RDP 2015-03: The Value of Payment Instruments: Estimating Willingness to Pay and Consumer Surplus 4. Distribution of Willingness to Pay for Card Payments
March 2015 – ISSN 1448-5109 (Online)
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The share of respondents in each willingness-to-pay range is shown in Figure 1. There is noticeable heterogeneity in respondents' willingness to pay for card payments.
Around 60 per cent of respondents indicated that their willingness to pay to use debit cards was less than 10 basis points when cash was an alternative. This proportion was lower for credit cards; around 47 per cent indicated a willingness to pay less than 10 basis points. For these consumers, cards appear to offer no additional value over cash at this price point ($50); cash may even be valued more highly as a payment method. At the other end of the distribution, around 5 per cent of respondents were willing to pay at least 400 basis points to use a debit or credit card, suggesting a small proportion of individuals value card payments quite highly.
The DCE data accords well with diary data on the surcharges that were paid during the week of the Survey. While respondents who were willing to pay 400 basis points or more to use credit cards made only 6 per cent of point-of-sale payments, these individuals paid 10 per cent of all point-of-sale surcharges recorded. Likewise, respondents who said they were unwilling to pay even a 10 basis point surcharge made 46 per cent of payments, but only paid 25 per cent of surcharges.^{[10]} This correlation between the answers to the DCE and behaviour observed in the diary gives us confidence in the use of the DCE to estimate willingness to pay. A more detailed crosscheck of the two types of data is limited by the small sample of surcharges that were paid and recorded during the Survey and the incomplete information regarding surcharges recorded in the diary. In particular, the diary data does not distinguish between a transaction that did not attract a surcharge and a transaction that did attract a surcharge, but in which an alternative payment method was used or the transaction discontinued. An additional crosscheck is whether the respondents were observed to have paid surcharges of the value that is consistent with their stated willingness to pay. As expected, a high level of consistency exists for the small number of payments that are similar to the scenario posed in the DCE.
An alternative way to view the data is to plot the percentage of respondents who are willing to pay the surcharge at each level of surcharge (Figure 2). The resulting cumulative distributions are analogous to demand functions.^{[11]} Across the range of surcharge values used in the DCE, these functions appear well-behaved; they are downward sloping and more elastic at lower price points than higher price points. At each level of surcharge, a higher portion of respondents are willing to pay for the use of a credit card than the use of a debit card, consistent with the additional benefits and features provided by credit cards.
This distribution accords with intuition. In Australia, debit cards do not generally offer any features other than enabling electronic funds transfer at the point of sale. Therefore, the willingness to pay for a debit card is likely to be indicative of the benefits associated with making a payment electronically instead of using cash. These benefits could include: a reduction in cash held or a reduction in the frequency of cash withdrawals due to the ability to access funds electronically at the point of sale; no need to manage change; consideration of tender times (for example, contactless transactions can be faster); or the automatic record of transactions. It should be noted, however, that individuals will also attach value to the benefits of using cash, which could include: privacy, the ability to manage finances; near universal acceptance at merchants; a fast tender time; or to avoid the potential theft of card details. The fact that 60 per cent of respondents reported that they would not be willing to pay even a 10 basis point surcharge to use a debit card instead of cash indicates that many consumers value the use of debit cards and cash similarly, or may even prefer to use cash for the $50 transaction considered in the scenario.
The benefits of electronic payments are shared by credit cards, so that the difference in the willingness to pay for credit cards and debit cards provides an estimate of the value of the additional features of credit cards as a payment instrument for the sample of credit card holders. Given the scenario, the features that should influence our measure of willingness to pay are the benefits that would be realised through the use of each respondent's card for a $50 purchase in a store. These may include access to credit, interest-free periods and reward points based on the value of the purchase. Other features, such as concierge services and travel insurance, may also motivate the use of the card for related purchases of car hire, holiday travel or entertainment services, but these are unlikely to be relevant given the scenario presented in the modified DCE. Any features of the card that are attached purely to ownership (for example, the payment of an annual fee) should not affect the decision of rational consumers to use the card in the scenario.
The role that credit card features play in influencing the willingness to pay for credit cards is depicted in Figure 3. The fact that individuals holding cards with more substantial features are generally willing to pay a higher surcharge suggests that individuals attach some benefit to the features of credit cards. In particular, at all levels of surcharge, holders of cards with more generous rewards are more likely to be willing to pay to use their cards.
4.1 Average Willingness to Pay
Since our data only indicate a range of willingness to pay for each respondent, the calculation of the average level of willingness to pay requires mapping the data to a continuous distribution. This is also the first step in undertaking the regression analysis completed in Section 5.
We use a standard regression framework for double-bounded willingness-to-pay data developed by Hanemann, Loomis and Kanninen (1991). In this framework, willingness to pay is specified as a latent variable in a discrete choice model. From this model, a likelihood function for the data can be written. Maximum likelihood estimation is then used to estimate the specified parameters (see Appendix B for the details, although a brief outline is given here). We assume willingness to pay is normally distributed; our choice of distribution is discussed further below.
In this model, consumer i's willingness to pay (our variable of interest) to use a card instead of cash is specified as a continuous latent (i.e. unobserved) random variable represented by:
Here, α is the unconditional mean willingness to pay and ε_{i} is the normally distributed random error term with σ^{2} variance. In this section, our focus is on estimating the unconditional sample average and no covariates are included in the model. Sections 5 and 6 expand on this specification by including covariates.
Our observable data are the set of variables that tell us which of the eight ranges of willingness to pay presented in Table 2 the respondent falls into:
where y_{i pl}_{,pu } is an indicator variable taking the value 1 if consumer i's willingness to pay lies within the range and 0 otherwise. p_{l} is the lower bound price of the range and p_{u} is the upper bound price of the range. The eight ranges of willingness to pay in basis points are:
The probability that respondent i has a willingness to pay between p_{l} and p_{u} is given by:
Here F() is the normal cumulative distribution function of ε_{i}. The likelihood function is detailed in Appendix B.
As a first step, two constant-only regressions (i.e. not containing any independent variables) are estimated separately for debit cards and credit cards. The purpose is to provide the summary statistics of our data – the estimate of the mean and variance of the willingness to pay for debit cards and credit cards for our sample. Plotting the estimated cumulative distribution function from the fitted normal distribution against our observed data suggests that our assumption of normality provides an appropriate fit for the data for the positive range of willingness to pay shown in Figure 4.
The fact that the willingness to pay of a large proportion of consumers falls in the lowest unbounded range proves to be a problem for estimation. Under the specification of a normally-distributed error, around half of respondents are estimated to have a negative willingness to pay for the use of debit cards and credit cards (i.e. the merchant would need to offer a discount for the use of cards to entice these respondents to pay with a card rather than cash).^{[12]} For these people, we must make a judgement about how accurate this model prediction is and whether this affects the results of greatest interest.
A priori, based on our assessment of the relative benefits of cards and cash, we would expect that willingness to pay for the use of cards is positive, zero or only slightly negative. Data on payment use collected in the Survey shows that 88 per cent of respondents used a card at the point of sale at least once over the week of the Survey. Given that cash is universally accepted at the point of sale, this statistic suggests it is unlikely that our respondents strongly prefer cash (i.e. have large negative willingness to pay). Our preferred option is, therefore, to truncate the distribution at zero; i.e. the mean is calculated averaging willingness to pay if it is predicted to be positive and zero otherwise (see Appendix B). Alternative assumptions consistent with a small negative willingness to pay for card payments are considered for sensitivity analysis.
If we were to assume that willingness to pay was strictly positive, then an alternative assumption could be the log-normal distribution. However, we find that the ‘fat tail’ of the log-normal distribution results in an unrealistically high proportion of individuals being predicted to be willing to pay more than 400 basis points, which skews the average willingness to pay upwards significantly. Accordingly, we judge the truncated normal distribution to be a more representative distribution of the underlying data than a log-normal specification. The comparatively better fit for the portion of respondents with a positive willingness to pay gives us more confidence in this approach. We nevertheless test our results in Section 5 against a log-normal distribution and find similar results. Alternate non-negative distributions are left for future work as they are less commonly used in the willingness-to-pay literature and present greater difficulty for convergence in maximum likelihood estimation.
Debit card | Credit card | Difference in means | |
---|---|---|---|
Minimum willingness to pay assumed to be: | |||
0 bps | 67 (0) | 96 (10) | 29 |
−10 bps | 61 (−10) | 91 (10) | 31 |
−20 bps | 55 (−20) | 87 (10) | 32 |
−50 bps | 38 (−50) | 74 (10) | 36 |
Memo items (0 basis points minimum): | |||
Full sample | 67 (0) | ||
Sample of people who only hold debit cards | 66 (0) | ||
Note: 938 respondents held a debit card, of which 605 respondents also held a credit card |
Table 3 provides the mean willingness to pay (post-truncation) for the use of debit cards and credit cards under a range of assumptions. Assuming that the minimum willingness to pay for a card payment is zero basis points, the median willingness to pay for using debit cards is zero while the mean is 67 basis points. For credit cards, willingness to pay is estimated to be higher on average; the median willingness to pay is 10 basis points and the mean is 96 basis points. We note that the mean willingness to pay for debit cards appears to be similar for both the sample of credit card holders and non-holders despite some differences in the demographic characteristics of these two groups. The average willingness to pay, however, is sensitive to the assumption of the minimum willingness to pay.
The difference in the willingness to pay for debit card payments and credit card payments is less sensitive to the assumption regarding the minimum willingness to pay. The difference suggests that the additional benefit of the payment-related features of credit cards for this group is around 30 basis points. These features include the monetary incentives given to consumers for the use of credit cards, namely the reward points that accrue and the interest-free period.
Footnotes
Under a simple probit model that regresses the probability that a surcharge is paid with independent variable dummies of the response to the DCE, point-of-sale payments made by individuals unwilling to pay a 0.1 per cent credit card surcharge are statistically significantly the least likely to have paid a surcharge. Individuals in each higher willingness-to-pay range were broadly more likely to have paid a surcharge than the preceding lower willingness-to-pay range, though the small sample means the effect is not necessarily statistically significant if comparing adjacent willingness-to-pay ranges. [10]
Each distribution is built on the assumption that all individuals make one payment where they consider the use of debit cards or cash and another where they consider the use of credit cards or cash. This is a more restrictive assumption than underpins a standard demand curve. We do not scale the data by the number of payments made by each individual as the focus on a $50 transaction is already stylised. [11]
Specifically, our model predicts that the willingness to pay for debit cards is distributed N(−76.3,252.2^{2}) and that willingness to pay for credit cards is distributed N(10.0,228.4^{2}). [12]