Theoretical approaches to scientific innovation, technological change in enterprises and economic development

The literary review regarding the main theoretical contributions on innovation and management of technological administration refers to the seminal ideas of Joseph A. Schumpeter, who highlights the central role of the “disruptive creation” of the entrepreneur in the process of economic development (^{Schumpeter, 1950}). This concept consists in highlighting the preponderant role played by the continuous waves of discoveries and innovations that occur among entrepreneurs with entrepreneurial spirit, and that allow them to obtain greater capacities and competitive advantages to position themselves with better market shares and even with temporary monopolies, by displacing the old production and organization schemes (^{Wernerfelt, 1984}; ^{Scherer, 1986}). According to this theoretical approach, innovation is the most relevant factor driving the economic growth and social welfare of a country or region (^{Mansfield, 1984}; ^{Griliches, 1986}; ^{Fagerberg, 1994}).

Until the 1970s, the predominant economic theory, based on neoclassical postulates, considered that technology was basically information and that its production process was exogenous to the economic system and innovative enterprises. This model of technological change conceptualized R&D as an isolated activity, carried out in research centers, and alien to market incentives. New technologies were considered public information and easily imitated. This model assumes that technology transfer is an automatic process without significant costs based on the “invisible hand” mechanism (^{Heijs and Buesa, 2016}).

An alternative theoretical model to the neoclassical linear model of technological change is the interactive or evolutionary model, developed in the 1980s, which implies radical changes for the technological management of companies or the design of technology policy by the public administration. Evolutionary theory is based on a strong critique of neoclassical theory. The evolutionary school censures neoclassical theory in the exogenous treatment of innovation as a determinant of growth. Likewise, this current of thought criticizes the simplistic neoclassical assertions that state that scientific information is a public good without cost, easily appropriable and that, ultimately, economic development tends towards a maximizing general equilibrium (^{Nelson and Winter, 1974}).

In evolutionary theory, technological change and economic growth are considered to be two interactive processes. Technological change is based on an evolutionary dynamic with gradual increases in technical efficiency, productivity, and process precision. This change occurs within a context with various agents and organisms of the system also known as the innovation ecosystem and the productive fabric, which develops and adapts from the technological capacities available in companies and R&D institutes, the conditions, opportunities, and business decisions (of entrepreneurs, engineers, and scientists) about future technological possibilities and their economic profitability (^{Dosi et al., 1994}; ^{Nelson, 2009}). Thus, technology transfer is a costly and cumulative process and follows historical trajectories of continuous change and improvement (^{Dosi, 1997}).

Increasing scientific complexity and interdisciplinarity demands innovation; companies and universities interact and cooperate in routines to improve their skills and technical capacities in environments of high tacit knowledge and difficult to code (Cohen and Levinthal, 1989; ^{Nonaka, 2008}; ^{Polanyi, 2009}). This demand for diversification in the different technological fields has become too costly in terms of time and financial costs for companies (^{Teece, 1992}). Thus, the set of actors involved in innovation cooperation processes includes companies, academic institutions, scientific laboratories, financial resource managers, intellectual property (IP) legal specialists, NGOs, and government agents (^{Nelson and Winter, 1982}).

In recent decades, the focus of the mission of universities in society has been radically transformed from being generators of basic research to actively participating in economic development (^{Etzkowitz and Viale, 2010}; ^{Stephan, 2012}). During the 1990s and early 2000s, the assessment of the impact and outcomes of university technology transfer focused on a multitude of factors including the economic outcomes of technological development (^{Roessner and Wise, 1994}; ^{Storper, 1995}; ^{Saxenian, 1996}); the generation of patents and radicalization of inventions (Henderson et al., 1998; ^{Shane, 2001}); and the role of government laboratories in the commercialization of technology (^{Kelley, 1997}; ^{Crow and Bozeman, 1998}).

Consequently, the literature has addressed the study of the series of agreements, licenses, start-ups, contracts, and conditions of use of intellectual property between universities, federal laboratories, and industry (^{Link et al., 2003}; ^{Lockett et al., 2005}; ^{Phan and Siegel, 2006}; ^{Siegel et al., 2007}). Other theoretical studies have also focused on technology transfer offices (TTOs) whose main function has been to facilitate knowledge transfer and commercialization through the licensing to industry of university inventions or other forms of IP (^{Colyvas et al., 2002}; ^{Friedman and Silberman, 2003}; ^{Siegel et al., 2004}; ^{Belenzon and Schankerman, 2009}).

Another series of studies have focused on analyses of flows of investment in research and development, and the positive impact on local economies of knowledge spillovers (^{Audretsch et al., 2005}; ^{Caldera et al., 2010}). In this manner, several studies indicate that public funding for university research has also been associated with higher levels of efficiency in TT (^{Etzkowitz, 2002}; ^{Powers and Mc Dougall, 2005}). In response, governments interested in fostering industrial activity and technological innovation have channeled significant public resources to universities and research centers. According to ^{Mowery and Nelson (2015}), higher levels of public investment in R&D lead to higher levels of discoveries with high industrial potential, implying a greater pool of protected inventions that can be commercialized through university technology transfer (^{Grimaldi et al., 2011}).

While some authors point out that the benefits of investment in research on economic development are not immediate and rather long-term (^{Feller et al., 1995}; ^{Heher, 2005}), it is also noted that the development of human capital and scientific and technological capabilities in a context of interconnected social networks is a relevant factor in the effectiveness of research and knowledge transfer (^{Autio et al., 1995}; ^{Lynn, 1996}; ^{Bozeman, 2000}).

A number of scholarly articles have examined the relationship between spending on intellectual property investments, patent enforcement and maintenance, and efficient university knowledge transfer (Carlson and Fridh, 2002; ^{Siegel, Waldman et al., 2004}; ^{Powers and McDougall, 2005}; Mc Devitt et al., 2014). Literature has also highlighted that strong patent portfolios help achieve sustainable competitive advantages and greater efficiency in the transfer of scientific research results (^{Nerkar and Shane, 2003}; ^{Schilling, 2010}).

Evaluation of performance in the transfer of research results

The academic literature has focused on analyzing the outcomes and productivity of research and development investment expenditures at three levels: (1) systematic; (2) university and its departments; and (3) scientific knowledge transfer units, e.g. TTOs.

The first level has focused on measuring the impact on industry and the national economy. In a seminal paper, Griliches (1979) proposes a methodology for estimating the impact of private and public expenditures on scientific research on gross product in the economy and in sectors with capital-intensive industries associated with knowledge. This author points out the need to mark differences between returns in basic and applied research, as well as the effects of knowledge transmission between companies—spillovers. For its part, ^{Heher (2005}, ²⁰⁰⁶⁾ estimates that the returns on investments in science and technology are positive and oscillate between 2% and 3% with delays of 10 years at the institutional level and up to 20 years at the national level.

At the second level are studies that have been carried out in various countries to measure administrative performance, productivity, and efficiency in universities and faculties. For example, ^{Glass et al. (2006}), analyzing data for 98 universities in the United Kingdom during 1996, indicate that ranges in efficiency levels have increased over a decade. In the United States, a wide range of academic articles have been developed focusing on the productivity of HEIs where the found variance in productivity is less than that observed in institutions in the United Kingdom. For example, ^{Reichmann (2004}) analyzes 118 American universities, finding that those with the lowest performance are only 32% less productive than the most efficient. This result reveals a greater degree of homogeneity in American universities than their European counterparts; on the other hand, Cobert (2000) in a study of the 24 main master’s degree programs in business administration in the United States showed differences of only 8% in educational efficiency. Finally, several studies including institutions in Canada (Mc Millan and Chan, 2006), Austria (^{Leitner et al., 2007}), Australia (^{Worthington and Lee, 2008}), among others, have also analyzed productivity and operational efficiency in higher education. The study in Canada analyzes 45 universities using the DEA and SFA methods, although it finds divergence of results in each method; on the other hand, it achieves consistent results in the order of the individual efficiencies of the universities. The study in Austria emphasizes that both large and small universities have efficiency levels, emphasizing that there is no simple scale level to determine establishment at the efficiency frontier. Finally, the study of 35 universities in Australia between 1998 and 2003 shows an annual growth in productivity of 3.3% mainly due to technological progress.

In a third group of studies, the main line of research revolves around the performance and productivity of technology transfer activities and the performance of TTOs. There are studies based on profit and loss (P/L) financial analysis of the technology transfer offices (^{Trune and Goslin, 1998}; ^{Abrahms et al., 2009}), and from the decade beginning in 2000, several studies use: (1) approaches based on production functions, and (2) the frontier production functions approach (^{Bonaccorsi and Dario, 2004}). While in the first case a function is constructed to estimate the average trend of the observations through the regression equation, in the second case, models are constructed based on an optimal reference point at the frontier. ^{Siegel and Phan (2004}) describe stochastic frontier analysis (SFA) and data envelopment analysis (DEA) as the two most widely used tools for carrying out this assessment.

While the DEA method uses linear programming to determine levels of efficiency, it is not limited by the assumptions linked to traditional parametric regression analyses, such as the assumption of independence between independent variables. These models incorporate organizational and external factors that directly or indirectly influence the performance of technology transfer. The other method recurrently used in the study of efficiency is the stochastic frontier analysis (SFA), which consists of a parametric model with two functions: (a) efficiency and (b) technical inefficiency (^{Aigner et al., 1977}; ^{Meeusen and Van Den Broeck, 1977}). The method estimates an efficiency boundary through the use of a production function and calculates the parameters of the production function through the use of regression. Being a parametric method allows constructing both hypothesis tests and statistical confidence levels.

Table 1 shows the main work carried out on the efficiency of university technology transfer and TTOs. The main input-output variables used in these models include research and development (R&D) expenses, licensing revenues, number of licenses, number of companies founded, royalties, number of research agreements, number of notifications of inventions, size of the TTO, intellectual property expenses, and patents applied and/or obtained. Each of the studies is detailed below, indicating methodology, sample, approach, and the combinations of variables used.

^{Thursby and Kemp (2002}) utilize the DEA method with the Malmquist approach, in order to track the change in total factor productivity by 112 units of TT in the USA in the period of 1991-1996. These authors use the size of the TTO and the income for federal R&D funding by science area as input variables; and industry funding income, number of licenses, license royalties, number of notifications, and patent applications as output variables. For their part, ^{Thursby and Thursby (2002)} applied a three-stage DEA model to 64 universities, evaluating in each phase the input variables that contribute to the growth of the output variables. ^{Anderson et al. (2007}) evaluated 57 universities during 2004; these authors used research expenditures as an input variable, and license income, number of licenses, number of options executed, number of start-up, and patents applied and granted with weighting adjustments as output variables. The results suggest that the total licensing revenues in 54 of the 57 universities analyzed could be increased by 659 million dollars, improving their efficiency indices.

There is a representative study using SFA evaluating TT efficiency in 89 universities in the USA between 1991 and 1996 (^{Siegel et al. 2003}). This study uses license income as a dependent variable and three independent variables: (a) disclosure of inventions, (b) number of personnel in the TTO, and (c) amount of legal expense associated with patents. In another study carried out by ^{Siegel et al. (2008)}, using SFA, 120 TTOs are evaluated in the United Kingdom and the United States, corroborating a lower efficiency in universities in the United Kingdom with respect to those in the United States.

Finally, some studies seek to take advantage of the complementary benefits of the two previous approaches. Thus, ^{Chapple et al. (2005}) applied both methods to evaluate the number of licenses in 98 universities in the United Kingdom, estimating a level of efficiency between 26% and 29% using SFA, and a range between 15% and 35% using DEA. This implies a significant margin of productive potential to reach the technical frontier. Meanwhile, ^{Glass et al. (2006}) also assessed the relative performance of technology transfer in UK universities using both SFA and DEA. They developed a two-stage model. In stage one, they used DEA for the initial efficiency assessment and identified inefficiency factors linked to environmental and management effects; while in phase two, they identified the statistical noise.

Most studies measuring the efficiency of technology transfer refer to universities in the USA. ^{Thursby and Kemp (2002}), ^{Thursby and Thursby (2002)}, and ^{Anderson et al. (2007}) use DEA to measure efficiency at each university; ^{Siegel et al. (2003}) apply the SFA method to study the factors that influence performance at the level of the overall set of universities observed. ^{Thursby and Kemp (2002)} identified 54 efficient universities out of a total of 81 universities, which represent 67% of the total. This study found positive variations in efficiencies over the period of 1991-1996. Efficiency showed an average annual growth of 7.9%, which could be divided into 0.4% of universities that managed to improve their productivity, and 7.5% as a result of the expansion of the efficiency frontier. On the other hand, ^{Anderson et al. (2007)} found only 7 efficient universities out of 54, which is equivalent to 13%. Both studies used the VRS (variable returns to scale) method. Four universities: Brigham Young University, California Institute of Technology, Georgia Institute of Technology, and Massachusetts Institute of Technology were identified as efficient by both studies.

The main difference in these studies of measuring efficiency in university technology transfer and technology transfer offices lies in the use as input or output of some variables. For example, while most studies use income for research as an input variable, ^{Glass (2006}) identifies it as an output variable. On the other hand, ^{Thursby and Kemp (2002}), establish the number of disclosures of inventions as an output variable to evaluate the efficiency of technology transfer from universities, while two studies, ^{Siegel et al. (2003}) and ^{Chapple et al. (2005}), define it as an input variable to measure the efficiency of the university technology transfer office. The reason lies in the process that leads to the disclosure of an invention by the faculty, and the role of the university technology transfer office.

These TTOs help encourage scientists to participate in their decision to disclose new discoveries, but in the end, it is the university faculties that have the power to approve whether the disclosure will be shared or not. It is only until the disclosure is done that the work of TTOs begins. Thus, the responsibilities of TTOs are to evaluate and value disclosure, intellectually protect technologies by applying for patent registration, sell licensing contracts for industry, collect royalties, and enforce contractual agreements with licensees. Therefore, disclosure is an input variable when the objective of the model is to measure TTO efficiency (^{Siegel et al., 2004}). On the other hand, disclosure should be considered an output variable in the efficiency measurement of University-Industry Technology Transfer (UITT) model.

On the other hand, ^{Anderson et al. (2007}) highlight the importance of comparative studies on efficiency indices of USA universities with respect to their counterparts in Canada, Europe, or Asia to determine sources of technological advantages in different geographies. This author anticipates similarities and discrepancies that USA universities have with other HEIs in different geographic regions. In addition, a group of countries with less developed UTT have also undertaken comparative studies to assess the productivity and efficiency of HEIs. For example, Agostini and Johnes (2009) analyzed the efficiency levels of universities in the United Kingdom and Italy, finding higher levels of productivity in the first country –(0.82 vs. 0.70) during the periods of 2002-2003 and 2004-2005. However, they also found that Italian universities improved their technical performance by approaching the efficiency frontier more systematically over the period than their English counterparts.

In another international study, ^{Zhang et al. (2011}) assess efficiency levels in 59 research institutes in China using the DEA method. The input variables used were expenditure on R&D, number of staff members, and equipment for science; the output variables were the number of postgraduate students, citations, and the number of international published articles. This study concludes that there were annual productivity increases of 12.5% between 1998 and 2005. On the other hand, using the same methodology, ^{Ali and Ahmad (2013}) measure the level of efficiency of 18 faculties at Qassim University in Saudi Arabia, indicating that the level of efficiency reaches on average of 68%, where only 3 faculties reach the maximum frontier level. In Portugal, ^{Monteiro (2013}) analyses 18 TTOs between 2007 and 2011, indicating that productivity grows in early stages of TT, e.g. notification of inventions and patent applications; however, it decreases in advanced stages, i.e. creation of spin-offs or new R&D agreements. Finally, developed countries, but only just beginning their formal processes at UTT, have also focused on measuring the efficiency of their TTOs. Thus, in a study in France, ^{Curi et al. (2015}) found that, while on average TTOs in this country have increased their productivity in the short term, newly created TTOs in medical school and hospital contexts show negative efficiency levels.

In Mexico, although studies to measure the efficiency of universities are limited (^{Güemes-Castorena, 2008}), a recent work combining the DEA methodology with that of artificial neural networks (ANN) evaluates 51 engineering faculties in Mexico in the period of 2003 to 2008. The study highlights a great dispersion between the most efficient units that reach 97% and the least efficient that achieve only 15% (^{Altamirano-Corro et al., 2014}).

In recent years, new approaches have been taken to measure productivity and efficiency. Thus, ^{Rossi (2014}) has incorporated new output variables to expand UTT results, including consulting contracts, development and training days, and public academic events. For its part, ^{Tseng (2014}) constructs a weighted index based on six input variables, such as TTO revenues, invention notifications, number of patent applications and grants, and number of licenses and startups created.

In summary and following the main theoretical works listed here, the following were chosen as input variables of the present model: research expenditure on R&D (^{Thursby and Kemp, 2002}; Thursby and Thurby, 2002; ^{Chapple et al., 2005}; ^{Anderson et al., 2007}; ^{Siegel et al., 2008}), number of professional employees employed at the TTO (Siegel et al., 2008; ^{Zhang et al., 2011}; ^{Monteiro, 2013}), and expenditure on intellectual property (^{Siegel at al., 2003}; ^{Chapple et al., 2005}; ^{Siegel et al., 2008}; ^{Monteiro, 2013}). As output variables: private expenditure on research and development and number of private university-industry agreements for research and development (^{Thursby and Thurby, 2002}; ^{Thursby and Kemp, 2002}; Agostini and Johnes, 2009; Monteiro, 2013; ^{Rossi, 2014}). It should be noted that other variables including the number of invention notifications, and the number of and income from licenses were discarded in this model due to unsystematic and practically null reports in Mexico.

Finally, it should be noted that variables related to the quality of the faculty, such as age and size of the transfer office, although resources associated with the level of human capital and the degree of experience of the TTO, which are expected to be highly correlated with TT products, these effects and their relationships are considered as factors and not input or output variables in the construction of DEA models.

Sample

The subjects of this study are 21 TTOs and industrial liaison offices in Mexican HEIs. It is necessary to point out the existing delay in Mexico with respect to the creation of TTOs with respect to other countries. It is from the conformation of the network of TTOs promoted by the CONACYT and the Ministry of Economy (SE for its acronym in Spanish) in 2011 that the first certified offices are established in different academic, business, and governmental institutions in the country. This implies a delay of more than 40 years with respect to the first TTOs founded in the United States as a result of the Bayh-Dole Act. Hence, the collection of variables that have traditionally been used in other empirical studies on TT is problematic.

The main source of data came through 2 requests for information sent to 19 public research centers attached to the National Council for Science and Technology (CONACYT for its acronym in Spanish) and to 10 of the main public and private universities in Mexico that operate in TT. These requests were made through the portal of the Federal Institute of Access to Information (IFAI for its acronym in Spanish) during the months of March to May 2014, and April to June 2017. In the first request, complete responses were obtained at 21 HEIs, of which 62% had a TTO certified by the CONACYT. In the second request, complete responses were obtained at 19 HEIs where all academic entities except one have a TTO operating within the institution.

A second source of information is the database requested from the CONACYT on the Innovation Stimulus Program (PEI for its acronym in Spanish) for the years 2012 and 2013, which complemented the information on the number and total amount of R&D&i agreements between industry and academic institutions. It should be noted that the PEI is made up of three programs called Innovatec, Innovapyme, and Proinnova, which bring together the main source of resources for innovation projects in the country. A third source of information comes from the Mexican Institute of Industrial Property (IMPI for its acronym in Spanish), an office that was asked through IFAI the total amount of expenses issued by academic institution for the application, review, granting, and maintenance of patents. Finally, both the information concerning the GDP and the R&D intensity indicator by state were extracted from the page of the National Institute of Statistics, Geography and Informatics (INEGI). Table 3 shows the descriptive statistics of the data for the DEA and SFA.

Measurement of variables

Data were obtained in the requested survey for each HEIs and/or PRCs concerning: (1) private expenditure on R&D in millions of current pesos, which is transformed into its natural logarithm; (2) number of contracts between private companies and universities; (3) public expenditure on R&D in millions of current pesos, which is transformed into its natural logarithm; (4) expenditure on intellectual property by TT units in millions of current pesos, which is transformed into their natural logarithm; (5) size, by number of specialized employees of the TTOs; (6) information on whether the institution has a medical school; and (7) degree of regional intensity in R&D measured by degree of regional inventions by state over the national total.

Finally, following ^{Siegel et al. (2003}), a series of internal (organizational) and external (environmental) factors were identified as control and measurement variables for the technical inefficiency model equivalent to the degree of R&D intensity, the percentage of regional GDP, the public or private status of the HEIs, and the existence of a medical school in the academic institution (^{Siegel et al. 2003}; ^{Chapple et al. 2005}).

Design of econometric models

In order to carry out the analysis, two complementary models are designed in order to incorporate the set of explanatory variables selected from the technology transfer mechanisms, which include a set of internal institutional and organizational variables (input) and of results (output). In this way, the relative productivity of the university-industry technology transfer (UITT) units is estimated. Thus, this study focuses on the stochastic frontier analysis (SFA) method developed by ^{Aigner et al. (1977}) and ^{Meeusen and Van den Broeck (1977}), complemented by the DEA method. Each method is described in more detail below.

DEA is a method of frontier analysis from nonparametric statistics, which was originally designed to measure not only the financial performance of organizations, but to include other quantitative and qualitative elements of inputs and outputs that are related to efficiency (^{Charnes, Cooper and Rhodes, 1978}). The DEA method has been used to measure the performance and efficiency of operational indicators in productive units, ranging from small communities (^{Marshall and Shortle, 2005}) to countries and nations (^{Golany and Thore, 1997}). DEA uses linear programming algorithms to create a boundary of efficient units, which “envelops” other relatively less efficient units.

One of the main advantages of the DEA method is that it allows the absence of a formal specification of a functional relationship between inputs and outputs. In addition, DEA allows a wide variety of inputs and outputs to be used without assigning an a priori value judgment to the costs and shadow prices of these inputs and outputs (^{Charnes et al., 1994}). The DEA formulation evaluates the relative efficiency of a productive unit by estimating for each unit the measurement of weighted outputs over weighted inputs. There are several variants of DEA programs. The basic model for estimating the boundary with constant returns to scale (CRS) and output orientation can be formulated through the solution to the following mathematical expression:

Where:

xim is the quantity consumed by productive unit i of input m

yis is the quantity produced by the productive unit i of output s

vm is the cost of input m

us is the price of output s

The previous model is usually simplified through the following equivalent linear program:

s.a

The above algorithm looks for the set of prices that minimize the production cost of unit i with respect to the value of its product, subject to the minimum cost being equal to 1. If unit i is efficient, the cost = 1; if inefficient, the cost is greater than 1. The indices are presented as their inverse to indicate the degree of inefficiency of values less than 1.

The most realistic variable returns to scale (VRS) model incorporates an additional element or independent term ei; when ei > 0, it implies that the objective function does not pass through the origin. Only if ei = 0 does the objective function pass through the origin and CRS is assumed. In this way, the VRS model is expressed through:

s.a

A way of measuring product scale inefficiencies of an inadequate size of the productive unit can be expressed by the following:

Also, with the data panel, data envelopment analysis can be used as a program to measure productivity change over time. Fare et al. (1994) suggest changing the geometric mean of two Malmquist indices as a measure of the Total Productivity factor, one of which is based on the technology in period t and the other on the technology in period t + 1, or

½

K=t o k = t+1the distance functions d (.) are defined as

=max_ø, λᴓ subject to

y

subject to

The second model called SFA generates a frontier production (or cost) function with a stochastic error term consisting of two components: a conventional random error or “white noise”, and a term representing frontier deviations, which is equivalent to relative inefficiency. SFA is often contrasted with data envelopment analysis (DEA). In SFA, a production function is estimated as follows: yi = Xiβ + εi (5), where sub-index i denotes university i; product X the input vector; β the vector of unknown parameters; and ε an error term with two components. εi = Vi - Ui, where Ui represents a non-negative error term to account for technical inefficiency, or the remnant necessary to produce a product at the frontier, given the set of inputs used, with Vi being a random symmetrical error term. The standard assumption (Aigner et al., 1977) is that Ui and Vi assume the following distributions:

That is, the term inefficiency (Ui) is supposed to assume a semi-normal distribution, i.e. universities are established (1) “at the frontier” or (2) below it. Some model variants include zero-truncated, exponential, and gamma distributions. An important parameter in this model is γ = σ2u / (σ2v + σ2u), the ratio of the standard error of the technical inefficiency to the standard error of statistical noise, which is limited between 0 and 1. It is worth pointing out that γ = 0 under the null hypothesis of an absence of inefficiency means that all variance can be attributed to statistical noise. In recent years, SFA models that allow the term technical inefficiency to be expressed as a function of a vector of environmental and organizational variables have been developed. This is consistent with the idea that frontier deviations, which measure relative inefficiency in technology transfer units, are related to institutional and organizational factors. The model assumes that Ui are distributed independently with zero truncations of N (mi, σ2 u) distribution with mi = Ziδ (8), where Z is a vector of environmental, institutional, and organizational variables that, according to our hypothesis, influence efficiency, and δ is a vector of parameters.

In our case, the econometric programs LIMDEP.10 and NLOGIT.5 have been used to estimate the parameters of the β and δ vectors through the maximum likelihood estimation (MLE) method, and from the simultaneous estimation of the production function and the equation with the terms of inefficiency. On the basis of these parameter values, relative productivity estimates are calculated. The specification of equation (5) is based on the framework of the knowledge production function developed by ^{Griliches (1979)}, adapted here to the income and number of contracts between universities and industry, used as a proxy of the outcome of the technology transfer between university-company. Thus, a log-linear Cobb-Douglas production function is established for the revenue/number of contracts with three inputs:

Where PRIVEXP is the amounts of private expenditure between industry and academia annually; PUBEXP is the total public expenditure on R&D+i annually; PIEXP is the expenditure on intellectual property including patent application, search, and maintenance TTOSIZE equals the average number of specialized employees annually in the TTO, with the term technical inefficiency (Ui) expressed as follows:

Where ENV and ORG are vectors of environmental and organizational factors, respectively, and μ is the classic disturbance term. However, there is a lack of systematic measures of ORG (Siegel et al., 2003). The estimated equation contains only the following environmental/ institutional factors (ENV):

Where MED and PUBLIC are dummy variables indicating whether the university has a medical faculty, and INDRDij and INDOUTij are índices of intensity in R&D of the anual industry, and the average growth of real anual production in state (j) of University i, respectively, during the simple period of 2012-2013.

In the search to verify the continuity of the previous results, 2 models were elaborated with a new sample for the period of 2014 to 2016. In contrast to the first sample for the years 2012 and 2013, 19 complete and consistent responses were obtained from HEIs in Mexico. The 6 institutions that did not respond or were inconsistent with respect to the first sample were: Centro de Investigaciones Biológicas del Noroeste (CIBNOR), Centro de Investigaciones Avanzadas (CINVESTAV), Colegio de Posgraduados (COLPOS), Universidad Nacional Autónoma de México (UNAM), Instituto Tecnológico de Estudios Superiores de Monterrey (ITESM), and Instituto Nacional de Ecología (INEEC). However, 4 new institutions were added with respect to the first sample including the Instituto Nacional de Energías Limpias (INEL), Universidad Autónoma Metropolitana (UAM), Centro de Investigación Aplicada en Tecnologías Competitivas (CIATEC), and the Instituto Politécnico Nacional (IPN).

In these models, the dependent variable used was the number of academic-industry contracts during the reference period, and the following independent variables were estimated: public expenditure through the PEI program, reported expenditure on intellectual property, and number of employees in the TTO of the HEIs. Both the first binomial negative regression model of variable effects and the second data model of dynamic panels were estimated using the statistical program STATA 12, based on a balanced sample of 19 groups of HEIs with a total of 57 observations.