measures. For instance, not having the right to appeal regulatory decisions should arguably always add to the overall restrictiveness of those policy measures, regardless of whether some minimum share of employees is required to be nationals.

All three principal nests (ownership, quantitative limits and operations) are then combined with a value of into an overall score per mode of supply. The rationale for using this parameter value is that at this specific stage, each constituent score should add to restrictiveness but moderately so (see Figure 1). An additional advantage of this modular structure, which follows our taxonomy, is ρρ= 3 that the distribution of restrictiveness (across economies and sectors) is easily made transparent at each stage of aggregation—or “CES nest” —showing which kinds of policy measures drive the overall distribution of STRI values, see Figure 4 in Borchert et al. (2019).

At this point we have aggregated all individual measure scores to one STRI value per economy, subsector and mode. The nested aggregation described thus far is in principle the same within each mode of supply, even though the nature and number of measures within CES nests (such as ‘ownership and control’) will differ across modes.

The next step is to combine the modal scores to one STRI value per economy and subsector. We do this with a weighted arithmetic average, with a set of weights that differs across subsectors, reflecting the relative importance of the three modes for the provision of a given service, see Table A6.2 in Annex 6 in Borchert et al. (2019). Setting the aggregation parameter to unity in equation (1) yields the arithmetic average as a special case of the CES with weights. We are therefore not stepping outside the framework we have consistently employed thus far. However, the aggregation ρρ of scores from different modes is different from the aggregation of measure scores because in any sector, one mode of supply will invariably be more important than others so that the symmetric treatment of measure scores is no longer appropriate for this step of the aggregation.

Finally, to complete the aggregation of scores from the level of individual measures to the modes and the subsector, we then compute STRI at the sector and economy levels, respectively. We do this using the weights provided in Table A6.1 of Annex 6 in Borchert et al. (2019).

Overall, the new aggregation methodology offers conceptual as well as practical improvements. Its modular structure affords the flexibility to accommodate a range of different tasks in one framework, from the aggregation of measures that are nearly additive to those whose incremental impact on restrictiveness is almost negligible. At the same time, the approach is extremely parsimonious and fully transparent. In addition, STRI scores thus constructed are reproducible, implying that comparable scores for new economies or sectors can be obtained as the STPD is continuously being expanded.

These improvements imply, however, that the new STRI scores are not directly comparable to the STRI scores published in the 2008-11 World Bank Database because of changes in methodology and sectoral coverage, respectively. A detailed comparison and a full decomposition of changes in STRI scores relative to the World Bank 2008-11 STRI is provided in Borchert et al. (2019). Both STRI data sets are publicly available from the I-TIP services portal.<sup>12</sup> We emphasize, however, that a comparison of policy restrictiveness over time using the World Bank STRI (as in Section 3 of the paper) requires a separate set of _comparable_ scores. Backward compatibility requires two steps: first, the 2008-11 STRI needs to be re-computed using the improved scoring and aggregation methodology. Second, the 2016 STRI needs to be purged of measures and subsectors, respectively, that were not part of the 2008-11 STRI. The STRI data sets thus adjusted are also available from the I-TIP services portal (see Annex 3 for a description of the 2016 STRI for all sectors with STRI for the subset of sectors for which data were collected in 2008-11).

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