The subject of this article is the relationship between the average growth rate of the money circulation velocity, V, and that of government expenditure, G. The figure below shows a distribution of average values for about 20 years in 33 countries. The average growth rate of G ranges from 2% to 10%, and the average growth rate of V ranges approximately less than 1% (one example is larger than 2%). In the past 20 years, it is concluded that "the growth rate of circulation velocity V is smaller than the growth rate of government expenditure G". This explains a direct proportional relationship between the growth rate of nominal GDP and the growth rate of G.
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| The x-axis shows the averaged growth rate of G, and the y-axis show the averaged growth rate of V. |
Our purpose for this article is to explain the direct proportional relationship between the growth rate of G and the growth rate of nominal GDP, as is shown in our previous article, "A relationship between nominal GDP growth rate and government spending growth rate."
In that article, the author showed that this direct proportional relationship can be explained under the money circulation, if the growth rate of V is equal to 0, and if the growth rate of G is equal to the growth rate of domestic investment, I. The above figure shows that the growth rate of V is small compared to the growth rate of G. This leads to the above direct proportional relationship.
Contents.
1. Data
For this analysis, our data are "Gross domestic product (GDP)," "Household spending," and "General government spending" of OECD. The followings are selected countries.
['AUS' 'AUT' 'BEL' 'CHE' 'COL' 'CRI' 'CZE' 'DEU' 'DNK' 'ESP' 'EST' 'FIN' 'FRA' 'GBR' 'GRC' 'HUN' ' IRL' 'ISL' 'ISR' 'ITA' 'JPN' 'KOR' 'LTU' 'LUX' 'LVA' 'NLD' 'NOR' 'POL' 'PRT' 'SVK' 'SVN' 'SWE' 'USA' ]
Our countries and period are not equal to those of Prof. Park's data introduced in "A relationship between nominal GDP growth rate and government spending growth rate." Each data have more countries. This is just a result of data selection.
We selected data of 2000-2020 of 33 countries, and some countries have shorter data period than this. For example, about Japan, there is no data on "General government spending" before 2004. The shortest period of our analyzed data is 2012-2019 for Costa Rica.
For averaged data, we excluded data of 2009 and 2020, in which global economic hazards happened.
2. Equations for the money circulation
Here we summarize equations for the money circulation, as described in "A three-piece set for understanding the money circulation" and "A relationship between nominal GDP growth rate and government spending growth rate."
From a unified picture of our three-piece set (the circular flow diagram, the definitions of nominal GDP [Y=C+G+I=C+T+S], and the quantity equation [Y=MV=PQ]), we obtained M=G+I. And from Y=MV, V=Y/(G+I)=1/(1-β) is obtained.
- M=G+I
- V=1/(1-β)
Next, when small variations, dY, dM, and dV are given to Y=MV, a relationship between the growth rates (variation rates) is obtained as follows,
- dY/Y = dM/M + dV/V.
On this formula, if we give dV/V=0 and M=G+I=aG (where `a' is an independent coefficient), then the following formula is obtained.
- dY/Y=dG/G
This formula explains the direct proportional relationship between the growth rate of nominal GDP and the growth rate of government spending, G. So, our initial purpose of this article is to verify the observed value of dV/V and the coefficient `a' of G+I=aG. However, since data on domestic investment, I, was not obtained from OECD, only the observed value of dV/V was verified.
3. Plots
This is the plots shown in the above.
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| The x-axis shows the averaged growth rate of G, and the y-axis show the averaged growth rate of V. |
The range of the growth rate of V is within ±1%. In contrast, the growth rate of G ranges from 2% to 10%. From this tendency, we can expect that the growth rate of nominal GDP show the direct proportional relationship with the growth rate of G. (And if G and I are always comparable.)
The following plot shows the distribution of the growth rate of nominal GDP and the growth rate of G from our data sample.
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| The x-axis shows the average growth rate of G, and the y-axis shows the average growth rate of nominal GDP. The gradient of the solid line is unity. |
This variance seems to be a little larger than Prof. Park's plot. However, our plot also shows a direct proportional relationship.
In this analysis, we excluded data of 2009 and 2020. This is because these years were in the economic hazards, and these values are significantly different from normal. The following plot shows temporal variations of the growth rate of nominal GDP (dY/Y) and the sum of the growth rate of G and the growth rate of V (dG/G+dV/V), on Japan.
France shows a good correlation.
As you can see at a glance in both plots, dG/G + dV/V fails to reproduce dY/Y, especially in 2009 and 2020. From this, we guess that the growth rate of I is largely different from the growth rate of G in these years. In 2009, there was the Lehman Shock, and in 2020, covid19 began to spread worldwide.
As summary, the growth rate of V is smaller than the growth rate of G, for the data of 20 years for 33 countries. This small value explains the direct proportional relationship between the growth rate of G and the growth rate of nominal GDP, under the money circulation.
This direct proportional relationship shows that the growth rate of nominal GDP in each country is effectively controlled by the growth rate of G. Therefore, the author considers that there is little meaning on studies of forecasting the growth rate of nominal GDP based on the "balance between demand and supply" using many parameters and many equations.
References
- OECD (2022), Household spending (indicator). doi: 10.1787/b5f46047-en (Accessed on 06 November 2022)
- OECD (2022), Gross domestic product (GDP) (indicator). doi: 10.1787/dc2f7aec-en (Accessed on 06 November 2022)
- OECD (2022), General government spending (indicator). doi: 10.1787/a31cbf4d-en (Accessed on 06 November 2022)
Link page: Contents for money circulation
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