https://sites.google.com/site/theorymb/
Abstract
The biggest drawback of modern economics is absence of the theory capable not only to explain but also to reliably predict macroeconomic indicators, including the beginning and depth of financial crises. In the "Theory of Macroeconomic Balance " (TMB) it is maid an attempt to construct such projections.
TMB unveils quantitative development patterns of market economies. Quasiconstants and formulas of this theory make it possible to predict the values of GDP growth rate, share of gross private investment in GDP, total return of stock market, the beginning and value of large fluctuations in stock market indices, and other economic indicators by 5-80 or more years .
Responses of experts
For reception of general representation about ТМB some positive responses about given work are resulted below. Certainly, critical remarks exist and will occur in future ,which the author accepts with gratitude and attention. The criticism becomes constructive if the reader has well understand the main ideas of the theory, promoted by these positive responses.
1. TMB unveils "code" of changes in stock market index over time.
2. ТМB would be more looks like a fiction novel, rather than scientific work, if not one "but": quasiconstants and formulas of this theory wonderfully correspond with historical statistics data of USA and other countries.
3. Share of investments in gross domestic product, GDP growth rate, profitableness of the stock market - are constants? The first idea - it cannot be even because the governments of different countries and managers of companies day and night work to increase these parameters and often - as they say - achieve successes. However ТМB convincingly proves that we live in economical world of constants.
4. Calculation instead of stock index forecast for 30 or 80 years forward from the point of view of the stock exchange speculator - is a fantasy.
5 Rate of technical progress was measured In TMB , which determines the rate of productivity and GDP growth.
6. Practical advantage of ТМB is to predict macroeconomic indices with a high degree of reliability and on this basis to liquidate economic crises and to reduce commercial risks by hundreds billions dollars.
7. In academic circles ТМB will cause a shock and aversion since it too strongly differs from traditional concepts in economic science . However thanks to phenomenal practical advantage this theory will be recognized among members of business-community.
8. Accuracy of formulas amazing. For example, the deviation between theoretical and actual values of market total return for 200 years was only several % of it summa.
9. ТМB is deductive theory, i.e. it has no in its basis compilation of statistical data but only logical reflections. This theory, alongside with laws of physics or chemistry, could arise on other planet, but nevertheless describe economic processes on the Earth.
10. Like a genie, released from the bottle, the publication of TMB bring back to life the powerful market forces that can dramatically reduce the volatility of markets and economic risks until the liquidation of major financial crises. And this will happen automatically and independently of government policies or opinions of the scientific community.
11. If only one investor will use TMB conclusions - he will get an exclusive competitive edge in remaining volatile (for other investors) stock market with the ability to extract huge extra profits. With his hand gambling becomes like a game of cards with marked deck.
12. It is surprising that the scientific community did not notice a simple fact of American post-war economic history - the constancy of private investment average rate and GDP growth trend .
13.With the advent of ТМB economics turns from descriptive to the exact science, similar with physics or chemistry.
14. In sine rate of market value relative to book value of assets (P / B) it is determined that the period of this sine wave is equal to its amplitude. That is, the percentage of incidence (relative to book value) of the market from the highest to the lowest point is equal to the length of the cycle, expressed in % of GDP growth. The difference of this rule with the 5 years average actual data over 20 century US cycles of is only 2%.
15.Publication of TMB will increase the debt instruments rate and the need to reduce public debt due to the sharp increase in the cost of its services in most countries.
The theory of macroeconomic balance
(« The Invisible hand » of Adam Smith becomes visible)
Representation that Earth is the sphere is obvious heresy since both professor of theology and ordinary peasant know that the Earth lies on three elephants. If the Earth is round, how the heretic asserts, why people do not fall from its opposite side?
(From the medieval treatise)
Table of contents
Responses of experts
Introduction
1. General theory of macroeconomic balance
1.1. Model
1.2. Criterion of optimality
1.3. Equation and formulas
2. Special theory of macroeconomic balance
2.1. Calculation of economical cycle duration
2.2. Total rate of return on investment
2.3. Forecast examplers
2.4. Historical statistics data approval
3. The table of quasiconstants of macroeconomic balance
4. Some additional conclusions
4.1. A compensatory hypothesis of "Great depression" reason
4.2. Capital intensity and technical progress
4.3. The program of countries with low GDP level growth acceleration
4.4. Globalization - a new level
5. Excel appendix
The conclusion
Introduction
During many decades USA economy develops with average rate 3 or hardly more than 3 % per year. But why not 2 % or 4 %? In 60th years Japan and last decade China gain 10 %, 12 % was maximal. Why not 13 or 15 %?
The share of private investments in US gross domestic product during the post-war period was in a narrow corridor of 14-17 %. Why not 13-18 % or wider? During accelerated development similar parameter was equal 1/3 for Japan and China and in separate years did not exceed 2/5 of gross domestic product. Why economy did not manage to break this barrier?
At last, the stock market. Why its total return without inflation in USA during last two centuries made 6 % and 6,5 %, no more and not less? How to calculate the dates of onset and magnitude of "bottom" and "peak" of stock market indices fluctuations?
The Theory of Macroeconomic Balance (ТМB) answers these and other questions, unveiling quantitative laws of market economy countries development.
1. GENERAL THEORY OF MACROECONOMIC BALANCE
In the given section the model of macroeconomic balance and statistical data confirming it,s basic conclusions will be considered.
1.1. MODEL
Our purpose is to construct econometrical model which, having minimum of variables, would explain quantitative interrelations between the basic macroeconomic parameters. A primary factor of the present model is communication between gross domestic product (Y) and a share of investments into gross domestic product (K). All product shares into two parts - investments К*Y and consumption (1-К) *Y. Such factors operating in economy, as cost of land , natural resources, taxes, ecology, population, employment, inflation, trading balance, historical features of countries and etc. are not considered.
Let's assume, that in each separate manufacturing site, making gross national product, owing to technical progress production increases by «stairs» as it is shown on picture 1. Each stair corresponds to the technological level. Replacement of old technology by new occurs in conditions of technological obsolescence. The owner of the capital may not carry out the investment, having left performance level Уо during a long time interval. And if he decided to invest the purpose was reception of additional product (the shaded area on рiс.1). At the next replacement of equipment this additional product disappears, since the equipment on which it has been made is dismantled, and the size of this product is included into base of a following cycle (see рiс.1).
YT YT
Y0
Yo
Pic.1 Pic.2
Let service life of the equipment be equal Т in each cycle, and rate of productivity be r ,then increase in productivity of new techniques against replaced will make:
Yт/Yо=exp (r*T) = Z
As the quantity borrowed in manufacture does not vary in time rate of growth of all economy will be equal to labor and techniques productivity r growth rate. If in separately taken manufacture site productivity changes by «stairs», in all economy where the set of manufactures work simultaneously , it is continuous function. In economy simultaneously function high-efficiency capital with productivity Yт, and less productive Yо (see pic.2). At the moment of old equipment replacement into new one it is updated only its active part. Other part of the assets involved in production can serve in new manufacture. There would be an inexcusable mistake each time during updating, for example, to destroy old building and to build new one on its place. If the old building allows to organize inside its walls manufacture with new technology refusal of it would be empty squandering. The rule operates in business: Capital is spent only for what it is impossible to manage without.
Thus, in structure of the general capital there is a certain share of the "old" capital which has passed from former cycles. At the given stage of model formation we shall not consider this "old" capital since growth of productivity, shown on pic.1 does not depend on it. We shall note only, that investor can receive it from the saved stock of former cycles in any necessary quantity thus not spending current investments. In the structure of active capital involved in manufacture we shall allocate two kinds, differing by character of reproduction. These are investments into a fixed capital (Ko) which after full amortization leave manufacture, and investments in stocks (Кz) which are constantly updated also amortization are not a subject. The general investments are equal to their sum: К=Ко + Кz.
Let Ymax is gross domestic product of all economy, where capital with maximal-possible performance level for given moment Yт functions only, and Y is gross national product of real economy in which productivity of separate manufactures changes from Yо up to Yт. We shall calculate Y and Ymax, meaning, that Yт=Yо*Z:
Ymax = Yо*Z*T (1)
Y = Yo* ST0ertdt =Yo * (Z-1)/r (2)
From (1) and (2) equality follows:
Y = Ymax * (Z-1) / (Z*r*T) (3)
Let's admit cost of the modern equipment for manufacture of product to be Ymax ,cost of stocks - Кmax*n , and necessary for manufacture equipment investment - equal Кmax,. The need for investments for each year of equipment service will make Кmax * (1+n)/Т. Actual investments will be less by Кmax*n/Т/Z since the stocks which were ensured the functioning the left equipment, will pass for service of the new equipment. Investments will make:
K = Kmax * (1+n-n/Z)/Ymax/T (4)
Considering that the stock of active capital Kfixt is the sum of the investments collected during period Т, we shall find its attitude to gross national product:
Kfixt = Ko/Z ST0ertdt = Ko * (Z-1)/Z/r (5)
( ST0 mean integral )
Apparently from рiс.1 the shaded part of production is the additional value which has resulted from investments:
S = (Z-1)/Z (6)
It is possible to calculate S in another way, as the sum of gross product growth rates for the period of service T of an active part of fixed capital (see рiс.2):
S = r/Z ST0ertdt = (Z-1)/Z (7)
Though the size of a product has arisen as the summa infinite in time annual increments, market recognize as S only part of it, limited by actual time of service capital operating. If there were no investments To there would be no also an increase of product S. Therefore all additional product S belongs to investor of capital To.
1.2. CRITERION OF OPTIMALITY
Criterion of optimality in model is maximization of product consumption, existing in various forms. At level of economy as a whole the consumption level should be the greatest during each moment of time: Y * (1-К) = MAX. As limiting value for consumption is the marginal level of product Ymax the criterion can be written down in following kind:
Y * (1-К) / Ymax = MAX (8)
Financial criteria are also important for effective functioning of the capital and economy. Additional product S breaks up on two parts: investments S*К and consumption S * (1-К). Increase of consumption S * (1-К) should exceed size of investments K, otherwise investment loses sense since expenses for increase in consumption will exceed the gain of consumption. In formalized view the criterion will become:
S * (1-K)> K (9)
Performance of this condition is necessary not only for economy as a whole but also its limiting value, i.e. the size of a gain of consumption should outperform expenses for this gain for each dollar of investments:
d (S * (1-K))> dK (10)
Financial criteria (9,10) in system of optimality criteria have the subordinated character in relation to economical one (8). They should be carried out only after performance of the basic economical criterion. This requirement is caused by the several reasons. First, economical requirement for a society is more important than narrower financial interests. Secondly, financial criteria cover only a part of gross product.
1.3. Equations and fomulars
Let's work out the equation satisfying economic stationary criterion (8), using (3) and (4):
Y * (1-К) / Ymax = (Z-1)/Z/r/T (1-Kfixt * (1-n-n/Z)/T) = MAX (11)
The economic sense of this equation is that comparatively new high-efficiency equipment is in operation by short-term service. There is rather new equipment with high efficiency in short-term service life ,and that conducts to increase in the general volume of manufacture. However after reduction of service life the share of a product going on the investment and reducing a share on consumption sharply increases. The task is to search such value of Тwhich has provided maximization of function at given values of r, n, Kfixt (11).
Let's solve (11), putting the first derivative on T to 0. Having discarded roots without sense we shall receive following parities Т, r, n, Kfixt at which consumption reaches the greatest value:
r*Kfixt = 1 / (n+Z / (Z-1-lnZ)) (12)
And also, considering (12) and (4) , (5):
Kz = n / (n+Z / (Z-1-lnZ)) (13)
Ko = Z / (Z-1) / (n+Z / (Z-1-lnZ)) (14)
K = (n+Z / (1+Z)) / (n+Z / (Z-1-lnZ)) (15)
Formulas (12) - (15) reflect optimum parities of macroeconomic parameters for any country with market economy.
Let's consider now what are greatest values of these parameters. For this purpose we shall copy the equation (9), using formulas (6) and (15):
((Z-1) / (Z-1-lnZ)-1) / n / (n+Z / (Z-1-lnZ))> (n+Z / (1+Z)) / (n+Z / (Z-1-lnZ)) (16)
In a limiting case, at n =0, or Кz =0 restrictions imposed by an inequality (16), lead to following quantitative values:
Z <2,3223 K <36,281 % r*Kfixt <20,658 % S <56,939 % (17)
Or, being expressed in terms of ТМB, it is possible to approve, that in any market economy investment cannot exceed 36,3 % size of gross domestic product, and the additional product( operating surplus) cannot be more than 57 % of GDP.
Differentiating the right and left parts of (16) according to criterion (10) and accepting parameter n as constant we shall receive limiting values of macroeconomic parameters:
n <((1-lnZ) (2*Z-1)-Z*lnZ / (Z-1)) / (2*Z*lnZ-lnZ*lnZ / (Z-1) - (Z-1) (2*Z-1)/Z) (18)
At n =0, or Кz =0
Z <1,44255 Ko <17,205 % r*Kfixt <5,287 % S <30,678 % (19)
For economic interpretation of received results we shall work out the equation of optimality criterion, using (12) and (14) at n = 0 and assuming, that capital intensity Kf is a constant:
(Z-1-lnZ) *lnZ/(Z-1) / Z/Kf = MAX (20)
Derivative of function (20) at least in an interval 1,4 <Z <2,4
Is positive. It means, that any gain dZ, and
dК, leads to increase value of function (20).
For economy which can increase investments without increasing capital intensity, their size will aspire to the top limit defined by formulas (16) and (17). These are economy of the countries with rather low level of development, but with the developed market infrastructure and the qualified labor , providing conditions for high rates of gross national product growth. These countries pass a stage of the accelerated development, borrowing technologies in the country - leader of technical progress. In process of their approach a level of the advanced country and exhaustion of growth conditions, rates of development and a level of investments decrease , country comes nearer to a level set by the formulas (18) and (19). At this level - level technically the countries - the main obstacle for the accelerated development absence of more productive technologies with a former capital intensity is advanced. Growth of rates is possible only at decrease in a capital intensity, since their product is set by constant r*Kfixt=5,287 % GDP (see (19)). Parameters of all other market economy countries are between the given marginal levels, carrying out movement to top level (if there are corresponding conditions), or to bottom (if the top level is already passed or country is rather high developed).
In the economy opened for foreign markets, cost of initial and ready products is equalized by the international price for these products. Cost of equipment in such open economy approximately is identical. Therefore the capital intensity (ratio of capital to production) in the different countries is approximately identical. A developing country, using high technology, can let out production with the same capital intensity, as country-leader of technical progress. As the gain of a capital intensity r*Kfixt at the country with the accelerated development is (20,658/5,287 see (17), (19)) =3,907 times more, than at the leader, and the size of a capital intensity is approximately identical, it means, that rate of growth of the "catching up" country can maximal be 3,9 times above the leader:
rjap <3,9* rus (21)
Annual capital investments K leads to increase additional product by r*S. Profitableness R of capital investments makes:
R = r*S/K (22)
In a limiting case for the country-leader (at Kz=0) R=1,78 r, i.e. average current profitableness of investments is 1,78 times above rate of GDP growth .
Cost of capital P functioning in economy is equal to the capitalized cost of net profit flow which it generates. Except for (S-K) the annual capitalized increase enters into this flow as r * (S-K). Using profitableness (22) for capitalization we shall find this increase:
r * (S-K) / R (23)
All capitalized cost of investor net profit flow will be equal:
P = (S - K+r * (S-K)/R)/R = K* (1-K2 /S2)/r (24)
Till now we considered reproduction proportions of "effective" capital part from which growth productivity directly depends, shown on pic.1. One shall remind, that reproduction factor Z is equal exp (r*Tz) ,where Tz is time of fixed capital effective work after which the equipment continues to work though do not influence on growth of productivity. We shall find now reproduction factor y = exp(rTY ), where Ty- full time of fixed capital life.
Depreciation in balanced economy is equal to actual leaving of equipment. If Depreciation exceed actual leaving of equipment it contains already part of profit since exceeds need for left equipment replacement. The difference between cost of invested means of production Ko and their pure gain r*P will be equal to size of leaving. Having divided cost of the invested basic means by left size we shall receive required factor of reproduction:
Ko / (Ko-r*P) = exp (r*Ty) = y (25)
Let's copy (25) using (24):
rTy=LN (Ko*S2/K3) (26)
Formula (26) is one of the major in TMB system. It is expressed by the sum of logarithmic % of GDP growth during equipment service life and defines the period of total return R on the invested capital. The economic sense of this cycle mean that at any external rejecting influences (as a rule aside decrease) on total return R the market mechanism will lead to its optimum size during service life of assets Ty. In other words assets during the life should bring optimum size of profit at any rejecting factors. Only in this case criteria (8-10) are carried out and the system of macroeconomic parameters is balanced.
r N
L
M A
E Kfixt
B C D
Рic.3
Let's consider now, what restrictions impose the macroeconomic interrelations, revealed above, on a course of technical progress. For this purpose on fig. 3 we shall draw curve AL under the formula (19): r*Kfixt=5,287 % in space of ordinates axes r (rates) and abscissa Kf (capital intensities). This curve expresses "resolved" by the theory mutual position of growth rate and an effective capital intensity. Curve AN expresses opportunities which are given with technical progress: the first derivative of this curve is positive, i.e. the increase in rate of growth (and labor productivity) is possible only through growth of a capital intensity. It is obvious that curves can be crossed only under 90o angle since only in this case the equally effective vector breaking balance is not formed. We shall prolong AN to cross with an abscissa in point E. Straight line АЕ, moving along curve AL, aspires to borrow higher position with as much as possible high growth rate r. Thus capital intensity Ktech in a point A (piece СЕ) in relation to rate of growth (piece LС or МВ) increases. The maximal-possible capital intensity is reached at zero leaving equipment funds or infinite term in time of their service. The attitude infinite in time of investments To sum to rates of growth r gives as a result К/r, i.e. capital intensity Ktech = К/r. The ratio of « technical progress » capital intensity Ktech to « permitted»capital intensity Kfixt is equal to the following:
К/r/ Kfixt = 17,205/5,287 = 3,254 ( 27 )
or
Кtech = 3,254* Kfixt ( 28 )
On the basis of similarity of triangles ЕАС and АСD we shall work out the equation of a parity of these two curves in a point A, crossed under a 90o angle:
ЕС/СА= СА/СD = Кtech/ r = r/ Kfixt
3,254* Kfixt* Kfixt = r* r r2 = 1,804* Kfixt * r ( 29 )
Puting in ( 29 ) data from ( 19 ) one shall get:
r = 2√ 5,287*1,804 = 3,088 ( 30 )
Thus optimum rate of country – leader GDP, providing both maximization of consumption level and the fullest use of technical progress acceleration opportunities of development, in a limiting case (Кz=0) makes 3,088 logarithmic %. For case Кz=0,5, that correspond with USA parameter during last decades, GDP rate will make 3,01 %.
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( This paper is not finished. To be continued in nearest future)
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The conclusion
On a question « what is market economy » from point of view of the given theory it is possible to give playful but not deprived answer: the economy is the huge computer which has been adjusted to solve some mathematical equations. Individuals in this computer work as calculating elements instead of semiconductors, and corresponding sums of money act instead of electric impulses of various force. Millions of people daily make decisions to purchase goods and services for themselves and their companies . Activity of these people is directed to solve the equations to optimize macroeconomic proportions despite of rejecting natural and social influence.
The market in ТМB appears not as function of many variables with high amplitude of unpredictable spontaneous fluctuations, but as the maintenance mechanism of certain macroeconomic proportions. Accuracy of this mechanism is comparable with the minimal size of available statistical data, that means it is comparable to accuracy of economic processes measurement tool.
According to ТМB source of profit is the increase of productivity provided by introduction of new technologies and technical progress. The share of country-leader operating surplus in GDP is a constant. For other countries the size of surplus is function of investments volume. It is automatically supported by a market mechanism and does not depend neither from policy of the government, nor from requirements of trade unions, nor from businessmen avidity.
The annual share of investments into gross domestic product of country-leader is a quasiconstant and makes 16-17 %, rate of GDP growth is equal to round 3,0%. The country from rather backward can pass in a number of the most developed countries, thus the share of investments can be 2 times above the leader. Maximal-possible rate of growth 3,9 times exceeds 3 % optimum rate of the leader. After achievement of developed economy level the given country reaches labor productivity level close to the country-leader. Rate of GDP growth would be less than 3 % if dynamics of labor force in the given country concedes to the leader.
The stock market of the country-leader has total return of 6-7 % and develops cyclically with the period 34-37years (for modern and future condition of macroeconomic proportions). Duration of a cycle depends on GDP rates and share of investments into inventories. In 19th century it last in 20 years, in 20th century - 30-35 years. Rises and fallings of US stock market average profitableness repeated with such periodicity.
What consequences of the given theory can last for economy and business? If the behavior of businessmen correspond calculations on the basis of quasiconstants the future condition of the market risks of sharp rises and falling of stock indexes considerably will decrease. Really, if investor is absolutely assured, that in nearest future will receive 6 % on invested capital he will not join general panic and get rid of assets during market collapse with a heavy loss for himself. But for liquidation of a panic it is necessary to believe in ТМB by all investors what is impossible. How events will develop in these conditions?
Among millions of investors always there will be a small group of those who has believed in ТМB and begin to put it into practice. It will give to these group advantage in « natural selection »of best investors which permanently goes in the market, and provide its quantitative growth. Members of this group, unlike other investors know that at some point x market grows will yield from 0% up to 12%, and begin to buy before the rally. An example of successful investors will gradually conquer other market participants. Purchases will start earlier and earlier of period x, calculated according to TMB, causing an increase in the prices (and profitableness!) until the day "x" and – in contrast – reducing the price and transactions yield committed after x. At last, existed in not informed world sequence periods with market total return 0-12-0% as the number of investors who use TMB strategy grow, changes to 6-6-6%. This means the end of large fluctuations and crises in the stock market. Gin of business cycles parameters knowledge is let out from a bottle and sooner or later will execute the mission to reduce risks and liquidate stock and financial markets crises.
The cumulative effect of stock market risks decrease can make 30 trillions dollars (= to the sum of capitalization losses in 2008-2009 which happens about one time in 35 years). Plus reduction of risks in other sectors of economy and reduction of smaller collapses fluctuation amplitude.
The size of stock market actual total return deviation from theoretical value is inversely proportional to number of businessman following TMB laws. Therefore the amplitude deviations will decrease in accordance with TMB ideas distribution among making economic decisions persons, from 40-70 % ,corresponding deep crisis, to 5-10 %, corresponding light recession, and even less.
Given publication of ТМB represents only the beginning of new era in economic forecasting development - an era of constants and reliable numerical calculations of future market conditions. At the same time the publication has shined only a top of an iceberg of deep laws in economic development, having left underwater part to future researchers. ТМB construction is at an initial stage, it may be necessary to correct and add something. However conclusions which are already received also accuracy of quantitative interrelations which takes place, give the basis to trust in efficiency of this theory.