3. Cities and Labour Productivity
It is well established that average productivity is higher in cities than in non-urban areas although there is still debate on the reasons for this advantage. Rosenthal and Strange (2004) summarise empirical evidence on the nature and sources of agglomeration effects that may give rise to urban productivity premia and Duranton and Puga (2004) survey the range of theories that have been used to provide microfoundations for agglomeration effects.
Duranton and Puga (2004) identify three sets of agglomeration mechanisms ‑ sharing, matching, and learning. Sharing includes the use of indivisible inputs such as infrastructure, the advantages of greater variety and specialisation, and risk-sharing. Matching covers improved matching between firms, between inputs and outputs, including the advantages of better matching through thick labour markets, and between suppliers and customers. Finally, learning includes a range of mechanisms that enhance knowledge generation, diffusion and accumulation.
The strength and scope of each of these mechanisms will vary across industries. Rosenthal and Strange (2004) document three dimensions along which the strength of agglomeration effects can vary – industry 'closeness', geographic proximity, and time lags. The term 'localisation' is commonly used to capture agglomeration effects that result from interactions between firms in the same industry, whereas 'urbanisation' refers to the broader set of effects that result from urban scale and diversity.
A commonly used summary indicator of the presence and strength of agglomeration effects is the positive relationship between employment density and productivity. While many theories of agglomeration suggest that density can lead to higher productivity, it is also possible that density is a consequence of productivity advantages. Cross-sectionally, such a relationship may arise due to the presence of local productive inputs (e.g., a harbour).
This distinction is important for the analysis of policies that seek to increase density as a means of improving productivity, since such policies depend on density being a driver of productivity change. It is difficult to distinguish the differing sources of the density-productivity relationship from cross-sectional data alone. For instance, Ellison and Glaeser (1999)'s finding that "there remain a number of highly geographically concentrated industries in which interfirm spillovers seem important" is based on the low explanatory power of measurable ‘natural advantages' in accounting for the concentration of industry employment across US states. Patterns of change over time are able to provide further insights into the potential for changes in density to raise productivity – do new firms choose to locate disproportionately in already dense areas? Are closures more likely in less dense areas? Are changes in density in an area associated with changes in productivity? Examining the dynamics of the density-productivity relationship for different industries can also provide guidance on the plausibility of different agglomeration explanations of productivity performance.
In the current paper, we document the cross-sectional (2006) relationship between density and productivity at two spatial scales – first between regions and Territorial Authorities, and second between area units within Auckland. We also investigate the covariation of density and productivity within areas across time by means of fixed effects and change regressions. A positive relationship over time is consistent with either agglomeration effects or the response of employment density to product demand shocks. A negative relationship may arise due to congestion effects, or due to labour supply shocks that lower average labour productivity.
In order to shed light on the relative importance of localisation and urbanisation effects, we estimate, for selected groups of industries, the elasticity of productivity with respect to overall employment density and own-industry density.
3.1 Price effects
Our measure of labour productivity is "value added per worker", where value added is the value of a firm's output less the value of non-durable intermediate inputs used in production. Excluded from intermediate inputs are compensation of employees, consumption of fixed capital (depreciation), and net indirect taxes. For a firm to be indifferent between locating in Auckland and elsewhere, value added would have to be higher in Auckland to cover the higher cost of labour and of property capital.9 The firm is able to achieve the necessary higher value added if agglomeration effects lead to higher output for the same level of inputs, due to any of the agglomeration mechanisms outlined above. Alternatively, value added may be higher in Auckland if firms are able to charge a higher price for their output or if they can secure intermediate inputs at lower prices. A higher value added per worker may also arise if Auckland firms use more capital per worker than non-Auckland firms.
A measured labour productivity premium in Auckland is likely to reflect a combination of these factors – higher physical or technical productivity, higher output prices, and possibly lower input prices or unit costs, and higher capital to labour ratios. Average labour productivity measures will also be influenced by the composition of employment. Average labour productivity in Auckland will be higher if Auckland has a higher proportion of firms in industries or performing functions (e.g. head office functions) that would be more productive wherever they are located.
It is not the purpose of this paper to distinguish fully between these sources of productivity differentials. It does, however, analyse the contribution of industry composition, and presents industry-specific analyses that suggest a diversity of causes of Auckland's productivity premium. Analysis of the impact of differing capital intensity and of local prices remain as priorities for future research.
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