The theory of exchangeability as a tool to build the new architecture of the
global monetary system
Bayzakov S.-Scientific Director
Economic Research Institute
PhD., Professor
GDP deflator nature in the theory of Friedman-Fischer
The existing model of nominal GDP according to official data is the sum of
the following:
NGDP1 + NGDP2+ NGDP3+ NGDP4 = NGDP.
NGDP i = p i *Q i
NGDPi is the nominal GDP as defined by the scalar multiplication of the
respective deflator - рi to their physical volumes – Qi in constant prices
NGDP1 is the final NGDP2 - is the
NGDP3 - is the
NGDP4 – balance
consumption by
final consumption final consumption on export-import
the household
by the government on investments
operations in
sector
physical terms
Constraints of the monetary theory of Friedman-Fischer for the audit of market
economy development sustainability
GDP deflator as nominal GDP growth rates divided by real GDP growth rates
has no relations to the actual prices of the current year:
𝑝(𝑡)
𝑁𝐺𝐷𝑃𝑡/ 𝑁𝐺𝐷𝑃0
=
(1)
𝑝(0)
𝑅𝐺𝐷𝑃𝑡/ 𝑅𝐺𝐷𝑃0
The nature of the deflator stems from the interpretation of the monetarism
model which by mathematical methods proves the constraints of the GDP deflator
(p(t)) and its inconsistency as a key tool for financial management in real economy
development:
p(t) x Q(t) = v(t) x M(t).
Thus, since NGDP=v*M, it is easy to get the formula of the GDP deflator
nature:
NGDPt/ NGDP0
pt
Mt /M0 vt
=
*
=
p0
Q t /Q 0 v0
RGDPt/ RGDP0
(2)
«Notice, - confirm our conclusion Saks and Laren – that we calculate the
index indirectly. We first take the nominal GDP (NGDP) in current prices, then
find the real RGDP in constant prices, i.е. Q= RGDP. So the price deflator
calculated this way is sometimes called a revealed price deflator of GDP»
[Saks J.D., Laren F.B. Macroeconomics, - M: Delo, 1996. P54].
GDP deflator nature in the theory of duality by Kantorovich Koopmans
GDP deflator serves as a financial regulator in the model of joint tasks by
Kantorovich-Koopmans which in a general case is reflected as follows:
Qt x pt = ct x Xt .
(3)
ct - is the coefficient of money velocity efficiency which expresses the contribution
of scientifric and technical progress (STP) to the real economy.
Xt - is the output from national accounts.
After the slight transformation the formula (3) is provided as an index of GDP
deflator measurement:
𝑝𝑡
𝑐 /𝑐
= 𝑡 0 ,
(4)
𝑝0
Where
𝑝𝑝0
𝑝𝑝0
=
𝑄𝑡 /𝑄0
𝑋𝑡 /𝑋0
𝑝𝑝𝑡 /𝑝𝑝0
means change in money purchasing power growth
Constraints of the theory of duality by Kantorovich Koopmans for audit of
sustainability in market economy growth
Constraints of the theory of duality by Kantorovich Koopmans for audit of
sustainability in economy growth is explained by excessive mathematic form of
interface for dual estimations as the prices of scarce resources as production inputs.
As seen from formula (4), the GDP deflator inside it is the efficiency coefficient of
the money velocity divided by money purchasing power.
That means here constraints of the theory of duality by Kantorovich
Koopmans is narrowing the economic contents of the task to manage the real
economy and excessive use of quantitative methods of analysis. But the theory of
duality developed by American mathematician Koopmans and Soviet academic
Kantorovich is the universal mathematic tool for analysis of economy and
monetary system. This mathematic tool is independent of ideological, political,
and social context of society. R.Benzel, being the member of the Sweden Royal
Academy of Sciences on the ceremony of Nobel prize winners Kantorovich
Koopmans in 1975 pronounced the key words yet not thought through and
realized: “the main economic problems are identical in all the societies”, and the
whole bunch of similar scientific problems can be investigated in its pure shape,
independent of political organization of the society where they are developed”.
Exchangeability theory – the base tool for market economy liberalization
In the formula (4) acquired after scientific rethinking of the GDP deflator
nature in the theory of duality by Kantorovich Koopmans we see the unity of two
mutually independent indicator for economy management. One of them is the
coefficient of scientific-technological risk of entrepreneurs in the real sector - с(t),
the other one – money purchasing power in the monetary system - pp(t). One of
them expresses the quality of the performance in the real sector, the other one – in
the financial sector.
The principle of mutual exchangeability of money and prices for goods and
services is formulated as follows: Multiple of money purchasing power index pp(t) on GDP growth rates in nominal terms prices (i1) equal the multiple of
economy progress с(t) on real growth rates (i2) :
pp(t) x i1 = c(t) x i2
(5)
This is the basic rule of economy development which is unique in the world
and supports overall liberalization of market economy and on the basis of labor
productivity and capital growth.
The Roadmap for justification of economic laws that allow to define the
prices
Step1. estimating the progress in economy found by the coefficient с(t):
c(t)= GDP/(QP+GDP)
Where GDP – GDP in current prices, QP – the cost of materials used for its
production. The sum QP+GDP = Х is the output from national accounts.
Step2. Index of real economy growth via money purchasing power, in Kazakh
interpretation is counted under the new formula (i3*),
i3* = c(t) x i2.
Index of real economy growth via money purchasing power is found with
account of scientific-technological risk/stimulus as multiple of real output growth
rates and scientific-technical progress coefficient.
Step3. The replacement of growth index i2 by the similar index i1/р(t) allows
to get a new real growth rate index i3*:
i3* = c(t) x i1 / р(t) =рр(t) x i1
This money purchasing power indicator pp(t) has no analogues in the world
and is defined on the basis of the growth rates i1 and i2, which shape the frame of
the GDP.
GDP deflator nature in the theory of exchangeability of money cost and
prices for goods and services
The targeted index of prices for goods and services and, accordingly, the
answer to the question by A.Marshall “what defines the equilibrium price of
goods” is found as the inverse of money purchasing power:
1/pp(t) = i1 / (c(t) x i2).
Inflation index (GDP deflator) is the scientific-technical progress coefficient
divided by money purchasing power:
p(t) = c(t) / pp(t) = i1 / i2.
Estimation of the net growth of the scientific-technical progress coefficient:
dc(t) = c(t) – 100%.
The scope of main formulas in practice of market economy management
1. To estimate the coefficient of scientific-technologic progress:
c(t) = CDP / (QP+GDP).
2. To estimate money purchasing power:
pp(t) = (c(t) x i2) / i1
3. To estimate prices for G&S:
1 / pp(t) = i1 / (c(t) x i2)
4. To estimate real economy growth:
i3 = pp x i1, или i3 = c(t) x i2
5. To estimate the GDP deflator:
р(t) = с(t) / рр(t)
6. To estimate the net growth of scientific-technologic progress coefficient :
dc(t) = c(t) – 100%.
The model of world reserve currency by IMF developed through purchasing
powers of national currencies
Since on each country through purchasing powers of national currencies is
known, then using basics of SDR calculation we have the following:
PP(СДР, t )  i 1 NGDP(i) /[ pp(1) * NGDP(1)  pp(2) * NGDP(2)  ...  pp(n) * NGDP(n)],
i n
Where n stands for the quantity of countries trade partners
Calculation of SDR in 2000-2010 on 35 countries (CIS, BRIC, ЕС 27, USA
and Japan) is given an the table below:
NGDP, USD bn.
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
100,0 99,8 104,0 116,7 130,1 138,5 148,8 165,8 179,7 175,2 200,9
RGDP, USD bn. PPP 100,0 99,1 102,2 106,0 108,2 106,7 108,5 112,6 114,6 120,4 128,7
SDR calculation, % 100,0 100,8 101,8 110,0 120,2 129,8 137,2 147,3 156,8 145,6 156,1
As seen from the table, the growth rates of nominal GDP on these 35
countries is 201%, whereas the real growth -128,7%. The calculated rate of SDR in
US dollars grew to 156% what is equivalent to USD purchasing power up to о 0.64
SDR.
The comparative analysis of economic growth in Kazakhstan and Germany in
2000-2008, 2000=100%
GDP deflator from official statistics
Economic growth from official statistics
Scientific progress contribution, %
Real growth index of prices for G&S
Economic growth through purchasing power of currencies
Kazakhstan
358,0
203,8
+9,5
327,0
223,0
Germany
168
111
-9
184
106
The example shows that even the advanced countries having the high-tech
production, may fall captured by negative aggregate contributions of the invested
inputs and organization of scientific progress management. This is shown by
+9.5% and -9% contribution of STP in Kazakhstan and Germany respectively. In
2008 as per 2000 prices.
As a result, the real economic growth rate under the purchasing power of
money in Kazakhstan was 223,0% against 203,8% according to official statistics.
In case of Germany the real economic growth rate was 106% against 111 %.
Roadmap for estimation of STP impact on appreciation of regional currencies
The example above is not the exception for a couple of countries. Current
growth rates of world economy after 2010 confirm that the previous decade’s
tempo is still preserved. It is seen from the analysis of 35 countries during the
period of economic crisis from the net growth of the coefficient с(t)%-100%. What
gives hope in it is just the tempos of the net growth in the development of
economies of G35, BRIC, Japan and USA in 2005-2010, which we provide below
(2000=100%):
2005
2006
2007
2008
2009
2010
CES (RUS-KZ-BEL)
2
2
1
0
-1
0
BRIC
ЕС 27
G35
USA
Japan
Great Britain
Germany
France
-2
-3
-2
1
-8
-2
-1
-3
0
-4
-3
1
-13
1
-4
-4
3
-4
-3
0
-10
0
-4
-3
1
-3
-2
-1
0
3
-9
-4
13
-4
3
8
2
-23
-2
-1
32
-2
7
4
12
-4
-6
-2
Liberal market economy – the acknowledged necessity
The model of monetarism is constrained by the growth of GDP deflator in
real economy:
Qt x pt = vt x Mt .
But this growth may be originating from the speculations in the monetary
system
The model by Kantorovich-Koopmans is constrained by objectively
conditioned estimates:
Qt x pt = сt x Хt .
But this growth in prices may be originating in excessive operational costs of
production.
The model of mutual exchangeability of money and prices for G&S is free
from constraints:
сt x RGDPt=ppt x NGDPt .
Liberal market economy becomes the acknowledged necessity: both sectors
of economy are interested in growing efficiency of their functioning, these interests
are not contradictory but mutually supportive.
The theory of exchangeability – the most progressive generation of models for
real economy management
As already shown, both the monetarism model: Qt x pt = vt x Mt , and duality
model: Qt x pt = сt x Хt are not the adequate models providing sustainable
development of real economy. The problems of monetary system development are
solved by use in a model of real economy development of the third dimension –
growth rates of economy based on the new formula of GDP deflator which reflects
the changes in real economy and changes in the monetary system:
𝑝𝑡
𝑐𝑡 /𝑐0
=
𝑝0 𝑝𝑝𝑡 /𝑝𝑝0
The final new model of sustainable development in real economy received by
“crossing” of the monetary model by Friedman-Fischer and duality principle by
Kantorovich-Koopmans is written as follows:
сt x RGDPt=ppt x NGDPt
Or the formula of money cost exchangeability and prices for G&S where the
GDP deflator in the concealed shape is presented as the efficiency of real sector
and financial sector performance:
с x I2= pp x I1
If William Petti told that “the labor is father of wealth, the land is its mother”,
then we can say” “the duality principle is the father of the scientific management
and the monetarism model is its mother”.