Davide Debortoli | Macro Paper Warehouse

Nonlinear Monetary Policy Tradeoffs

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

This paper measures how the inflation-unemployment tradeoff associated with monetary policy varies with both the sign of the monetary intervention (easing versus tightening) and the state of the business cycle (booms versus recessions) for the US economy over 1973:M1 to 2019:M6. The motivation is that standard linear Phillips-curve estimates implicitly impose a constant tradeoff, yet a flat Phillips curve would simultaneously predict that (i) stimulating activity during a recession costs nothing in terms of inflation and (ii) reducing inflation costs very large amounts of unemployment — both empirically extreme predictions that have very different policy implications. The paper challenges both extremes.

Heterogeneity and Aggregate Fluctuations: Insights from TANK Models

By building three nested HANK economies and then constructing a deliberately simple two-agent counterpart for each, this paper argues that what household heterogeneity does to aggregate output can be read off the differential behaviour of just two household types, hand-to-mouth and unconstrained, and that idiosyncratic income risk itself contributes little. The nesting isolates three ingredients in turn: idiosyncratic income risk alone (HANK-I, with a natural debt limit so no constraint binds), an occasionally binding borrowing constraint (HANK-II), and a portfolio choice between liquid bonds and partly illiquid equity subject to an adjustment cost and a short-sale constraint (HANK-III). In HANK-I the whole gap from the representative-agent model runs through a single “risk shifter” term in the aggregate Euler equation, and that term barely moves: output volatility under HANK-I exceeds RANK’s by a factor of only 1.22 with a correlation of 0.97, because the squared elasticity of individual consumption to idiosyncratic income is strongly convex in consumption, so the households whose risk actually responds carry a small weight in the aggregate. The paper is blunt that the standard two-agent model is not a good approximation: in TANK-I the output response to an expansionary monetary shock is “highly amplified… almost trebling the effect on impact,” and the response to a technology shock has the wrong sign, because TANK-I misses the interest rate exposure channel entirely and reverses the sign of the income distribution channel. Three changes repair it — hand-to-mouth households are held permanently against the borrowing limit and so service interest on a constant debt, they are given productivity below the unconstrained (0.56 against a normalized mean of one), and they receive dividends on the same rule as in HANK — and the resulting TANK-II tracks HANK-II closely, with a volatility ratio of 1.10 for monetary shocks and near-unit correlation, while also reproducing the effect of tightening the borrowing limit from 30% to 50% constrained. Adding portfolio choice changes the answer again: because wealthy hand-to-mouth households can smooth cash-on-hand by liquidating equity at a cost, dividends no longer pass one-for-one into their consumption, the income distribution channel weakens, monetary shocks are amplified, and a positive technology shock now lowers output — a prediction the authors immediately flag as contrary to existing evidence and as hinging on their counterfactual constant-real-rate assumption. Splitting the hand-to-mouth into poor (weight 0.05) and wealthy (0.25) restores the approximation in TANK-III. Section 6 relaxes the constant real rate for a Taylor rule with φ_π = 1.5 and φ_y = 0.125, and the models converge dramatically; the mechanism is stated as a proposition, since the natural level of output is invariant to idiosyncratic risk and the shared Phillips curve displays divine coincidence, so under strict inflation targeting every model delivers the identical output path. The caveats are the authors’ own and are load-bearing: the result applies to environments where precautionary saving responds little to aggregate shocks, countercyclical income risk is absent from the analysis, only monetary and technology shocks are studied, heterogeneity is not allowed to touch the supply side, and nothing normative is claimed — the irrelevance proposition concerns output, not the real interest rate, and not welfare.

Monetary Policy with Heterogeneous Agents: Insights from TANK models

This paper asks how much of the HANK literature’s message about aggregate behaviour survives in a far simpler model, and answers by first identifying exactly what heterogeneity does. Building on a framework related to Werning (2015), the authors show that a heterogeneous-agent economy departs from its representative-agent counterpart along precisely two dimensions: the difference in average consumption between constrained and unconstrained households at any point in time, and the dispersion of consumption within the subset of unconstrained households. Both appear as “wedges” in an Euler equation for aggregate consumption, so each can be traced in response to any aggregate shock and its quantitative significance measured rather than asserted. A two-agent (TANK) model, with fixed shares of “Ricardian” households who trade financial markets freely and “Keynesian” households who consume current labour income each period, captures the first wedge and ignores the second entirely. The paper’s central finding is that this omission costs little for aggregates: in a canonical HANK calibration the first form of heterogeneity fluctuates substantially with aggregate shocks and is well captured by TANK, while the second remains roughly constant, because unconstrained agents limit their consumption swings by borrowing and saving. Quantitatively, with constant transfers the real-interest-rate elasticity of output on impact is about 70 percent larger in HANK than in RANK, and 64 percent larger in TANK – close agreement – and the two models track each other across alternative transfer rules and borrowing limits, which the authors read as TANK remaining a “good approximation to the richer HANK model” throughout (the widest gap between them is under the loosest borrowing limit, 1.23 against 1.46). Two analytical payoffs follow. Heterogeneity may amplify or dampen the effects of aggregate shocks, depending on the share of constrained agents and the cyclicality of fiscal transfers, but independently of the degree of nominal rigidity or the conduct of monetary policy. And a benevolent central bank’s welfare criterion acquires a third term penalising fluctuations in consumption heterogeneity, which generally cannot be stabilised alongside inflation and the output gap – so the divine coincidence fails. The authors are careful about the size of that last result: for standard calibrations the optimal policy still implies minimal fluctuations in inflation and the output gap, and is “nearly identical” to the representative-agent optimum. The manuscript is marked Preliminary and Incomplete, and its comparisons are restricted throughout to the responses of aggregate variables to aggregate shocks; it makes no claim that TANK reproduces HANK’s distributional detail.