Economics/ 8. Mathematical methods in economics

Post-graduate student, Servetnyk N.

Taras Shevchenko National University of Kyiv, Ukraine

The Cyclicity of GDP in Developed and Developing Countries

Cyclicity is the one of the key tendencies of dynamic development, which must be considered analyzing economic development of world and national economy under globalization.

The research identifies length of economic cycles in Ukrainian and world economy. There were taken some time series, such as gross domestic product of development countries: USA, Germany, and Russia. USA was chosen as the third most developed country in the world [2]. It has the largest economy in the world, which although is currently in the slumps, is still progressing at an average rate. Germany is the most important as economic country in Europe. Russia has very close relationships with our country.

There is great number of methods to identify cycles in GDP. The most interesting are those, which let to explore periods of rise and fall of GDP.

The statistical analysis was done using the method of LOG filters. It shows the instability and difficulties in forecasting of the development of Ukrainian and Russian economies.

Fig. 1. GDP cycle in Ukraine and Russia

Source: https://www.bank.gov.ua, http://www.gks.ru

Large spread in GDP fluctuations of Ukraine and Russia under crisis indicates higher risks than in Germany or USA. It caused by undeveloped market relations in Ukraine and Russia, which are depend on external influence of world market, but haven’t any influence on it.

Fig. 2. GDP cycle in USA and Germany

Source: https://www.destatis.de, http://www.bea.gov/

To identify the cycles the method of Hurst exponent is used. It helps to analyze the character of mentioned fluctuations and assign them a numerical characteristic – Hurst exponent. There are three growth cycles for Ukraine, Russia, and Germany and four – for USA. Coefficients of the trends are shown in the Table 1. Minimum value of GDP for all countries is in 2^nd quarter of 2009.

Table 1

	Ukraine			Russia			USA			Germany
Period	H	b	R^2	H	b	R^2	H	b	R^2	H	b	R^2
2000 - 3dQ2001	1,064	-0,463	0,921	0,996	-0,436	0,796	0,849	-0,449	0,647	1,007	-0,429	0,901
3dQ2001 – 2005	0,258	0,122	0,325	0,258	0,133	0,172	0,103	0,644	0,142	0,076	0,301	0,054
2005 - 2008	0,512	-0,234	0,480	0,247	0,137	0,006	0,784	-0,414	0,873	0,687	-0,466	0,606

Source: authorial calculation

GDP in researched countries has different behavior under the crisis in 2007 – 2009. For instance, GDP in Germany, Ukraine and USA have stable oscillations on the first statistical cycle (Hurst exponent is more than 0,5) and sharply reduce their stability on the second statistical cycle (Hurst exponent is less than 0,5). Fluctuations of GDP in Russia save their characteristics on the second and third statistical cycles.

Now let to examine the coincidence of cycles in different countries. In Germany growth phase was observed during 1987 – 1993, after which there was a phase of recession lasting to 2003. The peak of growth took place in 2005 and from 2006 economy in this country develops with acceleration. The year 2012 saw the first period of weak growth for the German economy since crisis year 2009. After that a consistent recovery process took hold, accompanied by rising capacity utilization in industry and a strong domestic demand. The common expectation among all the estimates for 2013 and 2014 is that a renewed flare-up of the Eurozone crisis is unlikely and the German economy is going to take a swing upwards from the current growth low [4, p.1].

The growth phase in USA began from 1997. The US economy is currently embroiled in the economic downturn which followed the financial crisis of 2007–2008.

At last let to analyze cyclicity of Ukrainian economy in comparison with economic cycles in country with close economic relationships – Russia. The growth phase in Ukraine and Russia began in 2004. It worth to emphasize, that world tendency is leveling the onset of phase cycles and increase of their impact. The most prosperous are considered that country of Western Europe, in which number of growth phases was more than half of periods of observations.

References

1. Peters E. The fractal analysis of financial markets: using of theory of chaos in investment and economics/E. Peters// - M.: I-trading, 2004. – 304p.

2. Answers [Online] http://wiki.answers.com

3. Bureau of Economic Analysis [Online] http://www.bea.gov

4. Economic Forecast Germany 2013 [Online] http://www.gtai.de

5. National Bank of Ukraine [Online] http://www.bank.gov.ua

6. Federal State Statistics Service [Online] http://www.gks.ru

7. Federal Statistical Office of Germany [Online] http://www.destatis.de