Cash or card? A structural model of payment choices
What this paper finds — and why it matters
Lippi and Moracci (2026) ask how euro area households choose between cash and card payments, and whether existing theoretical models can explain observed behavior. They draw on ECB payment diary surveys (SUCH and SPACE waves I–III, 2015–2024) covering transaction-level records that include purchase size, payment method chosen, cash on hand before each transaction, and merchant acceptance of cards. This granular data allows the authors to isolate unforced payment choices — transactions in which the consumer had sufficient cash, the merchant accepted cards, and the consumer held a card — from mechanically constrained ones.
The authors document three empirical patterns. First, roughly 39% of individuals in the sample violate the simple transaction-size threshold rule of Whitesell (1989): their largest unforced cash payment exceeds their smallest unforced card payment. Second, between 27% and 49% of unforced transactions are settled by card across survey waves, contradicting the “cash burns” policy of Alvarez and Lippi (2017) under which cards are used only when cash is exhausted. Third, and most novel, the probability of card use rises sharply as implied residual cash holdings (m′ = m − s) approach zero — that is, when a cash payment would nearly deplete the wallet. This suggests a precautionary motive: consumers maintain a cash buffer to cover purchases at merchants who do not accept cards.
To rationalize these facts, the authors build an inventory-theoretic model with a compound Poisson expenditure flow (random arrival times and random transaction sizes drawn from a lognormal distribution), imperfect card acceptance (fraction ϕ of merchants accept cards, set at 0.89 for 2023–24), a fixed cost b per cash withdrawal, a fixed cost κ per card transaction (sign unrestricted), and a utility penalty u per missed purchase. The optimal policy takes an (s,S) form for withdrawals and a state-dependent threshold for payment choice. When 0 < κ < b, the agent uses cards for purchases large enough that paying cash would push balances below a threshold m̃, thereby avoiding a costly withdrawal or the risk of missing a future purchase. The critical transaction size above which cards are used, s(m), rises with cash on hand, generating the interaction the data reveals.
The model is calibrated by minimum distance to four moments from the 2023–24 SPACE wave: average cash balances relative to daily expenditure, annual withdrawal frequency, the unforced card expenditure share, and realized purchase frequency. The estimated annual cost of managing consumption transactions for the average euro area household is approximately 15 euros — a remarkably small burden. Three counterfactual experiments quantify welfare implications. Removing card access raises the annual cost from 15 to about 50 euros, implying a card ownership value of roughly 35 euros per year. Near-universal card acceptance (ϕ = 0.99) reduces the annual cost by nearly 75%, from 15 to about 4 euros, while average cash holdings fall from 130% to about 20% of daily expenditure. A complete ban on cash would cost the average consumer approximately 60 euros per year more than the current mixed system. A cashless equilibrium requires both near-universal acceptance (ϕ above 99%) and card costs at or below zero (κ ≤ 0); neither condition alone is sufficient given the estimated magnitude of the missed-purchase cost u.
Q: What is the central empirical puzzle the paper addresses? A: Existing models predict either a pure transaction-size threshold (Whitesell 1989) or a pure cash-burns rule (Alvarez and Lippi 2017). The data shows both rules are violated: 39% of individuals with observed unforced transactions of both types violate the threshold rule, and 27–49% of unforced transactions are paid by card despite available cash. Neither model alone accounts for the novel finding that card usage spikes precisely when a cash payment would nearly exhaust the wallet.
Q: What data does the paper use and what is its key advantage? A: The authors use ECB payment diaries from four survey waves: SUCH (2015–16) and SPACE I, II, III (2019, 2021–22, 2023–24). For each transaction the diary records payment method, purchase size, and cash on hand, along with merchant acceptance of each payment method. Critically, the combined information on cash holdings and acceptance allows the authors to distinguish forced from unforced payment choices, which is essential for identifying the behavioral determinants of payment method selection.
Q: What is the novel empirical fact the paper contributes? A: The paper documents that the probability of card use increases sharply as implied residual cash (m′ = m − s) approaches zero. This pattern holds across all survey waves. It is consistent with a precautionary motive: consumers use cards to avoid depleting a cash buffer that provides insurance for encounters with merchants who do not accept cards.
Q: How does the theoretical model generate the precautionary motive for cash? A: Cards are accepted in only fraction ϕ of stores; when a merchant does not accept cards and the consumer lacks cash, the purchase is missed at utility cost u. This creates an incentive to maintain positive cash balances. Combined with a fixed withdrawal cost b and a fixed card cost κ, the agent optimally targets a cash level m* and withdraws before the wallet empties (trigger m̄ > 0), holding a buffer against card-rejection events.
Q: What is the key proposition characterizing the optimal payment policy? A: Proposition 1 establishes three regimes. When κ ≤ 0, the card always dominates and is used for all purchases. When κ ≥ b, cash always dominates and cards are used only for forced transactions. In the intermediate case 0 < κ < b, a threshold m̃ ∈ (m̄, m*) divides behavior: for m < m̃ the agent uses cash for all transactions; for m ≥ m̃ the agent uses a card for any purchase exceeding a size threshold s(m), where s(m) is increasing in m. The threshold s(m) distinguishes this policy from Whitesell (1989)’s fixed threshold.
Q: How does the payment threshold s(m) vary with cash on hand, and why? A: s(m) is the purchase size above which the value loss from paying cash — pushing the agent closer to m̄ and raising the probability of a missed purchase or costly withdrawal — exceeds the fixed card cost κ. As m rises, a larger cash payment is needed to trigger this concern, so s(m) increases. This means card use becomes less frequent as cash balances grow for most of the state space, consistent with the empirical finding that cash probability rises with cash on hand.
Q: What are the calibrated parameter values and what do they imply? A: The withdrawal cost b is estimated at 0.003 EUR — very small. The per-transaction card cost κ is about 60% of b, meaning cards are cheaper to use per transaction than visiting an ATM. The cost of a missed purchase u is approximately 1 EUR. The arrival rate λ is calibrated so that about 2% of purchase opportunities are missed under the estimated card acceptance rate of 0.89. These values imply that the payment system imposes a small but non-trivial welfare burden, concentrated in the precautionary costs of maintaining cash.
Q: What is the estimated annual cost of managing consumption transactions? A: Under the optimal policy for 2023–24 parameters, the annual cost C is approximately 15 euros per household. This decomposes into opportunity costs of holding cash (RM), withdrawal costs (bn), card usage costs, and the disutility from missed purchases. The authors characterize this as “remarkably small,” suggesting the current payment system is relatively efficient from the household’s perspective.
Q: How does this cost compare across demographic groups and over time? A: Until 2019 the estimated annual cost was around 20 euros; it stabilized around 15 euros from 2021–22 onward, with the decline driven primarily by households holding less cash in the post-pandemic period. Across age groups, education levels, income brackets, and gender, each subgroup faces a very similar cost as a proportion of their expenditure, indicating limited distributional variation in payment system costs.
Q: What is the welfare value of owning a payment card? A: Setting ϕ = 0 (cash-only economy), the annual cost rises from 15 to approximately 50 euros. The value of card ownership is therefore approximately 35 euros per year. The savings come primarily from lower opportunity costs of holding cash (since card access reduces the precautionary motive) and lower disutility from missed purchases; withdrawal cost reductions play a negligible role.
Q: What happens under near-universal card acceptance (ϕ = 0.99)? A: Average cash holdings fall from about 130% of daily expenditure to about 20% of daily expenditure, a reduction of approximately 110 percentage points. The unconditional card expenditure share rises by 17 percentage points to about 93%, mostly through an increase in forced card transactions (agents more often lack cash). Unforced card expenditure falls by about 10 percentage points because the precautionary motive for using cards — preserving a cash buffer — weakens when acceptance is near-universal. The annual management cost falls by nearly 75%, from 15 to approximately 4 euros.
Q: Under what conditions does a cashless economy emerge? A: The model identifies two jointly necessary conditions: card acceptance near universal (ϕ above 99%) and card costs at or below zero (κ ≤ 0). Raising ϕ alone from the estimated 0.89 to 0.99 reduces cash use substantially but does not eliminate it, because the estimated cost of missed purchases u is large enough that consumers still maintain a small cash buffer. For κ ≤ 0, cash holdings M/e are insensitive to κ and depend only on ϕ. With current card usage costs, even near-universal acceptance would not produce a cashless economy.
Q: What is the cost of a complete cash ban? A: Under a cashless policy, the annual cost is approximately 75 euros — about 5 times the 15-euro baseline and about 25 euros more than the cash-only cost of 50 euros. A complete ban on cash would increase transaction management costs by approximately 60 euros per year for the average consumer. This is because at ϕ = 0.89, nearly 11% of purchase encounters would result in missed transactions.
Q: How does card acceptance affect cash management in the model and data? A: As ϕ falls, the precautionary motive for holding cash strengthens: the withdrawal trigger m̄ rises, average cash holdings increase, and withdrawals occur when the wallet is still substantially full. This prediction is qualitatively consistent with the empirical finding that in areas with lower card acceptance, individuals hold higher cash balances and withdraw at higher residual cash levels.
Q: What are the main limitations the authors acknowledge? A: Three caveats are identified. First, the model has no exogenous cash inflows (wage payments, gifts); incorporating Miller-Orr-style inflows could affect cash resilience estimates. Second, the card cost κ is fixed and independent of transaction size s; allowing κ(s) = κ₀ + κₛ·s would better capture reward-program economies relevant for the US. Third, merchant card acceptance is treated as exogenous; endogenizing it as a game between merchants would allow a joint welfare evaluation of acceptance decisions, payment choices, and cash management.
Unforced transactions: Transactions in which both cash and card payments are feasible — specifically, cash holdings exceed the purchase size, the merchant accepts cards, and the consumer holds a card. Isolating unforced transactions is necessary to identify behavioral determinants of payment choice, stripping out mechanical constraints imposed by cash insufficiency or merchant non-acceptance.
Precautionary cash buffer: A positive cash balance maintained above the withdrawal trigger (m̄ > 0) to insure against purchases at merchants who do not accept cards. In the model, this buffer arises because card non-acceptance combined with insufficient cash results in a missed purchase at utility cost u; the precautionary motive is stronger when ϕ is lower.
Transaction-size threshold s(m): The purchase size above which a consumer with cash holdings m optimally pays by card (when cards are available and 0 < κ < b). Unlike the fixed threshold of Whitesell (1989), s(m) is increasing in m, generating a novel interaction between cash on hand and payment method choice that the ECB diary data confirms.
Cash burns policy: The policy of Alvarez and Lippi (2017) in which cards are used only when cash is fully exhausted (m = 0). The paper documents that 27–49% of unforced transactions are settled by card across survey waves, constituting a systematic violation of this rule that the model resolves by introducing transaction-size heterogeneity and a precautionary motive.
Imperfect card acceptance (ϕ): The exogenous fraction of merchants willing to accept card payments, set at 0.89 for 2023–24 in the calibration. Imperfect acceptance is the primary driver of the precautionary demand for cash; it also determines the frequency of missed purchases under a cashless policy and is the key parameter governing whether a cashless economy can emerge.
Annual transaction management cost (C): The total yearly household cost of operating within the payment system, defined as C = RM + bn + κ·(number of card purchases) + u·(number of missed purchases). Estimated at approximately 15 euros for the average euro area household in 2023–24, decomposed across opportunity costs of cash holdings, withdrawal costs, card usage costs, and missed-purchase disutility.
Ss withdrawal policy: The optimal cash replenishment rule characterized by a trigger level m̄ and a target level m*. The agent withdraws whenever cash falls to m̄, resetting balances to m*. A strictly positive trigger (m̄ > 0) reflects the precautionary motive: the agent refills before cash is exhausted in order to maintain insurance against card non-acceptance events.