Decomposing Simulation Results with Respect to Exogenous Shocks

Abstract

When a general equilibrium model is solved, there areoften a large number of exogenous shocks. The changein each endogenous variable obviously depends on thesedifferent shocks.We point out a natural way of decomposing thechanges (or percentage changes) in the endogenousvariables as sums of the contributions made by thechange in each exogenous variable. The change in anyendogenous variable is exactly equal to the sum of thecontributions to this change attributed to each of theexogenous variables.The contribution of a group of exogenous variablesto the change (or percentage change) in any endogenousvariable is defined to be the sum of the contributionsof the individual exogenous variables in the group. Ifall the exogenous variables are partitioned intoseveral groups that are mutually exclusive andexhaustive, the change (or percentage change) in anyendogenous variable is just the sum of thecontributions made by these groups.We introduce, and motivate, these decompositions inthe context of a published GTAP application in which10 regions remove import tariffs and non-tariffbarriers to imports. We use the methods given in thispaper to report numerical values for the contributionsto the welfare gains of various regions due to tariffreductions by particular regions or groups of regionsin this simulation. We show how the values obtainedvia the decomposition are related to the estimates inthe published study of the contributions to welfaregain due to certain groups of tariff reductions.We describe a practical procedure for calculatingthe contributions of individual exogenous variables orgroups of exogenous variables to the changes (or thepercentage changes) in all of the endogenousvariables. This procedure, which applies to a widerange of general equilibrium models, is now automatedin GEMPACK in a version that will be made publiclyavailable in the future.The contributions that make up the decompositionare defined as integrals. As such, they depend on thepath by which the exogenous values move from theirpre-simulation to post-simulation values. We proposeone natural path, namely a straight line between thesetwo points. Along this path, the ordinary rate ofchange is constant for each variable.