Patents and Innovation Counts as Measures of Regional Production of New Knowledge Zoltan J. Acs Merrick School of Business University of Baltimore and U. S. Bureau of the Census, U.S.A. Luc Anselin Regional Economics Applications Laboratory (REAL) and Department of Agricultural and Consumer Economics University of Illinois at Urbana-Champaign, U.S.A. Attila Varga Department of Economics University of Pécs, Hungary January 2000 First Revision May 2001 Second Revision October 2001 Abstract The role of geographically mediated knowledge externalities in regional innovation systems has become a major issue in research policy. Although the process of innovation is a crucial aspect of economic growth, the problem of measuring innovation has not yet been completely resolved. A central problem involved in such analysis is the measurement of economically useful new knowledge. In the U. S. information on this has been limited to an innovation count data base. Determining the extent to which the innovation data can be substituted by other measures is essential for a deeper understanding of the dynamics involved. We provide an exploratory and a regression-based comparison of the innovation count data and data on patent counts at the lowest possible levels of geographical aggregation. JEL Classification: O31, H41, O40 Keywords: function. innovations, patents, high technology R&D, knowledge production Correspondence to: Zoltan J. Acs Merrick School of Business University of Baltimore Baltimore, MD 21201 zacs@ubmail.ubalt.edu 1 1. Introduction Advances in the state of knowledge have been responsible for much of the economic development historically. Economically useful new knowledge that leads to innovation – product, process and disruptive – plays an important role in economic growth, international trade and regional development. In order to understand the exact role that knowledge and therefore innovation plays in the economy the measurement of knowledge inputs and knowledge outputs is critical. Our understanding of the role of knowledge in economic activity has traditionally been guided by the state of the measurement of knowledge. However, such data have always been incomplete and, at best, represented only a proxy measure reflecting some aspect of the process of technological change. Simon Kuznets observed in 1962 that the greatest obstacle to understanding the economic role of technological change was a clear inability of scholars to measure it. Measures of technological change have typically involved one of the three major aspects of the innovative process: (1) a measure of the inputs into the innovation process, such as R&D expenditures; (2) an intermediate output, such as the number of inventions which have been patented; or (3) a direct measure of innovative output. During the 1950s and 1960s our understanding of the economy was advanced by developing measures of research and development (R&D), an input measurement, as a proxy for innovative output. R&D suffer from measuring only the budgeted resources allocated towards trying to produce innovative activity. During the 1970s advances made in the use of patent data, an intermediate measure of economic activity, as a proxy for economic output1. Although patents are good indicators of new technology creation, they do not measure the economic value of these 1 For a review of the patent literature see Griliches, 1990. 2 technologies (Hall, Jaffe and Trajtenberg 2001). According to Griliches (1979) and Pakes and Griliches (1980, 378) “patents are a flawed measure (of innovative output) particularly since not all new innovations are patented and since patents differ greatly in their economic impact.” In contrast to proxies of innovation activities such as R&D expenditures or patents, literature-based innovation output measures provide a direct indicator of innovation. These indicators originate in the work of Pavitt, Robson and Townsend (1987) and Edwards and Gordon (1984). The methodology has been further developed by Acs and Audretsch (1993) and Kleinknecht (1991). Sampling the new product sections of trade and technical journals generates literature-based innovation output indicators. The advantage of these indicators over patents and R&D expenditures is that they document the ultimate end of every innovation process: the commercialization of technical ideas. However, they also suffer from some shortcomings2. One potential problem is that these indicators might under-represent large firm innovations because those firms might feel less need to announce their new products than small companies. Literature-based innovation output measures are very expensive to produce and therefore are available for only select years and in select countries. It is widely emphasised in the national innovation systems literature (e.g., Lundvall 1992, Nelson 1993, Patel and Pavitt 1994, Edquist 1997, Freeman 1988) that technological advance in industry is significantly influenced by several external factors resulting in specific innovation systems. An innovation system includes not only networks of innovative companies with research organisations, suppliers and customers, but also several institutional factors, such as the way publicly financed 3 research is organised in a given country, or the nation’s system of schooling, training and financial institutions. Production of economically useful new technological knowledge results from collective actions of different actors of the system connected by various linkages ranging from informal to formalized network relationships. There are many channels through which knowledge can flow between the actors of the system including technical collaboration among firms, universities and public research institutions, diffusion of knowledge and technology to enterprises via adoption rates for new technology or personnel mobility within and between the public and the private sector (OECD, 1997). The way different actors of the system are linked tends to depend to a large extent on nation-specific formal (e.g., regulatory frameworks) and informal (e.g., rules, conventions and norms) institutions, hence the focus is on the national dimension. Economic geographers have long been concerned with issues related to the spatial distribution of new knowledge creation. They have studied the location of innovative activity (Malecki, 1981 1991, Sweeney 1987), the location of high technology industry (Glasmeier 1988, Hall and Markusen 1985), and the dynamics of regional innovative complexes (Stohr 1986). Also, several case studies have been written on regional innovation complexes, such as Route 128 or Silicon Valley (Dorfman 1983, Saxenian 1994).3 An important finding of this literature is that innovation activities are not equally distributed in space. Production of new scientific and technological knowledge has a predominant tendency to cluster spatially (e.g., as exemplified for the US by Varga 1999 or for the European Union by Caniels 2000). Sensitivity of the transmission of new knowledge to distance seems to provide a principal reason for the development of regional innovation clusters: the most recent and as such the most 2 Coombs, Narandren and Richards (1996) provide an excellent overview of literature based innovation 4 valuable type of technological knowledge tends to have such a complex, uncertain and non-codified form that it cannot be fully articulated and may only be transferred through personal interactions (Polanyi 1966, Dosi 1988, Feldman 1994). As such, spatial proximity could be instrumental in facilitating knowledge flows among the actors of a system of innovations. This has inspired researchers to extend the innovation system framework to the regional dimension by directly studying knowledge flows within regional innovation systems (e.g., Acs 2000, Acs and Varga 2002, Braczyk, Cooke and Heidenreich 1998, de la Mothe and Pacquet 1998, Padmore and Gibson 1998, Padmore, Schuetze and Gibson 1998). If knowledge is not easily accessible at every point in space, the location of knowledge production and the characteristics of knowledge diffusion become a crucial issue in understanding economic development. This explains why the extent to which knowledge flows are indeed bounded within geographic limits has received a particular attention in the economics literature. It is shown in Glaeser, Kallal, Scheinkman and Shleifer (1992) that economic growth in US cities is directly related to localized interindustry knowledge flows. Strong evidence is provided both for the US (Jaffe, Trajtenberg and Henderson 1993, Almeida and Kogut 1999) and for Europe (Maurseth and Verspagen 1998, Verspagen and Schoenmakers 2000) that knowledge flows measured by patent citations are bounded within a relatively narrow geographical range. It is also indicated in several recent studies that companies are indeed attracted to the close proximity of external knowledge inputs such as universities (Audretsch and Stephan 1996, Zucker, Darby and Brewer 1998). A powerful approach to empirically model the characteristics of localized knowledge flows as well as to test for their influence on regional innovation is the output indicators. 5 knowledge production function framework initiated by Griliches (1979, 1986). This framework has been widely applied in empirical studies of regional innovation in the US (Jaffe 1989, Acs, Audretsch and Feldman 1991, Anselin, Varga and Acs, 1997, 2000, Varga 2000), in Italy (Audretsch and Vivarelly 1994, Capello 2001), in France (Autant-Bernard 1999) in Austria (Fischer and Varga 2001b) and in Germany (Fritsch 2002). A central empirical problem involved in such an analysis is the measurement of economically useful new knowledge. In the US information on this has been limited to the literature based innovation count database developed by the Small Business Administration4. Unfortunately, this database has not been maintained over time and it is available only for one year, for 1982. Determining the extent to which the innovation data can be substituted by other, more accessible measures is essential for a deeper understanding of the time dynamics involved in regional innovation. The purpose of the current paper is to test whether the patent data developed by the United States Patent and Trademark Office is in fact a reliable proxy measure of innovative activity at the regional level as compared to the literature-based innovation output indicator developed by the US Small Business Administration. There is some evidence that patents provide a fairly reliable measure of innovative activity at the industry level (Acs and Audretsch 1989), and some evidence that patents and innovations behave similarly at the state level (Acs, Audretsch and Feldman 1991) however this has not been tested at the sub-state level. Since most of the US states constitute quite large spatial units this level of geographical aggregation is not sufficient to study the nature of those knowledge flows that are supposed to be locally bounded (Varga 1998). The study by Anselin, Varga and Acs (1997) was carried out at an appropriately low level of spatial aggregation, at the level of US metropolitan 3 For a review of the literature on economic geography see Gordon, Feldman and Gertler, 2000. 6 statistical areas (MSAs) and as such it is considered the first attempt within the knowledge production function framework that provides an explicit account for the effects of localized knowledge flows on manufacturing innovation. To measure knowledge output it utilized the US SBA innovation count data. As such, this study provides a suitable base to compare the performance of the patent and the direct innovation measures in accounting for the effects of localized knowledge flows on regional innovation. The correlation between the PTO patent and SBA innovation counts at the MSA level is reasonably high (0.79) and this could be taken as a first indication that patents might be a reliable measure of innovation at the regional level. However, this correlation coefficient value is not high enough to guarantee that the role of different regional actors in knowledge creation would turn out fairly similar with both measures if applied in the same empirical model. This is why we proceed by replacing innovation counts with the patent measure in the same model as in Anselin, Varga and Acs (1997) to be able to directly compare the results of the two measures of new technological knowledge and assess the extent to which patents may be used as a reliable proxy. This is important, since the patent data are readily available over time and can be used to study the dynamics of localized knowledge flows within regional innovation systems. Thus, it is our objective to provide some insight into the reliability of the patent data as a proxy for regional innovative activity (a second best solution). We approach this by using patents as the dependent variable in a spatial model of knowledge production, estimated for 125 U.S. Metropolitan Statistical Areas (MSA) in the same base year as our model for innovation counts. The paper’s central finding is that the 4 For a detailed description of the US SBA innovation database and its advantages over the traditionally 7 two measures of technological change (patents and innovations) produce very similar results in regression models of regional spillover activity. In the remainder of the paper, we first briefly describe the data, followed by an outline of the knowledge production function model. Analytical results for both innovations and patents are compared in the third section. A summary concludes the paper 2. The Data The original innovation database consists of 8,074 innovations introduced into the United States in 1982. Of these innovations, 4,476 were identified as occurring in manufacturing industries. These data are classified according to four-digit SIC industry, the firm, and the location of the innovation. A private firm, The Futures Group, constructed the data base and performed quality-control analyses for the Small Business Administration by examining over 100 technology, engineering, and trade journals, covering each manufacturing industry. From the sections in each trade journal listing innovations and new products, a database consisting of the innovations by four-digit SIC industry was formed. The entire list of trade journals used to compile these data is available from the authors. The Small Business Administration defines an innovation as “a process that begins with an invention, proceeds with the development of the invention, and results in introduction of a new product, process or service to the marketplace” (Edwards and Gordon 1984, 1). Because the innovations recorded in 1982 were the result of inventions made, on average, 4.3 years earlier, in some sense the innovation database represents the inventions made around 1978 that were subsequently introduced to the market in 1982. The data were also checked for duplication. In fact, 8,800 innovations were used patent data see Edwards and Gordon 1984, Acs and Audretsch 1990, 1993 and Varga 1998. 8 actually recorded, but it was subsequently found that 726 of them appeared either in separate issues of the same journal or else in different journals. Thus, double-counting was avoided. The innovation data were classified according to the industry of origin based on the SIC code of the innovating enterprise. The Futures Group assigned the innovation to an industry based on the information given in the trade journal. When no such information was given and the relevant industry could not be determined from other sources, no industry was assigned to the innovation. The data were then classified into innovations by large firms, defined as firms with at least 500 employees, and innovations by small firms, defined as firms with fewer than 500 employees. For example, an innovation made by a subsidiary of a diversified firm would be classified by industry according to the SIC industry of the innovating subsidiary (establishment) and not by the SIC industry of the parent firm (enterprise). However, the innovation would be classified by size according to the size of the entire firm and not just by the size of the subsidiary. Because sixty-seven innovations could not be classified according to firm size, the number of total innovations does not always equal the sum of large- and small-firm innovations. There are several other qualifications that should be made concerning the innovation data. The trade journals report relatively few process, service, and management innovations and tend to capture mainly product innovations. The most likely effect of this bias is to underestimate the number of innovations emanating from large firms, since larger enterprises tend to produce more process innovations than do their smaller counterparts (Utterback and Afua 2000). However, because it was found that the large-firm innovations are more likely to be reported in trade journals than are small-firm innovations, the biases are perhaps at least somewhat 9 offsetting. One potential concern might be that the significance and “qua!ity” of the innovations vary considerably between large and small firms. Based on 4,938 of the innovations, each innovation was classified by Edwards and Gordon (1984) according to one of the following levels of significance: (1) the innovation established an entirely new category of product, (2) the innovation is the first of its type on the market in a product category already in existence, (3) the innovation represents a significant improvement in existing technology, and (4) the innovation is a modest improvement designed to update and existing product. To provide a test for any biases that might arise in the assignment of the innovation significance classification, The Futures Group undertook telephone interviews based on a subset of 600 innovating companies that were randomly selected. Of these selected companies, 529 were reached and 375 telephone interviews were actually carried out. Of those selected companies not participating in the telephone interview, the most frequent reason for not participating was the inability of The Futures Group to contact the innovating firm or targeted person responsible for the innovation. The respondents of the interviews tended to rate their innovation as being more important than the rating assigned by The Futures Group. For example, while The Futures Group did not assign any innovations to the most significant category, twenty-five of the interviewed firms considered their innovation to be worthy of the highest significance rating. Confronted with this disparity in ratings, Edwards and Gordon (1984, 66) conclude, “The liberalism on the part of the respondents, especially in the assignation of l’s, may be attributed to product loyalty on the part of some respondents and, perhaps, unfamiliarity with other products on the market on the part of some of the non-technical respondents. Alternately, The Futures Group may really 10 have underrated the innovations.” The telephone interviews also enabled the length of time between the invention and innovation to be determined, so that it could be tested whether this time interval varies systematically with firm size. Not only was the mean number of years to innovation 4.3 for both large and small firms, but a chi-square test leads to the conclusion that the time interval between invention and innovation is independent of firm size (Edwards and Gordon 1984). The patent data used in this paper are obtained from the United States Patent and Trademark Office (PTO) for 1982. The extract was supplied by the Center for Regional Economic Issues (REI) at Case Western University. Application year, location of inventors, assignee characteristics and industrial classification of the patent are the main pieces of information used from the PTO files. Corporate patents were selected, that is patents assigned to a US or non-US non-government organization, but excluding patents assigned to universities5. Following standard practice, patents with multiple inventors were assigned to the first inventor’s city (Jaffe, 1989). All data were aggregated by counties and by Metropolitan Statistical Areas (MSAs).6 In Anselin, Varga and Acs (1997) the focus was on research spillovers. It explains the choice of “high technology industries” (i.e., industries relying dominantly on R&D in innovation) for the study. Data availability constrained us to define high technology by an aggregate of five two-digit SIC sectors, chemicals (SIC 28), industrial machinery (SIC 35), electronics (SIC 36), transportation 5 In selecting corporate and excluding university patents we followed Jaffe (1989). The vast majority of patents (78.4 %) is assigned to corporations, 1.1 % to individuals and 18.4 % are unassigned (Hall, Jaffe, Trajtenberg 2001). Given that for 1982 the share of high technology patent applications assigned to individuals or unassigned is 6.4 % of all patent applications we do not expect significant differenences in the results if individual patents would be included. Since in Anselin, Varga and Acs (1997) as well as in Jaffe the focus was on the influence of university research spillovers on manufacturing innovation we excluded university patents. 6 An MSA includes the core city and surrounding counties together forming a local labor market area. 11 Figure 1. The spatial distribution of innovations, 1982 Figure 2. The spatial distribution of patents, 1982 12 these two-digit high technology industries. Patents were classified to the appropriate SIC sector based on the concordance between SIC and PTO codes provided by the US Patent and Trademark Office.7 The spatial distribution of patent and innovation counts, shown in Figures 1 and 2, demonstrates a striking similarity, both at the state and county geographical scale. The same 10 states exhibit the bulk of innovative activity, respectively 80% of the total US activity for innovations and 70% for patents (order given is for patent counts): California, New Jersey, New York, Pennsylvania, Illinois, Ohio, Texas, Michigan, Massachusetts and Connecticut. The similarity between the two measures is further confirmed by a correlation of 0.88 at the county level. A particular striking (but familiar) feature illustrated in Figure 1 is that the bulk of patenting activity in the US occurs on the coasts, and especially on the West Coast in California and in new England, stretching into the Mid-Atlantic Region. In sharp contrast no patenting activity is registered in large parts of the Midwest. MSAs in the traditional manufacturing belt show strong pockets of patenting activity, although much less concentrated than on the coasts. Figure 2 illustrates analogous patterns for innovation counts. 3. The Model In the knowledge production function (KPF) framework knowledge creation is modeled as a functional relationship between the inputs of the knowledge production process and its output that is economically useful new technological knowledge. The unit of analysis can equally be the firm (such as in Griliches 1979) or larger 7 Because a patent can have multiple PTO sequence numbers, a single patent may appear under more than one SIC code. Duplicate patents within high technology sectors and at the aggregate level of the high technology industry sector are eliminated. 13 geographic areas where innovating firms reside (such as a country, a state or a metropolitan area). When interest is in the characteristics of interactions between the actors of an innovation system (such as manufacturing firms, research laboratories, business services or academic institutions) the analysis is based on a geographic area assumed to cover the spatial range of supposed interactions. In the choice of the geographical unit research is usually constrained by data availability. The advantage of the KPF analysis over survey based studies of regional innovation systems (e.g., Cook 2002, Diez 2002) is that it can provide an account of innovation-related interactions based on a large number of geographical areas with the fraction of costs given the use of secondary data. On the other hand since the applied data do not refer to actual interactions much care should be taken on the econometric specification. To compare whether the patent measure performs similarly to the direct measure of innovative activity we used in our 1997 and 2000 papers (Anselin, Varga and Acs 1997, 2000) we apply an identical knowledge production function model to both measures. In its initial form as first was used in studying regional innovation by Jaffe (1989) this is a two-factor Cobb-Douglas production function that relates an output measure for “knowledge” to two input measures: research and development performed by industry, and research performed by universities. This framework was later extended in Feldman and Florida (1994) to account for other knowledge sources of the region. Formally, this is expressed as: log (K) = α + β log(R) + γ log(U) +δ log(Z) +ε (1) 14 Table 1. Descriptive statistics Minimum Maximum Average Standard Deviation PAT 1 1,244 133 205 INN 1 374 25 54 RD 10 26,780 2,274 4,400 URD 3 325,474 31,596 51,680 LQ 0.16 3.77 1.10 0.66 LARGE 0.10 15.38 3.61 2.59 BUS 567 293,879 21,105 38,428 Notes: PAT is granted patent counts sampled by application date; INN is innovation counts; RD is professional employment in industrial R&D laboratories; URD is university research expenditures in thousands of US dollars; LQ is location quotient; LARGE is the percentage of large firms; BUS stands for employment in Business Services (SIC73). 15 where K is a proxy for knowledge (either patents or innovation counts), R is industry R&D and U is university research, with εΚ as a stochastic error term. Z typically includes a measure of the concentration of a given activity (a proxy for innovation networks of manufacturing firms) and a measure of business services activities in the local economy (reflecting the local base of financial, legal, marketing or technical knowledge at business service firms). The analysis is usually carried out for aggregate cross-sectional units (e.g., states, MSAs), possibly for several points in time and/or disaggregated by sector. A positive and significant coefficients for β, γ and δ indicate positive effects of different regional knowledge sources on industrial innovation. Table 1 provides descriptive statistics of the main variables used for estimation. There are two sources of knowledge we include in the regression model, university research expenditures and private sector R&D. Our data for university research expenditures (URD) follow the common approach in the literature and are compiled from the NSF Survey of Scientific and Engineering Expenditures at Universities and Colleges for the year 1982 (National Science Foundation, 1982)8. Industrial research and development (RD) is a proxy measure based on data on professional employment (i.e., professional research staff with technicians and auxiliaries not included) in high technology research laboratories in the Bowker directories (Jaques Cattell Press, 1982). While imperfect, this approach allowed us to construct a private R&D variable (see also Bania, Calkins and Dalenberg 1992, pp. 218-219 for a similar approach)9. 8 The survey is conducted annually by the NSF Division of Science Resources Studies (SRS). The survey population for 1982 included approximately 500 universities and colleges, which accounted for at least 95% of all separately budgeted research and development in the academic sector. Responses were received from about 97% of the surveyed institutions. The response rate was slightly higher, however, among S&E doctorate-granting institutions that account for approximately 98 % of all academic R&D. Data for nonrespondents were imputed based on response patterns from peer institutions and past data submissions (National Science Foundation, 1982). 9 We tested for contemporaneous rather than lagged effects of the input variables on innovation outputs for the simple reason that 1982 is the first year that the Classification Index of Industrial Research Laboratories of the United States allows for appropriate industry level aggregations. This choice is supported by the trends in R&D lab location. As evidenced by Malecki (1980), location patterns of 16 As indicated in Anselin, Varga and Acs (1997), our proxy variable is remarkably similar to R&D expenditures used in Jaffe (1989) yielding a correlation of 0.91 for the 29 states common to both studies. Clearly, the use of lab employment as a proxy for expenditures assumes a constancy of the labor intensity and capital/labor ratio of R&D across the units of observation. To the extent that this is not the case, it will tend to yield misspecifications in the form of heteroskedastic error terms, which will merit special attention in our analysis. As in Anselin, Varga, and Acs (1997) our final data set included those 125 MSAs for which there were innovations in the high technology sector as well as both private industry R&D and university research expenditures. This reflects the motivation to focus on the strength and spatial extent of local geographic spillovers for MSAs where an innovative complex is already in place. Also, from a technical point of view, the use of a Cobb-Douglas function (KPF) in loglinear form precludes zero values for any of the variables in the sample. The Appendix table lists patent and innovation counts as well as patent-innovation ratios for the metropolitan statistical areas included in the study. Since we were particularly interested in the geographic scope of knowledge externalities and did not want to constrain this to purely within-MSA effects, we constructed new spatially lagged explanatory variables that we called “ring variables” (Anselin, Varga and Acs, 1997). These variables are designed to capture the effect of university research and private R&D in counties surrounding the MSA, within a given distance band from the geographic center of the MSA. Based on information of commuting patterns, two distance bands were considered: 50 and 75 miles. Specifically for any MSA i, the lagged variables URD50i and RD50i are the sums of R&D laboratories tend to be stable for a relatively long period of time. This suggests that the spatial 17 the university research and private R&D in those counties surrounding the MSA (and not part of the MSA) whose geographic centers are within 50 miles of the geographic center of the core MSA county. Similar measures were constructed for a 75 mile range as well (URD75, RD75). Since we did not have any a priory information on the spatial extent of knowledge flows from an MSA we regressed equation (1) with both of the ring variables for industrial and university research and selected the particular combination that provided the highest regression fit. The effect that local economic characteristics have on innovation is measured by a location quotient for high technology employment (LQ)10; employment in business services (SIC 73), BUS; and the percentage of large firms [firms with employment exceeding 500] (LARGE). The first two variables are included to capture local knowledge related interactions in innovation and are expected to have a positive sign (Feldman and Florida, 1994). The third is to assess the effect of firm size and is expected to have a negative sign (Acs, Audretsch and Feldman, 1994). All of the above variables are compiled from County Business patterns data for 1982 (Bureau of the Census, 1983). Similar to the approach taken in our previous work, the estimation of equation 1 is carried out within a systematically applied spatial econometric framework (e.g., Anselin, 1988a, Anselin and Florax, 1995, and Anselin and Bera, 1998). We believe that this approach is particularly useful in the study of the spatial patterns of knowledge spillovers. When models are estimated for cross-sectional data on neighboring spatial units, the lack of independence across these units (or, the presence distribution of R&D employment between 1977 and 1982 did not change significantly. 10 A location quotient relates local and national importance of an industry, based on its relative share in the local and in the national economy. Formally: LQ = (EMPHTMSA/EMPTOTMSA )/ (EMPHTNATION/EMPTOTNATION), where EMPHT and EMPTOT stand for employment in high 18 of spatial autocorrelation) can cause serious problems of model misspecification when ignored. The methodology of spatial econometrics consists of testing for the potential presence of these misspecifications and of using the proper estimators for models that incorporate the spatial dependence. The two forms of spatial autocorrelation that are most relevant in applied empirical work are so-called substantive dependence, or dependence in the form of a spatially lagged dependent variable, and nuisance dependence, or dependence in the regression error term11. 4. Regression Results In our 1997 paper we found that both university research and private R&D exerted a positive effect on innovative activity in an MSA, however, there is a clear dominance of private R&D over university research. The spatial lagged university research variable for a 50-mile range remains positive and significant. However, there is no evidence that the effect of private R&D on MSA innovative activity spills over from technology and total employment, respectively. LQ > 1 shows that high technology industry employment is more concentrated in the MSA than on average in the nation. 11 The spatial lag model can be expressed as: y = ρWy + Xβ + ε where y is a vector of observations on a dependent variable, Wy is a spatially lagged dependent variable for spatial weights matrix W, ρ is a spatial autoregressive coefficient, X is a matrix with observations on the explanatory variables with coefficients β, and ε is an error term. The weights matrix W is typically constructed from information on contiguity between two spatial units, but more general definitions are used as well, leading to a large range of potential specifications. The resulting spatial lag Wy can be considered as a (spatial) weighted average of the observations at “neighboring” locations. Ignoring a spatially lagged dependent variable yields inconsistent and biased estimates for the β coefficients in the model. The second form of spatial dependence is often expressed as a spatial autoregressive process for the error term in a regression model, or: y = Xβ + ε with ε = λWε + u where λ is a spatial autoregressive coefficient and u is a standard spherical error term. Ignoring spatial dependence in the error term does not lead to biased least squares estimates, but the estimate of their variance will be biased, yielding misleading inference [for further discussion, see, among others, Anselin, 1988a]. 19 outside the MSA. All three local economic variables are highly significant and have the expected sign. To the extent to which patent counts are reliable measure of innovative activity, we would expect to see similar results when the patent measure is substituted for the number of innovations in the regression model. Disparate results would, on the other hand, suggest that, whatever else patents may measure, they do not provide a reliable indication of the actual amount of innovation activity in a MSA. The regression results are reported in Table 2 for the logarithms of respectively the number of patents (in columns 2, 4 and 5) and the number of innovations (in columns 1 and 3) as the dependent variable, based on data for 125 US Metropolitan Statistical areas (MSAs). Two different specifications were estimated: the model in the first two columns of the table with only the two research variables included in the right hand side and a spatial model (columns 3, 4 and 5). In the latter, the base model is augmented with the spatial lags for university and private R&D (only the most significant of respectively URD50, URD75, RD50 and RD75 are reported in columns 3 and 5) 12. The base model in columns 1 and 2 confirms the strong significance of both private R&D 20 Table 2 The Knowledge Production Function OLS Regression Results for Log (Innovations) and Log (Patents) at the MSA Level (N=125, 1982) Model Constant Log(RD) Base Base Spatial Spatial I. Spatial II. Log(Innovations) Log(Patents) Log(Innovations) Log (Patents) Log(Patents) -1.045 -0.417 -1.134 -0.923 -0.816 (0.146) (0.319) (0.172) (0.371) (0.392) 0.540 1.414 0.504 1.311 1.283 (0.054) (0.117) (0.055) (0.120) (0.120) Log(RD50) 0.154 (0.055) Log(RD75) Log(URD) 0.001 0.161 (0.041) (0.089) 0.112 0.115 0.132 0.150 0.170 (0.036) (0.078) (0.036) (0.078) (0.077) 0.037 0.041 (0.018) (0.038) Log(URD50) Log(URD75) 0.036 (0.068) R2-adj 0.599 0.642 0.611 0.653 0.661 Log-Likelihood -65.336 -162.749 -69.402 -158.744 -157.401 White 1.183 14.103 9.024 38.708 23.751 D50 1.465 0.280 0.936 0.027 0.001 D75 2.688 0.715 2.178 2.022 1.598 LM-Err 12 The results for the innovation regression are from Anselin, Varga and Acs (1997) and included for comparison purposes. All estimations were carried out by means of the SpaceStat software package (Anselin 1998). 21 1.691 0.028 1.102 0.258 0.178 D50 5.620 5.318 1.026 0.063 0.065 D75 2.968 0.269 1.485 3.407 1.430 IDIS2 2.039 0.072 0.659 1.491 1.289 IDIS2 LM-Lag Notes: Estimated standard errors are in parentheses; critical values for the White statistic with, respectively 5 and 14 degrees of freedom are 11.07 and 23.69 (p=0.05); critical values for LM-Err and LM-Lag statistics are 3.84 (p=0.05) and 2.71 (p=0.10); spatial weights matrices are row-standardized: D50 is distance-based contiguity for 50 miles; D75 is distance-based contiguity for 75 miles; and IDIS2 is inverse distance squared. 22 and university research on the level of innovation and patents in an MSA. There is a clear dominance of the coefficient of private R&D over university research, showing an elasticity that is almost five times higher. This difference is even more pronounced for patents than for innovations. In the patents equation, there is some evidence of heteroskedasticity, but more importantly, there is a strong indication of misspecification in the form of a spatial lag for 50 miles (at p<0.05) for both patents and innovations13. The significant LM-lag statistic in both equations suggests that the extent of knowledge flows go well beyond MSA borders. To explicitly account for this effect RD and URD ring variables are added to the model (i.e., in columns 3 and 5 where the particular combinations of ring variables provide the highest regression fit). As a result, adjusted R2 improves slightly with no spatial dependence remaining. However, there is a striking difference between the effects of the ring variables on innovations and patents. University research outside the MSA has a positive and statistically significant effect on innovation, but the R&D effect from outside the MSA is insignificant. On the contrary, for patents, RD50 has a positive and statistically 13 We assessed this by means of a Lagrange Multiplier test for spatial error or lag dependence using three spatial weights. D50 and D75 are distance-based contiguities for 50 and 75 miles, respectively. These matrices are intended to capture remaining spatial dependencies within commuting distances around the MSAs. The third one, IDIS2, is an inverse distance squared weights matrix. It captures spatial effects that might come from the whole geographic area of the regression. As evidenced in a large number of Monte Carlo simulation experiments in Anselin and Rey (1991), the joint use of the Lagrange Multiplier tests for spatial lag and spatial error dependence provides the best guidance for model specification. Several statistics have been developed to test for spatial lag dependence. The LM-LAG statistic suggested by Anselin (1988b) tests for spatial lag dependence in the context of an OLS regression. It has the following form LM-LAG = (e’Wy/s2) 2/ (RJρ−β) where e is a vector of OLS residuals, y is the dependent variable of the regression, and RJρ−β = [T + (WXβ)’M(WXβ)/ s2], where WXβ is a spatial lag of the predicted values from the OLS regression, and M = I - X(X’X) -1 X’ is the projection matrix. The statistic is distributed as χ2 with one degree of freedom. The Lagrange Multiplier test for spatial error dependence is suggested by Burridge (1980) and has the following form LM-ERR = (e’We/s2)2/T where e is a vector of OLS residuals, W is a spatial weights matrix, s2 = e’e/N, and T = tr(W’W + W2) with tr as the matrix trace operator. The statistic is distributed as χ2 with one degree of freedom. 23 Table 3 The Extended Knowledge Production Function Regression Results for Log (Innovations) and Log (Patents) at the MSA Level (N=125, 1982) Model Constant Log(RD) Extended Spatial Extended Spatial Extended Spatial Log(Innovations) Log(Patents) Log(Patents) OLS OLS ML-Heteroskedastic Error -1.523 -1.623 -1.694 (0.206) (0.444) (0.429) 0.294 0.852 0.788 (0.057) (0.124) (0.119) 0.120 0.113 (0.049) (0.048) 0.113 0.155 0.142 (0.033) (0.070) (0.065) 0.046 0.077 (0.059) (0.055) 0.655 1.501 1.416 (0.165) (0.340) (0.288) 0.333 0.589 0.626 (0.057) (0.124) (0.124) -0.336 -0.309 -0.260 Log(RD50) Log(RD75) -0.025 (0.038) Log(URD) Log(URD50) 0.036 (0.015) Log(URD75) Log(LQ) Log(BUS) Log(LARGE) 24 (0.095) (0.198) (0.192) R2-adj 0.718 0.750 0.763 Log-Likelihood -40.821 -136.800 -136.001 White 31.235 57.404 Wald 9.301 LM-Err D50 0.085 0.006 0.043 D75 0.116 2.019 2.559 IDIS2 0.001 0.690 0.829 D50 0.497 0.008 0.160 D75 1.406 1.194 1.509 IDIS2 0.487 2.411 1.686 LM-Lag Notes: Estimated standard errors are in parentheses; critical values for the White statistic with 35 degrees of freedom is 49.52 (p=0.05); critical values for LM-Err and LM-Lag statistics and the Wald test on heteroskedasticity are 3.84 (p=0.05) and 2.71 (p=0.10); spatial weights matrices are rowstandardized: D50 is distance-based contiguity for 50 miles; D75 is distance-based contiguity for 75 miles; and IDIS2 is inverse distance squared. 25 significant coefficient, while the coefficient for university research outside the MSA is insignificant. For comparison purposes we also included the patents equation with the same ring variable structure in column 4 as in the innovations equation in column 3. It is clear that the spatial pattern of industrial and university research spillovers in column 3 is not replicated with the patents measure. Table 3 presents results for the extended knowledge production function that also includes a vector of local economic characteristics. For innovation counts, since no specification problems were discovered, the final model is estimated with OLS. The patent equation incorporates heteroskedasticity in the form of a random coefficients model14 that is estimated by means of Maximum Likelihood. In the followings we provide a comparative perspective on the behavior of the two innovation measures in the KPF model of localized knowledge interactions. 1. In several important “technical” aspects such as the explanatory power of regression equations, the form of spatial dependence or the sensitivity of parameters to changes in the variable structure the two measures behave in a strikingly similar manner. Regression fits of the two final models in Table 3 are almost identical, with adjusted R2 of 0.72 for innovation counts and 0.76 for patents. The structure of spatial dependence is also very similar as both equations exhibit significant spatial lag dependence within 50 miles from the MSA centers but not for the other two weights matrices. Change in the values of elasticities with respect to industrial and university research resulting from the inclusion of 14 A common specification of heteroskedasticity is the so-called additive heteroskedasticity specification where the error variance is expressed as a linear function of a set of explanatory variables: Var(ε) = Zγ , where Var(ε) is a N by 1 column vector of the error variances, Z is a N by P matrix with the heteroskedastic variables as columns, and γ is a corresponding vector of coefficients. In the case of the random coefficients model the elements of the Z matrix are the squares of the explanatory variables in the regression. Estimation of the model is followed Amemiya’s three-step FGLS method (Amemiya 1985). When errors are normally distributed the FGLS procedure can be shown to be equivalent to maximum likelihood (Anselin 1998). 26 local economic variables follows a very similar pattern for the two measures. With both patents and innovations the elasticity with respect to private R&D drops with about 40 percent while the drop in the university research parameter is about 15 percent for both measures. 2. With the exception of the variable LARGE which is significant in the innovation equation but not in the final patent model, the rest of the local economic variables are highly significant in both equations. In addition, all economic variables exhibit the expected sign: positive for specialization in high technology (LQ) and the importance of business services (BUS), and negative for the presence of large firms (LARGE). In other words, ceteris paribus, MSAs dominated by the presence of large firms tend to show less innovative activity. 3. Some systematic differences in the performances of the two innovation measures can also be observed in Table 3. It is apparent in the final models that all the parameters representing certain knowledge flows in the region yield significantly higher values for patents than for innovations. For the private R&D variable the estimated parameter in the patents equation is about 2.5 times higher than the respective parameter in the innovations equation while the elasticity with respect to university research is about one-third higher for patents than for innovations. Also, parameter values for the variables log(LQ) and log(BUS) are about twice as high in the patents equation. Since the patent count data reflect an earlier phase of innovation while the direct innovation measure represents the whole process this systematic difference in parameter values could well be associated with the empirical finding of survey-based regional innovation system studies that the reliance of innovative firms on external knowledge sources decreases significantly 27 as the innovation process approaches its end (e.g., Fischer and Varga 2001a, Fischer, Diez and Snickars 2001). 4. Although R&D spillovers dominate over university research spillovers in both equations, R&D dominance is substantially less pronounced for innovation than for patenting. The estimated coefficient for the industrial R&D variable is about six times higher than the respective coefficient for university research in the patents equation (as shown in the last column of Table 3) whereas for innovations the elasticity with respect to R&D is only around three times greater than the respective elasticity for university research (first column in Table 3). This pattern is replicated for research spillovers emanating from surrounding areas: the effect of localized R&D spillovers extends the MSA border for patents but not for innovations whereas innovation relies on university research activities of neighboring counties but patenting does not. This relatively higher weight of local university research in innovation can be related to the fact that in the later stages of innovation the need for applied research collaboration (e.g., conducting tests by university researchers or using university research facilities) is more pronounced than in earlier stages where basic research collaboration is more dominant. The two types of research collaborations exhibit different spatial patterns as evidenced in Mansfield (1991, 1995). To collaborate with universities in applied research firms tend to choose local academic institutions whereas basic research collaboration can be carried out over larger distances. Since patenting reflects more the earlier stages of innovation whereas the direct innovation measure accounts for the whole innovation process, the relatively higher weight of local universities in innovation than in patenting could reflect the different spatial patterns of basic and applied research collaboration. 28 5. Conclusion The empirical evidence suggests that patents provide a fairly reliable measure of innovative activity. With respect to regression fit, sensitivity of estimated parameters to changes in the variable structure or the type of spatial dependence the two measures provide very similar results in the KPF context. Also, the signs and significances of those variables representing knowledge sources in the MSA follow similar patterns for both of the measures. However, when patents are applied to measure innovation in the regression context some caution is suggested while interpreting the results: for all the local knowledge-related variables the knowledge production function with patents over-emphasizes the effects of localized interactions. Also, the influence of local university research spillovers is under-represented as compared to the effects of R&D spillovers. 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Brewer, 1998, Intellectual human capital and the birth of U.S. biotechnology industry, American Economic Review 88, 290-306. 36 Appendix: Number of new product innovations, counts of patents and the patentinnovation ratios for US MSAs and for high technology sectors, 1982 Metropolitan Statistical Areas Innovation Patent PatentInnovation Ratio Akron 7 194 27.71 Albany-Schenectady-Troy 1 290 290.00 Albuquerque 2 7 3.50 Allentown-Bethlehem-Easton Pa.-N.J. 7 90 12.86 Anaheim-Santa Ana-Garden Grove 108 332 3.07 Ann Arbor 7 62 8.86 Atlanta 26 100 3.85 Austin 12 161 13.42 Baltimore 12 124 10.33 Bellingham 1 9 9.00 Benton Harbor 1 30 30.00 Binghamton N.Y.-Pa. 2 48 24.00 Birmingham 1 19 19.00 Bloomington-Normal 2 2 1.00 Boston 282 801 2.84 Bridgeport 67 304 4.54 Bryan-College Station 2 2 1.00 Buffalo 24 124 5.17 Burlington 3 27 9.00 Charlotte-Gastonia 6 53 8.83 Chicago 164 1244 7.59 Cincinnati Ohio-Ky.-Ind. 13 158 12.15 Cleveland 54 297 5.50 37 Colorado Springs 6 30 5.00 Columbia 1 4 4.00 Columbus 20 126 6.30 Dallas-Fort Worth 77 343 4.45 Davenport-Rock Island-Moline Iowa-Ill. 5 36 7.20 Dayton 11 75 6.82 Daytona Beach 1 3 3.00 Denver-Boulder 26 195 7.50 Detroit 51 560 10.98 El Paso 7 5 0.71 Fort Collins 6 17 2.83 Fort Lauderdale-Hollywood 9 69 7.67 Fresno 1 3 3.00 Gainesville 1 12 12.00 Galveston-Texas 2 6 3.00 Grand Rapids 4 62 15.50 Greensboro-Winston-Salem-High Point 5 52 10.40 Greenville-Spartanburg 10 59 5.90 Hamilton-Middletown 4 40 10.00 Hartford 27 251 9.30 Houston 29 590 20.34 Huntsville 3 18 6.00 Janesville-Beloit 2 10 5.00 Jersey City 11 11 1.00 Johnson City-Kingsport-Bristol Tenn.-Va. 2 47 23.50 Kalamazoo-Portage 5 113 22.60 Kansas City 12 57 4.75 Knoxville 1 9 9.00 Lafayette-West Lafayette 1 15 15.00 Lancaster 4 123 30.75 38 Lansing-East 4 9 2.25 Lincoln 2 11 5.50 Lorain-Elyria 2 30 15.00 Los Angeles-Long Beach 161 576 3.58 Louisville 7 68 9.71 Madison 4 24 6.00 Melbourne-Titusville-Cocoa 11 40 3.64 Memphis Tenn.-Ark.-Miss. 3 23 7.67 Miami 4 41 10.25 Milwaukee 34 247 7.26 Minneapolis-St. Paul 80 558 6.98 Nashville-Davidson 5 22 4.40 Nassau-Suffolk 120 184 1.53 New Bedford 6 38 6.33 New Brunswick-Perth Amboy-Sayreville 30 214 7.13 New Haven-West Haven 19 143 7.53 New London-Norwich 1 79 79.00 New Orleans 1 29 29.00 New York N.Y.-N.J. 222 562 2.53 Essex county 143 834 5.83 Newburgh-Middletown 3 16 5.33 Newport News-Hampton 2 8 4.00 Norfolk-Virginia Beach-Portsmouth Va.-N.C. 1 8 8.00 Northeast 2 12 6.00 Oklahoma City 1 24 24.00 Orlando 5 28 5.60 Paterson-Clifton-Passaic 25 49 1.96 Peoria 1 32 32.00 Philadelphia Pa.-N.J. 139 748 5.38 Phoenix 29 223 7.69 39 Pittsburgh 39 436 11.18 Pittsfield 2 36 18.00 Portland 1 8 8.00 Portland Oreg.-Wash. 22 110 5.00 Portsmouth-Dover-Rochester 5 35 7.00 Providence-Warwick-Pawtucket 15 36 2.40 Provo-Orem 3 11 3.67 Raleigh-Durham 8 79 9.88 Reading 1 36 36.00 Reno 1 9 9.00 Riverside-San Bernardino-Ontario 13 40 3.08 Rochester 32 397 12.41 Sacramento 7 17 2.43 St. Louis 13 207 15.92 Salem 1 17 17.00 Salt Lake City 10 55 5.50 San Antonio 3 25 8.33 San Diego 59 148 2.51 San Francisco-Oakland 75 480 6.40 San Jose 374 659 1.76 Santa Barbara-Santa Maria-Lompoc 9 30 3.33 Santa Cruz 2 15 7.50 Seattle-Everett 34 182 5.35 South Bend 5 46 9.20 Spokane 3 4 1.33 Springfield 3 13 4.33 Springfield-Chicopee-Holyoke 3 31 10.33 Stockton 2 9 4.50 Syracuse 9 79 8.78 Tacoma 2 8 4.00 40 Tampa-St. 12 81 6.75 Toledo Ohio-Mich. 6 79 13.17 Trenton 29 240 8.28 Tucson 9 55 6.11 Tulsa 12 71 5.92 Waco 3 1 0.33 Washington DC 21 156 7.43 Waterloo-Cedar Falls 1 31 31.00 Wichita 5 17 3.40 Wilmington Del.-N.J.-Md. 11 215 19.55 Worcester 17 76 4.47 Youngstown-Warren 1 25 25.00 Sources: Innovation data come from the US Small Business Administration, patent data are from the US Patent Office