Working Paper Series no. 894: Aggregation Across Each Nation: Aggregator Choice and Macroeconomic Dynamics

Goods trade is central to structural international macro models, including those used for policy analysis (e.g. the GIMF model used at the International Monetary Fund). One of the most primitive assumptions needed within these models is how agents allocate their consumption across domestic and foreign goods, i.e. how these goods are ‘aggregated’ together. The precise nature of this aggregation determines the make-up of cross-border trade, and can affect how demand responds to changes in international relative prices.

The ‘go-to’ choice of aggregator within workhorse international policy models is the constant elasticity of substitution (CES) aggregator, which is governed by two parameters. First, the share of expenditure on each good, which captures ‘home bias’—the idea that countries tend to spend proportionally more on their domestic goods even if prices are equal. Second, the ease with which consumers can substitute between goods produced in different countries—the ‘trade elasticity’—which governs how relative demand responds to relative prices.

A major reason for this aggregator’s wide usage is its tractability, which comes from the fact that the trade elasticity is given by a constant parameter. However, the flipside of this simplicity is that the value of the trade elasticity becomes crucially important for the dynamics of international macro models. In fact, both the sign and size of spillovers from shocks in these models depend on this value. In other strands of the literature, many argue that the trade elasticity can vary with a range of factors (e.g. the level of consumption, the time horizon over which substitution can occur, and income levels). Considering such alternative aggregators, with more parameters and greater flexibility than CES, could allow for richer dynamics and help to alleviate this challenge.  

In this paper, we take these alternative aggregators to the workhorse international macro model and assess the implications of how trade aggregation is modelled. How does the precise form of the aggregator influence macro dynamics and the international transmission of shocks?

We find that— when linearizing these non-linear relationships—just two sets of parameters are key for macro dynamics: the long-run share of domestic vs. foreign goods in expenditure and the trade elasticity. Since these are precisely the parameters captured in the CES aggregator, our results indicate that the specific aggregator choice has only a limited impact on global macroeconomic model dynamics. This means that, while the precise formulation of the aggregator is irrelevant, the choice of these parameters is important.

In many settings, once you pin down the two sets of sufficient statistics that we identify, it is very hard to overturn the results attained using the standard CES aggregator. This is true in models with only two countries, and in models in which countries are assumed to be perfectly symmetric.

Conversely, by considering models with more than two countries in which countries are asymmetric, we get around this ‘aggregator irrelevance’. In these settings, aggregator choice can be important and departing from the CES aggregator can deliver richer dynamics. Indeed, when countries differ in size, or other structural features, there is no longer just a single bilateral trade elasticity to consider, but potentially different elasticities across every pair of goods being traded. As a result, the cross-border transmission of shocks will depend not only on bilateral trade between two countries, but also on their indirect linkages via third countries. While the standard CES aggregator imposes that the elasticity is the same across all pairs of goods, alternative aggregators can allow for realistic differences in the trade elasticities across different pairs of goods, and therefore qualitatively change the macro dynamics, as is visible in Figure 1.