DP12601-3 | Heterogeneity and Determinacy: Amplification without Puzzles

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Using an analytical (heterogeneous-agent New-Keynesian) HANK model, I find the closed-form conditions for determinacy with interest-rate rules and for curing NK puzzles. The latter requires self-insurance against idiosyncratic uncertainty and procyclical inequality: the income of constrained agents moving less than proportionally with aggregate income. With countercyclical inequality, good news on aggregate demand gets compounded, making determinacy less likely and aggravating the puzzles---a Catch-22, because countercyclical inequality is what HANK (and TANK) models need to deliver desirable amplification. A similar dilemma applies to a distinct, "cyclical-risk" channel: procyclicality cures the puzzles, countercyclicality aggravates them. The Catch-22 is resolved if these two channels co-exist and go in opposite directions---subject to sufficient conditions on their relative strength provided here. Even when both channels are countercyclical (with amplification, but much-aggravated puzzles and stringent determinacy requirements) a Wicksellian rule of price-level targeting ensures determinacy and cures the puzzles---while preserving HANK amplification.