agglomeration externalities and technical efficiency in italian regions

Qual QuantDOI 10.1007/s11135-014-0056-1

Agglomeration externalities and technical efficiencyin Italian regions

Massimiliano Agovino · Agnese Rapposelli

© Springer Science+Business Media Dordrecht 2014

Abstract The aim of the present work is to estimate an aggregate production function forthe 20 Italian regions by emphasizing the role that agglomeration externalities (localizationexternalities and urbanization externalities) and spatial spillovers have in influencing thetechnical efficiency of the production process. To this purpose, we use the stochastic frontierapproach. The results highlight the relevance and the positive impact that localization andurbanization externalities have in improving the efficiency level of the production processof Northern and Central Italy regions. Furthermore, spatial spillovers represent a source ofdevelopment and growth both for Northern-Central regions and Southern regions. Finally, weshow that the beta-convergence analysis of regional performance depends on the structuralcharacteristics of each economy (Northern-Central Italy and Southern Italy), and these struc-tural differences imply that Northern-Central and Southern macro-areas will have differentsteady states with regard to production performance.

Keywords Agglomeration externalities · Spatial spillovers · Stochastic frontier · Technicalefficiency · Italian regions · Convergence

JEL Classification R10 · O1 · D24

1 Introduction

In recent years territory has been seen as an independent production factor able to enter theproduction function and to affect the efficiency of classic production factors, i.e. labor andcapital. With regard to this issue, De Groot et al. state that “The productivity of the open urbaneconomy depends also on spatial factors, internally through density and infrastructure andexternally through spatial interaction with other cities and regions. Resources, production

M. Agovino (B) · A. RapposelliDepartment of Economics, University “G. D’Annunzio” of Chieti-Pescara, Viale Pindaro 42,65127 Pescara, Italye-mail: [email protected]

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M. Agovino, A. Rapposelli

factors and geography then combine with an industrial structure characterised by specialisa-tion, competition and diversity, to yield innovation and productivity growth that encouragesemployment expansion. … In the presence of economic diversity and increasing returns, cap-ital and labour are not flowing in opposite directions, as in static neoclassical theory. Instead,the city attracts capital too. Many aspects of this self-reinforcing and virtuous process yieldbenefits that are external to individual market transactions and such externalities are thereforecentral to agglomeration processes” (De Groot et al. 2007, p. 2).

The principle of agglomeration is mainly associated with the concept of externalities. Ifthese externalities are designed in their positive sense, i.e. in terms of benefits, they can beidentified in the so-called agglomeration economies. It is well known that the traditional clas-sification (Hoover 1937; Richardson 1969) divides these agglomeration economies in internaleconomies, i.e. economies of scale, and external economies, i.e. localization economies andurbanization economies. Economies of scale are defined as internal benefits because theyare related to the internal organization of the productive activity of firms and they are notcaused by factors external to them, such as proximity of other firms or presence of partic-ular services. In contrast, localization and urbanization economies are defined as externalbenefits or economies. In particular, the former type of economies are derived from bene-fits external to the individual firm but internal to the sector they belong to, while the latterare derived from benefits external both to the individual firm and to their sector. In short,economies related to the internal production of the firm, that arise from its resources, itsinternal organizational capacity and its management efficiency, can be controlled directlyby the firm, while external economies depend on production relations generated outside ofthe firm and are not controllable by it. Hence, traditional literature identifies three types ofagglomeration externalities: localization externalities, also known as Marshall externalitiesor MAR (Marshall 1890; Arrow 1962; Romer 1986), “represented by all those advantagesthe territory can bring to the firm production if it is organized into an agglomeration char-acterized by localization” (Camatti 2009) and urbanization externalities, also called Jacobsexternalities (Jacobs 1969), “represented by all those advantages the territory can bring tothe firm production if it is organized into an agglomeration characterized by urbanization”(Camatti 2009). The existence of these two typologies of territorial externalities is one of thekey factors of agglomeration, through the action of increasing returns that are generated byinteractions and spillovers between firms. Finally, the literature considers Porter externalities(Porter 1990), that are based on the assumption that “the competition among firms at locallevel represents a source of positive externalities as it encourages the production and theadoption of innovations.” (Cingano and Schivardi 2005).

Several empirical studies have tried to determine which is the most important character-istic of the production structure in generating externalities, focusing on the role of sectorspecialization (localization externalities) and production variety (urbanization externalities)(Cingano and Schivardi 2005). In particular, Glaeser et al. (1992) demonstrate, in their seminalwork conducted on a sample of American cities, that localization externalities have a negativeeffect on growth, while urbanization externalities have a positive effect on it. Subsequent stud-ies extended to other countries (as, for instance, Combes 2000 for the case of France; Bradleyand Gans 1998 in Australia; Cainelli and Leoncini 1999; Cingano and Schivardi 2005; Paciand Usai 2001 and Pagnini 2005 in Italy) confirm the negative relationship between produc-tive specialization and growth, while the relationship between urbanization externalities andgrowth seems ambiguous.

In this regard, the present study aims at estimating an aggregate production function forthe 20 Italian regions by emphasizing territorial externalities’ role in influencing the technicalefficiency of the production process. In addition, among the factors that may influence the

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Agglomeration externalities and technical efficiency

production process, we also consider spatial spillovers, starting from the reasonable hypoth-esis that they do not exhaust their effects only within the local economy in which they aregenerated but they also spread to neighbouring regions. More specifically, in this paper wewant to answer the following questions: which is the role of specialisation and diversificationof regional economic structures? How important is the interdependence (spatial spillovers)between contiguous economic areas? Is there convergence in the performance of Italianregions?

To this end, the stochastic frontier approach seems suitable to explain whether the per-sistent regional disparity, in terms of productivity, is due to differences in technology levels,factors endowments or efficiency (Mastromarco and Woitek 2006). Our work differs fromprevious empirical literature because it is the first one, to the best of our knowledge, thatevaluates, by means of technical efficiency scores estimates, the effect of agglomerationexternalities on the production performance of Italian regions.

The paper is organized as follows. In Sect. 2 we define some measures used for agglomer-ation externalities, in Sect. 3 we present the methodologies used, in Sect. 4 we introduce thedata and the results of stochastic frontier analysis, in Sect. 5 we provide the spatial econo-metric analysis of production performance in terms of beta-convergence, and in Sect. 6 weconclude.

2 Agglomeration externalities

Since early empirical studies (Glaeser et al. 1992; Henderson et al. 1995) the focus on theidentification of the agglomeration externalities intensity has been developed in terms of someindicators. The empirical literature usually refers to three types of territorial externalities,MAR (Marshall, Arrow, Romer) externalities, Jacobs externalities and Porter externalities.

MAR externalities are generated through knowledge spillovers between firms within thesame industry. In this case the spatial agglomeration of the industry, and hence its regionalspecialization, tends to stimulate knowledge spillovers between firms and, therefore, thegrowth of that local industry (Cainelli and Leoncini, 1999). This theory suggests the presenceof a monopolistic market: in fact it allows people to protect their innovations and to makebetter use of them. These externalities are given by the following indicator:

M ARit = max j t(si j t/s jt

)

where si j t denotes the ratio between the number of employed people in sector j in region iat time t and the total number of employed people in region i at time t , while s jt denotes theratio between the number of employed people in sector j at country level at time t and thetotal number of employed at country level at time t (Duranton and Puga 2000).

Jacobs externalities (Jacobs 1969) are based on the assumption that the industry varietyis able to promote the long-term development through cross-fertilization of ideas betweendifferent productive activities. Competition is the market form most appropriate to this typeof externalities, because only competition allows firms to increase their knowledge levels andthus to survive (Cainelli and Leoncini, 1999). Such externalities are commonly expressed bythe inverse of the Hirshman-Herfindal index (Duranton e Puga, 2000)1:

Jit = 1

/∑

j

∣∣si j t − s jt∣∣

1 The more the production structure of the corresponding region reflects the national economy diversity, themore the Hefindal index increases (Cirilli and Veneri 2009).

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Furthermore2, since it is likely that the externalities produced in a specific local economy donot exert their effects only within it but they can affect the performance of other locations(Pagnini 2003), we include an additional variable whose purpose is to quantify the exter-nalities associated with industrial agglomeration processes; therefore we take into accounta variable expressing spillover effects generated by the concentration of employment in theregions close to a given region and whose effect is an improvement of local growth, produc-tivity and efficiency (Guiso and Schivardi 2007; Battese and Tveteras 2006). We denote thisvariable with the following expression:

W Ei,t =∑

k �= j

Ek,t d−1j,k

where Ek,t represents the number of employed people of location k at time t, d j,k is thedistance between two generic locations and j and k represent the subscripts that identifythe element of the distance matrix W. This index is simply a lagged variable in space. Inparticular, we use as a measure of the distance from one region and others the inverse of thedistance expressed in km. This distance matrix has an interesting economic meaning: theincrease of distance reduces the strength of ties between a given region and neighbouringregions.

In other words, this index implicitly assumes that spillover effects, apart the distance,just depend on employment levels (the concentration of employment), regardless the typeof employment of neighbouring regions. Conversely, factors such as quality of employment(skilled/unskilled workers) and/or employment specialization, or other similar factors, mayplay a role in determining the spillover effects. Unfortunately, the non-availability of morespecific data does not allow us to have a more polished index when estimating the effect ofspatial spillovers.

Besides, it is important to highlight that the lack of disaggregate data regarding the employ-ment variable could generates bias in the econometric analysis. In particular, if we assumethat skilled workers generate a higher increase in the production than unskilled workers,considering in the analysis a homogenous employment indicator such as the number of totalworkers (both skilled and unskilled) rather than a disaggregated one, could falsify towardsthe top or towards the bottom to the effect on production. In other words, if total employmentis driven by unskilled (or skilled) workers, we may observe a misrepresentation of spillovers’effects on production towards the bottom (or the top). However, the non-availability of dis-aggregate data with regard to the quality of employment (skilled/unskilled workers) does notallow to control for this effect.

3 Methods

In this paragraph we introduce the methodologies used in our analysis. First of all, thestochastic frontier approach allow us to verify the impact of agglomeration externalities on theperformance of the regional production processes (Sect. 3.1). Second, the beta-convergence

2 Porter externalities (Porter 1990), which represent a cross between MAR and Jacobs thesis, are expressed

by the following indicator: Pi jt = (f irmi j t

/si j t

)/(

∑

i

∑

jf irmi j t

/∑

i

∑

jsi j t

)

, where f irmi j t indicates

the number of firms in sector j in region i at time t . Due to the unavailability of the number of firms by sector,we are not able to get this indicator and therefore it will be omitted from our analysis.

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analysis allow us to verify the existence of convergence in the Italian regional performance(Sect. 3.2).

3.1 Stochastic frontier analysis

Building on the work of Mastromarco and Woitek (2006), we consider a standard growthmodel with externalities. In particular, we assume a Cobb-Douglas production functionwhere, besides considering production, labor and the stock of capital (respectively, Yi,t , Li,t

e Ki,t ), we also include territorial externalities (M ARi,t and Ji,t ) that, together with techno-logical progress denoted by Ai,t , represent the total factor productivity level (TFP3) (Cinganoand Schivardi 2005). This relation is given by Yi,t = F

(Ai,t , Li,t , Ki,t , M ARi,t , Ji,t

).

Assuming that agglomeration externalities and technological progress are external to firms,we model them in the following way:

Yi,t = Ai,t ∗ M ARβ3i,t ∗ Jβ4

i,t ∗ f(Li,t , Ki,t

)

TPFi,t = Ai,t ∗ M ARβ3i,t ∗ Jβ4

i,t (1)

Consequently, the function we estimate under spatial spillovers hypothesis is the followingone:

Yi,t = Ai,t ∗ M ARβ3i,t ∗ Jβ4

i,t ∗ W Eβ5i,t ∗ f

(Li,t , Ki,t

)

TPFi,t = Ai,t ∗ M ARβ3i,t ∗ Jβ4

i,t ∗ W Eβ5i,t (2)

Our analysis will proceed in two steps. First, we consider a model where inefficiency is afunction of agglomeration externalities only (Eq. 1), then we implement a model that alsoincludes spatial spillovers among the factors leading to inefficiency (Eq. 2). Finally, wecompare how the spillover effects affect the determination of efficiency.

We model agglomeration externalities as a spillover effect that increases the productivity ofall inputs by increasing efficiency (Hulten and Schwab 1993). Our Cobb-Douglas productionfunction will have the following form:

Yi,t = �i,t ∗ Lβ1i,t ∗ K β2

i,t , i = 1, . . . , 20; t = 1970, . . . , 1993 (3)

where �i,t = Aτi,tωi,t , where A denotes the level of technology, τi,t is an efficiency measure,with 0 ≤ τi,t ≤ 1, and ωi,t is a measurement error.

Writing Eq. (3) – the frontier function- in logarithms we obtain:

yi,t = α + β1li,t + β2ki,t + εi,t + ηi + ηt , i = 1, . . . , 20; t = 1970, . . . , 1993 (4)

We also include a time effect ηt that allows for uniform influence of shocks, and a set ofregional dummies with the aim of capturing the unobserved heterogeneity of regions (ηi ).

with εi,t = vi,t − ui,t

where ui,t = − ln(τi,t

)is a non-negative random variable and νi,t = ln

(ωi,t

). Expected

inefficieny – inefficiency function - is given by:

E[ui,t

] = zi,tλ (5)

where ui,t are assumed to be independently but not identically distributed, zi,t is the vectorof variables which influence efficiency and λ is the vector of coefficients (Mastromarco and

3 TFP measures the output growth attributable to technical progress and to efficiency in the combination ofproduction factors.

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Woitek 2006). A single-stage Maximum Likelihood allows us to estimate both the parametersof the production function and those in Eq. (5) (Kumbhakar et al. 1991; Battese and Coelli1995).

We consider four different specifications for ui,t4. In the first model, inefficiency is a

function of MAR externalities and of Jacobs externalities:

E[ui,t

] = λ0 + λ1 M ARi,t + λ2 Ji,t + ηi + ηt (6)

The second model also takes into account spatial spillovers:

E[ui,t

] = λ0 + λ1 M ARi,t + λ2 Ji,t + λ3W Ei,t + ηi + ηt (7)

The third model takes into account the differences in the reaction of inefficiency dependenton the region (Mastromarco and Woitek 2006). We consider a slope dummy variable Di,t ,which is equal to one for Northern and Central Italy regions and is equal to zero for Southernregions5 (Mastromarco and Woitek 2006). This specification allow us to verify whether theimpact of externalities is stronger in Northern and Central regions rather than in Southernones.

E[ui,t

] = λ0 + (λ11 + λ12 Di,t

)M ARi,t + (

λ21 + λ22 Di,t)

Ji,t + ηi + ηt

Di,t ={

1 i f i = C N0 i f i = S

(8)

Finally, the fourth model adds spatial spillovers to the third model (8):

E[ui,t

] = λ0+(λ11 + λ12 Di,t

)M ARi,t +

(λ21 + λ22 Di,t

)Ji,t +(λ31 + λ32) W Ei,t +ηi +ηt

(9)Externalities modelled in this way are interpreted as determinants of inefficiency becausethey directly explain the inefficiency results of regions.

3.2 Spatial analysis of beta-convergence

In this paragraph we develop a spatial econometric analysis of beta-convergence. In thecase we consider 6 , beta-convergence implies that the regional performance growth rateis connected with the initial efficiency score. In particular, there is beta convergence whenlow performance regions grow faster than high performance ones, resulting in the formereventually catching up to the latter in production performance 7.

In our analysis we consider econometric models which include spatial effects. Thesemodels are relevant if there are spatial spillovers among neighbouring regions (spatial depen-dence), or when an artificial spatial framework (regions in our case) does not correspond tomarket processes (nuisance dependence) (Anselin and Rey 1991; Rey and Elias 2011).

4 Since there are a multitude of regional-specific and time-specific factors that could influence the efficiencyof regions, we control, also in the inefficiency function, for the time effect (ηt ) and the regional dummies (ηi ).5 Northern and Central Italy (NC): Piemonte (PIE), Valle d’Aosta (VDA), Lombardia (LOM), Liguria(LIG),Trentino Alto Adige (TAA), Veneto (VEN), Friuli Venezia Giulia (FVG), Emilia Romagna (EMR),Toscana (TOS), Umbria (UMB), Marche (MAR), Lazio (LAZ). Southern Italy (S): Abruzzo (ABR), Molise(MOL), Puglia (PUG), Campania (CAM), Basilicata (BAS), Calabria (CAL), Sicilia (SIC), Sardegna (SAR).6 The analysis of beta convergence is usually focused on per capita income (see Arbia 2005).7 It is important to highlight that in this study we only deal with absolute convergence.

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We start the convergence analysis with an OLS model, followed by diagnostic spatial testswhich allow to control for spatial effects. Here the OLS model is:

ln

(Yi,t+1

Yi,t

)= α + β ln

(Yi,t

) + δSOUTH + ηi + ηt + εi,t (10)

where the dependent variable is the yearly performance rate (efficiency scores), the regressoris the logarithm of performance of region i at time t , ηi represents a specific regional effect, ηt

represents a specific temporal effect and εi t is the stochastic error term. In addition, becausethe geography of Italian regions is characterized by a strongly polarized structure, we includea dummy variable (SOUTH), with the aim of identifying Southern regions. This allows usto control for the differences that characterize the two regional areas (Central-Northern Italyand Southern Italy).

In order to assess spatial effects we implement four tests, in particular the LangrangeMultiplier tests. Two of them (LM-Lag and Robust LM-Lag) allow us to assess whether thespatial lag model is a better alternative than the OLS model; on the contrary, the two lastones, i.e. LM-Error and Robust LM-Error allow us to test whether the spatial error model isthe best alternative to the OLS model. The robust version of these tests has to be consideredonly when the standard version (LM-Lag and LM-Error) is significant (Rey and Elias 2011).

Overall, we consider three models with spatial effects (Rey and Elias 2011): each of themallows for a different interpretation of the convergence process.

In particular, we consider the spatial error model:

ln

(Yi,t+1

Yi,t

)= α + β ln

(Yi,t

) + δSOUTH + ηi + ηt + (I − ζ W )−1 ui,t (11)

where ζ is a scalar spatial error coefficient, u ∼ N(0, σ 2 I

), W is the contiguity matrix, ηi

and ηt are defined as above. Equation (11) captures the possible effect that the performancegrowth rate in a given region where the shock occurred may affect the performance growthrate of other regions through the spatial transformation (I − ζ W )−1.

The spatial lag model is:

ln

(Yi,t+1

Yi,t

)= α + β ln

(Yi,t

) + δSOUTH + ρW ln

(Y j,t+1

Y j,t

)+ ηi + ηt + εi,t (12)

where ρ is the scalar spatial auto regressive parameter, and ηi and ηt are defined as above.Finally, we consider a spatial cross-regressive model where the spatial lag of efficiency

score is added to the original specification:

ln

(Yi,t+1

Yi,t

)= α + β ln

(Yi,t

) + δSOUTH + τW ln(Y j,t

) + ηi + ηt + εi,t (13)

where τ is the parameter associated with the cross-lag term, ηi and ηt are defined as above.We consider the last specification, as the omission of the cross-lag term could determinespatially correlated errors. This model allows us to tackle the question of spillover effects ina different way from the spatial lag model.

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4 Data used and stochastic frontier analysis results

The analysis will be conducted on the data of the 20 Italian regions for the period 1970–938. Data has been obtained from CRENOS (Centre for North South Economic Research)9. The output measure is regional GDP at constant 1985 prices, the capital stock is alsoexpressed at constant 1985 prices, the measure for labor input is the number of employedpeople. Moreover, since the number of employees in different production sectors is useful forcomputing the indexes that express territorial externalities, we also consider the employeesin five manufacturing sectors10, the employees in four service sectors11, the employees in theconstruction sector, the employees in the fuel and power products sector and the employeesin mining and chemical sectors. All variables are expressed in logarithms.

Although our data are quite outdated, Italy always represents an important case of studyand reference for regional scientists. The interest of the Italian experience lies in the differentconvergence path of the two groups of regions: those intermediate for the geographicalposition and the level of development in the 50’s, the North-East and Central regions, and thefarthest and least developed regions of Southern Italy. Within a general long-term pattern ofregional inequality, these two groups of regions have behaved differently. The first ones startedto converge very soon and very quickly, so that at the beginning of the 90’s they were perfectlyintegrated with the regions that were initially, in the 50’s, the most developed,ones, i.e. regionslocated in the North-West of Italy. In this case the neoclassical adjustment mechanism, basedon decreasing returns of capital, may be accepted as a satisfactory explanatory hypothesis.On the other hand, Southern regions also converged but in a more restricted period. In thiscase, regional policy, rather than the neo-classical equilibrating forces, has been the principalexplanatory factor.

We believe that data can tell us important things about Italian economic dualism and themethodology used will allow us to get additional information on the time period analyzed.

It is well known that administrative data aggregate individuals on the basis of arbitrarygeographical boundaries reflecting political and historical situations. The choice of the spa-tial aggregation unit is therefore essential as different choices may lead to different results inthe estimates. Regional data cannot be considered “independently generated” (Anselin 1988;Anselin and Bera 1998) because of spatial similarities of neighbouring regions; thus, stan-dard estimation procedures12 can provide biased estimators of the parameters. The regionaldimension could be sometimes too wide to correctly identify the specialization of a specificterritory. We cannot exclude that a region, especially if particularly extended, is character-ized by different specialization in different districts. Hence, the aggregation at regional levelreduces the information and does not give rise to the heterogeneity present in highly dis-aggregated data. On the contrary, aggregating data at provincial level will allow for spatialeffects, such as spatial spillovers, to be properly modelled (Arbia 2005). However, since dataat provincial or district level (e.g. local labour systems) are not available, we are forced touse at regional data.

8 The observation period is restricted to the years 1970-93 because at the moment more recent data are notavailable.9 Regio-IT1970-2004 and Regio(cap)-IT_70-94 (www.crenos.it).10 Minerals and non-metallic mineral products; Metal products and machinery and transport equipment;Food, beverages, tobacco; Textiles and clothing, leather and footwear; Paper and printing products; Wood,rubber and other industrial products.11 Trade, hotels and public establishment; Transport and communication services; Credit and insuranceinstitutions; Other market services.12 That is, estimates that do not take into account spatial dependence.

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www.crenos.it


Table 1 Statistical summary

Variable Mean SD Min Max Observations

GDP (Yi,t ) Overall 10.04341 1.1109 7.3804 12.1599 N = 480

Between 1.1224 7.5797 11.9080 n = 20

Within 0.1865 9.6031 10.3773 T = 24

Capital (Ki,t ) Overall 11.9989 0.9735 9.5124 14.0232 N = 480

Between 0.9623 9.8894 13.6795 n = 20

Within 0.2570 11.3282 12.5375 T = 24

Labour (Li,t ) Overall 6.5820 1.0297 3.9627 8.30825 N = 480

Between 1.0533 4.0413 8.2473 n = 20

Within 0.0627 6.4052 6.7208 T = 24

MAR Overall 0.3658 0.2525 0.0267 1.0649 N = 480

Between 0.2484 0.0720 0.8878 n = 20

Within 0.0706 0.1153 0.6432 T = 24

J Overall 1.7220 0.5528 0.4961 3.3571 N = 480

Between 0.5159 0.9124 2.8145 n = 20

Within 0.2284 0.9525 2.4151 T = 24

WE Overall 7.02893 0.1530 6.6568 7.4044 N = 480

Between 0.1460 6.7551 7.3453 n = 20

Within 0.0557 6.9160 7.1151 T = 24

MAR Marshall, Arrow, Romer externalities, J Jacob externalities, WE spatial spillovers

Table 1 reports the statistical summary of the logarithm of the variables analysed. We showthe variance decomposition in two components: the between or inter-regional variability,that embodies the permanent differences among regions and the within or intra-regionalvariability, that relies on time observations by country and that considers the position ofeach region at each date compared to his average over the whole period. We may note thatthe between variability is higher than the within variability for all variables considered. Inparticular, we may observe that the range of variation of specialization externalities (MAR)is quite large (about 1, with a minimum value which tends to zero and a maximum valueslightly greater than one): this highlights the presence of regions characterized by low levelof specialization that are opposed to highly specialized regions. The range of variation of thediversification externalities (J) is almost three times the range of specialization externalities(2.8, with a minimum value of 0.5 and a maximum value slightly higher than 3): also in thiscase we observe two opposite situations, i.e. regions characterized by little diversificationand regions that are very diversified. Finally, the variable measuring spatial spillovers (WE)presents a much smaller range of variation (0.7, with a minimum of 6.6 and a maximum ofabout 7.5). This highlights a minor difference, in terms of spillover, among Italian regions;besides, we may note that the spillover effect has a wide spread and that it is independentfrom regional specialization and diversification.

In Table 2 we report the estimates results of the models considered13. The Likelihoodratio test, rejecting the null hypothesis in all four cases, confirms the presence of technical

13 We implement the same analysis controlling for a country-specific deterministic trend; in particular, wedefine a tdi variable, where t is a polynomial in time and di is a regional dummy. The results are similar tothose reported in Table 1; for reasons of space we do not show them, interested readers can request them tothe authors.

123


inefficiency (for critical values of the test see Kodde and Palm 1986). In addition, the signif-icance of the parameter γ , i.e. the ratio between the variance of the inefficiency term σ 2

u andthe sum of the total variance σ 2

v + σ 2u = σ 2, shows that 86 % (column 1), 72 % (column 2),

74 % (column 3) and 12.5 % (column 4) of the output change among Italian regions is dueto differences in their technical inefficiencies. Log Likelihood values, being higher, alwayslead to prefer the model with spatial spillovers to the one without them.

With regard to the first model, all parameters of the production function are significant andhave the correct sign. In particular, the elasticity of capital is equal to 0.53 while labor elasticityis equal to 0.55 (column 1). The effects of MAR and Jacobs externalities have a negativeeffect on efficiency, leading to a reduction. With regard to MAR externalities, the negativeeffect of specialization on efficiency could be explained by the fact that a high specializationgenerates low flexibility and poor adaptability of products, technologies and infrastructurewhen the sector is in decline; on the contrary, more flexible sectors would be more able toconvert their operations (Combes 2000). The negative effect of specialization on the efficiencyrefers to industrial and services sectors (see footnotes 6 and 7) (Combes 2000). Jacobsexternalities, with their positive sign, show that a higher level of production diversificationmakes regions less efficient. Combes (2000) observes a positive relationship with urbanizationeconomies only for the high-tech industrial sector, while he verifies a negative relationshipfor traditional industrial sectors. The negative impact of Jacobs externalities on the efficiencyof the production process is supported both by the work of Henderson (1997) and Combes(2000), who found the presence of urbanization economies only for new industries, not forthe nature ones.

By examining column (2) we can note that MAR and Jacobs externalities as well as beingsignificant, still retain their negative impact on efficiency. On the contrary, the coefficientassociated with spatial spillovers, as well as being significant, has a negative sign thus showingits positive effect on efficiency. It is evident that the externalities associated with industrialagglomeration through spillover effects generated by the concentration of employed peoplein the regions close to a given region have a positive effect on the production process ofthat region. In our case, given the positive impact of spatial spillovers on efficiency, we lookat what is called “concentrated development”, that is expected when regions get a positivebenefit from external growth opportunities (Capello 2009).

With the introduction of regional effects in the other two specifications of the model(columns 3 and 4), the reading of the results becomes more complicated. For this reasonwe introduce a different way of interpreting this results, as suggested by Mastromarco andWoitek (2006):

dτ = −τλidzi

zi(14)

Hence, we can express the results as change in efficiency due to a percentage change inexternalities. For example, by calculating (14) in terms of mean efficiency (equal to 0.8553,column 1 in Table 2), we obtain that a 10 % increase in MAR and Jacobs externalitiesleads to an efficiency change equal to −4 % (MAR) e −0.4 % (Jacobs). This highlights thenegative impact of both externalities and the higher impact of MAR externalities comparedwith Jacobs externalities.

In Table 3 we report the results of (14) for the different estimates proposed. By observingcolumn 2, in addition to verifying the continuing negative impact of MAR and Jacobs exter-nalities on efficiency, we may note that spatial spillovers have a positive effect, equal to 4 %,on efficiency.

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Tabl

e2

Res

ults

Var

iabl

esB

asic

mod

elR

egio

nalm

odel

With

outs

patia

lsp

illov

ers

(1)

With

spat

ial

spill

over

s(2

)W

ithou

tspa

tial

spill

over

s(3

)W

ithsp

atia

lsp

illov

ers

(4)

Fron

tier

func

tion

Con

stan

t0.

1675

*(1

.749

9)0.

4540

***

(4.3

512)

0.02

53(0

.331

5)0.

4497

***

(6.1

125)

Cap

ital

0.53

29**

*(3

5.21

12)

0.45

85**

*(2

5.40

18)

0.55

39**

*(4

6.90

51)

0.45

95**

*(3

5.69

03)

Lab

or0.

5534

***

(39.

0471

)0.

6454

***

(34.

1017

)0.

5341

***

(49.

1599

)0.

6387

***

(47.

2472

)

Tim

eef

fect

yes

yes

yes

yes

Reg

iona

ldum

mie

sye

sye

sye

sye

s

Inef

ficie

ncy

func

tion

cost

ant

−0.1

061*

*(−

2.44

48)

3.14

56**

*(1

1.73

04)

0.27

20**

*(6

.498

0)2.

3795

***

(10.

3614

)

MA

R0.

4660

***

(13.

0338

)0.

3675

***

(8.5

651)

0.07

84**

(2.2

987)

−0.0

086

(−0.

2122

)

J0.

0470

**(2

.987

3)0.

0597

***

(3.6

942)

−0.0

379*

*(−

2.10

69)

−0.1

016*

**(−

4.73

08)

WE

−0.4

606*

**(−

11.5

209)

−0.2

867*

**(−

8.33

64)

D*M

AR

−0.4

426*

**(−

6.89

38)

−0.2

713*

**(−

4.15

69)

D*J

−0.0

429*

**(−

4.90

71)

0.07

06**

*(2

.752

7)

D*W

E−0

.026

1***

(−2.

7709

)

Tim

eef

fect

yes

yes

yes

yes

Reg

iona

ldum

mie

sye

sye

sye

sye

s

σ2

0.00

82**

*(1

0.03

89)

0.00

57**

*(1

0.10

64)

0.00

45**

*(1

0.52

32)

0.00

31**

*(1

7.54

73)

γ=

σ2 u

σ2 v+σ

2 u0.

8662

***

(20.

3906

)0.

7202

***

(9.1

487)

0.74

21**

*(1

0.43

78)

0.12

52**

*(8

.668

4)

LR

test

ofσ

2 u=

037

1.22

50**

*50

3.10

71**

*64

2.00

08**

*71

1.41

07**

*

Log

likel

ihoo

d54

1.72

4560

7.66

5667

7.11

2571

1.81

74

Mea

nef

ficie

ncy

0.85

530.

8562

0.87

060.

8874

***,

**,*

:1%

,5%

,10

%;(

):ts

tatis

tics

123


Table 3 Efficiency change compared to percentage change in externalities

Externalities Italy (basic model) NC (regional model) S (regional model)

(1) (2) (3) (4) (3) (4)

MAR −4 % −3 % 3 % 2.4 % −0.7 % Not significant

J −0.4 % −0.5 % 0.7 % 0.3 % −0.3 % 0.9 %

WE 4 % 2.8 % 2.5 %

By focusing on regional analysis, we observe that in the case without spatial spilloversthe differences between the two areas of the country are substantial (column 3). In particular,we verify that the productive efficiency of Central and Northern Italy is positively influencedby both specialization and urbanization externalities (Paci and Usai, 2000, Henderson et al.1995). We find an opposite situation for Southern Italy, where the effect of both externalitiesresults to be negative. The only thing that unites the two Italian areas is given by the minorweight of Jacobs externalities compared to MAR externalities.

Finally, in the fourth model (column 4), we observe that MAR externalities have no effecton Southern regions, whereas Jacobs externalities register a positive impact on efficiency. It isworth stressing that spatial spillovers produce a positive impact on both areas of the country,more pronounced in Central and Northern Italy than in Southern Italy (2.8 vs 2.5 %).

Two main findings arise from these estimates results. First of all, regional productiondynamics are highly interdependent (spatial spillovers are significant and positive). Sec-ond, their link intensity grows as the distance among regions reduces. In particular, regionssurrounded by neighbours with a high propensity to growth tend to have a greater develop-ment, all other things being equal. The opposite effect is obtained for regions surroundedby neighbours with a low propensity to growth. These findings open new directions forfuture research, particularly in the investigation of the sources of spillovers between geo-graphical regions. Their existence also raises a question about the design and the aim forpolicies to stimulate development at the local level. In particular, policies with the aim ofencouraging local development should consider the externalities that may occur betweenneighbouring areas as a result of their actions, and if they turn out to be positive the com-petent authorities should facilitate their dissemination. In this case, due to spillover effects,it would develop a “domino effect” that would involve not only the region where localdevelopment policy has been implemented, but it would also positively affect neighbouringregions.

4.1 Importance of spatial spillovers on regional efficiency

In this section we want to answer the following question: how important are spatial spilloversin determining the efficiency of individual regions? In this regard we report in Table 4 theefficiency ranking for each region, by considering the results arising from the assumptionson the ui,t term (presence and absence of spatial spillovers) in Eqs. (6) and (7).

The efficiency ranking analysis for the year 1993, the most recent one, identifies thepresence of three groups of regions. The first group is composed by regions that show thesame position in the rankings, i.e. Piemonte, Emilia-Romagna, Veneto, Friuli Venezia Giulia,Liguria, Marche, Puglia, Calabria and Sicilia (indicated by (*)). The second group consistsof regions which benefit from the positive effects of spatial spillovers, thus improving theirranking and their efficiency score: Valle d’Aosta, Trentino Alto Adige, Abruzzo, Umbria,Molise, Basilicata and Sardegna (indicated by (+)). The third group includes regions located

123


Table 4 Efficiency scores and efficiency ranking, 1993

Macro Area Regions Without spatial spillovers With spatial spillovers

Efficiency score Efficiency ranking Efficiency score Efficiency ranking

Northern Italy PIE (*) 0.9356 7 0.9382 9

Northern Italy VDA(+) 0.8803 12 0.9714 3

Northern Italy LOM(−) 0.924 9 0.9078 12

Northern Italy TAA(+) 0.8956 11 0.9418 8

Northern Italy VEN(*) 0.9191 10 0.9148 10

Northern Italy FVG (*) 0.9737 2 0.9791 2

Northern Italy LIG (*) 0.9868 1 0.9891 1

Northern Italy EMR(*) 0.9627 3 0.9626 4

Central Italy TOS (−) 0.9509 5 0.9467 7

Central Italy UMB(+) 0.9455 6 0.9581 6

Central Italy MAR(*) 0.9583 4 0.9587 5

Central Italy LAZ (−) 0.9306 8 0.9145 11

South Italy ABR(+) 0.8778 13 0.8912 13

South Italy MOL(+) 0.7597 18 0.8054 16

South Italy CAM(−) 0.7664 17 0.7581 19

South Italy PUG (*) 0.8279 15 0.8173 15

South Italy BAS (+) 0.7181 19 0.7616 18

South Italy CAL (*) 0.6929 20 0.7111 20

South Italy SIC (*) 0.7709 16 0.7788 17

South Italy SAR (+) 0.829 14 0.8621 14

(−), (+), (*) first, second and third group, respectively

at the bottom of the ranking as they suffer a loss of efficiency due to the presence of spatialspillovers: Lombardia, Toscana, Lazio, Toscana, Lazio and Campania (indicated by (−)). Thisresult is justified by the fact that “... there are cases where the growth potential developedby a region adversely affects the growth of neighboring regions which become donors oftangible and intangible resources, and thus become subject to gradual impoverishment andeconomic decline” (Capello 2009).

These results are very important because they reveal substantial differences among Italianregions due to the presence of spatial spillovers. In particular, their effects is not obvious:in fact, some regions benefit from their presence, while some others are indifferent or sufferfrom a negative effect in terms of efficiency.

By observing Figs. 1 and 2, we can note that spatial spillovers affect the results in terms ofefficiency. In particular, after considering spatial spillovers, we may note a reduction of theconcentration and an increase of the diffusion process of efficiency among Italian regions. ForNorthern and Central regions, we can observe a kind of osmosis between “donor” regions,which lose efficiency, and “receiving” regions, which gain in efficiency (Capello 2009).The concepts of donor and receiving regions find their justification in our results, that arealso in line with Pagnini’s findings (2005). In particular, Pagnini (2005) concludes that thegeographical spread of growth has strong elements of geographical viscosity. Based on thisresult, it is interesting to check whether, for example, at the origin of industrial take-offof some Central and North-East regions there has been their geographical proximity to theNorth-West regions, which still in the sixties showed high rates of employment growth in

123


Fig. 1 Efficiency scores without spatial spillovers, year 1993

Fig. 2 Efficiency scores with spatial spillovers, year 1993

some areas. The next two decades, the North-West regions would begin to show signs ofa slowdown for the effect of congestion costs due to the high employment density, andthis could largely explain the loss of efficiency of these regions. Central and North-Eastareas, however, would carry in their growth thanks to the self-propelling push which derivedfrom the spillovers generated between groups of neighboring regions characterized by highgrowth.

For example, we can see how Lombardia changes from a dark grey in Fig. 1 (a moreefficient region in the model without spatial spillover) to a light grey in Fig. 2 (a less effi-cient region in the model with spatial spillover): in this case, we can identify this regionas a donor one. On the contrary, Trentino Alto Adige changes from a light grey in Fig.1 (a less efficient region in the model without spatial spillover) to a dark grey in Fig. 2(a more efficient region in the model with spatial spillover): in this case, we can iden-tify this region as a receiving region. This result is justified by the fact that Lombar-dia (a donor region) mostly borders on North-East regions (Veneto, Trentino Alto-Adige,Emilia Romagna) that turn out to be, considering Pagnini (2005) hypothesis, receivingregions; these regions would exploit the ability to produce spillovers of Lombardia therebyimproving their production capacity. The presence of growing congestion costs in theNorth-West of Italy and the proximity of regions unable to develop spillovers could havereduced the productive efficiency of Lombardia. We do not obtain the same result forPiemonte, which mostly borders on North-West regions: in this case, Piemonte could nothave suffered a loss of efficiency in its production process because the growth of con-

123


Fig. 3 Evolution of efficiency scores at macro-area level. a model with spatial spillovers. b model withoutspatial spillovers

gestion costs could have been partly damped by the proximity of regions able to developspillovers.

5 Is there convergence in the performance of Italian regions? Beta-convergenceanalysis

An important question is the following one: is there a convergence process in the performanceof Italian regions?

Before we proceed with the beta-convergence analysis we introduce a brief analysis ofefficiency scores of Central-Northern Italian regions and Southern ones. In particular, inorder to examine the change of efficiency over time, Fig. 3 plots the mean efficiency scoresfor each year for North-Central regions (NC) and Southern regions (S). In the observationperiod, production in North-Central regions with a mean efficiency score equal to 0.90, iscloser to the common frontier than Southern regions, which show a lower mean efficiencyscore (0.80). In addition, we may observe a constant trend of efficiency scores that revealsa persistent gap in terms of performance between North-Central and Southern regions. Thedualism between the North-Center and the South of Italy that emerges from the analysisof the productive performance does not seem to decrease over time and consequently noconvergence process seems to be taking place among the two macro-areas. This result is

123


true for both estimated models (Fig. 3a and b). In other words, spatial spillovers do not helpSouthern regions to catch-up with North-Central regions.

Now we verify by more sophisticated tools the presence (or the lack) of the convergenceprocess in the Italian regional performance.

In particular, Table 5 shows the results of the OLS estimates for Eq. (10) for the efficiencyscores of both models (without and with spatial spillovers).

For both models, the parameter beta is significant with the expected negative sign, there-fore indicating a process of convergence. In addition, the dummy variable that controls forthe South has a negative sign and is significant: this shows that the convergence process hasoccurred not only at national level but also in Southern Italy, which has begun to convergein the direction of its own steady-state. These results confirm the presence of two clusters ofregions and, therefore, the presence of a polarization process in terms of productive perfor-mance.

However, for both models the diagnostic tests for spatial effects, both the standard andthe robust version of the LM-Error test, did not reject the null hypothesis of absence ofspatial relation in the error term. In addition, the diagnostic test for checking a potentialspatial relation in the dependent variable (LM-Lag and Robust LM-Lag) never rejects thenull hypothesis, both in the standard and in the robust version, and therefore it exclude apotential spatial relationship in the dependent variable.

In summary, for both models the tests exclude the presence of spatial effects in the con-vergence process. However, these tests tell us nothing about the cross-lagged term, thereforewe provide to estimate Eq. (13).

We conclude our analysis by considering the estimates of Eq. (13). For both models, theparameter beta is significant with the expected negative sign and with a higher impact thanprevious estimates. The parameter associated with the dummy that controls for the South issignificant, with negative sign, and its value is similar to the one estimated in Eq. (10).

The parameter associated with the spatial lag of the regressor is not significant (τ ). Thediagnostic tests for spatial effects, both in the dependent variable and in the error term, do notreject the null hypothesis of no spatial effects, both in the standard and the robust version.

As a consequence, for both models (without and with spatial spillovers) the best fittingmodel to the data is the classical equation (10) of convergence, because of the lack of signif-icance of the cross-lag.

These results show a persistent dualism on the regions performance in the productionprocess. Dualism persists also after controlling for the spatial spillovers (model with spatialspillovers).

The lack of a convergence process and the possible formation of a polarization process isusually attributed to the possibility that the two subareas of Italy (North-Centre and South)converge toward different steady states (Cosci and Mattesini 1995). In literature, mainlyhistorical and structural factors are considered as causes of divergence, such as the lackof infrastructure and the high crime rate in Southern Italy (Cosci and Mattesini 1995).The policy implication of our analysis is that, in the context of a regional-level produc-tion frontier, there is evidence that agglomeration economies and spatial spillovers are notsufficient to ensure the convergence process, consequently infrastructure investment (roads,airports, railroads and subway, ports, electrical lines and water, and telecommunication) andreduction of crime and corruption may positively influence technical efficiency (Mastro-marco and Woitek 2006). Unfortunately, the aim of this work is not to assess the impactof infrastructure and crime rate on regions’ performance, but future research will exam-ine the impact of these factors on the convergence process of the performance of Italianregions.

123


Tabl

e5

Res

ults

With

outs

patia

lspi

llove

rsW

ithsp

atia

lspi

llove

rs

OL

Sm

odel

(Eq.

10)

Spat

ialc

ross

-reg

ress

ive

mod

el(E

q.13

)O

LS

mod

el(E

q.10

)Sp

atia

lcro

ss-r

egre

ssiv

em

odel

(Eq.

13)

β−0

.048

***

(−3.

465)

−0.0

52**

*(−

3.67

6)−0

.036

***

(−2.

955)

−0.0

42**

*(−

3.34

7)

τ−1

.216

(−1.

44)

−1.4

51(−

1.57

)

SOU

TH

−0.0

10**

*(−

3.29

8)−0

.010

***

(3.3

03)

−0.0

07**

(−2.

812)

−0.0

07**

*(−

2.90

8)

Reg

iona

ldum

mie

sye

sye

sye

sye

s

time

dum

mie

sye

sye

sye

sye

s

LM

-Lag

0.68

03[0

.409

]0.

8210

[0.3

65]

0.65

40[0

.419

]0.

8702

[0.3

51]

Rob

ustL

M-L

ag2.

3593

[0.1

25]

2.45

88[0

.324

]1.

5621

[0.2

11]

1.24

21[0

.344

]

LM

-Err

or0.

8115

[0.3

68]

1.12

53[0

.289

]0.

7321

[0.3

92]

1.11

61[0

.291

]

Rob

ustL

M-E

rror

2.49

05[0

.115

]2.

7025

[0.1

25]

1.64

03[0

.200

]1.

3434

[0.2

56]

Log

likel

ihoo

d1.

2658

e+00

31.

2669

e+00

31.

3534

e+00

31.

3553

e+00

3

***,

**,*

sign

ifica

ntat

1%

,5%

,10

%;(

):ts

tatis

tics;

[]:p

valu

e

123


6 Conclusions

In this paper, we have examined the influence of agglomeration externalities and spatialspillovers on the production process of Italian regions. To this purpose, we have esti-mated a stochastic frontier production function on 20 Italian regions data for the period1970–93.

The results point out substantial differences in the Italian macro-areas. More specifically,we have verified that localization externalities and urbanization externalities positively affectthe productive efficiency of Central and Northern Italy regions. Hence, these results showthat production is positively affected by those sectors where the region appears to be spe-cialized and that a higher level of regions diversification favors the production process: “…it is important to make clear that these two externalities are not necessarily opposed, sincespecialization is a particular feature of a certain sector within a [regions] whilst diversity isa characteristic of the whole area” (Paci and Usai, 2000). On the contrary, the efficiency ofSouthern Italy regions suffers the positive influence only by diversification economies (aftertaking into account spatial spillovers).

Moreover, the spatial autoregressive term among the regressors reveals that spatialspillovers has a strong impact in determining a growth of efficiency of the production process.This highlights that the externalities produced in a specific local economy do not exert theireffects only within this location but that they cross the boundaries to influence the perfor-mance of other locations (Pagnini 2003). In fact it is rather restrictive to assume that spillovereffects run out only within the local economy in which they are generated, and it seems log-ical to assume that the interdependence degree between these economies is inversely relatedto distance.

In particular, “This spillover effect indicates that the spatial association patterns are notneutral for the economic performances of [Italian] regions. The more a region is surroundedby dynamic regions with high [employment], the higher will be its [productivity]. In otherwords, the geographical environment has an influence on growth processes. This corrobo-rates the theoretical results highlighted by the New Economic Geography.” (Baumont et al.2001).

Substantial differences among Italian regions arise when we take into account spatialspillovers effects on individual regions. In particular, spatial spillovers show a negative effecton the efficiency level of some regions, called the donor ones.

In addition, our results show a persistent dualism on the regions performance in theproduction process. In particular, we observe a polarization process due to the possibil-ity that the two subareas of Italy (North-Centre and South) converge toward differentsteady states. Since the agglomeration economies and spatial spillovers are not sufficientto ensure the convergence process between North-Centre and Southern regions, we rec-ommend policies that would help the Mezzogiorno to be more competitive and to catch-up, in terms of productive performance, with the more developed regions of North-CentreItaly.

Another interesting issue is related to the delay with which agglomeration externalitiesaffect production (Combes 2000). In this respect, Henderson (1997) shows that the mostsignificant impacts of localization externalities occur after three or four years, while thoserelated to urbanization externalities show increased persistence that extends up to eight years.In future work we could refer to a dynamic stochastic frontier model estimated by using thegeneralized method of moments (GMM) (Ahn et al. 1994; Ahn and Schmidt 1995; Ayed-Mouelhi and GOAIED 2003; Schmidt and Sickles 1984).

123


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