applied, would **not entirely** close off a sector-mode (e.g. combination of ENT, LMT or other quotas for mode 4 entry, assuming that such entry is allowed in the first place).

# **Aggregation**

In the first version of the World Bank database (2008-11), the associated STRI relied on an assessment of groups of measures, which were included in a ‘policy summary’. The automatized aggregation methodology described here follows a similar approach. The overall restrictiveness of a group of policy measures, say at the sector-mode level for a given economy, results both from the **types** of measures applied as well as from the **number** of measures applied. The severity of measures is captured directly in the scores assigned to individual measures, as shown in Table 1. A major restriction, such as a quantitative limit, may attract a score of 0.5 whereas a minor measure affecting only transparency would be scored much lower (0.125). In a second step, the set of individual measure scores needs to be aggregated for a given sector-mode or even an entire economy.

Aggregation of this kind is a challenge in a wide range of fields. In consumer theory, individuals aggregate the utility from the consumption of a bundle of goods. In production theory, firms produce a good by combining a range of intermediate inputs. In each case, the aggregation of utility or inputs is achieved by a mapping—the utility function or the production function, respectively—that exhibit well-established properties. In particular, the marginal contribution of an additional unit to the aggregate (utility, output, or indeed restrictiveness) is typically positive but smaller than that of a previous unit.

One of the most widely used mappings in economics for both utility and production functions is the ‘Constant Elasticity of Substitution’ (CES) functional form, which generically combines an array of elements according to � .<sup>24</sup> NN αα 1/αα ii= (1, ... , NN) xxii XX= ��ii=1 xxii A function of the CES type, commonly used as a utility or production function, also has desirable properties for aggregating policy restrictiveness. For instance, adding a restrictive measure to a set of other restrictive measures should increase the overall restrictiveness index. At the same time, adding -say- a tenth restriction to a set of nine restrictions should conceivably have less of an impact on overall restrictiveness than applying the first or second restriction to an otherwise open sector. This is the equivalent of ‘diminishing returns,’ such that adding more restrictions should add progressively less and less to the overall index number.

progressively less and less to the overall index number. Against the backdrop of these intuitive underpinnings, we combine individual measure scores for group according to ii mm kk STRI<sup>kk</sup> = ��NN (kk)�ρρkk�1/ρρkk (1) ii ii=1�mm The parameter governs the way in which constituent scores are combined. In other applications, these groups k are sometimes referred to as “CES nests” and different values of ρ can be assigned kk to group k depending on the context. Specifically, it determines the marginal contribution of adding ρρ another non-zero measure to the set of policies to be aggregated. By virtue of the functional form in equation (1), higher values of lead to smaller incremental contributions of additional measures to aggregate restrictiveness. Figure 1 illustrates the role of this parameter on a set of 10 individual measures with a score of 0.25 each, for alternative values of ρρ ranging from 1 to 10. It is readily seen from equation (1) that for unit values of , the aggregate score is the simple sum of constituent scores, i.e. 2.5. For high values of , the aggregate score of a group of individual measures with a ρρ score of 0.25 each will be only marginally above 0.25. For values of ρρ around 3, the aggregate score is slightly above 0.50. Column 2 of Table 3 shows the aggregate score that emerges for different ρρ combinations of measures with a value for . ρρ ρρ= 3

> 24 The parameter takes on different interpretations according to the context in which the function is used; for instance, in consumer theory, it is related to , the elasticity of substitution among products consumed. ρρ σσ

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