Evaluating Historical Episodes using Shock Decompositions in the DSGE Model

Evaluating HistoricalEpisodes using ShockDecompositions in theDSGE Model Zamid Aligishiev, Michael Ben-Gad, and Joseph Pearlman WP/25/51 IMF Working Papersdescribe research inprogress by the author(s) and are published toelicit comments and to encourage debate.The views expressed in IMF Working Papers arethose of the author(s) and do not necessarilyrepresent the views of the IMF, its Executive Board,or IMF management. 2025MAR IMF Working Paper Western Hemisphere Department Evaluating Historical Episodes using Shock Decompositions in the DSGEModelPrepared byZamid Aligishiev,Michael Ben-Gad, and Joseph Pearlman* Authorized for distribution by Gustavo AdlerMarch2025 IMF Working Papersdescribe research in progress by the author(s) and are published to elicitcomments and to encourage debate.The views expressed in IMF Working Papers are those of theauthor(s) and do not necessarily represent the views of the IMF, its Executive Board, or IMF management. ABSTRACT:We present alternative methods for calculating and interpreting the influence of exogenousshocks on historical episodes within the context of DSGE models. We show analytically why different methodsfor calculating shock decompositions can generate conflicting interpretations of the same historical episodes.We illustrate this point using an extended versionof Drautzburg and Uhlig’s (2015) model of the U.S. economy,focusing on the periods 1964–1966, 1979–1987, 2006–2009, 2016–2020 and 2020–2023. We argue that thebest method for analyzing particular episodes is one which isolates the influence of the shocks during theperiod under consideration and where the initial conditions represent the system’s distancefrom balancedgrowth path at the beginning of the episode. RECOMMENDED CITATION:Aligishiev, Z., M. Ben-Gad, and J. Pearlman. 2025. Evaluating HistoricalEpisodes using Shock Decompositions in the DSGE Model. Working Paper WP/25/51. International MonetaryFund, Washington D.C. Evaluating Historical Episodesusing Shock Decompositions inthe DSGE Model Prepared byZamid Aligishiev,Michael Ben-Gad, and Joseph Pearlman1 1Introduction Dynamic Stochastic General Equilibrium (DSGE) models estimated using Bayesian techniquesare now a standard framework for analyzing the behavior and evolution of macroeconomies. Inreduced form these are state space models where the evolution of each variable over the entiresample period can be represented as the combined effects of the different exogenous shocks overtime.1In this paper we describe alternative methods for calculating shock decompositions forhistorical subsamples.We argue there is one that is particularly suited for this purpose butwhich surprisingly has rarely been employed by the DSGE literature.This preferred methodisolates the contribution of each shock solely within the subsample. Two common approaches are typically applied in the DSGE literature to analyze historicalepisodes using shock decompositions. One is to simply present or focus on a subsample of thehistorical decomposition for the entire sample, as in Del Negroet al.(2013), Brzoza-Brzezinaand Kolasa (2013) or Cardaniet al.(2022).An issue with this approach is that it does notseparate the impact of the shocks of interest during a particular time span from the impactof those that preceded them.Due to the recursive nature of DSGE models, the impacts ofthese previously occurring shocks can be considerable. An alternative approach employed, bye.g.Drautzburg and Uhlig (2015) - henceforth DU, is to calculate the change in the entiresample decomposition from a particular start date.As we demonstrate below, although thisdifferencing procedure nets out the levels of the variables from an initial starting point of interest,it does not completely isolate the decomposition from the impact of prior shocks, which may bepersistent; the persistence of even relatively minor disaggregated shocks during a few previousperiods can skew the interpretation of individual episodes quite significantly.A third shockdecomposition method is to isolate the effects of shocks within that time span from those ofshocks that occurred earlier. This approach has a direct correspondence with the state spaceform of the model and so is a natural one to employ; but it has neverthless been overlookedby the literature. The purpose of this paper is to correct this oversight.2We demonstrate howinterpretations of a particular episode can differ depending on the shock decomposition chosenby applying all three versions to an updated and extended version of DU’s (2015) model, whichwe describe below. Why does this matter? We think this is important for two reasons. The first is the centralityof responses of agents and government to innovations in the DSGE framework. When lookingat a model’s explanation of a particular episode it is therefore the effect of innovations in thatepisode that should be highlighted. If one believes that monetary policy was unexpectedly tightduring, e.g., the term of U.