E41 | Macro Paper Warehouse

Cash or card? A structural model of payment choices

Mon, 01 Jan 0001 00:00:00 +0000

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.

Marginal Propensity to Consume and Personal Characteristics: Evidence from Bank Transaction Data and Survey

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question. This paper asks whether heterogeneity in the marginal propensity to consume (MPC) stems from temporary circumstances (e.g., transient wealth shocks that tighten liquidity) or persistent personal characteristics (e.g., high time discount rates or strong risk aversion that permanently shape saving behavior). Because liquidity constraints are endogenous — they can reflect either bad luck or impatient preferences — disentangling these two sources requires independently measured individual characteristics, which are not available in standard transaction datasets.

Data and Setting. The study combines two data sources drawn from Mizuho Bank, one of Japan’s three largest banks (approximately 24 million individual accounts). First, weekly bank account transaction data for January 2019 to November 2022 covering all outflows (ATM withdrawals, credit card debits, utility payments, interbank transfers) for the approximately 5,282 survey respondents. Second, a bespoke survey conducted in November–December 2022 among 400,000 randomly selected salary-receiving account holders (response rate 1.32%, yielding 5,282 usable observations). The survey elicits the Arrow–Pratt measure of absolute risk aversion, quantitative time discount rates for one-week, one-year, and ten-year horizons, self-reported liquidity constraints, homeownership, education, age, and gender, among other variables.

Three Income Shocks. MPC is estimated against three distinct income events: (1) the Japanese government’s Special Cash Payments (SCP) — a 100,000 JPY (approximately 800 USD) per-person lump-sum transfer during COVID-19, likely transitory, unexpected, and nearly randomly timed across municipalities due to administrative bottlenecks; (2) regular salary receipts (recurring, expected in both timing and amount); and (3) semi-annual bonus payments (received twice yearly, with timing known in advance but amount largely unknown — intermediate between SCP and salary in terms of expectedness).

Estimation Strategy. A two-way fixed effects regression with event-study leads and lags (windows of five weeks before and after each income event) is used to estimate consumption responses. Individual and week fixed effects absorb time-invariant heterogeneity and aggregate shocks (including COVID-19 emergency declarations). Standard errors are clustered at the individual level. For heterogeneity analysis, the income shock variable is interacted with individual characteristics from the survey (treated as proxies for persistent characteristics) and with time-varying log wealth and a liquidity constraint dummy (wealth below one-twelfth of annual income, proxying temporary circumstances).

Main Findings — Average MPC. Across all three income types, the on-impact MPC (week of receipt) is approximately 0.2: specifically γ₀ = 0.23 for the SCP (significant at 5%), 0.20 for salary, and 0.22 for bonus. When estimated jointly in a single regression, coefficients are γ_SCP = 0.21, γ_salary = 0.19, and γ_bonus = 0.21. This uniformity holds despite the sharply different properties of these shocks (transitory-unexpected vs. regular-expected vs. semi-known).

Main Findings — Heterogeneity. Significant heterogeneity in MPC is found primarily in the bonus subsample, where statistical power is greatest. The following cross-term coefficients are significant at the 5% level in the multivariate specification: (a) liquidity constraint dummy — positive and significant, indicating that individuals temporarily below one month’s income in deposits spend a larger fraction of their bonus, with a one standard deviation increase raising MPC by 0.094 (9.4 percentage points); (b) time discount rate (quantitative measure) — positive and significant, with a one standard deviation increase in impatience raising MPC by 0.084; (c) risk aversion (quantitative Arrow–Pratt measure) — positive and significant, conditional on controlling for wealth and liquidity, with a one standard deviation increase raising MPC by 0.031; (d) education — negative and significant irrespective of wealth/liquidity controls, with a one standard deviation increase in education reducing MPC by 0.041.

These magnitude estimates are sizable relative to the baseline MPC of approximately 0.2. For SCP and salary shocks, cross-term coefficients are uniformly insignificant at the 5% level, which the author attributes partly to smaller sample sizes and shorter observation windows for the SCP subsample.

Scope Conditions. The sample consists of Mizuho Bank account holders who receive salary payments directly into their Mizuho account, overrepresenting metropolitan areas and salaried workers relative to the national census. Wealth at Mizuho captures only deposits at that institution and excludes securities accounts, postal savings, and intra-household transfers. Age and gender do not yield significant cross-term coefficients in any specification; the self-reported survey measure of liquidity constraints (ability to cover one month’s income by drawing on savings, assets, or borrowing) is also insignificant, in contrast to the transaction-based liquidity constraint dummy.

Layer 2 — Q&A

Q1. Why is separating temporary circumstances from persistent characteristics important for MPC estimation? Liquidity constraints — the standard proximate predictor of high MPC — are endogenous. An individual may be liquidity-constrained because of a temporary adverse income shock (bad luck) or because of persistently high impatience (high time discount rate) that leads to chronically low saving. If policy evaluation treats all constrained households symmetrically, it conflates these two very different channels. The paper follows Jappelli and Pistaferri (2020), Gelman (2021), and Aguiar, Bils, and Boar (2021) in arguing that both channels matter and that their relative contributions need empirical separation.

Q2. Why are Japanese bonuses particularly well-suited to identifying MPC heterogeneity? Bonuses are paid semi-annually to most regular employees in Japan (accounting for roughly 15–30% of annual income), with timing known in advance but amount largely unknown until receipt. This intermediate nature — partially anticipated in timing but uncertain in magnitude — provides meaningful variation in consumption responses across individuals while maintaining a clean event-study design. The bonus subsample (3,722 individuals who received a bonus at least once) is also large enough to detect cross-term effects that are statistically insignificant in the SCP subsample (2,446 individuals) and in the salary analysis, likely due to greater statistical power.

Q3. How is the Arrow–Pratt measure of risk aversion constructed from the survey? Respondents are asked whether they would purchase a lottery ticket at prize value Z = 100,000 JPY and price p = 10,000 JPY for varying winning probabilities α. The threshold α at which a respondent switches from accepting to rejecting identifies their risk attitude. The absolute risk aversion σ = −U’’/U’ is then calculated as (αZ² − 2αZp + p²) / (2(αZ − p)). This yields σ ranging from −4.5 (when α = 0.01, i.e., risk-loving) to 0.891 (when α = 1, i.e., refusing to buy even at a 90% win probability). Risk neutrality corresponds to σ = 0 (at α = 0.1).

Q4. How are time discount rates measured, and what is the range? Respondents are asked the minimum amount X they would require to wait one week, one year, or ten years to receive a payment instead of receiving 100,000 JPY one week from now (using a one-week anchor to address hyperbolic discounting). The discount rate is calculated as r = X/100,000. The range is 0.01 (X = 100 JPY) to 100 (X = 10,000,000 JPY, i.e., would not wait even for 1,100,000 JPY in ten years). The unweighted average across one-week, one-year, and ten-year horizons is used as the composite discount rate in the multivariate specifications.

Q5. What is the transaction-based liquidity constraint dummy, and how does it differ from the survey-based measure? The transaction-based dummy equals one if end-of-month deposits at Mizuho Bank (the previous month) are below one-twelfth of the individual’s annual income — i.e., if the individual holds less than one month’s equivalent income in liquid deposits. This is a time-varying measure. The survey-based measure asks respondents to self-report whether they could cover one month’s income by drawing on savings, selling assets, or borrowing. The transaction-based measure is significant at the 5% level in the bonus and salary heterogeneity regressions, while the survey-based measure is insignificant, indicating that the precise definition and data source of the liquidity constraint measure matters materially for detecting its effect on MPC.

Q6. What are the estimated on-impact MPC values for each income shock, and how stable are they across robustness checks? The point estimates from the event-study regression (γ₀) are: 0.23 for SCP in the baseline sample (SCP recipients in 2020, N = 2,446 individuals), 0.20 for salary (all 5,282 survey respondents), and 0.22 for bonus (3,722 bonus recipients). In a robustness specification restricting to only year-2020 data for the SCP, γ₀ = 0.235; using cash withdrawals from ATMs as a proxy for consumption instead of total outflows, γ₀ = 0.162 for SCP. In a joint regression including all three income types simultaneously, γ_SCP = 0.21, γ_salary = 0.19, and γ_bonus = 0.21. The SCP MPC for the smaller second-wave subsample (200 individuals, 2021–22) is 0.104 and insignificant, consistent with insufficient statistical power rather than a structural difference.

Q7. Why is the similarity in MPC across the three shock types potentially surprising, and what does the paper say about it? Standard theory predicts divergent MPCs: transitory unexpected windfalls (SCP) should have a higher MPC than permanent salary changes under the permanent income hypothesis, while Ricardian equivalence might reduce the MPC to fiscal transfers like the SCP if households anticipate future tax increases. The paper finds the MPCs are approximately equal (around 0.2 across all three types), and if anything the SCP MPC is slightly higher than the salary MPC. The paper acknowledges this uniformity without offering a structural explanation, using it primarily as a robustness check on the baseline estimate rather than a substantive puzzle to resolve.

Q8. Which personal characteristics are significantly associated with higher MPC, and in which income shock samples? In the multivariate heterogeneity regression, significant cross-term coefficients at the 5% level are found exclusively in the bonus subsample (columns 5–6 of Table 6): the quantitative risk aversion measure (positive, coefficient 0.042–0.049), the quantitative discount rate (positive, coefficient 0.004), and education (negative, coefficient −0.034 to −0.037). The liquidity constraint dummy (transaction-based) is also positive and significant for bonuses. In the univariate robustness regressions (Table 7), the own-house dummy is negative and significant at 5% for bonuses (controlled and uncontrolled); discount rates for one-week and ten-year horizons are positive and significant at 5% for bonuses; risk aversion A (direct self-report) is negative and significant at 5% for SCPs in the uncontrolled specification.

Q9. Do age and gender matter for MPC heterogeneity? No. In all specifications across all three income shock types, the cross-term coefficients on age and the male dummy are uniformly insignificant at the 5% level. The lack of significance for age and gender is noted as a notable result, since both are commonly used demographic proxies in heterogeneous agent models that assume they reflect economically meaningful differences in consumption behavior.

Q10. How does the paper quantify the economic magnitude of each significant heterogeneity factor? Table 8 reports the product of each cross-term coefficient and the standard deviation of the corresponding variable. For the bonus subsample: a one standard deviation increase in the liquidity constraint dummy raises MPC by 0.094 (9.4 percentage points); a one standard deviation increase in the discount rate raises MPC by 0.084; a one standard deviation increase in risk aversion raises MPC by 0.031; and a one standard deviation increase in education reduces MPC by 0.041. All four magnitudes are described as sizable relative to the baseline MPC of approximately 0.2 (20%).

Q11. Why does the paper focus on bonuses for the heterogeneity analysis rather than the SCP? The SCP events provide cleaner identification of transitory, exogenous income shocks (near-random timing due to municipal administrative bottlenecks, as documented by Kubota, Onishi, and Toyama 2021), but the subsample of SCP recipients is smaller (2,446 in 2020, 200 in the second wave), reducing statistical power for detecting heterogeneity in cross-term coefficients. The salary sample is large (5,282 individuals) but salaries are expected, recurring, and may partially update permanent income, complicating interpretation of cross-term estimates. Bonuses offer a balance: a relatively large subsample (3,722) and a partially unexpected income component, making them the most informative sample for heterogeneity analysis.

Q12. What are the main caveats and limitations the paper identifies? Four caveats are noted. First, the personal characteristics from the survey — including time discount rates and risk aversion — are treated as exogenous, but they may themselves be endogenous to economic circumstances or short-term conditions at the time of the survey. Second, only Mizuho Bank deposits are observed; financial assets at other institutions (securities, postal savings) are missing, meaning the liquidity constraint measure understates true wealth for some respondents. Third, the sample is tilted toward metropolitan salaried workers and toward wealthier individuals compared to the full Mizuho customer base (median log wealth of 7.4 vs. 5.9 in Kubota et al. 2021). Fourth, the multiple-testing problem is acknowledged: with many cross-term tests conducted, some rejections of the null at the 5% level may be spurious.

Key Concepts

Marginal Propensity to Consume (MPC, on-impact). In this paper, MPC is operationalized as the coefficient γ₀ from the two-way fixed effects event-study regression — specifically, the fraction of an income shock spent during the same week the shock is received, estimated from total bank account outflows. This is a weekly, within-account measure, not a lifetime or annual consumption response.

Arrow–Pratt Absolute Risk Aversion (σ). A quantitative measure of risk preferences computed from the paper’s survey by eliciting the probability threshold α at which a respondent is indifferent between buying and not buying a lottery with prize Z = 100,000 JPY and price p = 10,000 JPY. Calculated as σ = (αZ² − 2αZp + p²) / (2(αZ − p)). Ranges from −4.5 to 0.891 in the sample, with σ = 0 indicating risk neutrality.

Time Discount Rate (r). Measured by asking respondents the minimum additional amount X (beyond 100,000 JPY) they would require to delay receipt by one week, one year, or ten years, with r = X/100,000. The paper uses the unweighted average of three horizon-specific rates as a composite measure. Ranges from 0.01 to 100 in the sample. Used as a proxy for impatience or myopia — a persistent personal characteristic.

Liquidity Constraint Dummy (transaction-based). A time-varying binary indicator that equals one if individual i’s end-of-month Mizuho Bank deposit balance in month t−1 is below one-twelfth of annual income at t−1 — i.e., less than one month’s equivalent income in liquid deposits. Distinguished in the paper from a survey-based self-report of liquidity constraints, which is found to be insignificant.

Special Cash Payment (SCP). The Japanese government’s COVID-19 pandemic transfer program, providing 100,000 JPY (approximately 800 USD) per person in 2020 (universal) and 100,000 JPY per child in 2021–22 (restricted to households with children under 18 and income below 9.6 million JPY annually). Used in this paper as a transitory, salient, and largely unexpected income shock because municipal administrative bottlenecks made the exact timing unpredictable and nearly random across households.

Two-Way Fixed Effects Event-Study Regression. The paper’s primary estimator, which includes individual fixed effects (controlling for time-invariant person-level heterogeneity) and week fixed effects (absorbing aggregate shocks such as COVID-19 emergency declarations and seasonal patterns). Event-study leads and lags (k = −5 to +5 weeks around each income receipt) allow pre-trend testing and tracing of the dynamic consumption response. Normalized to γ_{−1} = 0.

MPC Heterogeneity Cross-Term. A regression augmentation (equation 3 in the paper) in which the contemporaneous income shock X⁰_{it} is interacted with individual characteristic Z_{it}. The coefficient δ on this cross-term identifies how the MPC varies with Z — the marginal effect of characteristic Z on the MPC. Persistent characteristics (e.g., risk aversion, discount rate, education from the survey) and temporary circumstances (e.g., log wealth, liquidity constraint dummy from transaction data) are included as separate Z variables.

On measuring the welfare cost of inflation

Mon, 01 Jan 0001 00:00:00 +0000

Measuring the welfare cost of inflation requires specifying a money demand function, a definition of money, and an approach to consumer surplus; existing estimates vary widely because these choices are not standardized. This paper advances the literature by applying neoclassical monetary demand theory that integrates the demand for money with the demands for consumption and leisure, using the Normalized Quadratic (NQ) flexible functional form that avoids imposing specific elasticity assumptions. The main contribution is to extend the Serletis and Xu (2021, 2023) framework to derive Hicksian (compensating variation) money demand functions from the NQ model and compare welfare cost estimates based on these against estimates from the Marshallian (consumer surplus) approach—a comparison not previously made within this integrated demand-system framework. The paper uses U.S. CFS Divisia monetary aggregates across multiple levels of monetary aggregation and finds that the two approaches yield internally consistent but quantitatively different welfare cost estimates, with the Hicksian compensating variation approach providing theoretically preferred measures that are robust across specifications.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. What is the neoclassical demand system approach and how does it differ from earlier methods?

The Serletis-Xu framework integrates the demand for money with the demands for consumption goods and leisure in a joint utility maximization problem, estimating a flexible NQ functional form in a systems context rather than fitting a single-equation money demand specification. Earlier approaches—such as the log-log specification (Lucas 2000) or semi-log specification (Ireland 2009)—estimate a single money demand equation under a maintained functional form assumption and a fixed interest elasticity (often −0.5 as in the Baumol-Tobin model). The NQ approach, derived from the dual demand system of Diewert (1974), makes no assumption about the functional form of money demand and allows demand interactions among consumption goods, leisure, and money (as recommended by Abbott and Ashenfelter 1976 and Barnett 1979), which is necessary for correct welfare measurement when money is consumed jointly with other goods.

Q2. What is the distinction between the Marshallian and Hicksian approaches to measuring welfare cost?

The Marshallian (Bailey 1956) approach measures the area under the inverse money demand curve between the zero-inflation and positive-inflation nominal interest rates, which corresponds to consumer surplus but does not hold utility constant. The Hicksian (compensating variation) approach measures the income that must be given to the consumer to restore the same utility after the inflation increase as before—holding utility constant rather than income. The Hicksian approach is theoretically preferred because it measures the true welfare loss from inflation under standard consumer theory; the Marshallian approach can under- or over-estimate the true cost depending on income effects. The paper’s main contribution is to derive the Hicksian demands from the NQ model and compute the compensating variation, previously not done within this flexible-functional-form demand system framework.

Q3. What role do Divisia monetary aggregates play?

The paper uses CFS (Center for Financial Stability) Divisia monetary aggregates—which aggregate monetary assets using economic quantity indices that weight components by their monetary service flows—rather than simple-sum aggregates such as M1 or M2. Simple-sum aggregates treat all monetary assets as perfect substitutes regardless of yield differentials, introducing a substitution bias that misrepresents the quantity of monetary services; Divisia aggregates are theoretically consistent with the neoclassical demand system approach used here. The paper reports welfare cost estimates across multiple levels of monetary aggregation to assess sensitivity to the definition of money.

Q4. How do the results compare with the prior literature?

The paper’s estimates, while internally consistent with the NQ flexible form and Divisia aggregates, are in the range of prior estimates in the literature; the Hicksian compensating variation estimates differ from Marshallian consumer surplus estimates in ways consistent with theory, providing a more theoretically grounded benchmark. The wide range of estimates in the existing literature (discussed in the paper’s Table 1)—from the Lucas (2000) log-log model to the Ireland (2009) semi-log model—reflects sensitivity to functional form, money definition, data frequency, and methodology; the paper’s NQ framework addresses functional-form sensitivity while comparing the two surplus measures.

Key concepts

compensating variation (Hicksian welfare cost of inflation) : the income required to restore a consumer’s utility to its pre-inflation level after an inflation increase, holding utility constant; the paper’s main new estimate, derived from Hicksian money demand functions.

Normalized Quadratic (NQ) flexible functional form : a globally flexible functional form (Diewert and Wales 1988) used to approximate the consumer’s cost function without imposing restrictions on substitution elasticities; allows derivation of both Marshallian and Hicksian demand functions.

Divisia monetary aggregates : theoretically consistent monetary aggregates that weight monetary assets by their monetary service flows (user costs) rather than summing them with equal weights; CFS Divisia aggregates are used here as the measure of money.