by V Papava · 2016 · Cited by 8 — economic growth by countries are not constructive due to the catch-up effect according to which countries with relatively low levels of economic development find
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saqarTvelos mecnierebaTa erovnuli akademiis moambe, t. 10, #4, 2016 BULLETIN OF THE GEORGIAN NATIONAL ACADEMY OF SCIENCES, vol. 10 , no. 4 , 20 16 © 20 1 Economics The Problem of the Catch-Up Effect and Post-Crises Economic Growth in the World Leading Countries Vladimer Papava Academy Member, Faculty of Economics and Business and Paata Gugushvili Institute of Economics, Ivane Javakhishvili Tbilisi State University, Tbilisi, Georgia ABSTRACT . According to the World Bank statistical data, the World leading country in economic growth, not only in the post-crisis period but during the last decades, is China. Appearing next af ter China in economic growth in the post-crisis period are Indonesia and India. The direct comparisons of economic growth by countries are not constructive due to the catch-up effect according to which coun tries with relatively low levels of economic development find it easier to achieve higher growth rates tha n countries with more advanced economies due to diminishing capital returns. For measuring the econom ic development of different countries, the indicators of appropriate gross domestic products per capita are used. The paper proposes the hypothesis of proportional overlap for the catch-up effect. The paper also contains proof of an invariance theorem. After the adjustment for the catch-up effect of the econom ic growth ratios, the World leading countries in economic growth are Australia, the U.S., Canada and Sa udi Arabia. © 2016 Bull. Georg. Natl. Acad. Sci. Key words: economic growth, catch-up effect, G20 countries, economic development The problem to reach the stable economic growth has been analyzed in a number of significant publica- tions [1-4]. In order to measure economic growth, it is par- ticularly important to use a more or less adequate method allowing an inter-country comparison. But such a comparison is complicated by the existence of the so-called ficatch-up effect.fl The goal of the pa- per is to resolve the problem of the catch-up effect. Such an approach gives very different results about the leading world countries in economic growth, with and without the elimination of the catch-up effect. In the paper, such an approach to the resolving of the problem is shown in the example of the leading G20 countries in economic growth in the post-crisis pe- riod. The list of G20 countries includes not only coun- tries but the EU as well. Because the paper is focused on the problem of the leading G20 countries in eco- nomic growth, further we examine only 19 countries from the G20. As it is known, economic growth is measured using the indicator: gross domestic product (GDP) growth rate ( r ). To calculate the indicator, the amount of increase in the real GDP ( 10 YYY , where 1 Y is the real GDP in the reporting period and 0 Y is the real GDP in the base period) should be divided by the amount of the base-period real GDP ( 0 Y ):
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98 Vladimer Papava Bull. Georg. Natl. Acad. Sci., vol. 10, no. 4, 2016 0 Y r Y (1) It is common knowledge that one of the problems in measuring economic growth is a comparison of the indicators for countries and regions. The es- sence of the problem is that due to diminishing re- turns on capital, with all other things being equal, it is easier to achieve higher rates of economic growth in countries with relatively low levels of economic development than in those with a more advanced economy. In economics, this phenomenon is known as the catch-up effect (for example, [5: 546-547]). To illustrate this effect, let us consider the indica- tors of economic growth in the G20 countries in the post-crisis period from 2010 up to 2013 (Table 1). According to the economic growth data for all of the countries listed in Table 1, the leading countries in economic growth during the post-crisis period are China, Indonesia and India. At the same time, nega- tive economic growth occurred in Italy and Japan with the lowest growth rates observed in France, the U.K. and the U.S. Naturally, a direct comparison of economic growth indicators does not give a true estimate of the real situation because the level of economic development differ significantly from country to country. A comparison of countries with different economic development levels is only possible by removing the catch-up effect from the economic growth rates. For this, it is necessary to find a coefficient that would enable us to make an appropriate adjustment of the economic growth rates for these particular countries. As it is known, the aggregate indicator of a coun- try™s economic development is the GDP per capita ( y ) whose amount is determined by dividing the GDP( Y ) by the population ( N ): . Y y N (2) It should be noted that in comparing countries and regions, the GDP is usually measured in US dol- lars. The figures for the GDP per capita are given in Table 2. For example, according to Table 2, the U.S. economy in 2013 was 7.8 times the economy of China (in terms of the GDP per capita), 15.6 times the Table 1. Indicators of Economic Growth in the G20 Countries in 2010-2013 (See [6]) No. Countries Year 2010 2011 2012 2013 1 Argentina 9.1 8.6 0.9 2.9 2 Australia 2.0 2.3 3.7 2.5 3 Brazil 7.5 2.7 1.0 2.5 4 Canada 3.4 2.5 1.7 2.0 5 China 10.4 9.3 7.7 7.7 6 France 2.0 2.1 0.3 0.3 7 Germany 4.1 3.6 0.4 0.1 8 India 10.3 6.6 4.7 5.0 9 Indonesia 6.2 6.5 6.3 5.8 10 Italy 1.7 0.6 – 2.3 – 1.9 11 Japan 4.7 – 0.5 1.8 1.6 12 Mexico 5.1 4.0 4.0 1.1 13 Russia 4.5 4.3 3.4 1.3 14 Saudi Arabia 7.4 8.6 5.8 4.0 15 South Africa 3.1 3.6 2.5 1.9 16 South Korea 6.5 3.7 2.3 3.0 17 Turkey 9.2 8.8 2.1 4.1 18 United Kingdom 1.9 1.6 0.7 1.7 19 United States 2.5 1.6 2.3 2.2
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The Problem of the Catch-Up Effect and Post-Crises Economic Growth 99 Bull. Georg. Natl. Acad. Sci., vol. 10, no. 4, 2016 economy of Indonesia and 35.4 times the economy of India . Due to the catch-up effect, with all other things being equal, it is much more difficult for the U.S. to achieve an economic growth of 1% than it is for each of these other countries. It is logical to assume that since the U.S. economy in 2013, for example, was 7.8 times larger in GDP per capita terms than the economy of China, it would be 7.8 times more difficult for the U.S., with all else being equal, to achieve the same economic growth as in China. This can be explained by the following hy- pothesis: If the level of economic development of one coun- try is times higher than the level of economic de- velopment of another country, achieving the same economic growth in the former will be times more difficult than in the latter [8: 6]. Let us call this assumption the hypothesis of pro- portional overlap of the catch-up effect or, in short, the proportional overlap hypothesis . For its math- ematical description, let us divide the GDP per capita of the i -th country ( i y ) by that of the j -th country ( j y ): . i ij j y y (3) Based on the essence of the above hypothesis, ij is the coefficient of proportional overlap by the i -th country of the catch-up effect of the j -th country. In short, let us call ij the coefficient of the propor- tional overlap . For the calculation of the coefficients of the pro- portional overlap, the fietalonfl country for these cal- culations first needs to be chosen. Given that Aus- tralia has the highest level of economic development (in terms of the GDP per capita) among the G20 coun- tries, it is logical, therefore, to use its indicator for making the basic calculations (see Table 3). If the actual economic growth in the j -th country is j r , then the economic growth in this j -th country corresponding to that in the i -th country, given the hypothesis of proportional overlap of the catch-up effect, will be: * . j ij ij r r (4) Consequently, * ij r is the adjusted economic growth of the j -th country that can be regarded as corresponding to the economic growth in the i -th country. Briefly, let us call * ij r the adjusted economic Table 2. Indicators of Economic Development Level (GDP per capita) in the G20 Countries in 2010-2013 (See [7] ) No. Countries Year 2010 2011 2012 2013 1 Argentina 11,460.4 13,693.7 14,679.9 14,715.2 2 Australia 51,800.9 62,133.7 67,524.8 67,458.4 3 Brazil 10,978.3 12,576.2 11,320.0 11,208.1 4 Canada 47,465.3 51,790.6 52,409.2 51,958.4 5 China 4,433.3 5,447.3 6,092.8 6,807.4 6 France 40,706.1 43,809.7 40,908.3 42,503.3 7 Germany 41,723.4 45,870.6 43,931.7 46,268.6 8 India 1,417.1 1,539.6 1,503.0 1,498.9 9 Indonesia 2,946.7 3,469.8 3,551.4 3,475.3 10 Italy 35,875.7 38,367.3 35,132.2 35,925.9 11 Japan 43,117.8 46,203.7 46,679.3 38,633.7 12 Mexico 8,920.7 9,802.9 9,817.8 10,307.3 13 Russia 10,709.8 13,324.3 14,090.6 14,611.7 14 Saudi Arabia 19,326.6 24,116.2 25,946.0 25,961.8 15 South Africa 7,175.6 7,830.5 7,314.0 6,617.9 16 South Korea 22,151.2 24,155.8 24,454.0 25,977.0 17 Turkey 10,135.7 10,604.6 10,660.7 10,971.7 18 United Kingdom 38,363.4 40,972.0 41,053.7 41,787.5 19 United States 48,377.4 49,803.5 51,495.9 53,042.0
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100 Vladimer Papava Bull. Georg. Natl. Acad. Sci., vol. 10, no. 4, 2016 growth of the j-th country . Table 4 reflects the indi- cator of adjusted economic growth. Table 5 reflects both indicators Πthe actual and the adjusted data of economic growth rates. As is evident from Table 5 , the actual economic growth in China, for example, in 2013 was 7.7% and only 2.5% in Australia even though the Australian economy was 9.9 times larger than the Chinese economy in GDP per capita terms. Consequently, the 7.7% growth of the Chinese economy corresponds to the Australian economic growth of 0.8% (7.7:9.9). Similarly adjusted indicators of economic growth in other G20 countries are also given in Tables 4 and 5. According to Table 6, the leading G20 countries in economic growth are Australia, the U.S., Canada and Saudi Arabia and not China, Indonesia and India. Table 3. Coefficients of Proportional Overlap of the Catch-Up Effect (Ratio of GDP per capita in Australia to Similar Indicators of Other G20 Countries) No. Countries Year 2010 2011 2012 2013 1 Argentina 4.519991 4.537393 4.599813 4.584267 2 Australia 1 1 1 1 3 Brazil 4.718481 4.940578 5.965088 6.018719 4 Canada 1.091343 1.19971 1.288415 1.298316 5 China 11.6845 11.40633 11.08272 9.909569 6 France 1.272559 1.418264 1.650638 1.587133 7 Germany 1.241531 1.354543 1.53704 1.457974 8 India 36.55416 40.35704 44.92668 45.00527 9 Indonesia 17.57929 17.907 19.01357 19.41081 10 Italy 1.443899 1.619444 1.92202 1.877709 11 Japan 1.201381 1.344778 1.446568 1.746102 12 Mexico 5.80682 6.338298 6.877793 6.544721 13 Russia 4.836776 4.663187 4.792188 4.616739 14 Saudi Arabia 2.68029 2.57643 2.602513 2.598371 15 South Africa 7.219034 7.934832 9.232267 10.19332 16 South Korea 2.338514 2.572206 2.761299 2.596851 17 Turkey 5.110737 5.859127 6.333993 6.1484 18 United Kingdom 1.350269 1.516492 1.644792 1.61432 19 United States 1.070767 1.247577 1.311266 1.271792 Table 4. Adjusted Economic Growth Rates No. Countries Year 2010 2011 2012 2013 1 Argentina 2 .013279 1.895361 0.19566 0.632598 2 Australia 2 2.3 3.7 2.5 3 Brazil 1.589495 0.546495 0.167642 0.415371 4 Canada 3.115429 2.083837 1.319451 1.540458 5 China 0.890068 0.815337 0.694775 0.777027 6 France 1.571637 1.480684 0.181748 0.18902 7 Germany 3. 302374 2.657723 0.26024 0.068588 8 India 0.281774 0.16354 0.104615 0.111098 9 Indonesia 0.352688 0.362987 0.331342 0.298803 10 Italy 1.177367 0.370497 Р1.19666 Р1.01187 11 Japan 3.912165 Р0.37181 1.244324 0.916327 12 Mexico 0.878278 0.631084 0.581582 0.168074 13 Russia 0.930372 0.922116 0.709488 0.281584 14 Saudi Arabia 2.760895 3.337952 2.228615 1.539426 15 South Africa 0.42942 0.453696 0.270789 0.186397 16 South Korea 2.779542 1.438454 0.832941 1.155245 17 Turkey 1.800132 1.50193 0.331544 0.6668 4 18 United Kingdom 1.407127 1.055067 0.425586 1.053075 19 United States 2.334776 1.282486 1.754031 1.729842
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The Problem of the Catch-Up Effect and Post-Crises Economic Growth 101 Bull. Georg. Natl. Acad. Sci., vol. 10, no. 4, 2016 The indicators presented in Table 3 are con- structed on the principle of choosing the economy of a so-called fi etalonfl country which , in our case, is Australia, the country with the G20™s highest GDP per capita. In this case, its economic growth indica- tor serves to rank similar indicators of other coun- tries. It will be interesting if the final results of the eco- nomic growth rate comparisons change in the case of using an average indicator for the group of coun- tries instead of those of the fietalonfl country. It is not difficult to show that the ratio of eco- nomic growth rates adjusted to remove the catch-up effect does not change regardless of how they were calculated Œ based on the indicators of any one country or on the average indicators of the group of countries . If the given group consists of m 1,2,, im countries, the average GDP per capita ( y ) is calcu- lated as follows: Table 5. Actual and Adjusted Economic Growths Rates No. Countries Year 2010 2011 2012 2013 1 Argentina actual data 9.1 8.6 0.9 2.9 adjusted data 2.0 1.9 0.2 0.6 2 Australia actual data 2.0 2.3 3.7 2.5 adjusted data 2.0 2.3 3.7 2.5 3 Brazil actual data 7.5 2.7 1.0 2.5 adjusted data 1.6 0.5 0.2 0.4 4 Canada actual data 3.4 2.5 1.0 2.5 adjusted data 3.1 2.1 1.3 1.5 5 China actual data 10.4 9.3 7.7 7.7 adjusted data 0.9 0.8 0.7 0.8 6 France actual data 2.0 2.1 0.3 0.3 adjusted data 1.6 1.5 0.2 0.2 7 Germany actual data 4.1 3.6 0.4 0.1 adjusted data 3.3 2.7 0.3 0.1 8 India actual data 10.3 6.6 4.7 5.0 adjusted data 0.3 0.2 0.1 0.1 9 Indonesia actual data 6.2 6.5 6.3 5.8 adjusted data 0.4 0.4 0.3 0.3 10 Italy actual data 1.7 0.6 – 2.3 – 1.9 adjusted data 1.2 0.4 – 1.2 – 1.0 11 Japan actual data 4.7 – 0.5 1.8 1.6 adjusted data 3.9 – 0.4 1.2 0.9 12 Mexico actual data 5.1 4.0 4.0 1.1 adjusted data 0.9 0.6 0.6 0.2 13 Russia actual data 4.5 4.3 3.4 1.3 adjusted data 0.9 0.9 0.7 0.3 14 Saudi Arabia actual data 7.4 8.6 5.8 4.0 adjusted data 2.8 3.3 2.2 1.5 15 South Africa actual data 3.1 3.6 2.5 1.9 adjusted data 0.4 0.5 0.3 0.2 16 South Korea actual data 6.5 3.7 2.3 3.0 adjusted data 2.8 1.4 0.8 1.2 17 Turkey actual data 9.2 8.8 2.1 4.1 adjusted data 1.8 1.5 0.3 0.7 18 United Kingdom actual data 1.9 1.6 0.7 1.7 adjusted data 1.4 1.1 0.4 1.1 19 United States actual data 2.5 1.6 2.3 2.2 adjusted data 2.3 1.3 1.8 1.7
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102 Vladimer Papava Bull. Georg. Natl. Acad. Sci., vol. 10, no. 4, 2016 mm iii ii mm ii ii yNY y NN (5) where i Y is the amount of GDP in the i -th country and i N is the population of the i -th country. . Taking into account (3), the coefficient of propor- tional overlap of the catch-up effect of the j -th coun- try ( j ) in the case of the average level of economic development of the countries can be calculated ac- cording to the formula: . j j y y (6) As in (4), the adjusted economic growth of the j -th country ( * j r ); i.e., the economic growth in the j -th coun- try corresponding to the growth of the group of the countries, given the hypothesis of proportional over- lap of the catch-up effect, is determined as follows: Table 6. Rankings of G20 Countries by Actual and Adjusted Economic Growths Rates No. Countries Year 2010 2011 2012 2013 1 Argentina actual data 4 3 – 4 15 7 adjusted data 7 – 8 5 15 – 17 10 2 Australia actual data 16 – 17 14 6 8 – 9 adj usted data 7 – 8 3 1 1 3 Brazil actual data 5 12 14 8 – 9 adjusted data 10 – 11 14 – 15 15 – 17 11 4 Canada actual data 13 13 13 11 adjusted data 3 4 4 3 – 4 5 China actual data 1 1 1 1 adjusted data 14 – 16 12 7 – 8 8 6 France actual data 16 – 17 15 18 17 a djusted data 10 – 11 6 – 7 15 – 17 14 – 16 7 Germany actual data 11 10 – 11 17 18 adjusted data 2 2 11 – 14 17 – 18 8 India actual data 2 5 4 3 adjusted data 19 17 18 17 – 18 9 Indonesia actual data 8 6 2 2 adjusted data 17 – 18 15 – 16 11 – 14 12 – 13 10 Italy actua l data 19 18 19 19 adjusted data 13 15 – 16 19 19 11 Japan actual data 10 19 12 14 adjusted data 1 19 5 7 12 Mexico actual data 9 8 5 16 adjusted data 14 – 16 13 9 14 – 16 13 Russia actual data 12 7 7 15 adjusted data 14 – 16 11 7 – 8 12 – 13 14 Saudi Arabia actual data 6 3 – 4 3 5 adjusted data 4 – 5 1 2 3 – 4 15 South Africa actual data 14 10 – 11 8 12 adjusted data 17 – 18 14 – 15 11 – 14 14 – 16 16 South Korea actual data 7 9 9 – 10 6 adjusted data 4 – 5 8 6 5 17 Turkey actual data 3 2 11 4 adjusted data 9 6 – 7 11 – 14 9 18 United Kingdom actual data 18 10 – 11 16 13 adjusted data 12 10 10 6 19 United States actual data 15 16 – 17 9 – 10 10 adjusted data 6 9 3 2
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104 Vladimer Papava Bull. Georg. Natl. Acad. Sci., vol. 10, no. 4, 2016 ekonomika mkveTri zrdis efeqtis problema da postkrizisuli ekonomikuri zrda msoflios wamyvan qveynebSi v. papava akademiis wevri, ivane javaxiSvilis saxelobis Tbilisis saxelmwifo universitetis ekonomikisa da biznesis fakulteti da paata guguSvilis saxelobis ekonomikis instituti msoflio bankis statistikuri monacemebis Tanaxmad, msoflios wamyvani qveyana ara marto postkrizisul periodSi, aramed bolo aTwleulebis ganmavlobaSi iyo CineTi . postkrizisul periodSi ekonomikuri zrdis mixedviT CineTis momdevno qveynebia indonezia da indoeTi. qveynebis uSualo Sedareba ekonomikuri zrdis mixedviT arakonstruqciulia mkveTri zrdis efeqtis gamo, romlis Tanaxmadac kapitalis klebadi ukugebidan gamomdinare, ekonomikurad naklebad ganviTarebul qveynebSi maRali zrdis tempebis miRweva ufro advilia, vidre ekonomikurad ufro ganviTarebul qveynebSi. sxvadasxva qveynis ekonomikuri ganviTarebis gasazomad gamoiyeneba mosaxleobis erT sulze mTliani Siga produqtis maCvenebeli. statiaSi wamoyenebulia mkveTri zrdis efeqtis proporciuli gadafarvis hipoTeza. statia Seicavs invariantulobis Teoremis damtkicebas. mkveTri zrdis efeqtis koreqtirebiT ekonomikuri zrdis koeficientebis Tanaxmad ekonomikur zrdaSi msoflios wamyvani qveynebia avstralia, aSS, kanada da saudis arabeTi. REFERENCES: 1 . Acemoglu D. (2009) Introduction to Modern Economic Growth. Princeton: Princeton University Press. 2 . Aghion P., Howitt P. (2008) The Economics of Growth. Cambridge: MIT Press. 3 . Barro R. J., Sala-I-Martin X. X. (2004) Economic Growth. Cambridge: MIT Press. 4 . Van den Berg H. (2012) Economic Growth and Development. London: World Scientific Publishing. 5 . Mankiw N. G. (2004) Principles of Economics. Mason: Thomson South-Western. 6 . fiGDP Growth (Annual %).fl World Bank, online at http://data.worldbank.org/indicator/NY.GDP.MKTP.KD.ZG . 7. fiGDP Per Capita (Current U.S.$).fl World Bank, online at http://data.worldbank.org/indicator/ NY.GDP.PCAP.CD. 8 . Papava V. (2014) Problems of Economic Transition. 57 , 3: 3-12. Received July, 2016
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