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In any month, each PBN can belong to only one enterprise and only one group. Allocating PBN labour input to different enterprises is straightforward, by aggregating across those months in which the PBN belongs to the enterprise. In addition, we wish to analyse productivity patterns by industry and location, so we group monthly PBN observations into distinct subsets for which enterprise-number, industry, and location (area unit) are constant. By construction, each plant belongs to only one enterprise during the year, and is allocated a proportion of that enterprise's value added and working proprietor input. Where enterprises belong to more than one group, it is not possible to tell how much of the enterprise's value added is associated with each group. The groups are therefore pooled for the purposes of aggregation of BAI value added, as described above.

Appendix Table 2 shows the distribution of activity across different group structures. Single plant enterprises that do not belong to an enterprise-group, in which there is no ambiguity in the link between reported value added and annual labour input, account for 76 percent of plant-year observations. Being relatively small, however, they account for only 55 percent of labour input and 37 percent of value added. Productivity is relatively low for these plants. In multi-plant enterprises not belonging to a group, labour productivity is close to the national average of $52,000, and plant size is also roughly average. These plants account for about one sixth of plants, labour, and value added.

Groups containing more than one enterprise are divided into two subsets in Appendix Table 2 – hierarchical and complex. Hierarchical groups are groups in which each enterprise in the group belongs to only one group during the year. For enterprises not having an AES postal record, productivity is constant within the group. Although these groups contain only 5 percent of plants, the plants contain, on average, 17.7 workers and account for 41 percent of value added and 23 percent of labour input. Productivity is thus high in these groups – just under $100,000 per worker. Complex groups are groups within which at least one enterprise belongs to more than one group. Such enterprises serve to connect two or more groups. Aggregation of BAI value added takes place within sets of connected groups. Complex groups are relatively large and productive, but account for only 2 percent of plants and 6 percent of value added.

Appendix Table 2: Group Structures (2006)

Appendix Table 3 shows summary statistics for three groups of firms that are less affected by the within-enterprise allocation algorithm. Single plant enterprises are not subject to any allocation of value added. They account for 55% of employment nationally, and Auckland's share of single-plant enterprises (30%) is only slightly lower than its share of total employment, reflecting the over-representation of multi-plant enterprises in Auckland. The Auckland labour productivity premium for single-plant enterprises (39%) is similar to the premium estimated for all enterprises (44%). Similarly, adjusting for industry composition, the Auckland premium for single-plant enterprises is 22% compared with 25% overall. The allocation algorithm appears to give a similar Auckland premium estimate to that based on single-plant enterprises for which there is no allocation.

Enterprises for which only AES postal returns are used (i.e.: no data from BAI is allocated within enterprise groups) account for 40% of Auckland employment. The AES contains a disproportionately large share of larger firms. A relatively high 39% of employment in AES-only enterprises is in Auckland. The Auckland premium is slightly lower for this group (27% raw, or 17% when adjusted for industry composition), possibly because AES also contains a relatively high share of multi-plant enterprises, so the advantage of being in Auckland may accrue in part to enterprises and plants affiliated with Auckland-based firms. It may also be that agglomeration is of particular value to smaller firms.

The third group of firms, which is least affected by the method of value added allocation contains single-enterprise firms for which data are sourced from AES. This group accounts for only 8 percent of employment, and has employment located in Auckland to the same degree as other AES-only firms (40%). The Auckland premium for this group is similar to that for AES-only enterprises generally (28% unadjusted and 15% adjusted for industry composition).

It would appear that the method of value added allocation is not driving the overall premium estimates. The overall estimates may, however, be masking some variation in agglomeration benefits by firm size, as suggested by the lower premium for the AES sample.

Appendix Table 3: Auckland Shares and premia (2006)