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Economy & Energy
No 39: August-September 2003 
ISSN 1518-2932

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Economical Forecasting.

Omar Campos Ferreira.

Adviser of the Minas Gerais State Secretariat of Science and Technology.


Economical systems are in general less predictable than the physical, cultural, industrial and technological ones about which we have developed a forecasting methodology described in articles in previous issues of Economy and Energy ( efficiency of internal combustion engines, publications concerning exergy analysis, industry perspectives and development of new technologies. The tripod supporting this methodology is composed of the basic laws of Thermodynamics (Mass/Energy Conservation and Non-Decrease of Entropy) and Prigogine’s Theorem (asymptotic approximation to states of dynamic equilibrium). Extending thermodynamic concepts to others areas of knowledge permits to forecast the behavior of systems of different natures.

In the absence of competition, the tripod for auto-calalytic systems are expressed by the logistic law, namely the differential equation:

                                   dK/dt = a K (K*-K),

where K is the number of catalytic elements of the reaction, K* is the maximum number of these elements and a is the cinetic parameter. In an auto-catalytic system, an element induces a reaction among the substances without participating in the reaction itself, resulting in the reproduction of the catalyst. Therefore, it is a process that accumulates catalyst at the cost of other substances. Capital has the properties of a catalyst since it is reproduced at the cost of work and raw materials. With no intention of dealing with the subject at a deep level, we have studied the capital accumulation in the Brazilian economy that is presented in what follows.

Carlos Feu et al. (“Brasil: o Crescimento Possível”, ed. Bertrand do Brasil,1996) have developed a simple macroeconomic model, with a forecasting character, that has been used in formulating scenarios of the Gross Domestic Product evolution in several studies (energy matrix elaboration, emission of greenhouse effect gases, electricity and fuel demand, regional planning,…). One of the premises of the model is that the main factor limiting growth is the insufficiency of endogenous capital, historically compensated by the inflow of external capital with medium term effects on the social-economical system that are under dispute (net transfer abroad of resources in the two last decades, loss of opportunities for generating jobs, inadequacy of imported technologies, …). Therefore, the analysis of this limitation is important in what concerns economical planning. In the present application we have used scenario data elaborated by the authors referred to the 1994 American dollar, a year when the exchange rate was balanced.

Graphic 1 shows the capital evolution from 1947 on, the year when the IBGE’s National Accounts was first published. 


Graphic 1.

According to the methodology used, described in several e&e articles (for example, “Technological Forecasting”, nº 30, Jan/Feb. 2002), we try at first to verify if the phenomenon that is under study follows a general law that orientates, as safely as possible, the extrapolations necessary to forecasting. The steps to verify the adequacy of the law begin with the calculation of the capital variation rate from the original series, in time intervals sufficiently long for “smoothing” the series, keeping the largest possible number of intervals in order to guarantee the reliability of adjustments to the equation:

                                   dK/dt = a K (K*- K)

We have used triennial rates of capital accumulation and have adjusted a 2o degree equation in K to the calculated rates and obtained the graphic 2 below. The maximum capital that can be accumulated in the present economic model was calculated to be 1940 billion US$. In 2000, the capital reached 87% of the maximum value, whereas the population reached 70% of the maximum value forecasted (E&E, nº 1, “Futurology”) suggesting a trend to economic stagnation. In similar circumstances, biological systems adapt themselves to adverse conditions in order to survive, which is the highest purpose of any species.

Graphic 2.

When one examines graphic 2 we note that at the end of the sixties, about 200 billion US$ were accumulated, a part of the curve suggesting a proximity to a maximum accumulation value. In a first article about the subject (“Capital Accumulation in the Brazilian Economy, e&e nº 9, July/August 1999), we have discussed the industrialization option chosen then by the system when there were many areas that were appropriate for colonization that permitted maintaining the adopted production model, for example the colonization of the north of Paraná State. According to that article, maintaining the previous model would have allowed the accumulation of the same capital stock of the agriculture-industry transition model but with a positive derivate as opposed to the stagnation trend observed today.

One can speculate about what had failed in the planning of the “Brazilian miracle” that produced GDP growth rates of up to 10% annually, besides the petroleum price crisis that seriously unbalanced the external trade balance. If we were to summarize the causes of the miraculous model failures we could suggest as the main cause the vulnerability of the economy at that time, depending on the external capital for support, a situation that is the same now in more unfavorable circumstances due to the size of the public debt. Since “the mill cannot grind with the water that is past” we should better study what happened then in order to, who knows, find out a way to solve the present crisis.

It should be noted that parts of graphic 2 are like parabolic curves that are compatible with a differential equation (between 206 and 808 and between 830 and 1120 billion US$). We have decided to study the subject further and analyze the accumulation process in successive pulses, assuming that part of the accumulated capital in one of the pulses is used to sustain the start of the next one and try to correlate the pulses with the several measures adopted to “put out the fire”. The pulses overlapping should reproduce the accumulation curve observed.

The first pulse cannot be entirely described since there are not data before 1947 but its initial phase can be inferred from the symmetry of the respective parabola. In order to take into account the mentioned interdependence of pulses in the ascending direction each one of them is extrapolated to the next interval until a null variation rate is observed. Graphics 3 to 5 show the original pulses and those corrected by the interaction with the previous one. It can be seen in graphic 3 that the 2º pulse is not considerably affected by the 1º one (the blue points coincide reasonably well with the red ones). In the abscissa axis are recorded the maximum values attained in the corrected accumulated pulses when separately considered.

The capital accumulation pulses.

Between 1947 and 1966, in the first part of the temporal scale, accumulation was interpreted, according to what is shown in graphic 3, as an accumulation pulse whose final value would be K* = US$ 376 billion (K* = 2 Kmax, where Kmax is the abscissa corresponding to the maximum point of the curve), with a correlation coefficient significantly larger than the one obtained as one examines the whole accumulation curve. In the same way, two subsequent pulses were identified as can be seen in graphics 4 and 5. It should be noted that the 3º pulse is strongly influenced by the 2º one. The correlation coefficient of the corrected pulses is very good for the two first ones and only reasonable for the last one when the main problems of the economy occurred. On the whole, the adjustments seem to be adequate to the interpretation that we are proposing, as it is demonstrated when we compare the original curve (graphic 2) with the curve built with the corrected pulses (graphic 6).

Graphic 3. 

Graphic 4.

Graphic 5.

                                   soma = addition, observado=observed

Graphic 6.

In graphic 7 it is shown the original accumulation rate curve and the curve made with the overlapping accumulation pulses and one can notice that the most significant differences occur in the interval from 1984, after the so-called second petroleum price shock, to 1993, still under the effects of the Collor Plan. In this interval, inflation menaced to rocket up, reaching 86% monthly at the end of 1989, and the inflation correction, that has always favored the capital, helped to compress consumption and increase the capital accumulation rate.

Graphic 7.

In order to ease correlating the pulses with the economical models adopted in Brazil in the analyzed interval, we also present in a temporal scale (graphic 8) the corrected pulses (up to this point, the capital was the independent variable in order to ease the mathematical treatment of the logistic differential equation). In the temporal scale, the parabola is converted into an approximate Gaussian curve and so it is not possible to compare the shape of the curves in different scales.

Graphic 8.

Another way to show the adequacy of the pulses composition would be to present the “capital x time” integrated curve. However the “accumulation rate x accumulated capital” or the “variation rate x time” differential form is more sensitive to the fitting of the model to the historical series, and so we find useless to show the rebuilt integrated curve.

The main advantage of the analysis by pulses is the clearness of how the different phases of the economic evolution can be correlated with the adopted economic policy. Then the 1º pulse would correspond to the phase starting after the end of the Second World War when Brazil had a high hard currency balance as a result of the “war effort”, of exports of primary products (iron ore, sugar, salt and natural rubber, for example) and of restrictions to imports (gasoline, wheat, copper, aluminum, chemical products, etc.) and of the consumption habits that had not been affected by the foreign models yet (consumption economy). The 2º pulse would correspond, in our interpretation, to the industrialization, started in the “JK years” and continuing during the military governments when the foreign capital was available and the so-called “cold war” would ease access to it due to geo-political motivations. The 3º pulse would correspond to efforts for recovering the economy with the sequence of short-lived “heterodox plans” starting with the Cruzado Plan and followed by the Summer I and II, Bresser and Collor Plans during which the efforts for containing inflation through consumption compression resulted in capital accumulation.

The capital stock would have reached in the 1º pulse, if totally acomplished, 376 B US$; the 2º one, 1.260 B US$ and the 3º one might reach 2.690 B US$.  Therefore, the capital stock would have grown at an average rate of 6,9% aa while the gross domestic product would have grown 6,9% aa and the population has grown 2,3% aa. Carlos Feu reasons that the Brazilian economy presents a capital productivity comparable to those of industrialized countries without having reached the equivalent per capita income.

The drop of capital productivity is a universal phenomenon explained by the progressive exhaustion of natural resources that are easily exploited, by the wear-down of installations and machines, by the need of adequating production to new demands of society, etc. What calls attention in the Brazilian economy is the fast increase of the capital/product ratio (the inverse of capital productivity) only comparable to that of Mexico among the Latin American economies.

Graphic 9 shows the evolution of capital and of product compared to the K/Y ratio and one can verify the sharp increase of K/Y notably coinciding with the 2º pulse of capital accumulation (graphic 8).  

                     Graphic 9.

In unitary terms (values per inhabitant), the economy evolution is shown in graphic 10. Since the start of the nineties, the product/inhabitant has practically stopped, whereas the capital/inhabitant continued to grow. It seems clear that the model started in the seventies is exhausted.

Graphic 10.

Graphic Edition/Edição Gráfica:
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Tuesday, 11 November 2008

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