Thomas Scherngell
email: thomas.scherngell@ait.ac.at

Yuanjia Hu
email: yuanjiahu@umac.mo

Collaborative Knowledge Production in China. Regional Evidence from a Gravity Model Approach

Keywords: JEL Classification: O38, L14, R15 Co-publications, collaborative knowledge production, Negative Binomial regional gravity model, Chinese regions räumliche Muster kollaborativer Wissensproduktion zwischen 31 chinesischen Regionen zu beschreiben und den Einfluss von geographischen, technologischen und ökonomischen Determinanten auf die Variation interregionaler Kollaborationsaktiviäten zu messen. Die Studie verwendet neue Daten aus der zeigen, das die Kollaborationswahrscheinlichkeit signifikant mit zunehmender geographischer Distanz abnimmt. Der Einfluss von technologischer Nähe ist jedoch wichtiger als geographische Distanzeffekte, während ökonomische Unterschiede

In this study we investigate collaborative knowledge production in China from a regional perspective. The objective is to illustrate spatial patterns of research collaborations between 31 Chinese regions, and to estimate the impact of geographical, technological and economic factors on the variation of cross-region collaboration activities within a Negative Binomial gravity model framework. We use data on Chinese scientific publications from 2007 with multiple author addresses coming from the China-National-Knowledge-Infrastructure (CNKI) database. The results provide evidence that geographical space impedes crossregion research collaborations in China. Technological proximity matters more than geography, while economic effects only play a minor role.

Introduction

The literature on the geography of innovation argues that knowledge flows between agents are geographically bounded since knowledge is in part tacit. Though the cost of transmitting codified knowledge may be invariant to distance, presumably the cost of transmitting noncodified knowledge across geographic space rises with geographic distance (see [START_REF] Audretsch | R&D spillovers and the geography of innovation and production[END_REF]. Also in scientific research collaborations spatial proximity may occur as an important determinant of the intensity of collaboration between two actors (see [START_REF] Katz | What is research collaboration?[END_REF]. Time and money required to engage in collaborations is limited which forces collaborating actors to be highly selective in choosing a collaboration partner. Thus, collaboration intensity between any two actors will not only be affected by learning opportunities, but also by the time and the coordination costs incurred by participating in collaborations (see [START_REF] Hoekman | The geography of collaborative knowledge production in Europe[END_REF]. [START_REF] Cummings | Coordination costs and project outcomes in multiuniversity collaborations[END_REF] illustrate the importance of coordination costs in research collaborations. These costs may increase with geographical distance, but also with the existence of institutional barriers or language borders, since long-distance collaborations are more time-consuming and yield additional travel costs (see, for instance, [START_REF] Hinds | Out of Sight, Out of Sync understanding conflict in distributed teams[END_REF].

From its beginning, the empirical literature on the geographic localisation of knowledge diffusion has faced numerous problems, particularly concerning the measurement of knowledge production and diffusion. KRUGMAN (1991, p. 153) states that "knowledge flows are invisible, they leave no paper trail by which they may be measured and tracked", pointing to difficulties in finding data on knowledge flows. However, during the 1990s the empirical research on the spatial diffusion of knowledge has significantly improved by using new indicators and introducing new (spatial) econometric methods. The pioneering study of [START_REF] Jaffe | Geographic localization of knowledge spillovers as evidenced by patent citations[END_REF] uses patent citations as a paper trail for knowledge flows in the United Europe at a regional level to identify various determinants of knowledge diffusion. In general, these studies provide evidence -as assumed by [START_REF] Breschi | Knowledge spillovers and local innovation systems A critical survey[END_REF] -that the localisation of knowledge flows is to a lesser extent related to geographical distance effects, than to institutional or technological conditions, i.e. geographical proximity is not a sufficient condition for knowledge flowing between agents, but still conducive.

Other empirical studies focus on research collaborations to investigate the geographic localisation of knowledge flows. [START_REF] Katz | Geographical proximity and scientific collaboration[END_REF] investigates the effect of geographical proximity for university collaborations in Canada, Australia and the UK, while [START_REF] Liang | Major factors affecting China´s inter-regional research collaboration Regional scientific productivity and geographical proximity[END_REF], [START_REF] Ponds R | The geographical and institutional proximity of research collaboration[END_REF] and [START_REF] Hoekman | The geography of collaborative knowledge production in Europe[END_REF] argue that the regional level is an appropriate choice since "Regions have played and will continue to play a key role in the advancement of S&T in China" (OECD 2007, p. 22). The region is an important unit in a Chinese science and technology policy context since recent policy efforts aim to reduce barriers to cross-region collaborations in science in order to support the development of an harmonised Chinese innovation system.

In The remainder of the study is organised as follows. The next section highlights some general aspects of scientific collaborations in China, sheds some light on the Chinese (regional) policy context, and provides a short literature review. Section 3 describes the empirical setting of the study and discusses in some detail the co-publication data used accompanied by some descriptive statistics. In Section 4 we analyse spatial patterns of collaborative knowledge production across Chinese regions. Our territorial breakdown is composed of 31 regions, including the 22 provinces of China, five autonomous regions and four municipalities. We use a slightly modified Jaccard similarity coefficient to identify the relative strongest collaboration links in terms of attractiveness. Section 5 continues to describe the regional gravity model that we use to estimate separation effects of cross-region collaboration activities. The dependent variable are observed cross-region collaborative intensities, the independent variables include origin, destination and separation variables, such as the geographical and technological distance as well as the economic gap between regions. We use a Negative Binomial model specification to account for the non-negative, integer nature of our dependent variable and to allow for the overdispersion in the data by letting each pair of regions parameter have a random distribution of its own. Section 6 presents the estimation results for all co-publications as well as for six different scientific fields, before we conclude with a summary of the main results, some policy implications and a short outlook in the final section.

Scientific research collaborations in China

In the current era of the knowledge-based economy, it is widely agreed that research collaborations, both in the industry and the science sector, but also between the science and the industry sector, are essential for the successful production of new knowledge (see, for example, OECD, 1992, among many others). In the science sector, co-publications accounted China follows this trend in the strategic orientation of its science and technology policy.

China faces two major barriers for research collaborations. First, there exist enormous regional disparities, both in the education as well as in the science sector. A considerable number of empirical studies on this issue confirm the essential inter-regional gap of education and research systems in China (see [START_REF] Tu | Factors and regional disparity of self-innovation capabilities in China[END_REF][START_REF] Zhang | Spatial inequality in education and health care in China[END_REF] (2007) points out that these regional patterns of R&D and innovation activities in China are not optimal from a social equity perspective, as innovation systems in lagging regions are underdeveloped. Thus, OECD (2007) also concludes that the national innovation system is not fully developed and still imperfectly integrated due to various barriers between the specific regional innovation systems. Second, regional protectionism is a widely documented phenomenon in China (see, for instance, [START_REF] Bai | Local protectionism and regional specialization Evidence from China's industries[END_REF]. [START_REF] Chen | The influence to the local S&T legislation from the view of CAST operation mode forum on science and technology in China[END_REF] disclose that regional policy makers follow a protectionism perspective in the orientation of their science policy. Also ZHANG (2003) considers regional protectionism as one of the major problems of cross-region collaborations in science and technology. One prominent instrument used by local governments to exert creeping protectionism is China's so-called hukou (household registration) system (see [START_REF] Chen | The influence to the local S&T legislation from the view of CAST operation mode forum on science and technology in China[END_REF]. This system has imposed strict limitations on ordinary Chinese citizens changing their permanent place of residence.

Employment, housing, and social benefits are commonly linked to hukou identification. Rural migrants to urban areas are often unable to obtain equal access to public services such as health care and education. Also the mobility of researchers for scientific knowledge production is affected by the hukou system. For instance, it is more difficult for researchers to move to another university located in a city for which they have no hukou. Furthermore, regional authorities at the province level play an important role to allocate S&T resources in China. 93% of public research institutions in China are mainly funded by local governments (NBS, 2007). Thus, research collaborations between research institutions located in different regions face significant barriers coming from regional protectionism (see also OECD, 2007).

The of administrative barriers to inter-regional collaborations, and the establishment of specific funding and coordinating organizations aimed to impel such inter-regional collaborative activities.

There exists a significant body of literature related to the analysis of scientific research collaborations in China. These studies can roughly be divided into three categories: policy initiatives aimed to support research collaborations 3 . However, our data are not completely without limitations. First, different scientific journals have different ways to deal with zip code information of authors. For instance, some journals only show the zip code information for the corresponding author, while some even do not provide any zip code information. Second, we found that some publications are inappropriately classified according to the six thematic fields given in the CNKI database. Further, more general limitations to the use of co-publication data are provided in [START_REF] Hoekman | The geography of collaborative knowledge production in Europe[END_REF]. Despite these shortcomings, we still consider our data appropriate and very useful given our research objectives, in particular due to the large sample size used.

By nature of our research question, we need to construct region-by-region co-publication matrices based on a two-step procedure: First, we produce a general region-by-region copublication matrix including all publications (i.e. irrespective of the thematic field), that we label Y, by aggregating the number of individual co-publications to the regional level 4 . y ij represents one element of Y denoting the number of observed co-publications between two region i and j. Thus, Y contains the co-publication intensities between all (i, j)-region pairs,

given the i =1, …, n = 31 regions in the rows and the j = 1, …, n = 31 regions in the columns 5 .

Second, the sector specific collaboration matrices for our six thematic fields are extracted from Y, by excluding all publications not belonging to the respective thematic field. We end up with six further n-by-n collaboration matrices for each thematic field, labelled Y (agr) for Agriculture, Y (eco) for Economics, Y (it) for Information Technologies, Y (med) for Medicine, Y (nse)

for Natural Sciences & Engineering and Y (soc) for Social Sciences.

Spatial patterns of Chinese research collaborations

This section sheds some light on spatial patterns of Chinese research collaborations as captured by co-publications. Figure 1 presents the cross-region network of knowledge flows across Chinese regions. It can be seen that the region of Beijing is the central hub in this spatial co-publication network. One line represents one co-publication link between two regions i and j, the size of the nodes corresponds to a region´s degree centrality, i.e. the number of links of one region from a projected network analysis point of view. At a first glance, the results indicate that co-publications spread out star-shaped from the region of Beijing to all other regions. This may not only be explained by the fact that most universities and researchers are located there. The total number of co-publication links of Beijing equals to 117,226, followed by the region of Jiangsu (60,072) and the region of Guangdong (58,166).

The highest cross-region interaction intensity is observed for the region pairs Beijing and Shandong (2,526), followed by Beijing and Shaanxi (2,341) and Beijing and Guangdong

(2,202).

Figure 1 about here

This exploratory spatial analysis reveals cross-region co-publication flows in terms of absolute link size. However, from social network analysis we know that we should consider the relative strength of the links between nodes, i.e. regions in our case. One appropriate measure to capture the relative size of the cross-region collaborative links is the Jaccard index (see, for instance, LEYDESDORFF, 2008). In our study the index is defined as 6

( )

1 ij i j ij ij J y y y y - • • = + - i, j = 1, …, n (1)
with

1 n i ij j j i y y • = ≠ = ∑ , 1 n j ij i i j y y • = ≠
= ∑ and y ij is the number of observed links between i and j.

The calculation of the J ij coefficient for our (i, j)-region pairs leads to interesting results concerning the spatial structure of cross-region co-publications in China. region Chongqing are highly focused on the region Sichuan, and vice versa. One may also conclude that different disciplinary specialisation and diversification patterns of regions play a role here. However, we cannot identify considerable differences in the disciplinary specialisation of the regions with respect to their publication intensity in our six scientific fields 7 . Thus, we conclude that there may exist -maybe historically well established -links between specific universities that are located in neighbouring regions and are characterized by a higher researchers mobility between them. The strongest connection according to the Jaccard index appears between the regions Chongqing and Sichuan in the western area of China. This pair belongs to the top 5 in all other thematic fields except from Social Sciences.

A very strong relative connection is also found for the region pairs Jiangsu and Shanghai as well as for Shanghai and Zhejiang. Beijing and Shandong is the only non-neighbour pair that appears twice (all co-publications and Natural Sciences & Engineering). These results may point to the existence of strong geographic localisation effects in Chinese co-publication activity.

ij ij ij Y X ε = + i, j = 1, …, n (2)
where Y ij is assumed to be a stochastic dependent variable corresponding to the observed collaboration flow

0 ij y ≥
between two regions i and j. X ij is a function that captures the stochastic relationship to other random variables sampled from a specified probability distribution dependent upon some mean, say ij

µ , with [ ] ij ij E Y µ = . ij ε is a disturbance term with the property [ | ] 0. ij ij E y ε =
For our empirical analysis, the next step is to develop an appropriate model for the systemic part of the model X ij . Since we are dealing with interactions between regions in a multiregional setting, the spatial interaction model of the gravity type is an appropriate

instrument. Thus, ij ij X µ =
is specified as a function of covariates measuring the characteristics of origin regions, destination regions, and their separation, given by ( )

ij i j ij X f O D S = i, j = 1, …, n (3)
where O i is a function characterising region i of interaction, D j is a function characterising region j of interaction, while S ij is a function characterising the separation between two regions i and j. We follow classical spatial interaction theory (see, for instance, SEN and SMITH 1995) and specify origin and destination functions by using power functions as α are the respective parameters to be estimated 10 . By nature of our research questions, the focus of interest is on the spatial separation function S ij that is specified as

1 i i O o α = i = 1, …, n (4) 2 j j D d α = j = 1, …, n (5)
( ) 1 exp K k ij k ij k S s β =   =     ∑ i, j = 1, …, n (6)
with ( ) k ij s representing a measure of separation between i and j. The k β are unknown parameters. By theory and our research questions, our interest is focused on K = 6 separation measures: (1) ij s denotes geographical distance between two regions i and j as measured in terms of the great circle distance between the capital cities of the regions 11 . ( 2) ij s is a dummy variable that is set to one if two regions i and j are physical neighbours, and zero otherwise 12 .

(3) ij s accounts for the economic gap of two regions i and j and is defined as (3)

ij i j s G G = -
where G i and G j is the Gross Regional Product in 2007 for region i and j, respectively 13 . Furthermore, we add two variables that control for the fact that China is characterized by huge disparities between the coastal area and the rest of China 14 . ( 4) ij s is a dummy variable that is set to one if either or both regions i and j are located in the coastal area of China, and zero otherwise, while (5) ij s is a dummy variable that takes values of ones if either or both regions i or j are located in the central area of China 15 , and zero otherwise. Finally, (6) ij s controls for the technological distance between two regions i and j. We use data from the Chinese Patent Office to measure this variable. It is constructed as a vector t(i) that measures region i's share of patenting in specific technological classes of the International Patent Classification (IPC) 16 .

We follow [START_REF] Moreno R | Spatial spillovers and innovation activity in European regions[END_REF] Integrating Equations ( 4)-( 6) into Equation (2) leads to the empirical model:

1 2 ( ) 1 exp K k ij i j k ij ij k y o d s ε α α β =   = +     ∑ . i, j = 1, …, n (7)
At this point, we are interested in estimating the parameters 1 2 , α α and k β that are elasticities of cross-region scientific collaborations y ij with respect to the origin variable o i , the destination variable d j and the separation variables ( )

k ij s .
Due to the integer non-negative nature of our data and distributional assumptions, OLS estimation procedures are not appropriate (see, for example, [START_REF] Long | Regression Models for Categorical Dependent Variables Using Stata[END_REF]. The Poisson distribution is widely considered as a reasonable description for non-negative integer values (see [START_REF] Maddala | Limited Dependent and Qualitative Variables in Econometrics[END_REF]. In our empirical setting, the Poisson density function is given by ( ) where 0 α is a constant, and assuming that

Pr ! ij ij y ij ij ij ij ij Y y X e y µ µ - = = , i, j = 1, …, n; 0, 1, 2, ... ij y = (8) with 0 1 2 ( ) 1 exp log( ) log( ) K k ij ij i j k ij k X o d s α α α µ β =   = = + + +     ∑ (9)
ij ij ij ij ij V Y X E Y X µ     = =     (10)
The parameters are estimated by standard Maximum Likelihood procedures using Newton

Raphson iterations (see [START_REF] Cameron | Regression Analysis of Count Data[END_REF].

Specification (10) implies a particular form of heteroscedasticity due to equality of the conditional mean and the variance of Y ij given X ij . This indicates that the independent variables are assumed to account for all individual deviations. However, in a multiregional setting the existence of unobserved heterogeneity is very likely and may lead to biased estimates (see [START_REF] Hausman | Econometric Models for Count Data with an Application to the Patents-R & D Relationship[END_REF]. A common strategy to overcome the problem of unobserved heterogeneity is to introduce a stochastic heterogeneity term, exp(ξ ij ), in the conditional mean leading to a probability distribution given by ( ) ( ) ( )

exp( ) * Pr exp( ) ! ij ij y ij ij ij ij ij ij Y y X y ξ µ µ = = - i, j = 1, …, n; 0, 1, 2, ... ij y = (11) with 0 1 2 * ( ) 1 exp log( ) log( ) K k ij i j k ij ij k X o d s α α α β ξ =   = + + + +     ∑ and ( ) exp( ) ij ξ Γ γ
( ) 1 * 1 1 ( ) Pr 1 ! ( ) y ij ij ij ij ij ij ij ij y Y y X y γ Γ γ θ θ Γ γ - - + = = -     i, j = 1, …, n; 0, 1, 2, ... ij y = (12)
ij ij θ γ γ µ - - = + . i, j = 1, …, n (13)
Model estimation is again done by Maximum Likelihood estimation procedures (see [START_REF] Cameron | Regression Analysis of Count Data[END_REF] for details on the ML estimation).

Estimation results

Table 3 presents the sample estimates of the gravity models for all co-publications (Y). The first column gives the results for the basic Poisson model without heterogeneity as specified by Equations ( 8)-( 10), the second column for the Negative Binomial model (Equations ( 12) and ( 13)). Standard errors are given in brackets, and parameters are estimated by Maximum Likelihood procedures, using Newton Raphson. The estimated value of the dispersion parameter γ = 0.957 with p < 0.001 in the Negative Binomial specification (second column of Table 3) indicates that the basic Poisson model has to be rejected. Assumption (10) is too restrictive to adequately model our cross-region co-publication data due to unobserved heterogeneity among the (i, j)-region pairs. Thus, we prefer the Negative Binomial model specification leading to a very large increase of the log-likelihood function as compared to the

Poisson model without heterogeneity. The Negative Binomial estimates are all significant and robust. However, the estimated standard errors are somewhat larger than for the basic Poisson model due to allowance for an additional source of variance. In the context of the relevant theoretical and empirical literature as well as within a Chinese policy context, the results provide new valuable insights into the mechanisms of the diffusion of scientific knowledge in China. First, geographical distance between authors exerts a significant negative effect on the probability that they collaborate with each other. The parameter estimate of 1 β = -0.354 tells us that for each additional 100 km between two authors, the probability for collaboration decreases by about 29.8%, holding all other variables constant. Since we are investigating knowledge flows within one country, this relatively high negative effect of geographical distance is somewhat surprising as compared to similar studies for regions located in different countries that find similar or even lower distance effects -using different indicators for knowledge flows between European regions, including co-publications (see [START_REF] Fischer | The geography of knowledge spillovers between high-technology firms in Europe. Evidence from a spatial interaction modelling perspective[END_REF][START_REF] Lesage | Knowledge spillovers across Europe. Evidence from a Poisson spatial interaction model with spatial effects[END_REF]2007;[START_REF] Ponds R | The geographical and institutional proximity of research collaboration[END_REF][START_REF] Scherngell | Spatial interaction modelling of cross-region R&D collaborations. Empirical evidence from the 5th EU Framework Programme[END_REF]. In an integrated research area collaboration patterns should be based solely on scholarly ground, and not impeded by geographical barriers. Thus, we conclude that China´s regional integration policy faces a big challenge, in particular -but not exclusively -because of negative geographical distance to inter-regional collaborative knowledge production. There seems to be a clear need for further harmonising the Chinese research and education systems. [START_REF] Maurseth | Knowledge spillovers in Europe A patent citation analysis[END_REF][START_REF] Fischer | The geography of knowledge spillovers between high-technology firms in Europe. Evidence from a spatial interaction modelling perspective[END_REF][START_REF] Lesage | Knowledge spillovers across Europe. Evidence from a Poisson spatial interaction model with spatial effects[END_REF][START_REF] Hoekman | The geography of collaborative knowledge production in Europe[END_REF][START_REF] Maggioni | Knowedge networks across Europe which distance matters?[END_REF]SCHERNGELL and[START_REF] Scherngell | Spatial interaction modelling of cross-region R&D collaborations. Empirical evidence from the 5th EU Framework Programme[END_REF][START_REF] Scherngell | Distinct spatial characteristics of industrial and public research collaborations Evidence from the 5th EU Framework Programme[END_REF]. This supports the conclusion that geographical proximity is not a sufficient condition for collaborations to occur between researchers, but still conducive. Regarding the impact of the economic gap between two regions on their collaboration probability ( 3 β = -0.048), we find -though significant -a rather small effect. As expected, the estimates for the mass terms (α 1 =α 2 =1.001) are close to one, indicating that a higher number of research staff in a specific region increases the likelihood of collaboration with other regions. and significant differences of the results across scientific fields. The most notable outcome is that the elasticity of the collaboration intensity with respect to geographical distance between collaborating researchers is lowest in the field of Information Technologies, maybe associated with a higher level of integration by using new information and communication systems.

However, for Information Technologies we also find the highest neighbouring region effects, i.e. though negative effects of geographical distance are relatively lower, collaborations in this field are subject to a specific type of localisation, namely an increasing collaboration probability between neighbouring regions. The highest elasticity of collaboration intensity with respect to geographical distance is identified for the fields Economics and Medicine, while for the other fields the magnitude of the geographical distance effect is closer to the average for all publications. Regarding the estimates for the other separation variables in the sector-specific models given in Table 4, the results of the model for all co-publications are generally confirmed, though some estimates are not significant anymore.

Table 4 about here

Closing comments and discussion

The empirical analysis of knowledge flows and knowledge diffusion in geographical and technological space is one of the key research areas of contemporary economic geography and economics of innovation. The study at hand adopts a regional gravity model framework to analyse the variation of cross-region collaborative knowledge production in China as captured by scientific co-publications. We focused on the question whether geographical space is a significant determinant of collaborative knowledge activities between Chinese regions, at the same time controlling for economic and technological differences. We use a Negative

Binomial model specification of our regional gravity model to allow for overdispersion in the data.

The analysis has produced a number of interesting results in the context of the relevant empirical and theoretical literature. The probability of collaboration between researchers significantly decreases by geographical distance. Furthermore, technological distance between regions shows a somewhat larger negative effect on cross-region collaborative activities, indicating that the collaboration probability increases between regions that are located close to each other in technological space. By this, our study confirms the hypothesis for the Chinese case that the localisation of knowledge flows is to a lesser extent related to geographical distance effects, than to technological conditions, i.e. geographical proximity is not a sufficient condition for collaborations to occur between researchers, but still conducive.

However, geographical effects are statistically significant across all scientific disciplines, though its magnitude varies. In the fields of Information Technologies and Natural Sciences and Engineering we find a lower negative effect of geographical distance. This may pertain to Furthermore, the results point to the existence of quite high barriers to collaboration between authors located in the central area and authors located in the coastal area of China. Effects of economic differences between regions are rather small but statistically significant.

The study at hand produces significant policy implications, and shows that there is much space for improvement in a Chinese policy context. Though we are investigating knowledge flows within one country, we find strong evidence for the negative effect of geographical distance on the variation of cross-region collaborative knowledge production in China. Thus, Chinese regional integration policy is claimed to establish further measures to ease barriers between regions, for instance by harmonising research and education systems. Two major factors that hinder inter-regional collaboration need to be addressed by the policy: First, regional protectionism still plays a crucial role. Thus, the central Chinese government needs to improve the supervision of the allocation of regional S&T resources by regional governments, and remove barriers for researchers mobility coming from inconsistencies because of different regional household registration systems. Second, regional economic and technological differences are significant factors. A series of measures has been taken to encourage cooperation between regions with different comparative advantages, but the strong negative effect of technological proximity to the variation of inter-regional research collaborations in the current study implies that there remains much space for improvement in this direction. Concerning economic effects, Chinese government has launched a series of policies to reduce regional economic disparities in the recent past, particularly The Grand Western Development Program starting in 1999. The empirical results imply that these measures may have to some extent achieved a positive feedback, at least in the context of cross-region research collaborations, though the impact of economic disparities is still 3 By focusing on publications with financial support, we delimit the scope of the study to a special form of copublications that is -to our view -a more suitable proxy for cross-region collaboration intensities since we take into account policy initiatives aimed to support research collaborations. By this our indicator comes more close to recently used indicators for knowledge flows between European regions as captured by joint R&D projects in the European Framework Programmes (see SCHERNGELL and[START_REF] Scherngell | Spatial interaction modelling of cross-region R&D collaborations. Empirical evidence from the 5th EU Framework Programme[END_REF][START_REF] Scherngell | Distinct spatial characteristics of industrial and public research collaborations Evidence from the 5th EU Framework Programme[END_REF].

them in the formal presentation. 7 The index of specialization calculated in this study is defined as ( )

1 2 i ik ik S y y = - ∑
, where y ik is the share of publications in the scientific field k in region i, and The model described in this section is equally applicable to Y (agr) , Y (eco) , Y (it) , Y (med) , Y (nse) , Y (soc) . We do not distinguish between them in our formal presentation.

9 Data for researchers, including researchers employed at any institution, come from the China Statistics Yearbook 2007 (NBS, 2007).

10 Note that due to symmetry of the origin and destination variables we have a special case with [α 1 =α 2 ].

11 According to [START_REF] Bröcker | How to eliminate certain defects of the potential formula[END_REF], we calculate the intra-regional distance as

(1) 0.5

(2 / 3) ( / )

ii i s A π = , where A i is denotes the area of region i, i.e. the intra-regional distance is two third the radius of an presumed circular area.

Note that we refrained adding an intra-regional dummy variable to the model due to high correlation with the logarithm of the geographical distance variable

(1) ij s .

12 Physical neighbours are defined to share a common border. Note that intra-regional observations are not part of this reference group, i.e. a region cannot be a neighbour to itself.

13 GRP data come from the China Statistics Yearbook 2007 (NBS, 2007).

14 These disparities -reported in a large number of empirical studies (see, for instance, [START_REF] Liu | Regional policy, regional openness and regional disparity in economic development[END_REF][START_REF] Xu | Spatial and temporal scale analysis on the regional economic disparities in China[END_REF] -cannot be captured by the other covariates. The differences do not only refer to economic disparities, but also to cultural, educational, social and institutional ones. For instance, [START_REF]China R&D A high-tech field of dreams[END_REF] provides empirical evidence that the vast majority of foreign invested R&D centers are located along the eastern coast. This might attract researchers to collaborate with other researchers located in these regions.

Thus, we strongly assume that it is important to account for a coastal area and central area effect in the model in order to avoid an omitted variable problem. 15 The coastal area includes the regions of Beijing, Fujian, Guangdong, Guangxi, Hainan, Hebei, Jiangsu, Liaoning, Shandong, Shanghai, Tianjin and Zhejiang. The central area is composed of the regions of Anhui, Heilongjiang, Henan, Hubei, Hunan, Jiangxi, Jilin, Nei Mongol and Shanxi. 16 The technological classes used correspond to the second-digit level of the IPC systems. 17 The additional parameter γ changes assumption (10) by

* * * ( | ) ( | ) [1 ( | )] ij ij ij ij ij ij V Y X E Y X E Y X γ = + which is a natural form of overdispersion in that the overdispersion rate is * * * ( | ) ( | ) 1 ( | ). ij ij ij ij ij ij V Y X E Y X E Y X γ = +
Note that when γ = 0, model (12) collapses to the standard Poisson specification as given by Equation (8).

18 Another way to deal with the problem of unobserved heterogeneity is to use quasi maximum likelihood estimation strategies. We prefer the Negative Binomial solution as it allows the likelihood ratio and other standard maximum likelihood tests to be implemented (see [START_REF] Ismail | Handling overdispersion with Negative Binomial & Generalized Poisson Regression Models[END_REF]. Notes The dependent variable is the cross-region co-publication intensity between two regions i and j. The independent variables are defined as given in the text. Note that due to symmetry of the origin and destination variables we have a special case with [α 1 =α 2 ]. The multicollinearity condition number yields a value of 4.023, while the Variance Inflation Factors (VIFs) for the variables range between 1.27 and 3.83, so we infer there are no multicollinearity problems (see [START_REF] Chatterjee | Regression Analysis by Example[END_REF].We tested the residual vector for the existence of spatial autocorrelation which can also be a problem in the context of interaction data (see [START_REF] Fischer | Modeling spatial autocorrelation in spatial interaction data. An application to patent citation data in the European Union[END_REF]. The respective Moran´s I statistic is insignificant, i.e. spatial autocorrelation in the error term does not exist. *** significant at the 0.001 significance level, ** significant at the 0.01 significance level, * significant at the 0.05 significance level. Notes The dependent variable is the cross-region co-publication intensity between two regions i and j in different scientific fields. The independent variables are defined as given in the text. Note that due to symmetry of the origin and destination variables we have a special case with [α 1 =α 2 ]. Technological distance is not included in the sector-specific models. We tested the residual vector for the existence of spatial autocorrelation which could be a problem in the context of interaction data (see [START_REF] Fischer | Modeling spatial autocorrelation in spatial interaction data. An application to patent citation data in the European Union[END_REF]. The respective Moran´s I statistic is insignificant, i.e. spatial autocorrelation in the error term does not exist. *** significant at the 0.001 significance level, ** significant at the 0.01 significance level, * significant at the 0.05 significance level.

F

  provide evidence that geographical proximity promotes knowledge diffusion processes.[START_REF] Breschi | Knowledge spillovers and local innovation systems A critical survey[END_REF] re-examine the geographical localisation hypothesis, and highlight the importance of additional factors, such as labour mobility, or institutional and cultural barriers. In this context, more recent empirical studies try to control for these additional factors in an advanced econometric framework. Notable examples are the studies of[START_REF] Maurseth | Knowledge spillovers in Europe A patent citation analysis[END_REF][START_REF] Maurseth | Knowledge spillovers in Europe A patent citation analysis[END_REF][START_REF] Fischer | The geography of knowledge spillovers between high-technology firms in Europe. Evidence from a spatial interaction modelling perspective[END_REF] analysing knowledge flows across European regions by using patent citation data of the European patent office.SCHERNGELL and[START_REF] Scherngell | Spatial interaction modelling of cross-region R&D collaborations. Empirical evidence from the 5th EU Framework Programme[END_REF][START_REF] Scherngell | Distinct spatial characteristics of industrial and public research collaborations Evidence from the 5th EU Framework Programme[END_REF]) make use of joint research projects funded by the European Framework Programmes as a proxy for knowledge interactions in

  use research collaborations as captured by joint scientific publications (co-publications) to analyse localisation effects of knowledge flows. The current study follows the research tradition focusing on research collaborations as captured by co-publications to investigate the geographical dimension of knowledge diffusion. The objective is to provide new empirical insights on the mechanisms of collaborative knowledge production in China by using new information on co-authored scientific publications, and to estimate how spatial, technological and economic characteristics affect the variation of collaboration activities between Chinese regions. We

  using Chinese co-publication data as a proxy for collaborative knowledge production in China, we build on recent work by LIANG and ZHU (2002) 1 but depart from this prior work in at least three major respects: First, we follow PONDS et al. (2007) and HOEKMAN et al. (2009) by employing a spatial interaction model of the gravity type to identify and measure separation effects of cross-region collaborative knowledge production, and use a Negative Binomial model specification due to the presence of unobserved heterogeneity in our crossregion co-publication data. This methodological framework enables us -in contrast to the study of LIANG and ZHU (2002) -to control for other determinants than geographical distance affecting cross-region collaboration intensities. Second, we make use of new unique data on scientific publications in China of the year 2007 extracted from the China National Knowledge Infrastructure (CNKI) database. Third, we investigate differences of spatial patterns of collaborative knowledge production and their determinants across six different scientific fields. Such differences may occur due to different collaboration behaviour across scientific fields, related to different epistemic and cognitive regimes (see, for instance,[START_REF] Thagard | Collaborative Knowledge[END_REF][START_REF] Wray | The epistemic significance of collaborative research[END_REF]. Differences in the geographical localisation of scientific disciplines may be related to the localisation of important research equipment, in particular in natural sciences, and to the use ofICTs. PONDS et al. (2007) provide evidence that geographical distance effects to collaboration differ across scientific subfields using Dutch copublication data.

  Conceptual and theoretical studies, empirical analyses of individual regions, and empirical research on interactions between regions. The first category generally employs qualitative methods to describe the current situation, including existing problems and policy recommendations, of scientific research collaborations in China (see, for instance,[START_REF] Wei | The cause, model and policy implications of cooperation and communication of science and technology among administrative regions in China[END_REF]. Briefly speaking, these studies point out the importance and significance of scientific research collaborations and encourage fostering inter-regional cooperation in science and technology. The second category of studies investigates individual regions with respect to their collaboration ability by measuring their knowledge absorption capabilities (see[START_REF] Wang | Scientific collaboration in China as reflected in co-authorship[END_REF] SU, 2007, among others). The third category expands the horizon of the second by focusing on cross-region interactions in research and science. As mentioned above, the most notable contribution in this context is the study of[START_REF] Liang | Major factors affecting China´s inter-regional research collaboration Regional scientific productivity and geographical proximity[END_REF]. They investigate factors affecting China´s cross-region research collaborations as captured by copublications and conclude that impact of geographical proximity is essential. Further studies that can be mentioned are[START_REF] Ma | A study on temporal and regional process of knowledge spillover[END_REF][START_REF]Decline of the center The decentralizing process of knowledge transfer of Chinese universities from 1985 to 2004[END_REF]. The first uses the location of keywords in scientific publications to investigate the geographical and temporal dimension region knowledge spillovers, while the second explores knowledge transfers from Chinese universities to the industry sector at a regional level.3 The co-publication data and some descriptive statisticsThis section discusses in some detail the co-publication data used in the study at hand and describes the empirical setting. Our study area is composed of i, j = 1, …, n = 31 regions, including the 22 provinces of China, five autonomous regions and four municipalities. The detailed list of regions is given in Appendix A, accompanied by a map on the spatial configuration of the study area. We use data on scientific publications from the China National Knowledge Infrastructure (CNKI) database, which is the most comprehensive and largest source of China-based information resources and publications. On a basis of random sampling, we use scientific articles published in 2007 covering six thematic fields that are Agriculture, Economics, Information Technologies, Medicine, Natural Sciences & Engineering, and Social Sciences. By using data on publications of the year 2007, the dataset reflects the current sketch of scientific knowledge production in China. Note that the year 2007 is not a special year with respect to differences in publication behaviour or changing patterns in regional protectionism 2 . Our random sample covers about 50% of all publications in 2007, leading to a sample size of 142,548 publications generating 758,682 co-publication flows. We use two-digit zip codes of the author address to trace the specific region of an author.It is worth emphasising that we only consider publications with financial support, as recorded in the CNKI database, provided by diverse funding sources, including the central government, local governments, high education institutions, research institutions, enterprises, social organizations, military organizations, international bodies, etc. By this, we take into account

  Figure 1 also illustrates a triangle of strong collaborative activities between the regions of Beijing, Shanghai and Jiangsu. Western regions show relatively lower participation rates. Appendix B presents a spatial collaboration map for each of the thematic subfields. The shows up as the central hub with respect to the number of links in all sectorspecific spatial networks. However, some sectoral differences are observable (see Figure B.1).

  is the number of researchers 9 in region i, and d j the number of researchers in region j. 1 α and 2

  and use the Pearson correlation coefficient given by r 2 = vectors of two regions i and j to define how close each other in technological space. Their technological distance is then given by

Figure 2

 2 Figure2visualizes the geographical distance decay probability on cross-region co-

  Figure 2 about here

  important research equipment, in particular in Natural Sciences and Engineering, and to the more intensive use of information and communication technologies.

1

  Thus, further policy initiatives, in particular The Grand Western Development Program for "the EleventhFive-Year" (2006[START_REF] Scherngell | Distinct spatial characteristics of industrial and public research collaborations Evidence from the 5th EU Framework Programme[END_REF], are intended to further reduce regional economic disparities19 .Concerning a future research agenda, at least two points come to mind: First, a dynamic analysis of collaborative knowledge production as captured by co-publications across Chinese regions would provide valuable insight into the evolution of the estimated effects over time.The influence of the above mentioned policy measures could be more accurately analyzed under the framework of a dynamic model. Second, analysing other indicators for cross-region knowledge flows, such as co-patents or patent citations, would be important to enrich our understanding on the mechanisms of knowledge diffusion in China. The study of[START_REF] Liang | Major factors affecting China´s inter-regional research collaboration Regional scientific productivity and geographical proximity[END_REF] uses co-publication data to analyse the effect of geographical proximity by means of some simple correlations. They find that geographical proximity is one the most important factors of cross-region knowledge flows. However, they do not control for other factors that may affect collaboration intensities. For instance, geographical distance may just be a proxy for technological distance(see FISCHER et al., 2006) 2 Research input, as captured by R&D expenditures, and research output, as captured by publications, in China shows a smooth upward trend over time from 1997 to 2007 (NBS/MOST, 2008).

iky

  is the respective average of China (see, for instance,[START_REF] Hallet | Regional Specialisation and Concentration in the EU[END_REF]. The average specialization index is 0.09, i.e. regions are highly diversified with respect to their publication intensity in different disciplines. The Herfindal concentration index shows values between 0.05 and 0.07 for the six fields, i.e. they are relatively equal distributed across Chinese regions.

Figure 1 .Figure 3

 13 Figure 1. Knowledge flows as captured by co-publications across Chinese regions

  for less than 10% of all publications at the beginning of the last century. In the 1990s, the share of co-publications has increased significantly to more than 60% of all publications (see[START_REF] Wagner-Doebler R | Continuity and discontinuity of collaboration behaviour since 1800 -from a bibliometric point of view[END_REF]. Over the last few years, several governments have taken series of measures to stimulate different kinds of research collaborations between firms, universities and research organisations. For instance, the European Union provides substantially increasing financial support to collaborative research activities in the Framework Programmes for Research and Development.

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Table 1

 1 As a prelude to the analysis the follows, Table1presents some descriptive statistics on crossregion co-publications. The mean number of collaborations between any two regions is 789.39, with a high standard deviation of 4,496.22. The statistics for skewness and kurtosis point to an extremely right-skewed distribution, indicating that there are relatively few region pairs with a high number of collaborations, while the majority of the region pairs show relatively low collaboration intensities. The same holds true for the sector-specific collaboration matrices. The coefficient of variation differs slightly across the different co-

	about here

  Table2presents the top 5 collaborative links in terms of the Jaccard index J ij for all co-publications and for copublications in different scientific fields. First, it comes out that the relative strongest links are different from the highest links in absolute numbers. Second, by far most of the relative strongest links correspond to collaborations between regions that are direct spatial neighbours.

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It is notable that the connectivity Beijing does not particularly stand out according to the Jaccard index, though Beijing has a rather central role for scientific knowledge production in China as illustrated by Figure

1

. This is mainly the outcome of the high geographical diversification of regions collaborating with Beijing, while, for instance, collaborations of the

Table 2 about here 5 The regional gravity model approach

 2 The exploratory analyses of the previous sections points to some interesting issues and reveals spatial patterns of cross-region collaborative knowledge production in China. The question that now arises is what are the determinants of the observed patterns? In this context we aim to let the variation of cross-region collaboration activities depend on a set of exogenous variables, including geographical, technological and economic characteristics. From this perspective, we are interested in models of the form 8

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Table 3

 3 likely to occur between regions that are close to each other in technological space. By this, our econometric analysis confirms the hypothesis for the Chinese case that the variation of cross-region knowledge flows is not only affected significantly by geographical distance, but to a somewhat larger extent by technological distance -as, for instance,

	about here
	A specific type of localisation is reflected by the estimate for 2 β = 0.254, indicating that
	collaboration probability increases between regions that are physical neighbours, while
	suggesting that this effect is slightly smaller in magnitude than the effect of geographical
	distance. The estimate for the coastal area dummy variable ( 4 β = 0.169) indicates that the
	mean collaboration probability between any two regions increases when at least one region is

proposed by

[START_REF] Breschi | Knowledge spillovers and local innovation systems A critical survey[END_REF]

and confirmed by various empirical studies for the European case (see, for instance,

Table 4

 4 presents the estimation results of the Negative Binomial gravity models for different scientific fields. The dispersion parameter γ is significant for all models, indicating that the Negative Binomial specification is the right choice. Note that we have excluded the technological distance variable for the sector specific models. The models highlight important

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 1 Some descriptive statistics on collaborative knowledge production among Chinese regions as captured by scientific co-publications

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Table 2

 2 Top 5 collaborative links in terms of the Jaccard index J ij for all cross-region copublications and for cross-region co-publications in different scientific fields.

	Region pair	J ij	Spatial neighbours	Region pair	J ij	Spatial neighbours
	All co-publications Y			Information Technologies Y (it)
	Chongqing and Sichuan	0.087	yes	Chongqing and Sichuan	0.165	yes
	Jiangsu and Shanghai	0.077	yes	Beijing and Jilin	0.093	no
	Shanghai and Zhejiang	0.062	yes	Beijing and Shanghai	0.092	no
	Henan and Shaanxi	0.058	yes	Hebei and Tianjin	0.091	yes
	Beijing and Shandong	0.058	no	Henan and Shaanxi	0.080	yes
	Agriculture Y (agr)			Natural Sciences & Engineering Y (nse)
	Jilin and Nei Mongol	0.125	yes	Chongqing and Sichuan	0.070	yes
	Shanghai and Zhejiang	0.111	yes	Beijing and Shandong	0.066	no
	Shanghai and Jiangsu	0.107	yes	Hebei and Tianjin	0.060	yes
	Anhui and Jiangsu	0.083	yes	Henan and Shaanxi	0.058	yes
	Chongqing and Sichuan	0.079	yes	Jiangsu and Shanghai	0.058	yes
	Economics Y (eco)			Social Sciences Y (soc)
	Chongqing and Guizhou	0.124	yes	Jilin and Liaoning	0.133	yes
	Anhui and Jiangsu	0.115	yes	Guizhou and Sichuan	0.125	yes
	Chongqing and Sichuan	0.096	yes	Hubei and Hunan	0.113	yes
	Henan and Hubei	0.074	yes	Heilongjiang and Jilin	0.106	yes
	Shanghai and Zhejiang	0.072	yes	Gansu and Ningxia	0.102	yes
	Medicine Y (med)
	Jiangsu and Shanghai	0.128	yes
	Chongqing and Sichuan	0.096	yes
	Guangdong and Hubei	0.082	no
	Jilin and Liaoning	0.068	yes
	Guangdong and Henan	0.059	no
	Note Spatial neighbours are defined to share a common border

Table 3

 3 Estimation Results of the regional gravity models for all co-publications [n 2 = 961 observations; asymptotic standard errors given in brackets]

	Basic Poisson model	Negative Binomial
	without heterogeneity	model

Table 4

 4 Estimation Results of the Negative Binomial regional gravity models for different scientific fields [n 2 = 961 observations; asymptotic standard errors given in brackets]

			Negative Binomial regional gravity models
		Agriculture Y (agr)	Economics Y (eco)	Information technologies Y (it)	Medicine Y (med)	Social sciences Y (soc)	Natural sciences & engineering Y (nse)
	α 1 =α 2	0.830 *** (0.060)	1.025 *** (0.061)	1.301 *** (0.069)	0.873 *** (0.058)	0.878 *** (0.061)	1.027 *** (0.044)
	ß 1	-0.324 *** (0.044)	-0.434 *** (0.040)	-0.225 *** (0.042)	-0.448 *** (0.043)	-0.368 *** (0.039)	-0.289 *** (0.032)
	ß 2	0.193 *** (0.151)	0.345 *** (0.133)	0.639 *** (0.141)	0.063 *** (0.145)	0.151 *** (0.131)	0.261 *** (0.115)
	ß 3	-0.027 *** (0.038)	0.033 *** (0.035)	-0.180 *** (0.036)	-0.025 *** (0.037)	-0.024 *** (0.034)	-0.057 *** (0.028)
	ß 4	0.001 *** (0.125)	0.434 *** (0.003)	0.625 *** (0.123)	0.250 *** (0.122)	0.304 *** (0.114)	0.224 *** (0.092)
	ß 5	-0.665 *** (0.115)	-0.781 *** (0.003)	-0.624 *** (0.110)	-1.152 *** (0.112)	-0.606 *** (0.000)	-0.767 *** (0.000)
	α 0	-12.582 *** (0.954)	-17.748 *** (0.976)	-23.771 *** (1.109)	-12.785 *** (0.924)	-15.129 *** (0.970)	-15.501 *** (0.697)
	γ	0.440 *** (0.022 )	0.614 *** (0.036 )	0.554 *** (0.032 )	0.467 *** (0.024 )	0.700 *** (0.047 )	0.803 *** (0.036 )
	Ps. R-sq.	0.570	0.694	0.714	0.674	0.708	0.715

Table 5

 5 List of regions used in the study

	ID Region	Capital	Type	ID Region	Capital	Type
	1 Anhui	Hefei	Province	17 Jilin	Changchun Province
	2 Beijing	Beijing	Municipality	18 Liaoning	Shenyang Province
	3 Chongqing Chongqing Municipality	19 Nei Mongol Hohhot	Autonomous Region
	4 Fujian	Fuzhou	Province	20 Ningxia	Yinchuan	Autonomous Region
	5 Gansu	Lanzhou	Province	21 Qinghai	Xining	Province
	6 Guangdong Guangzhou Province	22 Shaanxi	Xian	Province
	7 Guangxi	Nanning	Autonomous Region 23 Shandong Jinan	Province
	8 Guizhou	Guiyang	Province	24 Shanghai	Shanghai	Municipality
	9 Hainan	Haikou	Province	25 Shanxi	Taiyuan	Province
	10 Hebei	Shijiazhuang Province	26 Sichuan	Chengdu	Province
	11 Heilongjiang Harbin	Province	27 Tianjin	Tianjin	Municipality
	12 Henan	Zhengzhou Province	28 Xinjiang	Urumqi	Autonomous Region
	13 Hubei	Wuhan	Province	29 Xizang	Lhasa	Autonomous Region
	14 Hunan	Changsha Province	30 Yunnan	Kunming	Province
	15 Jiangsu	Nanjing	Province	31 Zhejiang	Hangzhou Province
	16 Jiangxi	Nanchang Province

We follow full counting procedure, i.e. a publication with n authors produces n(n-1)/2 links that we count. For instance, for an article with three authors in three different regions, we count three links: from region a to region b, from b to c and from a to c. When all three authors are located in one region we count three intraregional links. Authors from the same institution are included when counting collaborations. They enter our calculations as intra-regional observations. However, bias in this direction does not play a role since the share of 'same institution'-collaborations is similar across all regions (between 27% and 31%).

Note that the n-by-n matrix is symmetric by construction (y ij = y ji ).

Note that Equation (1) is equally applicable to the sector specific networks. We do not distinguish between

The Five-Year Plans of China are a series of economic development initiatives, for example, The First Five-YearPlan (1953Plan ( -1957)), The TenthFive-Year Plan (2001[START_REF] Li | Regional differences and types of science-technology talent resources distribution in China[END_REF] and The EleventhFive-Year Plan (2006[START_REF] Scherngell | Distinct spatial characteristics of industrial and public research collaborations Evidence from the 5th EU Framework Programme[END_REF]. The Grand Western Development Program for "the TenthFive-Year" (2001[START_REF] Li | Regional differences and types of science-technology talent resources distribution in China[END_REF] has been completed.

Acknowledgements

. We gratefully acknowledge Manfred Paier (AIT, Foresight and Policy Development Department) and Bernhard Dachs (AIT, Foresight and Policy Development Department) for valuable comments that helped improving this work, and Changyu Liang (ZTE) for assisting in developing the co-publication database and the collaboration matrices. Yuanjia Hu gratefully acknowledges Josef Fröhlich (AIT, Foresight and Policy Development Department), Yitao Wang (University of Macau), and Eurasia Pacific Uninet (EPU) in Austria for supporting this research.

< R1 -General Regional Economics < R -Urban, Rural, and Regional Economics, R15 -Econometric and Input-Output Models|Other Models < R1 -General Regional Economics < R -Urban, Rural, and Regional Economics

Appendix A

This study disaggregates China's territory into 31 regions composed of 22 provinces, five autonomous regions and four municipalities. Due to data limitations we have to exclude the special administrative regions Hong Kong and Macao.