Economy & Energy
Year IX -No 65:
October - November 2007
Texto para Discussão:
Capital Stock in Brazil and Capital Productivity after the National Accounts Revision made by IBGE
Carlos Feu Alvim
In the previous issue of this periodical [ref. 1] it was examined the best way of making compatible the old and new National Accounts series of IBGE in order to form long series for Brazil. So a “backward extrapolation” of the National Accounts data before 1995 was made, so that they could be used in the projetar_e software that makes economic projections.
In the present study these data are used (1947/2007 period), using the projetar_e software, to analyze: 1) the role of the internal and external savings in the investment accumulation; 2) capital stocks; 3) capital productivity. Using the productivity capacity as a proxy of the utilization factor, it is suggested a procedure to calculate the trimester index of capital productivity.
2 – Investments in Brazil considering the National Accounts Revision
In the projetar_e software investments are considered the values of the Gross Fixed Capital Formation (FBKF) of National Accounts. The FBKF values are use in “Construction” and “Machines and Equipment” (includes “Others”). Figure 1 shows the evolution of investments in these aggregates in the period from 1947 to 2007.
It should be pointed out that the National Accounts revision has reduced the FBKF share in construction in five percent GDP points (from 13% to 8% of the GDP in the 1995/2005 period) but has increased the FBKF share in machines and equipment (about 2% of GDP). The FBKF share in the GDP decreased about 3% and as a consequence there was a considerable change in the proportional share of the items in investment. With the “backward extrapolation” these changes also have had repercussions on values before 1995.
In the revised values shown in Figure 1 the investments in machines and equipment exceeded those of construction until the beginning of the “lost decades” of the eighties and nineties and exceeded them again at the start of the present decade.
Figure 1: Investments Evolution (gross formation of fixed capital) in Brazil;
the 2007 values are based on the first three trimesters; the share
of machines and equipments in investment in the last
two years was assumed to be equal to that of 2005.
It is also interesting to notice the share of internal and external savings in investments. Investment is the sum of the internal savings (share of the GDP that is not internally consumed) and the external savings (transfers from abroad). The evolution of the share of both types of savings is shown in Figure 2.
Figure 2: Evolution of the internal and external savings regarding
the capital formation in Brazil, with strong predominance of the former
The internal savings path has grown until the beginning of the nineties when it had a sudden drop in the economic crisis of the Collor Administration. With the implementation of the Real Plan, consumption was favored and the internal savings was reduced. Regarding the external savings, there was between 1995 and 2000 a net ingress of 2% of the GDP. However, as the internal savings was reduced to 15% in this period, the investment level was 17% of the GDP, well below the 20% level at the beginning of the eighties.
This external resources increase that occurred in Brazil, as well as in other Latin American countries that have adopted the so called economical opening, relieved the pressure on the goods and services balance. At the time it was expected that this input of external resources would bring about larger growth. However, particularly after the Real Plan, consumption was stimulated that together with inflation control brought about popularity to the Plan but not growth.
Similar to what happened in the period of the “economical miracle” of the military regime, the input of external resources was charged in the subsequent years This is evident in Figure 3 where it is shown the evolution of the accumulation of external savings along time in dollars of 2006.
Figure 3: Accumulated external savings along the 1947 - 2007
period showing from 1970 two large cycles of input and input of
savings resulting in - 230 billion dollars of 2006.
Between 1947 and 1970, the accumulated flow of external resources was practically zero. In the seventies the external savings was financed by loans that flowed from the international financing system. The petroleum shocks in 1979, the decrease of commodities prices and the interest rate shock in the eighties have aggravated the inherited debt from the external capital input. Data in Figure 3 show that the positive flow until 1982 was 91 billion dollars and between that year and 2004 there was a net remittance of resources abroad of 234 billion dollars. The outflow of resources was more than twice and a half of the inflow. In 1994, the net accumulated result was 143 billion negative.
In the nineties another cycle of external savings input was started, this time financed by direct investments and “in portfolio”. However, an external liability was being accumulated in the form of investments that were highly volatile. The economic crisis in Russia, Argentina and Asia aggravated the charging of this liability because after the 2001 crisis the liability was under the impact of high internal interest rates and of the dollar exchange rate.
In Figure 3 it is shown that between 1994 (Real Plan) and the 2001 crisis there was a net inflow of 105 billion dollars at 2006 values, according to data from the goods and services balance. From 2002 on the flow of external resources was reversed and until the end of 2007 (preliminary values) 169 billion dollars were sent abroad.
It should be pointed out that it should no be expected external investment to last forever. Those who lend money want return in the form of interest rates as well as those who invest directly expect remittance of profits and dividends. If investments result in production increase, the resulting remittance would be paid by this additional production. The disproportion between inflow and outflow is a cause of concern in the Brazilian case.
As it has been pointed out in other opportunities, there is no medium or large size country whose growth was boosted by external savings. External savings, as China’s example has demonstrated, is important as far as it permits to add technology and market to local product. Its importance for development is more qualitative than qualitative and depends on the economic and technological policy of the country that receives it.
The capital stock calculation is made according to what is described in reference 2 and corresponds to the sum of past investments, depreciated according to its lifetime. Investments are depreciated using a logistic scrapping curve that adopts an average life of twenty years for machines and equipment and forty years for construction. An estimate of investments before the initial year (1947) is also adopted according to the description of reference 2.
The values obtained for the capital stock are shown in Table A1 (in values relative to the 1980 GDP) and in Table A2 (values in US$ bi of 2006) in the Annex. In Figure 4 it can be observed the behavior of the capital stock values from 1947 to 2006.
Figure 4: Capital stock (K) and GDP, where it can be observed the change that occurred from 1973 onward when K grows quicker than the GDP.
The capital stock approximately follows the GDP until 1962 (one dollar of capital stock generated about 0.9 dollars of the GDP). With the political-military crisis of 1963/1964 there occurred a decrease of the GDP but the product evolution was “parallel” to the capital stock. From 1973 onward (beginning of the economical miracle) the capital stock and the product began to show divergent behaviors with the reduction of the capital productivity, as shown below.
Figure 5 shows that the machine and equipment (include others) and construction stocks had similar values until the beginning of the eighties when the economic stagnation, that lasted two and a half decades, started. From that point on, the construction goods stock became predominant relative to that of machines and equipment.
Figure 5: Construction and machines and equipment capital stocks were approximately equal until 1982 (when recession started)
but differed from this year onward.
In Table A2 it is also shown the age of goods that form the capital stock of machines and equipment. This evolution is shown in Figure 6. The average age of construction goods grows after a minimum of 7.6 years at the beginning of the eighties and in 2007 its average age reached 12 years.
Figure 6 – The average age of capital goods depends on the historical investment values and on the scrapping curve and has a minimum value
corresponding to the largest investments of the seventies
The average age of machines and equipment had a minimum value of 4.8 years when the investment rate was higher (mid 1970s) and was stabilized around 6.6 years in the last years. It should be noticed that depreciation fixes the need of investments to restore the stock. The higher the average age is, the higher is the investment depreciation rate, as shown in Figure 7.
Figure 7: The depreciation rate of the capital stock, as well as the
average age of goods depend on the historical values of investments
and on the scrapping curve; generally when the set of
goods is younger the depreciation rate is smaller.
It should be noted that the changes in the National Accounts accountability has increased the share in the capital stock of machines and equipment (with lower lifetime) relative to construction goods. Therefore, the average depreciation rate to be considered on the capital stock changed from about 4% to 5.7% annually.
Summarizing: the National Accounts revision has caused important changes in the capital goods stock in the Brazilian economy. The construction goods have been reduced and those of machines and equipment have been increased. Therefore the share of machines and equipment has increased due to the increase of the annual depreciation rate.
The Y/K ratio (GDP/Capital Stock) can be taken directly as a measure of the capital productivity. However, this procedure does not differentiate a structural change (in the capital productivity itself) from a conjuncture change that would be due to the use of the productive park. In the projetar_e software the historical data of this variable is fitted along time. The adjusted values are considered as capital productivity. The variation around this fitting (annual value/adjusted value) is considered as the utilization factor.
It is expected that the capital productivity so measured is related to the structural variation in production. In the case of productivity growth, for example, the variations could be connected both with the relative share in the sectors (favoring those with higher Y/K) and with technological changes and/or management changes in specific sectors that favor the productivity of the invested capital or still a durable valuation of the country’s products abroad.
The methodology used by the program to make projections has identified the decrease in the capital productivity (from 1970s onwards) as the main cause of stagnation in the 1980s and 1990s. Figure 8 shows the annual values and the fitted ones.
As indicated in Figure 8 (and also in Figure 4) until mid 1970s one dollar of capital stock has generated 0.85 dollar in the GDP. This value decreased to a plateau of 0.47 dollar in the 1990s. This means that for one unit of the capital stock generated a little more than half of the production generated in the previous plateau.
In the 1990s, in order to restore the capital stock depreciation (about 5% annually) it was necessary to invest 12.1% of the GDP to maintain the same capital stock, everything else kept constant, and the same GDP (zero growth).
As the investment was 17% there was a surplus of 5% to effectively increase the capital and the GDP. The GDP expected growth was about 2.5% annually. This is what really happened in the 1990s.
Figure 8: Capital productivity and fitting of the projetar_e software
showing the decrease from 1973 onwards, the stabilization in the
1990s and the recovery in the last four years.
A good question is why was it possible to grow 4.4% in the last four years when investments remained 17% annually?
As investments were on the same plateau, the same 2.5% growth would be expected. The difference is that in the last four years the capital productivity grew 6% with the same repercussion on the GDP. As the capital productivity increased, the expected GDP increase would be 4.0% annually.
It can also observed in Figure 8 that the low growth in 2001 (1.3% annually) kept production below the expected level, therefore there was a recovery margin in the capital productivity factor utilization. However in the last years the capacity factor is 2% above the expected value. The software assumes that the economy will return to normal capacity factor in the next years.
The variation of the effective production relative to the expected one (real GDP/ expected GDP) is calculated by the program and defined as the utilization of the productive capacity. It should be related to the “Utilization of the Industrial Installed Capacity” (UCI) that was calculated by the Fundação Getúlio Vargas (FGV) from 1970 until 2005 and is presently calculated by the National Industry Confederation -CNI (monthly index). It should be noticed that the utilization factor evaluated by the program includes the whole economy as opposed to those of the FGV and CNI that refer only to industry. There is a good correlation among the three indexes as can be observed in Figure 9 that presents the values normalized to the 1992-2005 average (years when the three indexes are available). Considering the diversity of inclusion of the utilization factor and of the UCI indexes, the coincidence is really surprising.
Figure 9: The utilization factor of the capital stock and the utilization of the industrial installed capacity present a similar behavior along time.
The relative coincidence of both indexes justifies an alternative procedure, namely to use the values of the Y/K ratio divided by the UCI (renormalized to the average) to reduce the capital productivity. The UCI index would be used as a proxy of the utilization factor.
The capital productivity index calculated by the program and that from the Y/K values (from the program as well) divided by the UCI (FGV and CNI) are shown in Table A2. The productivity evolution from 1947 to 2007 (preliminary data for the last two years) is shown in Table A3. Figure 10 shows the behavior of the capital productivity values according to the adjustment and those of the division of Y/K by the UCI index.
The series show that the decrease trend of capital productivity observed along the series has been reversed in the last years. According to the economic theory, the capital productivity decrease is expected when the country becomes more intensive in one factor and in the same way it is expected that the capital productivity improves when the country is more open and imports goods that incorporate technology from technology frontier countries.
Figure 10: Capital productivity calculated using the fitting of Y/K data compared with values obtained by dividing Y/K by the industrial capital utilization index (UCI)
In the construction of a productivity index that might have a quarterly periodicity (according to the Quarterly National Account series of IBGE), one could use directly relative values of (Y/K)/UCI as an index to determine the capital productivity variation (estimated by the fitting) relative to the previous year. This procedure is necessary because the fitted values depend on having the final data of the year or at least three quarterly values, as was made for 2007.
It should be mentioned that IPEA publishes in its data base capital stock values that are calculated using investment depreciation in a methodology similar to that of our program. Data are calculated from a L. Morandi study (ref 3) and updated in the system. It is possible to establish an evaluation of the capital productivity from these values by dividing the values found by the UCI calculated by CNI.
The values calculated by IPEA are 15% higher than those of e&e. Data from 1995 onwards are practically coincident when it is considered the productivity relative to one specific year. The difference in the capital stock calculation is due to the origin of the investment series used. IPEA calculates the values using the old National Accounts series while the present study considers a “backward extrapolation” (ref. 2) between the old and new National Accounts. It should be remembered that the new series supplied by IBGE has lower investment weight in the GDP and has changed the investment composition and therefore has increased the capital productivity by decreasing the relative quantity of this input and has increased the depreciation rate by concentrating investment in goods that that have a faster depreciation (machines and equipment).
The capital productivity values calculated by the program’s fitting and the values obtained by dividing Y/K (from e&e and from IPEA) by UCI (from CNI) are shown in Table 1 for the year 2000. Figure 11shows the evolution of these data between 1992 and 2007.
Table 1: Values of the Capital Productivity relative to year 2000
Figure 11: Capital productivity from Y/K fitting (e&e) and
(Y/K)/UCI using Y/K data from e&e and IPEA and UCI data from CNI
It can be observed that the capital productivity values obtained dividing the K/Y program value and those of IPEA by the UCI value have a good coincidence because the relative values of the two series are practically equal. It is also important to observe that data from IPEA and from CNI lead to a capital productivity estimate that has a minimum value around year 2000 and is growing since then, corroborating the behavior obtained by the procedures adopted in the present study.
An interesting data supplied by the program is the capital stock/GDP (capital/product ratio) behavior considering construction and machines and equipment goods in the GDP stock. The evolution curves of the K/Y ratio (inverse of capital productivity, Y/K) are shown in Figure 12.
Figure 12: Construction and machines components of the capital / product ratio
In spite of the fact that explicit product data regarding construction and machines and equipment so that one can calculate the productivity per capital component, it can be inferred from Figure 12 that the capital productivity decrease (increase of the capital/product ratio) in the 1970s and 1980s is mainly due to the construction component. In this period, the stock of construction goods increased without the corresponding increase of the GDP. On the other hand, the machine and equipment stock/product ratio increased in the 1970s but remained relatively stable after the 1982 crisis and started to decrease again at the start of the 1990s.
So from the beginning of the nineties onwards the capital productivity of machines and equipment has grown gradually. On the other hand the construction goods stock as a proportion of the GDP remained stable in this decade.
Therefore the data suggest a gain in capital productivity in sectors that use machines and equipment intensively (like industry) and stagnation in sectors connected with construction goods. So it seems that there is much room for productivity gain in activities related to infrastructure.
It was suggested a procedure for calculating the capital productivity index for the Brazilian economy.
From the analysis carried out here it is concluded that the Brazilian sustained growth depends on increasing the capital productivity and on increasing the annual investment rate.
The investment increase can be attained in part by reducing the transfer abroad (of goods and services) considering that, according to the evaluation made by the program, the net external liability has been considerably reduced as compared to the value at the beginning of the century. Lower transfers, according to the model adopted here, means larger availability of resources for investments.
Simulations made by the projetar_e program confirm the importance of increasing capital productivity, mainly in a context where the infrastructure begins to show saturation regarding productive capacity.
Therefore, with some capital productivity increase and investment increase through the reduction of the external savings deficit or increase of the internal savings, one can reach the sustained growth of 4.5 to 5% annually.
On the other hand, in case capital productivity returns to the levels of the beginning of the century, growth will return to the unsatisfactory value of 2.5% annually.
Table A1: Capital Stock and GDP – Values Relative to the 1980 GDP
Table A2: Capital Stock and GDP – Values in 2006 US$bi
Table A3: Capital Productivity
1 – Feu, Aumara – “Retropolando” as Contas Nacionais até 1947: Como Compatibilizar os Dados da Nova Série do Sistema de Contas Nacionais do IBGE com Modelos de Longo Prazo, como o projetar-e. , № 62 issue of the e&e periodical
2 – Bases para Programa de Incremento de Produtividade de Capital, № 56 issue of the e&e periodical.
3 – Morandi, L. et al, Tendências da Relação Capital/Produto na Economia Brasileira, IPEA, Boletim Conjuntural, October 2000.
 In the No 56 issue of this periodical there is a description of the projetar_e software that has been used by the e&e Organization for different prospective studies.
 Values for 2006 and 2007 are estimated.
 The program considers in the projections this historical dependence between the annual growth of the GDP and the largest share of machines and equipment in investment.
 1- [Consumption + Stock Variation]/GDP
 (Imports – Exports) of goods and services/GDP.
 Values in 2006 dollars were obtained from the GDP of that year, expressed by the average exchange rate of that year.
 Even though both the capital’s average age and the depreciation rate depend on the historical investment and the scrapping, there is no direct relationship between the two magnitudes in spite of the fact that both vary in the same sense.
 In what concerns the GDP fraction necessary to invest in order to maintain production, there has been a significant change because, as will be shown in what follows, the capital stock/ product ratio was reduced (to approximately 2), and it is necessary to invest about 11% of the GDP to maintain the same production (zero growth).
 17% of investment – 12% of depreciation.
 There was a change in the methodology in the UCI series of CNI. The main change observed in the data was in the level and not in movement; therefore the series presented in the graphic connects the new and the old series through the variation.
 The absolute values of IPEA’s capital stock are about 15% higher than e&e data, with consequences on the Y/K ratio relative values; however they are equal within the data error margin.
 K/Y = (Km&e + Kconstr)/Y = Km&e /Y + Kconstr/Y
Graphic Edition/Edição Gráfica:
Friday, 25 April 2008.