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Is There a Rural–Urban Divide? Location andProductivity of UK ManufacturingMarian Rizov a b & Patrick Paul Walsh ca Department of Economics and Statistics , Middlesex University Business School ,London, NW4 4BT, UKb Agricultural Economics and Policy Group , Wageningen University , , Hollandseweg 1,NL-6706 KN, Wageningen, the Netherlandsc UCD SPIRe and Geary Institute , Newman Building, Belfield, Dublin 4, Ireland E-mail:Published online: 05 Jul 2010.
To cite this article: Marian Rizov & Patrick Paul Walsh (2011) Is There a Rural–Urban Divide? Location and Productivity ofUK Manufacturing, Regional Studies, 45:5, 641-656, DOI: 10.1080/00343401003713449
To link to this article: http://dx.doi.org/10.1080/00343401003713449
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Is There a Rural–Urban Divide? Location andProductivity of UK Manufacturing
MARIAN RIZOV∗† and PATRICK PAUL WALSH‡∗Department of Economics and Statistics, Middlesex University Business School, London NW4 4BT, UK.
Email: [email protected]†Agricultural Economics and Policy Group, Wageningen University, Hollandseweg 1, NL-6706 KN Wageningen,
the Netherlands‡UCD SPIRe and Geary Institute, Newman Building, Belfield, Dublin 4, Ireland. Email: [email protected]
(Received January 2009: in revised form November 2009)
RIZOV M. and WALSH P. P. Is there a rural–urban divide? Location and productivity of UK manufacturing, Regional Studies.
Aggregate productivity of manufacturing industries by urban, rural less sparse, and rural sparse locations in the UK is computed
from firm-specific total factor productivities, which are estimated by a semi-parametric algorithm, within four-digit manufactur-
ing industries, using the FAME data set over the period 1994–2001. The productivity differentials across location categories are
analysed by decomposing them into industry productivity effect and industry composition effect. The analysis indicates that at the
end of twentieth century, a rural–urban divide in manufacturing productivity still remains, but there is a tendency for convergence
between rural and urban location categories, possibly due to increased competitive pressure. The industry composition effect is
positively correlated with the industry productivity effect, suggesting that locations with high productivity are also characterized
by industrial structure enhancing productivity.
Total factor productivity Structural estimation Rural–urban definition UK manufacturing
RIZOV M. et WALSH P. P. Est-ce qu’il y a un clivage urbano-rural? L’emplacement et la productivite de l’industrie au R-U,
Regional Studies. On calcule la productivite globale de l’industrie au R-U en fonction des emplacements urbains, des emplace-
ments ruraux moins eparpilles et des emplacements ruraux clairsemes a partir des productivites globales des facteurs specifiques
aux entreprises et estimes a partir d’un algorithme semi-parametrique pour les industries a quatre chiffres, employant l’ensemble
de donnees FAME sur la periode allant de 1994 jusqu’a 2001. On analyse les ecarts de productivite a travers les categories d’empla-
cement en les decomposant en l’effet productivite industrielle et l’effet composition industrielle. L’analyse indique qu’a la fin du
vingtieme siecle, il restait un clivage urbano-rural pour ce qui est de la productivite industrielle, mais il y avait une tendance a la
convergence entre les categories d’emplacement rurales et urbaines. Cela pourrait s’expliquer par une augmentation de la
competitivite. L’effet composition industrielle est en correlation etroite avec l’effet productivite industrielle, ce qui laisse supposer
que les emplacements a forte productivite se caracterisent aussi par une productivite qui ameliore la structure industrielle.
Productivite globale des facteurs Estimation structurelle Definition ruralo-urbaine Industrie au R-U
RIZOV M. und WALSH P. P. Gibt es eine Kluft zwischen dem landlichen und stadtischen Raum? Standort und Produktivitat des
britischen Produktionswesens, Regional Studies. Mit Hilfe des FAME-Datensatzes fur den Zeitraum von 1994 bis 2001 berechnen
wir anhand der firmenspezifischen Gesamtfaktorproduktivitaten, die mit Hilfe eines semiparametrischen Algorithmus geschatzt
werden, die Gesamtproduktivitat von produzierenden Branchen auf vierstelliger Ebene in urbanen sowie in gering bzw. sparlich
besiedelten landlichen Gebieten Großbritanniens. Wir analysieren die Differentiale der Produktivitat in Bezug auf verschiedene
Standortskategorien, indem wir sie in eine Auswirkung auf die branchenspezifische Produktivitat und eine Auswirkung auf die
Branchenzusammensetzung aufteilen. Aus der Analyse geht hervor, dass zum Ende des zwanzigsten Jahrhunderts hinsichtlich der
Produktivitat der produzierenden Branchen weiterhin eine Kluft zwischen Stadt und Land besteht, aber zugleich die Tendenz
Regional Studies, Vol. 45.5, pp. 641–656, May 2011
0034-3404 print/1360-0591 online/11/050641-16 # 2011 Regional Studies Association DOI: 10.1080/00343401003713449http://www.regional-studies-assoc.ac.uk
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einer Konvergenz von stadtischen und landlichen Standortskategorien zu beobachten ist, was moglicherweise auf den erhohten
Konkurrenzdruck zuruckzufuhren ist. Die Auswirkung auf die Branchenzusammensetzung steht in positiver Korrelation zur
Auswirkung auf die branchenspezifische Produktivitat, was darauf schließen lasst, dass sich Standorte mit hoher Produktivitat
auch durch eine Branchenstruktur auszeichnen, die die Produktivitat verbessert.
Gesamtfaktorproduktivitat Strukturelle Schatzung Landlich-stadtische Definition Produktionswesen in Großbritannien
RIZOV M. y WALSH P. P. ¿Existe una division entre zonas rurales y urbanas? Lugar y productividad de la industria manufacturera
britanica, Regional Studies. A partir de la productividad total de los factores a nivel de empresas, que se estima mediante un algo-
ritmo semiparametrico, calculamos la productividad agregada de las industrias manufactureras en zonas urbanas, zonas rurales con
muy poca poblacion y zonas rurales con poblacion escasa en el Reino Unido para las industrias manufactureras de cuatro dıgitos
con ayuda de los datos de FAME durante el periodo de 1994 a 2001. Analizamos los diferenciales de productividad en las diferentes
categorıas de lugares al descomponerlos en el efecto de la productividad industrial y el efecto de la composicion industrial. El ana-
lisis indica que al final del siglo XX, todavıa existe una division rural–urbana en la productividad manufacturera pero hay una
tendencia a la convergencia entre las categorıas de zonas rurales y urbanas, posiblemente debido a un aumento de la presion com-
petitiva. El efecto de la composicion industrial esta positivamente relacionado con el efecto de la productividad industrial, lo que
indica que las zonas con una alta productividad se caracterizan por una estructura industrial que mejora la productividad.
Productividad total de los factores Estimacion estructural Definicion de zona rural y urbana Industria manufacturera
britanica
JEL classifications: D24, R11, R30
INTRODUCTION
From the late 1950s to the end of the century, there hasbeen a shift of employment from urban to rural areasand a rise in rural wages which has arguably also beenassociated with a growth in productivity of all types ofrural businesses in the United Kingdom (KEEBLE,2000; NORTH and SMALLBONE, 2000; ANDERSON
et al., 2005), in other parts of Europe (ROPER, 2001;TERLUIN, 2003; TERLUIN et al., 2005), and in theUnited States (ACS and MALECKI, 2003). Authorsargue that this trend has slowed down and even reversedrecently (for example, WEBBER et al., 2009). Therefore,the question if differences in aggregate productivitybetween urban and rural locations still remain andwhat are the factors affecting rural–urban productivitydifferentials is of high importance for policies aimingat welfare improvement and economic growth.
Traditional studies commissioned by the Departmentof the Environment, Food and Rural Affairs (DEFRA)in England and Wales have usually been concernedwith productivity differentials at local authority levelusing aggregate data. However, there are methodologicaland data problems associated with the area approach suchas whether to use a workplace or a residence-basedmeasure, and how to incorporate both earnings andprofits in the measure of productivity. The alternative isto estimate business productivity using micro-data atfirm or plant level and then aggregate productivitymeasures to the level of rural and urban locationcategories. Recently, WEBBER et al. (2009) estimatedlabour productivity using plant-level data and investigatedthe presence and causes of differences in productivityacross the 2004 DEFRA-defined urban, rural lesssparse, and rural sparse location categories.1 The main
finding is that there is a productivity divide across urbanand rural locations – plants in less sparse and sparserural location categories are 13.5% and 21.6% less pro-ductive than plants in urban locations, respectively.2
Similar to the work of WEBBER et al. (2009), thepresent paper uses micro-data. However, the widelyavailable data set used in the study – FAME of theBureau van Dijk – is different from the Office forNational Statistics (ONS) census data employed byWebber et al. The advantage of the data over thoseused by Webber et al. is that FAME contains consolidatedfirm-level accounts which avoid problems withidentifying plants within multi-plant firms. Given theultimate goal to study productivity differences betweenaggregated rural and urban areas and the economicimportance of large (multinational) multi-plant firms(MARKUSEN, 1995), the present authors believe thatassuming homogeneity of plants within multi-plantfirms is a less costly trade-off compared with excludingall multi-plant firms from the analysis. Furthermore, astructural estimation algorithm is applied to panel data,covering the 1994–2001 period, and the analysis oflocation and performance is extended by estimatingtotal-factor productivity (TFP) at the firm level, whichis a more comprehensive direct measure of firm perform-ance compared with the labour productivity estimatedfor only one year (2004) by WEBBER et al. (2009).
Previous studies attempting to link location and pro-ductivity apply a two-stage analysis. In the first stage,authors estimate firm productivity, and in a secondstage they proceed to link productivity to locationcharacteristics. In the view of the present authors,testing for a relationship between location and (unob-servable) productivity, ex-post, is admitting that there is
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information that should have been used in the structuralmodel of the unobservable while estimating theproduction function in the first instance. Therefore, toestimate unbiased and consistent measures of firm pro-ductivity, the present authors rely on a behavioural fra-mework that builds on models of industry dynamics(ERICSON and PAKES, 1995) and the link between pro-ductivity and density of economic activity (CICCONE
and HALL, 1996). Following the econometric model-ling ideas of ACKERBERG et al. (2007), the frameworkof the present paper underlines the estimation strategyand helps to specify timing and relational assumptionsfor firm decisions in a manner similar to OLLEY andPAKES (1996). The present econometric applicationfollows the work of ACKERBERG et al. (2007) as wellas an extension suggested by RIZOV and WALSH
(2009). Market structure (factor markets, demand con-ditions, and prices) and investment climate (includinginstitutions) are explicitly allowed to differ across ruraland urban locations. It is found that there is indeed arural–urban productivity divide which is due to bothdifferences in industry composition and industry (andfirm) productivity as rural industries lag behind theirurban counterparts. The aggregate rural–urban pro-ductivity differentials are mostly determined by industryproductivity differences, while differences in industrycomposition across rural (especially, less sparse) andurban locations are less pronounced.
The paper is organized as follows. In the next section,a brief analysis of the relevant literature is undertaken toclarify the link between the productivity and the densityof economic activity and a model of (unobservable)productivity is explicitly formulated. The econometricframework section introduces the semi-parametricestimation methodology applied in the paper, while thefollowing section describes the data and variables usedin the econometric analysis and reports results of estimat-ing production functions within four-digit industries.Distributions of productivity estimates by locationcategory are also presented. The penultimate sectionanalyses the spatial patterns of aggregate productivityand factors affecting it by the means of decompositionsin levels and in changes for each location category. Thefinal section concludes.
LOCATION, DENSITY OF ECONOMIC
ACTIVITY, AND FIRM PRODUCTIVITY
The origins of the analysis relating the location andeconomic performance of firms can be traced back atleast to the work of MARSHALL (1920), who statesthat urbanization and, thus, the geographical concen-tration of economic activities in urban agglomerationscan result in a snowball effect, where new entrantstend to agglomerate to benefit from higher diversityand specialization in production processes. There arealso benefits to firms from co-locating in close
proximity to other firms in the same industry. Bothurbanization and localization economies can be con-sidered centripetal forces leading to the concentrationof economic activities. However, HENDERSON
(1974), building on the work of MILLS (1967), demon-strates that, in an equilibrium, disamenities fromagglomeration may offset the productivity advantages,thus acting as centrifugal forces. For example, theseinclude increased costs resulting from higher wagesdriven by competition among firms for skilled labour,higher rents due to increased demand for housing andcommercial land, and negative externalities such ascongestion.
A second branch of the literature on agglomerationhypothesizes economies of scale internal to firms(ABDEL-RAHMAN, 1988; FUJITA, 1988; RIVERA-BATIZ, 1988). Models with internal increasing returnsbuild on theories of the firm and its market and com-monly employ the well-known formalization of mono-polistic competition by SPENCE (1976) and DIXIT andSTIGLITZ (1977) to demonstrate that non-transportableintermediate inputs produced with increasing returnsimply agglomeration. In a related model, KRUGMAN
(1991) demonstrates that agglomeration will resulteven when transportation costs are small, if mostworkers are mobile. The essence of all these models isthat when local markets are more active, a largernumber of producers of the differentiated intermediateinputs break even and the production of final goods ismore efficient when a greater variety of intermediateinputs is available.3
While previous studies focus on returns to economicmass such as city size, CICCONE and HALL (1996) focuson spatial density and show that density, which isdefined as the intensity of labour, human and physicalcapital relative to physical space, rather than size is amore accurate determinant of productivity. Densityaffects productivity in several ways. If technologieshave constant returns themselves, but the transportationof products from one stage of production to the nextinvolves costs that rise with distance, then the technol-ogy for the production of all goods within a particulargeographical area will have increasing returns – theratio of output to input will rise with density. If thereare externalities associated with the physical proximityof production, then density will contribute to pro-ductivity for this reason as well. A third source ofdensity effects is the higher degree of beneficial special-ization possible in areas of dense activity. A closelyrelated work by CARLINO and VOITH (1992) findsthat TFP across US states increases with urbanization.More recently, CICCONE (2002) for Europe andFINGLETON (2003) for Great Britain report a positiveassociation between employment density and pro-ductivity. For the case of Great Britain, RICE et al.(2006) explain regional productivity differences byproximity to economic mass. They argue that thedetailed modelling of proximity, measured by driving
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time, to economic mass is more general than themeasures of the population density in their own orneighbouring regions and that this enables them toderive economically meaningful inferences about thespatial scale over which the productivity effects ofagglomeration operate.
The present paper follows the models of CICCONE
and HALL (1996) and RICE et al. (2006) in directly relat-ing productivity to density of economic activity andproximity to economic mass. Given that the strategy isto control for unobservable productivity while estimat-ing production functions, rather than explicitly identi-fying effects, proxy is used as a categorical variablebased on the DEFRA definition. In 2005, DEFRAbrought out both a new classification and a new defi-nition of rural as described in DEFRA’s (2004) strategypaper. The classification is based on settlement mor-phology, while the definition is based on the density ofthe population. In principle, it is possible to have sixtypes of rural locations – town (less sparse); town(sparse); village (less sparse); village (sparse); dispersed(less sparse); and dispersed (sparse) (DEFRA, 2005a) –but, in practice, this grouping cannot be readily under-taken for analytical purposes (DEFRA, 2005b) and thecombination of the classification and the definitionmakes little sense for policy analysis. In this study,similar to that of WEBBER et al. (2009), the new ruraldefinition is used; a distinction is made between sparseand less sparse locations to allow comparisons to bemade between broadly different types of rural locationbased on the density of the population. The sparseand less sparse rural categories are then comparedwith data for urban locations to examine principaldifferences in plant productivity between rural sparse,rural less sparse, and urban locations.
Table 1 presents summary statistics of key locationcharacteristics (density of the population of workingage, business density, etc.) by urban, rural less sparse,and rural sparse categories according to the DEFRA
definition. There are clear differences across locationswith respect to various characteristics of density ofeconomic activity, with urban locations exhibiting thehighest density and rural sparse locations being theleast dense in economic activity. The main hypothesisis that productivity is high in locations with a highdensity of economic activity or that have, in somesense, proximity to a large economic mass. It is arguedthat the DEFRA definition of location controls for allthese effects and encompasses various agglomerationmechanisms driving productivity.4 For example, onemechanism can be technological externalities; firmslearn from a co-presence with other firms in relatedactivities, so innovating and implementing new technol-ogies efficiently. Another mechanism can be via thickcapital and labour markets which work more efficientlyby having lower search costs and generating improvedmatching of buyers and sellers. A third mechanism canbe simply that in the presence of transport costs, firmsgain from having good access both to their customersand to their suppliers of intermediate goods and services.The aim of the present paper is not to seek to identifyeach of these effects separately, but merely to controlfor their combined impact by using location-specificinformation in modelling firm productivity.
Next, this section explicitly builds the productivityand location relationship into a (structural) model ofunobservable productivity. The productivity of a firm,j, at a point in time, t, following OLLEY and PAKES
(1996) and extensions outlined in ACKERBERG et al.(2007), is specified as a function:
vjt = h(ijt, kjt, ajt, ljt, rt)
of a firm’s capital, kjt; labour, ljt; age, ajt; investment, ijt;and the economic environment that the firm faces at aparticular point in time, rt; and the function is treatednon-parametrically in the estimation algorithm.OLLEY and PAKES (1996) derive the function of
Table 1. Indicators of density of economic activity by location category, 1997–2001
Indicator Urban Rural less sparse Rural sparse
Density of the population of working age (number of residents/km2) 1778.1
(1454.8)
252.2
(223.8)
37.0
(29.6)
Business density (stock of value added tax registrations/km2) 262.2
(157.5)
12.7
(11.6)
2.5
(2.0)
Job density (number of jobs/resident of working age) 2.6
(1.8)
0.8
(0.7)
0.7
(0.6)
Proportion of knowledge-intensive business services in all businesses (%) 16.4
(12.2)
14.9
(11.5)
13.1
(8.4)
Proportion of employees in knowledge-intensive business services (%) 14.5
(8.7)
11.4
(7.6)
7.7
(6.1)
Proportion of the population with a higher education (%) 21.8
(9.4)
19.9
(5.1)
17.5
(2.3)
Capital investment by local authority (£/resident) 3425.3
(1352.4)
3190.0
(1401.3)
2812.2
(1331.9)
Note: Summary statistics are aggregated from information at local authority (LAD) level (434 observations in total); standard deviations (SD) are
reported in parentheses. The population of working age comprises men aged sixteen to sixty-four, and women aged sixteen to fifty-nine.
Source: Office for National Statistics (ONS).
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productivity by inverting the investment demand func-tion of the firm, which itself is a solution to the firm’smaximization problem.5 The economic environmentcontrol, rt, could capture characteristics of the inputmarkets, characteristics of the output market, or indus-try characteristics such as the current distribution of thestates of firms operating in the industry. Note that theOlley–Pakes formulation allows all these factors tochange over time, although they are assumed to beconstant across firms in a given period.
This paper extends the Olley–Pakes model of(unobservable) productivity in two ways. First, itextends the information content of the economicenvironment control to vary by type of firm accordingto the DEFRA definition of rural and it denotes thisby rjt, where a subscript index j is added. Introducinglocation-specific market structure in the state spaceallows for some of the competitive richness of theMarkov-perfect dynamic oligopoly model ofERICSON and PAKES (1995). Note also that introducinga richer location-specific market structure in the pro-ductivity function does minimize the deviations fromthe original Olley–Pakes scalar unobservable assump-tion necessary to invert the investment function, andit may help with the precision of the estimates.
Second, this section relaxes the scalar unobservableassumption all together following the modelling ideas ofACKERBERG et al. (2007) and an application to firmproductivity and trade orientation by RIZOV andWALSH (2009). Furthermore, the model of productivityis adjusted to allow for exporting status, ejt, to be anadditional (endogenous) control variable in the statespace that is driven by lagged productivity, as in MELITZ
(2003). This formulation leads to modelling productivityas a controlled second-order Markov process:
p(vjt|vjt−1,vjt−2)
where firms operate through time-forming expectationsof future vjt’s on the basis of information from twopreceding periods.6 The productivity function thenbecomes:
vjt = h(ijt, kjt, ajt, ljt, eji, rjt) (1)
The selection to exporting can reveal better productivitydue to higher-quality products, know-how, anddistribution networks that are needed to overcome sunkcost to get into foreign markets. The propensity toexport is specified as a non-parametric function ofijt−1, kjt−1, ajt−1, ljt−1, rjt−1 and a vector of other firm-specific characteristics such as the type of ownership,corporate governance, and industry groupings. Similarly,location choices may also be endogenous. Therefore,the propensity of firms to locate in urban, rural lesssparse or rural sparse areas is specified as a non-parametricfunction of firm-specific (ijt−1, kjt−1, ajt−1, ljt−1, ejt−1) and
location-specific characteristics (Table 1) measuringdensity of economic activity at local authority (LAD)level. In addition, NUTS-3 (Nomenclature des UnitesTerritoriales Statistiques) regional dummy variables areincluded partially to control for spatial spillovers andproximity to economic centres. Equation (1) uses thepropensity to export, eji, estimated from a probit model,and the propensity to locate in an area with a higherdensity of economic activity, rji, estimated from anordered probit model, rather than the observed eji and rjiwhich allows one to treat the exporting and locationdecisions as endogenous controls.7
ECONOMETRIC FRAMEWORK
To compute unbiased and consistent firm-level (totalfactor) productivity measures, one first needs to gener-ate unbiased and consistent estimates of productionfunction parameters. However, estimating productionfunction parameters is complicated due to the fact thatproductivity is not observed directly in the data. Thefirst complication arises because unobservable pro-ductivity determines input levels, which is the classicsimultaneity problem analysed by MARSHAK andANDREWS (1944). The second complication arisesout of the fact that firms survive based on unobservableproductivity type, amongst other factors. If an ordinaryleast-squares (OLS) estimator is used, simultaneitymeans that estimates for variable inputs such as labour,when considered a non-dynamic input, will beupward biased, assuming a positive correlation withunobservable productivity. Exit will depend on pro-ductivity type as well as the capital stock representingsunk cost. Thus, the coefficient on capital is likely tobe underestimated by OLS as higher capital stocksinduce firms to survive at low productivity levels(OLLEY and PAKES, 1996). Besides the two biases, apotential problem afflicting productivity measure isassociated with the spatial dependency of observationswithin a geo-space. Spatial dependency leads to thespatial autocorrelation problem in statistics since –like temporal autocorrelation – this violates standardstatistical techniques that assume independence amongobservations (ANSELIN and KELEJIAN, 1997). Further-more, spatial dependency is a source of spatialheterogeneity, which means that overall parametersestimated for the entire system might not adequatelydescribe the process at any given location.
To deal with the estimation problems outlined above,a semi-parametric estimation algorithm is employedin the spirit of OLLEY and PAKES (1996) followingextensions given in ACKERBERG et al. (2007) and anapplication by RIZOV and WALSH (2009). As inOLLEY and PAKES (1996), a log–linear productionfunction is specified:
yjt = b0 + bkkjt + baajt + bl ljt + vjt + hjt (2)
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where the log of firm j value added at time t, yjt, ismodelled as a function of the logs of that firm’s statevariables at t, namely: age, ajt; capital, kjt; and labour,ljt. Investment demand, ijt, determines the capital stockat the beginning of each period. The law of capitalaccumulation is given by:
kjt+1 = (1 − d)kjt + ijt
while age evolves as ajt+ 1 ¼ ajt + 1. The error structurecomprises a stochastic component, hjt, with zeroexpected mean, and a component that represents unob-served productivity, vjt, as specified in equation (1).Both vjt and hjt are unobserved, but vjt is a statevariable, and thus affects a firm’s choice of variables –the decision to exit and investment demand – whilehjt has zero expected mean given the current infor-mation, and hence does not affect decisions.
Substituting equation (1) into the production func-tion (2) and combining the constant, kjt, ajt, and ljtterms into function f(ijt, ejt, kjt, ajt, ljt, rjt) gives:
yjt = f(ijt, ejt, kjt, ajt, ljt, rjt) + hjt (3)
Equation (3) is the first step of the estimation algorithmand can be estimated as in OLLEY and PAKES (1996)with OLS and applying semi-parametric methods thattreat the function f(.) non-parametrically, using a poly-nomial.8 Even though the first stage does not directlyidentify any of the parameters of the production func-tion, it generates estimates of f(.), fjt, needed in thesecond stage where expected (unobservable) pro-ductivity can be written as:
vjt(b0,bk,ba,bl) = fjt − b0 − bkkjt − baajt − bl ljt
(4)
Next, to clarify the timing of production decisions, vjt isdecomposed into its conditional expectation given theinformation known by the firm in two prior periods,t – 2 and t – 1, and a residual:
vjt = E[vjt|vjt−2,vjt−1] + jjt = g(v_jt−2,v_
jt−1) + jjt
By construction, jjt is uncorrelated with information int – 2 and t – 1 and thus with kjt, ajt, and ljt, which arechosen before time t. The specification of the g(.) func-tion is determined by the fact that productivity follows asecond-order Markov process, as discussed in the pre-vious section. Note that the firm’s exit decision inperiod t depends directly on vjt and thus the exitdecision will be correlated with jjt. This correlationrelies on the assumption that firms exit the marketquickly, in the same period when the decision ismade. If exit is decided in the period before actualexit occurred, then even though there is a selection
per se, exit would be uncorrelated with jjt.9 To
account for endogenous selection on productivity, theg(.) function following the work of ACKERBERG et al.(2007) and RIZOV and WALSH (2009) is extended asfollows:
vjt = g′(v_jt−2,v_
jt−1, Pjt) + jjt (5)
where Pjt is a propensity score that controls for theimpact of selection on the expectation of vjt, that is,firms with lower survival probabilities that do surviveto time t likely have higher vjt’s than those withhigher survival probabilities. Pjt is estimated non-parametrically by using a probit model with a poly-nomial approximation. Note that the state variable setis extended with location and trade status informationwhich captures the effects of important determinantsof firm exit decision.
The capital, age, and labour coefficients are ident-ified in the second step of the estimation algorithm.Equations (5) and (4) are substituted into equation (2)using expressions for the estimated values, fjt−1,fjt−2, which gives:
yjt = bkkjt + baajt + blljt + g′(fjt−1 − bkkjt−1
− baajt−1 − blljt−1, fjt−2 − bkkjt−2 − baajt−2
− blljt−2,_Pjt) + 1jt (6)
where the two b0 terms have been encompassed intothe non-parametric function, g′(.) and 1jt is a compositeerror term comprised of hjt and jjt. The lagged f vari-ables are obtained from the first step estimates at t – 2and t – 1 periods. Because the conditional expectationof vjt, given information in t – 2 and t – 1 periods,depends on vjt 2 2 and vjt 2 1, one needs to use esti-mates of f from two prior periods. Equation (6) is esti-mated with a non-linear least-squares (NLLS) estimator,approximating g′(.) with a polynomial.10
Finally, having estimated unbiased and consistentproduction function coefficients, one can back out anunbiased and consistent measure (residual) of TFP as:11
TFPjt = yjt − bkkjt − bl ljt
In the model of unobservable productivity, spatial andtime dependencies have been explicitly incorporatedby merging spatial interactions with disaggregatedmodelling of productivity at the firm level. In termsof verifying whether variations in location and exportstatus make firms more productive, the authors havecontrolled in the model of productivity for marketstructure-specific shocks (such as demand conditions,factor markets, exit barrier) that are different acrosslocations and export status. Note that these factors
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remain constant across firms in the same location andexport status within a given industry and time period.
DATA AND PRODUCTIVITY ESTIMATES
As discussed in previous sections, the analysis classifieslocations as in WEBBER et al. (2009) into urban, ruralless sparse, and rural sparse following the 2004DEFRA definition of rural. The production functionsare estimated using the FAME data set of the Bureauvan Dijk. The data set covers all firms at CompaniesHouse in the UK and includes information on detailedunconsolidated financial statements, ownership struc-ture, location (by post code), activity description, anddirect exports. The data used in the analysis containannual records on more than 80 000 manufacturingfirms over the period 1994–2001. The coverage ofthe data compared with the aggregate statistics reportedby the UK Office for National Statistics (ONS) is verygood as regards sales (86%) and employment (92%).12
The manufacturing sectors are identified on the basesof the current 2003 UK Standard Industrial Classifi-cation (SIC) at the four-digit level and range between1513 and 3663. All nominal monetary variables areconverted into real values by deflating them with theappropriate four-digit UK SIC industry deflatorstaken from the ONS. Producer price index (PPI) isused to deflate sales and the cost of materials, as well
as asset price deflators for capital and fixed investmentvariables.13
In this paper, the goal is to estimate unbiased andconsistent TFP measures at the firm level, withinfour-digit industries, and to document the aggregateproductivity gaps between urban, rural less sparse, andrural sparse locations. The strategy of the empiricalanalysis implies that one runs regressions within four-digit industries which leaves the forty-one largestfour-digit industries with a sufficient number of obser-vations to apply the estimation algorithm. The esti-mated sample accounts for almost 60% of themanufacturing sales and 56% of the employment inthe data. After lags are applied and observations withmissing values deleted, there are 23 841 remainingobservations for 6722 firms. The correlations betweenthe ONS aggregate statistics series and the estimatedsample series are as follows: value added (used in theregressions as dependent variable), 0.94; employment,0.97; and exports, 0.95.
The descriptive statistics calculated from the esti-mated FAME sample of manufacturing firms arereported in Table 2. Average firm characteristics arecompared across urban, rural less sparse, and ruralsparse locations. Urban firms, compared with theirrural counterparts, are larger in terms of value added,employment, and capital, and they invest more. Urbanfirms are also more likely to export and to be ownedby foreign investors.14 These characteristics are in
Table 2. Descriptive statistics of firm-specific variables by location category, 1997–2001
Variable Urban Rural less sparse Rural sparse
Firm characteristics
Value added (£, thousands) 17333.3
(22381.2)
8606.5
(4644.5)
3532.3
(913.6)
Total assets (£, thousands) 18646.9
(48926.1)
12966.2
(8397.9)
3030.1
(666.1)
Investment (£, thousands) 4675.1
(14716.6)
4493.9
(4095.9)
582.6
(112.9)
Number of full-time-equivalent employees 425.3
(261.8)
248.7
(68.6)
137.9
(24.6)
Share of exporting firms 0.56
(0.50)
0.55
(0.50)
0.46
(0.50)
Share of foreign owned firms 0.26
(0.44)
0.23
(0.42)
0.11
(0.31)
Age of the firm 29.0
(22.4)
29.1
(22.8)
36.9
(33.3)
Industry composition
List of top-four, four-digit SIC industries ordered
by market share
3663 2852 2112
2222 3663 1513
2852 3162 1551
3162 2222 2524
Market share of top-four industries (C4) (%) 37.7 38.0 35.1
Number of observations (total ¼ 23 841) 21 469 1747 625
Note: Values are shown as mean (standard deviation – SD). Definitions of four-digit Standard Industrial Classification (SIC) industries are as
follow: 1513, Meat and poultry meat products; 1551, Dairy products; 2112, Paper and paper products; 2222, Publishing and printing; 2524,
Miscellaneous plastic products; 3663, Miscellaneous manufacturing; 2852, General mechanical engineering; and 3162, Miscellaneous electrical
equipment.
Source: FAME, Bureau van Dijk.
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accord with the measures of density of economicactivity reported in Table 1. Interestingly, industry con-centration characterized by the market share of the top-four four-digit industries does not show substantialdifferences across rural and urban areas. However,there are important similarities and differences in thecomposition of the top-four industries dominatingeach type of location. In the urban and rural lesssparse locations, the following are dominant: publishingand printing (2222), general mechanical engineering(2852), miscellaneous electrical equipment (3162), andmiscellaneous manufacturing (3663). The rural sparselocations are dominated by: meat and dairy production(1513 and 1551), paper and paper production (2112),and miscellaneous plastic production (2524). Thefinding that the industry composition is very similarin urban and rural less sparse areas is significant andpoints to the fact that there is indeed a divide, but it isacross rural areas by their level of sparsity.
A summary of the aggregated coefficients, over theestimated forty-one industry production functions, bylocation category are reported in Table 3. Coefficientestimates from all forty-one industry regressions, thenumber of observations, and test statistics are reportedin Appendix A. The aggregated coefficients onlabour, capital, and age reported in Table 3 are weightedaverages using value added as the weight. They confirmthe differences across urban and rural locations with
respect to the shares of capital and labour in output.The coefficient on labour declines systematicallyacross urban and rural areas as its value is 0.71 forurban firms and 0.66 for firms in rural sparse areas.The pattern of the capital coefficient is just the opposite,but differences are quite small: 0.25 for urban firms and0.26 for firms in rural sparse areas.
Aggregate productivity measures by location categoryclearly show that urban firms are the most productive;the TFP of urban firms is 3.75, while it is 3.26 and3.08 for firms in rural less sparse and rural sparse areas,respectively. Furthermore, not only the mean, but alsothe whole distribution of urban firm TFPs dominatethe corresponding distributions of rural firm TFPs.Fig. 1 illustrates the distributions of firm TFPs acrossthe three categories of urban and rural locations bymeans of kernel density estimates. The Kolmogorov–Smirnov two-sample tests for stochastic dominance aresignificant at the 5% level and confirm the fact thatfirms in urban locations are most productive.
SPATIAL VARIATION IN AGGREGATE
PRODUCTIVITY
The discussion in previous sections and the informationreported in Tables 1–3 as well as Fig. 1 suggest thatthere is a systematic relationship between productivity
Fig. 1. Firm productivity distributions by location category, 1997–2001Source: Authors’ own calculations
Table 3. Production function coefficients and productivity estimates aggregated by location category, 1997–2001
Coefficient Urban Rural less sparse Rural sparse
Labour 0.709 (0.057) 0.696 (0.064) 0.665 (0.081)
Capital 0.246 (0.038) 0.250 (0.042) 0.255 (0.050)
Age 0.021 (0.070) 20.124 (0.090) 20.126 (0.108)
Aggregate productivity 3.752 (0.971) 3.259 (1.021) 3.084 (1.019)
Note: Reported coefficients and aggregate productivity are weighted averages, using value added as weight, from forty-one industry regressions on
firm-level data. The R2-statistics of all industry regressions are very high, close to 1 (see Appendix A). Standard errors (standard deviations for
productivity) are reported in parentheses.
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and the spatial characteristics of rural and urbanlocations related to density of economic activity. Thissection analyses differences in aggregate productivityacross rural and urban locations by applying a decompo-sition of the spatial variation in levels following RICE
et al. (2006).15 Further, it explores sources of pro-ductivity by analysing changes in the decompositionindexes. Spatial variation in aggregate productivityderives from two main sources: differences in the indi-vidual firm productivities within each industry, result-ing in different average productivities across industries;and differences in the industry composition in eachlocation category.
Let qrk be the weighted average, using firm value
added as the weight, of individual firm productivities(TFPs) in location, r, and industry, k.16 Let the totalvalue added in location, r, be denoted by:
Sr = Skskr
and the share of industry, k, in the total value added inlocation, r, be:
lkr = skr /Sr
The average productivity of industry k for the economyas a whole (that is, aggregating across all locations, r) isgiven by:
�qk =∑
rskr q
kr /∑
rskr
while:
�lk =
∑rskr /
∑rSr
is the share of industry k in the total value added for theeconomy as a whole. Aggregate productivity, qr, is aweighted average of industry productivities in location
r using industry value added as the weight. This aggre-gate productivity can be decomposed as:
qr ;∑
kqk
r lkr
=∑
kqk
r�l
k +∑
k�qklk
r −∑
k�qk�l
k
+∑
k(qk
r − �qk)(lkr − �l
k) (7)
The first term on the right-hand-side of equation (7) isthe average level of productivity in location r con-ditional on the industry composition being the sameas for the economy as a whole; this is referred to asthe productivity index. The second term is theaverage level of productivity of location r given itsindustry composition, but assuming that the pro-ductivity of each industry equals the economy-wideaverage for that industry. It is referred to as the industrycomposition index. The remaining terms measure theresidual covariance between industry productivitiesand industry shares in location r. It is important topoint out that a comparison between productivity andindustry composition indexes, while taking intoaccount the residual covariance terms, in equation (7)can provide useful information about the determinantsof aggregate productivity in various locations.
The productivity index and the industry compo-sition index are computed as specified above for theurban, rural less sparse, and rural sparse locations inthe UK, and the results are reported by location cat-egory in Table 4, panel A. Note that values reportedare normalized by the term:
∑k�qk�l
k
from equation (7). While variation in aggregate pro-ductivity by location reflects differences in both pro-ductivity and industry composition, the spatialvariation observed in the productivity index derives
Table 4. Aggregate productivity decompositions by location category, 1997–2001
∑k
qkrl
kr
∑k
qkr l
k∑
kqklk
r −∑
kqkl
k∑
kDqk
rDlkr
(A) Levels, average for 1997–2001
Urban 1.005 1.000 1.004 1.000 0.001
Rural less sparse 0.873 0.873 0.899 1.000 0.101
Rural sparse 0.825 0.765 0.819 1.000 0.241
(B) Changes, 1997–1998
Urban 0.027 0.029 0.024 0.022 20.004
Rural less sparse 20.046 0.084 20.060 0.022 20.048
Rural sparse 0.047 0.153 20.230 0.022 0.146
(C) Changes, 2000 2 2001
Urban 0.024 0.008 0.022 0.013 0.007
Rural less sparse 0.002 0.011 20.042 0.013 0.046
Rural sparse 0.066 0.078 0.091 0.013 20.090
Note: For definitions of decomposition components, see equation (7).
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entirely from spatial variation in industry (firm) pro-ductivity and is independent of differences in industrycomposition. A higher value of the productivity indexin a given location would suggest that industries inthis location are more productive. The spatial variationin the industry composition index derives entirely fromdifferences in the industry composition across locationsand is independent of variation in productivity. A highervalue of the composition industry index in a givenlocation implies that the more productive industriesare represented by larger industry shares in that location.The last covariance term in equation (7) providesinformation about the link between industry sharesand productivity; a positive sign of the term in a givenlocation means that the more productive industries arealso larger.
The results in Table 4, panel A, are computed asaverages for the 1997–2001 period and confirm thefact that urban locations, with the highest density ofeconomic activity, have the highest aggregate pro-ductivity. The rural less sparse locations lag behind inaggregate productivity by 13.2%, while rural sparselocations are the least productive, with aggregate pro-ductivity lower by 18% compared with the urbanlocation category. The productivity index and theindustry composition index are also lower for bothrural less sparse and rural sparse location categoriescompared with the urban location category as thedifferentials for the productivity index are 12.7% and23.5%, while the differentials for the industry compo-sition index are 10.5% and 18.5%, respectively. Themagnitudes of the differentials suggest that rural sparselocations are characterized by both the lowest pro-ductivity and the worst industry composition. Thecovariance term is positive for all location categories,but its magnitude is the largest for the rural sparselocations suggesting a substantial unexplained realloca-tion of industry shares towards more productive indus-tries or increases in productivity of larger industries.From a policy viewpoint, efforts to increase firm andindustry productivity, through technological innovationand competition, rather than modify industry compo-sition, might be more fruitful given the larger scopefor improvement in the productivity index comparedwith the industry composition index.17
To explore further the factors affecting aggregateproductivity, by location, changes over time of thedecomposition indexes are analysed in equation (7).Table 4 report results for two periods: in panel B, forthe 1997–1998 pre-euro period; and in panel C, forthe 2000–2001 post-euro period. The euro wasadopted by the UK’s main trading partners at the begin-ning of 1999, which resulted in a real appreciation of theexchange rate of the pound sterling against the euroover the 2000–2001 period, and led to an increase incompetitive pressure on both exporters and non-expor-ters (through increased import competition). By com-paring changes of aggregate productivity in the two
periods, with distinct exchange rate regimes and inter-national trade conditions, one can derive importantresults concerning the impact of economic conditionson the productivity of various types of location. Specifi-cally, one can establish the magnitudes of contributionsby both industry productivity and industry compositionchanges to the aggregate productivity of urban, rural lesssparse, and rural sparse locations.
The results shown in Table 4, panels B and C, showsubstantial heterogeneity in responses by type oflocation. Aggregate productivity in urban locationsincreases at a similar pace in both pre- and post-europeriods, by 2.7% and 2.4%, respectively. There are dra-matic changes in productivity of rural less sparselocations, with a shift from a negative growth of 4.6%in the pre-euro period to a positive but close-to-zerogrowth in the post-euro period. The rural sparselocations are characterized by the highest growth ratesin aggregate productivity – 4.7% before the euroimplementation and 6.6% after that. There is evidenceof rural sparse locations catching up with rural lesssparse and urban locations in terms of aggregate pro-ductivity over the entire period of analysis. It alsoseems that rural sparse locations are resilient to econ-omic shocks and respond well to increases in competi-tive pressure, which can be seen, in this case, as asubstitute for the impact of density of economic activity.
The sources of aggregate productivity growth varyby type of location. For the urban location category,improvements in both productivity and industry com-position indexes are evident before and after theimplementation of the euro. There is a relatively sub-stantial decline in the growth of the productivityindex in the post-euro period suggesting that, duringperiods of increased competitive pressure, the within-industry productivity improvements become lessimportant than the adjustments in industry compositionwhere more productive industries expand. For rural lesssparse locations improvement in the productivity indexis more important in the pre-euro period and there is adecline in the effect after the implementation of theeuro, similar to the urban location category. There isalso evidence of a relative improvement in the industrycomposition in rural less sparse locations underincreased competitive pressure. Despite this, however,the growth in the industry composition index remainsnegative over the period of analysis, suggesting thatthe large surviving industries in rural less sparselocations are relatively less productive. The negativegrowth in the residual covariance term in the pre-euro period also supports the view that the reallocationof industry shares leads to a deteriorating industry com-position in the pre-euro period. However, the growthin the residual covariance turns positive in the post-euro period, implying that there is a shift of industryshares in favour of more productive industries underincreased competitive pressure. Aggregate productivityin rural sparse locations is positively affected by
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improvements in the productivity index in a mannersimilar to other location categories, but the magnitudeis much larger. The impact of the industry compositionindex is interesting; the growth in the compositionindex shifts from negative in the pre-euro period topositive in the post-euro period, implying an improve-ment in the industry composition under increased com-petitive pressure in the economy. However, the growthin the residual covariance term exhibits an oppositepattern by becoming negative in the post-euro period.This is interpreted as evidence that there are in therural sparse locations less productive industries thatmanage to survive and even expand.
CONCLUSION
The focus of this paper is on evaluating the pro-ductivity gap between rural and urban locations inthe United Kingdom using micro-data. A structuralmodel of the unobservable productivity is builtemphasizing the link between productivity andspatial density of economic activity, and the semi-parametric estimation approach proposed by OLLEY
and PAKES (1996) is adapted to estimate the parametersof production functions at the firm level, within four-digit UK manufacturing industries, for the period1997–2001. Market structure is allowed to differ byendogenous export status and location choices, andproductivity is modelled as a controlled second-orderMarkov process which greatly enhances obtainingunbiased and consistent estimates of the productionfunction parameters and, thus, backing out unbiasedand consistent total-factor productivity (TFP)measures at the firm level. The firm TFPs are aggre-gated by location category following the 2004 Depart-ment for Environment, Food and Rural Affairs(DEFRA) definition of rural and it is found thataggregate productivity systematically differs acrossurban, rural less sparse, and rural sparse locations asthe magnitudes of the differentials are 13.2% and18.0%, respectively. The results are in line withseveral recent studies, notably WEBBER et al. (2009),and, in broader sense, RICE et al. (2006).
Next, aggregate productivity is decomposed intothe productivity index and the industry compositionindex. The productivity index is the highest in urbanlocations suggesting that (firm and industry) pro-ductivity is strongly influenced by the density ofeconomic activity and proximity to economic mass.The industry composition index captures the extent
to which manufacturing production in differentlocation categories is allocated to industries that aremore or less productive compared with the averagefor the UK economy. Because the industry compo-sition index is positively correlated with the pro-ductivity index, it is evident that locations with highproductivity are also characterized by industrial struc-ture enhancing productivity. However, the correlationis not perfect. Even though industry composition (ofthe top-four industries) in urban and rural less sparselocations is very similar, differences in both aggregateproductivity and productivity index remain. Further,analysing changes in the decomposition indexes overtwo periods, before and after implementation of theeuro by the UK main trading partners, revealssubstantial heterogeneity in responses across locationcategories under increased competitive pressure. Themain finding is that there is a tendency of ruralsparse locations to catch up with the urban and ruralless sparse location categories in terms of aggregateproductivity over the period of analysis.
Evidence is also found that increased competitivepressure as a result of changes in trade conditionsafter implementation of the euro by the UK’s maintrading partners has acted as a substitute for the roleof density of economic activity in enhancing industrycomposition, especially in rural sparse locations.From a welfare and economic growth policy view-point, the ultimate interest is in the ability of variouslocations to convert efficiently the set of resourcesavailable into output, and improvements in the useof resources by reallocating them from less to moreproductive industries can be just as effective in increas-ing aggregate output as are the productivity improve-ments within individual firms and industries.However, in the light of the decomposition results,efforts to increase firm and industry productivity,through technological innovation and within-industrycompetition, rather than relying on induced changesin industry composition, might be more fruitfulgiven the larger scope for improvement in the pro-ductivity index compared with the industry compo-sition index in rural locations.
Acknowledgements – The authors thank David North
and Arie Oskam for discussions on earlier drafts. Useful
comments made by anonymous referees are acknowledged.
The financial support from the Mansholt Graduate School
of Social Sciences and the British Academy is also acknowl-
edged. The usual disclaimer applies.
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APPENDIX A
Table A1. Production function coefficient estimates within four-digit Standard Industrial Classification (SIC) industries
SIC Parameters SIC Parameters SIC Parameters
(1) (2) (3) (1) (2) (3) (1) (2) (3)
1513 bl 0.55 1551 bl 0.82 1584 bl 0.77
RS SE 0.06 RS SE 0.08 SE 0.10
bk 0.31 bk 0.24 bk 0.21
SE 0.05 SE 0.08 SE 0.07
ba 0.04 ba 20.03 ba 20.04
SE 0.05 SE 0.10 SE 0.15
R2 0.98 R2 0.99 R2 0.98
n 308 n 203 n 162
1589 bl 0.77 1591 bl 0.62 1598 bl 0.66
SE 0.06 SE 0.07 SE 0.07
bk 0.21 bk 0.37 bk 0.31
SE 0.04 SE 0.05 SE 0.04
ba 0.13 ba 0.07 ba 20.17
SE 0.06 SE 0.09 SE 0.06
R2 0.98 R2 0.98 R2 0.98
n 416 n 108 n 154
1822 bl 0.70 2112 bl 0.67 2121 bl 0.56
SE 0.10 RS SE 0.08 SE 0.04
bk 0.21 bk 0.28 bk 0.33
SE 0.06 SE 0.04 SE 0.03
ba 20.11 ba 20.12 ba 0.09
SE 0.15 SE 0.08 SE 0.08
R2 0.98 R2 0.98 R2 0.99
n 502 n 246 n 459
2125 bl 0.84 2211 bl 0.66 2212 bl 0.80
SE 0.11 SE 0.05 SE 0.06
bk 0.10 bk 0.18 bk 0.23
SE 0.06 SE 0.03 SE 0.04
ba 20.16 ba 20.10 ba 0.02
SE 0.04 SE 0.05 SE 0.06
R2 0.98 R2 0.96 R2 0.99
n 168 n 723 n 408
2213 bl 0.83 2215 bl 0.68 2222 bl 0.68
SE 0.08 SE 0.04 U, RLS SE 0.03
bk 0.15 bk 0.26 bk 0.30
SE 0.04 SE 0.03 SE 0.02
ba 20.07 ba 0.02 ba 20.12
SE 0.10 SE 0.04 SE 0.03
R2 0.95 R2 0.97 R2 0.98
n 813 n 259 n 2355
2320 bl 0.55 2413 bl 0.62 2416 bl 0.49
SE 0.02 SE 0.09 SE 0.09
bk 0.32 bk 0.33 bk 0.35
SE 0.02 SE 0.05 SE 0.05
ba 0.11 ba 20.15 ba 0.09
SE 0.08 SE 0.09 SE 0.06
R2 0.99 R2 0.97 R2 0.98
n 170 n 480 n 466
2430 bl 0.42 2441 bl 0.86 2442 bl 0.80
SE 0.06 SE 0.05 SE 0.11
bk 0.50 bk 0.06 bk 0.13
SE 0.07 SE 0.03 SE 0.05
ba 20.12 ba 0.01 ba 0.15
SE 0.04 SE 0.04 SE 0.07
R2 0.98 R2 0.96 R2 0.95
n 226 n 395 n 133
(Continued )
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Table A1. Continued
SIC Parameters SIC Parameters SIC Parameters
(1) (2) (3) (1) (2) (3) (1) (2) (3)
2451 bl 0.42 2452 bl 0.42 2466 bl 0.75
SE 0.07 SE 0.06 SE 0.08
bk 0.41 bk 0.34 bk 0.24
SE 0.08 SE 0.08 SE 0.04
ba 0.30 ba 0.20 ba 20.25
SE 0.06 SE 0.12 SE 0.11
R2 0.85 R2 0.98 R2 0.98
n 109 n 257 n 621
2524 bl 0.66 2710 bl 0.70 2811 bl 0.55
RS SE 0.03 SE 0.08 SE 0.05
bk 0.29 bk 0.22 bk 0.32
SE 0.02 SE 0.05 SE 0.03
ba 0.02 ba 20.24 ba 0.18
SE 0.04 SE 0.10 SE 0.06
R2 0.98 R2 0.98 R2 0.97
n 1398 n 323 n 587
2852 bl 0.67 2912 bl 0.65 2922 bl 0.48
U, RLS SE 0.02 SE 0.04 SE 0.06
bk 0.16 bk 0.10 bk 0.33
SE 0.02 SE 0.02 SE 0.04
ba 0.06 ba 20.05 ba 0.25
SE 0.02 SE 0.04 SE 0.06
R2 0.96 R2 0.97 R2 0.98
n 2005 n 460 n 497
2924 bl 0.73 2971 bl 0.44 3002 bl 0.77
SE 0.05 SE 0.08 SE 0.05
bk 0.18 bk 0.52 bk 0.25
SE 0.04 SE 0.10 SE 0.04
ba 20.05 ba 20.36 ba 20.30
SE 0.06 SE 0.14 SE 0.10
R2 0.98 R2 0.95 R2 0.96
n 466 n 168 n 597
3110 bl 0.46 3162 bl 0.62 3220 bl 0.62
SE 0.04 U, RLS SE 0.04 SE 0.08
bk 0.50 bk 0.30 bk 0.30
SE 0.04 SE 0.03 SE 0.05
ba 20.13 ba 20.06 ba 20.26
SE 0.04 SE 0.06 SE 0.08
R2 0.97 R2 0.97 R2 0.97
n 384 n 1669 n 382
3320 bl 0.74 3410 bl 0.52 3430 bl 0.74
SE 0.04 SE 0.08 SE 0.10
bk 0.15 bk 0.36 bk 0.18
SE 0.02 SE 0.05 SE 0.06
ba 20.01 ba 0.16 ba 20.36
SE 0.04 SE 0.06 SE 0.21
R2 0.97 R2 0.98 R2 0.81
n 1107 n 241 n 347
3530 bl 0.73 3663 bl 0.69
SE 0.06 U, RLS SE 0.03
bk 0.17 bk 0.24
SE 0.04 SE 0.02
ba 20.16 ba 20.11
SE 0.06 SE 0.05
R2 0.97 R2 0.98
n 371 n 2698
Note: Reported R2-statistics and number of observations (n) are from the last step of the estimation algorithm; SE, standard error. Location
categories: U, urban; RLS, rural less sparse; and RS, rural sparse. Industries for which U, RLS or RS are reported are in the top-four industries
for one or more location categories.
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NOTES
1. The 2004 DEFRA rural–urban definition is also
extended to Scotland and Northern Ireland.
2. HARRIS and LI (2009) estimate total factor productivity
of UK firms and discuss the role of research and develop-
ment and absorptive capacity at a regional level, but they
do not consider the 2004 DEFRA definition and do not
focus on the rural–urban divide.
3. FUJITA and THISSE (2002) and ROSENTHAL and
STRANGE (2004) offer extensive surveys of the literature
on economics of agglomeration and its implications for
productivity.
4. H. M. TREASURY (2001) has defined five generic micro-
economic drivers that account for area-based differences
in performance: employment and skills; investment;
innovation; enterprise; and competition. COURTNEY
et al. (2004) regroup H. M. Treasury’s classification in
an attempt to accommodate less tangible elements of pro-
ductivity specifically in rural locations. They also postu-
late five main drivers. Economic capital embraces
infrastructure and innovation and human capital accom-
modates employment, skills and enterprise. Their other
three drivers are social capital (for example, networks
and partnerships), cultural capital (political consensus,
civic engagement), and environmental capital (quality
of living space). Whilst H. M. Treasury drivers apply at
the aggregate area level, they are less good at explaining
productivity at the firm level.
5. The invertability of the investment function requires the
presence of only one unobservable which OLLEY and
PAKES (1996) refer to as scalar unobservable assumption.
This assumption means that there can be no measure-
ment error in the investment function, no unobserved
differences in investment prices across firms, and no
unobserved separate factors that affect investment but
not production. However, the monotonicity needed in
the work of Olley and Pakes does not depend on the
degree of competition in the output market; it just
needs the marginal product of capital to be increasing
in productivity.
6. Note that the fixed effects estimator can be seen as a
special case of the Markov process p(.), where pro-
ductivity, vjt, is set to vj and does not change over time.
7. Results from estimating propensities to export and to locate
in areas with a high density of economic activity are avail-
able from the authors upon request.Given the availabilityof
two extra controls, besides the investment variable, the
authors also experimented with a third-order Markov
process, but the estimation results were very similar to the
second-order Markov process results reported here. Thus,
it is concluded that a second-order Markov process
approximates well the model of productivity.
8. OLLEYand PAKES (1996) show that kernel and polynomial
approximations of the unobservable produce very similar
results. In the present estimations, a computationally
easier fourth-order polynomial is used throughout.
9. Note that the first stage of the estimation algorithm is not
affected by selection because by construction hjt, the
residual in equation (2), is not correlated with firm
decisions as it is not observed by firm managers.
10. WOOLDRIDGE (2009) presents a concise one-step for-
mulation of the original OLLEY and PAKES (1996)
approach using a generalized method of moments
(GMM) estimator which is more efficient than the
standard Olley–Pakes algorithm; however, it is less flexible.
11. Estimating the age coefficient is only used to separate out
cohort from selection effects in determining the impact
of firm age on productivity and, therefore, the contri-
bution of age is not netted out from TFP.
12. Based on the analysis of HARRIS and LI (2009), FAME is
biased towards larger companies, particularly in the non-
exporting populations. Even though the aggregations are
size-weighted over company productivity, this is a caveat
of using the data.
13. KATAYAMA et al. (2003), and related studies, point out
that production functions should be a mapping of data
on inputs and outputs. However, most studies tend to
use revenue and expenditure data and use industry-
level deflators for output, raw material, and capital
assets to get back the quantity data needed. It is clear
that inputs and outputs can be priced differently for
different firms within narrowly defined industries. This
results in inconsistency discussed by KLETTE and
GRILICHES (1996) in the case of common-scale estima-
tors. Note, however, that allowing for endogenous
trade orientation in the unobservable, as in RIZOV and
WALSH (2009), and introducing location information
in the state space will control for a persistent pricing
gap across locations and between exporters and non-
exporters in their use of inputs and their outputs
within four-digit industries. Furthermore, FOSTER
et al. (2008) find that productivity estimates from quantity
and deflated revenue data are highly correlated, and that
the bias vanishes on average and estimated average pro-
ductivity is unaffected when aggregate deflators are used.
14. A company is marked as an exporter if one observes in
the data exporting by the firm in any year within a
three-year moving window. RIZOV and WALSH (2009)
also use these data to study productivity and trade orien-
tation and here a similar classification scheme will be
followed where exporters are defined as firms that con-
sistently export over the entire period of analysis. In
fact, out of 6722 firms in the sample, exporters represent
between 46% and 56% across the three categories of rural
and urban locations.
15. OOSTERHAVEN and BROERSMA (2007) offer detailed
discussion of decomposition methods.
16. Note that industry productivity is determined by indi-
vidual firm productivities and firm market shares
within the industry, as discussed by OLLEY and PAKES
(1996) and RIZOV and WALSH (2009), among others.
Thus, there could be two sources of industry pro-
ductivity: within-firm productivity increases and a real-
location of market shares towards more productive firms.
17. There is a large body of literature on international (and
regional) specialization which predicts that general
technology (Ricardian) and factor supply (Heckscher–
Ohlin) differences jointly determine comparative
advantage and, thus, specialization, measured as industry
composition. Recent papers, starting with HARRIGAN
(1997), show that the estimated impact of non-neutral
technology differences is large and in accord with the
theory, suggesting that Ricardian effects are an important
source of comparative advantage and a determinant of
industry composition.
654 Marian Rizov and Patrick Paul Walsh
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