Payment data, information disclosure, and privacy

Layer 1: Overview

Research question and motivation: Digital payments generate vast, high-frequency, transaction-level data that several central banks (Bank of Canada, Swiss National Bank, Eurosystem members) already use for nowcasting, and regulatory initiatives (the EU’s PSD2, the UK’s Open Banking Standard, prospective CBDCs) are broadening system-wide data access. The paper asks how improved aggregate-demand forecasts enabled by payment data affect economic activity and through which channels; what the optimal communication policy for disseminating such forecasts is and how it depends on the monetary-policy stance; whether a competitive market in which private banks produce and sell forecasts is socially optimal; and how privacy concerns over individual transaction data affect optimal policy.

Model setup: The authors build a Lagos-Wright / Rocheteau-Wright general-equilibrium monetary model with infinitely-lived buyers and sellers (unit measure each) and periods split into a centralized market (CM) and decentralized market (DM). Each period a stochastic fraction theta_t of buyers becomes ‘active’ and wants the DM good; theta_t takes two values, theta_B < theta_G (bad/good aggregate state) with unconditional mean E[theta_t] = theta-bar. Sellers can pay an effort cost kappa to raise productivity from theta_L to theta_H. Payments use bank deposits fully backed by one-period government bonds costing g > beta (g is the policy variable; r = 1/g - 1). DM terms of trade follow the Kalai (1977) bargaining solution with buyer bargaining power sigma. No agent observes theta_t directly, but aggregating payment data across all banks yields a noisy binary signal s in {o,p} (optimistic/pessimistic), producing an unbiased forecast theta-tilde_t in {theta-tilde_G, theta-tilde_B} with E(theta-tilde_t) = theta-bar.

Main findings (qualitative, as the paper is theoretical with an illustrative calibration): Disclosing forecasts affects welfare through two channels. (1) Demand channel: buyers hold more deposits when expecting high demand, so disclosure raises deposit-holding volatility; even though buyer utility is strictly concave, aggregate welfare w(theta) can be convex or concave. The sign hinges on the statistic T(x) = [u’’(x)]^2 / [u’’’(x)(u’(x)-1/theta)]: w(theta) is convex if T(x) < 1/3 and concave if T(x) > 1 over the relevant range (Lemma 4). (2) Investment channel: sellers underinvest because they capture only fraction (1-sigma) of DM surplus, so disclosure that encourages (discourages) investment raises (lowers) welfare (Lemma 3, thresholds kappa_1 < kappa_2 < kappa_3). Crucially the welfare effect is state-dependent in the monetary stance: with a low bond price/high deposit rate (low g) disclosure tends to reduce welfare (it mainly adds downside volatility and can weaken investment), while with high g (low deposit rate) disclosure tends to raise welfare (Proposition 1; thresholds g, g-bar). Calibrating to the U.S. economy 2016-19, disclosure improves welfare when the utility curvature parameter gamma is small and g is large; the discrete investment channel is inactive over most of the parameter space (Figure 2).

Policy/theoretical implications: A central bank that controls disclosure can do better than binary reveal/withhold by sending noisy messages, a form of Bayesian persuasion (Kamenica-Gentzkow 2011): by committing to send the pessimistic message mb even when the forecast is optimistic (P^b < 1), it raises the posterior theta-tilde_b and induces investment, improving welfare when the investment channel is strong (Figures 4-5; numerical cases g = 1.05 and g = 1.00). A competitive market where private banks pay fixed cost C to produce and sell the forecast yields zero profits and always reveals undistorted information; provided C is below a threshold C-bar the forecast is always produced and sold, possibly causing excessive information production relative to the social optimum. Privacy: a fraction eta of buyers with high privacy costs use cash, shrinking recorded transactions and lowering forecast precision, but this need not reduce welfare; concave privacy costs can make deposit buyers’ preferences less concave, turning welfare convex so disclosure helps via the demand channel, partially but not fully offsetting the privacy cost.

Layer 2: Deep Dive

What is the modeling/identification strategy, and what are the main threats to it?

This is a theoretical general-equilibrium paper, not an empirical identification exercise. The strategy is to embed payment-data-derived forecasting and central-bank communication into a Lagos-Wright/Rocheteau-Wright monetary search model. Aggregate demand theta_t is a two-state random variable realized at the start of the DM; agents make CM decisions (deposit holdings, investment) under a common prior theta-bar unless a forecast is disclosed. The ’threat’ analog is robustness of the comparative statics to functional-form and parameter assumptions; the authors discipline curvature via the statistic T(x) and use a CRRA-type utility u(x)=(x+gamma)^{1-sigma_u}… so that conditions map cleanly into the parameter gamma. They acknowledge agents in reality observe many macro indicators, but assume the only payment-data-based information is the unbiased binary signal, to isolate the informational value of payment data.

What are the two main channels, and how are they distinguished?

The demand channel works through buyers’ deposit holdings: optimistic forecasts raise deposits and DM consumption x, pessimistic forecasts lower them; its welfare sign depends on the convexity/concavity of w(theta), governed by T(x) (convex if T<1/3, concave if T>1). The investment channel works through sellers’ discrete investment decision: because sellers capture only (1-sigma) of surplus they underinvest, so disclosure that pushes investment up raises welfare and disclosure that pushes it down lowers welfare. They are distinguished analytically by shutting one off: Lemma 4 and Proposition 1 set theta_L = theta_H to isolate the demand channel; Lemma 3 isolates the investment channel via the cost thresholds kappa_1 < kappa_2 < kappa_3.

How does the welfare effect depend on monetary policy stance?

The bond price g (inverse of the deposit rate, r = 1/g - 1) is the key policy variable. When g is small (high deposit rate, cheap to hold deposits), consumption x is near its upper bound x*(theta) already under theta-bar, so an optimistic forecast barely raises x while a pessimistic one sharply lowers it, making welfare locally concave and disclosure welfare-reducing; low g also makes DM surplus large so sellers already invest, and a low theta-tilde_B can discourage investment, hurting welfare. When g is large (low deposit rate, costly deposits), x is low under theta-bar so an optimistic forecast substantially raises trade volume, making welfare convex and disclosure welfare-improving (Proposition 1, thresholds g and g-bar). Hence optimal forecast communication should be designed jointly with conventional monetary policy.

How does the Bayesian persuasion / noisy-message result work?

Instead of fully revealing theta-tilde_t, the central bank sends messages m in {mg,mb} under a committed, publicly known policy phi, choosing posteriors P^g = P(theta-tilde_G|mg) and P^b = P(theta-tilde_B|mb). Lemma 6 gives the policy implementing constant posteriors (requires P^b + P^g != 1). By lowering P^b below 1, the bank sometimes sends mb even when the forecast is optimistic, raising the posterior theta-tilde_b conditional on mb and encouraging sellers to invest; this can outweigh the demand-channel loss when the investment channel is strong. Lowering P^g below 1 adds beneficial noise via the demand channel when w is concave (low g). Numerical exercises with g = 1.05 (welfare locally convex, full transparency P^g=P^b=1 optimal when only demand channel active) and g = 1.00 (welfare locally concave, noisy messages welfare-improving) illustrate this (Figures 4-5).

Why do buyers and sellers always want to buy the forecast even when disclosure can lower welfare, and what is the market failure?

Lemma 5 shows buyers’ willingness to pay rho^b_t > 0 always and sellers’ rho^s_t >= 0. Knowing theta-tilde_t lets buyers tailor deposit holdings (avoiding the cost of carrying a fixed level since g > beta) and lets sellers tailor investment, yielding strictly higher private surplus. But neither internalizes the social benefit (the increase in total DM surplus), so private willingness to pay can exceed the social value. Proposition 3 shows that for C <= C-bar the forecast is always produced and sold in the competitive equilibrium (banks earn zero profit), which can lead to excessive information production relative to the social optimum. The market always fully reveals; it cannot replicate the central bank’s optimal noisy (persuasion) policy.

What is the selective-disclosure result?

When the production cost C is neither large nor small, the break-even price may exceed only one side’s willingness to pay, so the forecast is sold only to buyers or only to sellers (Proposition 3). A buyer-only outcome can improve welfare if the forecast helps via the demand channel but hurts via the investment channel; a seller-only outcome helps if the reverse holds. Online Appendix C.3 shows both are possible, but these market outcomes generally do not coincide with the social optimum, so implementing welfare-improving selective disclosure may require the central bank to control the payment data.

How does forecast precision affect outcomes?

Raising phi_o (precision of the optimistic signal) requires lowering phi_p, sharpening the forecast under both realizations. Through the demand channel, dE[w]/dphi_o = phi-tilde(theta_G-theta_B)[w’(theta-tilde_G)-w’(theta-tilde_B)], which is positive when w is convex and negative when concave. Through the investment channel, more precision raises theta-tilde_G but lowers theta-tilde_B, which can raise or lower investment depending on kappa. With private banks, Proposition 4 shows buyers’ and sellers’ willingness to pay rises with precision, making production (and possible over-production) more likely and selective disclosure less likely. Under Bayesian persuasion, higher precision weakly raises welfare (it expands the feasible policy set); but if private banks also disseminate, the central bank’s persuasion is constrained because agents’ posteriors cannot contain less information than the private forecast.

How are privacy and cash modeled, and what is the effect on welfare?

A fraction eta in (0,1) of buyers (‘cash buyers’) face sufficiently large privacy costs from deposit-based payments and use lower-return cash; the rest (‘deposit buyers’) prefer deposits. Cash use shrinks the share of recorded DM transactions, lowering forecast precision (unless cash and deposit buyers’ demand is perfectly correlated). By the precision results this can raise or lower welfare; with private production it makes excessive information less likely, while under central-bank noisy-message disclosure lower precision shrinks the feasible policy set and can reduce welfare. If the privacy cost is increasing and concave in DM consumption x, deposit buyers’ net DM utility becomes less concave, making w more likely convex, so disclosure can improve welfare via the demand channel and the optimal policy may switch from non-disclosure to disclosure. This partially but not fully offsets the negative welfare impact of the privacy cost.

What are the equilibrium-multiplicity and underinvestment results in the benchmark?

With no data sharing, all decisions are state-independent under theta-bar. Strategic complementarity (more sellers investing raises buyers’ deposits, which raises investment payoff) can generate multiple stationary equilibria (lambda=0, lambda=1, and a mixed lambda in (0,1)) when kappa and theta-bar are intermediate (Figure 1). The lambda=1 equilibrium is highest-welfare and Pareto optimal, and the authors impose a refinement selecting it. Sellers can underinvest: there exists kappa for which lambda=0 is the unique equilibrium even though lambda=1 would be socially better, because sellers receive only (1-sigma) of DM surplus. This underinvestment drives the investment-channel welfare results.

How does the paper relate to and differ from closely related work?

Versus Andolfatto-Berentsen-Waller (2014) and Andolfatto-Martin (2013), where assets pay stochastic dividends and information is disclosed at the start of the DM so nondisclosure is always optimal (consumption smoothing), here the forecast is revealed at the start of the CM and affects deposit and investment decisions, so disclosure can be welfare-positive or -negative. Versus Choi-Liang (2023), whose non-monotonic disclosure effects arise from a money-adoption coordination margin, here non-monotonicity arises from how disclosure shapes marginal deposit holdings and investment. It extends the payment-data literature (Garratt-van Oordt 2021; Garratt-Lee 2020; Kang 2024; Amendola-Araujo-Ferraris 2025; Wang 2020, 2023; Cheng-Izumi 2025; Ahnert-Hoffmann-Monnet 2024) by focusing on the macroeconomic forecasting value of payment data and optimal disclosure, and connects to central-bank communication work (Morris-Shin; Jarocinski-Karadi 2020 information channel; Aruoba-Drechsel forthcoming).

What are the CBDC and privacy-protection implications and their scope conditions?

CBDC can serve as an institutional alternative source of payment data: transactions are recorded on a digital ledger, potentially letting the central bank observe flows directly, and can reduce coverage gaps from financial exclusion (the paper cites the 2021 FDIC survey: 4.5 percent of U.S. households, about 5.9 million, were unbanked). CBDC data could improve welfare via the demand and investment channels. Because privacy is a primary public concern, the authors recommend privacy-preserving architectures: adding statistical noise (differential privacy), randomizing data on the buyer’s device before transmission, keeping data decentralized with only model updates shared (federated learning), and clear governance/consent. Scope condition: incentivizing a cash-to-deposit/CBDC shift is welfare-improving only under sufficient privacy protection and only under the conditions (e.g., concave privacy cost, high g) that make disclosure beneficial; legal hurdles to central-bank access of payment data remain, which CBDC issuance could circumvent.

What extensions and robustness checks are reported?

Correlated signals: the central bank and private banks may receive correlated but non-identical signals (e.g., the bank has confidential surveys); Online Appendix B.4 shows this does not change the main results because information affects allocations only through agents’ beliefs about theta_t at decision time. The model is calibrated to the U.S. 2016-19 (Online Appendix B.2) for the quantitative figures. Online Appendix C.2 provides a continuous-investment version (under which the investment channel is always active and welfare responses are smoother); the paper deliberately presents the discrete-investment case to highlight the channels. Online Appendix C.1 gives additional noisy-message numerical exercises, and C.3 shows selective-disclosure cases. An alternative to the lambda=1 refinement is a government ‘revenue backstop’ subsidy (Online Appendix B.2).

Key Concepts

Demand channel: The mechanism by which disclosing the aggregate-demand forecast changes buyers’ deposit holdings and hence DM consumption volatility; its welfare sign depends on whether aggregate welfare w(theta) is convex or concave, governed by the curvature statistic T(x), not merely by the concavity of buyer utility.

Investment channel: The mechanism by which disclosure changes sellers’ discrete decision to invest in higher productivity; because sellers capture only fraction (1-sigma) of DM surplus they underinvest, so disclosure that encourages investment raises welfare and disclosure that discourages it lowers welfare.

T(x) statistic: A normalized log-curvature measure, T(x) = [u’’(x)]^2 / [u’’’(x)(u’(x)-1/theta)], that disciplines the curvature of w(theta): w is convex when T(x) < 1/3 and concave when T(x) > 1 over the relevant consumption range, capturing how quickly the marginal DM surplus falls as consumption rises.

Bayesian persuasion via noisy messages: In the paper’s sense, the central bank commits to a publicly known communication policy (choosing posteriors P^g and P^b) that deliberately garbles the forecast - e.g., sending the pessimistic message even when the forecast is optimistic - to shift agents’ expectations (especially to induce socially efficient seller investment), exploiting that Bayes’ rule constrains only the average posterior.

Excessive information production: The outcome under a competitive market for forecasts where, because banks earn zero profit and both buyers and sellers are willing to pay for the forecast even though it may lower aggregate welfare, the forecast is always produced and sold whenever the cost C is below a threshold, over-supplying information relative to the social optimum.

Cash buyers / privacy cost: Buyers facing sufficiently large privacy costs from deposit-based (recorded) payments who choose lower-return cash; their use reduces recorded transactions and forecast precision, but a privacy cost that is concave in consumption can make deposit buyers’ preferences less concave, turning welfare convex so that disclosure becomes optimal and partially offsets the privacy cost.

Aggregate state theta_t: The two-valued (theta_B bad, theta_G good) random fraction of buyers who become active and demand the DM good, equal to the level of aggregate demand; realized at the start of the DM with unbiased forecast theta-tilde_t derived from aggregated payment data.