Decomposing Simulation Results with Respect to Exogenous Shocks

When a general equilibrium model is solved, there are often a large number of exogenous shocks. The change in each endogenous variable obviously depends on these different shocks. We point out a natural way of decomposing the changes (or percentage changes) in the endogenous variables as sums of the contributions made by the change in each exogenous variable. The change in any endogenous variable is exactly equal to the sum of the contributions to this change attributed to each of the exogenous variables. The contribution of a group of exogenous variables to the change (or percentage change) in any endogenous variable is defined to be the sum of the contributions of the individual exogenous variables in the group. If all the exogenous variables are partitioned into several groups that are mutually exclusive and exhaustive, the change (or percentage change) in any endogenous variable is just the sum of the contributions made by these groups. We introduce, and motivate, these decompositions in the context of a published GTAP application in which 10 regions remove import tariffs and non-tariff barriers to imports. We use the methods given in this paper to report numerical values for the contributions to the welfare gains of various regions due to tariff reductions by particular regions or groups of regions in this simulation. We show how the values obtained via the decomposition are related to the estimates in the published study of the contributions to welfare gain due to certain groups of tariff reductions. We describe a practical procedure for calculating the contributions of individual exogenous variables or groups of exogenous variables to the changes (or the percentage changes) in all of the endogenous variables. This procedure, which applies to a wide range of general equilibrium models, is now automated in GEMPACK in a version that will be made publicly available in the future. The contributions that make up the decomposition are defined as integrals. As such, they depend on the path by which the exogenous values move from their pre-simulation to post-simulation values. We propose one natural path, namely a straight line between these two points. Along this path, the ordinary rate of change is constant for each variable.