G32 | Macro Paper Warehouse

Diversion Risk, Markups, and the Financing Cost Advantage of Trade Credit

Thu, 01 Jan 2026 00:00:00 +0000

This paper provides a theory and evidence for why firms with higher markups extend more trade credit, focusing on a financing cost channel that is distinct from existing competition-based explanations. In the model, diversion risk creates a wedge between the bank borrowing rate and the deposit rate. Under cash in advance, the buyer must borrow the full invoice amount (production cost times markup); under trade credit, the seller instead borrows only her production costs. Since higher markups amplify the difference in borrowing needs between these two payment forms, they make trade credit more attractive—and this advantage strengthens with the buyer’s borrowing rate, generating a unique interaction prediction. Empirical tests using detailed Chilean export transactions matched with firm-product markup estimates (De Loecker et al. 2016 methodology) find that a one standard deviation rise in upstream markups increases trade credit by 13 days, with the extensive and intensive margins contributing roughly equally; this effect strengthens with the destination country’s borrowing costs. Results are robust to instrumenting markups with plant-product level physical productivity and replicate in U.S. Compustat data with the real Effective Fed Funds Rate as the borrowing cost proxy.

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

In depth

Q1. Why does a higher markup make trade credit more attractive?

Under cash in advance, the buyer must pre-pay the full invoice price (production cost times markup), requiring borrowing equal to the markup times production cost; under trade credit, the seller instead borrows only her production costs to finance production while the buyer pays later from sales revenues, requiring no pre-payment borrowing at all. Because diversion risk causes banks to charge more than the deposit rate for loans, a higher markup amplifies the savings in financing costs from using trade credit rather than cash in advance, making trade credit strictly preferred whenever the markup and interest rate spread are both positive. This mechanism is operative even if the seller and buyer face identical borrowing rates and even if goods are no harder to divert than cash (distinguishing it from Burkart and Ellingsen 2004, where trade credit dominates because goods are harder to divert).

Q2. What is the unique empirical prediction that distinguishes the financing cost channel?

The model uniquely predicts that the positive effect of upstream markups on trade credit should increase with the buyer’s borrowing rate: when borrowing is expensive, the relative financing cost advantage of trade credit (which reduces total borrowing) is larger, so higher markups generate even more trade credit use. This interaction prediction distinguishes the financing cost channel from competition-based theories (Demir and Javorcik 2018; Giannetti et al. 2021) which predict higher upstream bargaining power (lower markups) → more trade credit, and allows identification even with a rich set of fixed effects because the interaction term is residual to seller, buyer, and destination fixed effects.

Q3. What do the Chilean export data show?

A one standard deviation rise in upstream markups increases trade credit by 13 days on average, with the extensive margin (probability of using trade credit) and intensive margin (trade credit maturity conditional on use) contributing roughly equally; crucially, the effect of markups on trade credit strengthens with the destination country’s borrowing costs, consistent with the unique interaction prediction of the financing cost channel. Markup estimates are constructed at the firm-product level using the De Loecker, Eeckhout, and Unger (2016) methodology applied to Chilean manufacturing survey data, which requires quantity-based information on inputs and outputs to avoid revenue-based measurement confounds; the extensive fixed effects structure (seller × product, buyer-country × product, and seller × buyer-country-year fixed effects) addresses omitted variable concerns.

Q4. How does the paper handle endogeneity of markups?

The paper instruments for firm-product markups using plant-product level physical productivity, which is a supply-side technological variable that affects markups through the cost side (more productive firms have lower marginal costs and thus higher markups for a given price) but is unlikely to directly affect payment choice; the IV results are quantitatively similar to OLS, supporting the causal interpretation of the markup effect on trade credit. Because markups estimated with revenue data can conflate productivity with demand shocks (the ‘De Loecker critique’), the Chilean quantity-based data are particularly valuable: firm-product quantities and input prices are directly observed in the manufacturing survey, enabling markup estimates that are free of revenue confounds.

Key concepts

financing cost channel of trade credit : the mechanism by which trade credit reduces the total bank borrowing needed for a transaction—because the seller borrows only production costs rather than the buyer borrowing the full invoice price—thereby lowering financing costs when diversion risk creates a borrowing-deposit rate wedge; the paper’s central contribution, distinct from competition-based explanations of trade credit provision. diversion risk and borrowing-deposit rate wedge : the risk that borrowers divert borrowed funds, which causes banks to charge a borrowing rate above the deposit rate; the spread between these rates determines the per-dollar financing cost saved by switching from cash in advance to trade credit, amplifying the role of markups in payment choice. De Loecker et al. (2016) markup estimation : a methodology for estimating markups at the firm-product level using quantity-based production data (physical inputs and outputs) rather than revenue data, avoiding the confound between productivity and demand shocks; used here to obtain the Chilean firm-product markup estimates.

Regulating Credit Lines in the Presence of Fire‐Sale Externalities

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

This paper provides a contract-theoretic rationale for the special liquidity regulation of bank credit lines—a form of lending that has received little attention in the regulatory literature despite being the most important source of firm liquidity risk management. In the model, banks choose pre-arranged funding (committed before drawdowns accumulate) and ex-post funding (raised as drawdowns occur) to finance firms’ liquidity needs through credit lines. In states with high liquidity needs, banks cannot raise sufficient ex-post funding to meet all drawdowns and renege on some credit lines, forcing liquidations. Because each additional liquidation depresses the equilibrium liquidation value for all liquidated firms—a pecuniary externality—competitive banks choose insufficient pre-arranged funding in the private equilibrium. A minimum requirement on bank pre-arranged funding per committed (undrawn) funds in credit lines restores constrained efficiency, despite making credit lines more costly; welfare improves because more firms receive funding in high-liquidity states. The optimal regulatory ratio is increasing in the frequency of high-liquidity-need states, the value lost in liquidation, and the sensitivity of liquidation values to forced sales, and decreasing in the premium on pre-arranged funding.

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

In depth

Q1. Why can banks not fully meet credit line drawdowns in high liquidity need states?

In high liquidity need states, where many firms simultaneously draw on their credit lines, the revenues that banks receive from credit lines (interest payments and fees from the small share of firms that need no drawdown) shrink relative to the total drawdown demand, and the resulting shortfall cannot be fully met through ex-post funding raised from new investors because bank revenues are the collateral for such funding. The model captures the systemic nature of correlated liquidity shocks: when drawdowns are idiosyncratic, banks can cross-subsidize from non-drawing firms and raise ex-post funding easily; when drawdowns are highly correlated, these cross-subsidy revenues vanish and ex-post funding is insufficient, making pre-arranged funding essential for maintaining credit line insurance.

Q2. What is the pecuniary externality and why does it lead to under-provision of pre-arranged funding?

When a bank reneges on a credit line and the borrowing firm is liquidated, the forced sale of the firm’s assets depresses the equilibrium liquidation value—a fire-sale externality that reduces the payoff for all other firms being liquidated simultaneously; competitive banks do not internalize this negative spillover because, individually, each bank takes liquidation prices as given, leading the private equilibrium to feature too little pre-arranged funding and too frequent reneging relative to the constrained social optimum. This is a classic pecuniary externality (Lorenzoni 2008): the externality does not operate through a technological channel but through prices (liquidation values), so it is invisible to competitive agents who treat prices as parametric.

Q3. How does the minimum liquidity requirement on credit lines restore efficiency?

A minimum requirement mandating that banks hold a specified amount of pre-arranged funding per committed (undrawn) credit line funds induces competitive banks to internalize the social value of additional pre-arranged funding—namely, that more pre-arranged funding reduces the number of liquidated firms and raises equilibrium liquidation values—and thereby implements the constrained planner’s solution. This regulatory tool resembles the Basel III LCR (which requires banks to hold liquid assets equal to 5%-30% of undrawn credit lines, depending on the type of credit facility) and the NSFR (which requires stable funding equal to at least 5% of undrawn credit lines); the paper provides the first theoretical justification for precisely this type of regulation for credit lines and characterizes how the optimal ratio depends on economic fundamentals.

Q4. What are the determinants of the optimal regulatory ratio?

The optimal minimum pre-arranged funding requirement per committed funds in credit lines is higher when: (1) the premium on pre-arranged over ex-post funding is lower (making additional pre-arranged funding less costly at the margin); (2) high-liquidity-need states are more frequent (making the insurance value of pre-arranged funding higher in expectation); (3) liquidations are more costly (larger welfare losses per uninsured firm); and (4) liquidation values are more sensitive to the number of liquidations (a steeper fire-sale externality). This comparative statics result is policy-relevant: it implies that the Basel III framework’s one-size-fits-all approach to credit line liquidity ratios cannot be optimal across jurisdictions with different economic fundamentals, and national authorities should calibrate requirements to local conditions.

Key concepts

credit line pre-arranged funding : bank funding committed before credit line drawdowns accumulate; provides insurance against high-liquidity-need states by ensuring the bank can meet drawdowns even when ex-post funding is insufficient; corresponds to equity-like stable funding in Basel III terminology. fire-sale pecuniary externality on liquidation values : the depression of equilibrium firm liquidation values caused by simultaneous forced sales when many firms are liquidated after banks renege on credit lines; not internalized by competitive banks, leading to under-provision of pre-arranged funding in the private equilibrium. optimal credit line liquidity requirement : a minimum ratio of pre-arranged funding to committed (undrawn) credit line funds that restores constrained efficiency by internalizing the fire-sale externality; shown to be an increasing function of the frequency of high-liquidity-need states, liquidation costs, and liquidation-value sensitivity.

Taxes Depress Corporate Borrowing: Evidence from Private Firms

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

Layer 1 — Overview

Research Question

Does corporate income taxation raise or lower corporate leverage? The canonical Modigliani-Miller (1963) view holds that the interest tax deduction makes debt more attractive, predicting a positive taxes-to-leverage relationship. Most prior empirical work using large public firms confirms this prediction. This paper re-examines the question using data on small private U.S. firms and finds the opposite: higher corporate taxes depress leverage, at least for small, financially constrained private firms.

Data and Identification

The primary dataset is the Federal Reserve’s Y-14Q supervisory collection (2011–2017), which covers the loan portfolios of the 33 largest U.S. banks and includes firm-level income statements and balance sheets for privately held, bank-dependent borrowers. The sample is restricted to domestic private C-corporations with prior-year assets above $100 million (to screen for pass-through entities), yielding 39,363 non-singleton firm-year observations. The median firm has $288 million in book assets and total debt-to-assets of approximately 38%. A supplementary dataset from the Shared National Credit (SNC) Program (1993–2018, 50,203 firm-year observations) provides a longer time series on syndicated loan commitments. Public firm comparisons use CRSP-Compustat (91,314 observations, 1989–2017).

The empirical strategy is a difference-in-differences event study using variation in state corporate income tax rates. A novel contribution is the manual collection of both enactment dates (when legislation was signed into law) and effective dates for each state tax change since 1975. Identification follows the narrative approach of Romer and Romer (2010) and Giroud and Rauh (2019) to exclude tax changes endogenous to local economic conditions. The specification includes firm and industry-by-year fixed effects, and the analysis uses heterogeneity-robust estimators (Borusyak et al. 2024; de Chaisemartin and D’Haultfoeuille 2020) to address staggered treatment timing.

Main Empirical Findings

For small private firms (below-median total assets, i.e., below $288 million), long-term debt-to-assets rises by approximately 4% in the year of tax cut enactment and remains elevated—at approximately 2%—four or more years later, indicating a permanent increase in leverage. This anticipation effect arises because firms respond to the law’s passage, not its effective date; results using effective dates are noisy and largely insignificant. The average tax cut during the sample period was 1.2 percentage points, representing approximately a 6% reduction in firms’ tax bills (given an average private-firm tax rate of 21%), and the implied leverage change of about 6% at year four is correspondingly large, consistent with a low-interest-rate environment in which small changes in marginal q translate into large investment and borrowing responses.

For large private firms (above-median assets), leverage shows no significant response to tax cuts in any event year. For public firms, evidence of any effect is scant, with at most transient significance and pre-trend issues that complicate interpretation.

Mechanism

The paper argues two tax-sensitive costs of debt offset the standard interest tax shield. First, a higher tax rate reduces after-tax profits, raising default probabilities and credit spreads endogenously; a tax cut thus lowers credit spreads and incentivizes more borrowing. Second, because external equity finance is either unavailable or very costly for small private firms, debt and capital are complements in financing investment: a tax cut raises the marginal product of capital, inducing firms to invest and borrow more. For small firms with low capital adjustment costs, this capital-debt complementarity dominates the direct loss of interest tax shield value. For large firms with high capital adjustment costs (estimated at nine times the small-firm value), investment responds sluggishly to tax changes, the complementarity effect is muted, and the traditional tax shield effect becomes relatively more important—producing the standard, slightly positive taxes-to-leverage relationship.

Bank-assessed default probabilities fall by 20–30 basis points (roughly a 10% decline from an average of approximately 2%) in the year of enactment or one year later for small borrowers, directly supporting the model’s credit spread mechanism.

Welfare Counterfactual

Removing the interest tax deduction from the estimated model (while retaining profit taxation and restricted equity access) causes leverage to fall from 0.36 to −0.26. Firms substitute into cash holdings, shrinking the capital stock. In equilibrium, hours worked rise, the real wage falls, and consumer welfare drops by approximately 1.8%. The interest deduction thus raises welfare in a second-best sense by offsetting other frictions that impede optimal capital accumulation.

Layer 2 — Q&A

Q1: Why do prior studies find a positive taxes-to-leverage relationship, and how does this paper differ?

Prior studies—including Titman and Wessels (1988), Heider and Ljungqvist (2015), and Faccio and Xu (2015)—predominantly use large public firms, for which the interest tax shield is the quantitatively dominant consideration. The present paper focuses on small private firms that face greater financial frictions (restricted equity access, higher default risk), in which two additional tax-sensitive costs of debt become quantitatively important. A further methodological difference from Heider and Ljungqvist (2015) is the use of firm fixed effects rather than first differences, which the authors argue is appropriate in a staggered DiD design.

Q2: Why use enactment dates rather than effective dates as the event?

Tax legislation is often signed into law one to two years before taking effect; in the sample of 125 tax packages since 1975, 33 became effective the following year and 13 became effective two or more years later. Firms that anticipate future tax changes will adjust leverage immediately upon enactment, not at the effective date. Results confirm this: event studies using enactment dates yield precise positive estimates for small firms (ranging from ~4% at year 0 to ~2% at year 4+), while results using effective dates are noisy and mostly insignificant. The paper therefore treats the enactment date as the economically relevant event and collects these dates as a novel contribution.

Q3: What is the economic magnitude of the leverage response for small private firms?

Small firms’ long-term debt-to-assets rises by almost 4% in the enactment year and remains elevated at approximately 2% four or more years after enactment, consistent with a permanent adjustment. The average tax cut during the period was 1.2 percentage points, representing roughly a 6% reduction in the average tax bill (given an average effective rate of 21% for private firms, per Zwick et al. 2016). The estimated coefficient of 0.021 in year four also implies approximately a 6% change in leverage, a large response that the paper attributes to the low interest rate environment amplifying the marginal q effect of even modest tax changes.

Q4: Do large private firms respond differently to tax cuts, and why?

Large private firms (above the median of $288 million in total assets) show no statistically significant leverage response to tax cuts in any event year, and this null is not attributable to wider confidence intervals. The model estimation explains this via capital adjustment costs: the adjustment cost parameter for large firms is estimated to be nine times larger than for small firms. With high adjustment costs, investment responds sluggishly to a tax cut, so the complementarity channel (more investment requires more debt) is suppressed. The traditional tax shield effect then becomes relatively more important, producing a slightly positive (or zero net) taxes-to-leverage relationship consistent with the large-firm data moment.

Q5: How does the model generate a negative relationship between taxes and leverage when the interest tax deduction is present?

Two mechanisms offset the tax shield. First, higher taxes reduce after-tax profits, pushing firms closer to the default threshold; this is capitalized into equilibrium credit spreads, raising the cost of debt. Specifically, for small firms, the model shows that once leverage exceeds approximately 0.47 of assets, the after-tax risky interest rate rises monotonically with the tax rate (rather than falling via the deduction effect). Second, capital and debt are complements in financing investment: because a tax cut raises the marginal product of capital, and because external equity is unavailable, firms substitute into capital by using more leverage. For small firms with low capital adjustment costs, both mechanisms outweigh the loss of interest tax shield value when taxes fall.

Q6: How are the model parameters estimated, and what are the key parameter values?

The model is estimated by simulated method of moments on the Y-14 small-firm sample, minimizing the distance between nine data moments and their model-simulated counterparts. The nine moments include the means and standard deviations of debt, investment, and operating income (all as ratios of assets), the serial correlations of investment and operating income, and the coefficient from a two-way fixed-effects regression of leverage on a tax-change dummy. The deadweight loss in default (ξ) is estimated at 0.6 for small firms and 0.32 for large firms, consistent with elevated financial frictions for small firms and in line with average recovery rates in Kermani and Ma (2023). Fixed operating costs (f) are approximately 0.15 for both samples, amounting to just under half of steady-state operating profits. The serial correlation of the tax process is estimated at 0.662, with innovation standard deviation of 0.022.

Q7: What is the model’s welfare counterfactual, and what does it imply?

The paper compares two economies both with profit taxation: one with the interest tax deduction and one without. Removing the deduction in the small-firm model causes leverage to fall from 0.36 to −0.26, as firms hold net cash rather than net debt. The capital stock shrinks, output falls, hours worked rise, and both the real wage and consumption decline. Consumer welfare drops by approximately 1.8%. Capital misallocation (measured following Hsieh and Klenow 2009) worsens from 0.89 to 0.88. The result has a second-best character: the interest deduction incentivizes debt-financed investment that partially offsets the distortion from restricted equity access.

Q8: What does the evidence on default probabilities add to the empirical case?

The Y-14 collection contains bank-assessed default probability estimates. In an event study covering Q1 2012–Q4 2018, the authors find that firms’ assessed default probabilities decline significantly by 20–30 basis points in the year of enactment or one year later for small borrowers (those with total loan commitments of $10–$100 million), representing approximately a 10% decline from the sample average default rate of around 2%. This decline peaks two years after enactment and persists for three years. No comparable decline is observed for larger loan size buckets. Separately, in SNC data, the probability of a non-pass (i.e., below-investment-grade supervisory) rating falls by 1.7–2.2 percentage points following tax cut enactments, persisting roughly three years. Together, these findings directly validate the model mechanism by which tax cuts lower default risk and credit spreads.

Q9: Are the results robust to alternative econometric methods that address heterogeneous treatment effects?

Yes. The paper applies the Borusyak et al. (2024) imputation estimator, which imputes fixed effects from untreated observations onto treated observations to remove negative weighting bias; for small firms and event years 0–3, it finds significant positive estimates comparable to the baseline. The de Chaisemartin and D’Haultfoeuille (2020, 2021) estimator, based solely on first-time switchers to treatment, yields an effect of 0.036 on leverage for small firms in the enactment year and no effect for large firms, consistent with the baseline. Results using the narrative approach (excluding Connecticut 2011 and 2015, New York 2014, and Rhode Island 2014 as potentially endogenous) produce slightly larger leverage estimates.

Q10: Are tax hike effects symmetric to tax cut effects?

Evidence on hikes is weaker because tax hikes are rare in the sample. In Y-14 data, hikes are associated with leverage declines for small firms in event year 4 and for large firms in event years 1, 2, and 4, but without sufficient pre-hike observations to identify pre-trends, these results are less credible than the cut results. In SNC data (which spans a longer period, 1992–2018), tax hikes are associated with large and significant reductions in total syndicated borrowing commitments of 6–7%, while cuts produce smaller and marginally significant increases. This asymmetry is consistent with the lower adjustment costs of reducing debt relative to increasing it.

Q11: What does the analysis of alternative model specifications reveal about the generality of the mechanism?

Three model extensions are considered. In a collateral-constrained model (no endogenous default), the cost of debt is lost financial flexibility (the future shadow cost of the borrowing constraint), which remains tax-sensitive. In a model with costly equity issuance (linear cost λ = 0.11 following Hennessy and Whited 2007), equity issuance is rare, so the model behaves nearly identically to the baseline. In a solvency-based default model (default when firm value turns negative rather than when liquidity is insufficient), the negative taxes-to-leverage result is preserved. A news-shock extension (Jaimovich-Rebelo 2009) incorporating the anticipation of future tax changes also produces lower leverage in response to higher anticipated taxes, consistent with the empirical anticipation effects, though with smaller magnitudes because the news shock variance is smaller than the total tax-change variance.

Q12: Why do contingent-claims models (Fischer-Leland-Goldstein class) always predict a positive taxes-to-leverage relationship?

In these models, shareholders have deep pockets, so negative cash flows can always be covered; this implies default is rare and the effect of taxes on the default put value is small relative to the direct interest tax deduction. Additionally, these models contain no capital stock, so there is no substitution mechanism between capital and a storage technology (i.e., cash/negative debt). Without endogenous investment, the only channel linking taxes to leverage is the tax shield, which necessarily implies a positive taxes-to-leverage relationship. This is why, as the paper notes, the result was “already hiding” in the Hennessy-Whited class of dynamic investment models but not visible in the contingent-claims literature.

Key Concepts

Interest Tax Deduction (Tax Shield) The paper uses this in the standard corporate finance sense: the after-tax cost of debt is reduced because interest payments are deductible against corporate income. In the model, debt proceeds are discounted at the after-tax interest rate, and the deduction is taken at the time of debt issuance. The paper’s contribution is to show this benefit can be outweighed by two tax-sensitive costs of debt, reversing the sign of the taxes-to-leverage relationship for small, constrained firms.

Tax-Sensitive Cost of Debt The paper defines two distinct tax-sensitive costs that offset the tax shield. First, taxes reduce after-tax profits, shifting the default threshold and raising equilibrium credit spreads; this is capitalized into the risky lending rate endogenously from the lender’s zero-profit condition. Second, taxes reduce the marginal product of capital, making debt-financed investment less attractive; because debt and capital are complements in a model without external equity, a higher tax rate lowers optimal capital and, with it, optimal debt.

Capital Adjustment Costs (ψ) Quadratic costs of changing the capital stock, parameterized as ψ(k’ − (1−δ)k)² / (2k). The paper identifies this parameter as the key determinant of whether leverage responds positively or negatively to taxes: for small firms, ψ is estimated to be near zero (insignificantly different from zero), enabling free substitution between capital and the storage technology (negative debt), so the complementarity channel dominates. For large firms, ψ is estimated to be nine times larger, suppressing this substitution.

Default Threshold In the model, default is triggered when the firm’s current after-tax profits plus recoverable capital are insufficient to repay debt: (1−τ)(y − wn − f) + (1−ξ)(1−δ)k < p. This threshold depends directly on the tax rate τ, so higher taxes move the threshold in the direction of default, raising credit spreads. The paper provides empirical support for this mechanism via the event study of bank-assessed default probabilities.

Enactment Date vs. Effective Date The paper distinguishes between the date tax legislation is signed into law (enactment date) and the date it becomes operative (effective date), which can differ by one to two years. The paper collects novel data on enactment dates from state legislative records. The empirical finding that firms respond to enactment rather than effective dates constitutes evidence of anticipation effects: firms adjust leverage upon observing future expected tax changes, not when the changes actually take hold.

Second-Best Welfare Effect of the Tax Deduction The paper uses this term to characterize the welfare result from the counterfactual: in an economy already distorted by profit taxation and restricted equity access, the interest deduction raises consumer welfare by incentivizing debt-financed capital accumulation. Removing the deduction causes firms to substitute into cash, shrinking the capital stock and lowering wages and consumption. This is a second-best result because the deduction is welfare-improving only because it partially offsets the distortions created by other frictions; in a frictionless world, no such second-best rationale would apply.

Y-14Q Supervisory Data The Federal Reserve’s supervisory collection from the 33 largest U.S. banks, covering loan portfolios and associated borrower financial statements for firms with commercial and industrial loans exceeding $1 million in commitment. The paper uses this dataset because it covers private, bank-dependent firms—a population not previously studied in the tax-leverage literature—and contains firm-level balance sheets, credit ratings, and default probability estimates.

Tokenomics: Optimal monetary and fee policies

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

The rapid proliferation of cryptocurrency tokens—roughly 10,000 outstanding with a total market capitalization around $3 trillion as of early 2024—raises new questions about the design of token monetary policy and fee structures. This paper makes two contributions. Empirically, using supply histories for approximately 2,000 tokens, it documents three systematic patterns: average token money growth rates decline with age and stabilize at about 0.2% per month; long-run money growth rates and convergence speeds are positively correlated across tokens in the cross-section; and tokens more widely held by retail investors have relatively lower long-run money growth rates and convergence speeds. Theoretically, the paper derives optimal issuance and fee policies for a profit-maximizing issuer in a dynamic model where commitment matters, showing that a fully committed (Ramsey) issuer who maximizes profits after the initial period makes choices that maximize the total utility value of all tokens, that without any commitment no equilibrium with a positive token price exists unless fees are charged, and that under partial commitment issuers with higher commitment credibility optimally choose lower long-run money growth rates and fee ratios.

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 are the three empirical facts about crypto monetary policies?

Fact 1: the average money growth rate across the ~2,000 tokens declines with cohort age and stabilizes at approximately 0.2% per month, with more recent cohorts converging faster to their long-run growth rates. Fact 2: in the cross-section of tokens, the estimated long-run money growth rate and the speed of convergence to it are positively correlated—tokens that will eventually have higher money growth also converge more quickly to that level. Fact 3: tokens whose circulating supply is widely distributed among retail investors (measured by the proportion of wallet addresses holding less than 0.1% of total supply) have both lower long-run money growth rates and lower convergence speeds. Together these facts suggest that the degree of decentralization of token ownership systematically influences the choice of monetary policy.

Q2. What are the main theoretical results about commitment?

Without any commitment, no equilibrium with a positive token price can be sustained if the issuer cannot charge user fees; fees create credibility by giving a Markov-perfect issuer an incentive to restrict future token issuance (to collect fees on legacy token holders), which supports a positive price. At the other extreme, with full commitment the Ramsey issuer maximizes profits subject to the full sequence of resource constraints, and a central analytical result is that at steady state the Ramsey issuer’s profit-maximizing choices are equivalent to maximizing the total utility value of all tokens outstanding. This equivalence—profit maximization = welfare maximization for token holders—holds because commitment prevents the issuer from diluting legacy holders; under full commitment, the issuer has no incentive to deviate from the policy that maximizes total token value.

Q3. What does partial commitment imply for policy design?

Under partial commitment (modeled as a probability of sticking to a given policy rather than re-optimizing), issuers with higher commitment probability optimally choose lower long-run money growth rates and reduce both the money growth rate and the fee ratio more slowly over time. This is because higher commitment credibility raises the present value of legacy tokens (users expect the issuer to honor its policy), which makes it optimal to extract less seigniorage and fewer fees in each period while sustaining a higher token price. The model is analytically solvable under partial commitment despite rich economic mechanisms, and the results help interpret Fact 3: tokens with more decentralized ownership (higher effective commitment due to governance constraints) exhibit lower money growth.

Q4. How do the model’s predictions compare with the Bitcoin and Ethereum cases?

Bitcoin exemplifies near-full commitment: its supply schedule is essentially deterministic and hard-coded, resembling the Ramsey policy, though the paper notes a non-zero probability of a fork that could alter the policy. Ethereum exemplifies frequent policy changes (the transition from proof-of-work to proof-of-stake altered issuance and burn rules significantly). Discretionary platforms like MakerDAO, which allow issuer discretion over token supply, more closely resemble the Markov-perfect benchmark. The paper’s framework covers this entire spectrum and predicts that tokens with more commitment (closer to Bitcoin) should have lower long-run money growth and slower convergence—consistent with the empirical facts.

Key concepts

token monetary policy : the issuer’s choice of the rate at which new tokens are minted over time (the money growth rate) and the fees charged per transaction; the paper shows these jointly determine the value of a token and the issuer’s profit.

Ramsey policy for tokens : the full-commitment profit-maximizing policy for a token issuer; a key result is that the Ramsey issuer’s profit-maximizing choices, after the initial period, are equivalent to maximizing the total utility value of all tokens.

partial commitment : a probabilistic commitment technology in which the issuer maintains a given policy with some probability and re-optimizes with the complementary probability; the paper uses this to model the spectrum between Bitcoin (high commitment) and more discretionary platforms.