In Chapter 5 I also use Urban Economics (UE) theory as a possible explanation of differences in individual wages across US regions. The version of urban economics as used here is based
38
on Ciccone and Hall (1996). This model assumes that increasing returns exist in the production of local intermediate goods. It is assumed that the production function for making a final good on a unit of land, say an acre, is:
𝑄 = 𝑀0𝐼(';0). (2.27)
Where M is the amount of labour used in making output Q, i is the amount of composite service input which is used and cannot be transferred outside the area. 𝛼 is the decreasing returns of the inputs based on the acre which can be thought of as congestion effects. 𝛽 is the distribution parameter which can be thought of as the agglomeration effect.
It is assumed that the service composite, given as i is produced from different individual services which are represented as 𝑥(𝑡). t indicates the type. Assuming a constant elasticity of substitution production function this yields the following:
𝐼 = `∫ 𝑥(𝑡)d '/b𝑑𝑡
% e
b
(2.28)
Where z describes the varieties of intermediate products produced of which there are 0 through z available. 𝜇 is a parameter which controls the substitutability between intermediate products. It is assumes that 𝜇 > 1. A larger value of 𝜇 indicates that there is less ability to substitute one product for another and that there is a higher degree of monopoly power for the producer of that product. Ciccone and Hall (1996) note that under the standard assumptions of the underlying Dixit-Stiglitz model the level of output at zero profits is:
𝑥 =b;'h (2.29)
Substituting this value into equation (2.27) yields:
𝐼 = 𝑧b𝑥 (2.30)
The share of employment in manufacturing is given as:
39
Where N is total employment per acre. The remaining share of labour makes intermediate services and is given as (1 − 𝛽)𝑁.
Ciccone and Hall (1996) note that as the total amount of labour given over to intermediate services and the amount each one produces is known it is possible to solve for the variety of services which gives:
𝑧 = (1 − 𝛽)';bb kh (2.32)
This suggests that the intermediate product variety, given as z, is proportional to density, as measured by the number of workers per acre.
If this equilibrium value for z is substituted into equation (2.29) to determine I, and this is substituted into the production function (2.26) for final goods this yields:
𝑄 = 𝜙𝑁l (2.33)
Where 𝜙 is a collection of the constant values in the production function and 𝛾 is the elasticity of the production function given as:
𝛾 = 𝛼[1 + (1 − 𝛽)(𝜇 − 1)] (2.34)
Equation (2.33) implies that increased density of employment per acre increased output density.
Numerous empirical studies have provided insights into the impact of density on wages and output. Díaz Dapena et al. (2018) provides an analysis of local labour markets for 2011 for Spain. A series of alternative estimation techniques, including instrumental variable estimation, is utilised to analyse the impact of employment density on wages. The results suggest that increased labour density results in higher wage levels.
Ciccone (2002) analyses the impact of employment density (agglomeration) on wages for five European countries; France, Germany, Italy, Spain and the UK. He compares these results to the results of similar, previous analyses of the US. His results indicate that labour density has a significant positive effect on wages, with this effect being present across the five countries
40
studied. While the average effect is slightly lower than that observed in the US the author concludes that a significant agglomeration effect is present.
Brülhart and Mathys (2008) provide an analysis similar to that of Ciccone (2002) but extend the analysis by utilising dynamic panel estimation techniques and also by disaggregating their analysis by sector. The findings suggest that there is evidence of strong urbanisation effects, but also some evidence of own-sector congestion effects (when considering sector by sector analysis).
Larsson (2014) uses geocoded data to analyse the impact of density on wages in Swedish cities at three alternative spatial scales. He finds that the impact of density varies, dependent upon the spatial scale considered, however, the effect is consistently significant and positive. The analysis is conducted on the neighbourhood, district and agglomeration scale which are 0.06km2, 1km2, and 10km2 respectively.
Faberman and Freedman (2016) use data on US firms to identify what they term the ‘urban density premium’. Their data allows them to control for firm level characteristics which may explain productivity. Using panel data for 1992 to 1997 they find that a significant ‘urban premium’ is present and that density impacts positively on productivity.
Groot et al. (2014) analyse wage data at the micro-level for the Netherlands for the period 2000- 2005. They analyse the impact of individual specific characteristics, industry effects, and employment density on wages. They find that, even when controlling for individual effects there is evidence that employment density results in increased wages. This effect also persists when controlling for Porter and Jacob types externalities. This type of analysis, and that of Faberman and Freedman (2016), is particularly relevant for my PhD as in Chapter 5 I also employ micro-level data.
Finally, as noted in the previous section Fingleton (2006) provides an analysis comparing the relative explanatory power of NEG theory against urban economic theory using data for Great Britain at the Unitary Authority - Local Authority Districts level for the year 2000. From the analysis, while market potential does have a significant positive effect on wages, urban economics is found to have more explanatory power. The significance of both indicators, and a rationale for considering both, is discussed further in Chapter 5.
41