Macro modeling with chain-type GDP

Abstract

The switch to chain-type GDP eliminated the substitution bias problem that plagued the fixed-weight aggregative data macroeconomists have been accustomed to working with. In this paper we review the essential differences between fixed-weight and chain-type measures of output, as well as the source of the substitution bias. The elimination of the substitution bias makes it worth facing the considerable difficulties occasioned by the switch. Therefore modelers must be prepared to take the necessary steps to re-structure their models to accommodate the new regime. The major tasks in this process are:

1) Re-estimate the behavioral relationships. Generally, where aggregates are employed on the left or right hand side of equations, eliminating the bias inherent in the fixed-weight data will improve the regressions. However, one must pay special attention to issues of scaling, especially where coefficients have familiar interpretations. For this reason, it makes sense to use dollar-denominated quantity indices where possible. 2) If more than one aggregation scheme is to be employed, and it may well be a good idea, modelers must be prepared to re-structure their models to remove any aggregate series from the simultaneous block of the model and reduce aggregation to a table-writing problem by making it totally post simultaneous. 3) Be prepared to add possibly thousands of lines of additional code to accommodate the new aggregation method. Even then, it will probably be necessary to incorporate aggregation residuals and PxQ residuals to insure that the model can replicate the official figures.

Finally, even today, more than two years beyond the switch to chain-type GDP in the US, there is a gross lack of appreciation for the problems related to working with chain-type GDP. To the extent that groups such as ours have handled the ugly details and incorporated into our models the needed modifications, perhaps we have made it a kind of black box. Indeed, this is the case in our system. Users can be totally ignorant of the details of chain-type GDP and still generate results that observe the rules of its construction.