Reward elasticity

The core measurable: how much deposits move when the reward rate moves — and why the two directions are estimated separately.

Argued in full in the whitepaper at §3.2, §3.3.

Definition#

Let R_P(t)be the incentive-derived reward rate, annualised, in excess of the pool’s organic yield.

ε_P = ∂ log L_P / ∂ log R_P

ε ≈ 0 — deposits ignore the subsidy, the liquidity is owned. Large ε — deposits track it and leave with it.

Incentivised stablecoin pools frequently sit between 1.5 and 4. At ε = 3.1, roughly three percent of deposits leave for every one percent the reward rate falls.

Estimation#

Emission rates change discretely, publicly and on a schedule, which is close to an experiment run on our behalf. For campaign c with rate changes at τ₁…τ_k:

Δ log L_P(τⱼ) = α + ε_P · Δ log R_P(τⱼ) + γᵀ Z(τⱼ) + uⱼ

Z controls for market-wide flows — aggregate stablecoin supply change, chain-level TVL change, a volatility index.

Without Z, a pool that shrank because the whole chain shrank would score as highly elastic. Pools with too few rate-change events are pooled hierarchically across their asset class and venue type, with shrinkage toward the class mean, and the attestation carries a LOW_DATA flag.

The asymmetry#

Elasticity measured on increases is not elasticity on decreases. Capital enters faster than it leaves — attention effects on the way in, exit friction on the way out. Two coefficients are estimated, ε⁺ and ε⁻, and only ε⁻ enters the hazard.

Elasticity is also not realised in a vacuum. At a scheduled cliff it is dampened by where else depositors can go and how expensive leaving is:

E[ Δ log L_P | t_e ] = ε⁻_P · log(1 − m_e) · φ(A_P, F_P)

m_e is the fractional reduction in reward rate. φ ∈ (0,1] rises with exit friction F and falls with the alternative yield spread A.

The rest of the feature vector#

Fourteen features, all from public state. Three carry disproportionate weight:

Feature	What it separates
Tenure Gini `G`	Two pools with the same median tenure: one a long-standing core plus a churning fringe, one where everyone arrived the same week. The first retains a floor; the second can empty completely.
Post-campaign retention `κ`	The highest-signal feature there is — a direct observation of the predicted quantity under a previous realisation. Unavailable for pools that have never seen a campaign end, which on a new chain is nearly all of them.
Bridge-in recency `ν`	Capital that bridged in recently has already demonstrated mobility and a willingness to pay to chase yield. It leaves the same way.

The others: incentive share of APR, time to campaign expiry, scheduled emission decay, median tenure, depositor concentration, alternative yield spread, exit friction, depth-to-TVL, cross-pool correlation, and gas subsidy status.