To understand the intellectual property rights, it is necessary to review the Trade Related Aspects of Intellectual Property Rights (TRIPS) (WTO, 2019), specifically those who protect and strength the intellectual property rights to rise their appropriability.

The WTO Agreement on TRIPS constitutes an attempt to reduce the differences in the way of protecting these rights in the different countries of the world and of some of them to common international standards. It complies with the minimum protection that each government must grant to the intellectual property of the other WTO Members².

In this sense, Foray (2004) explains that the technological knowledge is different to the production of standardized goods and services. This difference is located in the non-exclusive and non-rival nature of knowledge consumption (Encaoua, Guellec & Martinez, 2006). Non-rival because it can be consumed by a large amount of people at the same time, and non-exclusive because it can be shared at a cost cero for most of the cases.

In this way, a strong Intellectual Property Right (IPR) is characterized by a strong system of appropriation of knowledge, where the imitation is difficult, and the exploitation of knowledge is high.

However, this strength in the IPR has some consequences such as the weak diffusion of knowledge (Aboites & Soria, 2008).

Because of the last, it is important to analyze the different instruments of knowledge appropriation, to be specific we analyze the instruments that are applied in the Mexican context, where the study is conducted. The Mexican legislation known as “Industrial Property Law” (DOF, 2018), recognize different IPR: patents, UM, ID, Industrial Secrets, Brands and Appellation of Origin. Although there are other IPR like copyrights in the “Author Copyright Federal Law” (DOF, 2018) and the Vegetal Variety in the “Vegetal Variety Federal Law” (DOF, 2012), nevertheless the most common IPR for the industries are patents, UM and ID.

Despite of the variety of IPR instruments, it is common for most of the industries to protect their knowledge by patents, UM and ID, mainly because brands are of public knowledge, appellation of origin cannot be imitated, and industrial secrets are not disposable in public databases. By another way, copyrights apply to a few industries (i.e., cultural and software), and vegetal varieties to a smaller amount of industries. In this sense, patents, UM and ID are in the Mexican case the most common IPR, and those, they will be taken for this study.

According to WIPO (2016), the patent system is designed to contribute to promoting innovation and the transfer and diffusion of technology, in favor of the inventors, the users of the inventions and to all the public. Once a state or regional office grants a patent, then the patent holder has the right to prevent a third party from exploiting the patent for a period of 20 years. In the form of compensation, the owner must release or disclose the invention to the public at the end of said period.

By another side, WIPO (2016) states that not all knowledge is patentable, therefore, requirements of: patentable matter, industrial application (utility), novelty, inventive step, disclosure of the invention. The first case refers to the impossibility of patenting exceptional cases, such as medical treatments. The second case refers to the practical industrial application. The third case refers to the fact that, in the invention, it must be observed a new feature so far not known in the body of knowledge. The fourth case concerns something that cannot be deduced by a person with general knowledge in the technical field in question. The last case refers to the fact that the invention, must be disclosed clearly and completely.

The rights conferred by a UM are similar to those conferred by a patent. WIPO (2016) states that utility model protection generally applies to minor inventions. Technical complexity and inventions expected to be marketed for only one period limited time. By another side, the requirement of “inventive step” to sometimes it is not contemplatedor is less rigorous.

One of the basic purposes protections of ID is to encourage design activity for the product elaboration. According to WIPO (2016), protection of ID that is contemplated in the laws only applies to designs corresponding to articles or products or that are integrated in them. This protection does not, therefore, prevent other manufacturers produce or do business with similar articles or products, this is due to the condition that in the latter it is not integrated or reproduced protected design.

The maximum term of protection for industrial designs varies between countries, and ranges from 10 to 25 years.

The use of patents, UM and ID has increased their usage as an appropria- tion mechanism, nevertheless there are some differences among industries and countries (Aboites & Soria, 2008). These differences are historical, Wyatt (1986) explains that in Japan the patent is a more important appropriation mechanism than in USA; Levin et al. (1987) explains that the differences in IPR mechanisms differ from one industry to another; Mansfield (1986) in his research find out that the propensity to patent is different from industry to industry.

In recent studies Encaoua et al. (2006) describes how the patent system can encourage the sequential innovation. Anton & Yao (2004) Shows that the value of disclosure is offset by the increase threat of imitation, these in scenarios where the property rights are weak. Heikkilä & Lorenz (2018) explains that the patents effects on the direction of technological change, productivity growth and welfare is disputable, and those the study of UM models is a necessary step to understand the knowledge production. Torres et al. (2016) study how the public grants have an impact on the patent activity and production, but it has no effects on the UM production, by another side the study shows that improving firm capabilities and combining them with public grants has an important effect on the UM production. Odman (2010) refers to UM as an alternative way to protect the patent system, remedying problems related to the appropriation of knowledge. Ribeiro & Shapira (2020) explains that patent system is a socially shaped institution, because it is the intersection between public and private interests.

The studies of ID and their IPR mechanisms are not new; Denicola (1983) signals the importance of copyright mechanisms to protectthe applied art and their differences from ID. By another perspective Reichman (1993) points out the importance of ID arguing that the realproblem that face some industries (mainly design industry, softwareand biogenetic) is the difficult to protect incremental innovation, thosea strong design law is indispensable to protect incremental innovations.

Frenkel (1999: 534), in addition explains that “industrial designersare currently faced with an intellectual property void: no matterwhere they turn –whether it is to copyright, trade dress, or design patent law- their work remains extremely difficult to protect”. Because theprotected features of designs must be in some way separable from thefunctional features that can be imputed to the product. Although thereare a few studies that remark the positive impacts of ID on competitiveness (Gemser & Leenders, 2000), there is a lack of studies pointing tothe effects of ID refered to IPR mechanisms.

Although the patents, UM and ID are different they remain been the best proxies to codified knowledge in most of the industries, and in most of the countries. In this sense, the different countries are mixtures of different kind of industries, especially in the developing countries, since there are some countries advocated to primary resources and other that are manufacturers. These differences point out to different dimension of the codified knowledge, starting from the different kind of variables and systems of innovation inside each country, in this case for Mexico.

There are different index and variables to measure the codified knowledge. In this study, we try to resume the main studies to understand the relations between codified knowledge and variables related to socioeconomic and research and development conditions.

Maybe the first study of codified knowledge was that of Schmookler (1952), where he proposes the patent as the main variable to measure the knowledge production in the economy. From this study there has been a discussion of the patent as a proxy variable for the codified knowledge, however it is the pioneering work to create new proxy variables or knowledge index in the actual state of art.

Griliches (1973; 1998) proposes a production function that uses as a proxy variable of knowledge the R&D expenditures combined with a stock of physical capital, that has as an output the production. Where one of the main problems were the market valuation of R&D expenditures to approach their effects on the national output.

Jaffe (1999) proposes a framework for the index in the economics of knowledge for the health public sector; he divides the index in three parts inputs (expenditures, use of particular organizational practices), outputs (papers, prizes, patents, new drug applications) and impacts (citations, expert evaluations, life expectancy, statistical analysis of healthcare expenditures, revenue growth, profitability). As it is seen, this view of Jaffe has three categories of variables including patents, its effects on socioeconomic variables and inputs for increasing the patenting activities.

Archibugi & Coco (2004) proposes the ArCo index to measure the knowledge, and this index is conformed by three variables 1) knowledge production (patent and scientific articles), 2) technological infrastructure (internet penetration, telephone penetration and energy consumption) and 3) human capital formation (enrollment in science and engineering, higher education tuition).

The World Bank (2008) presents two index, the knowledge index (KI) and the knowledge economic index (KEI), where the KI becomespart of the second index KEI, but both index has outputs between 0 and 10. KI is conformed of literacy, high school and professional, payment of fees and income, patents, scientific articles, telephones, PCs andinternet users. KEI is conformed of KI, tariffs regulatory quality andlaw authority. In this index, there are two main topics, the institutionalaspects integrated in the KEI index and the economic and social aspects related to codified knowledge.

In this sense, the different index and proxy variables are proposed in a specific context, where the measurement is possible or feasible, and in the major cases these measurements recognizes three categories or aspects that has to be taken into account for the relations between codified knowledge (patents, UM and ID), inputs for knowledge and effects of codified knowledge.

The variables described above are some of the most cited works on the measure of codified knowledge. However, the main problem is that these variables and index are only proxies, this means that the index and information depend on the availability of information on each country.

For this reason, the proposed model is shown in the Figure 1.

Figure 1
Proposed Model
Source: Own Elaboration.

The model in Figure 1, take into account codified knowledge in the form of patent, UM and ID, which means that take almost all the codified knowledge information. By another side, it takes into account effectvariables like population density, GDP per capita and gross fixed capital formation, which are some of the most important socioeconomic variables in Mexico. Finally, it takes into account the input variables such as public education Budget, S&T Budget, Public Labs, Research Centers, postgraduate degrees of excellence (research and professional degrees), staff dedicated to science and technology, national researchers, postgraduate scholarships, internet bandwidth.

The model describes two variable groups, one (the left side) thatshows the codified knowledge (Patents, UM and ID), but a second group (the right side) that shows the rest of variables. So that, there area double side effect, by one side codified knowledge determining the economic and education and scientific variables, but by another side, this model shows the effect of economic and education and scientifi cover the codified knowledge. In the model and the theory described above, there is a relation between codifi ed knowledge and input variables, as well as codified knowledge and effect variables, so the Figure 1 resumes all of these relationships.

The canonical correlation analysis is a multivariate model to find relationships between two set of variables. The model was propose by Hotelling (1936) to find the maximum projections for each set of variables in a linear way.

In this case it consist in a two column vectors X = {Patent, UM, ID} and Y = {population density, GDP per capita, gross fixed capital formation, public education Budget, S&T Budget, Public Labs, Research Centers, staff dedicated to science and technology, national researchers, postgraduate scholarships, internet bandwidth}. So, the target is to find linear transformations of scalars u1=aTx and v1=bTy that maximizes the relationship of the scalars.

(1)

It is common to replace the expressions xy^T, xx^T and yy^T by estimates from samples of the matrices X and Y, which gives as a result the canonical correlation.

(2)

Where R_xy, R_xx and R_yy are correlation matrices of the random variables x and y, and the correlation matrix is expressed as follows:

(3)

Therefore, the maximization problem is reduced to maximize the nume- rator in equation 2, which leads to solve the eigenvalues and eigenvector of the next equation:

(4)

Which gives a number of canonical correlations equal to the minimum number of variables in the vectors, for this case three dimensions which then are uncorrelated between them (an orthogonal condition for the solution).

Table 1
Variable Description

Source: Own Elaboration.

The canonical correlation analysis has been applied to a variety of problems in economics (from describing macroeconomic relations, to relations between macroeconomics and stock prices, to microeconomic problems), which at the time is not a new tool (it´s been applied since 1980s to economic problems), in this sense, here we propose to analyze the relationship between codified knowledge to input variables and effect variables.

Table 2
Correlations Between Variables

Source: Own Elaboration.

With the information in Table 1, the canonical correlation analysis was performed; the results are shown in the next section.