Abstract. The temporal and regional process of knowledge spillover that hasa distinct geographical performance is an important process proposed by thetheory of new economic growth. Based on two case studies on the keywordsof sustainable development and knowledge economy, it is found that it isimproper for traditional theories to estimate the spillover intensity only byknowledge gaps. Three important findings have been discovered on the basisof the case studies. Firstly, not only is knowledge spillover related toknowledge gaps, but also the regional demands determined by geographicalcharacteristics. Secondly, similar to many economic geographical phenom-ena, the space of spillover intensity is exponentially decreasing. Thirdly,knowledge driven by regional demands is active rather than the ramificationof trading. Finally, a new model describing the spillover intensity betweenregions has been proposed in this paper.

JEL classification: O31, O33

1. Introduction

Regional interaction is a classical theme which reflects the interaction betweenregions (Wilson 1967; Haynes 1987; Wang et al. 1991; Wang 2000). After thedevelopment of the Wilson theory, regional interaction was generally re-garded as the relations of material transportation between regions. AlthoughWang (2000) emphasized that the relations included not only population andmaterial, but also capital as well, all of which were related to physical capital.Grossman and Helpman (1991) noted that knowledge spillover was essentialfor the common growth of regional economy, which make known that theknowledge spillover between regions is a major pattern of regional interactionand plays the same role as classical spatial interaction. It is one of the keyelements to understand regional geographical processes. As a new theme ofknowledge-based era, knowledge spillover becomes the focus of debate ofgeographers in recent years Beckman (1995) van de Klunder and Smulders(1996), Caniels (2000), Wallsten (2001), Bretscger (1999a).

Ann Reg Sci (2004) 38:595–606DOI: 10.1007/s00168-003-0186-1

A study on temporal and regional processof knowledge spillover

Zheng Wang 1,2, Cuifang Ma 1, Guilan Weng 3, Ying Wang 2

1 Institute of Policy & Management, Chinese Academy of Sciences, Beijing 100080, China2 Geocomputation Key Laboratory of GIS Sciences, CEDD, East China Normal University,Shanghai 200062, China (e-mail: lliwang@public.bta.net.cn)3 Urban and Regional Planning Department, Peking University, Beijing 100871, China

Received: June 2003/Accepted: November 2003

Verspagen (1992) and Caniels (2000) emphasized that regional spilloverhad the characteristics of diffusion and discussed regional knowledge spilloverwith the theory of center place and therefore introduced the spatial factor intothe general spillover theory. Further, Verspagen (1992) and Caniels andVerspagen (2001) defined the spillover intensity with knowledge gaps. That is,the spillover intensity of knowledge is satisfied with the following equation:

sij ¼di

rije�ð

1di

Gij�liÞ2 i 6¼ j ð1Þ

where sij is the knowledge spillover coming from region j to region i. dðkÞi is thelearning capacity in region i. rij is the spatial distance between region i and

region j. GðmÞij is the knowledge gaps which is defined as follows:

Gij ¼ lnKj

Kið2Þ

Here, Kj is the knowledge store in region j.However, Bretschger (1999b) came up with a key problem: There are no

data or statistics which give information on knowledge diffusion in space withspillover; in other word, Formula (1) describing the regional process ofknowledge spillover has not been verified by practical experiences. Further-more, after summarizing the studies on spillover, several unsolved problemshave been found as follows:

1) If the spillover is defined by the knowledge gap, then whether it is theonly factor that results in the generation of spillover. Or whether there areany other factor rather than the knowledge gap that affects the knowledgespillover. Especially, whether the basic realm of economy –‘‘demands’’ stillplays some roles in the process.

2) The interaction between spatial factors, knowledge diffusion andknowledge spillover has been ascertained by theories. How dose the spatialprocess of knowledge spillover accomplish in reality?

3) Since regional spillover acts as a geographical process, how do geo-graphical factors play their roles.

To explore the above problems and fill the vacant of practical study,two technological concepts, Sustainable Development (SD) andKnowledge-based Economy (KE), which can act as the representative ofnew technological concepts and have been broadly endorsed by scholars,have been selected as two objects to study the mechanism and the processof knowledge spillover.

The integrated concept of SD was come from the research report, OurCommon Future, issued by the United Nation in 1988. However, the pre-vailing of SD concept in China started from 1991, which can serve as thestarting point of the diffusion of the concept. After the 21st-Century Agendaof China passed by the Chinese State Council in 1993, the concept of Sus-tainable Development has been widely accepted by Chinese scholars. Con-sidering the concept was firstly introduced and issued by the Chinese centralgovernment in Beijing, it has a definite starting point of spatial diffusion.Moreover, because of the lack of natural resources and overpopulation, alllocal governments feel great challenges from the nature. As a result, theacceptance of the new technological concept SD had a potential coherence.Therefore, it is reasonable and representative to choose the concept SD tostudy the mechanism of spatial and temporal diffusion.

596 Z. Wang et al.

In 1996, the Knowledge-based Economy (KE) was first appeared in theinternational organization documents used by the Organization of EconomicCooperation and Development, whose headquarter is in Paris. Knowledge-based Economy is the economy that is based on the producing, distributingand using of knowledge and information. Currently, knowledge has beenconsidered as the driving force of improving productivity and realizing theeconomic growth. It is believed that Knowledge-base Economy (KE) wasfirstly advanced by US President Bill Clinton in 1997 and therefore KE, as atechnological concept, has the clear starting point of diffusion. Because KEhas the obvious starting point during its process of diffusion and belongs todifferent academic realm from SD, it has also been chosen as another studyobject,. These two concepts, SD and KE, are both related with economicgrowth, however, they relate to the physical geographical factors and eco-nomical geographical factors respectively, and hence display different spatialdiffusion process.

Another important reason to choose these two concepts as the studyobjects is that the diffusion of these two concepts was impelled by governmentand their diffusion was not impeded by patent right and technological pro-tection. For this reason , the diffusion process can be regarded as a generalprocess and can serve as a representative of diffusion process.

Technologically, this paper is based on the statistics of the science litera-ture center of Chinese Academy of Sciences. All papers with the keyword SD,published from 1991 to 2000, and with the keyword KE, published from 1997to 2000, have been statistically counted in terms of their publication quantity.

To simplify the expression, Sustainable Development papers or SDP rep-resents those papers with the keyword SD and Knowledge-based Economypapers or KEP with the keyword KE.

2. Temporal and regional evolution of knowledge spillover

2.1. The temporal evolution trend of knowledge diffusion

To find out the mechanism of knowledge spillover, the temporal trend of thenumber of SDP is showed in Fig. 2.1. From Fig. 2.1, it is found the diffusionspeed of the concept SD was very slow during the first two years. However,the diffusion speed increased significantly after 1996 and reached its peak in

Fig. 2.1. The evolution of number of SDP

A study on temporal and regional process of knowledge spillover 597

1999. After that, it began to decrease. The dynamic diffusion process revealsthat, at the very beginning of the concept diffusion in China, its diffusionspeed is relatively slow, which indicates that concept has not been widelyaccepted by the academia at that time. Later, the speed of diffusion increase,indicating that the new concept is generally accepted by scholars and widelydiffuses throughout China. This kind of processes is confirmed by the evo-lution of SDP, The whole process from the beginning, growth and peak todecline is shown in Fig. 2.1.

Similar to the situation of SDP showed in Fig. 2.1, Fig. 2.2 shows thetemporal trend based on the number of published papers with the keyword ofKnowledge-based Economy. Comparing Fig. 2.2 with Fig. 2.1, we find that thediffusion speed of KEP is much faster than that of SDP. After the first KEPpublished in 1997 and a slow diffusion in 1998, there is a rapid growth interms of diffusion in 1999. By 2000, a whole development process has beenaccomplished from beginning, growth and peak to decline.

2.2. The regional evolution of SDP

To carry out regional analysis, SDP has been classified by the writer’s insti-tutes and the number of the published papers to explore the mechanism ofspatial spillover. The quantitative regional distributions of SDP in 1991, 1993and 1997 have been shown in Figs. 2.3, 2.4 and 2.5 respectively to scrutinizethe regional evolution process of concepts SD and KE. Since SDP first ap-peared in Beijing, Beijing was regarded as the diffusion center of the conceptSD.

It was until 1993 that the concept of SD was recognized broadly andcaught much attention by the push of the government. From Fig. 2.4, it isobvious that the papers with concept SD mostly appeared in the regionswhere the environment is fragile. This phenomenon has a profound geo-graphical context. The natural environment of these regions is very fragile.The mix of farming and feeding and the degeneration are so serious that therelationship between human and nature are very intense in these regions(Zhao and Chen 2000). The findings here are a little bit different from thetheoretical mechanism of the already familiar spatial diffusion. According tothe traditional mechanism of diffusion, it is difficult to explain the phenom-enon that concepts first diffuse to regions where economy and technology areunderdeveloped. This phenomenon is inconsistent with those Grossman and

Fig. 2.2. The evolution of number of KEP

598 Z. Wang et al.

Fig. 2.3. The distribution of SDP in 1991

Fig. 2.4. The distribution of SDP in 1993

A study on temporal and regional process of knowledge spillover 599

Helpman (1991) first thought in principle. It is indicates here that the geo-graphical characteristics of knowledge spillover is the result of regional needsand the spillover is self-independence. Environment is so fragile and envi-ronment tension is so strong in those regions that government and scholarsare more sensitive to environment issues. It is justified that the concept SDfirst diffused to these regions was determined by natural geographical factors.That is to say, knowledge spillover was subject to the new factor–demandfactor, ‘‘created’’ by geographical condition. The appearance of demandfactor in spillover process is related to regional interest and thus makes dif-ference from diffusion process.

After 1994 the diffusion speed of the concept increased and new charac-teristics of regional distribution appeared. That is, there are different kinds ofregional distributions in terms of SDP. The first kind of regional distributionincludes those regions mentioned above where the environment pressure isvery strong and the relationship between human and nature is very intensesuch as Ganshu, Shanxi or Heilongjiang provinces where the natural envi-ronment is very fragile. Since the practice of sustainable development canrelieve the relationship between human and nature and can also promoteregional development, it was quickly paid much attention by people in theseregions. Another kind of regional distribution contains the coastal developedregions where the diffusion speed of SDP is at the peak. In these regions, thereare convenient communication system and strong technological basis. Theconcept SD first diffused to these regions due to their convenient communi-cation system and developed economy. Up to 1997, the concept SD haddiffused to almost all regions in China and the number of SDP started todecline distinctly in 2000. However, the knowledge gap oriented and demands

Fig. 2.5. The distribution of SDP in 1997

600 Z. Wang et al.

oriented functions could be identified from the spatial distribution and dif-fusion trend.

From the perspective of economic geography, the spatial decline ofspillover intensity needs further examination. To exclude the noise of de-mands, we divided the area of China into three kinds of regions: regionswhich are less than 500km from Beijing, regions which are between 500 to1000km from Beijing and regions which are more than 1000km from Beijing,the diffusion center of SD. The dynamic changes of SDP in these three regionsare shown in Fig. 2.6. It is clear that the distribution of concept SD isdeclining with the increase of the distance to the diffusion center. Althoughthe development of electronic technology has largely reduced the barrier ofspatial distance, face to face communication, besides communication viawritten format, is still necessary in the process of concept diffusion. Therefore,the less the spatial distance is, the higher intensity the spillover is. For the timeand economy concern, scholars in provinces far from Beijing have feweropportunities to learn and exchange the concept with other via face-to-facecommunication in Beijing. As a result, it is difficult for new concept to diffusedirectly from Beijing to those remote provinces in China. Usually, a conceptdiffuses to these regions gradually from nearby regions, which are closer toBeijing, the diffusion center. Because of the friction between regions in theprocess of diffusion, the speed of diffusion in these regions is lower than thatin those nearby regions. Consequently, similar to general geographical phe-nomenon, the knowledge spilling obviously follows the rule of spatial decline.

2.3. The regional evolution of KEP

The first paper with the keyword Knowledge-based Economy appeared inWuhan, the capital city and political and cultural center of Hubei province,which is located in a developed area of China, where information commu-nication is frequent. As an economic center of central China, new ideas comeout quickly and the revolution which overthrew the Qing-imperialism brokeout there in 1912.

By 1999, the concept KE has accomplished the whole process of spatialdiffusion in China. Figure 2.7 shows the spatial distribution of KEP in 1999in China. It shows that KEP has diffused to almost all regions of China. Thediffusion center is located in Hubei province and there are also many KEP

Fig. 2.6. The dynamic change of SDP with distance to the center

A study on temporal and regional process of knowledge spillover 601

diffused to Liaoning, Guangdong, Shanghai and Shangdong, where theeconomy is well developed. However, the KEP number is comparatively smallin Ningxia, Qinghai, Xizhang and Xinjiang. After careful analyzing thespatial pattern, we found that the diffusion is declining with the increase ofthe distance (see Fig. 2.8). This phenomenon can be attributed by two factors:the drive of needs and the friction of distance. The concept of knowledgeeconomy started to decline in 2000 and the concept of new economy becamethe focus of discussion emerged in Beijing.

As a summary, there are several characteristics of the regional evolution ofthe two concepts, SD and KE.

First, the diffusion centers of spillover usually appear in large main eco-nomic cities in china. Second, knowledge spillover is obviously related to theneeds generated from the factors that come from physical geography and theeconomic development. Third, spatial distance impedes the spillover andhence the spillover intensity declines with the increase of distance.

3. The model of regional spillover

Based on the above study, we can begin to model the regional spillover ofknowledge. A measurement of the amount of knowledge stored in a region isneeded. Many studies show that it is inappropriate to indicate the amount ofstored knowledge by the number of papers in publications. GDP per capita

Fig. 2.7. The distribution of KEP in 1999

602 Z. Wang et al.

was selected to serve as an index of stored knowledge because the amount ofstored knowledge, as an economic factor, should be expressed as an economyvariable. If we accepted the existence of knowledge economy, we must realizethat GDP reflects the amount of stored knowledge for Gross DomesticProduct (GDP) in a certain year is the result of accumulated knowledge ofeconomy system. It is found that the difference of GDP is consistence withknowledge levels between regions. Therefore, GDP could be selected as anindex to represent the extent of stored knowledge. Within the theory of neweconomy development, generally, it is difficult to measure many variablesdirectly, thus indirect representations are necessary to unravel the mechanismof the theory. Certainly, further studies are needed to determine these vari-ables.

Verspagen (1992), Caniels and Verspagen (2001) supposed that the declinewith the distance is in inverse proportion. Wilson (1967) approved that thedecline with the distance was in negative exponent and Wang (2000) made amore reasonable proof while avoiding the ‘‘pitfall’’ that the spillover of re-gions to themselves is infinite. Consequently, the basic model of knowledgespillover is identified in Eq. (3) which will be compared to the inverse pro-portion decline model expressed in Eq. (4).

sij ¼ die�ð l

dðkÞi

GðkÞij �liÞ2þ l

dð1Þi

GðdÞij �brij

ð3Þ

sij ¼di

rbij

e�ð l

dðkÞi

GðkÞij �liÞ2þ l

dð1Þi

GðdÞij

ð4Þ

Where GðkÞij is knowledge gap and GðdÞij is demand gap and ecological gap,measure by the ratio of regional ecological levels, in the issue of sustainabledevelopment (the sustainable development study group of CAS). b is spatialresistance.

The Eq. (3) has been changed to Eq. (5) by taking logarithm on its bothsides.

ln si ¼ ln d� brij �1

dðkÞ2

i

GðkÞ2

ij þ2l

dðkÞi

GðkÞij þ1

dð1Þi

GðdÞij � l2i ð5Þ

According to Eq. (5), the regression to the sum of SDP and KEP has beencarried out and the result is shown in Table 3.1. The same transformation hasbeen performed to Eq. (4).

Fig. 2.8. The dynamic change of KEP with distance to the center

A study on temporal and regional process of knowledge spillover 603

According to the result on F-test and t-test in Table 3.1, the knowledgegaps, the distance and the square of knowledge gaps are statistically signifi-cant. But the parameter of ecology gaps is not statistical significant. However,if only SDP is taken into consideration, the ecology gaps would statisticallypass the t-test. The results are showed in Table 3.2. It is clear that knowledgespillover is closely related to demands.

On the other hand, if the distance decline is considered as the exponent ofNewton expression in Eq. (4) rather than Wilson’s exponent, the results aredifferent and they are shown in Table 3.3.

Table 3.1. The regression result of the spillover level with SDP+KEP and the factor

Correlation coefficient R = 0.890602

df SS MS F

Regression analysis 4 24.10206 6.025516 22.0509Residual 23 6.284862 0.273255Sum 27 30.38693 F critical value is 2.80 t critical

value is 1.714Coefficient Standard error t statistic Lower 95%

Intercept 5.246545 0.236942 22.14273 4.756394rij 0.00034 0.000165 2.08769 0.00069

GðkÞij 0.910858 0.142551 6.389701 0.615969

GðkÞij 2 0.14076 0.096116 1.46452 0.3396

GðdÞij 0.40661 0.438667 0.926921 0.50084

Table 3.2. The regression result of the spillover level with SDP and the factors

Correlation coefficient R = 0.87519

Df SS MS F

Regression analysis 4 24.11927 6.029816 18.81817Residual 23 7.369779 0.320425Sum 27 31.48904 F critical value is 2.80 t critical

value is 1.714Coefficient Standard error t statistic Lower 95%

Intercept 3.51861 0.256579 13.71354 2.987836rij 0.00024 0.000179 1.36793 0.00061

GðkÞij 0.98485 0.154365 6.379999 0.665522

GðkÞij 2 0.16377 0.104082 1.57343 0.37908

GðeÞij 0.957606 0.475023 2.015914 0.02505

Table 3.3. Results of Newton’s model and Wilson’s model

Distance forms SDP+KEPcorrelationcoefficient

SDP correlationcoefficient

KEP correlationcoefficient

SDP+KEP F

1=rb 0.876027 0.867635 0.811501 18.9730expð�brÞ 0.890602 0.87519 0.835953 22.0509

604 Z. Wang et al.

According to Table 3.3, it is found that Wilson potential is much moresuitable for knowledge spillover than Newton potential. The reason is thatknowledge spillover takes place between regions in a 2-dimension geo-graphical phenomenon. It is proved that Newton potential would takefunctions only in a 3-dimension space (Wang 1980). But there is no significantdifference in the regression result. It is noted that the knowledge spilloverbetween regions does not take place in a continual space and the positionpotential theory may not be sufficient. However, Newton potential is feasiblein the case of simple situation.

Knowledge are products with difference and the demand for them are alsodifferent, therefore, the intensity model of regional knowledge spillover couldbe expressed as follows:

sij ¼ aie� 1

dðkÞi

GðkÞij �li

� �2

þPMm¼1

1

dðmÞi

GðmÞij �brij

ð6Þwhere sij is knowledge spillover from region j to region i, di is learning

capacity, rij is spatial distance between regional i and region j, GðkÞij represents

knowledge gaps and GðmÞij is the m-th need gaps of between i and region j a; bare regional parameters.

4. Conclusion and Discussion

In this paper, we carried out a case study in China to identify the spatialevolution processes of two concepts of terms- Sustainable Development andKnowledge-Based Economy. The process of knowledge spillover has beenanalyzed with the focus on restrictions coming from the natural geographicalfactors (ecology conditions) and economic geographical factors (spatial dis-tance). From the analysis, some findings have been discovered as follows:

1) Although knowledge gap are first factor for knowledge spillover, it isinappropriate to define knowledge spillover solely by knowledge gaps. The‘‘demand factors’’ generated from the physical geographical factors andeconomic geographical factors are important on the process of knowledgespillover and they express rather good correlated relationship. That is tosay, the discovering and utilizing of knowledge of our society has much todo with the social demands and thus the knowledge spillovers are geo-graphical oriented.

2) The key format of Wilson’s spatial interaction (1967) was defined in theform e�br. According to our study, the spatial decline of knowledgespillovers, a new economic geographical phenomenon, is according to theWilson’s model.

3) Finally, based on case studies, a new model of spillover, in which the geo-graphical factors have been considered, has been identified on the basis ofrevision of classic spillovermodel and it is a new formof regional interaction.

The case studies on knowledge spillovers are a kind of pro-active attemptsand there is no previous related study up to now. Therefore, there areinevitable some limitations in this study. First, on selection of samples, it isdifficult to define clearly the start points of the new concepts mostly. The

A study on temporal and regional process of knowledge spillover 605

concepts of SD and KE have been selected to explore the integrated evolutionprocess. However, the evolution processes of these two concepts are short-term processes. Whether the mechanism found in this study is appropriate tobe adopted in long-term processes requires further studies. On the other hand,whether the mechanism found in these two selective concepts, both are sci-entific terms, is appropriate to be applied to technological concepts needsfurther studies.

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