The Role of Complex Analysis in Modelling Economic Growth †
<p>In our theoretical framework, capabilities are crucial in explaining the economic performances of countries. As can be observed on the left, conceptually, we can visualize capabilities as an intermediate layer in a tripartite country-capability-product network. Capabilities are non-measurable entities, and information on them can be inferred by building an empirical country-product network through international trade data. As can be seen on the right, such a bipartite network can be interpreted as the projection of the tripartite network. In the country-product network, a <math display="inline"><semantics> <mrow> <mi mathvariant="script">C</mi> <mo>→</mo> <mi mathvariant="script">P</mi> </mrow> </semantics></math> link is established if and only if the country has a revealed comparative advantage in exporting the product [<a href="#B44-entropy-20-00883" class="html-bibr">44</a>,<a href="#B45-entropy-20-00883" class="html-bibr">45</a>].</p> "> Figure 2
<p>The binary matrix of countries and products built from the worldwide 1998 export flows of the BACI dataset [<a href="#B48-entropy-20-00883" class="html-bibr">48</a>]. The rows and columns of the matrix are ranked according to the Economic Fitness-Complexity algorithm (EFC). The rows are sorted by increasing country fitness and the columns by increasing product complexity. In such a way, the matrix acquires a triangular-like shape: countries with more diversified export baskets are more competitive, while countries specialized in a few products—which generally are also exported by every other country—are the less competitive. Source of the figure: Tacchella et al. [<a href="#B44-entropy-20-00883" class="html-bibr">44</a>]. With the permission of Publisher Elsevier.</p> "> Figure 3
<p>The colour-map represents the tridimensional relation between fitness, GDP per capita and subsequent GDP per capita growth rate, where <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>t</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> years is considered. Countries with low fitness are not able to achieve subsequent high growth rates, irrespective of their initial GDP per capita level. For countries with intermediate fitness, higher GDP per capita results in mildly higher growth rates. Countries with high fitness are able to grow at very high rates, especially when their GDP per capita is low or intermediate. Fitness, when it is put into relation with GDP per capita, is able to suggest future growth in a way not fully captured by the sole information contained in the GDP per capita.</p> "> Figure 4
<p>The colour-map represents the tridimensional relation between fitness, capital intensity and subsequent GDP per capita growth rate, where <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>t</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> years is considered. When the combined effect of fitness and capital intensity is taken into consideration, the latter loses explanatory power, and the growth profile of countries is almost completely explained by their fitness level. Higher fitness leads to higher growth rates, and countries with high fitness and intermediate capital intensity are able to achieve the highest growth rates.</p> "> Figure 5
<p>The colour-map represents the tridimensional relation between fitness, employment ratio and subsequent GDP per capita growth rate, where <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>t</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> years is considered. Only the highest levels of employment ratio, after a critical threshold of <math display="inline"><semantics> <mrow> <mi>l</mi> <mi>o</mi> <mi>g</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mi>M</mi> <mi>P</mi> <mo stretchy="false">/</mo> <mi>P</mi> <mi>O</mi> <mi>P</mi> <mo stretchy="false">)</mo> <mo>∼</mo> <mo>−</mo> <mn>0.65</mn> <mo>%</mo> </mrow> </semantics></math>, have a positive effect on economic growth. This is clearly visible from the horizontal variation of colour from red to green in the upper portion of the plot. For lower values of <math display="inline"><semantics> <mrow> <mi>E</mi> <mi>M</mi> <mi>P</mi> <mo>/</mo> <mi>P</mi> <mi>O</mi> <mi>P</mi> </mrow> </semantics></math>, the dominant variation of the colour is vertical: the higher the fitness, the higher the growth rate.</p> "> Figure 6
<p>The colour-map represents the tridimensional relation between fitness, life expectancy and subsequent GDP per capita growth rate, where <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>t</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> years is considered. Life expectancy values <math display="inline"><semantics> <mrow> <mo>≳</mo> <mn>73</mn> </mrow> </semantics></math> years have a positive effect on growth rates. When life expectancy <math display="inline"><semantics> <mrow> <mo><</mo> <mn>73</mn> </mrow> </semantics></math> years, fitness determines the colour contour: the higher the fitness, the higher the growth rate. However, also high fitness countries show a higher growth rate when life expectancy <math display="inline"><semantics> <mrow> <mo>></mo> <mn>60</mn> </mrow> </semantics></math> years.</p> "> Figure 7
<p>The colour-map represents the tridimensional relation between fitness, human capital and subsequent GDP per capita growth rate, where <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>t</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> years is considered. Fitness and human capital appear positively correlated in some regions of the plots, and complementary in others. Low and intermediate fitness corresponds to low human capital. While, when <math display="inline"><semantics> <mrow> <mi>l</mi> <mi>o</mi> <mi>g</mi> <mo stretchy="false">(</mo> <msub> <mi>F</mi> <mi>c</mi> </msub> <mo stretchy="false">)</mo> <mo>></mo> <mo>−</mo> <mn>4</mn> </mrow> </semantics></math>, increasing fitness affects positively the GDP per capita growth rate, even for low human capital levels.</p> "> Figure 8
<p>The colour-map represents the tridimensional relation between fitness, total factor productivity and subsequent GDP per capita growth rate, where <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>t</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> years is considered. For <math display="inline"><semantics> <mrow> <mi>l</mi> <mi>o</mi> <mi>g</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mi>F</mi> <mi>P</mi> <mo stretchy="false">/</mo> <mi>G</mi> <mi>D</mi> <mi>P</mi> <mo stretchy="false">)</mo> <mo>≳</mo> <mo>−</mo> <mn>11</mn> </mrow> </semantics></math>, as can be noted by the horizontal movement of colour from red to green, fitness is the prevailing factor. Keeping Total Factor Productivity constant, high fitness corresponds to greater growth rates. For <math display="inline"><semantics> <mrow> <mi>l</mi> <mi>o</mi> <mi>g</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mi>F</mi> <mi>P</mi> <mo stretchy="false">/</mo> <mi>G</mi> <mi>D</mi> <mi>P</mi> <mo stretchy="false">)</mo> <mo><</mo> <mo>−</mo> <mn>11</mn> </mrow> </semantics></math> from the diagonal variation of colour, we deduce that fitness and TFP are complementary in affecting future growth rates. In this area, very low fitness brings low growth, independent of the TFP level. For low and intermediate fitness countries, TFP has a negative impact on economic growth. This could be due to TFP measurement errors. Finally, we detect a complementarity between fitness and TFP for highly competitive economies: high fitness leads to high growth rates, especially when TFP is high.</p> "> Figure A1
<p>Estimation errors of the growth rate colour-maps in <a href="#sec4-entropy-20-00883" class="html-sec">Section 4</a>. Two layers of information are represented in the figures. (1) In the grey scale, the Nadaraya–Watson growth rate estimation error. White indicates a standard error of <math display="inline"><semantics> <mrow> <mn>0.2</mn> <mo>%</mo> </mrow> </semantics></math> or less and dark grey a standard error of <math display="inline"><semantics> <mrow> <mn>0.4</mn> <mo>%</mo> </mrow> </semantics></math> or more. (2) The iso-lines of the growth rate levels, represented in the same palette of the colour maps (lowest in dark red, highest in dark green).</p> ">
Abstract
:1. Introduction
2. Economic Growth, Capabilities and Complexity
3. Materials and Methods
3.1. Measuring Fitness
3.2. Empirical Strategy
3.3. Sources of Data
4. Empirical Evidence
4.1. Fitness and GDP per capita
4.2. Fitness and Capital Intensity
4.3. Fitness and Employment Ratio
4.4. Fitness and Life Expectancy
4.5. Fitness and Human Capital
4.6. Fitness and Total Factor Productivity
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A. Non-Parametric Graphical Analysis: Estimation Errors
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Used Variable | Mean | Median | St. Dev. | Source & Variable Names | Description |
---|---|---|---|---|---|
Growth Rate | 0.08 | 0.09 | 0.18 | PWT 9 Penn World Tables 9.0 [54] (based on and ) | Annual growth rate of GDP per capita ( at constant 2011 national prices in 2011 U.S. $ million, in millions). In levels, formula: . |
−1.03 | −1.00 | 0.26 | PWT 9 Penn World Tables 9.0 [54] () | Employment ratio ( in millions, in millions). In natural logarithm, at year . | |
8.54 | 8.56 | 1.17 | PWT 9 Penn World Tables 9.0 [54] () | Income per capita ( in 2011 U.S. $ millions, in millions). In natural logarithm, at year . | |
10.16 | 10.31 | 1.52 | PWT 9 Penn World Tables 9.0 [54] () | Capital intensity ( in 2011 U.S. $ million, in millions). In natural logarithm, at year . | |
1.94 | 1.82 | 0.66 | PWT 9 Penn World Tables 9.0 [54] () | Human capital (human capital index, based on years of schooling and returns to education, adimensional). In levels, at year . | |
−11.46 | −11.53 | 1.79 | PWT 9 Penn World Tables 9.0 [54] () | Total factor productivity-GDP ratio ( at constant national prices with 2011 = 1, at constant 2011 national prices in 2011 U.S. $ million). In natural logarithm, at year . | |
62.92 | 66.18 | 10.97 | WDI World Development Indicators, The World Bank Group [55] (Life expectancy at birth, total) | Life expectancy at birth (in years of life). In levels, at year . | |
−2.39 | −1.16 | 4.37 | PIL-FF 1963-2000 [36] (fitness scores) | Fitness (PIL’s group computation from EFC algorithm [6] based on UN-COMTRADEexport data [56], adimensional). In natural logarithm, at year . |
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Sbardella, A.; Pugliese, E.; Zaccaria, A.; Scaramozzino, P. The Role of Complex Analysis in Modelling Economic Growth. Entropy 2018, 20, 883. https://doi.org/10.3390/e20110883
Sbardella A, Pugliese E, Zaccaria A, Scaramozzino P. The Role of Complex Analysis in Modelling Economic Growth. Entropy. 2018; 20(11):883. https://doi.org/10.3390/e20110883
Chicago/Turabian StyleSbardella, Angelica, Emanuele Pugliese, Andrea Zaccaria, and Pasquale Scaramozzino. 2018. "The Role of Complex Analysis in Modelling Economic Growth" Entropy 20, no. 11: 883. https://doi.org/10.3390/e20110883