## BUSINESS CYCLE MAIN PRINCIPLES

**The CMI model is a unique synthesis of econometric (non-structural) and theoretical (structural) models that preserves the main advantages of both classes of models while allowing us to avoid their main drawbacks at the same time (see the section Competitive Advantages of the CMI model). **

#### In Brief

Within the model, we proposed an original way to measure the rate of market (competition) imperfection that is at the base of the CMI model. At the base of this method is a calculation of the natural (normal) price (P_{0}) that corresponds to the perfect market, even if the perfect market was never formed in the real world. Well-known models posit rationality (perfection) of market valuations but are unable to verify their rationality (perfection) rate. The rationality (perfection) rate can be approximately identified post-facto only and with a considerable time lag, if at all. Money as a product of exchange that is highly dependent on psychological laws evaluates exchange processes directly. At the same time, production expenditures or technology (that depends on physical and chemical laws) can only be evaluated in monetary terms indirectly. As a result, the accuracy of technology evaluation in monetary terms directly depends on the exchange perfection, the rationality of market valuations, and the market imperfection rate. In the case of perfect markets (competition) only, market valuations rational are automatically both for exchange and production.

#### Energy equivalent of the cost

To calculate the “natural” price we introduce chemical exergy units (in addition to monetary ones) to evaluate production cost. Exergy cost consists of two components only for sectors of the economy that extract natural resources: 1) an absolute value or chemical exergy component (in defiance of monetary estimation) and 2) a production cost component (in the same way a monetary one). For the rest of the economic sectors, these absolute values are equal to zero. Chemical exergy characterizes the absolute values of natural resources that they have, even ones that have not been extracted from the Earth and used in GDP production. These values are the kind of natural constants for our planet, which were tabulated for main natural resources (Shargut, 1987)[1].

To calculate the exergy cost vector, we used well-known “input-output” tables, which allow us to calculate all kinds of production resources in exergy units in the same way we can in monetary units.

If we use the “input-output” matrix to calculate production cost in monetary units, it will be impossible to determine a set of technologies that minimize this cost, because the square matrix of equations that determine production costs has right sides that equal zero. It means that the system of equations has no unambiguous solution. In other words, any technology can be optimal in monetary estimation depending on relative prices for production resources. If we use the same square matrix of equations to calculate a vector of exergy costs, the right sides of the equations will not equal zero for economic sectors that extract natural resources (they will equal to chemical exergy of corresponding natural resources). Therefore, we can get an unambiguous solution for the square matrix of equations that determine production costs in exergy units, i.e., we can get only one set of technologies that minimize production costs in exergy units.

At the base of market prices is the money supply according to the well-known monetary equation. On the other hand, at the base of exergy costs is the sum of the chemical exergy of natural resources that were extracted in corresponding sectors of the economy. If we multiply ones, exergy cost by the quotient of division money supply on this sum of chemical exergy values (this quotient of division is the same for all sectors of the economy), we would recalculate exergy units in monetary ones saving unchanged inter-industrial proportions that were determined by the vector of exergy costs. In such a way we determine the vector of “natural” prices (P_{0}). Thus, monetary aggregate (Mcmi) can be allocated between sectors of the economy in proportion to relative exergy costs (not market mechanism), as relative market prices.

#### Market and natural price correlations

In general, we can distinguish three possible correlations between the market price (Р_{і}) and natural (Р_{0і}) price over time (t) for a certain market of i-sector of an economy (Fig. 1, a,b,c). As we can see from the figure, cases “a” and “c” (in contrast to case “b”) are not perfect despite supply and demand balancing or equilibrium. In Fig. 1a current market price permanently exceeds the “natural” price, and, vice versa, in Fig.1c “natural” price always is above the market price. Figure 1b corresponds to the case of a perfect market if ∆P → 0.

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Fig.1. Scheme of three possible correlations between market (Р_{і}) and “natural” (Р_{0і}) prices over time (t) for some market of i-sector of an economy.

In general, for any i-sector of the economy, we can present the market price (Р_{i}) as

Р_{i }= Р_{0i}± ΔР_{і }(1)

where Р_{0i} – natural price for the i-sector of the economy and ΔР_{і }– corresponding deviation of market price from the natural price.

As is proportional to e_{min,i }with coefficient k_{0}, any deviation from natural price will lead to the overuse of resources in energy terms (∆e_{i}).

According to the CMI model, the less the natural price deviates from the market price, the less the imperfection rate in a market of the i-sector of the economy is. The case when the gap (ΔР_{і }) is equal to zero (natural and market prices coincide) corresponds to the case of a *perfect* market. Thus, micro equilibrium on a separate perfect market is considered here as an ordinary balance between supply and demand that is established when ± ΔР_{і } → 0 and ∆e → 0. Obviously, in the real world, it is impossible to establish and preserve all markets to be perfect at the same time. The quantity of (∆e_{i}) is proposed here as a measure of the imperfection rate for a separate market in any market conditions.

#### THE MACRO EQUILIBRIUM

Switching to the macroeconomic level it is natural to assume that the real state of the economy, at which the minimum number of resources is used in GDP production, should not depend on the selected measure of those resources. Thus, there is the following determination of macroeconomic equilibrium: long-run macroeconomic equilibrium is determined as a state where “natural” (Р_{0}) and market (P) price levels or their GDP deflators are numerically equal.

Also, this state of the economy might be considered *the equivalent of perfect markets (perfect competition)*. In this state, the production cost is as in exergy units, so in monetary terms is minimum and economic profit is zero which corresponds to well-known features of perfect competition. *Thus, the macro equilibrium that is equivalent to perfect competition for the whole economy can be reached even, if all separate markets are imperfect.*

#### HOW TO READ TRENDS BY THE VALUE OF THE CUMULATIVE MARKET IMPERFECTION

If the market price index is higher (lower) than the “natural” price index, the production resources overrun (as compared to a technologically achievable minimum) in exergy units have appeared. This overrun provides physical limits for amplitude and termination as recovery, so a recession in the business cycle (see below for details). Quantitatively this overrun is proportional to the value of ∆Р = Р_{о} – Р, which can be considered as the aggregate rate of market imperfections.

Thus, according to the CMI model the initial driving force of macroeconomic dynamics (∆Р = Р_{о} – Р) can generally be determined as:

where Р, Р_{о} – price indexes for actual market and “natural” prices, correspondingly.

Money supply that provides quantitative equality of “natural” and market price indexes forms the monetary aggregate of *non-neutral money supply* (M_{cmi}) in (1). Fundamental importance is not so much the absolute value of M_{cmi}, as its growth rate, is approximately equal to the *sum of growth rates for real GDP and inflation* that averaged over the business cycle. According to the CMI model, the value of М_{смі} directly effects on real GDP growth rate. In contrast, monetary aggregate (M2 – М_{смі}) might be considered *neutral *one, because it does not affect the real GDP growth rate.

Figure 1 presents a theoretical scheme of the CMI model of the business cycle in monetary units. According to the CMI model, if **∆Р > 0**, there is an economic growth phase of the business cycle, if **∆Р < 0**, we will see a recession. The points where **∆Р = 0** are the turning points of the economic cycle, i.e., the points of the beginning (ending) of recessions. Thus, the value of the cumulative market imperfection (∆Р = Р_{о} – Р) is *the initial driving force of macroeconomic dynamics for all market conditions and for all moments of real-time*. However, *macro equilibrium or perfect market state could be reached for a moment only* and in the short run, there is no force that will hold an economy in this state once it was disturbed.

Fig. 1 the CMI model of the business cycle.

5 critical points: E_{1 }, E_{2 }, E_{3}– macroeconomic equilibrium points, recession starting and end points;

O_{1}, O_{2} – local maximum and minimum points, economic growth tendency changing;

∆P – cumulative market imperfection, the driving force of macroeconomic dynamics

E_{1}, E_{2}, E_{3}, O_{1}, O_{2} – 5 critical points for the business cycle.

## THE INTERRELATION BETWEEN THE VALUE OF THE CUMULATIVE MARKET IMPERFECTION AND GDP

The greater the value of ±∆Р, the greater the hidden overrun of production resources in exergy units and, therefore, the smaller the rate of economic growth should be observed. Thus, the condition for maximizing the rate of economic growth (real GDP) is the approximation of the ∆Р value to zero in (1). In the point where **∆Р**→ mах, the overrun of production resources in exergy units is maximum, too. It causes a macroeconomic trend change (correction) returning the direction of ∆Р from its maximum to zero again. As ∆*Р* decreases further into the negative, the potential for recession increases and businesses start to feel the pressure of lower-than-normal revenues. During this period statistics usually generate mixed signals and speculations on financial markets increase as the national bank starts stimulating an economy. Even as the real growth rates decline, this does not limit speculations, which are fueled by Ponzi finance (Minsky 1992)[2]. Thus, the recession is originating within the boom stage of the business (economic) cycle. However, any external (a war, a pandemic, an earthquake, etc.) or internal (action of regulators, speculations, etc.) shocks can initiate a recession when its fundamentals had formed already (when ∆*Р* had become negative). While the value of ∆*Р remains positive, any internal or external shock can be absorbed by an economy without recession initiating.*

Thus, a *business cycle* is formed, and each critical point does not only have an economic basis, but also a physical grounding. In theory, we can see economic growth deceleration just before the point of **∆Р **→ mах and its acceleration just after this point.

The value of ∆P determines fundamental macroeconomic trends that could be strengthened (weakened) by occasional events (external or internal shocks). That is why, regardless of one and the same initial driving force of macroeconomic dynamics, the *configuration of every business cycle should be unique in real-time*. Besides, *every cycle should be asymmetric*, which was revealed empirically by Knoop (2004)[3], for example. It would make the CMI model a more realistic one.

## Comparison of the business cycle models

To compare the basic principles of the business cycles dating on the CMI model, by the American model of Mitchell – Burns, and by Austrian Schumpeter’s model, Figure 2 presents a simplified version of the classical business cycle model, elaborated by the US National Bureau of Economic Research (NBER) that is used by the US and most European countries for the recession official dating. Figure 3 presents Austrian Schumpeter’s view on dating principles of the cycles (Niemira, 1995)[4].

Fig.2 Classical business cycle scheme by the US NBER (Niemira,1995, www.nber.org). Peak, trough – 2 critical points for the business cycle.

Fig. 3. Schumpeter’s view of the business cycle (Niemira, 1995).

Inflexion points – 3 critical points for the business cycle.

By comparing figures 1, 2, and 3, one can see that the CMI model contains common elements attributable to the American and Austrian schools. The CMI model has five critical points: three pivot points (E_{1}, E_{2}, E_{3}), which mark the beginning and the end of the growth and recession, and two inflexion points, which mark local peaks of the growth (O_{1}) and the trough (O_{2}) of the recession phases. From this point, we can consider the CMI model as some synthesis of American and Austrian models. Points “peak” and “trough” in Fig.1 were marked to show the relationship between the CMI and NBER classical business cycle models.

## The CMI model differences

However, we can single out some elements that are specific to the CMI model only.

The main distinctive feature of the CMI model is that critical points in the CMI model could be identified well in advance before their statistical confirmation, i.e., with “*the time lead period”*. This period between the CMI model signal of the origin of a recession and its official beginning by NBER dating is characterized by high economic growth and the formation of various bubbles in financial markets. The time lead period appearance in the CMI model is explained by forecasting within this model not so much the final output of the economy directly (as we can see in most traditional models) as stimuli to produce this output. It let us

*able to forecast accurately future events in an economy using statistical data from the past*.

One more distinctive feature of the CMI model is the exogeneity of market prices (P). It means that the actual market price is a result of the effect of all market factors for every moment in time. This exogeneity provides the ability to adequately describe macroeconomic dynamics under *any combination of market conditio*ns. That is, within the framework of the CMI model, *we do not need to accept any assumptions that limit the scope of its use* (ceteris paribus, flexibility-inflexibility of prices and wages, the perfection of competition, the neutrality of money, etc.), which are inherent for well-known models of macroeconomic dynamics. Thus, the CMI model *could be applied to all kinds of market conditions and to any economy.*

To prove the distinctive features noted above see *Empirical Verification of the CMI model* section.

[1] Szargut J., Morris D. (1987) Cumulative Exergy Consumption and Cumulative Degree of Perfection of Chemical Processes. *Energy* *Research*, Vol.11, 245-261

[2] Minsky H.P (1992) The Financial Instability Hypothesis. Levy Economics Institute, Working Paper 74

[3] Knoop T.(2004) Recessions and Depressions: Understanding Business Cycles- Praeger Publishers, Westport, US.

[4] Niemira, M., & Klein, P. (1995). Forecasting financial and economic cycles. NY: John Wiley & Sons, Inc.