The degree of economic development pattern of economy

In this article, we explore the concept and measurement of the degree of economic development pattern (DEDP) of economy, which refers to the extent to which the development of an economy can serve as a reference for other economies. Utilizing 76 macroeconomic indicators across 217 economies, the economic development paths in a standardized space of economy is compared to identify variations in DEDP through the regression analysis on the relationship between the similarity of development paths and the growth rate on gross domestic product (GDP) per capita. To measure DEDP of economy from different perspective, two types of metrics are constructed. One is the determination coefficient of regression analysis, which exhibits significant positive correlations with population size of economy, uncovering differences of development paths among economies of varying population sizes. The other type of metrics is based on the consistency on regression coefficients and effectively explains disparities among economies in the growth rate on GDP per capita, economic complexity index and economic fitness. These findings reveal the differences in development paths among different countries from the perspective of referentiality for development patterns, suggesting the potential existence of the paths with more universal meaning to economic development.


Introduction
'Economic development pattern' refers to the overall approach or strategy that a country or region uses to achieve economic growth, social development, and sustainable progress [1].Every country strives to find a development path that fits its unique national conditions and can sustain long-period growth momentum.Based on their environment, resources, culture, social and economic systems, and other factors, countries have gradually explored various economic development patterns in their long-term development practices.Among them, some countries that achieved rapid growth for a long period, such as Japan after World War II, South Korea in the late twentieth century, and China in the last four decades, have developed several remarkable economic development patterns that have attracted extensive attention from scholars and been partly used for reference by other countries [2][3][4].Although different countries must fully consider their own national conditions when choosing their economic development paths and patterns, and there are often failures when learning from the development patterns of other countries [5], it is noteworthy to identify a set of common features in these successful economic development patterns, such as promoting market integration [6], giving full play to government's active role [7], emphasizing infrastructure and public services [8], adopting an open economic system [9], strengthening investment in education and technology [10], and promoting innovation and scientific and technological development [11].These shared characteristics are indicative of fundamental principles underlying economic development and constitute focal points for cross-country learning, thereby indicating the potential existence of a generalizable pattern in economic development.
At the same time, the research in development economics and growth economics also put forward a series of development theories based on the general sense, such as the neoclassical growth model [12], institutional change theory [13], endogenous technological change theory [14], market growth theory [15], trying to give the interpretation of economic development driving from a universal sense.However, there are

Data and construction of the development paths in a standardized space
The calculation of the similarity between the benchmark economy and other economies in terms of their economic development patterns is a crucial step in determining an economy's DEDP.The economic development patterns of an economy usually are hidden within its development paths.To establish metrics for an economy's DEDP based on the development paths, the process involves three fundamental steps: firstly, the development paths of each economy are constructed in a standardized space based on multiple macroeconomic indicators of economies.Subsequently, the similarities of development paths between different economies are calculated.Finally, the metrics of DEDP are determined through regression analysis that examines the relationship between economic growth and the calculated similarities, as well as the further analysis based on the results of regression analysis.
The development paths of each economy are obtained from a comprehensive transformation of multiple macroeconomic indicators.We employed a total of 76 macroeconomic indicators across 11 indicator categories such as transportation, market integration, foreign trade, military, innovation, social assets, labor force, sub-industry, human development level, urbanization, and finance, as shown in table A1 in appendix.In addition to these indicators, the data also includes per capita gross domestic product (GDP per capita) and population data of each economy.In the 76 macroeconomic indicators used in this study, the human development index was sourced from the United Nations Development Programme website (www.undp.org), while the remaining indicators were obtained from the World Bank database (www.worldbank.org).This dataset covered a total of 264 countries, regions, and organizations, with 217 being national entities or regions (they are called 'economies' in this article), and spanning a period of 61 years (from 1960 to 2020).We also collected two new emerging product-level-based macroeconomic indexes of economies: ECI and economic fitness.ECI is a measure of an economy's capacity [17].The ECI data is sourced from the 'Economic Complexity and International Development' project by the Harvard Growth Lab (https://atlas.cid.harvard.edu).It covers 133 countries and spans a time period of 26 years, from 1995 to 2020.Economic fitness is a metric for product complexity that is calculated by the data of product-level exports of economy and shows well predictive ability on economic growth [18,19].The data of economic fitness of each economy is collected from Databank of the World Bank (https://databank.worldbank.org),covering 149 economies from 1995 to 2015.
For the 76 macroeconomic indicators, we first performed the following steps as preprocessing.Firstly, among these macroeconomic indicators, if an indicator is derived from the sum of per capita indicators, it will be restored as a per capita indicator.Subsequently, we replaced each indicator with its ratio to the corresponding world average to eliminate the impact of changes in statistical scope and measurement capabilities across different years for each indicator.Given the heterogeneity of these indicators, we further use the logarithmic value of the ratio as the processed indicator value I 0 for each indicator.Similarly, for the GDP per capita of each economy, due to its heterogeneity, we also convert it into the logarithm of the ratio to the world average value, which is called the logarithmic relative GDP per capita (denoted by g), as the indicator of the economic development level of each economy.
We construct a standardized space that enables the comparison of each indicator across different economies and years within it.We plot the trajectories of each economy in the space of I 0 vs. g for every indicator.As the example shown in figure 1, numerous macroeconomic indicators exhibit a strong dependence on g, showing the strong impact of the economic development level of economy.Under such circumstances, identical values on the indicator in economies with distinctly different levels of development can conceal underlying systemic disparities.Consequently, the validity of direct comparisons based solely on the absolute value of I 0 is greatly reduced.So the first step of the construction is to eliminate the impact of economic development levels on these indicators, the method is as follows: For an indicator (e.g. the kth indicator I 0 k ), plot the trajectories of every economy in the space of I 0 k vs. g.And then, we set a narrow sliding window with each data point as the center of the horizontal coordinate.For example, the left border and right border of the sliding window for the ith data point with coordinate (g i , I 0 k (g i )) is g i − w/2 and g i + w/2, where w is the width of the sliding window.The average value ⟨I 0 k ⟩(g i ) of I 0 k for all data points in the sliding window can be considered as the global expected value of I 0 k at g = g i .By using this method, we obtained the global expected value of all data points.Compared with the original indicator value I 0 k (g i ) (the ith data point, say), the deviation of each data point from its global expected value expresses the difference to the average behavior on the relationship I 0 k vs. g and can better reflect the systemic differences across economies with different economic development level, because the hidden characteristics in the I 0 k of each economy covered by the impact of economic development level are revealed.Several previous studies in mining urban characteristics and innovation ability have confirmed the effectiveness of the relative indicators constructed based on this type of deviation [24][25][26][27].We further standardize this deviation for each data point within its corresponding sliding window: where σ(I 0 k (g)) is the standard deviation of the value of I 0 k (g) of all data points in the sliding window.The curve of I D k of each economy still contains the impact of the fluctuation in the indicator's global level over the years.To exclude this impact, for each economy (economy i, say), the difference between I D k and the global average value at each year (year Y, say) is calculated: where of all economies at year Y. Through this calculation, all indicators are converted into a set of standardized new sequences I R that excludes both the impact of economic development level and world fluctuations.
These I R exhibit the development paths of every economy in a 76 dimensional standardized space and will be the base of the following similarity analysis.An example of the trajectories of the indicator I 0 and the corresponding relative indicator I R for economies in the space I 0 vs. g and I R vs. g are respectively plotted in figures 1(a) and (b), and their corresponding curves of I R over year are shown in figure 2. Since these I R mainly are constructed by the relative level between I 0 and the corresponding global expected level, they are called 'the relative indicators' in the following discussion.

The similarity and the regression analysis
In the calculation of the similarity in the development paths between two economies, we use the following three measures to describe the features in the path of a relative indicator: the level, the trend, and the variability.For the kth relative indicator I R k (Y), the level value is directly set as I R k (Y).The trend κ(Y) refers to the regression coefficients obtained from linear regression on the relationship between I R k (y) and year y in a sliding year window with m years width and Y as the middle year (the regression model is I R k (y) = κ(Y)y + c), while the mean of regression residuals ζ(Y) is used as a measure of variability at year Y.
The similarity in the path of the relative indicator between two economies is quantified by the Euclidean distance.For the relative indicator I R k , the distance between economy i and economy j at year Y is: where d I , d κ and d ζ respectively are the difference on the standardized values of the level I R k , the trend κ and the variability ζ: By setting an economy (e.g. economy i) as the benchmark economy and employing the above approach, we can obtain the similarity of other economies relative to the benchmark economy on each relative indicator.And then, for each relative indicator (e.g. the kth relative indicator I R k ), we calculate the z-score standardize value of the similarity of other economies (e.g. economy j) relative to the benchmark economy (economy i) on I R k : where ⟨S i k ⟩ and σ(S i k ) are the average value and the standard deviation of the set of the similarity relative to the benchmark economy (economy i) on I R k , respectively.Noticed that, for economy's missing indicator, its standardize value of the similarity is just set to 0.
Finally, by using the z-score standardized value of the similarity of other economies relative to the benchmark economy (economy i) in every relative indicators as the independent variable and setting their average growth δg per year on the relative GDP per capita g as the dependent variable, we perform multivariate regression analysis.The regression model is: where the subscript j denotes economy j (j ̸ = i), the subscript k denotes the kth relative indicator, q i k is the regression coefficient, and ϵ i is the error term of benchmark economy (economy i).Given the correlation among the similarities in different relative indicators, the ridge regression method is employed to mitigate multicollinearity concerns.The determination coefficient R 2 i of this multivariate regression analysis is adopted to be the metric of DEDP of the economy i.

Correlation analysis
Setting the width of sliding year window m = 11, we calculated the value R 2 of each economy in the term from 1960 to 2020, and obtained effective values of R 2 of 207 economies.The global average of R 2 is 0.326, with some economies with higher DEDP reaching a level over 0.56, suggesting that the degree of similarity in development paths between other economies and these high DEDP economies can largely explain the differences in their speed of economic development, also indicating the higher prediction accuracy on the predicted value E(δg) of δ using the regression model of equation (5).The relationships between the predicted value E(δg) and actual δg of various economies when using several high-DEDP representative economies as benchmark economies are plotted in the figure 3, where the Pearson correlation coefficients r and the Spearman correlation coefficients ρ between E(δg) and δg are over 0.7 for some benchmark economies.The values of R 2 , r and ρ of 30 economies with the highest R 2 are listed in table 1.
We examined the relationships between R 2 and population size of economy.The logarithmic average ⟨log 10 p⟩ of population over years in this term (from 1960 to 2020) as a measure of an economy's population size in this analysis.As shown in figure 4, R 2 exhibits a significant positive correlation with population size ⟨log 10 p⟩ of economy, with a Pearson correlation coefficient of 0.474 (the significance level P < 0.001) and a Spearman correlation coefficient of 0.482 (P < 0.001), and the partial correlation coefficient controlling the effect of the average g over years (⟨g⟩) is 0.477 (P < 0.001), indicating that the populous economies usually have higher level of economic development pattern.As shown in figure 5, certain economies with low R 2 values exhibit significant missing indicator issues.Consequently, we repeat the above correlation analysis after excluding a subset of economies with substantial missing indicator.For a given economy, the economy's missing indicator rate µ is defined as the proportion of indicators that do not include that economy out of the total number of indicators.The correlation coefficients (Pearson correlation coefficient r and Spearman correlation coefficient ρ) and the partial correlation coefficients r (g) (controlling the impact of ⟨g⟩) in the cases after excluding the economies with higher µ are listed in table 2 (the threshold of µ is 50% and 30%).Although the correlation between R 2 and ⟨log 10 p⟩ is slightly weakened after excluding high-µ economies, it is still significant.These results further confirm the significant positive correlation between R 2 and population size of economy.
The correlations between each economy's R 2 and other macroeconomic indicators that are relevant to long-term economic development are also observed.These indicators include δg, the average value ⟨g⟩ of g over years in the period from 1960 to 2020, the average value ⟨K E ⟩ of ECI over years in the period from 1995 to 2020, and the logarithmic average value ⟨log 10 F⟩ of economic fitness over years in the period from 1995 to 2015.However, R 2 does not show any significant correlations with these indicators.

The consistency analysis based on regression coefficients 4.1. The consistency analysis based on the global average regression coefficients
Equation ( 5) as a regression model that all the independent variables are standardized, the absolute value of the regression coefficient is correlated to the effect of the factor on the dependent variable.The regression coefficients of each indicator for each benchmark economy are plotted in figure 5. Due to the lower S means higher similarity, the negative regression coefficient indicates that economies with smaller differences in this indicator compared to the benchmark economy are more likely to have faster economic growth.Conversely, for positive regression coefficients, the opposite is true.It can be observed that there is high-level consistency in the regression coefficients obtained from different benchmark economies.We therefore calculate the average ⟨q⟩ of regression coefficient q of each indicator, and the indicators with high absolute value of ⟨q⟩ are listed in table 3, most of which are the trade indicators, showing the strong impact of international trade on economic development.
Figure 5 also implies that there is a degree of consistency between the regression coefficients for the different benchmark economies.For the sequence {q} of regression coefficients of each benchmark economy    and the sequence {⟨q⟩} of average regression coefficients, we use the correlation coefficient (Spearman correlation coefficient ρ C ) between them to be the measure of their consistency.In the calculation of correlation coefficients, for the economy with missing indicators, the corresponding indicators are removed from the sequence {⟨q⟩} of average regression coefficients, and then we calculate the correlation coefficients between the remaining part of the two sequences.This consistency is an indicator for another aspect of DEDP of the benchmark economy, which measures the difference in direction of its explanation with the global average explanation direction when using the similarity S to explain economic growth.This consistency (measured by ρ C ) is positively correlated with R 2 (figure 6(a)), and the Pearson correlation coefficient r and the Spearman correlation coefficient ρ are 0.390 and 0.227, respectively.ρ C also exhibits a weak correlation with the population size ⟨log 10 p⟩, as indicated by the correlation coefficients of r = 0.247 and ρ = 0.240.Moreover, we find that a significant correlation between ρ C and δg, with Pearson correlation coefficient and Spearman correlation coefficient of 0.308 and 0.301, as shown in figure 6(b).Although the correlation is not strong, the partial correlation coefficients r (g) and r (p) remain significant (r (g) = 0.309 and r (p) = 0.307, both with P < 0.001) after excluding the effects of ⟨g⟩ and population size More remarkable, the consistency is also significantly correlated with ECI and economic fitness of economy.As illustrated in figures 6(c) and (d), ρ C exhibits positive correlations with both ⟨K E ⟩ and ⟨log 10 F⟩ of the benchmark economy, with Spearman correlation coefficients of 0.467 and 0.618, respectively.Excluding the impact of ⟨g⟩ and population size (⟨log 10 p⟩), the partial correlation coefficients r (g) and r (p) between ρ C and ⟨K E ⟩ are 0.547 and 0.449, respectively (as shown in figure 6(c)).Additionally, the partial correlation between ρ C and ⟨log 10 F⟩ is also significant (r (g) = 0.321, r (p) = 0.323, see figure 6(d)).These results indicate that the economy with a high ECI or economic fitness usually has a high level of consistency in the direction of its explanation when using similarity S to explain long-term economic growth.

The consistency analysis based on regression coefficients of benchmark economy
The consistency mentioned above is defined on the benchmark of the global average of regression coefficients.However, using the global average of regression coefficients as the benchmark may not necessarily lead to the best explanatory power.We therefore try to extend the benchmark to the regression coefficients of each economy.That is, by designating an economy (e.g. economy i) as the coefficient benchmark economy, the consistency of the other economy (e.g. economy j) based on the regression coefficients of economy i is measured by the Spearman correlation coefficient ρ E C | j i between the sequence of regression coefficients {q} j of economy j and {q} i of the coefficient benchmark economy (economy i).In the calculation of similarity, for the case with missing indicators, a method that is similar to the above calculation is adopted: in each pair of economies, if one or two economies have missing indicators, the missing indicators in both sequences of the two economies are removed, and the remaining part of the two sequences is used in the calculation of correlation coefficients.
By successively setting each economy as the coefficient benchmark economy, we calculate the consistency ρ E C of every economies' sequence of regression coefficients relative to that of the coefficient benchmark economy, resulting in the consistency set {ρ E C } for the coefficient benchmark economy.Subsequently, the correlations between the consistency set {ρ E C } of each coefficient benchmark economy and several macroeconomic indicators associated with economic growth, including δg, ⟨K E ⟩, ⟨log 10 F⟩, and the average annual changes δK E of ⟨K E ⟩ and average annual changes δ log 10 F of ⟨log 10 F⟩, are observed.Using ρ δg P , ρ K P , ρ F P , ρ δK P , and ρ δF P , to represent the Spearman correlation coefficient between {ρ E C } with δg, ⟨K E ⟩, ⟨log 10 F⟩, δK E , and δ log 10 F, respectively, they assess the explanatory power on these macroeconomic indicators through the regression coefficients of the coefficient benchmark economy, which also serves as a comprehensive set of metrics for evaluating the DEDP of the coefficient benchmark economy from the perspective of explaining the corresponding macroeconomic indicators.
The  coefficient benchmark economies, their consistency set {ρ E C } exhibits remarkable strong correlations with these macroeconomic indicators, particularly ⟨K E ⟩ and ⟨log 10 F⟩.For example, ρ K P of Austria and ρ F P of Germany are as high as 0.730 (P < 0.001) and 0.786 (P < 0.001), respectively, as shown in table 4, indicating a strong explanatory power for both ECI and economic fitness serving the regression coefficients of these economies as benchmarks.The highest values of ρ δg P and ρ δK P are also over 0.4, indicating that Poland and Vietnam, serving as benchmarks, can also explain the growth of GDP per capita and ECI growth, respectively, to a certain extent.The highest ρ δF P is 0.278 (Oman) and remains significant (P < 0.001).In addition, from table 4, we observe that the economies with higher-level metrics of explanatory power for without factor control, as shown in each panel of figure 8, indicating that these correlations are not a result from other relationships that are relevant to variations in GDP per capita or population size of economy.
The other two metrics ρ δK P and ρ δF P also show significant correlations with δK E and ⟨K E ⟩, respectively, with Spearman correlation coefficients of 0.363 (P < 0.001) and −0.505 (P < 0.001), as shown in figure 9. Notably, the relationship between ⟨K E ⟩ and ρ δF P is the only instance of a significant negative correlation (see figure 9(b)).This finding is pertinent as the majority of economies with a higher ρ δF P belong to the developing economies, which typically exhibit a lower level of ECI.
At last, the notations for main indicators and metrics used in sections 3 and 4 are summarized in table 5.

Conclusion
The method for constructing a metric of DEDP can be summarized as follows: in a standardized multiple indicator-year space, the similarity between the development paths of economies in each indicator is defined and calculated.And then, we utilize different economies as benchmark economy to assess the explanatory power (measured by the determination coefficient R 2 ) of the similarity relative to the development paths of the benchmark economy on the economic development speed of each economy using regression analysis, constructing DEDP metrics based on this explanatory power and the consistency of the sequence of the regression coefficients.The data basis in the construction of DEDP integrates 76 economy-level macroeconomic indicators across 11 categories, providing comprehensive coverage of the external representation of macro-economy in different fields.Since all indicators have undergone relative transformation, that is, the standardized deviation of each indicator relative to the global expectation level is used as the benchmark, and the fluctuations of the world's overall level with each year are excluded, all the indicator data among countries with different levels of economic development in different years are incorporated into a comparable standardized framework [24][25][26][27], ensuring the consistency and comparability of the similarity of macroeconomic indicators between economies defined on this deviation.It is important to note that, this approach in the construction of DEDP metrics can be easily generalized to the analysis of other socio-economic indicators.For example, by incorporating more socio-economic indicators into the current framework, a high level of explanatory power and prediction accuracy for economic growth and social development would be achieved.One of the main findings of this study is the significant positive correlation between R 2 and the population size of an economy.This result suggests that there may be significant disparities in the development paths of economies with different population sizes.In comparison to economies with a smaller population size, the development paths of populous economies are more suitable for serving as a comparative benchmark to explain variations in economic development speed across economies.This implies that the development paths of economies with a larger population size be closer to  The partial correlation coefficient controlling the impact of the logarithmic average population size over years (⟨log 10 p⟩) General correlation rµ The Pearson correlation coefficient for the economies where the missing indicator rate µ is no more than certain threshold General correlation ρµ The Spearman correlation coefficient for the economies where the missing indicator rate µ is no more than certain threshold economic development patterns that hold universal significance.In previous studies, it has been observed that numerous factors that are crucial for economic development often require the support of a large population size.For instance, the establishment of large internal markets [28,29], the availability of human resources [30], cross-regional industrial division and economic diversification [31], as well as technological development and innovation activities [27,32,33] often depend on a sufficient population size.This suggests that populous economies are more likely to leverage the support of their large population to coordinate various factors comprehensively and promote economic development in a multifaceted and comprehensive manner.This could be the underlying reason why the development paths of populous economies are more comparable.
The analysis of the consistency of the sequence of the regression coefficients reveals another perspective for exploring the DEDP of economies.A set of consistency-based metrics, especially the metric ρ E C based on the consistency of the sequence of regression coefficients of the coefficient benchmark economy, as well as explanatory power metrics (ρ δg P , ρ K P and ρ F P ) derived from the correlation between ρ E C and macroeconomic indicators, exhibit strong correlations with the growth rate of GDP per capita, ECI, and economic fitness, offering robust explanations for the differences in these macroeconomic indicators across economies.It is worth noting that these consistency-based metrics and R 2 effectively decouple the impact of economic factors and that of demographic factors in economic development patterns: the consistency-based metrics focus on the effective explanations for differences in macroeconomic indicators, while R 2 uncovers the differences in development paths among countries with varying population sizes.This decoupling is unexpected, since we have not directly integrated the separation of these two types of factors into the construction algorithm of the DEDP metric.
More importantly, our findings provide rather significant and strong implications in terms of catch-up policies for the developing countries.Because the economy with higher R 2 reflect that, using their development paths as the benchmark, the differences between other economies' development paths and the benchmark are strongly positively correlated with the speed of economic growth, it implies a potential development strategy for other economies is to try to approach these high-R 2 economies in their development paths.Of course, since development paths are constructed in a standardized space, this 'approach' does not mean directly attempting to replicate the macroeconomic indicators of high-R 2 economy, but rather requires a combination of the domestic economic development stage and current situation.
These results also imply that there may exist one or more virtual development paths in the macroeconomic indicator space that leads to the maximum DEDP metrics.In this case, the difference between the actual development paths of an economy and the DEDP-maximized paths can explain the development speed of each economy to the greatest extent.In other words, the DEDP-maximized paths represent a development model with significant reference value for all economies' development and are likely corresponding to a universal pattern in economic development.The DEDP-maximized paths are more suitable as the absolute benchmark for further analysis and as a guide for the economic development direction of individual economies.The construction and analysis of the DEDP-maximized paths remains to be further studied.
At last, it should be noted that, in the construction of DEDP metrics, the similarity S between economy's development paths used in the regression analysis is defined independently for each macroeconomic indicator, rather than combining them into a single similarity metric.This approach results in difficulties in visually associating the changes in DEDP metrics with those in macroeconomic indicators, thereby posing challenges in the interpretability of the DEDP metrics.The consistency-based metrics, in particular, exhibit weaker interpretability due to their reliance on the similarity of regression coefficients from different coefficient benchmarks.In subsequent studies, further examination is essential to elucidate the distinct manifestations of these DEDP metrics along economic development paths, with the ultimate objective of shaping strategic guidance for the economic development direction of diverse economies.

Figure 1 .
Figure 1.The trajectories of each economy in the space of economic indicator (merchandise imports (current US$) as an example) and the logarithmic relative GDP per capita g.The indicator shown in panels (a) and (b) is the original indicator and the correspond relative indicator, respectively.The color curves and the gray curves respectively correspond to representative economies and other economies, and the black dashed lines show the sliding-window-averaged curves (window width w = 0.2).

Figure 2 .
Figure 2. The curves of the relative indicator (merchandise imports (current US$) as an example) of each economy over the years (1960-2020).The color curves and the gray curves correspond to representative economies and other countries respectively.

Figure 3 .
Figure3.The relationships between the actual δg and the predicted value E(δg) of δg for each economy in different benchmark economies.The benchmark economies of panels (a)-(f) are China (the mainland), the United States of America, Japan, Republic of Korea, Russia and Brazil, respectively.The color data points and the gray data points correspond to representative economies and other countries respectively.The dashed lines show the linear-fitting curves.One, two, and three asterisks represent significance levels of P < 0.001.

Figure 4 .
Figure 4.The correlation between each economy's DEDP R 2 and the logarithmic population size ⟨log 10 p⟩, where the color points and the gray points respectively correspond to representative economies and other economies, and the dashed line is the linear fitting curve.Three asterisks represent significance levels of P < 0.001.

Figure 5 .
Figure 5.The regression coefficients of each indicator for each benchmark economy.Economies are listed in R 2 value from highest to lowest.The values listed in the bottom are the average ⟨q⟩ of the regression coefficients of each indicator.

Figure 6 .
Figure 6.The correlations between benchmark economy's consistency (ρC) based on global average regression coefficients and their R2 (panel (a)), δg (panel (b)), ⟨KE⟩ (panel (c)), and ⟨log 10 F⟩ (panel (d)).The color points and the gray points in each panel respectively correspond to representative economies and other economies, and the dashed lines show the linear fitting.Three asterisks represent significance levels of P < 0.001.

Figure 7 .
Figure 7.The examples with the strongest correlations (the highest Spearman correlation coefficient) between the consistency set {ρ E C } of the coefficient benchmark economy and the macroeconomic indicators (δg, ⟨KE⟩, ⟨log 10 F⟩, δKE, and δ log 10 F) of economies.The panels in the first row (panels (a)-(c)), the second row (panels (d)-(f)), the third row (panels (g)-(i)), the fourth row (panels (j)-(l)), and the fifth row (panels (m)-(o)) show the examples of the correlations between {ρ E C } and δg, {ρ E C } and ⟨KE⟩, {ρ E C } and ⟨log 10 F⟩, {ρ E C } and δKE, and {ρ E C } and δ log 10 F, respectively.The color points and the gray points respectively correspond to representative economies and other economies, and the dashed lines show the linear fitting.One, two, and three asterisks represent significance levels of P < 0.05, P < 0.01, and P < 0.001, respectively.

Figure 9 .
Figure 9.The correlations between ρ δK P and δKE, ρ δF P and ⟨KE⟩.The color points and the gray points respectively correspond to representative economies and other economies, and the dashed lines show the linear fitting.Three asterisks represent significance levels of P < 0.001, respectively.

10 F
logarithmic relative GDP per capita of economy The macroeconomic indicator ⟨g⟩ Economy's average g over years in the period from 1960 to 2020 The macroeconomic indicator δg Economy's average growth per year of g in the period from 1960 to 2020 The macroeconomic indicator ⟨log 10 p⟩ Economy's logarithmic average of population over years in the period from 1960 to 2020 The macroeconomic indicator ⟨K E ⟩ The mean of ECI of economy in the period from 1995 to 2020 The macroeconomic indicator δK E The average annual change of ⟨K E ⟩ of economy in the period from 1995 to 2020 The macroeconomic indicator ⟨log 10 F⟩ The logarithmic average of economic fitness of economy in the period from 1995 to 2015 The macroeconomic indicator δ log The average annual changes of ⟨log 10 F⟩ of economy in the period from 1995 to 2015 Metric of economy's DEDP R 2 The determination coefficient of the multivariate regression analysis based on equation (5) Metric of economy's DEDP ρ C The consistency between economy's regression coefficients and the global average of regression coefficients, measured by Spearman correlation coefficient Metric of economy's DEDP ρ E C The consistency between economy's regression coefficients and the regression coefficients of the coefficient benchmark economy, measured by Spearman correlation coefficient Metric of economy's DEDP ρ δg P The explanatory power on δg through the regression coefficients of the coefficient benchmark economy, measured by the Spearman correlation coefficient between {ρ E C } of the coefficient benchmark economy and δg of economy Metric of economy's DEDP ρ K P The explanatory power on ⟨K E ⟩ through the regression coefficients of the coefficient benchmark economy, measured by the Spearman correlation coefficient between {ρ E C } of the coefficient benchmark economy and ⟨K E ⟩ of economy Metric of economy's DEDP ρ F P The explanatory power on ⟨log 10 F⟩ through the regression coefficients of the coefficient benchmark economy, measured by the Spearman correlation coefficient between {ρ E C } of the coefficient benchmark economy and ⟨log 10 F⟩ of economy Metric of economy's DEDP ρ δK P The explanatory power on δK E through the regression coefficients of the coefficient benchmark economy, measured by the Spearman correlation coefficient between {ρ E C } of the coefficient benchmark economy and δK E of economy Metric of economy's DEDP ρ δF P The explanatory power on δ log 10 through the regression of the coefficient benchmark economy, measured by the Spearman correlation coefficient between {ρ E C } of the coefficient benchmark economy and δ log 10 F of economy General correlation r The Pearson correlation coefficient General correlation ρ The Spearman correlation coefficient General correlation r (g)The partial correlation coefficient controlling the impact of the average GDP per capita over years (⟨g⟩) General correlation r (p) , where I R * , κ * and ζ * denote the z-score standardized value of I R k , κ and ζ, respectively.The mean of D

Table 1 .
The list of 30 economies with the highest R 2 .All of correlation coefficients have the significance P < 0.001.

Table 4 .
The list of top 20 economies on the five indicators (ρ ) of explanatory power of coefficient benchmark economy.One, two, and three asterisks represent significance levels of P < 0.05, P < 0.01, and P < 0.001, respectively.
P , and ρ δF P * ⟨log 10 p⟩ respectively, suggesting that this consistency possesses a certain degree of explanatory power in terms of economic growth.

Table 5 .
Notations and descriptions of main indicators and metrics used in the paper.

Table A1 .
List of macroeconomic indicators.