Ahmet Faruk

Luis Carlos Castillo-Téllez

Dilek Demirbaş
email: dilek.demirbas@istanbul.edu.tr

Mustafa Disli
email: mdisli@hbku.edu.qa

FOREIGN TRADE, EDUCATION AND INNOVATIVE PERFORMANCE: A MULTILEVEL ANALYSIS

Keywords: Multilevel, Innovative Performance, Open Economy Variables, Innovation Systems, Multilevel Regression Models, Development. JEL Classification: O31, O32

This research analyses the innovative performance of 5273 companies across 64 different economic sectors and 32 different regions in Colombia. We assess the different effects on the innovative performance of firms by analyzing firm, sector, and regional level determinants. The study involves the multilevel approach of the innovation process considering the structure and behavior of innovation systems in developing countries. We furthermore focus on technology transfer from foreign trade and the role of education in the process of innovation. We find that education and open economy variables have a significant relationship with innovation performance at the firm and regional levels.

INTRODUCTION

What is the role of education and the impact of open economy variables (OEV) on the innovative performance of Colombian manufacturing firms? In support of the innovation system (IS) theory, it has been found that both education and foreign trade are crucial in the development of new knowledge, technology transfer, and knowledge spillovers [START_REF] Keller | International Trade , Foreign Direct Investment , And Technology Spillovers[END_REF][START_REF] Lundvall | Epilogue: Which way now? In Handbook of Innovation Systems and Developing Countries: Building Domestic Capabilities in a Global Setting[END_REF][START_REF] Srholec | A Multilevel Analysis Of Innovation In Developing Countries[END_REF][START_REF] Srholec | Understanding the diversity of cooperation on innovation across countries: multilevel evidence from Europe[END_REF]. Recent contributions to the literature not only have shown that in Colombia that educational institutions need to have the ability to transfer knowledge to the industry [START_REF] Vélez-Rolón | Open innovation community for university-industry knowledge transfer: A Colombian case[END_REF], but also confirmed that imports have a positive relationship with science, technology, and innovation activities [START_REF] Guevara-Rosero | Trade, innovation and agglomeration. A case study for Colombia[END_REF] Seminal studies on the (IS) theory were developed by Lundvall (1985) and Freeman (1982). While Lundvall analyzed innovation at the micro-level where the user-producer interactions shaped the development of new technologies and products. Freeman (1982), from a macroperspective, underlines the relation between innovation and international trade, emphasizing the importance of building a technological infrastructure at the national level. From this perspective, company innovation is at the center of analysis but seen in a larger context of the network of institutions whose interactions enable the diffusion of new technologies. Firms are exposed to a context in which international trade [START_REF] Laurin | The internationalisation of smes and the relationships between imports and exports[END_REF] and capital mobility [START_REF] Keller | International Trade , Foreign Direct Investment , And Technology Spillovers[END_REF] become a bridge of technology transfer between the global knowledge networks and the IS. In addition, universities play a significant role in the formation of human capital and scientific research. These education institutions provide skilled labor while they are also a source of specific knowledge transfer for different industries (OECD, 2012;UNCTAD, 2014). In Latin America, however, cross-country analysis of innovation performance at the firm level has encountered two main constraints. First, the enforcement of new legislation that controls the access to microdata files in different countries [START_REF] Guillard | La experiencia en Encuestas de Innovación de algunos países latinoamericanos[END_REF]. Second, differences in data collection procedures among Latin American countries often prevent meaningful comparisons across countries [START_REF] Guillard | La experiencia en Encuestas de Innovación de algunos países latinoamericanos[END_REF]. So far, studies for Colombia that relate innovation systems with multilevel models have been limited to two levels, i.e., firm and regional levels [START_REF] Barrios-Aguirre | El ambiente regional y empresarial en el desempeño innovador de las firmas manufactureras colombianas: ¿Quien es mas importante? Conferência Internacional LALICS[END_REF][START_REF] Zuluaga Jiménez | Ambiente regional y desempeño innovador de las firmas. Una propuesta de análisis multinivel[END_REF] This study adds to the literature by considering an additional dimension of sectoral innovation which allows us to perform a three-level analysis (i.e., firm, sector and region). Accordingly, the main objective of this research is to determine if OEV and education variables have a significant relationship with the innovative performance of Colombian manufacturing firms in light of multilevel analysis. This paper presents a multilevel quantitative technique to analyze the innovative performance of the manufacturing industry in Colombia based on the theory of regional and sectoral IS. In particular, the microdata from the Technological Development and Innovation Survey (EDIT) 2007-2008 and merging different datasets mainly provided by the National Department of Statistics (DANE) allows us to build a database that has a hierarchical structure in which companies can be classified according to their economic activities (or sector) and regions in which those firms have their headquarters. By doing so, this study examines 5273 firms operating in 64 different economic sectors and 32 regions in Colombia.

The major conclusion of this study reveals that at the first level, firms with foreign capital harm innovation performance unless these firms allocate the foreign capital inflows to R&D activities. At the sectoral level, however, the model did not bring enough statistical evidence about the influence of OEV variables on innovation performance. At the regional level, foreign trade has a positive influence on innovation performance due to technology transfer. In addition, tertiary education plays a significant role in the development of innovation at the firm and regional level, hence indicating the importance of strengthening the universityindustry collaboration in the Colombian innovation system. This paper is organized as follows. In the methodology section, the multilevel regression model and variables are introduced. In the second section, the estimation of the model and the results will be presented and discussed. Then in the final section, the conclusion summarizes the results and policy implications.

METHODOLOGY

From multilevel analysis to multilevel modeling

In general, individuals interact in a social environment to which they belong, as a result of this individuals are influenced by this social environment and vice versa [START_REF] Gupta | Innovation at and Across Multiple Levels of Analysis[END_REF]. In other words, individuals are nested within social groups at different levels creating a hierarchical interconnected structure. A commonality among multilevel regression models1 is the hierarchical structure of data with one single result or dependent variable at the lowest level and independent variables at higher levels [START_REF] Gelman | Data Analysis Using Regression and Multilevel/Hierarchical Models[END_REF][START_REF] Hox | Multilevel Analysis: Techniques and Applications[END_REF]. Multilevel Poisson regression analyses have been used by different disciplines that study embedded data of multilevel phenomena. The reliability of the model depends on the quality of the data as well as the adopted methodology in the estimation process. As the innovation process happens in the firm, sectors, and regions there are some unobserved conditions by the model. Heterogeneity or variations across individuals such as firms, sectors, and regions are unobserved by the model [START_REF] Hox | Multilevel Analysis: Techniques and Applications[END_REF][START_REF] Wooldridge | Econometric Analysis of Cross Section and Panel Data[END_REF]. However, if we use multilevel models with random parameters and mixed effects the unobserved individual-specific heterogeneity is assumed to be unrelated to the explanatory-variable vector. Following [START_REF] Gupta | Innovation at and Across Multiple Levels of Analysis[END_REF] in the field of innovation, the hierarchical structure is visible as firms appeared to be the individuals that are clustered in sectors, and these sectors are allocated within regions.

Taking into account the challenges to explain the causalities of the variables of interest, this study proposes the following hypothesis: H1: The innovative performance of firms is significantly related to open economy variables even though the interpretation of these variables from the regional, sectoral and firm dimensions could generate different results when analyzing developing economies.

According to [START_REF] Fagerberg | Working Paper Series Innovation and Economic Development[END_REF] education is one of the main components of the social capabilities in IS. Thus the second hypothesis is: H2: From the multilevel dimension higher education such as a doctorate, master, undergraduate, or associate degree are expected to contribute to the firm's innovation performance.

Determinants of innovation from a multilevel dimension

From the multilevel dimension, each of the three levels will encompass a set of determinants that are linked to the main components of the RIS [START_REF] Padilla-Pérez | Regional Innovation Systems in Developing Countries: Integrating Micro and Meso-level Capabilities[END_REF], the building blocks of Sectoral Innovation Systems (SIS) [START_REF] Joseph | Sectoral Innovation Systems in Developing Countries: The Case of ICT in India[END_REF][START_REF] Malerba | Sectoral Systems of Innovation and Production[END_REF][START_REF] Srholec | A Multilevel Analysis Of Innovation In Developing Countries[END_REF] and the firms' characteristics [START_REF] Hadhri | Determinants of innovation activities in small and open economies: the Lebanese business sector[END_REF].

Regional level determinants

The regional level determinants encompass characteristics outside the firm that can influence innovation performance. Within the context of developing countries, the determinants tend to change due to the existence of heterogeneity among countries and regions [START_REF] Srholec | Understanding the diversity of cooperation on innovation across countries: multilevel evidence from Europe[END_REF]. According to the characteristics of the Colombian IS, the following determinants will be tested within the econometric model.

Following the literature, imports and exports bring along technological and knowledge spillovers that have a positive effect on productivity and innovative performance, nevertheless, the relationship between international trade and innovation in developing countries can bring positive or negative results [START_REF] Bernard | Exceptional exporter performance: cause, effect, or both?[END_REF][START_REF] Hadhri | Determinants of innovation activities in small and open economies: the Lebanese business sector[END_REF][START_REF] Keller | International Trade , Foreign Direct Investment , And Technology Spillovers[END_REF][START_REF] Lefebvre | Innovative Capabilities as Determinants of Export Performance and Behaviour: A Longitudinal Study of Manufacturing SMEs[END_REF][START_REF] Padilla-Pérez | Regional Innovation Systems in Developing Countries: Integrating Micro and Meso-level Capabilities[END_REF][START_REF] Vogel | Higher productivity in importing German manufacturing firms: Self-selection, learning from importing, or both?[END_REF]. Coverage on higher education and human capital formation is crucial in the process of innovation [START_REF] Lundvall | The origins of the national innovation system concept and its usefulness in the era of the globalizing economy[END_REF][START_REF] Vélez-Rolón | Open innovation community for university-industry knowledge transfer: A Colombian case[END_REF]. In developing economies, however, the lack of basic and advanced educational systems and the failure of governments to allocate resources for research and higher education hinder innovation performance [START_REF] Kuhlmann | Introduction : governance of innovation in emerging countries : understanding failures and exploring options[END_REF]. Technological unemployment happens when cutting-edge technology disrupts labor markets and creates jobs with high-income cognitive tasks and displace low-income manual occupations and routine tasks [START_REF] Frey | The future of employment: How susceptible are jobs to computerisation?[END_REF]. Evidence from seven Latin American countries, however, shows that investment in science and technology does not affect the unemployment rate [START_REF] Aguilera | Technological Unemployment: An approximation to the Latin American Case[END_REF]. The distance to the capital city and other main cities explain that geographical proximities to production, skilled labor, high wages, and institutions make interactions, flows of information, and knowledge more effective [START_REF] Ascani | Regional Economic Development : A Review[END_REF][START_REF] Feldman | Innovation in cities: Science-based diversity, specialization and localized competition[END_REF]

Sectoral level determinants

The interactions between the building blocks within the Sectoral IS and the main components of the Regional IS play a significant role in the exchange of information, knowledge, and technology as such that innovation within sectors takes place [START_REF] Joseph | Sectoral Innovation Systems in Developing Countries: The Case of ICT in India[END_REF]. At this level, the following determinants were tested in the econometric model. Similar to the regional level, international trade (export rate, trade openness index, foreign capital) brings knowledge and technology spillovers that influence innovative performance. Maleçrba (2005) states that firms are embedded in heterogeneous sectors in which they use different technologies, networking, and institutions. Furthermore, trade may bring different effects that could change according to industry characteristics and composition (ICTSD, 2016). Regarding the concentration of knowledge, Pavitt's Taxonomy distinguishes sectoral innovation patterns considering four types of innovative-firms: science-based, specialized-suppliers, supplierdominated, and resource-intensive [START_REF] Bogliacino | The Pavitt Taxonomy revisited : patterns of innovation in manufacturing and services[END_REF]. On the other hand, [START_REF] Gera | Employment Performance in the Knowledge-Based Economy[END_REF] argue that some sectors demand higher R&D investment than others industries, identifying three knowledge intensity groups: high, medium, and low-knowledge industries. The concentration of innovation takes place on economies of scale, specialized suppliers, and science-based industries, where innovation activities are more intense than sectors that are dominated by suppliers [START_REF] Urraca-Ruiz | Patrones sectoriales de cambio técnico en la industria española[END_REF]. A recent study reveals how digital technologies are redesigning the concentration of innovation activities [START_REF] Paunov | On The Concentration Of Innovation In Top Cities In The Digital Age[END_REF].

Firm-level determinants

Innovation performance depends on the characteristics of the firm and the synergy with the regional and sectoral innovation system. [START_REF] Hadhri | Determinants of innovation activities in small and open economies: the Lebanese business sector[END_REF] found that determinants of innovative performance can change according to the context in which firms are exposed. The following determinants found in the literature are included in our regressions. The size of companies has a positive relationship with R&D investment [START_REF] Schumpeter | The Theory of Economic Development: An Inquiry into Profits, Capital, Credit, Interest, and the Business Cycle[END_REF][START_REF] Schumpeter | Capitalism, Socialism and Democracy[END_REF]. [START_REF] Cohen | A reprise of size and R and D[END_REF] and [START_REF] Cohen | Chapter 18 Empirical studies of innovation and market structure[END_REF] claim that larger companies have access to different external technological resources and a higher budget to invest in R&D. Next to size, [START_REF] Hadhri | Determinants of innovation activities in small and open economies: the Lebanese business sector[END_REF]suggest the inclusion of control variables such as education, networks, human capital, and others. According to [START_REF] Powell | Networks of Innovators[END_REF], networks foster the trade of knowledge. Nowadays technology and information flows are important to acquire the knowledge needed to develop and commercialize new products. For this reason, interorganization partnerships are important in the development of networks [START_REF] Ardito | From Technological Inventions to New Products : A Systematic Review and Research Agenda of the Main Enabling Factors[END_REF]. Networks in the era of digital globalization can furthermore generate a suitable environment for innovation performance [START_REF] Manyika | Modeling the global economic impact of AI[END_REF]. Evidence also suggests that R&D expenditure generates a positive effect on innovation and productivity [START_REF] Baumann | The link between R&D, innovation, and productivity: Are micro firms different?[END_REF][START_REF] Macgregor-Pelikánová | R&D Expenditure and Innovation in the EU and Selected Member States[END_REF][START_REF] Prodan | Influence of Research and Development Expenditures on Number of Patent Aplications: Selected Case Studies in OECD countries and Central Europe, 1981-2001[END_REF]. In developing countries, however, the resources allocated to R&D are relatively low [START_REF] Morero | The role of public policies in promoting innovation and innovation complementarities in developing countries: the case of the Argentinian software industry[END_REF]. In this situation, the government should create public policies aimed to increase firms' capabilities to absorb foreign knowledge to improve innovation performance and development [START_REF] Morero | The role of public policies in promoting innovation and innovation complementarities in developing countries: the case of the Argentinian software industry[END_REF]. Human capital is crucial in the innovative behavior of firms. [START_REF] Romijn | Determinants of innovation capability in small electronics and software firms in southeast England[END_REF] mentioned the need to have trained and skilled people in areas such as engineering, science, and others. Firms in emerging economies, however, do not have access to a labor force with technological-oriented skills that are needed in the development of high-quality goods and services [START_REF] Morero | The role of public policies in promoting innovation and innovation complementarities in developing countries: the case of the Argentinian software industry[END_REF]. In a low-resource context, where there is less collaboration between universities and industry, firms also will have to make more efforts to build up their human capital [START_REF] Albats | Companies' human capital for university partnerships A micro-foundational perspective Companies' human capital for university partnerships: A micro-foundational perspective[END_REF][START_REF] Marotta | Human Capital and University-Industry Linkages' Role in Fostering Firm Innovation: An Empirical Study of Chile and Colombia[END_REF]. Finally, the role played by foreign direct investment FDI in innovative performance is significant. Literature in innovation [START_REF] De Marchi | Regional Innovation Systems or Innovative Regions? Evidence from Italy[END_REF][START_REF] Keller | International Trade , Foreign Direct Investment , And Technology Spillovers[END_REF][START_REF] Morero | The role of public policies in promoting innovation and innovation complementarities in developing countries: the case of the Argentinian software industry[END_REF][START_REF] Padilla-Pérez | Regional Innovation Systems in Developing Countries: Integrating Micro and Meso-level Capabilities[END_REF] has mentioned how emerging economies have created policies to attract FDI to promote growth, development and facilitate technology transfer. Nevertheless, in some countries, these policies are designed to boost sectors related to commodities extraction. For example, OECD (2014)indicates that a substantial amount of FDI in Colombia has been captured by the mining sector rather than technologically oriented sectors.

DATA AND EMPIRICAL METHODOLOGY

Data

The data was taken from different official sources such as DANE, National Department of Planning (DNP); Ministry of Education; Ministry of Commerce, Industry and Tourism; Directorate of Taxes and National Customs (DIAN), and Procolombia. The latest publicly available version of this survey is the EDIT (2007EDIT ( -2008)). In recent years, however, the Colombian government has issued certain laws that restrict access to these databases.

First or firm-level data, that comprises 5273 firms, is obtained from EDIT (2007EDIT ( -2008)). The second or industry-level data contains 64 groups of economic activities identified according to the International Standard Industrial Classification of All Economic Activities, Rev.3 (ISIC Rev3). The third or regional level data include variables of the 32 departments of regions from Colombia.

To build the database, this research develops the following measurements. The dependent variable is the total count of innovations. This variable is the result of the summation of all nine types of innovations (see Table 1) that every firm was able to achieve during the period of the survey, this categorization can be found in the EDIT 2007-2008 survey.

Table 1. Types of innovation

1. New goods or services for the company 2. New goods or services for the national market 3. New goods or services for the international market 4. Goods or services significantly improved for the company. 5. Goods or services significantly improved for the national market. 6. Goods or services significantly improved for the international market. 7. New or significantly improved methods of production, distribution, delivery, or logistics systems, implemented in the company. 8. New organizational methods are implemented in the internal functioning, in the knowledge management system, in the organization of the workplace, or the management of external relations of the company. 9. New or significantly improved marketing techniques (channels for promotion and sale, or significant changes in packaging or product design), implemented in the company to expand or maintain its market.

(Changes that affect the functionalities of the product are excluded). Source. EDIT 2007EDIT -2008 The EDIT 2007EDIT -2008 survey classifies three types of innovation (Radical, Incremental, and Strategic)2 and measures the innovation performance by counting the accumulation of innovations within two years. The dependent variable used in this research is the total count of innovations, which is the summation of the three above-mentioned types. Table 2 gives the summary statistics of the dependent variable. According to EDIT 2007-2008 survey, 40% of the firms reported on average 46,338 innovations while 60% of the firms did not innovate at all. Table 2 shows that the total count of innovation is a discrete variable that contains non-negative values, with a distribution that describes a Poisson process 3 (see Figure 2).

Figure 1. Histogram of the total count of innovations

Source. Calculations based on EDIT 2007EDIT -2008 The independent variables at the sectoral and regional level had the following treatment, the continuous variables between 2007 and 2008 were averaged and standardized (see Table 3). Most of the independent variables at the firm, sector, and regional level are continuous (see Table 5 for summary statistics). However, some variables are discrete which in this case dummy variables are included. 3 Winkelmann (2008) describes the Poisson process as a special event count in which a stochastic process is carried out. This stochastic process is the accumulation of random variables (in a probability space) at a certain period.

Models of count data

These regression models are for non-negative integer or counts, for instance, the dependent variable as count of innovations takes values without upper explicit limit [START_REF] Winkelmann | Econometric analysis of count data[END_REF], for this type of data the Poisson Regression Model (PRM) is the appropriate one. This model assumes in this case that innovation is an event and behaves as a Poisson Process, which is a stochastic process that calculates the probability of the occurrence of an event in a certain period [START_REF] Winkelmann | Econometric analysis of count data[END_REF].

As we see in Table 2, the variance is larger than the mean and 3146 zero values were found, these excessive zeros make the sample violate the equidispersion assumption in the PRM, in which the mean is equal to the variance. To solve this problem, the Zero Inflated Poisson Model (ZIP Model) or Zero Inflated Negative Binomial Model (ZINB Model) which is an extension of PRM has been used [START_REF] Lee | Multi-level zero-inflated poisson regression modelling of correlated count data with excess zeros[END_REF][START_REF] Winkelmann | Econometric analysis of count data[END_REF]. This amount of zeros in the survey are common in developing countries. According to [START_REF] Ricyt | Ibero-American Network for Science and Technology Indicators[END_REF], in countries like Argentina, Brazil, and Chile, only less than 40% of their firms innovate. The Colombian case is not very much different from that, approximately 60% of the companies did not innovate according to the survey EDIT 2007-2008.

Applying the multi-level zero-inflated Poisson ZIP model

Following the literature [START_REF] Hox | Multilevel Analysis: Techniques and Applications[END_REF][START_REF] Hur | Modeling clustered count data with excess zeros in health care outcomes research[END_REF][START_REF] Lambert | Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing[END_REF][START_REF] Lee | Multi-level zero-inflated poisson regression modelling of correlated count data with excess zeros[END_REF][START_REF] Long | Regression Models for Categorical and Limited Dependent Variables[END_REF][START_REF] Wang | Multilevel Models: Applications using SAS®[END_REF], this paper will use multilevel models with mixed-effects that involve count data since that is the nature of the dependent variable. To run a multi-level model with a high number of zeros, [START_REF] Long | Regression Models for Categorical and Limited Dependent Variables[END_REF] suggests to classified these zeros into two groups. First, we have structural zeros with a probability, which represents companies that always have zero innovation counts, given that these companies structurally do not comply with the technological capabilities to innovate. Second, circumstantial zeros with probability may occur even though companies comply with the technological capabilities to develop innovations, they do not achieve their innovation goals at the end of the period, or because innovation was still underway at the time of the survey.

Following [START_REF] Lambert | Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing[END_REF], the ZIP technique can run a Poisson and a logit model simultaneously. The Poisson model allows us to find not only the circumstantial zeros but also the arrival rate or innovation count, while the logit model estimates the probability when firms do not innovate. Traditionally, this type of model can be generated from an approximation of a generalized linear mixed model by the maximum likelihood technique [START_REF] Wang | Multilevel Models: Applications using SAS®[END_REF] (see also [START_REF] Hur | Modeling clustered count data with excess zeros in health care outcomes research[END_REF] and [START_REF] Lee | Multi-level zero-inflated poisson regression modelling of correlated count data with excess zeros[END_REF]).

In multilevel models, the variables are expressed in a linear system of equations as below4 .

(1) (2) (3)

Where represents the count of innovation for firm i (level 1) operating in sector j (level 2) and headquartered in region k (level 3). is a vector of variables at the firm level, represents the intercept in the first level that changes according to the sector's determinants , and is the intercept in the second level which varies according to the region determinants . Integrating equations 1, 2, and 3 gives us:

(4)

This model is similar to an ordinary linear regression model with fixed effects and random coefficients .

The maximum likelihood (ML) method is commonly used to estimate multilevel models. The ML technique is generally robust and gives estimates that are asymptotically efficient and consistent [START_REF] Hox | Multilevel Analysis: Techniques and Applications[END_REF]. The advantages and limitations when using multilevel models are generally associated with the quality and the structure of the data. As the innovation process happens at different levels, there are some unobserved conditions by the model which is also known as unobserved heterogeneity. The differences between firms, sectors, and regions are unknown by the model. Multilevel models with random parameters and mixed effects assume, however, that the unobserved individual-specific heterogeneity is unrelated to the explanatory-variable vector. By considering the hierarchical structure of the data, multilevel models prevent type I errors and aggregation biases which consist of making statistical inferences at the individual level from aggregate data [START_REF] Wang | Multilevel Models: Applications using SAS®[END_REF]. Notes: The ISIC level belongs to the sector level and CD to the regional level.

EMPIRICAL FINDINGS

Two scenarios have been used to test both hypotheses. In the first scenario, the economy is closed and therefore the model includes ten variables at the firm level, three at the sectoral level, and five at the regional level. In the second scenario, there is an open economy and therefore the model includes the same variables as the first model plus the OEV variables: three OEV at the firm level, two at the sectoral level, and one at the regional level were added.

After running the first model under the assumption of a closed economy, we can identify in Table 4 that nine out of the ten firm-level variables are significant. We find that that the percentage of the variable of national private capital invested in R&D and personnel with an associate degree that involves R&D are negatively associated with innovative productivity of firms. In addition, in the second level, two out of three variables are significant. The sectors with more intensity in R&D and a high level of knowledge intensity influence in a positive way the innovative performance of industrial manufacturing firms. Previous studies such as [START_REF] Savrul | The Effect of R&D Intensity on Innovation Performance: A Country Level Evaluation[END_REF] and [START_REF] Zawislak | Technological intensity and innovation capability in industrial firms[END_REF] have also confirmed that sectors with more R&D and knowledge-intensive have positive effects on innovation. Finally, at the third level, all five variables are significant. Two of these variables such as distance to the capital and research groups have negative effects. First, [START_REF] Concilio | Cities as enablers of innovation[END_REF], [START_REF] Florida | The city as innovation machine[END_REF][START_REF] Rammer | Knowledge proximity and firm innovation: A microgeographic analysis for Berlin[END_REF] have explained that capital cities are hubs of science and technology. Hence, considering the results companies that are more distant from capital cities tend to innovate less. Second, in Colombia, R&D activities are supported by research groups and universities. The latest report of the Colombian Ministry of Science, Technology, and Innovation (2020) shows that on average only 5% of the research groups are involved in high intensive technology sectors while social sciences and education reach 37%. Therefore, the interpretation of the negative effect that research groups bring to innovation performance to manufacturing firms has reflected to some extent in the lack of technology-oriented research groups.

After running the second model with the assumption of the open economy, firm-level OEV in Table 4 is significant. However, from the multilevel perspective, some variables are different from the expected results. For example, companies with foreign capital have a decrease in the total count of innovation by times the expected number of companies with no foreign capital. It was expected that companies with more foreign capital would have a positive effect on the innovation count of firms. The interpretations can change according to the country's FDI agenda, according to the Colombian Central Bank for 2007-2008 the mining and oil extraction sector captured almost 50% of the total FDI, while the manufacturing industry only attracted on average 16.5% of the total FDI for the same years. Even though firms demand FDI, this investment does not go to the innovative sectors in the manufacturing industry hurting the innovations counts. Blanco-Estévez (2015) concluded that Latin American firms invest only 0,60 dollars per 100.000 dollars in income in R&D while emerging countries in Asia invest 17 dollars.

Additionally, if the percentage of private foreign capital invested in R&D was to increase one percent, the expected number of innovations would increase by a factor of . According to [START_REF] Morero | The role of public policies in promoting innovation and innovation complementarities in developing countries: the case of the Argentinian software industry[END_REF] in developing countries, local firms are not getting enough R&D investment from the local private sector. In this case, local firms will demand foreign R&D investment. Holding the rest of the variables constant, if the firm increases its proportion of foreign capital by one percent then the count of innovations will increase by a factor of .

The Schumpeterian hypothesis of size [START_REF] Schumpeter | The Theory of Economic Development: An Inquiry into Profits, Capital, Credit, Interest, and the Business Cycle[END_REF][START_REF] Schumpeter | Capitalism, Socialism and Democracy[END_REF] is proven right in both scenarios. Control variables such as networks, partner cooperation, patents, and intellectual property rights maintain a significant and positive relationship, complying with previous studies such as [START_REF] Baker | Innovation, Intellectual Property, and Development: A better set of approaches for the 21st century[END_REF], [START_REF] Balachandran | Networks and innovation: Accounting for structural and institutional sources of recombination in brokerage triads[END_REF], [START_REF] Galaso | Munich Personal RePEc Archive Collaboration Networks and Innovation : How to Define Network Boundaries[END_REF].

In terms of education, at the firm level, the model includes four variables. While holding the rest of the variables constant, if a firm hires one additional employee with a bachelor, master, and Ph.D. degree in both scenarios, firms will increase their innovations by a factor of and under closed and open economy, respectively. If a firm hires one additional employee with associate degree firms will increase innovations by a factor of and under closed and open economy, respectively. Furthermore, firms that hire one more employee in the R&D department with a bachelor's, master and Ph.D. degree in the scenario of an open economy, firms will increase their innovations by a factor of . Conversely, companies that hire one more employee in the R&D department with an associate degree the firm will decrease their innovations by a factor of and for a closed and open economy respectively. If we look closer at EDIT 2007-2008 bulletin only 0.1% of the personnel employed in the industry reached doctoral level; 0.4% had a master degree; 12% had bachelor's degree and 9.1% had an associate degree. Not to mention the 31,4% of the companies that could not access skilled personnel.

At the sector level, only two variables are significant. Sectors with a high level of knowledge intensity have positive effects in both scenarios. The intensity of R&D also generates a positive effect on the innovation counts. Nevertheless, the model does not show enough evidence to determine the impact of the OEV in the sectors. At the regional level, all variables are significant. Control variables such as distance to the capital and the number of active research groups have a negative relationship, which decreases the propensity to innovate. The unemployment rate, coverage in higher education, the commercial opening index, and the national investment in R&D keep a positive relationship.

Education plays an important role in the process of innovation, keeping the rest of the variables constant the model shows that if the coverage of higher education in the region increase by one percent the firms will increase the count of innovation by a factor of and under both scenarios closed and open economy respectively.

When the commercial opening index at the regional level increases by one percent, the firms will increase the counts of innovation by a factor of Even though the results of the commercial opening index of the region have a positive effect, it is important to mention that in Colombia high technology imports represented 19.8% while medium technology imports reach 35.7% for the years 2007-2008. On the other side, DANE showed that high technology exports in Colombia represented only 2,3% of the total exports which is low compared with the average in Latin America with 11%. The Colombian economy has a high dependence on coal and oil, as commodities represent almost half of the total exports. Table 6 in the appendix used it as robustness checks and shows the results for the three types of innovations. As seen, OEV still has a significant relationship with innovation performance. Our focus firm-level variables hold even after controlling for OEV variables in Table 6. We have also run the logit estimation for robustness in Table 7. Looking at our result running robustness checks in Table 6 and Table 7 we conclude that our findings are rather robust for alternative modeling strategies.

CONCLUSIONS

This study examines the role of education and the impact of open economy variables (OEV) on the innovative performance of Colombian manufacturing firms. Consistent with the expectations of Hypothesis 2, we find that the role of education is key for innovation performance and development. As the econometric model at the firm level shows a positive relationship between innovation and higher education, it is important to strengthen the link between universities and industry. Promoting university-industry collaboration will improve technological capabilities, the acquisition and the adoption of new knowledge and technology, R&D activities, and the development of new products. All these advantages can be obtained, if the governments apply the best policy agenda that stimulates university-industry linkage.

Even though there is a positive relationship between coverage in higher education and innovation performance of firms, the quality of education and the enrolment rate in Colombia needs to catch up with OECD country members. Despite the absence of evidence at the sectoral level, the model with OEV variables shows that there is a positive relationship with innovation counts at both regional and firm-level. This confirms that that trade and foreign direct investment have a positive impact on innovation through knowledge and technology transfer to local firms. Furthermore, our findings are supportive of Hypothesis 1. Even though there is a significant relationship between the dependent variable with open economy variables, the interpretations may bring different insights. According to the results, we can conclude that even though firms have a percentage of foreign direct investment, it does not necessarily mean that it positively influences innovation unless firms allocate a fraction of these FDI flows in R&D activities. At the regional level, since the commercial opening index of the region is significant, we can conclude that foreign trade has a positive impact on the innovation performance of firms. This positive impact is related to technology transfer. Despite the positive impact of foreign trade on innovation, Colombia must strengthen the technological capabilities to boost high technology exports.

After analyzing the education and foreign trade variables. We can conclude that Colombia has a fragmented IS with a weak institutional structure, and low interaction between policymakers, industry, universities, research centers, and other components and building blocks of the system. Given de complexity of the behavior of IS in emerging economies, Colombia needs to align its economic development agenda. Promoting science, technology, and innovation policies without leaving out the environmental factors, the population's welfare, and development. Following the same research line of innovation systems in emerging economies, different research questions for future studies are also arising. For example, how can we measure university-industry cooperation in Colombia? How can we evaluate the technological capabilities of the Colombian system? What is the performance of innovation in other sectors such as agriculture and services? What are the impacts of digitalization on innovation performance?

  Employees with associate degrees involve in R&D divided by the total employees. Source: EDIT 2007-2008. (Standardized) Intellectual property and patents. Summation of all types of intellectual property and patents that the company reported. Source: EDIT 2007-2008. (Standardized) Foreign R&D Financing. The total of own, foreign, and public resources divided by the total of foreign resources invested in R&D. Source: EDIT 2007-2008. (Standardized) 2 Knowledge intensity: High. According to the Gera and Masse classification (1996). Source: DANE Methodology Indicators of Industrial Competitiveness by Intensity of Knowledge. (Dummy) The intensity of knowledge: Low. According to the Gera and Masse classification (1996). Source: DANE Methodology Indicators of Industrial Competitiveness by Intensity of Knowledge. (Dummy) Intensity of R&D. Amount of large companies that invested in R&D is divided by the number of companies that invest in R&D in the sector. Source: EDIT 2007-2008. (Standardized) Sectors with foreign capital. The number of companies with foreign capital is divided by the number of companies in the sector. Source: EDIT 2007-2008. (Standardized) Commercial Opening Index of the sector. It is the average of imports plus exports as a share of GDP for the years 2007-2008. Source: DANE, Competitiveness indicators, foreign trade. (Standardized) 3 Unemployment rate by department Average unemployment rate by department (2007-2008) Source: DANE, labor market. -2008 of the higher education coverage rate. Source: Ministry of Education, SNIES (National Information System of Higher Education) Database. (Standardized) Commercial opening index of the region. It is the ratio between the average of imports plus exports and the GDP for the years 2007 and 2008. Source: DANE, foreign trade. (Standardized) National investment by region in R&D Average of the R&D Investment by the department for the years 2007-2008. Source: OCYT. (Standardized) Distance to the Capital. Kilometers away from the capital of each department of the region. Source: Google Earth. (Standardized) Research groups Average of active research groups between 2007-2008. Source: Observatory of Science and Technology OCYT. (Standardized)

Table 2 . Descriptive statistics of the total count of innovations

 2

	Variable

Table 3 . List of independent variables by level

 3 Employees with Ph.D., Master, and Bachelor degree involve with R&D divided by the total employees. Source:EDIT 2007-2008. (Standardized)

	Level Variables			Description
	1	Firms with foreign capital.	Companies with more than 25% of foreign capital will be considered a foreign company, this
					variable is binary where 1 are foreign companies and 0 otherwise. Source: EDIT 2007-2008.
					(Dummy)
		Size.			According to the number of employees, the average is taken between 2007-2008. Source: EDIT
					2007-2008. (Standardized)
		Percentage	of	national	The total of own, foreign, and public resources divided by the total of private resources invested in
		private capital invested in	R&D. Source: EDIT 2007-2008. (Standardized)
		R&D.
		Percentage of foreign private	The companies that within their total capital have a percentage of private foreign capital invested in
		capital invested in R&D.	R&D. Source: EDIT 2007-2008. (Standardized)
		Internal Networks.		The companies' departments that participate in innovations developments, internal networks that
					the firm used over the total of networks (Int + Exter). Source: EDIT 2007-2008. (Standardized)
		External Networks.	External networks (clients, suppliers, universities, chambers of commerce, etc.) that the firm uses
					over the total of Int + Exter networks. Source: EDIT 2007-2008. (Standardized)
		Partner cooperation.	If the company had partner cooperation or not. Source: EDIT 2007-2008. (Dummy)
		Level	of	education:	Employees with Ph.D., Master, and Bachelor degrees are divided by the total employees. Source:
		Bachelor, Master, and Ph.D.	EDIT 2007-2008. (Standardized)
		Level of education: associate	Employees with associate degrees are divided by total employees. Source: EDIT 2007-2008.
		degree.			(Standardized)
		Level	of	education:
		Bachelor, Master, and Ph.D.
		involve in R&D.
		Level of education: associate
		degree involve in R&D.

Table 4 : Results of the multi-level Zero Inflated Poisson ZIP model

 4

	VARIABLES	Poisson without OEV	ISIC	CD	Poisson with OEV	ISIC	CD
	Observations	5,273	5,273	5,273	5,273	5,273	5,273
	Number of Groups		64	32		64	32
	Constant	2.292*** (0.075)	0.991*** (0.113)	1.024*** (0.037)	2.295*** (0.105)	0.980*** (0.115)	1.023*** (0.037)
	Firms with foreign capital				-0.180*** (0.026)
	Foreign R&D Financing				0.028*** (0.002)
	Percentage of foreign private capital				0.0134***
	invested in R&D				(0.000)
	0Size	0.104*** (0.002)			0.112*** (0.002)
	Percentage of national private capital	-0.087***			0.151***
	invested in R&D	(0.004)			(0.020)
	Internal Networks	0.065*** (0.007)			0.060*** (0.007)
	External Networks	0.022*** (0.006)			0.018*** (0.006)
	Partner cooperation	0.095*** (0.011)			0.100*** (0.011)
	Level of education: Bachelor. Master and	0.132***			0.128***
	PhD	(0.005)			(0.005)
	Level of education: associate degree	0.022*** (0.006)			0.031*** (0.006)
	Level of education: Bachelor. Master and	0.006			0.007*
	PhD involve in R&D	(0.004)			(0.004)

Table 6 : Results of the multi-level Zero Inflated Poisson model for innovation types

 6

				Radical			Incremental			Strategic
	VARIABLES		Innovations	ISIC	CD	Innovations	ISIC	CD	Innovations	ISIC	CD
				with OEV			with OEV			with OEV
	Observations		5.273	5.273	5.273	5.273	5.273	5.273	5.273	5.273	5.273
	Number of Groups			64	32		64	32		64	32
	Constant			1.150*** (0.234)	-1.283*** (0.389)	0.123** (0.0479)	1.222*** (0.235)	-1.479** (0.602)	0.123** (0.0501)	0.529*** (0.194)	-1.406*** (0.463)	-0.181*** (0.0527)
	Firms with foreign	0.0400			-0.584***			0.118*
	capital			(0.0384)			(0.0586)			(0.0616)
	Percentage of foreign private capital invested in R&D	0.0165*** (0.00140)			0.0147*** (0.00113)			-0.00944*** (0.00124)
	Foreign	R&D	0.0439***			-0.0484***			0.00796
	Financing			(0.00273)			(0.00957)			(0.00768)
	Size			0.0954*** (0.00402)			0.101*** (0.00602)			0.252*** (0.00730)
	Percentage of national private capital invested in R&D	0.261*** (0.0300)			0.0316 (0.0243)			-0.154*** (0.0240)
	Internal Networks		0.136*** (0.0109)			0.158*** (0.0205)			0.230*** (0.0236)
	External Networks		-0.0203** (0.00986)			-0.0606*** (0.0165)			0.107*** (0.0188)
	Partner cooperation	-0.243*** (0.0164)			0.0727*** (0.0235)			0.0323 (0.0285)
	Level of education: Bachelor, Master and PhD	0.0929*** (0.00855)			0.290*** (0.0117)			0.0639*** (0.0157)
	Level of education:	0.189***			-0.0293**			-0.0113
	associate degree		(0.00855)			(0.0146)			(0.0173)
	Level of education:
	Bachelor, Master and	0.0302***			0.00143			-0.00700
	Ph.D. involve in	(0.00596)			(0.00865)			(0.0106)
	R&D
	Level of education: associate degree involve in R&D	-0.306*** (0.0107)			-0.119*** (0.00991)			0.0503*** (0.00945)
	Intellectual property	0.0109**			0.0186***			0.0103
	and patents			(0.00549)			(0.00601)			(0.00845)
	Knowledge intensity:	-0.0276			-0.146			-0.335*
	High			(0.207)			(0.208)			(0.171)
	Intensity		of	0.0297			-0.0962			-0.176
	knowledge: Low		(0.255)			(0.280)			(0.211)
	Intensity of R&D		0.0472 (0.128)			0.130 (0.139)			-0.0557 (0.105)
	Sectors with foreign	0.00602			0.0199			0.0350
	capital			(0.142)			(0.143)			(0.109)
	Commercial Opening	0.115			0.0319			0.0325
	Index of the sector		(0.0743)			(0.0707)			(0.0574)
	Unemployment rate	1.464***			0.434			0.328
	by department		(0.325)			(0.335)			(0.274)
	Coverage in higher	-0.205			-0.0571			-0.183*
	education			(0.161)			(0.163)			(0.107)
	Commercial opening	-0.194			-0.0834			-0.0595
	index of the region		(0.148)			(0.149)			(0.107)
	National investment	0.321			0.347			0.0159
	by region in R&D		(0.248)			(0.252)			(0.184)
	Distance	to	the	-0.0490			-0.150*			0.0394
	Capital			(0.0860)			(0.0910)			(0.0667)

Table 7 : Results of the Logit model for innovation types

 7

	VARIABLES	Logit without OEV	ISIC	CD	Logit with OEV	ISIC	CD
	Observations	5,273	5,273	5,273	5,273	5,273	5,273
	Number of Groups		64	32		64	32
	Constant	0.602*** (0.208)	-1.596*** (0.283)	-14,18 -161,228	0.450* (0.259)	-1.642*** (0.297)	-21,88 -340000000000
	Firms with foreign capital				-0.338 (0.267)
	Percentage of foreign private				-0,007
	capital invested in R&D				(0.006)
	Foreign R&D Financing				-0.127 (0.092)
	Size	-0.414*** (0.067)			-0.408*** (0.067)
	Percentage of national private	0,010			-0,069
	capital invested in R&D	(0.047)			(0.118)
	Internal Networks	-1.421*** (0.0454)			-1.422*** (0.045)
	External Networks	-0.698*** (0.042)			-0.694*** (0.042)
	Partner cooperation	-0.713*** (0.118)			-0.705*** (0.118)
	Level of education: Bachelor,	0.157***			0.155***
	Master and PhD	(0.053)			(0.053)
	Level of education: associate	0,0544			0,0534
	degree	(0.048)			(0.048)
	Level of education: Bachelor,	-0.837***			-0.834***
	Master and PhD involve in R&D	(0.0905)			(0.0906)
	Level of education: associate	-0.170***			-0.170***
	degree involve in R&D	(0.0537)			(0.0539)
	Intellectual property and patents	-0.118 (0.0874)			-0.120 (0.0869)
	Knowledge intensity: High	-0,0463 (0.144)			-0,0116 (0.176)
	Intensity of knowledge: Low	0.103 (0.184)			0,0932 (0.183)
	Intensity of R&D	-0,0252 (0.102)			-0,0206 (0.107)

Random coefficient models, variance component models, hierarchical linear models, mixed effect models, and so on(Hox et al.,

2017).

DANE defines radical innovations as new goods or services; incremental innovations as goods and services that are significantly improved and strategic innovations are new organizational methods applied to management and production processes.

Usually, multilevel models have cross-level interaction effects. To have a deeper understanding of these effects, we refer toGelman and Hill (2007) and[START_REF] Hox | Multilevel Analysis: Techniques and Applications[END_REF].

Appendix