Analysis of the Growth in the Number of Patents Granted and Its Effect over the Level of Growth of the Countries: An Econometric Estimation of the Mixed Model Approach

Abstract

The purpose of this paper is to identify and measure the impact of the variables affecting the increase in the number of patents as a way to advance the development of policies in countries in terms of sustainable development based on innovation. An econometric estimation of a mixed model was used to measure the impact of patent development on the countries analyzed in this research. The findings suggest that economies that have some relevance in research and development have increasing numbers of patents. Thus, the empirical findings relate to the theoretical models that state that comparative advantages may be dynamic due to technological innovation. Finally, this paper shows that innovation is a central parameter to engage in research and develop a knowledge-based economy.

1. Introduction

Economic growth processes are predominant in state policies, such as the possibility of solving current social problems and economic problems; therefore, the priority is their link to activating economic growth. The stimulation of innovation, development and investment are key issues in the needs and efficiency of contemporary challenges [1].

The research of Pinto and Taixeira [2] shows the results research and the link between growth with (a) the result of holistic research in a positive and significant way impacts on economic growth; (b) both the academic knowledge of the scientific areas that most resemble capital goods (physical sciences, engineering, and technology, life sciences or social sciences) or final goods (clinical, preclinical and sanitary basis or arts and humanities) promoting economic performance; (c) the overall impact of research output is particularly high in the fields of engineering and technology, social sciences and physics; and (d) the impact of research results on economic growth is mainly through processes of structural change involving the reallocation of resources to the industrial sector.

Another variable linked to research and development and economic growth, according to [1], is that the impact is much greater on well-developed economies under conditions of sustainable economic development and globalization. According to [3], the impact of aggregate R&D spending on economic growth follows an inverted U-shaped curve because the analysis presented by the research is based on what they call the Swedish paradox, in that most research indicates that R&D leads to innovation, which leads to economic growth, but some academics have a different opinion, indicating that high investment in R&D will not bring high economic growth, although according to [4], based on a study conducted in China, innovation has a lagging impact on economic growth. According to Alibekova et al. [5], despite the strong efforts of the government of Kazakhstan in building innovation infrastructure, there is a low level of innovation activity.

According to [6], public investment in innovation and development (R&D) could boost growth and well-being, in the productivity associated with a country or region, according to [7], for [8,9]. Additionally, according to [10], science and technology innovation factors have a strong multiplier effect on regional economic development; hence, the input of new type of a practical patent significantly improves the regional economic level in the current period, and the lag phase effect is further improved.

Innovation and development have an impact on the competitiveness, innovation, growth and production [11] of countries, especially when markets change and become turbulent [12]. Ref. [13] makes an observation indicating that additional public R&D encourages private R&D and productivity, and that higher internal rates of return are generated by private R&D changes and could therefore accelerate growth.

Innovation and development in OECD countries imply a positive link [14]. Additionally, investment in R&D is related to corporate income taxes within certain levels according to [15] and the relation between publications and R&D expenses is linked by optimal thresholds [16].

Factors related to innovation systems have a considerable impact on organizations, which is generally identified in Latin American countries, and recognition processes and ways of doing innovation can be explained by the complexity of the conditions under which they arise [17]. There are factors that are considered the basis for R&D [9], such as the number of patent applications (per million inhabitants), high-tech exports (% of exports) and the number of articles in technical and scientific journals (per million inhabitants). According to [18], it is proposed that there is a mutual dependence between innovations through the number of patents and countries’ economic performance measured by GDP [19].

Countries are characterized by different levels of developed technology, which is the main factor revealing their different competitive patterns and long-term economic divergence [20,21]. Therefore, the incentive for R&D and consequently for patenting and publications is a factor that would allow a greater growth and production of such countries.

For granting of licenses, the possibility of higher innovation under licensing compared to no licensing decreases; in this case, the companies’ heterogeneity is crucial to assess whether licensing incentives R&D cost-reducing investments [22].

According to [23], innovations are more concentrated than inventions, which in turn are more concentrated than production, gauged by employment levels. Moreover, innovations are concentrated in regions that already have high production and invention levels.

According to [24], countries rise in their economic scale, rise in R&D intensity and increase GDP income. In addition, Ref. [25] indicates that the indicators associated with R&D spending and the number of researchers have a statistically significant positive impact on states’ exports and have a positive effect on international market access when R&D includes international partners [26].

The paper [27] indicates that there are long-term equilibrium relationships in the panel data format, unlike the situations of countries and individual groups, between R&D and international trade. According to [28], there is a stable long-term relationship between technological innovation and its determinants (such as the digital economy, bank finance, R&D spending, GDP and financial risk, which according to [29] incorporates country risk).

Product cycle models also relate technology to international trade and provide an explanation for intra-sector trade [30]. Innovations in technology generate results that would be the source of a comparative advantage for a country. The first phase is carried out in more advanced countries, with higher per capital income and higher costs, creating new products and developing new processes. The paper [31] assumes that all developed countries have access to the scientific knowledge necessary for the creation of new products and emphasizes geographical proximity and market information in terms of external economies. According to [32], in the process of innovation building, special relations play an important part, the regional and local levels are emphasized because of the importance of actors’ interactions in the process.

Some authors link economic growth through sustainable energy-based innovations, so innovation that sustains energy savings would allow green economic growth [33]. Government policies promoting more knowledge complementarity and coordination between environmental fields will help promote more knowledge transfer, allowing more sustainable development [34].

Table 1. Variables used in the literature in relation to patents grants.

Concept	Relationship	Reference
Innovation Expenditure	R&D investment is shown across countries on a comparative basis as a % of GDP	Coccia [8], Baneliene and Melnikas [1], Basu and Getachew [6], Dobrzański et al. [9], Hu [35], Hudson and Minea [36], Bertrand [37]
OECD Member	Research shows that patent generation is linked to OECD membership, especially when mentioning R&D investments. Additionally, OECD membership is related to levels of research output	Baneliene and Melnikas [1] Ulku [14] Kapidani and Luci [38] Mtar and Belazreg [39] Choi and Zo [40] Mamede et al. [41]
Growth	The economy of the countries is linked to performance as measured by GDP and GDP per capita	Kijek and Matras-Bolibok [7], Klas [18], Simionescu et al. [19], Mitchell [24], Yuan et al. [28], Lechthaler [33], Coccia [15], Zanakis and Becerra-Fernandez [29], Baneliene and Melnikas [1], Jian et al. [4], Yu et al. [3], Breul [42]
Trade Openness	It is suggested that R&D implies a positive relationship in international markets and intra-industry trade, leading to comparative advantages	Ziesemer [13], Tsouri et al. [26], Das and Chatterjee [27], Vallina-Hernandez et al. [30], Coccia [11], Hammadou et al. [12], von Tunzelmann [20]
Geographical Area	Regions indicate the relationship between certain groups of countries, linked geographically, that allow the identification of the existence of interactions between them, which are related to the generation of innovation	Furman [17] Turkina et al. [43] Hajek et al. [32]
Scientific Publication	R&D relates to the generation of human capital that is capable of developing innovations, measured by the number of research outputs	Dobrzański et al. [9] de Frutos-Belizón [44]

corresponds to a list of variables used in the models developed in this research, which is set out below.

The purpose of the research is to identify and measure the impact of the variables affecting the increase in the number of patents as a way to advance the development in policies of countries in terms of sustainable development based on innovation.

This paper is organized as follows. Section 1 presents the introduction, which includes a literature review. The materials and methods are presented in Section 2. The results are shown in Section 3. Section 4 presents the discussion and conclusions of this research.

2. Materials and Methods

This research uses the total patent grants of 99 countries from 1996 to 2018, extracted from the WIPO database [45]. Based on this information, we build a dependent variable that shows the impact of each country’s policies on incentivizing innovation production measured by the number of patents granted within a country in a specific year; specifically, we measure the percentage change in the number of patents by the logarithm of the total patent grants per year.

Figure 1 shows the evolution over time of the granted patents of the countries in the sample. We can observe a sustained increase over time in the production of innovation, which indicates an increase in the capacities acquired by all countries for the development of new products focused on the development of innovation.

Figure 2 shows the evolution over time of the granted patents for the countries in the sample. We observe that the area associated with the Asian region corresponds to the region with the highest production, followed by the European continent and the North American region. On the other hand, the regions with the lowest production of granted patents are Africa and Latin America.

When analyzing the temporal evolution of the number of patents, by means of Figure 3, we can observe certain trends measured by geographic region. The Asian, Middle East and Latin American regions show the highest growth trends, while Eastern Europe and Africa show stagnation in the growth of the number of patents granted.

To measure the impact of policies on the number of patents granted, we consider a series of variables of influence according to recent literature that has been obtained from the database provided by the World Bank [46].

The first relevant variable is the logarithm of the GDP per capita, which allows a comparison of the impacts of percentage changes in income level between the different countries in the sample. The second variable considered is the expenditure on education as a percentage of GDP, which shows an approximation of each country’s policy on educational issues. R&D as a percentage of GDP corresponds to an approximation of the intensity that each country gives to research and development and its impact on innovation production. International trade as a percentage of GDP corresponds to an approximation of the level of interaction that the countries in the sample have with respect to other countries. Finally, the level of credit as a percentage of GDP shows the capacity of each country to leverage resources and its possible impact on innovation policies for each year of the sample.

On the other hand, we also consider the natural logarithm of the number of citable documents per country as an approximation of the effect of academic activity on innovation production; the data were extracted from the Scimago database [47], which is built on the basis of data from Scopus of April 2021.

Table 2. Correlation between the principal variables of the model.

Variables	ln(Patent)	ln(GDPpc)	ln(Cite)	R&D	Trade	Credit
ln(Patent)	1.000
ln(GDPpc)	0.610	1.000
ln(Cite)	0.693	0.889	1.000
R&D	0.671	0.685	0.727	1.000
Trade	−0.008	0.245	0.284	0.105	1.000
Credit	0.215	0.053	0.025	0.094	−0.229	1.000

shows the correlation between the main variables used in the research and Figure 4 shows the scatter plot between the variables under study. We can observe a high level of correlation between the natural logarithm of patents granted with respect to the logarithm of GDP per capita, the natural logarithm of generation of citable documents and the level of R&D expenditure, which justifies the incorporation of these variables into the model.

We can also observe that there is a strong correlation between GDP per capita and the natural logarithm of the number of citable documents and R&D expenditure, as well as a significant correlation between the natural logarithm of citable documents and R&D expenditure. These high correlations indicate potential multicollinearity problems, and therefore, the results should be treated with caution.

To estimate the functional relationship of the model based on Equation (1), we propose a mixed model to explain the response variable Y in terms of a set of explanatory variables (see [48,49]). The functional relationship of the model is defined as follows:

$$Y_{ij}={\beta }_0+\sum _{s=1}^S{\beta }_s{x}_{sij}+\sum _{k=1}^K{\tau }_k{t}_{kij}+\sum _{h=1}^H{\rho }_h{r}_{hi}+u_{i0}+{\epsilon }_{ij},$$

(1)

where $Y_{ij}$ corresponds to the dependent variable measured by measuring the number of patents granted from each country i over time j; ${\beta }_0$ corresponds to a baseline parameter of the model; and $\beta$ is a parameter vector that corresponds to the parameters related to macroeconomic variables that define the behavior of country i in period j. $x_{1ij}$ corresponds to the natural logarithm of GDP; $x_{2ij}$ corresponds to the natural logarithm of GDP per capita; $x_{3ij}$ corresponds to each country’s credit as a percentage of GDP; $x_{4ij}$ corresponds to each country’s education expenditure as a percentage of GDP; $x_{5ij}$ corresponds to the trade ratio of each country as a percentage of GDP; $x_{6ij}$ takes a value of 1 if the country is an OECD member, zero if it is not; $x_{7ij}$ corresponds to the logarithm of the number of citable documents; $x_{8ij}$ corresponds to R%D spending as a percentage of GDP;

On the other hand, $\tau$ is a parameter vector that corresponds to year dummies from 1996 until 2018 and is used as a control for the specific effect that a specific period may have had on innovation output at the global level.

Finally, $\rho$ is a parameter vector that indicates whether country i belongs to a specific geographical region and allows us to analyze the natural clustering of innovation production in specific areas of the world. $r_{1i}$ corresponds to the African region; $r_{2i}$ corresponds to the Asiatic region; $r_{3i}$ corresponds to the Eastern Europe region; $r_{4i}$ corresponds to the Latin America region; $r_{5i}$ corresponds to the Middle East region; $r_{6i}$ corresponds to the Northern America region; $r_{7i}$ corresponds to the Pacific region; and $r_{8i}$ corresponds to the Western Europe region.

For the estimation of the random factor of the mixed model $(u_j+{\epsilon }_{ij})$, we assume that $u_{0j}$ is orthogonal to ${\epsilon }_{ij}$. The random effect $u_{i0}$ corresponds to the change in level invariant in time associated with each country i that represents a change in the overall average ${\beta }_0$; ${\epsilon }_{ij}$ is a normally and independently distributed error term observed for country i in period j.

The structure of the variance of the model is as follows:

$$Var\left(\begin{array}{c}u\\ \epsilon \end{array}\right)=\left(\begin{array}{cc}G& 0\\ 0& {\sigma }_{\epsilon }^{2}R\end{array}\right),$$

(2)

where G corresponds to the variance-covariance matrix of u that represents the random portion of the associated country level model, and $\epsilon$ corresponds to a multivariate normal matrix with mean 0 and variance ${\sigma }_{\epsilon }^{2}R$. In the estimation procedure, the random factor u is not calculated directly, but we can characterize it by the elements of G, which are estimated from the average variance in the residual ${\sigma }_{\epsilon }^2$, and the variance in the residual is contained within R.

In principle, we are not interested in the innovation production of each country in particular, and we consider a random effect to be associated with each of the countries in the sample. The fixed part of the model represents the average behavior of the countries with respect to the innovation development phenomenon.

3. Results

This section presents the results of the econometric estimation of the mixed model defined as the estimation of the number of patents granted.

The four models estimated consider the following explanatory variables: (i) the logarithm of GDP; (ii) the logarithm of GDP per capita; (iii) level of credit as a percentage of GDP; (iv) expenditure on education as a percentage of GDP; and (v) international trade as a percentage of GDP, in addition to taking into account the fixed effect of the years. The case of the second specification incorporates (vi) membership or non-membership in the OECD group of countries. The third specification incorporates (vii) the logarithm of the number of citable documents and (viii) R&D as a percentage of GDP. Finally, the fourth specification considers the geographic region to which the observation belongs (ix–xv).

Table 3. Parameter estimate and the corresponding p-value (in parenthesis) of the indicated model, as well as statistical indicators of goodness-of-fit and significance.

	Model 1	Model 2	Model 3	Model 4
ln(GDP)	−14.59 **	−15.22 **	−13.12 **	−13.39 **
	(0.024)	(0.017)	(0.036)	(0.031)
ln(GDPpc)	14.58 **	15.07 **	12.74 **	13.01 **
	(0.024)	(0.019)	(0.041)	(0.036)
Credit	−0.000920	−0.00228	−0.00222	−0.00200
	(0.759)	(0.442)	(0.439)	(0.482)
Education	−0.0753 *	−0.0937 **	−0.101 **	−0.0960 **
	(0.084)	(0.029)	(0.014)	(0.020)
Trade	−0.00303	−0.00355 **	−0.00505 ***	−0.00580 ***
	(0.106)	(0.048)	(0.003)	(0.000)
OECD		4.772 ***	2.401 ***	1.436 ***
		(0.000)	(0.000)	(0.009)
ln(Cite)			0.820 ***	0.785 ***
			(0.000)	(0.000)
R&D			0.306 **	0.301 **
			(0.013)	(0.013)
Asiatic Region				2.412 ***
				(0.000)
Eastern Europe				1.775 ***
				(0.006)
Latin America				0.742
				(0.233)
Middle East				0.103
				(0.899)
Northern America				4.905 ***
				(0.001)
Pacific Region				1.861
				(0.191)
Western Europe				2.589 ***
				(0.001)
Constant	4.838 ***	4.442 ***	14.81 ***	13.44 ***
	(0.000)	(0.000)	(0.000)	(0.000)
log()
Var(Constant)	1.174 ***	0.925 ***	0.679 ***	0.542 ***
	(0.000)	(0.000)	(0.000)	(0.000)
log()
Var(Residual)	−0.357 ***	−0.362 ***	−0.382 ***	−0.383 ***
	(0.000)	(0.000)	(0.000)	(0.000)
LR test vs. linear model
${\chi }^2\left(1\right)$	1748.1	1788.0	1494.9	1354.2
$Prob>{\chi }^2$	<0.001	<0.001	<0.001	<0.001
N	1004	1004	1004	1004

p-values in parentheses. * $p<0.10$, ** $p<0.05$, *** $p<0.01$.

shows the results of the regression analysis for the four specifications that allow us to identify the effects of the dependent variables on granted patents. It is observed for all models that the scale effect, measured by the logarithm of GDP, has a significant and negative effect, indicating that larger countries tend to decrease their innovation output.

On the other hand, the effect of per capita income, measured as the logarithm of GDP per capita, has a significant and positive effect for all the estimated models. Measuring the level of income is a sign of the level of development of countries, which indicates that the higher the development of a country, the greater they tend to develop innovation as measured by patents granted.

Similarly, the effect of spending by nation on education, measured in terms of expenditure as a percentage of GDP, is significant and has a positive sign. This shows that the greater the relevance of education in a country, the more innovation production will be reflected and shows that education is a relevant variable in public policies when considering the development trajectories of countries.

The terms of trade of countries, measured in terms of transaction volume as a percentage of GDP, can indicate the technological interaction between countries. In this sense, countries with a higher level of exchange can internally incorporate the technologies of the countries with which they trade. For Models 2–4, this variable is significant and has a negative sign, showing that greater trade openness has an effect on the absorption of technologies and that this has a negative effect on the need to develop new technologies.

Membership in the OECD group of countries indicates the level of development of member countries. In principle, the more developed countries have greater installed capacity that allows them to have a higher level of innovation production. A positive and significant value is observed for Models 2–4, showing that the level of development of the countries has a positive influence on the production of granted patents.

The effect of scientific and applied research conducted in universities, research centers and companies can be captured by means of two specific variables. For Models 3 and 4, we can observe that the logarithm variable of the number of citable papers and R&D expenditure as a percentage of GDP is significant and has a positive sign; therefore, scientific and applied research is necessary for a greater impact on innovation production.

By analyzing the scale effect provided by GDP, the wealth effect provided by GDP per capita, and R&D investment policies, we can observe a related effect between R&D investment and the wealth effect of countries. In contrast, to what happens with larger, but not wealthy, countries, where their policies focus on other basic priorities and not on innovation. Therefore, interaction has been observed in the size effect, wealth, and innovation policies of the countries in the sample.

A relevant element of the analysis carried out in this research corresponds to the clustering effect that can be observed. In this sense, we can observe that, depending on the specific zone to which the country belongs, the relations of technological, commercial and scientific exchange differ. We can observe that the Asian, European and North American regions have a significant and positive impact, showing that the geographical area influences the development of innovation production.

When reviewing the specification of the models, whether it corresponds to an ordinary linear model or a mixed model, we can mention that the likelihood ratio test, which allows verifying the level of fit between the two models, shows that for all specifications, the null hypothesis is rejected; therefore, there are significant differences between the restricted model (ordinary linear model) and the mixed model, therefore, modeling based on a mixed model is preferred.

4. Discussion and Conclusions

In the literature, it is possible to observe two rather different styles of research in their attempts to assess the contribution of research and development (R&D) expenditures to economic growth: historical case studies and econometric estimates of production functions containing an R&D variable. There have been a number of detailed case studies of particular innovations tracing out their subsequent consequences [50,51]. Much can be and has been learned through such studies. They are, however, very data- and time-expensive, and are always subject to attack as not being representative since they tend to concentrate on prominent and successful innovations and fields. Thus, it is never quite clear what general conclusions one can draw on the basis of such studies. The econometric production function approach tries to meet these objections by abandoning the interesting detail of specific events and concentrating instead on total output or total factor productivity as a function of past R&D. The present investigation tries to be a contribution to the second option, that is, through econometric multivariate production mixed model functions, the impact of the variables affecting the increase in the number of patents as a way to advance the development of countries, will be quantified.

Thus, the patents registered between between 1996 and 2018 show an advance in patenting, in accordance with Figure 1, which implies an advance in the development linked to the generation and registration of applied research. This relates to [8], which links the R&D base to patent applications (per million Inhabitants).

Starting from Figure 2, clusters can be identified, which have been generated according to the number of patents, by geographical area, and the focus of patents in Asia and Europe is observed. In the case of Asia, clusters are related to what is specified by the cluster [4] Cluster generation was developed without applying a specific model and was generated only with the number of patents, since there is a focus on geographical areas in the generation of patents. For the authors [17,43], there is a focus on studies of regions linked to R&D, as their research focuses on considering regional sectors in the analysis.

In relation to the variables considered in the research, the correlation reflects a high relationship between the number of patents and GDP per capita, as stated [3], the citations that are made to publications, and the variable R&D according to [14]. According to the authors [18,19], the GDP variable is a reflection of the economy of the countries, allowing clusters to be generated according to a link with their economic development. In the case of the innovation variable, indicators have been proposed [20,21], such as the number of research projects and the number of patents granted because countries that invest in R&D expect greater growth and production through technological improvements generated by innovation processes.

The results of the statistical modeling of the evolution of the number of patents granted show the importance of incorporating variables associated with research and development, variables associated with the level of development, size of the countries and variables associated with the geographical area in which each country is located. Model 4 corresponds to the model that contemplates all the variables and shows a high level of significance, which implies that they should be incorporated for adequate modeling.

This research generates new lines for future work, such as identifying which areas of research and development mostly affect the level of growth of the countries and, through a cluster analysis, verifying findings on the territorial or cultural aspects that affect the interaction and production of innovation. On the other hand, as future research it would be important to study if the results obtained for each of the evolution of the study variables serve to predict the behavior of another variable, and check if they have a unidirectional or bidirectional character, for which it would be necessary to compare and deduce whether the current and past behavior of one of the series used in this research predicts the behavior of another series, for example, the causality of the variables for which their correlation was analyzed in this research could be analyzed in future research using the methodology described by [52].