Francesco Quatraro Brick

Francesco Quatraro
email: francesco.quatraro@unito.it

O33 -Technological Change: Choices and Consequences|Diffusion Processes < O3 -Technological

Keywords: Diffusion JEL Classification Codes: O33, R11 Regional Innovation Capabilities, Growth Retardation, Diffusion La diffusion des capacités O33; R11 Die Diffusion des regionalen Innovationspotenzials: Belege anhand der Daten von italienischen Patenten In diesem Beitrag wird die Diffusion des regionalen Innovationspotenzials Region gestattet eine Kombination der Schumpeterschen Perspektive der Innovation und Geschäftszyklen mit der Theorie der Wachstumspole. Das Innovationspotenzial breitet sich werden empirische Belege aus den italienischen Regionen mit Diffusion von Innovationspotenzial in spät industrialisierten Regionen rascher voranschreitet als in früh industrialisierten Regionen. Ebenso werden die Rolle von Forschung und Entwicklung sowie die komplementären Änderungen in der Wirtschaftsstruktur untersucht. JEL Classification Codes: O33, R11 Regionales Innovationspotenzial Wachstumsverzögerung Diffusion Innovación regional Capacidades Retraso del crecimiento Difusión JEL Classification Codes: O33, R11

This paper investigates the diffusion of regional innovation capabilities within the manufacturing sector. The competence-based theory of the region allows for combining the Schumpeterian view upon innovation and business cycles and the growth poles theory. Innovation capabilities spread within the region after the expansion of the propulsive sector, due to learning dynamics. Adopting a methodology for the analysis of diffusion processes, the paper presents empirical evidence on Italian regions. The results show that in late-industrialized regions the diffusion of innovation capabilities is faster

Introduction

Different schools of thought have stressed the importance of innovation to regional competitive advantage in the last decades. On the one hand, the concept of learning regions refers to the capacity of areas featured by systemic ties, to enhance the creation of new knowledge and foster innovation [START_REF] Asheim | Industrial districts as 'learning regions': A condition for prosperity[END_REF]. On the other hand the Regional Innovation System (RIS) approach, drawing explicitly upon the notion of national innovation systems, has emphasized the relevance of interactive learning for the different kinds of actors involved in the innovation process [START_REF] Cooke P | Regional innovation systems: Institutional and organizational dimensions[END_REF].

Besides these perspectives, a new one recently emerged which extends the concept of firms capabilities to the regional domain. [START_REF] Foss | Higher-order industrial capabilities and competitive advantage[END_REF] proposed the concept of "higherorder capabilities", i.e. capabilities going beyond the scope of single firm command, which may be key to regional competitive advantage. The idea has been further articulated in the competence-theory of the region, where new knowledge is created by combining both internal and external resources. The density and the quality of network relationships, as well as the appropriate institutional endowment, are the main pillars of regional capabilities. These have to be accumulated over time, as they stem from daily activities and interactions of economic agents [START_REF] Foss | Higher-order industrial capabilities and competitive advantage[END_REF][START_REF] Lawson | Towards a competence theory of the region[END_REF][START_REF] Lorenz | Collective learning, tacit knowledge and regional innovative capacity[END_REF].

In particular, innovation capabilities may be defined as the degree of technological accumulation and the efficiency of search processes [START_REF]Sources, procedures and microeconomic effects of innovation[END_REF]. They emerge out of the learning process, and refers to the ability to both absorb and create technological knowledge [START_REF] Lall | Technological capabilities and industrialization[END_REF]. Areas characterized by institutional variety, high degrees of proximity among the innovating agents, low communication costs and relevant knowledge externalities, will hence show better technological performances, other things being equal [START_REF] Antonelli | Collective knowledge communication and innovation: The evidence of technological districts[END_REF][START_REF] Patrucco | Institutional variety, networking and knowledge exchange: Communication and innovation in the case of the Brianza technological district[END_REF][START_REF] Boschma | Knowledge Networks and Innovative Performances in an Industrial District. The Case of a Footwear District in the South of Italy[END_REF]. The appreciation of regional innovation capabilities provides an interesting bridge with Schumpeter's business cycles theory. The geographical bearings of Schumpeter's analysis have been emphasized by [START_REF] Perroux | Note sur la notion de 'pole de croissance[END_REF] and further articulated at regional level by [START_REF] Thomas | Growth pole theory, technological change and regional economic growth[END_REF]. On the one hand radical innovations enable sustained economic growth by creating new industries within the regional economy. On the other hand it allows firms within an industry to gain competitiveness.

Innovation efforts tend to emerge with a sensible delay with respect to the expansion stage of the industry within which they are generated. This is due to a delayed diffusion of innovation capabilities [START_REF] Schumpeter | Business cycles. A theoretical, historical and statistical analysis of the capitalist process[END_REF]. Industries grouping around the dynamic core then develop the set of competences and skills that make it possible the systematic application of knowledge to economic activities through the working of interactive learning and network externalities. Innovation capabilities hence gradually emerge within the propulsive industry, and then spread to closely related industries.

In this paper we enquire into the emergence of regional innovation capabilities within the manufacturing sectors, by grafting the regional capabilities approach into the analytical framework of innovation diffusion [START_REF] Griliches | Hybrid corn: An exploration in the economics of technological change[END_REF][START_REF] Mansfield | Technical change and the rate of imitation[END_REF]. We specifically focus on the diffusion of innovation capabilities within the manufacturing sectors, using patent applications as a reliable proxy. The context of the analysis consists of the 20 Italian regions in the 1981-2003 period.

The case of Italy within this picture is very peculiar. Indeed, already in the 1970s eminent scholars maintained that the Italian economic system was characterized by a 6 dualism in the industrial structure. On the one hand North-West regions were the cradle of modern industrial firms, and during the 1980s the manufacturing sectors had already completed their growth phase, leaving the floor to service industries. On the other hand, North-Eastern-Central (NEC) regions showed a delayed process of manufacturing activities, carried out mostly by small and medium sized enterprises (SMEs) often operating in peculiar economic and social environments [START_REF] Fuà | Industrializzazione nel Nord Est e nel Centro[END_REF]. It follows that the Italian case provides a good benchmark to investigate the patterns of diffusion of innovating capabilities, and its relationships with the stages of industrial development.

In this context, the contribution of this paper to the literature is twofold. On the one hand it aims at rejuvenating a field of enquiry which has been lacking appropriate consideration since the 1980s. For this reason, the debate about the economic development of Italian regions has somehow missed the important opportunity of investigating cross-regional differences in the light of the economics of innovation. On the other hand, such an analysis is also relevant for its theoretical implications concerning the relationships between development patterns and technological change.

The remainder of the paper is organized as follows. In Section 2 we articulate the theoretical framework and the working hypotheses. Section 3 presents the background economic context. Section 4 discusses the methodology and the data. In Section 5 we present the results of the empirical analysis. Finally the conclusions follow in Section 6. quest for innovations aims at opening new markets 2 . Although mainly focused on the demand side, an important link is identified therein, i.e. the one between innovation as a process of creative destruction and the reduction of industry's growth rates [START_REF] Kuznets | Secular Movements in Production and Prices[END_REF][START_REF] Burns | Production trends in the United States since 1870[END_REF].

In the retardation theory framework new industries emerge as an effect of radical innovation. This generates a cycle which terminates when the related technological opportunities are exhausted. Of course, not all industries declines at the same time, and performances of a region are strictly related to its leading industry 3 . When the expansion stage is exhausted, a clustering of innovations emerges within sectors, as an effect of delayed diffusion of innovation capabilities, which spread like a disease [START_REF] Schumpeter | Business cycles. A theoretical, historical and statistical analysis of the capitalist process[END_REF]. Innovating efforts are then stimulated in the decreasing stages of the business cycles by creative response mechanisms of firms which perceive the threat of new emerging sectors in the economic environment [START_REF] Schumpeter | The creative response in economic history[END_REF].

The recent research on innovation capabilities enhances the understanding of the process through which they emerge in regional contexts. Within a context shaped by Schumpeterian competition, firms dynamic capabilities stand for the "ability to integrate, build, and reconfigure internal and external competences to address rapidly changing environments" (TEECE et al., 1997: p. 516). Innovation and technological capabilities specifically denote the firm's capacity to combine internal and external sources of both tacit and codified knowledge, directed towards the introduction of product and process innovations (LALL,1992;[START_REF] Antonelli | The microdynamics of technological change[END_REF]. The emphasis on external linkages calls the attention upon factors going beyond the firm level. Higher-order innovation capabilities relates to knowledge which resides in the region, and "emerge in a historical process from the systemic interaction among firms" (FOSS, 1996: p.3). The different institutions involved in the innovation process need time to learn to interact. This requires iterate interactions, the development of common communication codes and the availability of effective channels to access external knowledge. Such a kind of learning is highly localized in the specific context in which it takes place. As a result, regional innovation capabilities are highly idiosyncratic and related to the conditions of the economic and institutional environment, and hence they are difficult to replicate in the same way in other regions [START_REF] Lorenz | Collective learning, tacit knowledge and regional innovative capacity[END_REF][START_REF] Antonelli | Collective knowledge communication and innovation: The evidence of technological districts[END_REF][START_REF] Romijn | Innovation, networking and proximity: Lessons from small high technology firms in the UK[END_REF].

Different propulsive industries feature diverse regional systems. Long after the growth stages, innovation capabilities come out as the result of learning activities, which gradually infect creative agents. The grafting of innovation capabilities framework into the diffusion theory provides suitable methodological tools to investigate such dynamics at the regional aggregate level. The pioneering work in this respect is the analysis of diffusion of hybrid corn across US states, carried out by [START_REF] Griliches | Hybrid corn: An exploration in the economics of technological change[END_REF].

Within epidemic models, bounded rationality, information asymmetries and networks effects are the major forces determining the characteristic S-shape of the diffusion process. Learning dynamics are gradual, and the working of communication channels is crucial to the diffusion of an innovation within a system. The increase in the number of adopters makes it available more information about the possible applications and 10 consequences of the innovation, and hence it helps the diffusion process within the particular subset of the social system which is defined by the potential adopters. This gradually reduces the uncertainty about the innovation, and stimulates its adoption [START_REF] Griliches | Hybrid corn: An exploration in the economics of technological change[END_REF][START_REF] Mansfield | Technical change and the rate of imitation[END_REF][START_REF] Hall | Innovation and Diffusion[END_REF].

According to the growth pole theory, industries tend to group around a central core of other industries, which act as catalyst to economic growth in the area. Proximity among firms enhances the probability of interactions and stimulates the flow of knowledge.

Innovation capabilities within local contexts are thus likely to emerge as the result of an endogenous process in which firms within the propulsive industry play as pioneers. The emergence of local competences can hence be seen as the outcome of learning processes occurring in time, triggered by local interactions and network effects.

Therefore the development of innovation capabilities by firms needs time to both ignite and propagate. In the early stages of the innovation cycle a few firms innovate and the system is characterized by low levels of technological performance. The stimulus to innovate spread to other firms, which realize the benefit from innovating within a competitive context. Where possible, they eventually commit financial resources to more formalized search activities. Where internal R&D is not feasible due to financial constraints, the availability of high quality public research centres within the region enhances the innovation capabilities of the system.

In such a context, the availability of effective protection tools may increase the returns to R&D. The higher returns to R&D in turn may well determine an increase in patenting activities [START_REF] Jaffe | The US patent system in transition: Policy innovation and the innovation process[END_REF][START_REF]Firms' decisions to innovate and innovation routines[END_REF][START_REF] Lerner | Unravelling the Patent Paradox[END_REF].

Moreover, patents also represent a tool through which firms can exchange knowledge on the markets, making it easier for interactive learning to work in environments characterized by the existence of strong systemic ties (LUNDVALL, 1992;[START_REF] Arora | Markets for technology[END_REF][START_REF] Peeters | Innovation strategy and the patenting behavior of firms[END_REF].

Drawing upon the argument elaborated so far, we may now spell out our hypotheses as follows:

1) Regional innovation capabilities emerge over time, as an outcome of the increase of innovation activities within the system, and the working of learning dynamics which enhance agents' capacity to interact and combine external with internal inputs. At the aggregate level this would amount to an initial exponential stage in which there is an explosion of technological performances, followed by a gradual saturation due to the infection of all potential innovators.

2) Regional innovation capabilities appear with a sensible delay with respect to the expansion of the propulsive industry within the area. This leads us to expect that over the same period, the speed of diffusion of regional innovation capabilities in an industry will be faster in areas where the expansion has come out late, than in areas where the same industry has developed earlier.

3) Regional innovation capabilities vary across different regions. In contexts characterized by the predominance of SMEs the interaction between firms and public research institutions is expected to be more crucial than in areas characterized by large firms. Italian regions in manufacturing sectors. However we firstly need to identify the different patterns the process of industrialization followed in different areas, in order to make it clear which one is early-industrialized and which is late-industrialized. This is the purpose of the following Section.

The Economic Context

In the 1950s most Italian regions were rural, and populated by a large share of smalland medium-sized enterprises, as opposed to North-Western regions, which specialized in manufacturing activities, carried out by large firms. Analyzing the distribution of growth rates and structural change at the regional level in the period 1950-1970, the Ancona School identified and found the clues of a successful diffusion process of manufacturing activities towards such rural regions in the North-East and eventually in Central Italy, along the Adriatic coast. For this reason they proposed to group such regions into a larger macro-area which has been eventually called NEC (North-East-Centre) 4 . At the same time, the growth of manufacturing industries was slowing down in the North-West, wherein the growth of business service industries was already in nuce [START_REF] Pettenati | I Modelli di Organizzazione Economica del Territorio[END_REF]FUÀ and ZACCHIA, 1983). argued that the widespread presence of small-and medium-sized firms contributed to create a favourable environment, characterized by low costs of living, intense utilization of labour potential, and the persistence of pretty informal labour relationships. Firms in turn benefited from these peculiarities in terms of lower costs and better business efficiency. Moreover they maintained that the small size scale and the specialization in labour-intensive activities, permitted in many ways swifter adaptation to changes in markets and technologies [START_REF] Fuà | Industrializzazione nel Nord Est e nel Centro[END_REF](FUÀ, , 1991a(FUÀ, and 1991b;;FUÀ and ZACCHIA, 1983;[START_REF] Garofoli | Lo Sviluppo delle aree periferiche nell'economia italiana degli anni Settanta[END_REF]1983).

On the other hand the relevance of the features of the social texture has been stressed, whereby the traditions rooted into the sharecropping system largely drawing on the informal institution of the "extended family" were persisting. The gradual diffusion of manufacturing did not seem to be paralleled by a simultaneous change of the social organization. Low wages and temporary jobs were accepted because of the weakness of labour market as an institution, substituted by the "extended family" which worked as a real self-regulatory system. In such a context dynamic pressures and attitude toward self-employment represented a key factor for the successful creation of manufacturing enterprises 5 [START_REF] Paci | Mercato del Lavoro e Classi Sociali in Italia. Ricerche sulla Composizione del Proletariato[END_REF]1992). The boosting role of institutional factors (above all embedded in the labour market) and the peculiarities of the economic structure, were maintained to lead to the set of positive-feedbacks well described by the industrial district theorists [START_REF] Brusco | The Emilian model: Productive decentralization and social integration[END_REF][START_REF] Becattini | Modelli Locali di Sviluppo[END_REF].

The Recent Evidence

To investigate the persistence of late industrialization and its geographical distribution, we use time series data on employment at the regional level, drawn from the Italian National Institute of Statistics (ISTAT). The issue of territorial diffusion of manufacturing activities can be addressed by looking at the dynamics of regional specialization index, defined as the region's relative share of employment within an industry. Formally it is defined as employment in sector i located in region j at time t (IL ijt ), divided by the region's total employment in all industries, compared to the same measure at the national level 6 .

In

Data and Methodology

The empirical analysis of the diffusion of regional innovation capabilities within manufacturing sectors in Italy, is based on the evidence about the evolution of patent applications to the EPO 8 . The limits of patent statistics as indicators of innovation activities are well known. The main drawbacks can be summarized in their sectorspecificity, the existence of non patentable innovations and the fact that they are not the only protecting tool. Moreover the propensity to patent tends to vary over time as a function of the cost of patenting, and it is more likely to feature large firms [START_REF] Pavitt | Patent statistics as indicators of innovative activities: Possibilities and problems[END_REF][START_REF] Levin R | Appropriating the returns from industrial research and development[END_REF][START_REF] Griliches | Patent statistics as economic indicators: A survey[END_REF].

Nevertheless, previous studies highlighted the usefulness of patents as measures of production of new knowledge, above all in the context of analyses of innovation performances at the aggregate regional level (ACS et al., 2002). Besides the debate about patents as an output rather than an input of innovation activities, empirical analyses showed that patents and R&D are dominated by a contemporaneous relationship, providing further support to the use of patents as a good proxy of innovation [START_REF] Hall | Patents and R and D: Is There a Lag?[END_REF].

The emergence of regional innovation capabilities manifest itself in high quality innovation processes, wherein firms commit internal resources to R&D and cooperate with other firms and R&D institutions. Patenting represents the last stage of this process. The application to the European Patent Office is a time-and resourceconsuming process, which is likely to exert an ex-ante selection of the innovations to be patented. This allows us to identify high-value innovations stemming from systematic more formalized innovation efforts, which are precisely the object of our analysis.

Table 2 provides empirical evidence of the regional diffusion of innovation capabilities 9 , over the time span 1980-2001. Absolute value data about patent applications are not that suitable for comparative purposes, due to cross-regional dimensional differences. In order to investigate the diffusion of innovation capabilities the data about patent applications need to be somehow normalized. Different alternatives could apply to the case. First of all we ruled out population statistics, in that their link with innovation variables is too weak and difficult to assess 10 . A variable related to the dimension of the production system would be more appropriate to our analysis. The alternatives are thus either the regional number of firms or the number of workers. The former seem to be inappropriate as there can be a bias towards those areas characterized by a large number of small and medium-sized firms, with the consequent underestimation of dimensions in areas characterized by a lower number of large firms. In Table 3 we report the breakdown of quinquennial growth rates of patent applications by region. It is evident that in most Italian regions in the period such growth rates were higher in the first five years, then it lowers in the second one, becoming even negative in the third one. The last quinquennial is then characterized by very low growth rates. It is moreover fair to note that in the first five years the growth rates of Piedmont and Lombardy were higher than those of Emilia-Romagna, Marches and Umbria, while in the last five years the situation is reversed, the latter showing higher growth rates then the former. The evidence in Tables 2 and3 shows that, with obvious cross-regional differences in absolute levels, the dynamics of patent applications across Italian regions are interpretable as a diffusion process. Insofar as patents are reliable indicators of innovative activity, the sequence of growth rates suggests that innovation capabilities have diffused in most Italian regions following an S-shaped time path, and that the patterns characterizing North-Eastern-Central regions are different from those characterizing North-Western regions.

INSERT TABLE 3 ABOUT HERE

In conclusion, the preliminary evidence about data applications appears to suggest that the territorial diffusion of manufacturing activities is still ongoing in the North-East-Central regions, as they are sustained by the diffusion of innovation capabilities, and the consequent advantages stemming from innovation. Emilia-Romagna seems to be the leading region in such a process, whereby Marches, Abruzzi and to some extent Umbria are the immediate followers. The case for a possible extension towards Molise and Puglia seems very difficult to assess, as the data up to 2001 are not very supportive. The regional aggregate data on R&D expenditure, both private and public, have been drawn from the ISTAT to provide a suggestive evidence of the increase in the availability of the knowledge stock accessible in the area 11 . To gain better understanding of the regional dynamics, in Tables 4 and5 we calculated a regional specialization index for public and private R&D expenditure, defined as R&D in sector i (public vs. private) located in region j at time t, divided by the region's total R&D expenditure, compared to the same measure at the national level. It is straightforward from the data that North Western regions are characterized by strong concentration of private R&D expenditure, with the only exception of the Liguria region. The Piedmont region turned out to have the highest value for the index, followed by Valle d'Aosta and Lombardy. Some regions with an index value above 1 can be found also in the North-East. They are Veneto and Emilia-Romagna, which is not so surprising considering that high tech sectors increasingly gained relevance in the area, due to the local positive feedbacks characterizing the upgrading from consumer goods to dedicated capital goods of the manufacturing activity in the area. In the remainder regions the value of the index is below one, above all in the regions along the Adriatic coast.

As far as the public R&D expenditure is concerned, of course in the North-West the only region that can be defined public-R&D-intensive is the Liguria one. It is worth noting that in the North-East, the value of the index for Emilia-Romagna and Veneto is just slightly below 1. This means that in the area the public and the private inputs for innovative activity are pretty balanced. The highest value for the index can be found in the regions along the Adriatic coast, and in Southern Italy in general. Thus the Italian case seems to be characterized by a clear and strong divide also according to the path of change followed by the old industrialized regions and the late industrializing ones. While within the former firms seem exposed to raising problems, unable to cope with the decline of performances in both domestic and international markets, in the latter they seem better able to take advantage of the new technologies by means of a process of creative adoption [START_REF] Quatraro | Change vs. decline: A comparative analysis of the evolution of TFP in Italian regions, with a particular attention to the case of Turin[END_REF].

Econometric Strategy

The econometric strategy is articulated in two steps. Firstly, in order to estimate the different rates of diffusion of patent application across Italian regions, we use the standard logistic equations proposed by [START_REF] Griliches | Hybrid corn: An exploration in the economics of technological change[END_REF] and [START_REF] Mansfield | Technical change and the rate of imitation[END_REF].

A similar exercise was put forth by [START_REF] Andersen | The hunt for s-shaped growth paths in technological innovation: A patent study[END_REF] in her analysis of differential growth rates at the industry level 12 . The logistic function can formally be written as follows:

t e K P β α - - + = 1 ( 2
)
where P is the level of adoption, t the time and K the ceiling. The features of this curve are well known, in that it is asymptotic to 0 and K, it is symmetric around the inflexion point and its time derivative is dP/dt = -b/(P/K)(K-P), which confers the S-shape. 2) is well suited to represent the diffusion process as the result of learning and imitation dynamics. It can be rearranged dividing both sides by (K-P) and taking logs, to obtain the following econometric specification:

t P K P t t β α + =       - ln (3)
Secondly, we investigate the relationships diffusion of innovation capabilities and structural change on the one hand, and the links with the availability of accessible knowledge stocks on the other. This is done by taking the estimated time coefficients from the logistic fit and regressing them as follows:

u TRA d FIN c MAN b a i i i i + ⋅ + ⋅ + ⋅ + = β (4) z GRPRD n GRPUR m GRGFI h e i i i i + ⋅ + ⋅ + ⋅ + = β (5)
Where β clearly stands for the estimated time coefficients of the logistic equation, and u and z are the respective error terms. In Equation ( 4) MAN, FIN and TRA are respectively the average annual growth rates of the employment share of manufacturing, finance business services and trade industries. In Equation ( 5) the rates of diffusion are instead regressed against the average growth rate of public and private R&D (respectively GRPUD and GRPRD), plus the average annual growth rate of gross fixed investment (GRGFI) as control variable accounting for the embodiment hypothesis. In order to investigate the patterns of diffusion of innovation capabilities within regional contexts we fitted the data by using the logistic function specified in Equation ( 3) 13 . Due to the problem of auto correlated disturbances affecting this kind of time series relationship, the choice of a Chi-square estimator seemed to be the most appropriate.

We thus carried out a feasible GLS regression by region, yielding the results displayed in Table 6. The coefficient β is interpreted as the rate at which local competences emerged over time. In this case, through the diffusion of patents applications, we obtain a measure of how fast the innovation capabilities have spread within each Italian region in the period 1981-2001. Although this measure is affected by the definition of K, nonetheless it can provide very useful information to understanding regional differences in economic and industrial dynamics. In particular, we start with a simple comparison among the different levels of β yielded in each region.

INSERT TABLE 6 ABOUT HERE

Within the relevant North-Western regions, Lombardy shows up the fastest rate of emergence, followed by Liguria and then Piedmont. A glance at the values featuring North-Eastern and Central regions is very instructive. Actually, within this subgroup the first rank goes to the Abruzzi region, immediately followed by Emilia-Romagna and Marches, while the Umbria region instead features a low coefficient. At a comparative level it is worth noting that the speed at which innovation capabilities spread within the Abruzzi region is 76.6% greater than that of Piedmont and 40% than that of Lombardy.

For what concerns the Emilia-Romagna region the magnitude of the difference is of 1% and +23% as compared to Lombardy and Piedmont respectively. The Marches region has a β value 25.2% higher than that of Piedmont, but almost equal to that of Lombardy. It must be also noted that the rate of appearance in Liguria is in between that of Piedmont and that Lombardy The results of the econometric estimations therefore provide strong support not only to the idea that the emergence of innovation capabilities followed a logistic path, but also to the hypothesis concerning cross-regional differences. Some regions in the North-East-Centre, specifically Emilia-Romagna, Marches and Abruzzi are characterized by diffusion rates systematically higher than those of Piedmont, and equal or higher to those of Lombardy. The Emilia-Romagna region, in particular, can be considered as the first region in the North-East-Centre side of Italy in which the diffusion of innovation capabilities took place, while Abruzzi and Marches seem to follow it with a slight delay 14 .

As far as the relationship between the emergence of innovation capabilities and the change in the economic structure is concerned, Equation (4) has been estimated through OLS with robust standard errors. The estimation yielded the following results:

β = 0. 157 + 3.911 • MAN** -5.610 • TRA + 1.128 • FIN (6)
(2.89) (-1.57) (0.59) F = 2.93, t of Student between parentheses. As expected the coefficient on the growth rate of the employment share of manufacturing industries is positive and significant, while the coefficients for the two service industries are not statistically significant. The evidence of higher diffusion rates of innovation capabilities in some NEC regions is hence to be related to the evidence, already presented in Section 2, about the enduring 24 growth of manufacturing activities in the area. This process could be thus interpreted as a specific stage in the development of manufacturing activities, according to which learning dynamics and the increasing international competition are likely to foster innovative efforts, as long as technological opportunities are at the same time on hand.

In this direction the availability of an accessible knowledge stock is supposed to be closely related to the diffusion of innovation capabilities. To this purpose Equation ( 5)

has been estimated through OLS with Huber-White heteroscedastic consistent standard errors. The econometric test yielded the following result:

β = 0.172 -0.026•GRGFI + 0.076 •10 -3 •GRPRD*** + 0.379•10 -3 •GRPUR *** (7) (-1.06) (3.05) (3.74)
F=84.9, t of Student between parentheses (coefficients on R&D are both significant at 1%). It is worth emphasizing that the coefficient on public R&D is far larger than that on private one. This confirms that faster rates of diffusion of innovation, and faster rates of public R&D, are at the heart of the process leading to faster growth rates in lateindustrializing regions. The stronger impact of public R&D also suggests that the absorption of formal inventive activity within firms' productive routine doesn't imply necessarily a parallel process of dimensional growth. It is likely that within areas characterized by local capitalism, firms may also outsource R&D services, particularly relying on the public knowledge infrastructure. In this direction, it is worth mentioning that also the organization of public R&D labs (say the National Research Council) is becoming more and more functional to the needs of local production systems, trying to

Concluding Remarks

In this paper we tried to shed new light onto the persistent process of diffusion of manufacturing activities, integrating the analysis with the study of the regional patterns of innovation within the NEC regions. While in the 1970s the explanations were mainly based on aspects related to institutional conditions and the structure of local economic and social systems, we proposed an interpretation in the light of the economics of innovation. The combination between the diffusion theory and the concept of growth poles has allowed us to appreciate the emerging development of innovation capabilities within the late-industrializing regions.

Growth poles theory suggest that regions are dominated by propulsive industries, which act as catalyst to economic performances of close economic activities. Core industries however are not evenly distributed across regions and they are not static, as mature industries within regional contexts are possibly characterized by slackening growth rates, while some other industries gain momentum [START_REF] Perroux | Note sur la notion de 'pole de croissance[END_REF][START_REF] Fuà | Industrializzazione nel Nord Est e nel Centro[END_REF].

The emergence of innovation capabilities within a regional context is strictly related to the relative stage of development of the propulsive industry and of its related industries.

Therefore, regions in which the process of industrialization occurred with some delay, are also likely to experience a delayed emergence of innovation capabilities within the manufacturing sectors. The competences about how to innovate spread over time as the The results obtained through the analysis of the diffusion of patent applications strongly support the hypothesis according to which the NEC regions are still exploiting the advantages of the late industrialization. The exploitation of the innovative potential stemming from learning dynamics is actually fed by the parallel growth of technological opportunities and the strengthening of the productive system. Indeed the thickening of the manufacturing production system and the increasing availability of accessible knowledge stock proved to be positive related to the rate of diffusion of innovation capabilities across Italian regions.

It is also fair to note that in the econometric test the impact of public R&D expenditure on the speed of diffusion of innovation capabilities, turned out to be far higher than that of private R&D expenditure. This suggests that the idiosyncratic features of the regions mostly affected by the process played a crucial role. The increasing availability of public knowledge represents a competitive advantage, provided the existence of conditions enabling knowledge communication and absorption. This is the case for many areas in the NEC regions, wherein the dynamics typical of industrial districts have allowed for the evolution towards either technology districts, or technology-based industrial districts.

Along the lines of Kuznets, industrial development does not take a unique shape, but followed different paths according to the specific regional characteristics of economic 2 It is fair to quote also the pretty similar analysis of industry lifecycles proposed by KLEPPER (1997).

3 The theory about the retardation of growth rates of mature industries was elaborated by KUZNETS (1930) by considering the evolution of industries within different countries. Like all models it maybe provides a simplified view of reality, which nonetheless enhances the understanding of evolutionary processes at aggregate levels. This perspective was then successfully articulated also at the regional level by Giorgio Fuà and subsequentely by the scholars belonging to the so-called School of Ancona, e.g. FUÀ (1977), [START_REF] Garofoli | Lo Sviluppo delle aree periferiche nell'economia italiana degli anni Settanta[END_REF] and PETTENATI (1991). [START_REF] Evangelista R | Sectoral patterns of technological change in services[END_REF][START_REF] Evangelista | Innovation in the service sector. results from the Italian innovation survey[END_REF][START_REF] Evangelista R | Sectoral patterns of technological change in services[END_REF] present the Italian evidence, emphasizing the very marginal role played by patents in innovation dynamics within service sectors. 9 Patent applications are classified according to the inventor's residence address. 10 As also emphasized by [START_REF] Kuznets | Secular Movements in Production and Prices[END_REF].

11 Time series concerning public and private R&D expenditure at the regional level are available since 1982 on. Moreover, it is worth noting that public expenditure is not comprehensive of expenditure by Universities, as these data are available since 1993 on.

12 S-shaped curves were used also in the study of business cycles, many years before they entered the study of technological change. It is fair to recall, in this direction, the works by [START_REF] Kuznets | Secular Movements in Production and Prices[END_REF] and [START_REF] Merton | Fluctuations in the rate of industrial invention[END_REF]. 13 The fit of the logistic equation through linear techniques allow for estimating two parameters, requiring the ceiling to be specified ex-ante. As a reference, we used the overall maximum value of the dependent variable, and we multiplied it by the annual average growth rate of added value in manufacturing industries. It is worth stressing that in some contexts the evolution of the industrial structure is led by the emergence of groups of firms within the districts, i.e. by peculiar forms of evolution of local capitalism [START_REF] Brioschi | From the industrial district to the district group: An insight into the revolution of local capitalism in Italy[END_REF][START_REF] Cainelli | Spatial agglomeration and business groups: New evidence from industrial districts[END_REF]. 350 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 1980-1984 1985-1989 1990-1994 1995-1999 Piedmont

  contribution by[START_REF] Schumpeter | The theory of economic development[END_REF], innovation has been regarded as crucial to the process of economic development. The main agents of innovation firstly were new firms created by risk-taking entrepreneurs and then large corporations, which sacrifice static to dynamic efficiency(SCHUMPETER, 1942).[START_REF] Perroux | Note sur la notion de 'pole de croissance[END_REF] integrated the role of technological change in his "growth pole" theory following Schumpeter's legacy. Regional economic systems are characterized by rounds of growth, i.e. periods in which firms within the propulsive industry grow at faster rates, propagating the positive effects across firms directly and indirectly relate to the propulsive industry. The main driving factor of such expansion is technical efficiency gained through innovation efforts.The competitive forces driving the expansion of such an industry however do not work indefinitely. Sooner or later growth rates starts declining and a new industry is likely to emerge, as an effect of the introduction of radical innovations within the system. Within the new industry firms will innovate to gain competitive advantages and gales of innovations show up at some point in time. In the positive climate related to the expansion of the industry one firm will introduce an innovation, stimulating other creative agents. THOMAS (1975) articulated the implications of Perroux' framework on regional economic growth using a product life-cycle perspective, wherein the saturation of product markets are the main responsible for the slowdown of growth rates and the

Figure 1

 1 Figure 1 summarizes the theoretical framework elaborated so far. Continuous lines refer

  proposed in the 1970s as conducive to the successful territorial diffusion of manufacturing activities towards the NEC. On the one hand it has been

  Thus we decided to take the number of patent applications per worker as the indicator of the level of diffusion of innovation capabilities within each region.INSERT TABLE 2 ABOUT HEREWith the help of Figure2, we focus on the differences among early-and lateindustrialized regions. As far as the former are concerned, the dynamics of Lombardy and Piedmont are characterized by high levels in the early 1980s in both of them, but in 1988 it can be noted a further speeding up of Lombardy which clearly overtake Piedmont, outperforming it until 2001. Around 1991 the growth of patent applications begins to slow down in both regions, but more markedly in Piedmont. The evidence about Emilia-Romagna is of much interest for the purpose of our analysis. Indeed the diffusion of patent applications seem to be more sustained all over the period observed.Innovation capabilities diffuse at a very fast pace, such that Emilia-Romagna outperformed Piedmont already in 1998 and Lombardy in 1999. Friuli-Venezia Giulia and Veneto are characterized by fairly opposite dynamics, as the former appears to grow sensibly along the 1980s and then slowing down in the 1990s, while the latter is characterized by modest growth rate until the late 1990s, and then a sudden acceleration. Finally Umbria, Marches and Abruzzi show up dynamics very similar to Veneto's, in that the hastening of growth in patent applications can be devised

  of the competencies and the reputation that such areas gained in some particular markets(CNR, 2005).

  dynamics, in which local interactions and networking play a crucial role.

  capitalization of the benefits stemming from innovation can be, in this light, interpreted as a distinct stage in the industrialization process, which characterizes an industry as old enough to properly manage emerging technological opportunities, but not so mature to incur in the slackening of growth rates. NOTES 1 Part of the background research for this paper has been carried out during my visiting periods at the CRIC -University of Manchester and at the Columbia University of New York. Preliminary versions was presented at the CESPRI lunch seminar at the Bocconi University of Milan on 10 May 2006, the CRIC "Monday afternoon" seminar at the University of Manchester on 7 July 2006 and the Annual CCC Doctoral Colloquium held at the GeorgiaTech College of Management in Atlanta on 13-15 April 2007. I wish to thank Cristiano Antonelli, Davide Consoli, Giovanni Dosi, Roberto Mazzoleni, Stan Metcalfe, Dick Nelson, Pier Paolo Patrucco and two anonymous referees for their useful comments. The usual disclaimers on errors and inadequacies apply.

4

  The grouping of Italian regions is as follows. North-West: Piedmont, Lombardy, Valle d'Aosta and Liguria. North-East: Veneto, Emilia-Romagna, Friuli Venezia-Giulia,Trentino Alto-Adige. Centre: about the nature of innovation activities within service sectors have recently received increasing attention. TETHER (2005) and CONSOLI (2007) offer good critical syntheses of it.

14

  These results are consistent with the empirical analyses carried out by PATRUCCO (2005) concerning the Emilia-Romagna technology district, the works by BELUSSI (2003) and by BELUSSI and ARCANGELI (1998) concerning both the North-Eastern regions, and BELUSSI (1999), QUATRARO (2005) and BOSCHMA and TER VAL (2005) for more recent evidence about Southern regions. The work at the aggregate level by CAINELLI and DE LISO (2005) is also particularly interesting in within Italian industrial districts.

  Figure 1 -The Conceptual Model

  In Emilia-Romagna and Molise its growth was sustained both in the 1980s and the 1990s, while in the Umbria region the index decreased until the first half of the 1990s, and then started increasing steadily. At the end of the observed period, it seems that North-Eastern and Central regions are characterized by specialization indexes very close to (and in the case of Marches even higher than) the values featuring North-Western regions. Moreover the trend appears to be soundly positive in the former, while the values in the latter are continuously decreasing since the early 1980s.

	the 1980s (respectively +13.6% and +19.6% in the period 1981-1991), slowing down in
	1990s (but still growing).
	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	INSERT TABLE 1 ABOUT HERE	O n l
	This is the reason why regions like Veneto, Emilia-Romagna, Umbria and Marches are y
	characterized by values just slightly lower than in the above mentioned North-Western
	regions. The main important aspect is that the North-Eastern and Central regions are
	characterized by specialization indexes increasing over time. It is worth stressing that in
	Veneto and Marches the specialization in manufacturing grew very impressively along

Table 1 we report the results of the calculations for manufacturing industries 7 . North-Western and NEC regions are characterized by well differentiated patterns. The former indeed show up decreasing values, both as an aggregate and singling out the regions. The Lombardy and Piedmont regions are characterized by the highest specialization indexes in 1982. It must be considered that, according to Fuà and his colleagues, the process of territorial diffusion started in the late 1960s.

Table 1 -Regional Specialization Index for Manufacturing Sectors †

 1

	2000 2001

2000 2001

	Piedmont	1.362 1.359 1.381 1.369 1.319 1.333 1.350 1.376 1.389 1.380 1.358 1.313 1.290 1.257 1.277 1.291 1.290 1.300 1.306 1.285 1.280 1.278
	Aosta Valley	0.720 0.737 0.781 0.823 0.786 0.744 0.711 0.655 0.668 0.594 0.578 0.583 0.579 0.558 0.561 0.531 0.538 0.548 0.567 0.554 0.536 0.548
	Lombardy	1.505 1.503 1.499 1.500 1.478 1.469 1.459 1.440 1.407 1.416 1.445 1.416 1.428 1.447 1.434 1.404 1.395 1.377 1.381 1.361 1.355 1.355
	Liguria	0.783 0.769 0.756 0.758 0.740 0.698 0.681 0.700 0.657 0.670 0.659 0.652 0.658 0.619 0.631 0.627 0.626 0.615 0.602 0.615 0.655 0.644
	North West 1.377 1.374 1.379 1.378 1.346 1.339 1.338 1.337 1.317 1.321 1.333 1.303 1.305 1.303 1.304 1.290 1.285 1.275 1.278 1.262 1.261 1.259
	Trentino-Alto Adige	0.657 0.655 0.641 0.643 0.696 0.656 0.654 0.697 0.724 0.698 0.691 0.688 0.725 0.709 0.708 0.701 0.709 0.718 0.705 0.713 0.716 0.733
	Veneto	1.230 1.198 1.213 1.213 1.265 1.343 1.320 1.307 1.326 1.344 1.346 1.361 1.349 1.383 1.360 1.372 1.384 1.397 1.397 1.403 1.381 1.370
	Friuli-Venezia Giulia	0.971 0.898 0.911 0.909 0.910 0.927 0.953 0.978 0.993 1.001 0.993 1.014 0.999 1.016 1.005 1.054 1.082 1.101 1.080 1.049 1.061 1.036
	Emilia-Romagna	1.112 1.141 1.157 1.162 1.213 1.220 1.222 1.270 1.280 1.274 1.247 1.196 1.200 1.207 1.215 1.218 1.218 1.222 1.233 1.242 1.249 1.257
	North East 1

.101 1.090 1.104 1.105 1.150 1.183 1.179 1.200 1.216 1.219 1.208 1.196 1.195 1.212 1.205 1.216 1.225 1.235 1.235 1.239 1.234 1.231

  Marche 1.154 1.133 1.168 1.186 1.224 1.239 1.239 1.342 1.323 1.365 1.328 1.355 1.333 1.371 1.329 1.339 1.347 1.332 1.349 1.376 1.351 1.390 Lazio 0.591 0.591 0.581 0.569 0.583 0.555 0.574 0.546 0.536 0.546 0.530 0.551 0.547 0.542 0.544 0.528 0.521 0.518 0.514 0.517 0.525 0.517 Abruzzi 0.799 0.802 0.792 0.814 0.831 0.811 0.820 0.805 0.831 0.812 0.830 0.926 0.910 0.925 0.935 0.935 0.975 0.986 0.988 1.021 1.034 1.013 Molise 0.505 0.532 0.526 0.536 0.569 0.565 0.541 0.642 0.683 0.696 0.699 0.673 0.735 0.726 0.737 0.763 0.776 0.787 0.817 0.833 0.820 0.837 Central Italy 0.

	Tuscany	1.155 1.176 1.161 1.213 1.199 1.212 1.230 1.187 1.167 1.104 1.126 1.132 1.168 1.170 1.162 1.157 1.158 1.150 1.153 1.131 1.131 1.142
	Umbria	1.133 1.072 1.075 1.132 1.135 1.106 1.049 0.959 1.014 1.006 1.005 1.042 1.057 1.020 1.001 0.992 0.998 0.990 1.011 1.026 1.052 1.058

913 0.914 0.906 0.918 0.922 0.911 0.919 0.899 0.888 0.881 0.872 0.890 0.897 0.898 0.891 0.883 0.882 0.875 0.877 0.876 0.879 0.884

	Campania	0.689 0.699 0.700 0.704 0.690 0.674 0.622 0.631 0.639 0.637 0.632 0.688 0.679 0.667 0.676 0.685 0.676 0.682 0.666 0.682 0.680 0.688
	Puglia	0.665 0.694 0.682 0.687 0.692 0.701 0.726 0.727 0.743 0.728 0.713 0.717 0.727 0.686 0.694 0.694 0.684 0.708 0.720 0.719 0.706 0.700
	Basilicata	0.441 0.436 0.465 0.453 0.439 0.458 0.477 0.429 0.420 0.440 0.498 0.493 0.482 0.492 0.544 0.657 0.678 0.685 0.698 0.748 0.793 0.837
	Calabria	0.363 0.369 0.387 0.370 0.388 0.346 0.388 0.362 0.342 0.312 0.348 0.389 0.393 0.359 0.371 0.377 0.366 0.363 0.351 0.358 0.385 0.392
	Sicily	0.502 0.507 0.507 0.493 0.482 0.485 0.471 0.457 0.462 0.482 0.460 0.476 0.466 0.465 0.467 0.457 0.446 0.452 0.450 0.467 0.470 0.471
	Sardinia	0.580 0.567 0.542 0.554 0.574 0.580 0.560 0.551 0.536 0.537 0.563 0.560 0.569 0.577 0.527 0.522 0.511 0.496 0.491 0.483 0.495 0.532

South 0.598 0.606 0.605 0.605 0.604 0.597 0.588 0.583 0.589 0.586 0.588 0.617 0.615 0.601 0.606 0.610 0.605 0.612 0.609 0.622 0.625 0.630

	F o r
	P
	e
	e r
	Source: Elaboration on ISTAT data. Note: † ISIC codes 15-37	R
		e
		v i e
		w
		O n l
		y

Table 3 -Patent Applications Growth Rates, by Region †

 3

  Missing values are due to high number of zeros in some regions.

			0.307	0.099	-0.013	0.047
	Aosta Valley		-	0.183	-0.116	-
	Lombardy		0.224	0.137	-0.019	0.050
	Liguria		0.251	0.069	0.075	0.025
	North West	0.250	0.123	-0.012	0.048
	Trentino-Alto Adige	0.220	0.116	0.036	0.057
	Veneto		0.272	0.095	-0.003	0.083
	Friuli-Venezia Giulia Emilia-Romagna North East Tuscany Umbria Marche F 0.169 0.186 0.209 0.281 0.153 0.462 o r 0.096 0.144 0.117 0.069 0.063 0.147	-0.021 0.051 0.021 -0.025 -0.093 0.015	0.011 0.078 0.071 0.049 0.082 0.050
	Lazio Abruzzi		0.186 -	0.093 0.183 P	0.004 -0.083	0.051 0.312
	Molise Campania Central Italy Puglia Basilicata	-0.243 0.231 0.251 -	-0.093 e 0.159 0.127 0.183 e r 0.183 -0.012 0.058 -0.037 0.000	-0.074 0.047 0.079 0.289
	Calabria Sicily Sardinia	South	-0.116 --0.257	0.000 0.170 0.030 0.134	0.085 0.030 -0.116 R 0.020 e	0.268 -0.025 0.085 0.051
	Italy		0.239	0.118	-0.002 v 0.059 i e
						w
						O n l
						y

Source: Elaborations on EPO data. Note: †

Table 6 -Results of GLS Estimation of Equation (3), by Region

 6 Statistics between parentheses.

	Dependent Variable:	ln	   	K	-t t P P	   
	Region					Const	Time	Wald-χ 2
	Piedmont				-218.49 (-7.95)	.110 (7.94)	63.01
	Aosta Valley				-444.82 (-1.94)	.221 (1.92)	3.71
	Lombardy				-292.13 (-8.82)	.142 (8.81)	77.67
	Liguria				-253.38 (-11.48)	.127 (11.42)	130.47
	Trentino Alto Adige				-212.29 (-11.32)	.106 (11.22)	125.80
	Veneto				-254.57 (-9.57)	.127 (9.53)	90.83
	Friuli Venezia Giulia				-223.69 (-6.85)	.112 (6.83)	46.69
	Emilia Romagna				-332.97 (-18.98)	.170 (18.95)	359.03
	Tuscany				-201.04 (-6.43)	.100 (6.38)	40.67
	Umbria				-161.70 (-6.68)	.080 (6.60)	43.60
	Marche				-279.33 (-8.89)	.139 (8.83)	77.92
	Lazio				-185.14 (-6.99)	.092 (6.93)	47.96
	Abruzzo				-376.36 (-7.03)	.188 (6.99)	48.83
	Molise				-474.67 (-1.91)	.235 (1.89)	3.57
	Campania				-231.80 (17.51)	.114 (13.05)	170.19
	Puglia				-232.66 (-8.98)	.115 (8.84)	78.18
	Basilicata				-750.42 (-3.18)	.374 (3.16)	10.00
	Calabria				-184.71 (-3.28)	091 (3.21)	10.28
	Sicily				-289.45 (-12.51)	.144 (12.38)	153.17
	Sardinia				-173.02 (-5.90)	.085 (5.77)	33.33
	Note: z

Tuscany, Abruzzi, Marches, Lazio, Umbria and Molise. South: Campania, Apulia, Calabria, Basilicata, Sicilia and Sardegna.5 The empirical analysis carried out by[START_REF] Garofoli | New firm formation and regional development: The Italian case[END_REF] addresses the issue of firms creation very exhaustively.6

Change|Research and Development < O -Economic Development, Technological Change, and Growth, R11 -Regional Economic Activity: Growth, Development, and Changes < R1 -General Regional Economics < R -Urban, Rural, and Regional Economics Regional Innovation Capabilities, Growth Retardation,

http://mc.manuscriptcentral.com/cres Email: regional.studies@fm.ru.nl

Regional Studies

F o r P e e r R e v i e w O n l y 22

Table 2 -Patent Applications per 1000 Workers, by Region, 1980Region, -2001Region, . 1980Region, 1981Region, 1982Region, 1983Region, 1984Region, 1985Region, 1986Region, 1987Region, 1988Region, 1989Region, 1990Region, 1991Region, 1992Region, 1993Region, 1994Region, 1995Region, 1996Region, 1997Region, 1998Region, 1999 Molise 0.000 0.017 0.017 0.000 0.009 0.000 0.000 0.016 0.008 0.026 0.008 0.009 0.017 0.009 0.027 0.000 0.018 0.036 0.036 0.054 0.026 0.017 Central Italy 0.007 0.015 0.020 0.030 0.028 0.033 0.042 0.047 0.049 0.057 0.068 0.079 0.080 0.071 0.065 0.068 0.072 0.075 0.093 0.104 0.127 0.122 Campania 0.001 0.005 0.006 0.005 0.004 0.006 0.006 0.009 0.012 0.015 0.014 0.011 0.016 0.023 0.020 0.024 0.019 0.025 0.026 0.031 0.040 0.035 Puglia 0.002 0.002 0.003 0.005 0.007 0.005 0.003 0.011 0.014 0.011 0.015 0.007 0.011 0.013 0.012 0.014 0.016 0.015 0.025 0.023 0.029 0.041 Basilicata 0.000 0.000 0.001 0.010 0.005 0.005 0.005 0.000 0.029 0.015 0.010 0.000 0.016 0.000 0.011 0.016 0.016 0.032 0.095 0.088 0.071 0.066 Calabria 0.003 0.002 0.003 0.002 0.002 0.005 0.005 0.014 0.011 0.005 0.005 0.005 0.008 0.009 0.008 0.003 0.002 0.016 0.010 0.017 0.021 0.013 Sicily 0.000 0.004 0.003 0.005 0.004 0.006 0.010 0.006 0.019 0.017 0.016 0.025 0.018 0.017 0.021 0.036 0.045 0.035 0.030 0.030 0.059 0.054 Sardinia 0.000 0.008 0.002 0.004 0.006 0.010 0.006 0.014 0.014 0.010 0.010 0.015 0.012 0.016 0.005 0.011 0.018 0.014 0.023 0.018 0.032 0.022 Source: [START_REF] Antonelli | Information and communication technologies and productivity growth: How to disentangle creative adoption from radical innovation[END_REF]


Ph.D Bruno Castanier

Ph.D Thomas G Yeung

Optimal Highway Maintenance Policies under Uncertainty

Keywords: maintenance optimization, gamma process, Markov semi-renewal

We develop an inspection and maintenance policy to minimize the cost of maintaining a given section of road or highway when there is a great deal of uncertainty in the degradation process. We propose to model the degradation of a section of road based on the proliferation and growth of cracks. We utilize a combination of a Poisson and gamma process to account for the tremendous amount of uncertainty and difficulty in predicting the proliferation of cracks. Our policy defines the optimal inspection interval as well as the minimum threshold at which to perform crack repairs. Furthermore, our policy contains a safety constraint to prevent the probability of a "catastrophic" failure from exceeding a pre-determined reliability value. Numerical calculations have shown that our model will extend the lifecycle of the road by performing preventive, conditioned-based maintenance to slow down the growth of cracks. Classical preventive maintenance policies usually shorten the lifecycle by forcing earlier renewals.

INTRODUCTION

In the year 2000, the United States had almost US$31 billion in highway maintenance expenditures [1]. In order to devise an effective maintenance/rehabilitation strategy, an accurate model for the degradation of roads is needed. Cracks, specifically longitudinal wheel-path cracks in the pavement, are the primary cause for road maintenance. Myers et al. [START_REF] Myers | Mechanisms of surfaceinitiated longitudinal wheel path cracks in high-type bituminous pavements[END_REF] reported that over 90% of road sections in Florida that are in need of repair have such cracks. The proliferation of a crack in asphalt concrete operates as follows. The traffic load applied to the pavement surface generates tensile stresses at the bottom of the asphalt layer. For new pavement, the tensile strength of the asphalt concrete initially exceeds the stress applied by the traffic load, and thus will remain free of cracks for a period of time. However, as the tensile strength of the road begins to degrade, fatigue cracks will initiate at weak spots at the bottom of the asphalt layer and overtime these cracks will propagate through the asphalt layer to the surface. The size of the crack will eventually reach some unacceptable level at which maintenance and/or rehabilitation becomes necessary. As cracks increase in size, contaminants are able to more easily infiltrate the road and disrupt the bond of pavement materials if they are not properly sealed, thus leading to further degradation.

We propose to develop an accurate model of road degradation using longitudinal surface cracks. We decompose the cracking process into two phases: 1) the crack initiation and 2) the crack propagation. Based on this degradation model we will formulate an optimal policy for highway inspection in conjunction with maintenance and rehabilitation actions.

MOTIVATION

The development of mathematical models for road maintenance became prevalent with the Pavement Management System (PMS) developed by Golbai et al. [START_REF] Golbai | A Statewide Pavement Management System[END_REF] for the Arizona Department of Transportation (ADODT) and Woodward-Clyde Consultants. The PMS contains a Network Optimization System (NOS) which consists of two Markov decision models. Wang and Zaniewski [START_REF] Wang | 20/30 Hindsight: The New Pavement Optimization in the Arizona State Highway Network[END_REF] report that the PMS achieved dramatic cost savings at the ADODT and has gone on to be implemented in various forms by other highway agencies.

Markov processes make up the majority of stochastic modeling approaches for pavement maintenance/rehabilitation [START_REF] Yang | Use of recurrent Markov chains for modeling crack performance of flexible pavements[END_REF]. The underlying degradation model of the Markov process is obtained either through statistical analysis of pavement data or some representative model. The greatest challenge in this approach is that an accurate degradation model is needed to construct the transition probability matrix of the Markov chain. Specifically a probability associated with each state transition.

Many degradation models also deal with the propagation of cracks in a wide variety of settings and are largely based on the Paris and Erdogan [6] equation. The transition probability matrix approach may be utilized with either the general or crack-specific approach, while the Paris and Erdogan (1963) equation applies specifically to propagation of cracks as a function of applied stress.

Wu and Ni [START_REF] Wu | Probabilistic models of fatigue crack propagation and their experimental verification[END_REF] found that a stationary Markov chain model with a transition probability matrix based on statistical data does not accurately describe a crack growth process. They also note that while the Markov chain approach is often criticized for its accuracy, Yang's model [START_REF] Yang | Use of recurrent Markov chains for modeling crack performance of flexible pavements[END_REF] and the polynomial model have parameters that are difficult to determine and must be obtained from a large sample of crack growth measurements and observations.

There is a tremendous amount of uncertainty in degradation models due to the variability in material properties, environmental conditions, and traffic patterns [START_REF] Yang | Use of recurrent Markov chains for modeling crack performance of flexible pavements[END_REF].

Due to the difficulty in estimating the underlying degradation of the Markov chain approach and parameters for the Paris and Erdogan equation we propose the use of gamma processes to model the crack growth. Gamma processes have recently received a tremendous amount of attention in the reliability and maintainability literature as means to the model degradation of many civil engineering structures under uncertainty [START_REF] Van Noortwijk | A survey of the application of gamma processes in maintenance[END_REF].

The use of a gamma process to model crack growth in conjunction with a Poisson for the appearance of a crack was first proposed by van Noortwijk et al. [START_REF] Van Noortwijk | Optimal Maintenance decisions for the sea-bed protection of the Eastern-Scheldt barrier[END_REF] for the modeling of scour holes of the Eastern-Scheldt barrier in the Netherlands. This work was then extended by van Noortwijk and Klatter [START_REF] Van Noortwijk | Optimal inspection decisions for the block mats of the Eastern-Scheldt barrier[END_REF] to allow the scour erosion to be decreasing rather than constant. We propose to further extend this model by applying it to road maintenance. We model the appearance of a crack in the road as a Poisson process and the propagation of the crack as a gamma process. The two previous models assumed that only one action was possible upon detection of a scour hole. No decision had to be made; a repair was automatically initiated. We allow for three possible actions: 1) do nothing, 2) maintenance: repair the crack, or 3) rehabilitation: completely resurface the section of road. Furthermore, we implement a safety constraint to ensure that the state of the road does not fall below a pre-determined threshold with a given reliability.

The evaluation of the size of a crack is a valuable metric for determining the optimal maintenance and rehabilitation strategy for roads [START_REF] Mei | Neural Network for Rapid Depth Evaluation of Shallow Cracks in Asphalt Pavements[END_REF]. The primary method used by most state departments of transportation in the United States to evaluate crack depths in pavement is core sampling. This method is time-consuming, costly, and destructive. Nondestructive techniques such as impact-echo or ultrasound do exist [START_REF] Schlengermann | Determination of crack depth using ultrasonics: An overlook[END_REF][START_REF] Sansalone | Determining the depth of surface-opening cracks using impact-generated stress waves and time-of-flight techniques[END_REF], however they are designed for use on concrete and not suitable for the asphalt pavement of roads. However, longitudinal surface cracks may be inspected visually and accurately without causing further damage to the road itself. It can also be assumed that a strong correlation exists between the length and the depth of the crack. The objective of this paper is to formulate an optimal inspection and maintenance/rehabilitation policy based on cracks in the road.

MODEL ASSUMPTIONS

Surface cracks can be detected via visual inspection. As previously mentioned, this has the advantage of being both non-destructive and extremely accurate. For our model, inspection is assumed to occur in a constant, periodic manner where the detection and measurement of a crack are assumed to be perfect. We denote the length of equivalent inspection intervals as •. A periodic inspection policy is chosen for practical purposes so transportation departments can effectively budget and schedule the funds and manpower necessary. Inspection is also assumed to occur instantaneously. In practice, a special vehicle outfitted with a video camera films the road so that the actual human visual assessment of the road can occur in a lab. This prevents road closures and allows for more accurate measurements than in the field. For our cost model formulation we let c s represent the fixed cost for inspecting a given length of road.

Let N i be the number of cracks that appear at the end of the i th period since the last inspection. Further, consider some

crack } , , 2 , 1 { i N j K ∈
where the length of the crack j at time t, t • 0 is denoted as L j (t) where l j (0) = 0 (l j denotes a specific instance of the random variable L j ). The arrival times (T 1 , T 2 , …) of initiated cracks are assumed to follow a Poisson process with intensity parameter • and thus be exchangeable and memoryless. While we recognize that the initiation of cracks overtime is most likely a non-stationary process, the stationary assumption is made to facilitate parameter estimation in practice. Once a crack has been initiated, its length propagation is modeled by a gamma process with shape function •t > 0 and scale parameter • > 0. This process denotes a constant crack growth with a linear trend. The initiation and growth process of a crack is shown in Figure 1.

Figure 1 -Crack Initiation and Growth Process 4 PROBLEM STATEMENT

As mentioned above, there are three possible actions after inspection occurs. It must first be decided whether to "do nothing" or take some action (i.e., maintenance or rehabilitation). No action will be taken during a given inspection period if the total length of all observed cracks is less than the decision variable •. We must optimize • in order to determine the maximum threshold in which it is optimal to take no action with the road. Therefore, the "do nothing" action is taken if:

( ) γ < ∑ = i N j j t L 1 .
(1)

If the decision is made that some action must be taken, then an evaluation must be made as to whether to maintain or rehabilitate the road. A rehabilitation action is defined as the complete resurfacing of the road to an as-good-as-new condition. Thus, rehabilitation is a complete renewal point. A maintenance action is defined as repairing each crack on an individual basis to an as-good-as-new condition. For our model, this is a semi-renewal point as we will be tracking the total number of repaired cracks as an indicator for when a rehabilitation action is needed.

Repairs, if carried out, are assumed to occur instantaneously and immediately after their detection and be perfect in nature. Let the cost of maintenance at the end of the i th time period be C m (i) with both a fixed and a linear variable cost component denoted c f and c v , respectively. Their

L j (t) T j λ t 1 t 22 ∆ L j (t 2 -t 1 )~ Γ(α(t 2 -t 1 ), β)
relationship is defined as follows:

( )

∑ = + = i N j j v f m t L c c i C 1 ) ( . (2)
The cost of rehabilitation, denoted c r , is a singled fixed cost per section of road under consideration and leads to a complete renewal of the process. Furthermore, it is assumed that c r >> c m,i such that c r + c m,i ~ c r . Stipulating that the cost of rehabilitation is much larger than the cost to repair individual cracks ensures our model will not choose to preemptively rehabilitate and also reflects the real world cost, man-power, and political problems associated with shutting down and resurfacing a section of road or highway. A rehabilitation action is considered to occur immediately upon recognition of the need and be instantaneous. The immediate and instantaneous assumption of the maintenance and rehabilitation actions is justified due to the relatively small amount of time required to carry out these actions in comparison to the total life of the road and the length of the inspection intervals. For quality and safety reasons, a rehabilitation action is deemed necessary when the total length of all cracks previously maintained, L m , plus the total length of cracks in need of maintenance exceeds a threshold l r . l r is a given parameter that will vary depending on the length of the section of road under consideration and the quality standards of a particular area. This is necessary to prevent the road from becoming a complete patch work of repaired cracks. It is a value set by considering a number of different points of view such as engineering, management, cost control, local government priorities, and how much past repair is deemed tolerable on a given section of road. Thus, rehabilitation will occur if the following is true

( ) r N j j m l t L L i > + ∑ =1 . (3)
Finally, we allow for a "safety rule" to ensure that our optimization model does not allow the probability of a given total length of all cracks in a section of road to exceed a specified safety threshold within an inspection interval. This requires two parameters: 1) the maximum total length of all cracks allowed at which point the road would be unsafe or unusable, denoted l s , and 2) the maximum allowable probability that the total length of all cracks will exceed the safety threshold l s . This maximum allowable probability is denoted p s . This safety rule is given by ( )

s s N j j p l t L i <         > ∑ =1 Pr . ( 4
)
The safety constraint also ensures that in our cost optimization model, the "do nothing" action is not taken at every inspection interval.

The possible actions in our model are summarized in Figure 2 based on a hypothetical scenario that begins with a brand new road. The first inspection occurs at time •. Since the road is new, there are no previously repaired cracks and thus L m (•) = 0 < l r and no rehabilitation action is taken. At end of • two cracks have formed, however, they are less than the repair threshold •, so no maintenance will occur either, leaving managers to "do nothing." At the end of 2•, the two initial cracks have continued to grow and a third has formed. There are still no previously repaired cracks and the total length of the three cracks does not exceed l r , so no rehabilitation action is performed. However, the total length of all three cracks now exceeds • and so a maintenance action is taken and the cracks are repaired. At the end of 3• two new cracks have formed. The previous cracks do not appear because they have been repaired. The total length of the two new cracks plus the total length of all previously repaired cracks do not yet exceed l r , so no rehabilitation action is performed. The two new cracks do exceed • so a repair action is taken. Finally at the end of the 4 th inspection cycle, three more cracks have formed pushing the total length of all existing cracks plus the total length of all previous repaired cracks over l r , and the rehabilitation action is taken to completely renew the road.

Figure 2 -Summary of Actions

The goal of the maintenance decision model is to determine the optimal inspection interval •, and the optimum maintenance threshold •, that minimizes the expected average cost per time period given by

( ) ( ) ( ) τ τ τ τ π R r v m f i t P c X E c P c c C E t t C + + + = = ∞ → ) ( ) ( lim ( 5
)
where E • (•) is the expectation defined by a Markov renewal cycle, P m and P R are the long-run probabilities associated with performing maintenance and rehabilitation, respectively, and E(X(•)) is the expected value of the cumulative length of all cracks at time •. The derivation of these values is discussed in the next section.

DETERMINING THE STATIONARY LAW

We propose to solve our model by making use of Markov semi-renewal theory which allows us to only consider the semi-renewal period in evaluating the optimal infinite horizon solution. We define an inspection point (τ, 2τ, …) as a semirenewal point of the Markov process. It is not a complete renewal as we are tracking the amount of crack repairs. We must determine the stationary law of the semi-renewal interval •. The stationary law dictates that the long-run probability distribution that governs the process for any time t in one inspection interval is equivalent for all other inspection intervals. We begin by defining the state of the system at time t,

) , 0 ( τ ∈ t : L j (t) τ τ τ τ
The initial state of the system in Markov semi-renewal theory can be specified based upon our knowledge of the system at a defined time t = 0. The stochastic processes being applied in our model allow for estimating the probabilities of system states before and after inspection and subsequent to any repairs or rehabilitation actions at any time t, based upon our specification of the initial state. The evolution of the system between 0 and t is referred to f t (x, n | x 0 , n 0 ) where x 0 is the initial cumulative length of all unrepaired cracks at the beginning of the inspection cycle and n 0 is the initial number of cracks.

We find that the expected length of crack growth in a given inspection period • given an initial number of cracks n 0 , and initial cumulative growth length x 0 , is given by

( ) ( ) β αλτ τ β α τ 2 2 0 0 + + = n x X E . (6)
It should be noted that

[ ) γ , 0 0 ∈ x , N n ∈ 0
, and y 0 < l r . To define the density function for multiple cracks, we introduce the function f *n (x) that represents the nth convolution of the function f(x). Thus,

N n t ∈ ∀
, the density function is given by (

t n n n n t X t e n n t x x f t n Ga n x f λ λ β α - - - - - • = ! * , | , 0 0 * 0 0 0 (7) ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
where Ga(•) denotes the density function of the gamma distribution and

( ) ( ) ( ) ( ) ( ) ( ) ∫ - Γ = - - - t u t x t X du u t x t e x f 0 1 α β β α β . ( 8
)
Finally, we define the stationary law in two parts. Let I denote a binary variable indicating whether a repair has been made since the last rehabilitation: I {y = 0} (no repairs), I {• • y < lr} (repairs have been made). The stationary law is denoted as π(x, y, z) which represents the long-run probability of being in state (x, y, z). It is given by where P R is given by

( ) ( ) ∫ ∫ ∫ ∑ ∑ ∞ ∞ - ∞ = ∞ = + = r r r l l y l n n R dxdy y n x dx n x P γ π π 1 1 , , 0 , , (10)
Recall that P R is the long-run probability of performing a rehabilitation action. Thus, using the stationary law, we can compute the probability of performing a maintenance action as

( ) ( ) ∫ ∫ ∫ ∑ ∑ - -∞ = ∞ = + = r r r l l y l n n r dxdy y n x dx n x P γ γ γ γ π π 1 1 , , 0 , , (11)
We implement a 4-step algorithm for computing the stationary law beginning with an arbitrary value of P R . The algorithm operates as follows:

1. Determine ( )

π π = (12)
where ( )

0 , 0 , 0 π is an estimate of ( ) y n x , , π
based on an arbitrary value of P R and is thus not a true density function as the probabilities do not sum to 1. It is normalized by P norm which will cancel out P R and leave the true value of ( )

y n x , ,

π

. A three-dimensional plot of the stationary law for a given set of parameters is shown in Figure 3. The x and y axes represent the x and y variables, respectively. The z-axis represents

( ) ∑ ∞ =1
, , n y n x π . In Figure 3 the semi-renewals are clearly seen as the value of y cycles through multiples of γ, in this instance γ = 10. The initial cycle after a rehabilitation has the highest probability of occurrence and each cycle after has a decreasing probability of occurrence due to the increase variability in the combinations of x and y values.

From the stationary law, the optimal policy is found by searching for the minimum cost over an iteration of potential • and • values. The cost function ( 5) is a convex function of these parameters and the algorithm may be terminated once the cost begins to increase (i.e., if the iteration starts from • = 0 and • = 0, the cost function will decrease until the optimum value is reached, after which the function will increase).

NUMERICAL EXAMPLE

Consider the following parameters for road degradation, maintenance costs and the limit on the maximum allowable repaired cracks: Due to the convexity one knows they have reach the minimum cost as the cost curve will continue to decrease as a function of increasing γ values until the minimum is obtained and subsequent values of γ will cause the cost function to increase.

• = 0.1 • = 3 • = 10 l r = 60 c i = 10 c f = 10 c v = 5 c r = 1000 ( ) ( ) ( ) ( )      = = = = t y t Y t n t N t x
0 0 0 2 1 0 , min 0 1 0 0 0 0 0 , min 0 1 0 0 0 0 0 0 0 0 0 0                               ⋅                 - + + + +           + + = ∫ ∑ ∑ ∫ ∑ ∫ ∑ -∞ = > ∞ = = < ≤ = = n x f

DISCUSSION

In this paper we have formulated an optimal inspection and maintenance policy for highways based on the state of the road. We are able to formulate this policy under conditions of great uncertainty as only 3 parameters are required for the degradation model, namely λ, α and β. This is a drastic reduction compared to other statistical and Markov chain approaches in the literature which require a tremendous amount of data for the statistical models. In practice one can easily estimate values of λ based on rate of appearance of cracks. α and β can also be easily be found and adjusted for various highway material compositions, traffic patterns, and environmental conditions without having to collect a large amount of data. Our policy is very easy to implement in practical settings as it gives maintenance managers the periodic inspection interval τ and clear guidelines on whether to "do nothing", repair, or rehabilitate after each inspection. Solving for the optimal policy can be done quickly as the equations and algorithm have been coded to run on a computer.

Figure 3 -Figure 4 -

 34 Figure 3 -Density Function of the Stationary Law