HANK After Cantillon: Two Hidden Premises and a Breakeven Condition

<p>The Heterogeneous Agent New Keynesian (HANK) literature claims that unanticipated monetary expansions benefit the poor by eroding their nominal debt — the balance-sheet channel. This claim rests on two premises built into the standard framework by construction: that new money reaches all agents simultaneously, and in equal proportion. Both exclude the Cantillon effect — the permanent redistribution from late to early recipients when money enters at a specific point and propagates with a lag. We embed staggered and potentially asymmetric receipt into a Two-Agent New Keynesian (TANK) model and derive the breakeven debt ratio at which the two channels exactly offset. The breakeven condition is linear in the receipt gap, with a slope that is analytically exact — independent of nominal rigidity, baseline income, and the functional form of the price adjustment rule. Under symmetric injection, the breakeven ratio at the empirical midpoint transmission lag of 18 months falls below the observed household debt-to-income range of 10–16, allowing the balance-sheet channel to survive. Under the income-growth divergence ratio of five to one documented during the QE period, the breakeven ratio rises beyond any observed household debt ratio by a factor of three to five. The HANK distributional claim is not a theorem. It is the simultaneous, symmetric-injection special case of a more general condition, and the burden of demonstrating that the true parameter values lie in the region where the claim holds rests with its proponents.</p>