RDP 2024-02: Valuing Safety and Privacy in Retail Central Bank Digital Currency 4. Statistical Method for Estimating Willingness to Pay
April 2024
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To estimate willingness to pay, we use the standard statistical method from the discrete choice experiment literature. Our explanation of the method begins with the core elements. The technical details follow in a separate section.
4.1 Core elements
Our method models the probability of a person choosing account A over account B as a function of the differences in utilities between the two accounts. In stylised form, that model is:
The parameters ${\beta}_{1},{\beta}_{2}$ and ${\beta}_{3}$ measure respondents' average sensitivity to the difference in the accounts' fees, provider, and privacy settings. We can thus compare our estimate of ${\beta}_{1}$ (sensitivity to price) with our estimates for ${\beta}_{2}$ and ${\beta}_{3}$ (sensitivity to account provider and privacy settings, respectively) to gauge the extent to which people are willing to forego lower account fees for more safety and privacy. This gives us estimates of willingness to pay for safety and privacy.
To explore heterogeneity in willingness to pay, we also estimate the coefficients of two extended models. In one, we interact all the initial right-hand-side variables with a respondent's age and household income, observing how willingness to pay changes along those dimensions. The other model is the same, except that instead of age and household income we interact the right-hand-side variables with a measure of cash use.^{[5]}
Our motivation for including age helps us to form a partial picture of generational differences in preferences, which are interesting to the extent that they help to forecast changes in aggregate privacy preferences over time. We say the picture is only partial because, without observing the same generations across multiple surveys, including age cannot help us to distinguish between differences that occur across generations and differences that occur within generations as people age.
Household income has a well-documented relationship to financial literacy (Stolper and Walter 2017) which, in turn, could be related to awareness of the various protections in place that make deposits safe already. Consistent with this, lower income people in the United States have a higher tendency to express concern over the safety of their bank deposits (Brenan 2023). But there are a range of other potential mechanisms at play here as well. For example, working in the other direction, household income could also be considered a proxy for a person's likelihood of having bank account balances over the deposit insurance threshold in Australia of $250,000 per account holder, per bank.^{[6]}
Finally, cash use could be related to privacy and safety valuations because cash offers an alternative option that is also a claim on the RBA and offers almost complete user anonymity. We have included cash in a separate model to age and household income, to preserve the intended interpretation of our results (more details on this in the next section).
Since we generate random variation in the account characteristics, we have the benefit of not having to worry about the most common statistical challenge in estimating causal relationships: bias from omitted variables. As with discrete choice experiments more generally, credibility concerns in our work are more likely to come from the set-up of the survey question generating the data and from problems in the sampling. We discuss what we judge to be the most likely areas of concern when presenting our findings.
4.2 Technical details
We model the utility derived by individual $i\in \left\{1,\mathrm{...},N\right\}$ from account $j\in \left\{A,B\right\}$ as a linear function of the account characteristics and a random error term. For our baseline model this has the form
where HighFee_{ij} is a dummy variable equal to one if account j has high fees ($25), and zero if it has low fees ($20). CommercialAcct_{ij} is a dummy variable equal to one if a commercial bank is the provider of account j, and zero if the RBA is the provider. AustracVis_{ij} is a dummy variable equal to one if transaction data for account j are visible to only AUSTRAC, and zero for all other privacy settings account j could have. More generally, all variables of the form {X}Vis_{ij} are dummies equal to one if transaction data for account j are shared only with entity (or entities) X, and zero for all other privacy settings. Finally, ${\epsilon}_{ij}$ is a random component to utility and ${\alpha}_{0}$ represents the utility derived from an a low-fee account, provided by the RBA, with full transaction privacy.
The probability of person i choosing account A (conditional on the account characteristics in the table presented to person i) equals the conditional probability that the utility derived from account A exceeds that of account B. That is,
We assume that ${\epsilon}_{iB}-{\epsilon}_{iA}\sim N\left(0,{\sigma}^{2}\right)$, and since the overall scale of utility does not matter, we normalise the variance to ${\sigma}^{2}=1$. The implied model for the conditional probability of choosing account A thus has the standard probit form
where $\text{\Phi}\left(\right)$ is the cumulative standard normal density function. In our specification we also include a constant, and test whether it differs from the predicted value of zero, to gauge the extent of ‘donkey voting’. A positive constant would, for example, indicate that respondents show some favouritism towards account A, which would be consistent with typical patterns of respondent inattention. (Note that Equation (5), with the constant added, is the detailed form of Equation (1).)
In any case, the corresponding willingness to pay for, say, having a claim on the RBA rather than a commercial bank, holding the other account characteristics constant, equals $5{\alpha}_{2}/{\alpha}_{1}$ (where the 5 comes from the difference in account fees). Likewise, the willingness to pay for full privacy, relative to sharing data with only AUSTRAC, is $5{\alpha}_{3}/{\alpha}_{1}$. We estimate these quantities by substituting in the individual parameter estimates generated by the standard maximum likelihood procedure for probit. Confidence intervals are produced via the delta method. The same techniques apply to all the estimates of willingness to pay presented in this paper. Those willingness-to-pay estimates are invariant to decisions about whether one models the probability of choosing account A or account B.
For our first extended model, we take the utility specification from Equation (2) and add interactions with age and income for each of the variables. Those interactions carry through the probit specification in predictable ways. We present the full list of variables with the probit estimation results. We copy this approach for the second extended model, except we interact with a measure of cash use instead of age and income. Cash use is explored in a separate model to age and income because it is a bad control for the age effects we intend to capture; some of the age effects could occur via preferences for cash, and we do not want to remove those effects from our estimates. Note also that the income variable we use is an approximation, since respondents only report income ranges, and 10 per cent of the sample has its income top-coded.
There is a growing tendency in the economics literature to favour linear probability models over probit, on account of the simplicity of their interpretation (Angrist and Pischke 2009). This simplicity comes at the expense of specifying marginal effects as being constant, when this cannot literally be true; there is an inherent nonlinearity due to the boundedness of probabilities that cannot be captured by the linear probability model. Being able to accommodate this feature becomes important in models where interaction effects are a focus (Ai and Norton 2003), as in our extension models. This argument motivates our preference for estimation using probit.
Footnotes
Exploring age and income relationships was included in our pre-analysis plan, although the set-up of the model has changed somewhat. The Online Appendix explains the rationale for the changes and includes the initially planned analysis. We conducted the cash use exercise in response to seminar feedback. [5]
Deposit insurance in Australia is provided under the Financial Claims Scheme (FCS), which is:
an Australian Government scheme that provides protection to deposit-holders with Australian incorporated banks, building societies and credit unions (known as authorised deposit-taking institutions or ADIs), … in the unlikely event that one of these financial institutions fails.
The FCS is a government-backed safety net for deposits of up to $250,000 per account holder per ADI. (APRA nd)
See APRA (nd) for further details of the policy. According to the latest (albeit dated) public estimates in Turner (2011), there are relatively few accounts in Australia with balances over the threshold.
[6]