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Why denser areas are more productive

Competitiveness & Growth 
PostDecember 2, 2016
Par Lionel Fontagné, Gianluca Santoni
A key driver of productivity is ease of resource allocation. This column uses firm-level data for France to show that misallocation has a spatial dimension: resource allocation and the associated effect on productivity are related not only to firms’ characteristics, but also to the environment in which they operate. Denser commuting zones seem to offer a better match between employers and employees, leading to more productive firms.
This article was first published on VoxEU.org, on November 20, 2016.

Is it selection, or the sorting of talents (Behrens et al., 2014) that leads only the most productive firms to locate in denser areas? Or do agglomeration economies explain why firms located in less dense environments are less productive?  Empirical evidence suggests that the main driver of differences in productivity is not selection (i.e. tougher competition inducing less productive firms to exit the market) but agglomeration economies (Combes et al., 2012). Usual suspects are the higher availability of services, better infrastructures, sharing of public goods, a denser labor market allowing better matching, and technology spillovers (Duranton & Puga2004). Using firm level data for France we confirm in a recent CEPII working paper (Fontagné and Santoni, 2016) that misallocation has a spatial dimension: resource allocation and the associated effect on productivity are related not only to firms’ characteristics but also to the environment in which they operate. Denser commuting zones seem to offer a better match between employers and employees.
A key driver of productivity is ease of resource allocation: in a perfectly competitive environment resources should flow freely from less to more productive firms, since those are most likely to survive in the market.  However, there are several factors that can hamper this continuous flow of resources:  recessions, labor and capital rigidity or adverse regulatory and competitive environments. The resulting resource misallocation implies that more efficient firms tend to be smaller than the optimal size while less efficient firms tend to be bigger than their optimum production scale.

The dispersion of revenue-based productivity (the product of physical productivity and the firm's output price) has been used as an indicator of the degree of resource misallocation at the sectoral level (Hsieh and Klenow, 2009). Alternatively, the gap between the marginal product value of each factor and its cost to the firm can be used as a metric of the degree of resource misallocation among firms within sectors. It measures the extent to which firms are not fully optimizing production (Petrin and Sivadasan, 2013).

Notwithstanding the distortions that are present in the economy as a whole such as labor market rigidities, firms in denser areas should be able to match with more productive and better paid workers. In relation to the difference between the wage and the value of the marginal product, a better matching should reduce the gap between the two at firm level. Using administrative data for the universe of legal units operating in the French manufacturing sector over the period 1993-2007, we show that this mechanism is at work: resource misallocation among firms within sectors is lower in denser French commuting zones.

Our evaluation of input allocation is performed using firm level balance sheet data to retrieve total factor productivity (TFP) estimations, from which we derive the marginal contribution of production inputs. Then, using firm (or industry) specific input prices it is possible to derive a monetary value for the firm level allocation inefficiencies. We use balance sheet data comprising information on the location of the establishment considered at the commuting zone level (‘Zone d'emploi’): 340 commuting zones were defined jointly by the National Institute of Statistics (INSEE) and the French Ministry of Labor for statistical purposes and were revised in 2011 based on the 2006 census[1].

We illustrate this stylized fact by plotting in Figure 1 the density of firms' TFP for two firm categories in 2000 (in the middle of our time window), in commuting zones below and above the median urbanization: the premium is 6.5% significant at the 1% level.

Figure 1: Urbanization and productivity by employment areas, single-plant firms (manufacturing only)
Source: authors' calculations.

For a given sector and year we report in Table 1 the mean absolute labor gap, defined as the distance from the social optimum allocation, where each firm is operating with marginal revenue equal to marginal costs and no frictions in the input markets. For the whole manufacturing sector over the period 1994-2007 this figure is slightly above 8,700 euro per firm at 2005 prices, with dispersion relatively high both between and also within industries, as shown by the coefficient of variation (CV). Instead of using perfect competition (zero gap) as the benchmark we are interested in knowing what the contribution to overall gains would be from achieving efficient allocation, i.e. the existing gaps are equal across all firms in a given sector. This results from the loosening of market constraints which allows the reallocation of one unit of labor (i.e. the marginal worker) across firms without changing the employment level or the structural frictions. This information is shown in column 4 (‘Contri’). For instance, in the case of machinery and equipment, resource allocation inefficiencies determine 50.2% of the mean absolute gap while structural frictions account for the other half of the overall gap.

Table 1: Average absolute labor gap by sector (years 1994-2007)

   Mean Gap > 0 CV Contri Obs
  (Euro) (%)   (%)  
Basic metals 9,052 19.4 0.994 38.3 8,557
Beverages 18,488 66 1.095 33.8 9,836
Chemicals 12,572 36.8 1.155 96.1 20,788
Computer  and Elect 14,123 12.2 0.776 23.6 25,965
Electrical  Equip 10,449 13.1 0.837 29.9 17,229
Fabricated  metal 8,226 17.8 0.894 38.1 145,354
Food products 6,644 27.7 1.093 62.4 133,132
Furniture 8,944 11.1 0.753 22.9 29,987
Leather products 7,056 28.2 1.32 76.7 8,937
Machinery  and Equipment 9,794 21 0.968 50.6 53,899
Motor  vehicles 8,727 19.9 1.088 52.2 14,335
Non-metallic  pro 9,525 20.5 0.998 57.8 33,452
Other Manuf 9,897 23.8 0.97 59.9 37,700
Other transport 8,656 25.8 1.115 56.9 6,206
Paper products 8,747 25 1.028 59.4 15,449
Pharmaceutical 19,022 21.9 0.897 63.4 4,300
Printing and rec 9,142 17.3 0.954 36.4 66,649
Repair and instal 8,031 20.8 1.025 49.1 74,799
Rubber and plastic 8,306 23.7 1.003 56.6 38,555
Textiles 8,815 22.8 1.14 60.9 26,441
Wearing apparel 9,648 29.8 1.196 85.0 33,714
Wood products 6,457 22.8 1.033 48.7 37,475
Source: authors' calculations.

We finally investigate whether firms in denser areas exhibit lower labor gaps, controlling for firm productivity and export status. To do so, we focus on the matching channel efficiency, and test whether in denser areas the thicker labor market also favors firm resource allocation efficiency, reducing the return to cost wedge. We follow Martin et al. (2011) and define two indicators for each single-plant firm located in a given commuting zone and operating in a given sector: ‘Urbanization’ is the number of employees in other industries within the same commuting zone, and ‘Location’, is the number of employees working in the same industry and the same commuting zone. However, we should be aware that that the typical worker in denser areas is more skilled. Worker sorting by skills across cities would thus induce attenuation bias in any OLS estimation.

Our instrumental variable approach confirms the role of agglomeration: a 10 percent increase in the degree of urbanization is associated with a decrease in the average gap of about 240 euro (out of a mean gap of 9,680 euro). Instead, location has no impact: intra-industry externalities do not induce firm level efficiency.
Behrens, K., Duranton, G., and Robert-Nicoud, F. (2014). Productive cities: Sorting, selection, and agglomeration. Journal of Political Economy, 122(3):507-553.
Combes, P.-P., Duranton, G., Gobillon, L., Puga, D., and Roux, S. (2012). The Productivity Advantages of Large Cities: Distinguishing Agglomeration from Firm Selection. Econometrica, 80(6):2543-2594.
Duranton, G. and Puga, D. (2004). Micro-foundations of urban agglomeration economies. In Henderson, J. V.and Thisse, J. F., editors, Handbook of Regional and Urban Economics, volume 4 of Handbook of Regional and Urban Economics, chapter 48, pages 2063-2117. Elsevier.
Fontagné, L. and Santoni, G. (2016). Agglomeration Economies and Firm Level Labor Misallocation. Working Paper CEPII, No 2016-24.
Hsieh, C.-T. and Klenow, P. J. (2009). Misallocation and manufacturing tfp in china and india. The Quarterly Journal of Economics, 124(4):1403-1448.
Petrin, A. and Sivadasan, J. (2013). Estimating lost output from allocative inefficiency, with an application to Chile and firing costs. Review of Economics and Statistics, 95(1):286{301.

[1] In the empirical analysis we use the zoning established in year 1990 prior to the estimation period (1994-2007) to limit possible simultaneity bias.
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