Moderate innovator trap – Does convergence of innovation performance occur in the world economy?

: Based on β and σ convergence analysis, we find high persistence of innovation gap for international innovation indices reported by the European Commission. Our research confirms the diverging scientific potential across the analyzed economies. On the other hand, estimation provides the evidence of convergence in case of R&D expenses and relative position on global technological frontier. We propose a simple fixed effect panel regression measuring relative innovativeness potential. Our model suggests that current ranking leaders i.e. Nordic countries (Sweden, Denmark and Finland) and Germany are likely to further outpace the United States. Central and Eastern Europe countries are achieving greatest relative gains, but are unlikely to exceed 70% of US potential. Peripheral Europe countries, South Africa, Turkey and Russia are projected to further lose innovativeness position, despite weaker initial position.


Introduction
An increasing research interest on the structural changes taking place in the world economy has been observed in the last years. In particular the emergence of high and medium-high technology industries in emerging markets, like China attracts greatest attention. The perspective of global growth convergence has begun to rise a question as developed economies are more and more based on the use of knowledge. The middle-income trap concept has been several times invoked [1], [2]. The idea highlights that developing economies have problems to exceed certain threshold of GDP per capita. The problem is commonly linked with exhaustion of benefits from imitating the solutions of the developed markets and lack of capacity to provide innovative solution.
In order to measure the level of innovativeness of different countries, the European Commission introduced the European Innovation Scoreboarda dataset consisting of 27 indicators describing e.g. scientific capabilities, Research & Development expenditure or intense of knowledge-rich activities. The studies analyzing trends in innovation potential of the European Union countries highlighted the divergence across regions. [3], [4]. This Paper extends the geographical scope of the research and includes other international economies scrutinized by the European Commission, aiming to answer the question if there is convergence in the world economy with respect to innovation performance of developed and developing countries.
We propose a simple fixed effect panel regression measuring relative innovativeness potential. Our model suggests that current ranking leaders i.e. Nordic countries (Sweden, Denmark and Finland) and Germany are likely to further outpace the United States. Central and Eastern Europe countries are achieving greatest relative gains, but are unlikely to exceed 70% of the US potential. Peripheral European countries, South Africa, Turkey and Russia are projected to further lose position comparing to other developed economies.
This paper is structured as follows: the next sections presents arguments arguing for possible divergence in the innovative activities. Section 2 describes European Commission Summary Innovation Indicesprobably the most comprehensive measure of various aspects of innovations. Secondly. It also presents methodology of our research and provides insight in different measurement techniques of convergence. Section 3 summarize results of the estimates. Section 4 discusses the results. Finally, section 5 concludes the paper.

Methods
During this section we introduce the European Innovation Scoreboarda ranking proposed by the European Commission to measure innovative potential of the EU28 economies as well as other international peers (including e.g. United States, Switzerland, Japan or China).
The innovative potential does not have a single measure. Most popular strain in macroeconomic theory associates innovation with a presence of national companies on the global technological frontier and achievement of the higher labor and multifactor productivity [5]- [7]. Firm level studies suggest that convergence is not always a case even in the developed economies. While [5] confirmed that the process of catching up exists based on UK industrial firms' data, numerous researchers provide evidence that technology gap between leading innovators and moderately innovative areas remains persistent in several industries [7], [8]. In a cross-country perspective, less productive firms tend to converge only towards the local (national) frontier rather than global one [9].
From the perspective of less developed countries, technological catch-up typically relies on Foreign Direct Investments (further FDIs) and their positive spillovers. Theoretically, technological transfer from developed economies with the labor turnover on emerging markets should improve human capital and regional potential output. Unfortunately, the FDIs are not costless and have their limitations. The most crucial barrier visible in the laggard countries is the lack of absorptive capacity [10]. Firms from developed countries typically shift the production to emerging states only for a product, where technical requirements are only slightly above current technological frontier of hosting economy [11]. There is often also a conflict of interest between needs of multinational companies providing capital and the native society needs. Authors highlight that an in-house Research and development (R&D) expenditures and motivations systems for domestic investments are required to benefit from foreign capital expenses [12], [13].
Another problem is related to regional system and network connections [14]. Knowledge intense industries are likely to cluster within narrow geographical areas. Numerous authors confirmed that intellectual property (PCT patents) is typically used by firms remaining in the geographical proximity to the inventor [15], [16]. Finally, more interconnected countries have greater capability to introduce and exports new products [17].
The European Innovation Scoreboard directly address all of the mentioned problems.
Therefore, we do believe the study should be most comprehensive and adequate to perform convergence analysis. The general summary innovation index for a European Union country is a synthetic indicator computed as an average of 27 subcomponents divided in the four pillars.
Due to the data limitations indices for international economies contains only 16 subcomponents.
The indices are reported annually typically in the middle of the year (June-July). The third pillar -Innovation activities (9 variables within EU, 8 internationally) is focused on three aspects. First aspect describes engagement of the Small and Medium Enterprises (SME) in the innovative activities. This group consist of two variablesfirst one describes product or process innovation second marketing or operational improvement. The data tables will use shortcut acronyms: respectively PP innovators and MO innovators, used by the European Commission. European countries report also whether innovative activities were done in-house or outsourced.
Secondly the survey promotes cooperation between entities and creating regional networks.
The three variables belonging to this aspect describes collaboration of SME enterprises, number of private-public partnerships co-publications per thousand inhabitants, and share of collaborative R&D expenses as a percent of the Gross domestic product (GDP).
The final aspect is dedicated to accumulating and using of intellectual property rights. Our aim is to determine whether cross-country convergence of innovation occurs. We introduce two measures of concurrences: β and σ [18], [19]. Secondly, we introduce simple relative models distinguishing between in-house innovative capacity and imitations [12].
The most popular concept of convergence (β) assumes that less developed countries/areas are growing more swiftly comparing to the more affluent peers. Let's denote as summary innovation index at the time t. We expect to see a positive relationship of average annual change during the period 2010-2017 and starting level 0 (index value at 2010).
Where 1 should take a negative value if convergence exist. On the other hand, a positive value of this parameter denotes divergence. We are going to repeat calculations for every single component creating summary innovation index.
Secondly, we also attempt to use another measure -σ-convergence. The idea of such indicator assumes that if convergence exists cross-country standard deviation should diminish over elapsed time. The downward trend should be visible, when using following formula.
We expect 1 parameter in equation (2) to have negative value, otherwise divergence occurs.
Similarly like in case of β-convergence the estimation will be repeated for all innovation index components.
Finally, subject literature tends to distinguish between capability of in-house innovation and imitations, we proposed a simple fixed-effects panel model: Where is a cross-country estimated fixed effect, The result of such exercise should present expected relative performance in case of no policy change scenario.

Results
This section discusses our findings on innovative capacity convergence. We proposed three measures determining if countries described as moderate innovators are catching up towards the innovation leaders.
The results of β convergence analysis is presented in the The estimate corresponding to the Summary Innovation Index does not differ from zero, suggesting quite persistent status quo between innovative potential across the countries. The analysis of subcomponents presents three major significant trends: 1) convergence of R&D expenditures in both business and public sector and related to them position of countries' production on the global technological frontier. 2) possible divergence of scientific potential with greater internationalization of research in developed countries.
3) The relatively stable position in case of using intellectual property rights (PCT patents, designs and trademarks) and SME activities, especially when it comes to product or process innovation.
The results of σ convergence analysis are available in the table 2. The data columns 2-9 contain cross country standard deviation observed in the subsequent years. Columns 10-11 present the estimated parameters. Column 12 answers if parameter 1 is statistically significant.  Model parameters are presented in table 3. Prob(F-statistic) 0 Periods included: 7, Cross-sections included: 31, Total observations: 217 Table 4 presents estimated cross-country fixed effects (column 2) and steady states (column 5). Similarly, to the results of β and σ convergence analysis minor changes are expected. On the other hand, peripheral Europe countries (Greece, Spain Portugal and Ireland) are projected to lose innovativeness position. The same problem is related to South Africa, Turkey and Russia despite their low initial position.

Discussion
Contrary to the research outcomes for the European Union countries [3], [4],

Conclusions
The research identified lack of convergence of innovative potential between countries.
According to the model the strong discrepancy between highly innovative North and less developed South of the European Union members is unlikely to vanish in the foreseeable future.
The problem is even stronger in comparison between developed and emerging economies. The uneven innovative potential is likely to limit growth opportunities in the emerging markets and solidify well-known middle-income traps.
Secondly, we identified strong divergence of scientific and research potential. This phenomenon may result in a problem of the brain drain i.e. migration of skilled individuals from the peripheral countries to the leading innovation centers in order to pursue career opportunities. The uneven distribution of skilled cognitive jobs is also likely to result in social tension between the regionssome prelude of this problem was already visible in the USA, where abandoned rust belt played decisive role in the election or France, where yellow jackets movement violently protested against inequality.
In order to prevent such events governments and international organizations such as the European Union should probably reconsider implementing deglomeration policies, aimed to provide incentives for multinational companies to diversify geographically knowledge intense activities. So far, such instruments were applied only regionallyfor example in post-war Germany.

Availability of data and materials
Data supporting the results reported in the article can be at the European Innovation Scoreboard a ranking proposed by the European Commission to measure innovative potential of the EU28 economies as well as other international peers (including e.g. United States, Switzerland, Japan or China).

Competing interests
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

Funding
The paper was prepared in the framework of the research project No 2016/21/B/HS4/03025 "Dynamics and factors of innovation gap between Poland and Chinainternational and regional dimensions", financed by the National Science Center, Poland.