EMPIRICAL ANALYSE S OF REGIONAL INNOVATION AND ECONOMIC GROWTH IN THE UNITED STATES By Giri Raj Aryal A DISSERTATION Submitted to Michigan State University in partial fulfilment of the requirements for the degree of Agricultural, Food, and Resource Economics Doctor of Philosophy 2018 ABSTRACT EMPIRICAL ANALYSE S OF REGIONAL INNOVATION AND ECONOMIC GROWTH IN THE UNITED STATES By Giri Raj Aryal Much of the innovation creation literat ure is focused on urban firms and areas or relies heavily on data based on these; l ess studied are rural firms or rural areas in this regard. The goal of this dissertation is to explore the drivers of rural - urban innovation gap and the link between regional innovation and econom ic growth and propose policies to mitigate regional innovation ecosystem deficiencies and impedim ents that contribute to the gap . In my first essay, I analyze heterogeneity in inventiveness across urban and rural counties is u sing a spatial autoregressive neg ative binomial regression model, considering spatial spillover effects , creative class population , industry characteristics, human capital, and other regional factors influencing innovation . Results indicate that drivers of invention, namely a college - educated labor force and diversity of high - tech industries are common across all counties types, but urban inventive advantage persists due to agglomeration economies, higher number of universities, and higher shares of high - tech firms, professional servic es and immigrants. Consistent with the creative class hypothesis, p opulation share of college gradu ates in creative disciplines also positively contributes to inventive output in urban counties. However, the effects of spatial spillover s and mobile phone technology penetration are stronger for rural counties, suggesting that policies promoting rural centers of innovation, technological diversity, and communication infrastructure in rural counties could help mitigate the urban - rural innov ation gap. My second essay explores the interdependence between regional innovation and economic growth by accounting for possible endogenous relationship s among regional innovation , income growth, employment and population . It draws on data for 3,038 counties in the 48 contigu ous states of the United States collected from several publicly available sources for 2009 - 1 3. Endogeneity tests using instrumental variable regressions show that regional innovation and economic growth have endogen ous relationships. Considering the endogeneity and estimating the system of simultaneous equations for regional innovation and economic growth using three stage least squares (3SLS) method, I find that innovation belongs to system of regional growth. Furth er, reduced form estimates of the 3SLS results suggest that policies promoting regional clusters of high - tech firms and capitalizing on the knowledge potential of the immigrants are likely to reinforce both regional innovation rates and economic growth. My third essay analyze s the characteristics that potentially influence innovation creation across rural and urban firm s employing a survey dataset from 2014 National Survey of Business Competitiveness combined with secondary d ata reflecting the regional business and innovative environments where these firms operate. The number of patent applications filed by these firms measures their innovation creation, and the paper employs a negative binomial regression estimation for analy sis. The findings of this essay show that, after controlling for industry, county and state factors, rural and urban firms differ in their innovation creation characteristics and behaviors, suggesting that urban firms capitalize on their resources better t han rural firms. O ther major findings of the essay provide evidence that (i ) for rural firms, the influence of university R&D is relevant to innovation creation, but their perception of university provided information is not significant and (ii) rural firms that are willing to try, but fail, in terms of innovation creation have a slight advantage over other rural firms less w illing to take on the ris k. Copyright by GIRI RAJ ARYAL 20 18 v To my parents, Prem Nath and Kaushila Aryal my brother, Sudarshan Aryal my si ste rs, Laxmi and Saraswati Aryal vi ACKNOWLEDGEMENTS First and foremost, I would like to express my profound gratitude for the incredible mentorship, guidance, inspiration, and motivation I received from my major advisor Dr. Satish Vasudev Joshi and my research supervisor Dr. John Thomas Mann II, who also jo intly funded the most part of my PhD study at Michigan State. Thank you for believing in me since the very beginning and insisting that I made progress even when I hit roadblocks as part of any long - term research. Also, sincere thanks to the res t of my adv isory committ ee Dr. Scott Loveridge , who also funded a part of my PhD study, and Dr . Mark Skidmore for precious comments on my research and technical as well as personal advice throughout my PhD career. I also extend my gratitude to the faculty and staf f of the Department of Agricultural, Food and Resource Economics (AFRE), Michigan State University, e specially the Graduate Secretaries, Ms. Debbie Conway and Ashleigh Booth , Travel Arranger, Nancy Creed, and the Graduate Chair s Dr . Scott Swinton and Dr. R obert Myers for consistent support and assistance while navigating the PhD study. I am forever indebted to my AFRE colleagues, Jina Yu, John Olwande, Jong - Woo Kim, Jungmin Lim, Mayuko Kondo, Miguel Castro, Nahid Sattar, among others , for the lasting bonds created through sharing struggles and common experience. I am also grateful to all my friends in East Lansing for the ir support by celebrating my successes and commiserating the failures during my doctoral program. Last but most importantly , I would like to a acknowledge my family who encouraged me to accept my offer of admission into the PhD program at MSU and supported me throughout the whole program. Specially, I wa nt to thank my remarkable parents, Prem Nath and Kaushila vii Aryal, for all the sacrifices they made for my educa tion and provided forever inspiration to work hard and fo llow fearlessly my dreams . I also wish to acknowledge my brothers, especially Sudarshan Aryal, who always encouraged and supported me to hold onto my aspi rations throughout the tough times of my academic and personal life. Finally, I would like to thank my dearest and caring sisters, Laxmi and Saraswati Aryal, for their unending love that relentlessly helped me move forward through the challenging situation s and cherish every small accomplishment. viii TABLE OF CONTENTS . xii ESSAY 1: DRIVERS OF DIFFERENC ES IN INVENTIVENESS ACROSS URBAN AND RURAL REGIONS ................................ ................................ ................................ ....................... 1 1.1. Introduction ................................ ................................ ................................ ............. 1 1.2. Review of Literature ................................ ................................ ............................... 3 1.3. Empirical Methods ................................ ................................ ................................ .. 7 1.4. Data and Variables ................................ ................................ ............................... 10 1.5. Empirical Results ................................ ................................ ................................ .. 15 1.5.1. Summary Statistics ................................ ................................ .................... 15 1.5.2. Regression Estimation Results ................................ ................................ .. 17 1.5.3. Rural Urban Comparative Advantage in Innovation ............................. 18 1.6. Summary and Conclusion ................................ ................................ .................... 21 REFERENCES ................................ ................................ ................................ ............................ 25 ESSAY 2: EXPLORING THE INTERD EPENDENCE OF INNOVAT ION AND REGIONAL ECONOMIC GR OWTH: A COUNTY LEVEL ANALYSIS .......................... 32 2.1. Introduction ................................ ................................ ................................ ........... 32 2.2. Literature Review ................................ ................................ ................................ . 34 2.2.1. Innovation and Economic Growth ................................ ........................... 34 2.2.2. Innovation and Regional Economic Growth ................................ ........... 36 2.2.3. Drivers of Regional Innovation ................................ ................................ . 38 2.2.4. Drivers of Regional Growth ................................ ................................ ...... 38 2.3. Modelin g and Estimation ................................ ................................ ...................... 43 2.3.1. Regional Growth Model ................................ ................................ ............. 43 2.3.2. Hypotheses ................................ ................................ ................................ .. 47 2.3.3. Estimation ................................ ................................ ................................ ... 51 2.4. Data ................................ ................................ ................................ ........................ 53 2.5. Results ................................ ................................ ................................ .................... 56 2.5.1. Regional Innovation and Economic Growth Interdependence .............. 58 2.5.2. Exogenous Factors of Regional Innovation and Economic Growth ..... 59 2.6. Summary and Conclusion ................................ ................................ .................... 63 REFERENCES ................................ ................................ ................................ ............................ 65 ESSAY 3: EXPLORING I NNOVATION CREATION A CROSS RURAL AND URBA N FIRMS: ANALYSIS OF T HE NATIONAL SURVEY O F BUSINESS COMPETITIVENESS ................................ ................................ ................................ ................ 72 3.1. Introduction ................................ ................................ ................................ ........... 72 ix 3.2. Literature Review ................................ ................................ ................................ . 75 3.3. Data ................................ ................................ ................................ ........................ 78 3.4. Methods ................................ ................................ ................................ .................. 85 3.5. Results ................................ ................................ ................................ .................... 87 3.5.1. Summary Statistics ................................ ................................ .................... 87 3.5.2. Regression Model Diagnostics and Interpretation of Results ................ 88 3.5.3. Rural and Urban Firm Innovation ................................ ........................... 91 3.6. Summary and Conclusion ................................ ................................ .................... 96 REFERENCES ................................ ................................ ................................ ............................ 99 x LIST OF TABLES Table 1.1 Variables Definition and Data Source ................................ ................................ ...... 11 Table 1.2 Summary Statis tics ................................ ................................ ................................ ..... 16 Table 1.3 Results from RENB - SAR Model on Full sample and Sub - samples by County Types ................................ ................................ ................................ ................................ ............ 19 Table 2.1 Variables Definition, Summary Statistics, and Data Source ................................ .. 55 Table 2.2 3SLS Results of the Estimation of the County Growth Model .............................. 57 Table 2.3 Reduced Form Estimates of the Parameters in the County Growth Model ......... 61 Table 3.1 Variables Description and Data Source ................................ ................................ ... 80 Table 3.2 Summary Statistics ................................ ................................ ................................ ..... 89 ................................ ............................. 90 Table 3.4 Negati ve Binomial Regression Results ................................ ................................ ..... 92 Table 3.5 Rural Innovative firms - Statistically Significant State Fixed Effects (Ref. State=CA) ................................ ................................ ................................ ................................ .... 95 xi LIST OF FIGURES Figure 3.1 Frequency distribution of firm - level total patent applications during 2011 - 13 (pooled sample) ................................ ................................ ................................ ............................ 86 xii KEY TO ABBREVIATIONS ACS American Community Survey BEA Bureau of Economic Analysis BLS Bureau of Labor Statistics CBP Community Business Patterns ERS Economic Research Service FCC Federal Communication Commission KPF Knowledge Production Function NAICS North American Industry Classification System NSBC National Survey of Business Competitiveness NSF National Science Foundation NUTS N omenclature of Territorial Units for Statistics OECD Organization for Economic Co - operation and Development R&D Research and Development RENB Random Effects Negative Binomial RKPF Regional Knowledge Production Function SBA Small Business Administratio n SBIR Small Business Innovation Research SD Standard Deviation USDA United States Department of Agriculture USPTO United States Patents and Trademark Office 1 ESSAY 1 : DRIVERS OF DIFFERENC ES IN INVENTIVENESS ACROSS URBAN AND RURAL REGIONS 1.1 . Introduction Innovation is central to economic competitive ness. Prior research identifie d and analyze d economic and non - economic factors driving innovation, and variations in innovation - related outputs across time and regions. Key drivers include p opulation densities, critical mass of educated and high - skilled employees, research and development (R&D) expe nditures by universities and private industries, innovation and communication infrastructure , and network externalities (Acs , et al. , 2002; Anselin , Varga, & Acs, 1997; Audretsch & Feldman, 2004; Barkley et al. , 2006; Carlino , et al. , 2007). It is no surpr ise that urban regions are more conducive to innovation due to scale economies, network externalities and knowledge spillovers, i.e. , the agglomeration effect (Carlino , et al. , 2001; Carlino et al., 2007 ; Feldman & Florida, 1994). When considering broader regions, however, questions about appropriate geographic units arise since the benefits of knowledge spillovers attenuate with distance (Rosenthal & Strange, 2004) . Many prior studies focus ed on larger geographic units, such as state or metropolitan statistical area (MSA) , which are likely to obscure the spatial (innovation) processes that occur within a region or across its regional Florida, 1994, p. 216). Further, e vidence suggests that spillover e ffects are l ikely more pronounced using smaller geographic units such as the county (Jaffe, et al. , 1993). On the other hand, more granular level studies may only consider smaller region s limiting the analysis of knowledge spillovers (Monchuk & Miranowski, 2010 ; Steph ens et al. , 2013), or do not explicitly analyze rural - urban differences in the rates of innovation (Zheng & Slaper, 2016) . Distinguishing innovation rates by county types may be relevant as urban or proximate to the urban counties fare better in terms of i nnovation and economic growth ( Monchuk & Miranowski, 2010; McGranahan, et al., 201 0; 2 Henderson & Executive, 2007; Henderson & Weiler, 2010; Henderson & Abraham, 2004; Stephens, et al., 2013 ). To address these gaps, I empirically analyze rural - urban gaps in innovation, focusing on differences in spillover effects and drivers of innovation among rural and urban counties in the U.S. This study contributes to the literature by analyzing regional heterogeneity of inventiv eness , measured as patents per capita of inventive class population , across urban, metro - adjacent rural, and rural remote areas , considering the spatial spillover effects, creative class population, industry characteristics, human capital, communication ac cess, and other state - level factors influencing innovation . I use a comprehensive county - level data set spanning the entire U.S., and empirically account for the spatial spillover (and spatial error correlation) and count nature of the dependent variable, by estimating a spatial autoregressive negative binomial regression model with county - level random effects . I find that the spillover effect of regional inventiveness is stronger for rural counties than for urban counties, implying externalities arising f rom innovative climate in their neighboring population share of college graduates in creative disciplines positively influences invention rates, is empirically supported only in urban areas but not in rural areas. This points to another source of rural disadvantage. I also find that the industry mix , in terms of professional services and manufacturing, positively influences inventiveness only in urban and metro - adjacent areas. Similarly, t he influence from the presence of 4 - year colleges and universities, share of high - tech firms, and new immigrants were statistically significant only for urban areas, likely reflecting the benefits of agglomeration economies. How ever, inventiveness in rural areas is positively associated with higher levels of mobile/cellular access compared to broadband services (via 3 cable or landline) in urban areas, suggesting that cellular services are substitute sources of knowledge and inform ation in rural areas. Additionally, the share of college - educated labor force and the diversity of high - tech industries influence inventiveness across all regions (urban, metro - adjacent rural, and rural remote). Finally, I do not find significant associat ions between tax burden, unemployment rate, and state - level venture capital on patenting rates in my study. 1.2 . Review of Literature I nnovation is a key driver of economic growth and regional development as the manifestation of new ideas and knowledge (e.g., in improved products and processes ) provide entrepreneurial opportunities leading to regional prosperity (Acs , et al., 2002; Feldman & Florida, 1994 ). Earlier research f ocused on the firm or industry unit of analysis, and found innova tion , m easured by patents, was positively associated with higher prod uctivity and profit (Bound et al. , 198 4; Griliches, 1990; Hall et al., 198 6 ; Hausman et al. , 1984; Pakes & Griliches, 1980; Scherer, 1965a, 1965b; C incera; 1997). Later research extended the Griliches (1979) knowledge production function (KPF) approach t o study geographically mediated knowledge spillover s, for example, between universit ies and the private sector ( Jaffe, 1989; Audretsch & Feldman, 2004). Increasingly, r egions came to be con sidered more appropriate units for analyzing the innovation process as my understanding of k nowledge spillovers and agglomeration economies across firms and industries evolved ( Audretsch & Feldman, 1996; Rosenthal & Strange, 2004 , Florida, et al. , 2016). W ithin the regional dimension of innovation, large cities and metro regions received greater scholarly attention since the co - location of firms and knowledge workers i n clusters of similar industries were assumed to facilitate spillovers of tacit knowledge due to proximity (Glaeser et al. , 1992; Henderson, 2003). 4 A major challenge for researchers analyzing innovation is identifying appropriate measures of the multi - faceted innovation process (Acs et al., 2002; Cameron, 1996; Cohen & Levin, 1989 ; Mann & Shideler, 2015 ). Typically used proxies to capture the different stages of innovation include : R&D expenditures for inputs, number of patents for invention output, and new product introductions for final innovati ve outputs (Aghion & Howitt, 1990; Acs & Audretsch, 2005a). At the same time , no single proxy can adequately capture the multi - dimensional and stochastic concept of innovation (Mann & Shideler, 2015). For example , R&D expenditures are often d irected toward imitation or technology adoption, in addition to generating inventions/patents (Mansfield , 1984; Kleinknecht,1987; Kleinknecht & Verspagen,1989). Reliable and comprehensive data on direct measures of innovative output s such as new product or service announcements are difficult to obtain (Acs, et al., 2002; Huang et al. , 2010). P atent statistics as innovation proxies are criticized because neither all inventions are patented nor do all patents lead to commercial ized final products (Griliches, 1990; Nagaoka et al., 2010 ) . Additionally , the implicit assumption of homogeneity of any chosen proxy measure in terms of relative contributions to actual technological change or economic value generated is inconsistent with reality (Acs & Audretsch, 2005b ; Cohen & Levin, 1989; Pakes & Griliches, 1980). In fact, Capello & Lenzi (2014) , in their analyses of the nexus between innovation and economic growth in 27 European counties, make the distinction between invention (e.g., patents) and innovation (e.g., co mmercialized output), and argue that less knowledge - intensive regions can achieve economic growth, as some regions may benefit more from new knowledge creation while other may benefit more from innovation commercialization. Despite these limitations, pate nts remain a popular output indicator o f the innovation process due, in part, to data availability and their consistent correlations with other proxies 5 (Autant - Bernard, 2001; Acs, et al., 2002; Czarnitzki et al. , 2009 ; Pakes & Griliches 1980; Parent & Lesa ge, 2008). For example, Acs et al. (2002 ) found that patent applications performed similarly to new product announcements . Parker et al. (2017) compare d 40 potential measur es of innovation and found that patent applications were stat istically similar in performance to the other 39 measures. Another related challenge, especially when analyzing relative innovation performance of regions, is the choice of the appropriate scaling when estimating innovation rates. Wojan et al. (2015) highlight conc erns about using patents per capita which assumes an inaccurate level of homogeneity across regions. For example, retirement communities or tourist towns cannot reasonably have the same innovation potential as equally populated technology/industrial cities or university towns. They show that urban areas appear to be more inventive when patents are scaled per capita, but patent ing rates scaled by the inventor class ( science, engineering and technical professionals) are more equally distributed across urban a nd rural regions 1 . Along a similar vein, Florida (2002) argued that the creative class , consisting of artists , musicians , architects, etc., also contributes directly and indirectly to innovation by allowing more creative collaborations and technology adapt ation to meet creative, non - technical professional needs. A number of regional scientists since then have explored the relationship between entrepreneurship and innovation pr oduction and the creative class . Th e rural - urban innovation gap can be explain ed in terms of the drivers of urban innovation , specifically that urban firms have better access to innovation inputs such as human capital, physical capital, knowledge stock, infrastructure, support services, and output markets ( Barkley et al., 2006 ; Hend erson & Weiler, 2010 ; McGranahan, et al., 2010 ; Monchuk & 1 I refer the interested reader in a more detail ed discussion and presentation of patenting rates across rural and urban regions to Wojan, Dotzel, & Low (2015), who include a number of helpful and informative figures. 6 Miranowski, 2010 ; Orlando & Verba, 2005). S mall populations and thin markets limit the ability of rural firms to capitalize on economies of scale. Further , hi gher population density and the concentration a nd diversity of industries provide more opportunities for communication between innovators. This leads to more synergistic knowledge spillovers and agglomeration economies in urban settings, the benefits of which are difficult, if not impos sible, to replicat e in rural areas. Rural regions, however, are also not homogeneous. E mpirical analysis suggests that spillover s arising from entrepreneurship and innovation creation are stronger in counties that have denser population and are more proxim ate to metro counties (Stephens , et al., 2013; Henderson & Weiler, 2010; Monchuk & Miranowski, 2010; Henderson & Executive, 2007; Fe ser & Isserman, 2006). Other studies posit that rural entrepreneurship is driven more by necessity than by innovative opport unity, which often leads to abandonment when better paying jobs arise (Acs, 2006; Henderson, 2002). Further, some of the behavioral factors analyzed include rural ownership characteristics such as multi - generational ownership and risk aversion ( Renski & Wa llace, 2012 ; Markley, 2001 ), and such factors may be less a ttractive to equity and venture capital investors. Although the extant literature taken together, identifies a large set of potential influencing factors driving the rural - urban innovation gap, ind ividual studies suffer from one or more of the following limitations: limited geographical coverage focusing mostly on urban areas or sub - regions; relatively large units of analyses (states or metropolitan areas); confounded innovation output measures due to normalization by population; and inadequate consideration of the count nature of patents, spatial spillover effects , correlated spatial errors and potential creative class contribution in model specifications. My study attempts to address these limitati ons by building on a recent working paper by Zheng & Slaper (2016). Using a similar comprehensive county - 7 level dataset, I analyze spillovers using a distance decay function. However, the focus of Zheng & Slaper (2016) is mainly on spillovers from Universit y R&D expenditures and the sensitivity of these spillovers to distance. Instead, I turn my attention to analyzing urban - rural gaps in invention rates, considering three county types, urban, metro - adja cent and remote rural. I normalize my output variable by the inventive class population and control for the potential creative class contribution . Finally, my econometric approach controls for the count nature of the dependent variable and spatial correlation; whereas, Zheng & Slaper (2016) relied on lin ear ord inary least square (OLS) estimations. 1.3. Empirical Methods The regional knowledge production function (RKPF) is central to a number of empirical studies of regional innovation and knowledge spillovers and can include region - specific factors that may infl uence regional innovative output s (Charlot et al. , 201 4; Buesa et al., 2010; Ponds et al., 2009; Varga, 2000). I assess the rural - urban differences in innovation using the extended RKPF framework where the dependent variable, a measure of in ventive output in rural and urban US counties, is modeled as a function of in ventive inputs, county - level regi onal characterist ics, and state - level fixed - effects. My dependent variable, inventions per inventive class, follows the spirit of Wojan et al. (2015) and is operationalized as the number of patent applications originating in a county normalized by the inventive class popul ation (where inventive class is measured as the number of degree holders in science and engineering fields excluding social sciences). The empirical model also include s indicator s classifying counties as metro, metro - adjacent rural, and re mote rural, to ex plore rural - urban differences , as well as state and temporal fixed - effects. 8 The RKPF model using patent applications per 1,000 inventive class population makes OLS assumptions inappropriate due to the count nat ure of patent applications (Hausman et al., 19 84 ) . U nder these conditions , OLS estimates are likely to be biased and inconsistent (Gr eene, 2003). On the other hand, count models are often estimated using a Poisson distribution. H owever, the conditional mean and variance of Poisson models are assumed e qual. Thus, w hen the dependent variable is over - dispersed, this assumption is violated leading to underestimated standard errors of coefficient estimates and spuriously high statistical significance (Hilbe, 2011). Regional patent data are essentially the c ounts and are right skewed with large portions of probability mass centered around zero. 2 To address this, I use a negative - binomial estimation procedure , as it can account for such over - dispersion and skewness by allowing the variance to be different than the mean ( Hilbe, 2011 ) . Following Hausman, et al., ( 1984 ), Hall et al., (1986), and Griliches (1990), I also employ a county - level random e ffects model instead of a fixed - effects model . This helps address the large number of counties with zero patent output during the study period and relatively short panel data. A fixed - effect regression model excludes these counties with time - invariant zero patents from analysis, which may introduce potential sample sel ection problems ( H all et al., 1986). My negative binomial regression model with county - level random - effects takes the form: , and (1) where Pat it are annual utility patent applications per inventive population in county i in year t ; x it represents the vector of innovation inputs; and z it represents the vector of other relevant regional 2 The smaller the geographical units of observations are, the higher number of zero pa tent observations are likely. In this county - level study as well, nearly two - thirds 64%, 37%, 77%, and 85% of the probability mass of the dependent variable (patent applications per inventive class) is centered at zero for combined, metro, metro - adjacent r ural, and remote rural data sets respectively. I do not include the figure on the distribution of patents to save space for remaining analysis, but it is available from authors upon request. 9 factors . The county - level random effects parameter i is assumed to follow a beta distribution ( Hilbe, 2011 ) . Regional patenting has been found to exhibit spatial dependence (Autant - Bernard, 2001; Parent & Lesage, 2008; Florida, 2014), that is, inventive activities in a regi on may have spillover effects on patenti ng rates in neighboring regions, and such spillover effects are likely to be more prevalent with more granular geographical units of analyses such as counties. These spillovers can arise from increased proximity, mob ility and interaction possibilities, and shared infrastructure and amenities that create an innovative climate. Hence, I hypothesize that innovation rates measured by patenting rates in one county influences patenting rates in its neighboring counties. I include a spatially lagged dependent variable to help estimate these spillover effects. Therefore, my estimated empirical model takes the form of the spatial - shown i n equation (2). 3 This model also accounts for spatial error correlation and is specified as: (2) where W t Pat it is the spatially lagged dependent variable, and is the spillover, or spatial dependence, coefficient to be estimated. When the neighborhood of each county does not change, as in my application, W t is identical each year . Thus, for any year W= w, 3 The spatial spillover effects arising from mobility of human c apital, R&D activities of colleges and universities , and the network of high - tech firms in surrounding regions may also play an important role in determining regional inventiveness. Recognizing this possibility, I initially considered a Spatial Durbin Model ( SDM ) where spillover effects of the independent variables, namely the high - tech variety, the number of 4 - year colleges and un iversities , and the share of bache , are included with the spatially lagged dependent variable in equation (2). However, I found that the spatially lagged independent variables displayed a very high degree of colli nearity . Inst ead, I decided to employ a n S AR model where the aggregate spatial spillover effects of the dependent variable (inventive outpu t) are modeled. Thus, my model assumes that the potential spillover effects from neighboring counties are adequately captured by t heir respect ive patenting rates. 10 , and is a nx1 vector whose j th element is a scalar resulting from a linear combination (weighted average) of patenting rates per inventive class in counties neighboring to county i . W eights take their values as: for all i =1 to n where d i,j is the geographical distance between centroids of counties i and j, and d is the threshold distance beyond which spatial dependence in terms of patenting rate is assumed to be zero. I empirically estimate equation (2 ) using maximum likelihood estimation procedures (Hilbe 2011), with xtnbreg command with random effects option in Stata® software. 1.4. Data and Variables My county - level dataset comprises several secondary sources and includes the 48 contiguous states in the U.S . for the period 2009 - 13 . 4 Table 1 lists key variables and their data sources. My dependent variable is patent applications per inventive class population, i.e. the number of college graduates in science and engineering in the county. Additionally, I classified counties into three groups using the 2013 USDA Rural - Urban Continuum Codes (RUCC). I classified c ounties with RUC C codes of 1, 2, and 3 as metro counties , 4, 6 , and 8 as metro - adjacent rural counties, and 5, 7, and 9 as remote - rural counties. 4 My sample includes 2833 counties as some were dropped due to missing observations across the different secondary data used. 11 Table 1 . 1 Variables Definition and Data Source Variables Description Source Year Patents per inventive class Utility patent applications per 1,000 four - year or higher college degree holders in selected S&E fields USPTO, ACS 2009 - 13; 2013 Splag patents per inventive class Spatial lag of patents per inventive class with distance decaying within 50 miles from county centroids USPTO, ACS 2009 - 13; 2013 High - tech variety Number of 3 - digit NAICS high - tech industries CBP 2009 - 13 High - tech share Share of high - tech establishments in total business establishments CBP 2009 - 13 Universities/colleges Number of four - year or higher college degree awarding institutions in a county NSF 2009 - 13 College plus education Share of 25 years and older people with ACS 2009 - 13 Arts share Share of four - year or higher college degree holders in selected Arts fields in total population ACS 2013 Foreign - born - non - citizen population Share of foreign - ACS 2009 - 13 Unemployment change Change in current year unemployment rate from BLS 2009 - 13 Tax burden Percent of personal income paid in tax Census of govts. 2007, 2012 High - speed broadband penetration Dummy (=1(high), if at least 60% of households had high - speed broadband connection; 0(low) otherwise) FCC 2009 - 13 Cellphone service penetration Dummy (=1 (high), if number of cellphone service providers is one s.d. above sample mean; 0(low) otherwise) FCC 2009 - 13 Manufacturing intensity Dummy (=1 (high), if share of population 16 years and older employed in manufacturing industries is one s.d. above sample mean; 0(low) otherwise) ACS 2009 - 13 Professionals service intensity Dummy (=1(high), if share of population 16 years and older employ ed in professional service industries is one s.d. above sample mean; 0(low) otherwise) ACS 2009 - 13 Average venture capital Average venture capital financing per business establishment, at state level NSF, CBP 2009 - 13 County types Classification of counties based on urban population and commuting patterns ERS 2003 ACS= American Community Survey: Census Bureau; BLS= Bureau of Labor Statistics; CBP= County Business Patterns; ERS= Economic Research Service - USDA; FCC= Federal Communications Commission; NSF= National Science Foundation; USPTO= U.S. Patents and Trademarks Office 12 Prior literature shows that human capital is strongly associated with invention rates ( Charlot et al., 201 4; Buesa et al., 2010; Ponds et al., 2009; Varga, 2000) . I use the share of my human capital measure, and I exp ect it to positively influence the regional rates of innovation. Wojan, 2007 ) individuals in creative occupations including artists and designers positively influence invention rates. Thus, I include the population share of college graduates in selected arts fields and hypothesized it to have a positive coefficient. Academic institutions act as centers of research, expertise and knowledge - based activities, and train highly - skil led labor force that facilitate inventive activities in other firms including small firms (Acs et al. , 1994). Further, universities are increasingly encouraging patenting by their faculty members ( Czarnitzki et al. , 2009). I include the number of private a nd public 4 - year colleges and universities as a control variable. I hypothesized it to have a positive coefficient indicating positive influence on patenting rates. To provide additional control s for the entrepreneurial and innovative environment in a county, I include variables for the share of high - tech establishments, the variety of high - tech industries represented , manufacturing intensity, professional service intensity, and venture capital per fir m . Note that I limit the industry focus to manufacturing and professional services, as these two industries account for a high level of patenting, and innovation rates in rural and urban areas were found to be more similar in manufacturing intensive areas (Wojan & Parker, 2017). The high - tech variety variable is based on NSF designated high - tech firms, and is the number of four - digit and six - digit high - t ech NAICS industries (out of the maximum 45) operating in the county (National Science Foundation, 2017) . The share of high - tech 13 establishments is calculated as the total number of these firms divided by the total number of all establishments in a county. Both High - tech variety and share of high - tech establishments are expected to positively influence innovat ion due to synergistic cross - fertilization of ideas across related and growing industries. The manufacturing intensity and professional service intensity variables are binary variables which are coded as 1 if the shares of the potential labor force (16 yea rs and older) employed in these sectors is at least one standard deviation above the sample mean (based on the combined geography types, metro, metro - otherwise. Both manufacturing intensity and professional service intens ity are expected to positively influence innovation production. I use state - level venture capital financing data from the NSF as a proxy for private investment, since private investment data are not readily available at the county level. The variable is no rmalized as venture capital investment per firm in thousands of dollars, and it is expected to be positively associated with patenting rates. Additionally, a growing body of literature examines the influence of immigrants on innovation production (Kerr, 20 13; Kerr & Lincoln 2010; Niebuhr, 2010). I include the variable Share foreign - born non - citizen population, as studies find that it i s mainly recent immigran ts that positively influence innovation creation . Communication infrastructure facilitates innovatio n and may be especially relevant for rural inventors where opportunities for face - to - face communications are less frequent with other innovators (Conley & Whitacre 2016 ). I use two indicator variables, one for high - speed broadband penetration and another f or cellphone/mobile service penetration drawing on Federal Communication Commission (FCC) data. Following Conley & Whitacre ( 2016 ), high - speed broadband penetration is coded as - speed connection and The second variable, cellphone service penetration which 14 has not been used on the prior literature to the best of my county penetration is more than one standard deviation above the sample mean (by county t ype) I hypothesize a positive association between invention rates and broadband access and cellphone penetration, especially in rural counties. A variable measuring loc al total tax burden , defined as ratio of per capita total local ta x to per capita personal income, is included to assess the impact of taxes on innovation production in a region. The tax burden data are from the Census of Governments for the years 2007 and 2012 . 5 While higher levels of local government services (e.g. education, roa ds, law enforcement, parks , etc.) are expected to facilitate innovation, it has also been argued that higher taxes inhibit innovation by reducing private resources and incentives for innovation effort s (Bartik 19 91; Mukherjee et al. , 2017) . I conjecture that the facilitation effect of public services will dominate the negative effects, and hypothesize a positive association between tax burden and rates of inventive outputs . Finally, I use the spatial lag of the dependent variable (derived from the spatial weighting method described in the methods section) to examine the spillover effects o f the inventive outputs in neighboring counties. I use the threshold of 50 miles 6 so that the spillover is assumed to occur across county boundaries if the county centroids are located within the distance. Given the discussion of prior literature above, I anticipate this measure to be positively associated with the innovation production in a county. 5 Since I have tax burden data only for 2007 and 2012, I used the 2007 tax burden for years 200 9 - 2011, and the 2012 tax burden for years 2012 - 2013. 6 Following Zheng & Slaper (2016), I tested the threshold of 100 miles, but it did not greatly affect the results, as the magnitudes, signs and significance of the coefficient estimates did not change. F or the sake of parsimony, I only include shorter distance in my modeling. The 100 - mile distance results are available on request. 15 1.5. Empirical Results 1.5.1 . S ummary Statistics Table 2 shows the summary statistics for all variables in the combined sample as well as each county type. Sim ple comparison of unc onditional means of the number of patent applications per inventive class population across urban and rural counties indicates that metro (urban) counties innovate significantly more than both types of rural counties; metro - adjacent ru ral counties innovate relatively more than the remote rural counties on average. However, all three county types display large heterogeneity (or dispersion) in the rates of patenting within their groups . 7 Simple correlation analysis (not shown , but available on request) also support the hypothesized associations between invention rates and various explanatory factors . Table 2 also shows differences among the three county types, with respect to the means of several explanatory variables expected to in fluence innovation rates. For example, means of patenting spillover, high - tech variety, 4 - year colleges and universities, which are hypothesized to positively influence the regional patenting rates , all show highest values for metro counties , followed by metro - adjacent and then by remote - rural counties. The means of people 25 - year old foreign - born population, share of arts degrees, and high - speed broadband penetration are highest in metro areas. Inter estingly, they are higher in remote rural areas compared to metro - adjacent rural areas. On the other hand, tax burden and cellphone service penetration, on average, are the highest in remote rural areas; while, the metro - adjacent counties are more manufact uring intensive among the three county types. 7 Coefficient of variation (dispersion) for metro counti es is (47.617/8.117)*100% =586% , for metro - adjacent counties it is (11 .026/0.819)*100% =635%, and for remote rural counties it is (5.753/0.819)*100% =702% 16 Table 1 . 2 Summary Statistics Variables Combined Metro Metro - adj. Rural Remote Rural Mean S.D. Mean S.D. Mean S.D. Mean S.D. Patents per inventive class 3.9 30.5 8.1 47.6 1.7 11.0 0.8 5.8 Splag patents per inventive class 8.2 17.7 14.6 23.2 6.2 12.9 1.9 9.1 High - tech variety 14.1 9.5 21.1 10.5 10.9 5.3 8.4 5.2 High - tech share (% points) 4.5 3.6 5.8 3.6 3.7 2.0 3.8 4. Universities/colleges 0.6 2.4 1.4 3.7 0.1 0.4 0.1 0.4 College plus education (% points) 13.0 5.4 15.5 5.8 10.8 3.8 12.3 4.9 Arts share (% points) 1.7 1.3 2.2 1.5 1.4 1.0 1.5 1.3 Foreign - born - non - citizen population (% points) 2.8 3.5 3.6 3.8 2.2 2.8 2.3 3.5 Unemployment change (in % points) 7.8 28.8 8.1 28.7 7.7 29.1 7.5 28.5 Tax burden (% points) 3.7 2.0 3.7 1.6 3.6 1.9 4.0 2.6 Manufacturing intensity (1=high; 0=low) 3% N/A* 2% N/A 5% N/A 3% N/A Professionals service intensity (1=high; 0=low) 3% N/A 6% N/A 1% N/A 1% N/A High - speed Broadband penetration (1=high; 0=low) 41% N/A 60% N/A 26% N/A 32% N/A Cellphone service penetration (1=high; 0=low) 20% N/A 16% N/A 19% N/A 27% N/A Average venture capital, state level, (in $1,000) 0.3 0.5 0.4 0.6 0.3 0.4 0.2 0.4 Observations 14165 5435 4760 3970 * N/A = Not applicable (for dummy variables; the means refer to frequencies in percent) These summary statistics suggest that the urban advantage in production of inventive outputs is driven by the higher levels of the factors that are found to be positively associated with regional innovation. However, regression analyses using empirical model (2) was carried out to test if this urban advantage persists after controlling for the differences in the levels of these innovation drivers between urban and rural areas. 17 1.5.2. Regression Estimation Results This section analyzes the advantage of urban areas in creating inventive outputs compared to the rural areas using the estimation results of the SAR model in equation (2). For this analysis, I first es timate my empirical model for the combined data set, with county level random - effects , state and temporal fixed - effects. I also include indicato r variables for metro - adjacent and remote - rural county types , with metro - counties serving as the reference categ ory. The first column of coefficient estimates in t able 3 show the maximum likelihood estimation results from my empirical model in equation (2) for the combined dataset. C oefficient estimates in the first column of table 3 suggest that urban areas are mor e inventive than both types of rural areas, with t he rates of inventive outputs shown to o ccur 48% [ = (e 0. 391 - 1)*100% ] and 104% [ = (e 0. 715 - 1)*100%] 8 more frequently in urban areas than the metro - adjacent and remote rural counties respectively. The positive statistically significant coefficient ( ) estimate of the spatially lagged dependent variable, indicates significant spillover effects of patenting rates in neighboring counties on the county patenting rate. That is, patenting in a county is positively influenced by conditions that favor patenting in neighboring counties. The coefficient estimates of the explanatory variables indicate statistically si gnificant positive association (at 5% or higher level) of patenting rates with several variables including high - tech variety, colleges and universities , college plus education, professional service intensity indicator, and spillover effects. Foreign - born p opulation is significant only at 10% level. The positive sign on patenting productivity of the inventive class. However, the variables related to the innova tion 8 See Hilbe (2011) for interpretation of the coefficients. Essentially, incident rate ratio=exp(coefficient estimate) and IRR is interpreted as the rate ratio for a unit c hange in independent variable of interest. 18 infrastructure (tax burden, high - speed broadband penetration, and cellphone service penetration) and manufacturing intensity do not show a statistically significant association . 1.5. 3. Rural Urban Comparative Advantage in Innovation The results fro m the combined sample generally support previous findings regarding the urban innovative advantage and drivers of innovation albeit with a more comprehensive dataset and a more refined count model estimation. However, in view of the persistent urban advant age in patenting rates and significant differences in levels of explanatory variables across county types revealed by the summary statistics, I estimate the regression model shown in equation (2) separately for the three subsamples by county type . The goal of these subsample estimations is to empirically explore diffe rences in the innovative capacities (patenting rates) of rural and urban counties that were otherwise iden tical within their subsamples. I conduct likelihood ratio test, suggested by Brooks and Lusk (2010), where null hypothesis is framed as various rural and u rban regions can be represent ed by common drivers of their innovative capacity (i.e., use of the combined model for analysis is appropriate). The a lternative hypothesis is that the paramet ers of various drivers across the three county types ( coefficient estimates columns 2 - 4 of t able 3 ) are dissimilar. The results from the likelihood ratio test rejected the null hypothesis in favor of the alternative hypothesis 9 , suggesting that there are some differences between rural and urban counties in terms of potential drivers of their patenting intensity. Thus, use of separate estimation models is justified. 9 The test statistics for the likelihood test is computed as two times the difference between the log - likelihood of model 1 and the sum of the log - likeliho ods of models 2 - 4 in tables 4 . For example, th e test stati stics is 466 {2*[ - 15283 - ( - 8694 - 4045 - 2311)] = 2* - 233= 466} . The chi - square critical value with 60 degrees of freedom and 99% confidence level (88.4 ) is less than the test statistic. 19 Table 1 . 3 Results from RENB - SAR Model on Full sample and Sub - samples by County Types Dep. Var.: Patents per inventive class Coefficient Estimates Combined Metro Metro - adj. Rural Remote Rural Metro - adj. Rural - 0.391*** - - - (0.082) Remote Rural - 0.715*** - - - (0.097) Sp lag patents per inventive class 0.005*** 0.003* 0.009** 0.010* (0.001) (0.002) (0.004) (0.006) High - speed b roadband penetration ( 1=high; 0=low ) 0.049 0.054 0.080 0.014 (0.035) (0.037) (0.097) (0.128) Cellphone service penetration ( 1=high; 0=low) 0.025 0.005 0.149* 0.240* (0.026) (0.026) (0.083) (0.133) Manufacturing intensity ( 1=high; 0=low) 0.021 - 0.083 0.377** - 0.522 (0.083) (0.094) (0.149) (0.412) Professional service intensity ( 1=high; 0=low ) 0.141*** 0.074* 0.496** 0.116 (0.039) (0.041) (0.200) (0.331) Arts share (in % points) 0.083** 0.100** - 0.013 0.112 (0.042) (0.048) (0.109) (0.110) High - tech variety 0.085*** 0.057*** 0.130*** 0.183*** (0.004) (0.005) (0.012) (0.016) High - tech share (in % points) 0.008 0.022** 0.002 - 0.079* (0.009) (0.011) (0.029) (0.040) Universities/colleges 0.063*** 0.086*** 0.020 - 0.311 (0.018) (0.019) (0.145) (0.223) College plus education (in % points) 0.100*** 0.092*** 0.100*** 0.112*** (0.011) (0.014) (0.028) (0.031) Foreign - born - non - citizen population (in % points) 0.023* 0.059*** 0.041 0.001 (0.012) (0.017) (0.026) (0.026) Unemployment change (in % points) - 0.000 0.000 - 0.002 - 0.001 (0.001) (0.001) (0.002) (0.003) Tax burden (in %points ) - 0.000 0.023 - 0.049 0.033 (0.015) (0.019) (0.038) (0.032) Average v enture c apital, state level (in $1,000) - 0.011 - 0.029 0.072 - 0.093 (0.042) (0.040) (0.225) (0.373) Constant - 1.875*** - 1.718*** - 0.433*** - 1.903 (0.296) (0.354) (0.090) (1.368) Time fixed effects Yes Yes Yes Yes State - level fixed effects Yes Yes Yes Yes Observations 14,165 5,435 4,760 3,970 Log likelihood - 15283 - 8694 - 4045 - 2311 Model DF 67 65 62 60 AIC 30706 17523 8220 4749 BIC 31235 17972 8640 5145 Standard errors in parentheses; *** p<0.01, ** p<0.05, * p<0. 1 20 My results in columns 2 - 4 of table 3 show that having high cellphone service penetration is important in rural areas (statistically significant coefficients at 10% level). However, high - speed broadba nd (via cable/landline) penetration does not appear to influence patenting rates. I find that the spatial spillover effects of patenting in neighboring counties are significant in all county types, but higher in rural counties (at 5% significance level in metro - adjacent counties and 10% in metro and remote rural counties). This suggests that the spillovers from inventive activities in surrounding counties likely have greater influence on invention rates in rural counties. I also find that the concentration of creative population, measured with the share of arts college degree holders in the county population, is positively associated with patenting rates in the urban and metro - adjacent areas, but not statistically significant in rural remote areas. My findin g supports the prior findings in the literature on the important role of creative class in the urban innovation and indicates why such a role is neglected in rural settings. The coefficient estimates of the manufacturing intensity and professional service intensity (positive and statistically significant) in column (3) of table 3 show that patenting is a more frequent phenomenon in both manufacturing and profession service industries located in metro - adjacent rural counties. In urban areas, only the profes sional service intensity is statistically significant but small in comparison. This provides weak support for the notion that differences in patenting rates between rural and urban areas may also be linked to differences in industry make up. I also find th e foreign - born - non - citizen population contributes to the innovation rate, but only in urban areas. The results (table 3) show that association of high - tech share with patenting rates is opposite in urban and rural counties, with the association being positive in metro counties but negative in remote rural counties. For metro - adjacent counties, it is positive but not statistically 21 significant. These suggest that increases in share of high - tech firms in total firms by a unit percentage point is likely to increase the patenting rates in metro counties by 2.2% [ = (e 0. 022 - 1)*100%], but the patenting rates in remote rural counties respo nd to the change with 7.6% [ = (e - 0. 079 - 1)*100%] lower patenting rates. On the other hand, the coefficient of high - tech variety is positive and statistically significant in all three county types. Compared to both types of rural counties, the influence of high - tech variety on patenting rate is lower in urban counties. These results suggest that diversity of high - tech industries rather than the absolute number of high - tech firms spurs innovation in remote rural counties, similar to metro - adjacent counties. H owever, metro counties benefit from both number and diversity of high - tech firms in terms of patent generation. Finally, I find that the share of population with a 4 - year degree or higher is a major driver of patenting rates in all three county types, but its influence appears to be stronger in the remote rural counties than in the metro - adjacent or metro counties. The coefficient estimates of the universities/colleges in columns (2) - (4) of table 3 show that the number of 4 - year private or public academic i nstitutions hosted by a county has statistically significant positive association with patenting rates in metro counties only. 1.6. Summary and Conclusion I analyze d regional heterogeneity in innovation rates and the drivers of such heterogeneity, using a comprehensive county level dataset covering the period 2009 - 13. I compare the rates of in ventive outputs among the urban areas and two types of rural areas, metro - ad jacent rural and remote - rur al areas of the U.S. using patent applications per 1,000 inventive class population (measured by the number of science and engineering graduates with four - year college or higher degree). I account for effects on rates of creation of inventive outputs in a county arising from the spatial spillover effects of inventiveness in surrounding counties by 22 using the spatially lagged variable of my measure of inventive output and including high - speed broadband penetration and cellphone serv ice penetration, which are likely to help facilitate the spatial spillover. I also account for patenting heterogeneity across industries by controlling the intensity of manufacturing activities and professional service provision. Additionally, I control ot her factors that are commonly found in the literature to be important in regional innovation such as advanced educational attainment, presence of colleges and universities, and high - tech firms. I conduct my econometric analysis using spatial autoregressive negative binomial count models of RKPF, aimed at identifying the drivers of differences in inventiveness across urban and rural regions. I find that urban areas on average are more inventive than the rural areas, even after accounting for the spatial spi llover effects, industry effects, and other common factors related to regional innovation. My results show that patenting is characterized by spatial spillover in urban and both types of rural regions, and the spillover effects are stronger in rural region s. This suggests that spatial spillover effects from inventive activities in neighboring areas are important in both urban and rural regions, but the rural communities may be more dependent on ideas and knowledge from adjacent areas, thus receiving higher spillover externalities compared to urban areas. Further, I find that higher penetration of cellphone service is likely to support inventions in rural areas. Lack of evidence on the supportive role of access to high - speed broadband connection does not sugg est that it is not important in facilitating regional inventions and its spillover. Instead, urban areas may already have provided such access or internet access; whereas, cellphone service providers may be substituting the access of high - speed broadband c onnection in rural areas. Additionally, the apparently smaller gap in patenting rates between metro and metro - adjacent counties (48%) compared to those between metro and remote rural 23 counties (104%) is likely driven by the larger share of manufacturing ind ustries that are expected to produce significantly more patents in metro - adjacent counties. Other results from this study confirm the prior findings in the literature that the diversity of high - tech industries and the percentage of population with advance d education al attainment are important contributors of inventiveness in all three county types - metro, metro - adj acent and remote rural counties. This suggests that the urban advantage in inventions is likely to arise from larger number of high - tech firms, advance educational institutions, and larger population share of new immigrants and creative class individuals. I do not find evidence of influence of tax burden, unemployment rate, and state - level venture capital on patenting rates in my study. My results provide two policy insights regarding regional in ventiveness and economic development. First, the results suggest that the policies intending to mitigate the rural - urban inventiveness gap should focus on building strong communication infrastructures in th e rural regions, as these infrastructures are likely to generate stronger spillover effects in the rural regions. Second, the key drivers of in ventiveness such as advanced education and diversity of high - tech industries play important roles in driving the rates of inventive outputs in urban and rural counties, with the importance (of both the variables) being more critical in rural areas. But, on average, these rural areas are less diverse and have lower levels of population share with advanced education. So, the similar policies promoting investments in education and attracting more diverse high - tech industry are effective in both urban and rural areas , but relatively larger investments may be needed in rural areas compared to urban areas, due to agglomera tion - related dis - economies in rural areas. More important but related to the second implication, an increase in the number of high - tech firms within the existing diversity is expected to spur the rate of invention output in metro areas but it is expected to have opposite influence in remote rural 24 c ounties. Therefore, the policies to promoting high - tech firms may further amplify the inventiveness gap between urban and remote rural areas if such policies fail to attract the firms from diverse high - tech industries. Finally, some caveats are in order in interpreting the findings of this study. I use patents/inventive population as an overall indicator of inventive capacity and productivity of a region, which is subject to criticism as discussed in the literature review. Further, the patent data I obtaine d from USPTO contain the residential address of the inventor(s). I used the county of residence of the first inventor, in case of multiple inventors, to match the patent data with other county level data. This may lead to bias in comparison as the place of work of the (first) inventor might be different from his/her place of residence. Additionally, my patent dataset does not distinguish between product or process innovations and this distinction might have implications for the growth effects of innovation, nor does the patents data provide information on whether the patent represented an incremental innovation or a radical invention. As the prior findings suggest that the incremental efficiency improving/cost reducing inventions are likely to occur more fr equently in rural areas, but the radical inventions are more l ikely in th e urban areas (e.g., Orlando & Verba, 2005). Such information may also reveal potential chain - patenting suspected to be occurring. Due to lack of more detailed data, I assume that the se effects are random. Finally, in my construction of spatial weight matrix, I do not distinguish among the spillovers across county types, for example if spillovers are prevalent more from urban to rural areas or vice versa, which might be an interesting topic for future research . 25 REFEREN CES 26 REFERENCES Acs, Z. (2006). How is entrepreneurship good for economic growth? Innovations: technology, governance, globalization , 1 (1), 97 - 107. Acs, Z. J., Anselin , L., & Varga, A. (2002). Patents and Innovation Counts as Measures of Regional Production of New Knowledge. 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Local academic knowledge transfers and the concentration of economic activity. Journal of Regional Science , 40 (2), 289 - 309. Wojan, T., & Parker, T. (2017). Innovation in the Rural Nonfarm Economy: Its Effect on Job and Earnings Growth, 2010 - 2014. USDA - ERS Report, ERR - 238. Wojan, T. R., Dotzel, K. R., & Low, S. A. (2015). Decomposing Regional Patenting Rates: How the Composition Factor Conf ounds the Rate Factor. Regional Studies, Regional Science , 2 (1), 535 - 551. 31 Zheng, P., & Slaper, T. (2016). University Knowledge Spillovers, Geographic Proximity and Innovation: An Analysis of Patent Filings Across U.S. Counties. Kelley School of Business Re search Paper No. 16 - 76. Retrieved from SSRN: https://ssrn.com/abstract=2857130 or http://dx.doi.org/10.2139/ssrn.2857130 32 ESSAY 2: EXPLORING THE INTERD EPENDENCE OF INNOVAT ION AND REGIONAL ECONOMIC GR OWTH: A COUNTY LEVEL ANALYSIS 2.1. Introduction R egional economic growth models have commonly accounted for the interdependency between the choice of households for their place of residence and the decision of firms to locate their business by modeling the equilibrium levels of populati on and employment induced by those decisions as being simultaneously determined . Carlino & Mills ( 1987 ) and Steinnis & Fisher ( 1974) used a two - equation system in which equilibrium levels of population and employment are determined simultaneously, influenced by s everal region - specific exogenous factors that the firms and households co nsider in their location decision s . It is possible within such partial equilibrium framework that some of these variables, mainly income, are simultaneously determined along with population and employment. Arguing that the quality and number of jobs that m ove to a region determine the equilibrium level of income in a region, Deller et al. (2001) account for this possibility of interdependent relationship of income with population and employment by modeling a system of three simultaneous equations, and by tr eating income as endogenous variable in the system. However, the above studies ignore the potential interdependent effect of innovation on regional economic growth. The role of innovation and innovative entrepreneurs in regional growth has been well docum ented in s everal empirical studies (e.g. Adelaja et al. , 2009; Feser & Isserman, 2006 ; Henderson & Weiler, 2010; McGranahan et al., 2010 ; Monchuk & Miranowski, 2010; Stephens et al., 2013; Young at al., 2014 ; 2013 ) and they have largely confirmed the expec ted positive association of population, employment, and income growth with innovation. Improvements in the innovation - led productivity of input factors including labor productivity result in income and employment growth (Ezell & Atkinson, 2010). Innovative industries are found to generate higher 33 displacement of lower - wage and lower - productivity jobs with better - paid and more productive ones (Helpman, 2004 ; OECD, 1994). The extant lit erature mentioned above has considered unidirectional positive influence of innovation rates on regional economic growth as measured by income, employment and population. These studies treat innovation as an exogenous driver of economic growth. However, I posit that innovation rates themselves are in turn influenced by economic opportunities and growth. Higher incomes and employment opportunities attract more technically qualified and creative class of people to the region and encourage synergistic creativ e cooperation resulting in higher innovation rates. In other words, I argue that innovation plays an important role in regional economic growth, and equilibrium innovation rates are in turn simultaneously determined with levels of income, employment and po pulation. Empirically, I consider the role of innovation in regional population, employment, and I extend their three - equation system to include innovation growth as an endogenous variable simultane ously determined along with population, employment, and income growth, wherein the growth in county level patent applications between 2009 - 13 serves as a measure of innovation, Additionally, I analyze the gaps in economic growth and innovation rates betwee n leading and lagging regions in cluding rural and urban regions, and factors influencing economic growth and innovation . The remainder of the article is organized as follows. In the next section, I review the literature on the relationship between innovat ion and economic growth and their determinants. The conceptual and empirical models are laid out in section three. Section four provides the 34 description of the data and variables. In section five, I present and discuss my findings. Section six concludes wi th policy implications and scope for further research. 2.2. Literature Review This section reviews the extant literature on the role of innovation in economic growth. It also contains a review of the factors influencing regional innovation and economic gr owth, which facilitates the choice of variables used in this study. 2.2.1. Innovation and Economic Growth Innovation is arguably a phenomenon as old as human history, as it is inherently human to produce new ideas for something better. However, the role of innovation in economic growth lacked scholarly attention until the emergence of Marxian - Schumpeterian theoretical perspective ( Fagerberg, 2003) . According to this perspective, innovations in firms occur as they strive to economy. These innovations spur possibilities for new businesses and further innovations, thus setting stage for long - run economic growth. In o ther words, it implies that innovation stimulates growth and the latter leads to more innovations as firms continuously seek to find new combination of resources to remain technologically competitive. Neither Marx nor Schumpeter applied their perspectives to explain the macro - level implications of innovation in terms of cross - country differences in economic growth, but several analyses from 1960s onwards suggested innovation as the major explanatory factor (Fage rberg, 1994, 2002; Fagerberg & Verspagen, 2002 ; Posner, 1961 ). approach to explain growth (e.g. Solow, 1956), but only were associated to the part of the growth 35 that cannot be explained by the contributions of t he accumulated traditional factors of production such as labor and capital 10 . In other words, the classical approach assumed the rates of innovations as exogenously determined in the economic system rather than explaining the mechanism that results to the t echnological change. Marxian - Schumpeterian perspective received renewed attention among the economists duction function. In the new growth models, innovation and technical change result from decisions of the profit maximizing agents to produce knowledge and utilize it as an input to production of final outputs. Thus, conceptually parallel to the Marxian - Sc humpeterian early growth models, these models, also known as rational actions of (innovative) entrepreneurs, who identify opportunities, introduce innovations, create c ompetition that demands further innovations, and offer more business opportunities for new entrepreneu rs (Acs et al., 2012; Carree & Thurik, 2003; Wennekers & Thurik, 1999; Wong et al., 2005). Theoretically, the relationship between innovation and economi c growth and development has been acknowledged by endogenous growth theorists for a long time beginning with Kuznets (1971) and Marshall (1990). Although perspectives differ on the mechanisms by which innovation influences economic growth, that is, whether knowledge is endogenous or exogenous in the system of economic growth, it is commonly recognized that change in knowledge and economic growth affect each other direct ly and indirectly (Howells, 2005 ). In the real world as well, innovation has been the central driver of prosperity and economic growth. 10 See Nadiri (1993) for a summary of the summary of studies using this app roach. 36 (Feldman & Florida, 1994). Innovation - led productivity has been estimated to account for nearly half of the U.S. GDP growth in past 50 years following the World War II (Mandel, 2004) and more than two - thirds of the income growth (Ezell & Atkinson, 2010). Improvement in labor productivity in innovative industries is associated wit h creation of better - paid jobs by displacing lower - paid ones 11 (Helpman, 2004 ; OECD, 1994). The influence of new ideas and products on - increasing rate. For example, it took 35 years for the telephone to reach a quarte r of the American population, but just 13 years for the cellphones, and seven years for the internet (Federal Reserve Bank of Dallas, 1996). America remains as the global economic leader due to its competitive advantage arising from its early adoption of an open and inclusive market economy that attracted talented workforce and innovative entrepreneurs from across the world (Ezell, 2009). Now that several compete o n traditional cost and quality terms, the ability to constantly create new and better products and services will confer the major competitive edge in the 21 st century. The fact that more than three dozen of countries have formulated innovation - led strateg ies for their economic growth and development in the first decade of the 21 st century (Ezell, 2009) suggests that innovation will become more powerful driver of economic growth in the future than ever before. 2.2.2. Innovation and Regional Economic Growth The models of endogenous growth recognize that knowledge is only partially excludable, as the firms producing it are unable to fully appropriate it. This knowledge spills over to the regional knowledge stock that benefits the surrounding firms (Acs et al. , 2012). The implications 11 See Capello & Lenzi (2013) for the discussion on potentially different roles of product and process innovations in employment growth. Data limitations do not allow us to analyze the difference in this analysis. 37 of this theoretical recognition combined with those from the Marxian - Schumpeterian perspective discussed above is that regional innovation and economic growth are interrelated, or they drive each other to continuous change. The kn owledge spillover from R&D activities of surrounding institutions such as universities and other firms served as an explanation for the source of knowledge input for small enterprises that were innovative but lacked their own R&D commitments ( Acs & Audrets ch, 2005; Jaffe, 1989 ) . Subsequently, the findings from a series of studies that knowledge spillover tends to be bounded by geographical distance ( Ans elin et al., 1997; Audretsch & Feldman, 1996; Jaffe et al., 1993) marked a major advance in inquiries int o the role of geography in innovation and growth. The economic growth of regions after the end of the World War II was focused more on the internal competition within a broad economic region than global competition. Various states in the U.S., and similarl y European nations, began to compete among each other to attract firms by investing in physical infrastructure (Ezell & Atkinson, 2010). This strategy provided the firms with efficiency gains through reduction in costs, especially transportation costs, and extended local markets. However, with increasing global economic integration and the advances in information and communication technologies, the regions are getting more interconnected and innovations are affecting broader geographies, and spreading fast er globally. For example, nearly half of U.S. productivity growth comes from improvements in technology in foreign countries (Eaton & Kortum, 1995). Therefore , the competitiveness of the regions that are integrating economically at global scale at ever - increasing pace lies more in the capability of firms and industries to create constantly new value in the global marketplace, which depends on regional 38 2.2.3. Drivers of Regional Innovation Regional innovation has been receiving increasing attention of academic scholars and innovation policy makers in the past two decades (e.g. Aud retsch, 1998; Feldman, 1 994; Jaffe, 1989 Krugman, 1991) with special focus on knowledge spillovers in geographically bounded areas (e.g. Acs et al. , 1992; Jaffe et al. , 1993 ) and on innovative activities of spatially concentrated industries (e.g. Audretsch & Feldman, 1996; Brenner , 2004; Porter, 1990). Feldman & Florida (1994) addressed the influence of local factors on regional innovativeness using the concept to understand regional innovation by combining the systemic nature of innovation within a geographic context. The empirical literature in regional innovation differs on the notion of agglomeration economies. One strand of literature argues that cre ation of new regional knowledge is based on the spillovers arising from - Arrow - (see Rosenthal & Strange, 2001) and the other explains it in terms of spillovers among ind ustries, also known a Frenken et al., 2007). However, the entire literature on regional innovation is in consensus with the major role of human capital, research and development (R&D) expenditures by private firms and univers ities, population and employment density, and industrial diversity (or concentration) as factors affecting regional innovativeness. 2.2.4. Drivers of Regional Growth To explain the observed regional population and employment patterns, early researchers s ought to understand the roles of factor prices, markets, fiscal characteristics ( Bartik, 1985; Helms, 1985; Plaut & Pluta, 1983; Romans & Subrahmanyam, 1979; Wheat, 1986 ) , agglomeration economies (Carlino, 1985), and public polic y ( Bartik, 1991). Most of t he early 39 models of regional growth considered population and employment separately. Carlino & Mills (1987) developed lagged adjustment models for county - level growth in which employment and populations are simultaneously determined. Their findings suggeste d that income was an important determinant of employment and population growth, while climatic conditions and local tax policies were important for population growth. Clark & Murphy (1996) applied the Carlino & Mills model to sectoral employments and popul ation growth at the county - level U.S. data and found evidence of simultaneous feedback between population density and employment density. Their findings showed that climate variables such as temperature and sunshine and local government expenditures had mi nor effects on both short - run and long - run growth in population. They also found stronger influence of employment density on population density than that of the latter on the former. Deller et al. (2001) extended the Carlino & Mills model to include change s in regional income levels as simultaneously determined along with changes in population and employment levels. Using the model to study the economic growth in nonmetropolitan U.S. counties, they found that a range of factors including natural resource am enities, property tax, education levels, distribution of income, and age played major role in regional economic growth. Their results of the negative relationships between the initial levels and growth in population, employment and income suggested that r ural areas were catching up to offer increased economic opportunities. Using the conditional convergence model, where the rate at which the poorer regions catch up the richer regions is assumed to be conditioned on several regional structural factors 12 , to study the county level income growth, Rupasingha et al. (2002) consider the role of social and institutions factors social capital, income inequality, ethnic diversity in addition to other 12 See Yeager (1999) for some examples of str uctural factors affecting economic convergence. 40 factors. They find that higher social capital, lower income inequ ality, and higher diversity were associated with higher income growth. The other variables they found to have positive association with income growth include higher level of human capital, lower local tax, and higher highway expenditure. Using the similar model of conditional convergence, Pede (2013) found that economic diversity, measured by the distribution of employment across sectors in the U.S. counties through several entropy indices, was positively associated with county level per capita income growt h. He also found positive association with respect to other variables such as percentage of bachelor's degree holders, and age composition of the population , and metropolitan indicator. Frenken et al. (2007) studied the role of industrial variety in region al employment growth was positively associated with the employment growth at NUTS - 3 level 13 . In their analysis of the determinants of income growth across U .S. labor markets using production function approach, Hammond & Thompson (2008) found little support for the role of public capital investment. Human capital investment had larger income growth in metropolitan regions than non - metro, but manufacturing inve stment had larger effect in the latter regions. They also found that regions with colleges and universities, lower tax rates, and higher level of household amenities accumulated larger pool of human capital. Komarek & Loveridge (2015) investigate the role of firm size distribution on the county - level growth in the US between 1990 and 2000 and find that the larger share of small firms had positive impact on employment growth but negative effect on income growth; medium sized firms affected the income growth positively. They suggest that small businesses are net job 13 NUTS stands for Nomenclature of Territorial Units for Statistics, a geocode standard, and the Netherlands has 40 NUTS - 3 units. 41 creators but pay lower wages. Additionally, they find larger pool of highly educated population, and urban counties were positively associated with the employment and income growth. The empirical literature on the relationship between innovation and regional economic growth at the regional level is relatively sparse compared to analyses at national level. Investigating the effects of urban to rural spillovers on regional economic growth, Feser and Isserman (2006) used a cross - section of 3,079 US counties and measured innovative activities with average utility patents over the 1990 - 95 period in region around a county in their set of explanatory variables. From their two - stage least square ( 2SLS) estimation, they found that high level of patenting w as associated with high level of employment growth during 1990 - 2000. They also found that growth spilled over more to the rural counties proximate to the highly - urbanized counties than those proxim ate to the less urbanized counties. Monchuk & Miranowski (2010) found that innovation, as measured by utility patents, were positively associated with employment and population growth in the Midwest regions during 1990 - 2005. Additionally, they found that increased rurality makes growth slower, although innovation positively affected the growth in rural regions. Adelaja (2009) analyzed a sample of 3,023 US counties by estimating a linear system of simultaneous equations. He found positive relationship of av erage patents held in a county during 1990 - 1993 with both its employment and per capita income growth during 1990 - 2000. In a test of the empirical relationship between technological change and employment growth at regional level of NUTS2 European countrie s, Capello & Lenzi (2013 ) report that product innovations lead to job growth in regions specialized in production sector, whereas process innovations dampen the job growth in regions with large cities. 42 Stephens et al. (2013) studied the role of several fa ctors including knowledge - based factors - proximity to universities, patenting rates, college graduates, creative workers, and high - tech employment share - in the growth of wage and salary employment in the economically lagging region of Appalachia. They d growth and these factors except the creative workers. Self - employment, as a proxy for entrepreneurship, was found to have very strong association with wage and salary employment growth. In an analysis o f the effect of the SBA lending on the growth of US countie s between 1990 and 2008, Young e t al. (2014) used citation - weighted patents per capita as one of the several control variables and reported negative association between patenting and county growth . In a study on the role of proximity to the nearest urban centers in the regional economi c growth, Partridge et al. (2008 ) examine the U.S. county level employment growth by differentiating distance effects for several tiers in the American urban hierarchy . They find that the regions more proximate to the urban centers grow faster than the distant regions and conclude that distance effects are stronger over time. In summary, the extant literature in regional economics has identified and empirically analyze d a number of drivers of regional economic growth measured by income, employment and population. A separate stream of literature has analyzed factors influencing regional innovation, including R&D inputs, spillover effects, and other socioeconomic drivers, and the unidirectional contribution of innovation to economic growth. Influential analyses (e.g. Deller et al., 2001) have analyzed the interdependence between income, population and employment. Although endogenous growth theorists have recognized and ana lyzed interdependence of innovation and national economic growth, surprisingly no research has empirically analyzed the 43 interdependencies between income, employment, population and innovation at the regional level using the general equilibrium framework. 2 .3. Modeling and Estimation This section presents the conceptual model of regional economic growth based on the general equilibrium framework, specifies the empirical regression model for this study, proposes the hypotheses to be tested, and discusses the estimation method. 2. 3.1 . Regional Growth Model Profit maximizing firms choose their location based on the factors that affect their production and distribution costs. The production cost depends on the supply of the inputs such as labor, cap ital, and land , and the distribution cost depends on the distance to the output markets. Capital input typically refers to physical capital. I allow knowledge capital to be a t on factors such as the population with higher education and the opportunity to collaborate with universities. According to endogenous growth theory, innovative firms intentionally decide to invest in innovation inputs such as human and R&D capital. So, the firms decide their extent of innovation jointly with other traditional decisions. On the consumer side, utility maximizing consumers derive their utility from the purchased goods and services that the firms provide, so their residential location decisi on depends on the supply of such goods and services. Equilibrium population and employment are determined by a host of factors that affect the location decision of the firms and the consumers. Carlino & Mills (1987) assume that the equilibrium levels of p opulation and employment are simultaneously determined while all other factors affecting them are exogenous. Deller et al. (2001) model simultaneous determination of income together with 44 population and employment. They argued the ir approach helps capture t he job quality and understand the regional growth process . In other words , people that mak e migration decisions consider the quality of life communities can support through the income levels that are determined by the opportunities to get existing work or start a new business. Innovative firms are likely to generate growth in overall income and employment through improved factor productivity ( Ezell & Atkinson, 2010 ) and displacement of low - wage jobs with better - paid jobs ( Helpman, 2004 ; OECD, 1994 ) . From a regional perspective, the regions are likely to vary in terms of their entrepreneurial culture leading to varying rates of innovation and job creation among regions . I therefore posit that innovation is endogenous in the system of regional growth. My model enables us to examine the role of innovation in economic growth, specifically whether it drives the growth of county - level regional economies, or is led by the regional economic growth, or is determined simultaneously along the growth process . I build upon the Carlino & Mills (1987) and Deller et al. (200 1 ) model for simultaneous system of regional growth. Following Deller et al. (2001), who add income to the two - equation system of Carlino & I add innovation to their three - equ ation system. With endogenous innovation, the general structural model expands to following system of four linear equations: (1) (2) (3) (4) w here , , , and represent equilibrium levels of the endogenous variables population, employment, personal income per capita, and innovation, and , , , and 45 contain the set of variables representing initial conditions of the dependent variable s and the exogenous regional char acteristics. The subscripts on the parameters and the superscripts on the set of exogenous variables identify their association with their respective dependent variables. Following Mills & Price (1984), Carlino & Mills (1987), and Deller et al. (2001), the population, employment, income, and innovation adjust to their equilibrium levels through a distributed - lag adjustment process as follows: (5) (6) (7) (8) where the subscripts and represent the values of the variables at a time and its one period lag (five years in my study) respectively, and levels of their respective variables with , , , . Rearranging equations 5 - 8 and substituting their equilibrium values from equations 1 - 4, the following system of equations can be derived: (9) (10) (11) 46 (12) w here , , , and . No te that the and in the system of equations 5 - 8 absorbing the speeds of adjustment, . The dependent variables , , , and in equations 9 - 12 are the change in the population, employment, per capita personal income, and innovation as measured by the number of patent applications per capita, between 2009 - 201 3 . The vectors , , , and contain several exogenous variables that represen t county - level characteristics at the initial period - year 2009 for all the e xogenous variables except tax, revenue, and highway expenditures, which correspond to the year 2007. I follow Carlino & Mills (1987), Deller et al. (2001), Monchuk Miranowski (2 010), Komarek & Loveridge (2015) , and Rupasingha et al. (2002) to design these vectors that include different sets of regional characteristics. I classify the various regional characteristics broadly into four types: Demand characteristics: Ethnic diversity, location - metro or nonmetro counties, income inequality, and share of expenditure in the construction and maintenance of highways. Supply characteristics: Percent of population between 25 and 44 years; number of non - farm proprietors; fi rm size (distinguished between percent of firms with less than 100 employees and greater than 100 employees); concentration of high - tech firms measured by the share of high - tech firms in total number of firms and the varieties of high - tech firms. Govern ment characteristics: Total tax per capita and the share of total county revenue earned from local, state, and federal governments 47 Innovation characteristics: Share of college educated population; expenditures in research and development by universities lo cated in own and neighboring counties; and small business innovation research (SBIR) awards received by small firms. The above grouping of regional characteristics by no means is assumed to contain mutually exclusive set of variables. For example, the shar e of college educated population is likely to determine the ability of firms to innovate and equally their ability to supply the goods and service demands in a region. Similarly, highway expenditure is as likely to represent regional demand as regional sup ply because improved transportation network connects the consumers to the broader regional markets and provides potential access to the substitutes to the goods produced by local firms while it might increase the supply efficiency of the local firms throug h reduction in transportation cost. But I assume that it affects more the ability of firms to satisfy Government characteristics and innovation characteristics are also eq ually likely to overlap with the demand and supply characteristics. 2.3.2 . Hypotheses The non - rivalrous nature of technology implied by the models of endogenous growth models (Aghio n & Howitt, 1992; Grossman & Helpman, 1993) imply a link between the innova tion and population growth. As the cost of invention is independent of the people benefitting from it (Arrow, 1962; Romer, 1990), growth in population implies technological progress (at the constant cost). On the other hand, the macroeconomic implication o f Malthusian model in relation to tech nology and population (Galor & Weil, 2000; Malthus, 19 59 ) is that the growth in population is limited by the level and growth of technology. Combining the implications of both these models, Kremer (1993) develops a model of population growth and 48 empirically finds that initial level of population is directly pro portional to the population growth and technological change. This background provides a basis for the test of my first hypothesis: Hypothesis 1 : Regional growth in population and patenting rates positively influence each other. The link between innovation and employment is not always clear. It greatly depends on the nature of the technology. The innovation in labor - saving process technology of a firm instantly reduces its labor demand but the compens ating effects may arise due to transfer of the improved pr oductivity to the consumers in the form of reduced output prices thereby stimulating demand (Harrison et al., 2008). This is expected to generate positive employment effects in other firms in ancillary industries due to increase in their level of activitie s but negative effects in competing industries if the firms fail to survive from the techn ological competition (Spezia & I expect that exit of incompetent firms wou ld set the stage for the entry of new innovative firms in the market, thus generating net positive employment effects. On the other hand, the innovation in the product side is expected to induce positive employment effects due to increase in demand for imp roved products. This effect might be weakened if the new products substitute the existing products in the market (Harrison et al., 2008). Also, similar compensat ing effects as in process innovation are likely to arise if the new product requires change in production methods. In this way , I expect the increase in innovation rates to generate higher level of employment. The growth in employment may lead to more economic activities, more competition, and the need for more innovations. This process can not be pe rpetual but constrained by the growth stage of the economy, implying that higher employment may not necessarily lead to more innovation rates. 49 However, as my study covers the economic recovery period, I expect the growth in employment to positively drive g rowth in innovation rates. Accordingly, my second hypothesis is: Hypothesis 2 : Regional growth in employment and patenting rates positively influence each other. Although commercialization of an innovation, in the long - run could be skill - saving as well a s skill - biased, I argue that the innovation creation, as measured by patenting rates within a five - year period in my study, is mostly skill - biased. My argument is inspired again by the endogenous growth models where human capital in the form of educated an d skilled people are needed to generate new economic knowledge. On the other hand, the wage inequality between college - educated workers and non - observed to have increased in the US 14 in the recent y ears. It is also observed that the within group wage inequality has also increased historically, Aghion (2002) argues in his model based on the Schumpeterian growth theory that the inequality is generated by the additional wage premium that is due to the r educed technological distance between the previous and current job of the group who get opportunit ies to learn by doing in innovative jobs. The combination of the idea from the endogenous growth theory and the observed wage premium for educated workers imp lies that workers in innovative firms enjoy wage premium over those in non - innovative firms. Consistent with this implication, improved labor productivity in innovative industries is argued to displace lower - paid unskilled jobs with better - paid ones (Harrison et al., 2008; Helpman, 2004; OECD, 1994). Building on these ideas, I expect that the growth in regional innovation enhances living standard of the regional population by means of income growth. I 14 Autor et al., (1998) show that the ratio of number of - - grew from an average rate of 2.5% during 1940 - 1970 to 3.05% during 1970 - 1995. In the meantime, the ratio of weekly wage rates of these groups fell by 0.11% during 1940 - 70 but increased by 25% during 1970 - 1995. 50 also expect that the regions with higher income le vel provide more business opportunities to the innovative firms to through higher demand for improved goods and potentially through higher source of financial capital. Thus, my third hypothesis is: Hypothesis 3: Regional growth in patenting rates and per capita personal income positively influence each other. From the results on the hypothesis tests 1 - 3, I will infer whether the innovation belongs in the three - equation system of regional economic growth as modeled by Deller et al. (2001). Combining the i mplications of the Malthusian model and the endogenous growth models discussed for laying out the first hypothesis, Kremer (1993) develops a model of population growth and empirically finds that initial level of population is directly proportional to the p opulation growth and technological change. Combining this finding and the expected positive association of innovation growth with population, employment , and income growth in the hypotheses 1 - 3, I also expect the initial levels of population, employment, i ncome, and innovation to have positive relation with their respective growth, for which reason the fourth hypothesis to be tested in this study is: Hypothesis 4: Initial levels of population, employment, income, and patenting rates are positively influenc e their respective growth rates. These hypotheses on the role of initial conditions provide the tests of regional convergence (or divergence) in terms of the measures of innovation and economic growth. Negative association means convergence, implying reduc ing regional gaps but positive association would suggest growing gaps. Further, I test the predictions of the endogenous growth theory regarding the roles of human capital and knowledge spillover from the universities and the clustering of high - tech 51 indust ries. The positive role of the human capital in innovation is straightforward from the implications of the models of endogenous growth and so is the role of universities in knowledge spillover (Jaffe, 1989; Mansfield, 1991). The positive role of proximity among firms in promoting knowledge spillover and innovation is undebated as knowledge spillover is defined as 1992). However, it is debatable whether such proximit y refers to the firms within the same industry (specialization) or across firms in different industries (diversity) 15 . (1969) concept, I expect the diversity of high - tech industries to be conducive to innovation and economic growth. These lead to my next three hypotheses. Hypothesis 5 : The share of regional population with college or higher education is positively related to innovation a nd economic growth. Hypothesis 6 : The expenditure in R&D by universities in a region is positively related to innovation and economic growth. Hypothesis 7 : The diversity of high - tech industries is positively related to the regional innovation and economi c growth. 2.3.3. Estimation First, I estimated individual equations 9 - 12 separately using instrumental variable regression 16 to test endogeneity of the variables in each equation. I conducted an endogeneity test using Durbin and Wu - Hausman tests, where the null hypotheses are that the variables modeled as endogenous can be treated as exogenous. Failure to reject the null hypothesis implies that the 15 See Glaeser et al. (1992) for the discussion of the concept on the role of industrial specialization and Jacob (1969) on the role industrial diversity in facilitating knowledge spillover and technological progress. 16 command to run instrumental variable regression, and post - estimation command estat endogenous to conduct endogeneity tests ( https://www.stata.com/manuals13/rivregresspostestimation.pdf ) 52 ordinary least square (OLS) estimat or of the equations provides consistent estimates. Alternatively, the rejection implies that the OLS estimates are inconsistent due to the correlation between the endogenous variables and the disturbance s in the equations (Greene, 2003 ), and instrumental variable techniques are required to account such correlation. Following the evidence of endogeneity in each equation, which I will discuss in the following results section, I estimate a structural model of county growth represented by the system of equati ons 9 12 using three - stage least square regression (3SLS) 17 to analyze the interdependence among the innovation and economic growth variables (hypothesis tests 1 - 3) . The 3SLS estimator also improves the efficiency of the parameters across the equations, whi ch are likely to be correlated through some unobservables in the equations (Wooldridge, 2010) such as the propensity to patent or the perception of the businesses about the potential of the regions for market growth, or the risk - seeking entrepreneurial cul tures of the regions. The correlation may arise, for example, by the simultaneous effects of the unobservable variable representing the entrepreneurial culture on the employment growth and innovation growth. In estimating 3SLS regression models, the variab les that are excluded from each equation are so chosen as to get an identified system of equations satisfying the exclusion restrictions 18 , using the Sargan - Hansen test 19 . The choice of the excluded variables is made based on these correlation with the variables which they serve as instruments for but are likely to be uncorrelated with the disturbance terms. The validity of the instruments or the overidentifying exclusion restrictions are tested using the Hansen 17 reg3 for my analysis in this study ( https://www.stat a.com/manuals13/rreg3.pdf ) 18 For an (over - identified) idendified model, the number of variables excluded from an equation should be (greater than) equal to the number of endogenous variables (see Wooldridge, 2010). 19 In Sargan - Hansen test, null hypothesis is that the instruments are valid instruments (uncorrelated with the disturbance term) and the excluded instruments are correctly excluded from the estimated equations. 53 het eroskedastic disturbances. Under the joint null hypothesis that the excluded instruments are valid (uncorrelated with disturbances) or the excluded instruments are correctly excluded, the - squared distributed. The failure to rejec t the null hypothesis satisfies the overidentifying restrictions. Finally, I estimate reduced forms of the structural coefficient estimates from 3SLS method to test the remaining hypotheses 4 - 7. The reduced form estimates are obtained by regressing each d ependent variable in the equations 9 - 12 on the set of exogenous variables in the system, or equivalently they are the coefficient estimates from the first stage estimation of 3SLS. The reduced forms of the structural coefficients include both the direct ef fects and indirect effects arising from interdependence among the e ndogenous variables (Carlino & Mills, 1987). 2.4. Data The empirical model is estimated using data for a sample of 3,038 counties in the 48 contiguous states of the United S tates. Seconda ry data are collected from several sources for the period during 2009 - 1 3 . Table 1 provides the specific sources of data for the variables used in this study, their definition, and summary statistics. The counties are classified into metro and nonmetro cate gories according to the Rural - Urban Continuum Codes (RUCC), 2013 developed by the Economic Research Service of USDA 20 . For the analysis in this study, metro counties - The number of the domestic utility patent applications per 10K population serves as my measure of the rate of innovation in the US counties. I aggregated the patent applications 20 2013 RUCC are accessible at: https://www.ers.usda.gov/data - products/rural - urban - cont inuum - codes.aspx Metro areas include all counties containing one or more urbanized areas: high - density urban areas containing 50,000 people or more; metro areas also include outlying counties that are economically tied to the central counties, as measured by the share of workers commuting on daily basis to the central counties. Non - metro counties are outside the boundaries of metro areas and have no cities with 50,000 residents or more . 54 originating from residential zip codes of the primary inventors to derive the county level patent applications. The university R&D expenditures data that come from NSF are available at city level. I matched the university cities with their associated counties. For example, if either a county does not have any city with college or university or t he institutions of higher learning do not spend in R&D activities, I assume in this study that the county has zero university R&D. I also account for the spillover effects of the university R&D from the counties hosting the university/colleges to their nei ghboring counties by constructing a spatially lagged university R&D variable based on a distance decay function within 100 miles from the county centroids. I employed the firms - related data including the variety of high - tech industries from US Census Bure establishments and their employments were derived by summing these variables at the three - digit level of industry codes across the 2012 North American Industry Classification Syste m (NAICS), 2012. I derived the number of high - tech establishments by summing at the six - digit level of industry codes across the 2012 NAICS codes that constitute high - tech industries, as defined by NSF. The data on foreign - born population and the populati on with college or higher degree come from the five - year estimates for 2009 of American Community Survey (ACS) 21 . I - born population variable. 21 ACS surveys 295,000 households randomly each year with no repeated household in five years and reports the estimates from data collected in five years . https://www.census.gov/content/dam/Census/programs - surveys/acs/about/ACS_Information_Guide.pdf 55 Table 2. 1 Variables Definition, Summary Statistics, and Data Source Variable Code Description Mean SD Source nonmetro RUCC 2003 county type (0=metro; 1=non - metro) N/A N/A ERS, USDA population Change in p opulation (1k), 2009 - 13 3 14.51 BEA employment Change in e mployment (1k), 2009 - 13 2.54 14.39 BEA income Change in p er c apita p ersonal i ncome ($1k), 2009 - 13 5.81 5.17 BEA innovation Change in p atents p er 10k p opulation, 2009 - 13 0.32 3.96 USPTO lagged_population Initial p opulation (1k), 2009 96 308.01 BEA lagged_innovation Initial patents p er 10k Population, 2009 2.3 30.1 USPTO lagged_employment Initial Employment (1k), 2009 54.72 191.13 BEA lagged_PCPI Initial Per Capita Personal Income ($1k), 2009 32.43 7.65 BEA nfarm_propri Number of Non - Farm Proprietors (1k), 2009 11.16 41.06 BEA urd University R & D expenditures ($1 M ), 2009 13.17 83.72 NSF splag_urd Spatial l ag of u niversity R&D e xpenditures ($1M), 2009 14.9 60.44 NSF sbir S BIR awards ($1 M ), 2009 0.61 5.2 SBIR pct_ht_estabs Percent of t otal e stablishments in h i - tech industries, 2009 5.07 2.71 CBP ht_variety Variety of Hi - tech Industries, 2009 13.39 9.64 CBP ethnic_diversity Ethnic Diversity by Race and Ethnicity, 2009 0.46 0.27 MCDC taxpercap Total t axes p er c apita ($1k), 2007 1.31 1.24 US Census pct_ig_rev Percent of t otal r evenue from f ederal, s tate, and l ocal g overnments, 2007 41.79 13.77 US Census pct_highway_expend Percent of t otal e xpenditure in h ighways, 2007 6.09 4.42 US Census pct_collegeplus Percent of p opulation with c ollege or h igher d egree, 2009 8.01 3.41 ACS pct_foreign_born Percent of f oreign - born p opulation, 2009 4 5.02 ACS income_ineq Gini Index of i ncome d istribution, 2010 0.43 0.04 ACS estct_pct_nlt100 Percent of t otal e stablishments with 1 - 19 employees, 2009 89.09 3.75 CBP est_pct_ngt100 Percent of t otal e stablishments with greater or equal to 100 employees, 2009 4.12 10.12 CBP pct_pop_25to44 Percent of t otal p opulation aged 25 - 44, 2009 0.22 0.94 ACS 56 The derivation of concentration measure of high - tech industries similar to HHI measure, which is widely adopted in the literature for representing industrial concentration (see Carlino et al., 2007), does not allow us to distinguish between the counties wi th zero employment and those with a completely specialized industry, as several counties in this study sample have zero high - tech employment. So, I created a high - tech variety variable that measures the number of three - digit level NAICs high - tech industry categories. Ranging in its value from 1 to 45, this variable essentially represents the concentration of high - tech industries after controlling the share of high - tech industries in total industrial employment and avoiding the zero - employment problem. I con structed the ethnic diversity variable is by creating an entropy index similar to Theil Index ( Audretsch et al., 2010 ) : where is the share of population identified as race r in region i at a time t , where {White, Black, Asian & Pacific Islander, American Indian, Other}. The entropy inde x could reach its maximum ( ) at = and its minimum (0) at = 1, that is when a single race forms the entire population of a region. The index measures the share and the variety of the races in the population. I used income inequality data represented by Gini Index from ACS for the census year 2010. 2.5. Results From the Durbin and Wu - Hausman endogeneity tests following the instrumental regression of equation 9, I found that patents growth and employment growth have an endogenous relationship with population growth, but I do not find statistical evidence of endogeneity of PCPI growth. From the similar tests in equation 10, I found that population growth was endogen ous with employment growth, while I did not find the statistical evidence of the 57 Table 2. 2 3SLS Results of the Estimation of the County Growth Model Variables Coefficient Estimates 0.134** - 0.224*** 0.156*** [2.39] [4.27] [2.95] 0.162* 0.597*** - 0.131*** [1.79] [5.12] [3.73] - 0.052 0.236*** - 0.058 [0.07] [2.82] [0.90] (per 10k pop.) - 1.830*** - 0.005 - 0.104 [4.61] [0.04] [0.80] Lagged population (1k people) - 0.008* - 0.028*** 0.019*** - 0.007*** [1.75] [14.85] [5.36] [5.77] Lagged employment (1k jobs) 0.086*** 0.015** 0.005 0.002 [7.41] [2.45] [0.89] [0.47] Lagged PCPI ($1k) - 0.086 - 0.093*** 0.155*** 0.039* [0.83] [3.75] [8.47] [1.95] Lagged patents (per 10k pop.) - 0.102*** - 0.003 - 0.01 - 0.056*** [4.68] [0.35] [1.32] [24.54] Nonmetro (1=yes; 0=metro) - 1.313 - 0.4 0.932*** - 0.216 [1.44] [1.57] [4.66] [1.13] Percent collegeplus (% points) 0.417*** 0.009 - 0.056 0.036 [3.06] [0.20] [1.39] [1.02] Percent foreign born (% points) 0.419*** 0.058** 0.096*** - 0.014 [5.87] [1.98] [3.83] [0.62] Tax per capita ($) - 1.936*** [5.19] Pct. highway expend. (% points) 0.105 0.186*** [0.70] [10.35] Pct. intergov. Revenue (% points) - 0.081** - 0.051*** [2.17] [8.37] Pct. est. w/ <100 emp (% points) - 0.712** 0.045 0.141 0.281*** [2.04] [0.35] [1.31] [2.66] Pct. est. w/ > 100 emp (% points) - 0.412*** 0.246*** - 0.241*** 0.220*** [4.08] [4.59] [4.47] [4.89] Pct. pop. age25 - 44 (% points) 1.167*** - 0.097 0.077 0.005 [3.81] [1.04] [0.97] [0.07] Income inequality (Ginni Index) - 1.783 - 1.962 [0.37] [0.83] Pct. high - tech firms (% points) 0.621*** 0.039 0.202*** 0.03 [4.37] [0.80] [4.96] [0.85] High - tech variety - 0.074 - 0.078*** - 0.108*** - 0.004 [0.57] [3.52] [5.32] [0.24] Ethnic Diversity (Theil Index) - 0.562 [1.53] 58 Table 2. 2 ) Non - farm proprietors (1k) 0.384*** - 0.242*** [22.37] [5.20] SBIR Awards - 0.062*** 0.012 - 0.028* [3.06] [0.61] [1.81] University R&D ($1M) 0.010*** [8.13] SPLAG univ R&D ($1M) 0.002 [1.31] constant 73.579** - 1.105 - 15.803 - 29.088*** [2.10] [0.08] [1.47] [2.77] R 2 0.55 0.9 0.07 0.2 N 3,038 3,038 3,038 3,038 endogeneity of the growth in PCPI and patenting rates. In equation 11, I found that population, employment, and patents growth were jointly endogenous, but not individually, with PCPI growth. Similarly, in equation 12, I found that population, employment, and PCPI growth were jointly endogenous, but not individually, with pate nt growth. 2.5.1. Regional Innovation and Economic Growth Interdependence To test the hypotheses 1 - 3, I analyze the 3SLS estimation results on the structural coefficients in table 2. The positive and significant coefficient of variable in nts equation (column 4), and negative and significant coefficient of variable in equation (column 1) show that relationship between regional growth in population and patenting rates is highly interactive. These findings suggest that gr owth in population leads to growth in regional innovation, but less innovative regions may experience relatively faster growth in population. Turning to my hypothesis 2, I find that employment growth negatively influences regional patenting rate, but I do not find statistical evidence of influence of patenting growth on regional employment. These findings suggest decreasing marginal patent productivity of 59 employees, or more frequent patenting by smaller firms, and offsetting of the job displacement effe cts of the labor - saving innovations with the job creation effects of the product improvement innovations. However, I do not find statistical evidence for the support of the hypothesis 3 regarding either the influence of innovation growth on income growth o r the influence of income growth on innovation growth. Combined, these findings show that innovation belongs to the regional growth ecosystem and the results from a growth study that does not account for this innovation effect is likely to suffer from spe cification bias (omitted variable bias in case of missing innovation variable and endogeneity in system of equations method). Beside my focus on my principal research questions, the results in table 2 show that population growth is directly proportional to employment growth, suggesting that people move to the regions with more employment opportunities and the increase in labor supply stimulates business growth. But the increasing supply of labor (also the skilled and educated workforce) is likely to have do wnward pressure on the PCPI growth due from lower wages. 2 .5.2. Exogenous Factors of Regional Innovation and Economic Growth Turning to the test of hypothesis 4, my findings from the reduced forms of the structural coefficients presented in table 3 show that the lower initial level of patenting rates is associated with higher patenting growth, suggesting that regional gap in inventive activities is shrinking. Also, I find that lower initial regional patenting rate is associated with higher growth in emp loyment and PCPI. Combined, I find that less innovative regions experienced higher growth rates in population, inventive activities, and employment. On the other hand, my results show that higher initial levels of PCPI lead to higher growth in PCPI but lo wer growth in population and employment. These results suggest that 60 prosperous regions generated relatively fewer number of jobs (but likely high - paying) and lower inflow of people. Combinations of these implications with the possible convergence in region al innovation rates (preceding paragraph) and better - paid jobs in innovative firms suggest the possibility of wage discrimination by the innovative firms based on the condition of regional prosperity. Turning to my hypothesis 5, I find that an increase in the share of population with four - year bachelor or higher degree is positively associated with the growth in population and inventive activities. Interestingly, the variable is negatively associated with the growth in PCPI. It is likely that some regions w ere not likely in situations to fully absorb the supply of fresh graduates during the recovery period following the great depression thus putting downward pressure on the wages earned by those fresh degree holders. I find that the expenditure by universiti es in R&D is positively associated with patenting rates (positive and statistically significant coefficient of University R&D my hypothesis 6 and suggesting that university research plays an important role i n accelerating innovative activities. The positive and statistically significant coefficient of the Percent high - tech firms in all four columns shows that high - tech businesses play a major role in generating innovations and economic growth. Further the ne gative and statistically significant coefficient of high - tech variety in the and equations, columns 2 and 3 respectively) suggests that the externalities generated from the R&D and other knowledge spillover are higher in regions with more specialized industries and are manifested in growth of regional employment and income. However, I do not find any evidence for the significant influence of such externality on growth in inventive activities. 61 Table 2. 3 Reduced Form Estimates of the Parameters in the County Growth Model Variables Coefficient Estimates Lagged population (1k people) - 0.004 - 0.027*** 0.004*** - 0.005 [0.27] [2.88] [2.63] [1.00] Lagged employment (1k jobs) 0.073** 0.026 0.002 0.01 [2.01] [1.36] [0.76] [1.05] Lagged PCPI ($1k) - 0.134*** - 0.070** 0.138*** 0.02 [4.00] [2.36] [3.45] [0.89] Lagged patents (per 10k pop.) - 0.001 - 0.005** - 0.007*** - 0.056*** [0.18] [2.10] [4.57] [3.83] Nonmetro (1=yes; 0=metro) - 0.716*** - 0.27 0.929*** - 0.376** [2.94] [1.53] [6.08] [2.03] Percent collegeplus (% points) 0.280*** 0.025 - 0.117*** 0.080** [4.54] [0.52] [2.59] [2.38] Ethnic Diversity (Theil Index) - 0.028 - 0.736** - 0.720*** - 0.317* [0.05] [2.18] [2.67] [1.70] Percent foreign born (% points) 0.388*** 0.141*** 0.093*** 0.036* [4.59] [2.63] [4.25] [1.80] Tax per capita ($) - 1.504*** - 0.085 0.299** - 0.262 [3.75] [0.37] [2.08] [1.54] Pct. highway expend. (% points) 0.079*** 0.019 0.191*** 0.006 [3.41] [1.34] [5.92] [0.44] Pct. intergov. Revenue (% points) - 0.072*** - 0.018 - 0.046*** - 0.001 [4.24] [1.63] [6.64] [0.18] Income inequality (Ginni Index) - 4.616 - 4.254* 1.432 1.716 [1.22] [1.74] [0.62] [0.94] Pct. est. w/ <100 emp (% points) - 0.944** - 0.014 0.339*** 0.113 [2.58] [0.06] [4.10] [0.92] Pct. est. w/ >100 emp (% points) - 0.593** 0.141 - 0.028 0.111* [2.22] [0.80] [1.10] [1.71] Pct. pop. age25 - 44 (% points) 0.866*** - 0.043 - 0.144 0.179 [3.49] [0.29] [0.43] [1.55] Pct. high - tech firms (% points) 0.490*** 0.142** 0.172*** 0.091** [5.06] [2.34] [3.68] [2.27] High - tech variety - 0.102 - 0.131*** - 0.164*** 0.008 [1.62] [2.97] [10.53] [0.56] Non - farm proprietors (1k) 0.125 0.396*** - 0.032*** - 0.031 [0.98] [5.71] [3.51] [1.34] University R&D ($1M) - 0.014 0.0001 0.001* 0.008*** [1.56] [0.03] [1.94] [3.15] SPLAG univ R&D ($1M) - 0.007 - 0.010** - 0.002** 0.002 [1.16] [2.09] [2.23] [1.23] SBIR Awards - 0.031 - 0.089 - 0.023* - 0.033 [0.20] [0.89] [1.92] [0.90] 62 Table 2.3 ) constant 99.863*** 5.994 - 35.033*** - 13.015 [2.73] [0.24] [4.26] [1.06] R 2 0.73 0.88 0.28 0.25 N 3,038 3,038 3,038 3,038 The t - stats in the square brackets are based on the robust standard errors; * p<0.1; ** p<0.05; *** p<0.01 Additional Findings on Regional Growth Drivers: The regions with higher racial diversity are associated with statistically significant decline in the number of jobs, PCPI, and inventive activities. My findings in terms of employment growth are consistent with those of Deller et al. (2001) but co ntrast with those of Carlino & Mills (1987) in that the former study found positive association between the percent black population, as a proxy to racial diversity, and employment but the latter study found negative association. However, in terms of income growt h, my percent black population and the income growth. The findings of this study show that the share of foreign born population is positively associated with the grow th in population, employment, PCPI, and inventive activities. I also find that the regions with higher total taxes are found to hinder population growth but support the income growth, probably through the externalities due to the higher spending on public goods. In terms of income growth, my negatively associated with population growth and the latte r study found negative association between the property tax and population growth. However, my finding of positive association The findings from table 6 show that the higher expenditures in highways and road networks attract more population and increase income levels likely because of the increased 63 access to the larger urban areas and labor markets. Further, I find that the share of revenues received from government agencies is found to have negative association with population growth and income growth. My findings on the relationship of the firm size show that the increase in the number of businesses, whether small or large, are associated with decline in population level, implying of small businesses is associated with increase in PCPI. The places with larger share of prime working age population are found to attract more population. Further, non - farm proprietors are found to create more but low - paying jobs, as shown by the significantly positive association of the variable with the employment growth but negative with the PCPI growth . 2 .6. Summary and Conclusion Theoretical and empirical consensus shows that innovation enhances economic growth at various geographical levels. It is equally likely that firms in growing regions are likely to have more resources out of higher profits to expend to the innovative activities and employ innovative workforce and such regions might provide better access for these firms to the financial resources and collaborations needed for innovation. So, it is likely that growing regions enhance innovative a ctivities. As existing literature presents evidence of simultaneity among population, employment, and income growth, it could be possible that innovation growth occurs simultaneously with one or more of the economic growth variables. To investigate this p ossibility, I extended the three - equation simultaneous equation model in the literature for population, employment, and income to four - equation model, where innovation is endogenously determined in the regional economy along with economic growth variables. The extended model 64 includes several variables identified in the literature to be related to economic growth and innovation. Using the Durbin and Wu - Hausman tests, I found that regional innovation and economic growth exhibit an endogenous relationship. Fr om the 3SLS estimation results, I found that growth in population leads to growth in regional innovation, but less innovative regions may experience relatively faster growth in population. I also found that employment growth negatively influences regiona l patenting rate, but there is no statistical evidence of influence of patenting growth on regional employment, suggesting decreasing marginal patent productivity of employees. My findings from the reduced form coefficients of the 3SLS estimates indicate t hat the lower initial level of inventive activities, measured by the patents per capita, are associated with higher growth in such activities, suggesting convergence between the leading and lagging regions in terms of inventive activities in the longer run . Compared to metro regions, growth in population and number of patent applications is significantly lower in the non - metro regions but the growth in income levels is higher. My major findings show that foreign - born population and high - tech firms in higher regionally concentrated industries are associated positively with both innovation and economic growth. 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Introduction Innovative firms are essential to sustain economic growth . Established firms must continuously innovate to survive the forces of creative destruction in t he face of new and disruptive technologi es . Innovation also serves as a mechanism for new firm entr y into emerging markets and enables these new entrants to compete with existing firms as well as other new entrants (Christensen, 2013; Schumpeter, 1942). The literature on regional innovation is p rimarily focused on urban innovation and based on firm data from urban areas that foster innovation creation and adoption; less studied is rural innovation and potential differences in innovation drivers between rural and urban areas (Dabson, 2011). Of the studies comparing rural and urban innovation, many conclude that r ural America lags in its inno vation performance (Orlando & Verba, 2005; Porter et al., 2004; Wojan et al., 2015). Economies need innovation - based entrepreneurship to ac hieve and sustain gr owth (Mann & Shideler, 2015 ), and competitiveness of the overall US economy builds on the rural - urban interdependency (Dabson, 2007, 2011). The rural - urban innovation gap has long - term consequences. For example, lower education rates and fewer economic opp ortunities for youth lead to sluggish wealth creation which in turn contribute to the persiste nce of rura l poverty (Lyons et al., 2018; Orlando & Verba, 2005; Porter et al., 2004; Ratner & Markley, 2014). Innovation in urban areas is generally explained in terms of the agglomeration effect supported by the higher population density as well as higher concentrations and diversity of firms and industries in these areas (Carlino et al., 2007; Gl aeser et. al., 1992; Orlando & Verba, 2005). Urban agglomeration fa 73 economies through enhanced communication and knowledge spillovers among innovative firms and industries, better supply of critical innovation resources such as human capital, extended bu yer and supplier networks, and financial and professional support services ( Aryal, et al., 2018; Orlando & Verba, 2005). On the other hand, scattered populations and less developed markets in rural areas restrict the opportunities for innovation by rural f irms. Related to the locational obstacles to innovation , rural firms have lower levels of skilled managers, professionals, and technicians and rural entrepreneurs are more likely to start new businesses based on necessity rather than opportunity , which f requently leads to a non - innovative enterprise that may be abandoned when better paying jobs arise (Acs, 2006; Henderson, 2002). Rural firms are also less likely to be growth - oriented, which may be attributed to owner characteristics such as embracing of t he multi - generational business ownership models or the tendency to avoid the risk associated with adopting and/or creating innovation ( Knickel et al., 2009; Renski & Wallace, 2012). Such business models are less likely to attract equity and venture capita l due to reduced interest or flexibility in potential exit strategies, a necessity for innovative startups (Markley, 2001). In terms of policy obstacles, rural economies are often framed as primarily agriculture - dependent , with substantial public resource s focused on cost - saving technologies for agriculture production (Mowery et al., 2010; Stauber, 2001). While these kinds of innovations are important for the growth and development of the US agricultural sector, dependence of rural economies on agriculture significantly declined after the industrial revolution , and this gave rise to a new diversity of rural industries. Thus, when policy makers overlook rural industrial diversity, this o versight likely negatively impacts non - agriculture related innovation in rural areas through missed opportunities for new firms and reduced competition for existing firms (Stauber, 2001). 74 To provide guidance for policy makers that helps mitigate the negative effects of the challenges highlighted above, it remains necessary to continue expand ing my understanding of the obstacles fa ced by rural firms in terms of innovation creation and adoption (Chatterji, et al. , 2014; Fortunato, 2014). This is the underlying motivation for this study. I develop my analytical models from firm - level data provided by the 2014 National Survey on Busine ss Competitiveness (NSBC). The NSBC data were made available by United States Department of Agriculture (USDA) for confidential access. It is a unique survey of the US firms, containing 257 variables from questions cover ing topics such as Research and Deve lopment (R&D) activities, innovation outputs, failed innovations, patents, other intellectual property protection, employee education levels , affiliated industry, location factors including local amenities, market share, location - based barriers, local gove rnment impact , among others. I combine selected innovation related firm variables from the NSBC data with county - level secondary data from the Bureau of Economic Analysis ( BEA ) , Bureau of Labor Statistics ( BLS ) , Small Business Administration ( SBA ) , and US Census Bureau , to capture the external business and innovation environment in which these firms operate. I use the number of patent application s as my measure for innovation creation and employ negative binomial regression model s to empirically test firm - level characteristics that influence innovation creation. Three models are estimated, one for combined sample of rural and urban firms ( N = 4,351), one for urban firms only ( N = 1,117), and one for rural firms only ( N = 3,234). In my empirical analysis, I first test whether there is a difference between the innovation - related characteristics of rural and urban firms once external regional factors are controlled . Further, I examine potential firm - level characteristics and behaviors that drive innovation across urban and rural firms . I find that there are difference s between rural and ur ban firms in terms of 75 influencers of their patenting activities , with urban firms exhibiting better capability to capitalize on their resources compared to rural firms. Additionally, I find evidence that the influence of university R&D is relevant to innovation creation in rural firms, but their perception of university provided information may not be significant . The remainder of this pa per is organized as fo llows. The next section provides a review of literature on firm innovation and its measure. The third section describes my research methodology including a de scription of the data, selection of variables , and the empirical model. Results are presented and discussed in section four, and section five conclude s with summary and policy recommendations . 3 .2. Literature Review During the 1950s through 1970s, innovation studies as well as policies directed towards improving innovation mainly focused on the role l arge firms play in driving the innovation process (Chandler, 1977; Schumpeter, 1942). The belief was that large firms , through scale economies , were best suited to bear the risk of R&D investment necessary to create new innovations. The role of small busi nesses in this process was viewed as minimal as they were argued to be handicapped by a lack of financial, physical, and human capital needed to innovate and commercialize new technologies (Galbraith, 1956). With the emergence of new technologies and as n ew evidence showing that small firms played a major role in job creation, this belie f evolved. Scholars recognized that scale economies also occurred through geographic proximity to a large number of small firms and this is as important to the innovati on p rocess as the scale economies of large enterprises. This new understanding recognized the importance of the links between entrepreneurship, small and large firms, and innovation creation in terms of driving technological progress ( Acs & Audretsch, 2005 ). From this view and based on the 76 knowledge production function framework formalized by Griliches (1979), business formation is a key starting point in the innovation process. While new firms are created exogenously, the innovation and technological chang e occurs through the performance of these firms standing (Arrow, 1962; Cohen & Levin, 1989; Scherer, 1984). Therefore, R&D efforts are considered as the most important inputs to innovation creation, but these efforts remain relevant to both new and established firms regardin g innovation creation (Cohen & Klepper, 1991; 1992). The focus on the firm as a central unit of the innovation process shifted to a broader geograph knowledge production function t o study the spillover of knowledge between univers ities and private in dustries (Audretsch & Feldman, 2004). Over the years, a wide theoretical consensus has emerged showing that knowledge spillover is an important source of innovation in urban areas (Audret sch & Feldman, 1996; Rosenthal & Strange, 2004). This led to wider scholarly interest in urban innovation studies as densely co - located firms tend to facilitate face - to - face interaction among knowledge workers and give rise to greater extent of spillover tacit knowledge spillover in urban areas (Glaeser et al., 1992; Henderson, 2003). On the empirical side, difficulty in measuring innovation an d technological progress, generally arising from data availability, made estimation of the knowledge production function challenging (Cohen & Levin, 1989; Kuznets, 1962). The available measures act as proxies reflecting one or more aspect of the innovation process. Firm - and regional - level innovation metrics are typically categorized as: (1) the inputs into the innovative process, such as R&D expenditures and the share of R&D employees in workforce; (2) an intermediate output, such as 77 the number of patent a pplications; or (3) direct measure of innovative output such as new p roduct announcements (Aghion & Howitt, 1990). Each category , and respective measure , has limitations, and this fact is well reflected in the literature. For example, tangible innovation creation appears lumpy relative to the levels of inputs such as R&D expenditures . (K leinknecht,1987; Kleinknecht & Verspagen,1989). Additionally, formal R &D budgets are not necessarily solely directed toward innovation creation; instead, they may include activities such as imitation and technology transfer (Mansfield, 1984). Similarly, patent applications and awards data , often used as a measure of innovat ion , are frequently criticized in the literature. For example, us ing number of patents as a measure of innovation suffer s from the implicit assumption of homogeneity regarding the R&D inve stment (Cohen & Le vin, 1989; Pakes & Griliches, 1980). Further, not all innovations are likely to result in patents nor are all patents likely to be used for a final innovative output, for example , they may be used as leverage for financing or held as defe nse against competing products (Nagaoka et al. , 2010). Challenges also arise in the use of direct measure s of innovative output such as new product or service launches in a market. Most notably, new product or service launches and similar output measures are expensive and labor intensive to measure (Acs, et al., 2002; Huang et al. , 2010) While patents as innovation measures have limitations , the literature maintains that patents remain a reliable metric for innovation creation (Acs , et al., 2002; Czarnitzki et al., 2009 ; Pakes & Griliches 1980). For example, Acs et al., (2002) compared patent applications to an SBA data set constructed from information in trade and technical journals on new products and reported that patents perform ed as well as this alternative innovation creation measure. Similarly, comparing 40 different p otential innovation measures constructed from 2014 NSBC data ( the 78 same data set as used in the current study), Parker et. al., (2017) showed that patent applicat ions were significantly correlated with the other 39 innovation measures . Additionally, current availability and the historica l use of patent data makes it a popular measure in terms of examining changes over time and for comparing different levels of aggr egation (e.g., inf luencers at the firm - level versu s the regional - level). 3 .3. Data Two types of variables are included i n my model - firm and county level . Firm - level data are from the 2014 NSBC conducted by the USDA. Respondents (N=10,929) are compris ed of US establishments with more than five employees in the tradable sectors that include mining, manufacturing, wholesale trade, transportation and warehousing, information, finance and insurance, professional/scientific/technical services, arts, and man agement of business. In total, there are 257 potential variables from survey questions cover ing topics such as R&D activities, innovation output (sales from new or improved products or services), failed innovations, patents, other intellectual property pr otection, employee education levels, affiliated industry, business - 2009 recession, market share, location - based barriers, and local government impact 22 . However, on ly a portion of the total 2014 NSBC observations were included in this study due to incomplete responses (1927), observations with missing location of the firm in terms of county FIPS (350), observations for which the respondents reported either they were missing responses relevant variables in my analysis (3404). 22 For details on th e survey, please refer to Wojan (2015) availabl e at https://www.oecd.org/sti/193%20 - %20SelfReportedInnovationSurveys_IncreasingReliability_ClearedManuscript.pdf 79 County - level data are intended to represent the regional business climate and include variables for university R&D , human capital, industrial structure, and selected demographic, and fiscal characteristics. The county - level data cover the 48 contiguous states not including the District of Columbia 23 . These data come from the US Census Community Business Patterns (CBP) and American Community Survey (ACS), the US Bureau of Economic Analysis (BEA), and National Science Foundation (NSF). When matching Firm - and county - level data by the county FIPS codes, 193 additional o bservations were dropped due to missing values within the county - level dataset. Thus, my effective sample for this study includes 4,351 establishments. Table 1 below includes variable name s , a brief description, and source, and the next few subsections pro vide details about variables selection and construction. Dependent Variable: Firm Innovation Creation . The 2014 NSBC included three questions about patenting that occurred between 2011 and 2013 , including whether or not the firm applied for one or more pat ents (binary), the number of patent applications filed (count), and the number of patents awarded (count). Part of my motivation for use of the self - reported patent counts is to make these study results comp arable to prior work, and patent counts allow for more modeling flexibility relative to a binary response as it includes magnitude ( Acs et al., 2002; Czarnitzki et al., 2009; Griliches, 1990; Trajtenberg, 1987 ). Of the two patent count options from the survey (applications and awards) , patent application s are frequently used in the literature as they reflect the most recent level of firm inputs. 24 Further, the patent award date relative to when the application is filed can occur in the same year or even decades from the application date (Hall et 23 Alaska and Hawaii were excluded because of missing observations for several counties; District of Columbia was also excluded as it has a sin gle county and I control for the state - level fixed effects using state dummies in my analysis. From the 48 included states, I also eliminated the counties with missing values for county - level variables 24 I considered scaling patents by the number of person s in the inventive class (engineers and other scientists), but nonscientific fields such as accountants. Thus, self - reported firm - level patent applic ation counts were used. 80 Table 3. 1 Variables Description and Data Source Variables Definition Source (Year) Firm - level Patent applications Total number of patent applications during 2011 - 13 NSBC (2014) Rural Locat ed in a non - metro county (1=yes; 0=no ) Academic information Academia as valuable source of new ideas (not at all valuable =0 , somewhat valuable =1 , very valuable =2 ) Employs individuals with at least bachelor education ( 1=yes; 0= no) Difficulty hiring Difficulty finding qualified applicants ( 0= very difficult; 1= somewhat or not difficult) High - tech (NSF def.) Firm belonging to high - tech industry ( 1=yes; 0= no) Firm size Establishment size (total number of employees) Firm age Establishment age (years in operation until 2013) Percent man. and prof. Management and professional employees as percent of full and part time employees on payroll (percentage points) Final innovative output Introduced innovation in product, service, production, or distribution method in past 3 years ( 1=yes; 0= no) Other IP activity Involved in other forms of IP protection than patents in past 3 years ( 1=yes; 0= no) Abandoned innovation Any improvement or innovation activities abandoned in past 3 years ( 1=yes; 0= no) R&D activity Conducted internally or hired, R&D and design services in past 3 years ( 1=yes; 0= no) Angel/venture funding Received some venture or angel capital financing in past 3 years ( 1=yes; 0= no) Rejected for loan Tried to borrow but received none from financial institutions in past 3 years ( 1=yes; 0= no) Green tech Production or service provision to any green energy sector ( 1=yes; 0= no) Internet sales Sold products or services over the internet ( 1=yes; 0= no) Export products Exported products/services internationally ( 1=yes; 0= no) Industry - level Fixed Effects I ndustry indicators at two - digit level NAICS (NAICS 21, 31, 32, 33, 42, 48, 51, 52, 54, 55, and 71) County - level Univ. R&D per cap. University R&D per capita NSF (2010) SPLAG univ. R&D per cap. University R&D per capita in neighboring counties NSF (2010) Percent pop. bach. degree Bachelor or higher degree holders as percent of population 25 years and over ACS (2010) High - tech variety High - tech Variety CBP (2010) Percent foreign born Foreign - born population as percent of total county population ACS (2010) Percent prof., sc., and tech. employment Employment in professional, scientific, and technological industries as percent of civilian employed population 16 years and over ACS (2010) Unemp. rate Unemployment rate BEA (2010) Total tax per capita Total taxes per capita Census of Govts. (2012) 81 al., 2005). This makes patent applications more consistent with other variables generated from the 2014 NSBC as they reflect input levels in the nearby period as when new applications were filed but not necessarily for those applications leading to awards if t he applicati on - award lags were many years down later . endogenous innovation efforts, patent awards depend on whether other firms/individuals were first movers with a similar patent appl ication. Th erefore , I selecte d patent applications as a better indicator of innovation output and use it as the dependent variable in my estimations . Independent Variables . I include a range of firm specific characteristics in my model including: locatio n ( rural / urban county), innovation creation actions and behaviors, and perceptions and characteristics related to human capital. First, firms located in rural counties are distinguished from those in urban counties. County classification is based on the 20 13 Rural Urban Continuum Codes (RUCC). In the combined model (discussed more in the methods section), an indicator for rural is included. The other two models include urban - only or rural - only firms. It is important to note that a goal of the 2014 NSBC was to collect data allowing for detailed analysis of rural firms while also making comparison of results to urban firms possible . T o achieve this, the survey over - sampled rural firms relative to urban firms. Thus, the rural - only model includes about 3 times t he number of firms as the urban - only model does, and the combined model is heavily weighted towards rural firms. Similar to prior literature, I anticipate that the rural parameter in the combined model is negative, and/or that differences in urban and rura l firm models necessitate separate models, that is, one for rural and one for urban firms. Second, I consider specific firm behaviors and activities in the innovation creation process. Aghion & Howitt (1990) identified three categories or stages of innovation development, Research and Development input ( R&D expenditure), intermediate R&D output 82 (patent), and final innovative output (new product or process), and the most innovative firms were act ive in each. I broaden their description of each category to include other ways in which these activities may occur and based on 2014 NSBC responses. Within my modeling framework, each category is represented with an indicator variable. The first category ( R&D input) includes in - house R&D , purchased external R&D , design activities, and design services. The second (intermediate R&D output) is made up of forms of IP protection other than patents (the dependent variable) and includes, industrial design, tradem ark, copyrights, trade secrets , and first . The third (final innovative output) was expanded to include producing any new or significantly improved goods or services, introduction of new or significantly improved methods of manufacturing, and use of new logistics, delivery and distribution methods for inputs, goods or services. Additionally, firms may choose to abandon an innovation at some stage of development, and I include an indicator for this decision. Lin et al., (2013) showed that in novative firms with mixed and complimentary IP strategy (form example, using multiple forms of IP protection) tent to be more successful. Additionally , and k eeping within the tradition of the f ramework described by Aghion & Howitt (1990), I identified firm - in an NSF - designated high - tech industry based on the 4 - and 6 - digit NAICS codes of firms provided by the 2014 NSBC (NSF, 2016). I expect that all these parameters to be positively associated with patenting activity. Third, I include a number of indic a tor variables based on activities that may influence innovation creation. M any businesses collaborate with academic institutions in conducting research activities . However, Howells, et al. (2012) showed that while these collabora tions benefited the firms, the firms did not necessarily acknowledge this benefit. It may be that the firm - level variables for academic obtaining academic information are negative and the county - 83 level controls for university R&D (discussed below) are posit ive, supporting Howells et al., (2012) finding. Similarly, the research findings and the extension outreach programs of universities can benefit firms by introducing them to new knowledge (Lyons et al., 2018). These results may be similar or different fr om what Howells et al., (2012 ) found. Firm s may also get access to angel or venture funding to help further develop and scale up an innovation, or they may be limited to pursuing more traditional forms of financing such as loans from financial institutions (Renski & Wallace 2012) . I expect the former to be positively associated with patenting, and the latter, which is framed as rejection for private financing (rejected for loan), to be negatively associated with patenting. I also include indicators for firms that said they sold their products or services via internet, exported their products or services, and energy, increasing energy efficiency, conservation of na tural resources, prevention, reduction, and cleaning up of pollution, and production of clean transportation fuels). I anticipate these indicators for broader market access and new markets (green tech) are positively associated with patenting. Fourth, the NSBC survey provides information about different aspects of human capital choices and perceptions. I include an indicator for firms that required individuals with at least bachelor degree for any of their occupational categories, and an indicator for firms that reported having difficulty in finding qualified applicants for their positions in the labor market. Following Aghion & Howitt (1990), I e) to be positively correlated with patenting, while the second (difficulty hiring) to be negatively associated with patenting. I include the share of management and professionals to total employees at the firms, a measure of establishment size (total numb er of employees), and the age of the firm. Based on the 84 finding in the literature (Aghion & Howitt, 1990 ; Henderson, 2003 ) I expect that these final variables are positively associated with patenting. Industry controls. Firms in different industries likel y vary in terms of their patenting propensity and intensity (Wojan et al., 2015) . I control for this heterogeneity across firms by including two - digit NAICS industries associated with the respondent firms in my sample. The industries included in the 2014 N SBC are: mining, quarrying, and oil and gas extraction (NAICS 21); food, beverage, textile, and animal products manufacturing (31); wood products, paper, chemical, petroleum, plastics and rubber, and nonmetallic mineral products manufacturing (32); metal, machinery, computer and electronic products, transportation equipment, furniture and related products, and miscellaneous manufacturing (33); wholesale trade (42); transportation (48), information (51), finance and insurance (52); professional, scientific, and technical services (54), management of companies and enterprises (55); and arts, entertainment, and recreation (71). County - level controls . To control for regional heterogeneity and the business environment in which the firms operate, I include univer sity R&D per capita in own county of firm location, university R&D in neighboring counties located within 100 - mile radius (variable constructed as a spatial lag of university R&D ), percentage of population with bachelor or higher degree of education, numbe r of high - tech establishments as a percentage of total establishments, variety of high - technology industries, foreign - born population as a percentage of total population, share of employment in professional, scientific, and technical services sector to tot al civilian employment, unemployment rate, and total taxes per capita. With the exception of the last two terms (unemployment and taxes which I anticipate to be negatively correlated with patenting), I expect these parameter to be positively associated wit h patenting. 85 Finally, I include state - level fixed effects to control for the heterogeneity among states. I use California as the reference state as it is well known for innovation centers such as Silicon Valley (Mann & Shideler, 2015). Since I construct s eparate models for rural and urban firms, I examine the state fixed - effects in terms of which states may provide a relative advantage or disadvantage to firms compared to California. The state fixed - effects are discussed more at the end of the results sect ion 5.3. 3 .4 . Methods I operationalize firm innovation by using the number of patent applications that firms reported filing between 2011 and 2013 as the dependent variable and are guided by the traditional literature on modeling paten ts counts (e.g., see Allison & Waterman, 200 2; Hall, et al. , 1986 ). As the number of patent applications is a count variable taking on only non - negative integer values, analyses using linear regression models are not appropriate. The violation of the assumptions of linear regression regarding homosc edasticity and normal distribution of residuals, which is atypical to count dependent variable like ours, is likely to lead to biased and inconsistent coefficient estimates (Greene, 2003). The count models such as Poisson and negative binomial are more app ropriate for analyzing count data such as the number of patent applications filed in a given year ( Allison & Waterman, 2002; Greene, 2003; Hall, et al. , 1986 ). Figure 1 shows that the distribution of patent applications data in my combined sample 25 of rural and urban firms is clearly right - skewed. Thus, I turn to Poisson and negative binomial process distribution in terms of constructing my regression models. However, based on my preliminary modeling evidence, specifically the likelihood ratio tests between the initial Poisson 25 The frequency distribution of total number of patent applications is similar for urban and rural sub - samples (not reported) 86 and negative binomial models (discussed more in the results section), indicate that patent applications data in my sample are over - dispersed. In the presence of such over - dispersion of the Figure 3 . 1 Frequency distribution of firm - level total patent applications during 2011 - 13 (pooled sample) dependent variable, the Poisson regression model is inappropriate as the over - dispersion likely causes spurious significance of the coefficient estimates due to underestimation of standard errors (Cameron & Trivedi, 1986). On the other hand, the negative binomial models allow over - dispersion (variance > mean) through its separate parameterization. Therefore, I settl e on the negative binomial model which has the following form expressed in terms of its log - likelihood function (Hilbe, 2011): 4034 113 66 52 9 22 27 21 7 0 500 1000 1500 2000 2500 3000 3500 4000 0 1 2 3 4 5 6-10 11-25 51-500 Number of establishments Number of patent applications 87 where represents the ou tcome variable for firm i , measured with reported patent applications it filed during 2011 - 13; represents the vector of explanatory variables, including firm - level variables, industry controls, county - level controls, and state indicators; and and represent overdispersion parameter and the vector of other model parameters to be estimated respectively. 3.5. Results Results and discussion are presented as follows. First, I include a brief discussion of the summary statistics of the model data. Second, I discuss the regression diagnostics and model selection. Third, I present the significant finding and their potential implications. 3 .5 .1. Summary S tatistics I report the d escriptive statistics in table 2 separately for the sample of firms located in coefficients for the combined sample are presented in table 3. The combined sample of 4,351 firms are across 1,562 US counties, and 25% (1,117 firms) are located in 422 urban counties and remaining 75% in 1,140 rural counties. Firms located in urban areas had higher values for the average number of patent applications (1.24) compared to t hose in rural area (0.27). Overall however, 93% (4,034 out of 4,351 firms, see figure 1) of the firms reported zero patent applications during the period 2011 - 13, and the average number of patent applications for my combined sample is 0.52. Firm age is neg atively correlated with patenting, and urban areas, on average, host younger firms compared 88 to rural areas. All other variables that are positively correlated with patenting, except direct innovation and green tech, have higher average values or frequencie s for urban regions compared to rural regions. The observations from the descriptive statistics indicate that rural firms innovate less frequently than urban firms. I also discuss selected variables in the context of th e parameter resul ts in section 3.5.3 . 3.5.2. Regression Model Diagnostics and Interpretation of Results As discussed in the methods section, I first estimated Poisson models separately for rural and urban firms and the combined sample. Most coefficient estimates were stati stically significant at the 5% and 1% levels (Poisson results not show n ). I then estimated negative binomial models, which allowed incorporation of the over - dispersion of the patents data. The results reported in table 4 for alpha (the over - dispersion parameters) provides a test of appropriateness of the Poisson models. The statistically significant alpha s in all three columns of the coefficient estimates demonstrated that the null hypothesis of zero dispersion is rejected at 1% si gnificance level, thus suggesting the statistically significant coefficients in the Poisson regression models were likely due to underestimated standard errors arising from the over - dispersed patent data. Additionally, I estimated four specifications of t he negative binomial regression model: (i) no county - level controls or state - level fixed effects, (ii) county - level controls only, (iii) state - level fixed effects only, and (iv) both county - level controls and state - level fixed effects. While I do not repor t the results from the first three specifications, (i ) - (iii), the model chosen is based on the AIC and BIC selection criter ia which identified the county - level controls and state - level fixed effects as the better specification of the four . 89 Table 3 . 2 Summary Statistics Variables * Combined Urban Rural Variables Combined Urban Rural Mean (SD) Mean (SD) Mean (SD) Mean (SD) Mean (SD) Mean (SD) Firm - level Variables Industrial (2 - digit NAICS) Patent apps. (counts) 0.52 1.24 0.27 21 2% 1% 2% (8.41) (16.12) (2.28) 31 5% 3% 6% Firm size (# employees) 55.04 63.57 52.09 32 9% 6% 9% (275.55) (398.94) (217.23) 33 18% 17% 19% Firm age (# years) 32.86 26.46 35.07 42 17% 21% 16% (28.09) (23.92) (29.07) 48 6% 3% 7% Percent man. and prof. (% points) 23.57 28.55 21.85 51 8% 5% 9% (21 .00 ) (25.22) (19.03) 52 4% 2% 4% Academic information 54 25% 34% 22% not valuable 13% 16% 12% 55 3% 5% 3% somewhat valuable 52% 48% 53% 71 3% 3% 3% very valuable 35% 36% 35% County - level variables Bachelor's degree (1=yes; 0=no) 56% 67% 52% Univ. R&D peer cap. ($) 94.05 187.07 59.62 Difficulty hiring (1=yes; 0=no) 26% 22% 27% (776.48) (512.11) (851.46) High - tech (NSF def.) 20% 31% 17% SPLAG univ. R&D peer cap. ($) 336.3 283.64 355.8 Final innovative output (1=yes; 0=no) 71% 70% 72% (994.36) (740.47) (1072.85) Other IP activi t ies (1=yes; 0=no) 33% 46% 29% Percent bach. degree pop. (% points) 9.15 11.89 8.13 Abandoned innovation (1=yes; 0=no) 26% 30% 25% (3.63) (3.72) (3.02) R&D activity (1=yes; 0=no) 60% 66% 58% High - tech variety 15.99 28.57 11.33 Angel/venture funding (1=yes; 0=no) 2% 2% 1% (9.94) (8.58) (5.28) Rejected loan (1=yes; 0=no) 5% 5% 5% Percent foreign born pop (% points) 4.71 8.57 3.28 Green tech (1=yes; 0=no) 33% 31% 34% (5.45) (7.32) (3.66) Internet sales (1=yes; 0=no) 48% 50% 48% Unemployment rate (% points) 7.28 7.15 7.32 Export products (1=yes; 0=no) 27% 35% 25% (2.46) (2.04) (2.59) Tax per capita ($) 1441.25 1686.57 1350.44 4,351 1,117 3,234 (955.72) (91354) (737.17) - metro samples are 1562, 422, and 1140 respectively 90 Table 3 . 3 91 Regression results a re presented in table 4 (below) for the combined, urban, and rural models. The beta coefficients and their statistical significance are shown in the first column under each group category and the incidence rate ratio minus 1 (IRR - 1) are shown in the second 26 . I report the IRR - 1 as this i s a straightforward method to interpret results (for recent examples in the literature using this method see Howell, 2017; Murray & Stern, 2007; Rothaermel & Hess, 2007). For example, under the combined model, the percentage of management and professional employees ( percent man. and prof. ) parameter is interpreted as a one - unit increase (in this case a 1% increase) in the share of management and professional employees is expected to inc rease patenting activity by 1%. 3.5 .3. Rural and Urban Firm Innovation To address my broader research question, I used a likelihood ratio test to empirically check for a difference in the innovation creation (patenting) behavio r of rural and urban firms that were otherwise identical in their characteristics. For this test, the null hypothesis is framed as rural and urban firms represented by common innov ation behavior parameters. Thus, I consider if the use of the combined mo del for analysis is appropriate, or are two models more appropriate, one for rural and one for urban . The test statistics for the first test is derived as two times the difference between the log - likelihood of model 1 and the sum of the log - likelihoods of mod el 2 and 3 ( - 1410.0 - 487.1 + - 858.1 = - 64.8, 2*| - 64.8| = 129.6) 27 . The critical chi - square value with 76 degrees of freedom and at the 99% confidence level (107.58) is less than the test statistic. Thus, I reject the null hypotheses in favor of using indivi dual urban and rural models in place of the 26 These are constructed as IRR - 1 = exp( ) - 1 ( Hilbe, 2011 ). 27 See Brooks and Lusk (2010) for the inferential approach using likelihood ratio test. 92 c ombined model. In other words, my test reveals that there are some differences between rural and urban firms in terms of potential influencers of patenting activities. Of the statistically significant firm - leve l parameters, participation in other forms of IP protection has the largest magnitude in difference between rural and urban firms ; however, both are positive and support the findings from Lin et al., (2013) . The IRR - 1 reveals that for urban firms, use of o ther fo rms of IP protection is correlated with a three - fold increase in patent activity compared to rural firms . In other words, other forms of IP protection appear much more important for urban firms in terms of their innovation creation. It may be that closer proximity to or higher density of other innovative firms contributes to this result. It could also be that since innovative urban firms compete in broader markets more frequently compared to innovative rural firms (revealed by the internet sale s and export products summary statistics and parameters), increased participation in other forms IP protection is necessary. These results may also be influenced by some of the o ther differences in characteristics in which urban firms have an advanta ge, fo r example, access to angel and venture funding, partici pation in green tech (urban firms show a greater magnitude impact on patenting activity although a higher portion of rural firms participate in this), and using R&D activity. It may be that private equ ity investors insist on more protections for the innovations developed and greater R&D investment motivate broader IP protection. Another interpretation of these results is that there is a connectedness between different innovation related activities, and that urban firms are able to better capitalize from the combined effort of these activities relative to rural firms. Thus, my results support prior studie s that demonstrate that urban firms have higher levels of innovative activity compared to rural firms . 93 Table 3 . 4 Negative Binomial Regression Results Variables (DV: Number pat. Apps) Combined Metro Non - metro Firm - level Beta IRR - 1 Beta IRR - 1 Beta IRR - 1 Rural 0.077 0.08 Academic information somewhat valuable - 0.612** - 0.46 - 0.167 - 0.15 - 0.251 - 0.22 very valuable - 0.699** - 0.50 - 0.588 - 0.44 - 0.201 - 0.18 Bachelors Degree 0.465** 0.59 0.219 0.24 0.550*** 0.73 Difficulty hiring - 0.233 - 0.21 - 0.285 - 0.25 - 0.140 - 0.13 High - tech (NSF Def.) 0.314 0.37 0.830** 1.29 0.042 0.04 Firm size 0.655*** 0.93 0.823*** 1.29 0.576*** 0.78 Firm age - 0.025 - 0.02 - 0.200 1.28 - 0.036 - 0.04 Percent man. & prof. 0.013*** 0.01 0.014* 0.01 0.011* 0.01 Final innovative output 0.255 0.29 0.462 0.59 0.465 0.59 Other IP activity 2.200*** 8.03 3.109*** 21.40 2.092*** 7.10 Abandoned innovation 0.452*** 0.57 0.066 0.07 0.473*** 0.60 R&D activity 1.299*** 2.67 1.593** 3.92 1.460*** 3.31 Angel/venture funding 0.983** 1.67 1.736* 4.67 0.319 0.38 Rejected for loan - 0.117 - 0.11 - 0.758 - 0.53 0.042 0.04 Green tech 0.195 0.22 0.696* 1.01 0.308* 0.36 Internet sales 0.393** 0.48 0.965*** 1.62 0.302 0.35 Export products 1.152*** 2.16 1.354*** 2.87 1.056*** 1.87 County - level Variables Univ R&D per cap. 0.083** 0.09 0.049 0.05 0.121** o.13 SPLAG Univ. R&D per cap. 0.046 0.05 0.126 0.13 0.000 0.00 Per. pop. bach. Degree - 0.005 0.00 0.039 0.04 - 0.048 - 0.05 High - tech variety 0.016 0.02 0.009 0.01 0.025 0.03 Per. foreign born 0.021 0.02 - 0.018 - 0.02 0.018 0.02 Unemp. Rate 0.035 0.04 - 0.142 - 0.13 0.082 0.09 Tax per capita 0.810** 1.25 0.895 1.45 0.596 0.81 Constant - 18.112*** - 17.309** - 17.860*** - 0.05 ln(alpha) 1.689*** 1.745*** 1.221*** 0.03 Industry - level Fixed Effects Yes Yes Yes State - level Fixed Effects Yes Yes Yes Number of obs. 4,351 1,117 3,234 Log - likelihood - 1410 - 487.1 - 858.1 Model DF 81 79 76 AIC 2985.78 1136.17 1872.22 BIC 3515.17 1542.66 2346.58 Standard errors in parentheses; *** p<0.01, ** p<0.05, * p<0.1 94 The results in this study also provide additional insight on this phenomenon, showing more detail on some of the nuances of how and/or why this may be occurring. One surprising result is that the urban - rural innovation gap is not seen in some of the county - level business environment control variables, such as high - tech variety or educated labor force in the urban areas. For example, using co unty - level regional model, Aryal et al., (2018) show these factors are positive and statistically significant for urba n and rural firms but to different degrees. T here are two firm - level results that also provide additional insight relevant ( and statistical ly significant) to rural firms in the context of my modeling of patenting activity, but not to urban firms. In terms of innovative activity, the difference in the human capital needs between r ural and urban firms may show that there is greater variability among rural fir ms. In short, innovative rural firms need educated employees but other rural firms rely less on an educated workforce; whereas, for urban firms both patenting and non - patenting firms depend on an educated labor force. The summary statistics showed that 67% of urban firms had firms). Thus , for urban firms, the employee standard appears higher which may imply that the distinction between different urban firms is more about field and less about whether or not the employee has the degree ( the opposite appears relevant for rural firms). bandon ed innovation is also positive and statistically significant for ru ral firms but not for urban firms. This implies that rural firms that expend effort, even if not successful, are more likely to create new innovations. From the summary statistics, only 25% of rural firms reported that they had innovation activities that w ere abandoned (compared to 30% of urban firms). This result may also reveal something about the level of risk 95 rural firms are willing or able to manage. In short, rural firms that are more willing to take on risk as evident from starting and abandoning inn ova tions innovate more frequently. For the county - level controls, only university R&D per capita is statistically significant for rural firms. This result is interesting considering that the coefficient estimate of the variable cademic information is n ot statistically significant (and negative). Howells, et al. (2012) reported that firms place a low value on the impacts of university technology transfer and partnerships, yet firms were shown to greatly benefit from these relationships. Given the results in my study, this may be especially true for rural firms. Finally, table 5 shows the statistically significant (10% or lower level) state - level fixed - effect parameter estimates for the rural firms model . While not the main focus this research, the results provide an interesting contrast to firms operating in urban areas. In both the urban and rural models, California is the reference state. Only Kentucky in the urban model was statistically differ ent than California (and negative). However, 16 states in the rural model were different than California and all were positive. California and Massachusetts historically are the leaders in innovation creation (Mann & Shideler, 2015), but much of the literature focusing on firm - or regional - level innova tion creation is relative to urban firms. The results of table 5 suggest that when it comes to rural firm innovation creation, many other states may be ahead of the traditional leaders. Interestingly, several of the tops states in this table are small in t erms of population (Wyoming, Montana, and Vermont). But larger states, such as New York and Texas also appear in this list. It may be that the location of some of these firms in rural areas benefit more substantially from urban spillovers (in the case of r ural areas adjacent to urban centers). On relative to California. 96 Table 3 . 5 Rural Innovative firms - Statistically Significant St ate Fixed Effects (Ref. State=CA) State Coeff icient Estimate IRR - 1 Wyoming 4.21 66.3 Nevada 3.64 36.9 Vermont 3.39 28.5 Montana 3.29 25.8 Alabama 3.18 23.1 Kansas 2.98 18.7 Missouri 2.82 15.8 New York 2.75 14.7 Texas 2.74 14.5 Iowa 2.73 14.3 Ohio 2.68 13.5 Colorado 2.67 13.4 Kentucky 2.57 12 .0 Mississippi 2.52 11.4 Tennessee 2.45 10.6 Minnesota 2.41 10.2 3 . 6 . Summary a nd Conclusion Much of the innovation creation literature is focused on urban firms or areas, or relies heavily on data based on these (NSF, 2016). Less studied are rural firms and areas in this context. The goal of this paper is to empirical ly test if and how much rura l and urban firms differ in terms of behaviors and characteristic that may influence innovation creation. To accomplish this goal, I use the 2014 NSBC and combine it with regional secondary data that reflect s the business and innovative environments in whi ch these firms operate. My overarching finding is that urban firms are able to better capitalize on firm characteristics and behaviors that may influence innovation creation relative to rural firms. This finding is revealed as most of the parameters that a re statistically significant for urban firms are also statistically significant for rural firms, but the magnitu des are higher for urban firms. While my main finding supports prior 97 studies that show rural firms lag behind urban firms, my study also provide s a few other insights as to how and why this is occurring . First, my results suggest that innovation creation within rural firms is influenced more by university R&D than for urban firms. At the same time, information from universities (for example from e xtension services) may not necessarily be perceived by firms as impactful with respect to innovation creation. This finding supports Howells et al. (2012) counterintuitive results with specific applications to rural firms that while firms may not perceiv e value from universities, they do benefit in economic terms from their interactions with universities. Second, rural firms that are willing to try, but fail, in terms of innovation creation have a slight advantage over other rural firms less willing to ta ke on the risk. This result is shown by the parameter (from the 2014 NSBC question asking firms if any innovation project had been abandon ed during 2011 - 2013 period). The implication is that rural firms that are more risk averse may degree appear to be more important for rural firms regarding innovation creation than for urban firms. However, I do not suggest here that an educated labor force is not important f or urban firm s in this regard. My summary statistics show that 2 out of 3 urban firms require a 4 - year degree for at least some positions compared to about half of rural firms. Instead, it is likely that for rural firms, having qualified workers capable of innovation creation is a higher barrier relative to urban firms. Fourth, there are several factors that suggest urban firms are more competitive than rural firms, for example, due to their proximity to other innovative firms or based on the degree/intensi ty of accessing broader markets (such as via exports and ecommerce). Thus, for urban firms mixed IP protection strategies appear much more important compared to rural firms. Combined, these findings suggest potential opportunities for policies directed tow ard rural firms 98 that can: (1) help mitigate the risk in innovation creation; (2) proved university support in terms of R&D, for example , access to intermediate R&D outputs suc h as licensing technologies; (3) provide qualified labor/assistance in terms of i nnovation creation or development ; and (4) help rural firms access broader markets . One example may be improving access to public or private equity for R&D, such as through the Small Business Innovation Research prog ram , or access to other kinds of program s designed to fund early stage R&D . Such improved access could occur with the aid of university - based training or research partnerships , and may include improved access to university developed technologies. Fifth , the states that typically lead innovation creation among urban firms and areas are not necessarily the same for rural areas. Although the evidence presented to support this notion is only suggestive (state - level fixed effects parameters ), it provides a topic for further research. For example, Wyoming, Vermont, and Montana appear in the top four of these rural leader states and all three are ranked near the bottom with respect to population, and Wyoming and Montana are lowest in populatio n density among the 48 contiguous states. 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