Abstract: Papers examining a developed nation’s labour productivity frequently ignore spatial effects. We present empirical results indicating that geographical proximity matters for plant-level productivity.distance; labour productivity

Don Webber

Paul White

English

Research Papers in Economics

  1 
Productivity and Proximity 
 
 
 
 
Don J. Webber
1 and Paul White
2 
 
1 School of Economics, University of the West of England, Bristol, UK 
2 Department of Mathematics and Statistics, University of the West of England, Bristol, UK  
 
 
 
 
 
 
Abstract: Papers examining a developed nation’s labour productivity 
frequently ignore spatial effects. We present empirical results indicating 
that geographical proximity matters for plant-level productivity. 
 
 
 
 
 
 
 
 
 
 
Acknowledgements: The authors thank Paul Dunne and Peter Howells for helpful 
comments on an earlier draft. This work contains statistical data from the Office for 
National Statistics which is Crown copyright and reproduced with the permission of 
the  controller  of  HMSO  and  Queen’s  Printer  for  Scotland.  The  use  of  the  ONS 
statistical data in this work does not imply the endorsement of the ONS in relation to 
the interpretation or analysis of the statistical data. This work uses research datasets 
which may not exactly reproduce National Statistics aggregates. Any errors are the 
authors’ responsibility. 
 
Keywords: distance; labour productivity 
 
JEL Classification: C21; R32 
 
Corresponding Author: Dr Don J Webber, School of Economics, Bristol Business 
School,  University  of  the  West  of  England,  Bristol,  BS16  1QY.  E-mail: 
Don.Webber@uwe.ac.uk. Tel.: (+44/0) 117 328 2741. Fax: (+44/0) 117 328 2289 
   2 
1.  Introduction 
 
Empirical analyses of within country spatial labour productivity variations typically 
focus on either agglomeration economies present within cities and their variations 
between conurbations, or the variation in and evolution of average labour productivity 
at an aggregate geographical level, such as the county, state, or prefecture. This may 
be due to a chosen focus on administrative regions or restrictive availability of data at 
a more disaggregated level. 
Both of these approaches avoid the explicit calibration of the trade-off 
between labour productivity and distance from the core. Evidence of such a trade-off, 
essentially linking productivity to proximity, has repercussions for economic theory 
(Bivand, 2008). For instance, theories of monopolistic competition often cite space as 
an insulating factor that allows spatially segregated firms to charge higher prices. The 
frequently cited example is the petrol/gas station where greater distances between 
forecourts mean drivers often pay higher petrol prices in rural areas rather than paying 
the additional cost of travelling to a cheaper forecourt. As such spatially segregated 
firms produce low quantities but charge high prices it appears that their productivity is 
high. This points to the possibility of a U-shaped relationship between productivity 
and proximity. Nevertheless the ability of a range of firms to compete on price in a 
region’s core city’s central business district reduces with greater transportation costs, 
which suggests the presence of a negative relationship as value added per worker 
would be squeezed to compensate for transportation costs. These relationships may 
well have changed over time (Glaeser and Kohlhase, 2004) but the death of the 
importance of distance may well be premature (Reitveld and Vickerman, 2004). 
In spite of these generalisations there is a lack of empirical evidence 
supporting the presence of a productivity–proximity trade-off. This paper fills this gap 
in the literature by presenting an empirical investigation into the influence of distance 
on labour productivity. We employ data for 16,410 plants within England which we 
match at the district level to distance data to the region’s core city’s central business 
district. 
 
2.  Model  
 
The natural logarithm of plant-level labour productivity is modelled using OLS 
regression.  Potential predictors include the natural logarithms of employment and 
capital stock per worker, local distance and a dummy variable to indicate plant status.  
The modelling strategy is to extend the regression model by including a quadratic 
term for local distance and to further extend by including a cubic term for local 
distance.  The inclusion of the quadratic term and the cubic term has the potential to 
induce a high degree of undesirable correlation between predictors.  For this reason 
we isolate the unique quadratic effect and the unique cubic effect using an orthogonal 
quadratic term and an orthogonal cubic term using the Gram-Schmidt 
orthogonalisation process (see Draper and Smith, 1981).  The model is extended by 
the inclusion of interaction terms between the multi-plant dummy variable and all 
other predictors so as to ascertain whether the rate of change of labour productivity 
differentially varies with the predictors according to plant status.   
   3 
3.   Data 
 
Factors influencing labour productivity ultimately act by influencing the operational 
performance of firms. Analyzing business performance at the plant-level overcomes 
the shortcomings of working with aggregate data, in particular by providing an 
unambiguous association between output and the workforce responsible for 
generating it. In this analysis we use data held by the UK government’s Office for 
National Statistics in their Annual Respondents Database (ARD) (ONS, 2002), which 
includes data on the number of employees, output and the amount of capital stock 
which relates to individual business units. Data on firm-specific capital stock is 
obtainable from the ONS and is matched with plant-specific data within the ARD. 
One issue with the ARD is the level at which the data are collected: we use the plant. 
However, plants can be members of larger firms and to control for this we employ a 
dummy equal to one if the plant comes from a firm with more than one plant and 
equal to zero otherwise. 
The district in which the plant is located is identifiable from the ARD. For 
simplicity, UK districts are sub-divisions of counties, and counties are subdivisions of 
regions – the UK has 9 administrative regions. We calculate the distance between 
each plant’s district location and the central business district of their region’s core 
city. Distance data is sourced separately from the AA website (www.theAA.com). 
Essentially this ‘local distance’ reflects the level of past infrastructural investment and 
is responsive to long term policy initiatives to improve transport infrastructure. The 
longer the period of time it takes to move goods to the location of consumption or 
intermediate productive use then the greater will be the incurred transportation costs 
and the less competitive the firm will be in the region’s core market place. 
 
4.  Results   
 
Table 1 provides means and standard deviations for the logarithm of labour 
productivity and for all potential predictor variables. The average distance from a 
plant’s district to a region’s core city’s central business district is 34 miles. This 
distance varies from zero (where the plant is located in the region’s core city’s central 
business district) to 195 (where the plant is located in the Isles of Scilly). 
Table 2 summarises the regression models without consideration of interaction 
terms involving plant status.  In Model 1a there is a statistically significant average 
increase in the logarithm of labour productivity with labour productivity increasing by 
a factor of 1.06 for multi-plant organisations compared with single plant organisations 
(p<0.001).  In regression Model 1a a doubling of capital stock per worker is 
associated with labour productivity increasing by a factor of 1.2 (p<0.001).  Also note 
that there is evidence of decreasing returns to scale from the employment variable. 
These effects are essentially constant irrespective of whether quadratic or cubic terms 
for local distance are included in the model (see Model 1a to 5a, Table 2). 
In the fitted model (Model 1a, Table 2) there is a statistically significant 
negative linear association between local distance and the logarithm of labour 
productivity (p<0.001), with a ten mile decrease in local distance being associated 
with labour productivity increasing by a factor of 1.03. The square of local distance 
produces an additional statistically significant unique effect (see Model 2a and Model 
4a, Table 2) and the same can be seen for the cube of local distance (see Model 3a and 
Model 5a, Table 2).  A graphical summary of the cubic model (for single and multi-  4 
plant firms) is given in Figure 1 and this graphic is based on the logarithm of capital 
stock per worker and logarithm of employment held at mean values. 
Table 3 summarises the regression models which include interaction effects 
with plant status and all other predictors.  All models in Table 3 capture a statistically 
significant interaction between plant status and logarithm of capital stock per worker 
on the logarithm of labour productivity with a doubling of capital stock per worker 
being associated with labour productivity increasing by a factor of 1.19 for single 
plant firms and increasing by a factor of 1.24 for multi-plant firms; this difference in 
effects is statistically significant (p<0.001).  Interestingly there is evidence from the 
interaction between plant status and logarithm of employment that single plant firms 
do not suffer from diseconomies of scale and that this is a characteristics of multi-
plant firms in general. Nevertheless in all models in Table 3 there is no differential 
effect between linear (p=0.245), quadratic (p=0.527) and cubic (p=0.614) local 
distance with logarithm of productivity and plant status. 
The repercussion of these results is that technological improvements that have 
facilitated declines in distance costs have not resulted in an eradication of the spatial 
labour productivity divide across English regions. 
 
5.  Conclusion 
 
The results from our regression analyses suggest that proximity to a region’s core city 
is negatively related to plant-level labour productivity within England. 
 
References 
 
Bivand, R., 2008. Implementing representations of space in economic geography. 
Journal of Regional Science 48, 1-27 
Draper, N. and Smith, H., 1981. Applied regression analysis, John Wiley and Sons, 
New York 
Glaeser, E.L. and Kohlhase, J.E. 2004. Cities, regions and the decline of transport 
costs. Papers in Regional Science 83, 197-228 
Reitveld, P. and Vickerman, R. 2004. Transport in regional science: The “death of 
distance” is premature. Papers in Regional Science 83, 229-248   5 
Table 1: Descriptive statistics 
  Mean  Median 
Log of labour productivity  3.289  3.342 
Log of capital stock per worker  3.297  3.373 
Log of employment  3.804  4.025 
Local distance in miles  34.290  28.000 
Local distance in miles
2  2111.991  784.000 
Local distance in miles
3  176844  21952 
Log of capital stock per worker * multi-plant dummy  1.254  0 
Log of employment * multi-plant dummy  1.974  0 
Local distance in miles * multi-plant dummy  11.649  0 
Local distance in miles
2 * multi-plant dummy  711.675  0 
Local distance in miles
3 * multi-plant dummy  59445.36  0 
n=16,410  
   6 
Table 2: Regression Models 
  1a  2a  3a  4a  5a 
Log (capital stock per worker)  0.275** 
(0.005) 
0.275** 
(0.005) 
0.275** 
(0.005) 
0.275** 
(0.005) 
0.275** 
(0.005) 
Log (employment)  -0.015** 
(0.004) 
-0.015** 
(0.004) 
-0.015** 
(0.004) 
-0.015** 
(0.004) 
-0.015** 
(0.004) 
Local distance in miles  -0.003** 
(2.35e-04) 
-0.004** 
(0.001) 
-0.008** 
(0.001) 
-0.003** 
(2.35e-04) 
-0.003** 
(2.35-e04) 
Local distance in miles
2  –  1.33e-05** 
(4.55e-06) 
9.37e-05** 
(2.07e-05)  –  – 
Local distance in miles
3  –  –  -3.66e-07** 
(9.19e-08)  –  – 
Orthogonal local distance
2  –  –  –  1.33e-05** 
(4.55e-06) 
1.34e-05** 
(4.54e-06) 
Orthogonal local distance
3  –  –  –   
 
-3.66e-07** 
(9.19e-08) 
Multi-plant dummy  0.058** 
(0.019) 
0.058** 
(0.019) 
0.057** 
(0.019) 
0.058** 
(0.019) 
0.057** 
(0.019) 
Constant  2.513** 
(0.022) 
2.538** 
(0.024) 
2.574** 
(0.025) 
2.515** 
(0.022) 
2.517* 
(0.022) 
F (prob.)  946.95** 
(<0.001) 
759.61** 
(<0.001) 
636.22** 
(<0.001) 
759.61** 
(<0.001) 
636.22** 
(<0.001) 
R
2  0.188  0.188  0.189  0.188  0.189 
 Notes: n=16,410. ** indicates statistical significance at the 1% level.   7 
Table 3: Regressions with compound variables 
  1b  2b  3b  4b  5b 
Log (capital stock per worker)  0.257** 
(0.005) 
0.257** 
(0.005) 
0.257** 
(0.005) 
0.257** 
(0.005) 
0.257** 
(0.005) 
Log (employment)  -0.005 
(0.005) 
-0.005 
(0.005) 
-0.005 
(0.005) 
-0.005 
(0.005) 
-0.005 
(0.005) 
Local distance in miles  -0.003** 
(2.87e-04) 
-0.004** 
(0.001) 
-0.009** 
(0.001) 
-0.003** 
(2.87e-04) 
-0.003** 
(2.87e-04) 
Local distance in miles
2  –  1.55e-05** 
(5.56e-06) 
1.06e-04** 
(2.51e-05)  –  – 
Local distance in miles
3  –  –  -4.08e-07** 
(1.11e-07)  –  – 
Orthogonal local distance
2  –  –  –  1.57e-05** 
(5.63e-06) 
1.68e-05** 
(5.64e-06) 
Orthogonal local distance
3  –  –  –  –  -4.16e-07** 
(1.13e-07) 
Log (capital stock per worker) 
     * Multi-plant dummy 
0.055** 
(0.008) 
0.054** 
(0.009) 
0.053** 
(0.009) 
0.055** 
(0.008) 
0.055** 
(0.008) 
Log (employment) 
     * Multi-plant dummy 
-0.031** 
(0.006) 
-0.032** 
(0.007) 
-0.034** 
(0.007) 
-0.031** 
(0.006) 
-0.032** 
(0.006) 
Local distance in miles 
     * Multi-plant dummy 
5.41e-04 
(4.66e-04) 
0.001 
(0.001) 
0.002 
(0.002) 
0.001 
(4.66e-04) 
6.14e-04 
(4.66e-04) 
Local distance in miles
2 
     * Multi-plant dummy  –  -5.81e-06 
(9.19e-06) 
-2.81e-05 
(4.12e-05)  –  – 
Local distance in miles
3 
     * Multi-plant dummy  –  –  9.45e-08 
(1.87e-07)  –  – 
Orthogonal local distance
2 
     * Multi-plant dummy  –  –  –  -6.38e-06 
(9.53e-06) 
-8.38e-06 
(9.54e-06) 
Orthogonal local distance
3 
     * Multi-plant dummy  –  –  –  –  1.18e-07 
(1.95e-07) 
Constant  2.547** 
(0.023) 
2.575** 
(0.025) 
2.615** 
(0.027) 
2.550** 
(0.023) 
2.552** 
(0.023) 
F (prob.)  639.59** 
(<0.001) 
481.06** 
(<0.001) 
386.90** 
(<0.001) 
481.07** 
(<0.001) 
386.93** 
(<0.001) 
R
2  0.189  0.190  0.191  0.190  0.191 
 Notes: see notes on Table 1 
 
 
 
 
 
   8 
240 200 160 120 80 40 0
20.0
17.5
15.0
12.5
10.0
7.5
5.0
Local Distance
L
a
b
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u
r
 
P
r
o
d
u
c
t
i
v
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t
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Single Plant
Multi-Plant
 
Figure 1: Local distance and labour productivity 

Productivity and Proximity

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