The geography of technological innovation dynamics

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Predictions

Geographic proximity and country diffusion

We analyse technology code diffusion timing to study the role of physical and political geography in technological innovation dynamics. Consider the MA where a specific technology code t first appears. We define the Mean Time Distance as the average time distance between the first appearance of t and its other first appearances in other MAs. After averaging over all technologies, we aggregate this mean on different spatial distance ranges to analyse the relationship with physical geography. On the other hand, to consider political geography, we calculate the average on the subsets of MAs belonging or not to the same country. In Fig. 1, we report our analysis on the Mean Time Distance.

Two important observations are in order. First, for the overall set of MAs, the Mean Time Distance increases on average with the geographical distance, signalling an important role of geography in the diffusion of technological innovation. Second, the Mean Time Distance is always shorter for the subset of MAs belonging to the same country, and it does not show a strong dependence from the spacial distance until the scale $10^3$ Km. After this scale, we see how a dependency from the spatial distance is stronger but more fluctuating (growing and then decreasing). This evidence is probably due to the distribution of MAs’ distances, which are affected by seas and oceans. In fact, until the scale $10^3$ Km, the distribution of distances (presented in Supplementary Information) follows a power law with exponent $\sim 2$, corresponding to an isotropic distribution in two dimensions. After that scale, the seas and oceans break the isotropy assumption, making the distribution less predictable and ultimately affecting Mean Time Distance. But also in this range, the MAs couples from the same country show a way lower Mean Time distance. Therefore, we can consider political geography as predominant over physical geography in the dynamics of technological innovation.

Role of countries: an improved model

In works concerning similarity and forecast on bipartite networks, it’s common to compute the prediction using the links between the items layer (technology codes, in our case), i.e., using $\omega ^{tec}_{at}$. However, mathematically, we have seen that it is possible to calculate a similarity between the nodes of both layers, i.e., also considering $\omega ^{MA}_{at}$. In the work of Albora et al.⁵², the authors show how a mean between the two scores can outperform the standard method. They also propose a linear combination of item-based and user-based estimations, showing how this method outperforms the others. In our case, to get the prediction, we utilised this last method, computing a linear combination of technology and MA densities instead:

$$\begin{aligned} S^{y+\delta }_{at} = \alpha \omega ^{tec}_{at} + \beta \omega ^{MA}_{at}. \end{aligned}$$

(4)

where $S^{y+\delta }_{at}$ is the forecast for the year $y + \delta $. If we consider MAs with no patent in the year y, regardless of the similarities used, the predictions obtained from $\omega ^{tec}_{at}$ and $\omega ^{MA}_{at}$ will always be zero by construction. This outcome is due to the presence, in the rows of ${\textbf {M}}$ matrices related to those MAs, of only 0s. Given the relevance of belonging to a country unveiled through our previous results, we included that information to predict when a given MA will start patenting a specific technology for the first time. To this end, we define:

$$\begin{aligned} \omega ^{C}_{at} = \sum _{a’}{M_{a’t}^{y}\frac{C_{aa’}}{\sum _{a}{C_{aa}}}}, \end{aligned}$$

(5)

where $C_{aa’} = 1$ if a and $a’$ belong to the same country, 0 otherwise and $\sum _a C_{aa}$ is the number of MAs in the same country as a, inserted to avoid size effects. $\omega ^{C}_{at}$ represents the average values of technologies done by the MAs of a specific country. As explained in the Method section, the higher the value of $\omega ^{C}_{at}$ is, the higher the probability that $M_{at}^{y+\delta } = 1$.

Our prediction model is thus a linear combination of the three previous contributions: technology similarity, MA similarity and information on belonging to the same country:

$$\begin{aligned} S^{y+\delta }_{at} = \alpha \omega ^{tec}_{at} + \beta \omega ^{MA}_{at} + (1-\alpha -\beta )\omega ^{C}_{at}. \end{aligned}$$

(6)

Also in this case, the higher the value of $S^{y+\delta }_{at}$, the higher the probability to have $M_{at}^{y+\delta } = 1$. Because of the Autocorrelation problem explained in the Method section, we decided to evaluate our predictions on the so-called activation elements, i.e., the matrix elements $M_{at}^{y} = 0$ and that in $y+\delta $ could become 1.

In Fig. 2, we compare the prediction for $\delta = 10$ of the four metrics of similarity defined above. We also compare our model (continue curves) and classic models, i.e., models using the items-items similarity $\omega ^{tec}_{at}$ (dotted lines). We can see how our model curves outperform all the dotted ones. In Supplementary Information, we also report the analysis done by using $\delta = 1$ and $\delta = 5$.

If we consider MA with no technologies in y, both $\omega ^{tec}_{at}$ and $\omega ^{MA}_{at}$ are 0 by definition. In this case, the predictions of our models are only due to $\omega ^{C}_{at}$, which represents the influence of countries.

In this specific case, we compared our results (Model) against a null model (Rand) and a model based on the spatial distance (Dist) to validate our findings. The null model prediction for each MA is a redistribution of the predicted technologies in the whole vector of the technological codes. If, for a given MA, we predict (0, 0, 1, 0), the null model would predict (0.25, 0.25, 0.25, 0.25). On the other hand, the spatial distance model uses geodetic distances between MA as similarities. In Table 1, we compare, for different values of $\delta $, the models’ performances on technological debuts of MAs by summing the areas under the curves for all years. Our model, informed on country membership, is the most successful in estimating future technologies made by an MA with a null technology portfolio.

Table 1 Models comparison.

Model analysis

In this section, we analyse the behaviour of the best parameters $\alpha $ and $\beta $ over the years. For each metric, we show in Fig. 3a the optimal values of $\alpha $ and $\beta $ over the years considering $\delta =10$. In Supplementary Information, we have reported the same analysis for $\delta =1$ and $\delta =5$. In this figure, we can see a common trend. Both $\alpha $ and $\beta $ tend to stay constant till the end of the 90s’. After that, their values tend to increase, as all four similarity metrics predicted. This analysis is confirmed by the descending behaviour, in Fig. 3b, of the term $1-\alpha – \beta $, representing the importance of belonging to a country. These pieces of evidence suggest that political geography has been highly important for the diffusion of innovation till around two decades ago. After that, the evidence indicates that the overall ecosystem of MAs became more global and based more on similarities between technologies and MAs. At the beginning of our period of observation in our data, the country term $1-\alpha – \beta $ has a positive contribution, but around the end of the 90s’, it tends to decrease and even becomes negative. We interpret this result as a change in the dynamics of technological innovation in countries where the similarity between technologies and MA starts to become more important than belonging to the country itself. This is likely because, instead of following national trends, many MAs could have begun to copy MAs in other countries. This phenomenon can be explained by the loosening of institutional barriers to international mobility, with a resulting globalisation of labour markets. Thus, when we observe that the role that borders play is diminishing in the development and diffusion of new technologies, this is mainly due to the erosion of institutional frictions that hinder international connectivity⁵³ and the strengthening of global collaboration networks⁵⁴. Together with these mechanisms also the general market globalisation plays a role. In fact, the enhancement of competitiveness to a global scale probably creates collective dynamics, even when there is no cooperation but competition, instead. This will probably give rise to innovation trends diffusing at the global scale. These considerations imply that the development of new technology takes place simultaneously at the global level to win primacy in its production.

The paths to technological innovation

In this last section, we focus on technological innovation paths, i.e., the paths followed by countries and metropolitan areas towards technological innovation. Though diversification is a good proxy for progress to technological innovation, we need another metric to represent similarities between the countries’ development strategies. We define, in particular, a metric that quantifies how competitive a country c is in a specific technology code t in year y relative to other countries, based on the number of MAs in c that patent with that technology code. Similarly, we can quantify how competitive an MA a is compared to other MAs. For each country, we define the following:

$$\begin{aligned} G_{ct}^y= \frac{C_{ct}/C_c}{C_{wt}/C_w}, \end{aligned}$$

(7)

$C_{ct}$ counts how many MAs in the country c do the technology t, and $C_c$ is the number of MAs in the country c. $C_{wt}$ counts how many MAs are in the entire database patent with the technology code t, and $C_w$ is the total number of MAs. Therefore, $G_{ct}^y$ measures the fraction of MAs in c that do the technology t compared to the entire word for the year y. We define with $\bar{G}_{c}^{y}$ the vector that represents the average of $G_{ct}^y$ over all technologies t, and it represents the competitive position of the country c for the year y. Similarly, for each MA, we define the following:

$$\begin{aligned} G_{at}^y= \frac{M_{a\in c,t}}{C_{ct}/C_c}. \end{aligned}$$

(8)

and, similarly, $\bar{G}_{a}^{y}$ is the average of $G_{at}^y$ over all technologies t and it represents the competitive position of MA a for the year y. For every year, $G_{ct}^y$ and $G_{at}^y$ are vectors with 650 entries, corresponding to the total number of technologies. Using UMAP, we reduced the dimensionality to one and defined the similarity embedding. We found that this embedding is strongly anti-correlated with the modules of $G_{at}$ and $G_{ct}$ (see the Supplementary Information for further information). This evidence implies that the lower the similarity embedding, the higher the competitiveness of countries or MAs. We can thus use the similarity embedding as a reverse measure of competitiveness and plot the time evolution of each country and each MA in a two-dimensional scatter plot determined by the two quantities: similarity embedding (a reverse proxy for competitiveness) and diversification. We report the results in Fig. 4 for countries and Fig. 5 for metropolitan areas. Each point on the two plots is a pair country/year and MA/year.

We have highlighted the paths over time, followed by a selection of countries and MAs. Two typical patterns emerge that we denote as the “upper” path and the “lower” path. This pattern is particularly evident for countries. A country or MA that moves from left to right increases its diversification but not the competitiveness in the technologies that it does. Instead, movements from the upper part to the bottom are associated with growth in terms of competitiveness, keeping fixed diversification. The main difference between the two typical paths is the order of these movements. In the “upper” path, we first observe an increasing diversification and then an increase in competitiveness. In the “lower” path, the opposite occurs: first, an increase in competitiveness followed by a diversification increase. We coloured with different shades of the same colour the evolution of some countries belonging to the two typical paths.

Finally, to highlight the technology difference between the “upper” and the “lower” paths of both figures, we divided the diversification into ranges of size 100 (except the last one). For each range, we focus on the highest and lowest 25th percentile and aggregate the technologies to the 1st digit, representing the general technological category. We compare the technological categories present in the two sets to highlight the most distinctive ones, i.e., those with the greatest difference in rank based on their frequency in the subset. For instance, if a technological category X is the most common in the top 25% set and the least common in the bottom 25% set, X will be considered as distinctive of the top set while, if it had been the most common in both sets, it would not have been considered distinctive. See Supplementary Information for more details.

In Fig. 5, we show the results for MAs. Unlike countries, we do not observe a point of accumulation between MAs. We observe how some MAs get closer to others, such as Moscow to Milan, Seoul to Tokyo or Shanghai to New York. From a technological point of view, results are consistent with countries. The upper part is dominated by manufacturing technologies, while at the bottom one, there is more evident dominance of Electricity technologies.

Let us now focus on interpreting the different pathways in terms of strategies and policies implemented by countries and metropolitan areas. A case of particular interest is that of China, where R &D investment led to a patent boom^55,56,57 and a consequent sudden increase in technological diversification. This sudden increase, however, was also paralleled by a deterioration in patent quality, as Dang et al.⁵⁵ pointed out. This evidence explains why the path of China first presents an increase in diversification (i.e., moving rightward on the horizontal axis), followed by a later increase in competitiveness (i.e., moving downward along the vertical axis). While adopting distinct policies and behaviours as discussed in Lacasa et al.⁵⁸, the other BRICS countries exhibit a similar trajectory to China. Lacasa et al.⁵⁸ elucidated that high-income countries such as the EU15, the United States, and Japan are more actively involved in cutting-edge technologies than all BRICS economies. Still, China stands out of the BRICS countries since it managed to acquire a remarkable global influence in innovation, positioning itself as an innovation leader among the BRICS countries⁵⁹, as demonstrated by Wang⁶⁰.

In the most recent period, China was the only BRICS country to bridge the gap in frontier technology activities, reaching levels observed in high-income countries. The remaining BRICS economies have yet to narrow this disparity in frontier activities compared to high-income economies. Across all technological fields, BRICS economies exhibit a similar, low degree of diversification. Among them, Brazil stands out with the lowest degree of global interaction, while India appears relatively more engaged in generating patentable knowledge than other BRICS economies. Overall, the technological advancement profiles of the BRICS countries between 1989 and 1997 show an unexpected uniformity, reflecting their limited involvement in cutting-edge technology activities and a low level of integration with the global economy at that time. China stands out also because it significantly expanded its scale of activities in behind-the-frontier and frontier technology, boosting a high percentage of patents in high-tech domains and holding a solid position in technological knowledge diversification within the BRICS group.

Shifting now our focus to the “lower” part of chat diversification-competitiveness, Israel provides an illustrative example. Israel’s consistently high investments in R &D have propelled it into a technologically advanced nation, as highlighted by Beyar⁶¹. According to OECD data (available at https://data.oecd.org/rd/gross-domestic-spending-on-r-d.htm), Israel has steadily increased its gross domestic spending on R &D since the early 1990s, ultimately achieving the top ranking in investment by the year 2000. Its observed trajectory can be attributed to the substantial investments in R &D, which improves the quantity (diversification) and the quality (competitiveness) of technologies.

2 days ago

0 4 12 minutes read