Source document: https://docs-lawep.s3.us-east-2.amazonaws.com/1697741931095.pdf (Georgia)
saqarTvelos mecnierebaTa erovnuli akademiis moambe, t. 10, #4, 2016 BULL ET IN OF THE GEORGIAN NATIONAL ACADEM Y OF SCIENCE S, vol.

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4, 2016 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 after 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 countries with relatively low levels of economic development find it easier to achieve higher growth rates than countries with more advanced economies due to diminishing capital returns.

For measuring the economic 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 economic growth ratios, the World leading countries in economic growth are Australia, the U.S., Canada and Saudi Arabia.

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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- countries in economic growth in the post-crisis pe- riod.

The list of G20 countries includes not only coun- tions [1-4].

In order to measure economic growth, it is par- tries but the EU as well.
Because the paper is focused on the problem of the leading G20 countries in eco- ticularly important to use a more or less adequate method allowing an inter-country comparison.

But nomic growth, further we examine only 19 countries from the G20.

such a comparison is complicated by the existence of the so-called “catch-up effect.” The goal of the pa- As it is known, economic growth is measured using the indicator: gross domestic product (GDP) 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 growth rate (r).
To calculate the indicator, the amount , where 1Y of increase in the real GDP ( 0Y is the is the real GDP in the reporting period and real GDP in the base period) should be divided by the Y Y   Y  0 1 amount of the base-period real GDP ( 0Y ): © 2016 Bull.

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98 Vladimer Papava Table 1.

Indicators of Economic Growth in the G20 Countries in 2010-2013 (See [6]) No.
Countries Argentina Australia Brazil Canada China France Germany India Indonesia Italy Japan Mexico Russia 13 Saudi Arabia 14 South Africa 15 South Korea 16 17 Turkey 18 United Kingdom 19 United States -0.5 4.0 4.3 8.6 3.6 3.7 8.8 1.6 1.6 Year 2012 0.9 3.7 1.0 1.7 7.7 0.3 0.4 4.7 6.3 -2.3 1.8 4.0 3.4 5.8 2.5 2.3 2.1 0.7 2.3 2013 2.9 2.5 2.5 2.0 7.7 0.3 0.1 5.0 5.8 -1.9 1.6 1.1 1.3 4.0 1.9 3.0 4.1 1.7 2.2 r  Y 0  Y (1) indicators does not give a true estimate of the real situation because the level of economic development 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).

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) According to the economic growth data for all of It should be noted that in comparing countries the countries listed in Table 1, the leading countries in economic growth during the post-crisis period are and regions, the GDP is usually measured in US dol- lars.

China, Indonesia and India.


At the same time, nega- tive economic growth occurred in Italy and Japan The figures for the GDP per capita are given in Table 2. with the lowest growth rates observed in France, the U.K. and the U.S. For example, according to Table 2, the U.S. economy in 2013 was 7.8 times the economy of China Naturally, a direct comparison of economic growth (in terms of the GDP per capita), 15.6 times the Bull.

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4, 2016 The Problem of the Catch-Up Effect and Post-Crises Economic Growth ... 99 Table 2.

Indicators of Economic Development Level (GDP per capita) in the G20 Countries in 2010-2013 (See [7]) No.
Countries Argentina Australia Brazil Canada China France Germany India Indonesia Italy Japan Mexico Russia 13 Saudi Arabia 14 South Africa 15 South Korea 16 Turkey 17 United Kingdom 18 United States Year 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 iy ) by that of the j-th country of the i-th country ( jy ): (   ij y .i y j Bull.

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4, 2016 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 “etalon” 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).
is If the actual economic growth in the j-th country jr , 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: * r ij  r j  ij .

(4) Consequently, * ijr 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 * ijr the adjusted economic (3) 100 Vladimer Papava 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 1 Argentina 2 Australia Brazil 3 Canada 4 China 5 6 France 7 Germany India 8 Indonesia 9 Italy 10 11 Japan 12 Mexico 13 Russia 14 15 16 17 Turkey 18 United Kingdom 19 United States Saudi Arabia South Africa South Korea 2010 4.519991 1 4.718481 1.091343 11.6845 1.272559 1.241531 36.55416 17.57929 1.443899 1.201381 5.80682 4.836776 2.68029 7.219034 2.338514 5.110737 1.350269 1.070767 Table 4.

Adjusted Economic Growth Rates No.
Countries Argentina Australia Brazil Canada China France Germany India Indonesia Italy Japan Mexico Russia 13 Saudi Arabia 14 South Africa 15 South Korea 16 Turkey 17 United Kingdom 18 United States 19 2010 2.013279 2 1.589495 3.115429 0.890068 1.571637 3.302374 0.281774 0.352688 1.177367 3.912165 0.878278 0.930372 2.760895 0.42942 2.779542 1.800132 1.407127 2.334776 Year -0.37181 0.631084 0.922116 3.337952 0.453696 1.438454 1.50193 1.055067 1.282486 2012 4.599813 1 5.965088 1.288415 11.08272 1.650638 1.53704 44.92668 19.01357 1.92202 1.446568 6.877793 4.792188 2.602513 9.232267 2.761299 6.333993 1.644792 1.311266 Year 2012 0.19566 3.7 0.167642 1.319451 0.694775 0.181748 0.26024 0.104615 0.331342 - -1.01187 0.916327 0.168074 0.281584 1.539426 0.186397 1.155245 0.66684 1.053075 1.729842 growth of the j-th country.
Table 4 reflects the indi- cator of adjusted economic growth.

Table 5 reflects both indicators – the 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.

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4, 2016 The Problem of the Catch-Up Effect and Post-Crises Economic Growth ... 101 Table 5.

Actual and Adjusted Economic Growths Rates No.
Countries Argentina Australia Brazil Canada China France Germany India Indonesia Italy Japan Mexico Russia Saudi Arabia South Africa South Korea Turkey 18 United Kingdom 19 United States actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data Year -0.5 - -2.3 - -1.9 -1.0 1.6 0.9 1.1 0.2 1.3 0.3 4.0 1.5 1.9 0.2 3.0 1.2 4.1 0.7 1.7 1.1 2.2 1.7 The indicators presented in Table 3 are con- structed on the principle of choosing the economy tries instead of those of the “etalon” country.
It is not difficult to show that the ratio of eco- of a so-called “etalon” country which, in our case, is Australia, the country with the G20’s highest GDP nomic growth rates adjusted to remove the catch-up effect does not change regardless of how they were per capita.

In this case, its economic growth indica- tor serves to rank similar indicators of other coun- calculated – based on the indicators of any one country or on the average indicators of the group of tries.

countries.
countries.

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- Bull.

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4, 2016 If the given group consists of m   countries, the average GDP per capita ( y ) is calcu-   1, 2, m i , lated as follows: 102 Vladimer Papava Table 6.

Rankings of G20 Countries by Actual and Adjusted Economic Growths Rates No.
Countries Argentina Australia Brazil Canada China France Germany India Indonesia Italy Japan Mexico Russia Saudi Arabia South Africa South Korea Turkey United Kingdom United States actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data actual data adjusted data Year 2010 4 7-8 16-17 7-8 5 10-11 13 3 1 14-16 16-17 10-11 11 2 2 19 8 17-18 19 13 10 1 9 14-16 12 14-16 6 4-5 14 17-18 7 4-5 3 9 18 12 15 6 2011 3-4 5 14 3 12 14-15 13 4 1 12 15 6-7 10-11 2 5 17 6 15-16 18 15-16 19 19 8 13 7 11 3-4 1 10-11 14-15 9 8 2 6-7 10-11 10 16-17 9 2012 15 15-17 6 1 14 15-17 13 4 1 7-8 18 15-17 17 11-14 4 18 2 11-14 19 19 12 5 5 9 7 7-8 3 2 8 11-14 9-10 6 11 11-14 16 10 9-10 3 2013 7 10 8-9 1 8-9 11 11 3-4 1 8 17 14-16 18 17-18 3 17-18 2 12-13 19 19 14 7 16 14-16 15 12-13 5 3-4 12 14-16 6 5 4 9 13 6 10 2 m m Y i i i y   y N i     iY is the amount of GDP in the i-th country (5) i m N N m i i i i where and iN is the population of the i-th country..
Taking into account (3), the coefficient of propor- development of the countries can be calculated ac- cording to the formula:   j y y j .
(6) As in (4), the adjusted economic growth of the j-th country ( * jr ); i.e., the economic growth in the j-th coun- tional overlap of the catch-up effect of the j-th coun- try corresponding to the growth of the group of the try ( j ) in the case of the average level of economic countries, given the hypothesis of proportional over- lap of the catch-up effect, is determined as follows: Bull.

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4, 2016 The Problem of the Catch-Up Effect and Post-Crises Economic Growth ... 103 r * j  r j a j .

(7) If the growth of the world economy is denoted by r , then, taking into account (1), we obtain: r    m  i m Y i i Y i 0 .

A comparison of (10) and (11), i.e., the ratio of the adjusted economic growth rates of the j-th and i-th countries corresponding to the economic growth of the group of the countries, is equal to: * j * r r i  r j r i  y j y i .
Comparing (9) and (12), we get: Let us consider the ratio of adjusted economic growth rates separately.

They are calculated based on a particular “etalon” country or on group averages.

* r ij r i  * j * r r i .

(12) (13) Inserting (3) in (4), * r ij  j .


r y j y i Based on (13), we can formulate the so-called in- variance theorem [8: 11]: The ratios of economic growth rates adjusted to remove the influence of the (8) Based on (8), the ratio between the adjusted eco- nomic growth of the j-th country corresponding to the economic growth of the i-th country and the ac- tual economic growth of the latter is as follows: * r ij r i  r j r i  y j y i .
(9) Similarly, inserting (6) in (7), for the j-th and i-th countries, respectively, we obtain: catch-up effect are the same in the case when the indicators of economic growth and the development level, that are used to calculate the coefficients of proportional overlap of the catch-up effect, belong to one selected country from the group of countries or are the average of this group; because the aver- age of the group is a constant, the ratio of economic growth rates adjusted to remove the influence of the catch-up effect does not depend on the choice of the r * j  * r i  r y j j y , r y i i y .
base indicators of economic growth and the devel- (10) opment level that are used to calculate the coeffi- cients of the proportional overlap of the catch-up (11) effect.

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4, 2016 104 ekonomika Vladimer Papava 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.

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Received July, 2016 Bull.

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4, 2016