This paper analyzes the monetary policy trade-off between defending purchasing power of consumers and keeping moderate debt cost to borrowers, in the framework of a heterogeneous agents New Keynesian open economy hit by a foreign energy price shock. Raising the interest rate indeed fights the real depreciation of domestic goods and wages due the energy shock, at the expense of higher interest payments for debtors. The trade-off can be resolved by implementing a milder interest rate policy during the crisis in exchange for a prolonged contraction beyond the energy shock time span: this interest rate smoothing approach allows to still enjoy a real appreciation today at the expense of a smoother effect on debt cost over time. This policy counterfactual is analyzed in a quantitative model of the UK economy under the 2022-2023 energy price hike, where the loss of consumers' purchasing power and the vulnerability of mortgage costs to higher policy rates have been elements of paramount empirical relevance.
Optimal monetary and fiscal policy are jointly analyzed in a heterogeneous two-agents New Keynesian environment, where fiscal policy is modeled in the form of lump-sum transfers set by the government. The main result is that transfer policy does not serve as a substitute for forward guidance - as it entails consumption dispersion costs - and does not affect its optimal duration. Transfers indeed influence the length of stay at the zero lower bound through two offsetting channels: a shortening channel works through an initial increase in transfers that mitigates the recession (reducing the need for forward guidance), and a lengthening channel works through a later transfer cut that curbs the undesired expansion (making forward guidance desirable for a longer horizon). Imposing a homogeneous transfer policy across agents does not change the stabilization outcome or the effect on the duration of forward guidance, nor does so allowing for cyclical income differences.
This paper proposes a new method to solve for optimal policy in heterogeneous agents New Keynesian models (HANK). It builds on the discretize-then-optimize method by Nuño, Gonzalez, Thaler, and Albrizio (2023), and reduces its computational complexity by leveraging the linearity of the first order conditions of the Ramsey planner in terms of the co-states of the problem. An application is carried out in the case of optimal management of energy shocks in HANK.