A toolkit for solving models with a lower bound on interest rates of stochastic duration

Abstract

This paper presents a toolkit to solve for equilibrium in economies with the effective lower bound (ELB) on the nominal interest rate in a computationally efficient way under a special assumption about the underlying shock process, a two-state Markov process with an absorbing state. We illustrate the algorithm in the canonical New Keynesian model, replicating the optimal monetary policy in Eggertsson and Woodford (2003), as well as showing how the toolkit can be used to analyse the medium-scale DSGE model developed by the Federal Reserve Bank of New York. As an application, we show how various policy rules perform relative to the optimal commitment equilibrium. A key conclusion is that previously suggested strategies -such as price level targeting and nominal GDP targeting -do not perform well when there is a small drop in the price level, as observed during the Great Recession, because they do not imply a sufficiently strong commitment to low future interest rates ("make-up strategy"). We propose two new policy rules, Cumulative Nominal GDP Targeting Rule and Symmetric Dual-Objective Targeting Rule that are more robust. Had these policies been in place in 2008, they would have reduced the output contraction by approximately 80 percent. If the Federal Reserve had followed Average Inflation Targeting -which can arguably approximate the new policy framework announced in August 2020 -the output contraction would have been roughly 25 percent smaller.

Aggregate Uncertainty, Hank, and the ZLB

“…We calibrate the shock size β L = 0.993 and the slope of the New Keynesian Phillips curve (κ (ω + σ )) to 0.01 to obtain initial output and inflation, in the HANK model with the ZLB, that match those of the Great Recession. 18 The shock reversal parameter µ is taken from Eggertsson et al (2021). 2023)), which might be of particular relevance in applications studying the recent inflation surge.…”

“…This analysis is similar to what McKay, Nakamura and Steinsson (2016) label as extended policy (where they choose q to minimize output loss on impact in a RANK economy) and to some extent goes in the direction of the state-contingency mentioned by Woodford (2012). Under the deterministic shock, such policy also corresponds to the "fixed length forward guidance" policy in Eggertsson et al (2021). However, the equivalence does not hold with the stochastic shock.…”

“…See for instanceAchdou et al (2022),Ahn et al (2018), and Kaplan, Moll and Violante (2018) among others.11 In both cases, the uncertainty regarding aggregate dynamics was unprecedented and we argue that our solution strategy is able to capture meaningful economic effects, as opposed to standard techniques.12 See for instance https://www.theatlantic.com/family/archive/2020/03/coronavirus-social-distancing-overback-to-normal/608752/.13 This aggregate shock structure is not novel Eggertsson and Woodford (2003). andEggertsson et al (2021) are other examples that have similar settings. A more structured shock process (a convolution of an AR(1) process ECB Working Paper Series No 2911…”

“…The methodology can be easily used in the presence of aggregate non-linearities other than the ZLB. For instance, non-linear Phillips curves in the presence of inflationary shocks (see Benigno and ECB Working Paper Series No 2911 Markov process in the spirit of Eggertsson et al (2021). This allows us to extend the existing solution strategy of Auclert et al (2021) and work around the curse of dimensionality in the aggregates.…”

“…In the baseline version of the model, the second step is skipped since shock Z is summarized by the discount factor shock to households and is assumed to only affect the heterogeneous agent block.27 This procedure is essentially different fromEggertsson et al (2021), where the expectation is explicitly solved ECB Working Paper Series No 2911…”