncertainty.

Incentive Compatibility Bias (including hypothetical bias):An incentive-compatible mechanism gives the respondent the incentive to respond truthfully and a disincentive for not revealing the truth. Incentive incompatibility arises, for example, when respondents are not responsible to pay their stated (or inferred) WTP. The willingness to pay is higher in such instances than when respondents are responsible to pay (Posavac 2001). Wertenbroch and Skiera (2002) show that this upward bias extends to such other non-incentive-compatible methods as open-ended and double-ended contingent valuation.

Strategic Response Bias: This arises when respondents anticipate a link between their response and the ultimate outcome and act so “as to maximize their utility taking into account how their responses may affect the decision” (Carson et al. 1997). The direction of strategic bias depends on the context of elicitation. When consumers perceive that stating a higher WTP will increase the likelihood of subsequently receiving a good, they are more likely to state a higher value than their true value (Posavac 2001). On the other hand, when anticipating a higher final price for a product, buyers might indicate a lower willingness to pay hoping to induce the seller to set prices lower (Monroe 1990, p.107).

Bias from Overlooking Buyer Uncertainty: This is an inherent bias of most methods (with the exception of Wang, Venkatesh, and Chatterjee 2007) due to the overlooking of buyer uncertainty while significant one exists.

In Table 3 we briefly point out the salient features of each method, their pros and cons, and representative studies that invoke these approaches. Under pros and cons, we note the biases that the methods control or ignore and their (in) ability to capture buyer uncertainty of an individual consumer. A key conclusion that we draw from the table is that ICERANGE approach appears to be a “best method” among available options based on its avoidance of the strategic, incentive compatibility biases, and buyer uncertainty.#p#分頁標題#e#

The direction of strategic bias depends on the context of elicitation:

(a) When consumers perceive that stating a higher WTP will increase the likelihood of subsequently receiving a good, they are more likely to state a higher value than their true value (Posavac 2001)

(b) On the other hand, “when facing a direct question as to which a set of prices would be preferred or acceptable, buyers often may indicate the lowest price option, since this would be a ‘rational’ answer.” (Monroe 1990, p.107), the reason for providing lower value than their true value is that consumers are trying to use strategic thinking to keep price low in the real market. This downward bias has been used to explain higher estimates of WTP from indirect mechanisms than those from simple self-explication (Chung and Rao 2000; Jedidi and Zhang 2002).

However, after taking all the above biases into consideration, the extant literature still cannot agree with each other on which method provides the “true” (or closest to “true”) value of WTP: As shown experimentally that simple self explication is biased upwards due to incentive incompatibility (Wertenbroch and Skiera 2002) or hypothetical bias (Posavac 2001), one may conclude that the “true” WTP should be lower than the estimate value from self explication.

This is, however, in contrary to the findings of indirect elicitation methods: the supposedly unbiased estimates of indirect elicitation (which is incentive indifferent as consumers has no incentive to either tell the truth or lie) turned out to have even higher value than those from self explication format (Chung and Rao 2000, Jedidi and Zhang 2002).

This raises further concern on whether it is sufficient to use these biases to explain the difference on estimates from alternative methods. Could it be the case that despite all these biases, different methods are simply measuring different points of a range of “reservation price” under buyer’s uncertainty?

The lack of convergence among extant methods can only partly be attributed to the two known biases. If, as shown empirically, simple self explication is biased upward (overestimation) due to incentive incompatibility or hypothetical bias, one may conclude that the “true” WTP should be lower than the estimated value from self explication. This is, however, not supported by the findings of indirect elicitation methods: the supposedly unbiased estimates of indirect elicitation turn out to be even higher than self-explicated measures (Chung and Rao 2003, Jedidi and Zhang 2002).

There is no easy way to reconcile these differences if buyer uncertainty is overlooked. On the other hand, it can only be explained when these estimates are tied to different purchase probabilities. The underlying uncertainty of consumer’s valuation is supposed to result in a range estimate of WTP that contains different point estimates of conventional methods within the range.#p#分頁標題#e#

Table 3, under salient features, contains the probability of purchase that the WTP measure (or estimate) implicitly maps on to. We surmise that without any elicitation bias, a WTP estimate associated with 50% of purchase probability would likely be higher than an alternative estimate associated with 100% of purchase probability.

As BDM and Vickrey auction procedures are tied to real choice (i.e., one has to buy the good if certain conditions are met), respondents may provide a value corresponding to their floor WTP with 100% of purchase probability (we will test this hypothesis in the next section). On the other hand, the nature of trade-off analysis in conjoint analysis and choice experiment—tied to indifference between buying and not buying—is likely to yield a higher estimate of WTP close to the “indifference” WTP with 50% of purchase probability.
 

Pricing implication when WTP estimated with buyer uncertainty overlooked

The purpose of this section is to prove analytically that ignoring buyer uncertainty in WTP estimation when it exists leads to sub-optimal pricing. To do so, we will set up a simple model of WTP, derive the closed form solution for optimal price and investigate the nature and extent of biases by ignoring buyer uncertainty.

Let the seller’s profit-maximizing price to an individual consumer be P. Let the consumer’s floor WTP (in Figure 1B) be a and the ceiling WTP be a+b, implying a range of b. Let the shape of the curve be S-shaped with the indifference WTP, at , halfway between the floor and ceiling WTP. In other words, the curve we assume is an S-shaped cumulative distribution function (cdf), a more widely accepted form in marketing than the ramp shaped (i.e., linear) cdf arising from a uniform density. The specific cdf we assume is:

for (1a)

and for (1b)

This functional form is better than, say, that normal cdf in that it is analytically tractable. Moreover, better than the normal and logistic cdfs, the one above is bounded between the floor and the ceiling WTP. The marginal cost is set to zero.

The seller’s profit would be:

Õ = aif P = a(2a)

Õ = if (2b)

Õ = if (2c)

Of the above possible levels for price, the optimal price occurs in the interval . Specifically, the seller’s optimal price to the consumer has the closed form solution:

Notice that the optimal price converges to a when b = 0. Notice that when the range is zero, the floor-, indifference-, and ceiling-WTP all converge to a. Obviously, the seller maximizes profit by setting the price at this point.

When the range is positive (b>0), we have the following proposition:

P1a:When a consumer is uncertain of her WTP, prices corresponding to the floor-, indifference- and ceiling WTP are all sub-optimal.

P1b:A price level corresponding to the floor WTP is biased downward, and those corresponding to the indifference or ceiling levels are biased upward. The price corresponding to the ceiling WTP has the most bias.
 

Empirical Evidence of WTP Elicitation Bias when Buyer Uncertainty is Overlooked

To demonstrate that conventional elicitation of WTP is likely to be biased due to overlooking of buyer uncertainty, we conducted two paper-and-pencil tasks. Our study 1 was in the context of a digital handheld. Our sample consisted of 87 MBA students, a relevant segment for this product category.

To assess whether the bias indeed exists when buyer uncertainty is overlooked, we asked each respondent three questions that map on to WTP associated with 100%, 50% and 0% purchase probability. In other words, we used a within-subjects design. The actual measures are provided in Appendix I. Specifically, we tested the following hypotheses:

H1a: Consumers’ mean indifference WTP is greater than their mean floor WTP.

H1b: Consumers’ mean ceiling WTP is greater than their mean indifference WTP.

There is some concern among marketing scholars that self-explicated measures of WTP, like the ones we used, could be downward biased as respondents might act strategically to keep prices low. The mitigating circumstance in our context is our interest in the differences between pairs of measurements, so the biases would largely cancel out.

We summarize the results in Table 2A. As seen here, and in support of Hypothesis 1(a), the mean indifference WTP exceeds the mean floor WTP by $44.67 (significantly greater than zero with p < 0.01). Further, in support of Hypothesis 1(b), the mean ceiling WTP is greater than the mean indifference WTP by $49.87 (p < 0.01). Together they support the Hypothesis 1 that WTP of individual consumers are better represented as a range of valuations, at least in the context of digital handhelds.

In Study 2, we address two potential problems with the earlier study: (a) As Study 1 is a within-subjects design, asking the three WTP related questions in succession might give rise to testing effects; (b) The digital handheld in Study 1 is just one category. Therefore, in Study 2, we used a between-subjects design with random assignment and considered three products: a digital camera, a ticket for a regular season NFL game and a bottle of French wine. We tested the following, considerably more conservative hypotheses.

H2a: (Mean Indifference WTP)Group j > (Mean Floor WTP)Group i

H2b: (Mean Ceiling WTP)Group k > (Mean Indifference WTP)Group j

The measures for a sample individual were: (1) What is the maximum price at or below which you would definitely buy the above shown <digital camera>? (At or below this price there is a 100% chance that you would buy.) (2) What is the price at which you would be indifferentbetween buying and not buying the above shown <NFL home ticket>? (At this price there is only a 50% chance that you would buy.) (3) What is the minimum price at or above which you would definitely not buy the above shown <French wine>? (At or above this price there is nochance that you would buy.)#p#分頁標題#e#

The sample for Study 2 consisted of 82 MBA students, without any overlap with the earlier sample. To avoid potential sequence bias, we rotated the products and the measures in the sense that respondents in each of the three groups provided the floor WTP in one category, the indifference WTP in another and the ceiling WTP in the third category. The page layout and filler questions ensured that the floor-, indifference- and ceiling-measures were “far apart.” The relevant results are in Table 2C.

Despite the conservative nature of this test, all six observed differences are in the hypothesized direction, with four of these differences statistically significant. The mean ceiling WTP is significantly greater than the mean indifference WTP for the football ticket ($49.38, p<0.01) and digital camera ($111.13, p<0.01). The mean indifference WTP is significantly more than the mean floor WTP for the football ticket ($16, p<0.01) and wine ($9.63, p<0.01).

We believe that the above theoretical and empirical evidence lend strong support for the bias that exists when buyer uncertainty (purchase probability) is overlooked during WTP elicitation.

Discussion

WTP is widely used concept in marketing and economics. The measurement of WTP is key to the pricing practice of marketing managers, especially value pricing and one-to-one pricing. However, when WTP is elicited using conventional methods (with the exception of Wang, Venkatesh and Chatterjee 2007), significant bias exist for all point estimates when buyers are uncertain about their valuation.

This paper reviewed the extant literature on the definitions and measurement methods of WTP. Our analytical model shows that when buyer uncertainty is present, point estimates can lead to serious bias and sub-optimal pricing. We further demonstrate that buyer uncertainty is evident for several popular consumer products.

In summary, researchers need to be careful when WTP is elicited under buyer uncertainty. The higher the level of uncertainty, the more bias the point estimate will be. The most severe bias happens when ceiling WTP is elicited.