Economy & Energy
Year VIII -No 44:
June-July 2004  
ISSN 1518-2932

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Capital Productivity:
A further Limitation for the Brazilian Growth

Simplified Methodology for Estimating the Evolution of Capital Productivity

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Capital Productivity: a further Limitation to Brazilian Growth

Carlos Feu Alvim


According to Aumara Feu (2003), capital productivity in Brazil at international prices was at the end of the 1990s 8% lower than that in the developed countries of the Organization for Economic Co-operation and Development (OECD)[1].

The low capital productivity in Brazil, when compared to that of the developed countries, does not reflect what is theoretically expected. From the neo-classic Solow (1956) and Sawn (1956) growth model and assuming that all countries have the same technologies available, the smaller the participation of one factor in the product the larger its productivity. Therefore, since Brazil is a country with relative scarce capital factor, as compared with the developed countries, a larger capital productivity would be expected in this country.

Incidentally, the low requirement for generating product would be the reason for expecting a lower difference in the per capita income among countries in the future: this would cause a higher response to investment in the developing countries. Effectively, the poor countries would increase their income which in turn would tend to converge to that of the richer countries, according to the absolute convergence theory, or at least it would diminish the disparity among incomes, according to the relative convergence theory[2]. Therefore, if the Brazilian capital productivity is lower that that of the developed countries it means that Brazil has lost the natural comparative advantage of a developing country.

Besides this introduction and the conclusion, the present article has three additional sections. Section 1 shows the expected behavior of the capital productivity vis-à-vis the labor productivity according to the Solow model, with and without technological growth, comparing the value predicted by the theory with the actual value verified in Brazil and some OECD countries. Section 2 examines the capital productivity evolution in six countries (including Brazil) with different development degrees using the simplified method for calculating the capital stock. Finally, Section 3 indicates which explanations could be given to the low capital productivity in Brazil and describes the experience in other countries that, in opposition to what is verified in this country, have managed to increase the capital productivity and promote the economic growth.

1. Capital Productivity vis-à-vis Labor Productivity

The productivity[3] of a production factor is given by the product relative to the stock of this factor. That is, that of labor corresponds to the ratio between the product and the labor force (Y/L) and that of capital, the ratio between the product and the capital stock (Y/K), composed of its machines, equipment and installations. In order to calculate this capital stock, using the permanent stock method, one adds the investments[4] and depreciates its value as a function of the goods’ age associated with it.

Concerning capital productivity in Brazil , according to different authors [5], it has considerably decreased in the last half of the last century and remained relatively constant from mid 1980s on. In 1999, according to Aumara Feu (2003), while Brazil could produce US$ 36[6] for each US$ 100 of the production goods stock, the OECD countries produced US$ 39 with the same one hundred dollars. That is, capital productivity in Brazil was 0.36 and that of OECD countries, 0.39.

On the other hand, regarding labor productivity, it has grown until the end of the 1970s but remained practically constant from then on. This behavior is observed considering the occupied population, as in Aumara Feu (2003), or the total one. In the present paper, aiming at simplifying data acquisition for the other countries, the total population will be used as labor proxy.

1.1 Relationship between Capital and Labor Productivities in the Solow Method

The economic growth models describe how the basic inputs, capital (K) and labor (L), combine to generate the product (Y). According to the Solow model, with Cobb-Douglas function, the participation of each factor in the product is constant along time. Therefore, according to the model, the labor (Y/L) and capital (Y/K) productivities combine so that when one increases the other one is reduced. Actually, assuming the constant income distribution between labor and capital, product growth per laborer means larger salary and an incentive for substituting this input for capital.

If the two factors are graphically represented in the simpler formulation, Cobb-Douglas function, with constant technology, one has the curve shown in Figure 1 where as the labor productivity grows the capital productivity decreases. In the same way, if one considers the logarithm of the two factors, one gets a straight line.


Figure 1 – Labor and Capital Productivity with Constant Technology and Cobb-Douglas production function represented in natural and log x log scale.

Figure 2 shows graphically the simulation results when technical progress is introduced in the Solow-Swan[7] model.  The curves represent annually different technological growth values.

Figure 2 - Capital Productivity vis-à-vis Labor Productivity in natural and logarithm scale with technological growth rate (g) equal to 0%, 1% and 2%annually. It should be noted that in the logarithm scale only the representation for g=0 is a straight line.

The graphics of Figure 2 simulate a situation near to that of a country with initial capital productivity near to 1 and US$ 3 mil[8] product per laborer. It should be observed that, according to the model, as the economy approaches equilibrium, the capital productivity variation tends to zero and the growth of the per capita product is equal to the technological growth. It should be noted that the bigger the technological growth the smaller the capital productivity decrease necessary to reach a certain income level per laborer. Figure 3 shows the capital productivity evolution as a function of the labor productivity in Brazil, in OECD as a whole and in some of its member countries.

Since in a general way the income per laborer of the countries increases with time, the temporal evolution is represented by the curves’ behavior from right to left.

       Brazil       Japan         USA          UK              OCDE    Canada

Figure 3 - Capital and Labor Productivity [9] – Brazil and OCDE countries -US$ 1990. Source: Aumara Feu (2003)

It can be noted that the set of OECD countries presents an initially decreasing capital productivity and that this value remained practically constant in the last two decades, around 0.4. That is, since the capital productivity remained constant and the labor productivity grew, in the two last decades the growth per laborer (within the used function) can be ascribed to technological growth.

Regarding the last years of the series, even though some OECD countries show a decreasing productivity path (like Japan and Canada), others present constant and even increasing productivities (like the USA and the United Kingdom).

From 1980 on, Brazil has been “skating” in the same product per laborer. The capital productivity decreased substantially in the seventies and eighties at current prices[10]. The same happened in different Latin American countries. A noticeable exception is Chile, whose path will be examined later. Japan is now experimenting a process of capital productivity decrease (similar to that of Brazil) in the last years, although with a much comfortable level regarding the product per laborer.

2.Evolution of Capital Productivity

Many of the analyzed OECD countries, considering the data available, are already in the steady state where the process of substituting labor for capital has been completed and the growth of income per laborer is due to technology variation. That is, these countries seem to have reached the stationary state.

The International Monetary Fund (IMF) data base has been used in the present section in order to increase the number of analyzed countries as well as a simplified procedure for calculating the capital stock, described separately in the present issue. In this way, it was possible to establish the evolution of the capital productivity and of the income per capita in different countries[11].

The analysis that follows is centered in two types of countries: (i) those that presented a significant variation in the capital productivity and (ii) those that seem to be relevant for understanding the Brazilian development process. The countries chosen were Japan, South Korea, Italy, Brazil, Chile and India.

Likewise, due to the data available, investment rates at current prices and product at constant prices were used. Therefore, we are not considering the difference in price variation of investments and product along time. According to Aumara Feu (2003), this form of calculation does not alter the trend verified in the series.

The result of the productivities evolution is shown In Figure 4 were it is verified, as in Aumara Feu (2003) for another group of countries, that the dispersion among capital productivity values decreases along time. This fact indicates a trend of capital productivity convergence for the studied countries.

Figure 4 - Capital Productivity Evolution for the Studied Countries. It should be noted that even though a  convergence of capital productivity in Japan is observed it would still  be half of that verified in India in the last year

The capital productivity values as a function of the per capita income (labor productivity) are shown in a logarithmic graphic in Figure 5.

Figure 5 - Capital Productivity as a function  of the Labor Productivity in Logarithmic Scale. The same straight line representing the behavior of a Cobb-Douglas function without technological growth describes in a satisfactory way the series evolution of the Italy, Japan and South Korea series.

It can be observed in Figure 5 that South Korea, Japan and Italy follow paths very similar to the Solow model forecasts without technological growth. Actually, the same straight line could describe, with good approximation, the values of the logarithmic graphic for Italy, Japan and South Korea[12].

On the other hand, Figure 6 shows the relationship between capital and labor productivities as well as the curve corresponding to the adjustment carried out in the previous figure. It is interesting to observe that, according to the growth accounting in the Solow model with Harrod-Neutra technology, only the negative technological progress would justify the curve behavior observed for Brazil.

Figure 6 - Capital Productivity X Labor Productivity (per capita product  as proxy) in linear scale.

3. Lessons for Brazil

Celso Furtado (2000) points out that:

"In the central economies the transformations take place simultaneously in the economic structures and in the social organization: social pressure makes labor remuneration follow the physical productivity increase of this labor, as this increase is denoted as an increase of the community’s average income. The increase of labor remuneration modifies the demand profile – and through that the allocation of productive resources – and conditions the destination of surplus – and in this way the technical progress orientation.

In the peripheral economies the productivity system modifications are induced from abroad. Due to the fact that these modifications are limited – in the formative phase that we are considering – to a re-ordination in the use of resources already available, its impact on the social structure is reduced or null.” (page 81)

 In the case of Brazil the representation of the two productivities in logarithmic scale shows that for Brazil the Solow model (with or without positive technological growth) does not fit well to the data. The fitting improves if one assumes negative technological growth along the period.

This verification could be explained by technological incorporation in a peripheral country without the corresponding qualification of the existing manpower. That is, the new technology would increase the capital necessary for generating one product unit without the corresponding decrease of labor quantity necessary for generation this product. As a consequence, the Solow residue, that is, the total productivity of the factors, would have to be negative in order to adequate itself to the growth accounting.

According to Aumara Feu (2003), what happened to capital productivity in Brazil can be described by a negative shock in the marginal capital  productivity. In this case all production resulting from capital, invested from a specific date on, would have the productivity reduced by the shock whereas the capital invested before this date, deducting depreciation, would go on generating a product with the previous productivity.

This probable negative shock in the marginal productivity at the end of the 1960s or beginning of the 1970s would be gradually incorporated in the capital productivity (composed of old investments, partially scrapped, but more productive, and new ones, less productive) generating a behavior similar to that presented by the calculated series of capital productivity in Brazil.

Clearly, this shock could be explained by the argument of a bad combination of technology and manpower’s skill in the developing countries. That is, the new technologies that were adopted in the developing countries would come from technological frontier countries, countries where capital and qualified manpower would be abundant factors, unlike the developing countries where these factors are scarce.

One evidence that the technology adopted in the developed and in developing countries, independently of the existing factors of each country, is more and more similar would be the convergence trend, previously pointed out, of the capital productivity.

In the developed countries, the choice of technology is made so that the use of the production factors is optimized relative to the remuneration factors in those countries. Actually, a loom imported brings implicit a relationship between capital/number of laborers and capital/product, decided as a function of the cost factors in the frontier countries. That is, when a developing country imports a loom it also imports the capital/product ratio of the country of origin. The same is true for the mechanized agriculture production or for the cars production or other products.

According to Acemoglu and Zibotti (2001), even when all countries have equal access to new technologies, the bad combination between technology and skill can lead to considerable differences in the total productivity of factors and laborer’s productivity. According to these authors, the bad combination between technology and skill of the manpower can explain part of the significant differences of laborer’s productivity observed.

Therefore, developing countries like Brazil are reaching the low level of capital productivity observed in frontier countries, long before presenting the productivity per laborer (per capita income) of these countries.

It can happen that the temporal convergence of the capital productivity, independently of the diversity of the labor remuneration among countries, is the inevitable consequence of globalization. In this case, the peripheral countries would be trapped in a situation that would condemn them to remain with a smaller per capita product. In Figure 6 two other countries, Chile and India, seem to be overcoming this kind of impasse, stagnation of the per capita income and drop of capital productivity, using strategies different from those of the further developing countries.

Figure 7: Capital productivity as a function  of the per capita income (amplification of the scale in Figure 6 in order to emphasize the three countries with smaller per capita income).

In what concerns Chile, its per capita product ,as can be observed in Figure 7, had a long stagnation period with reduction of capital productivity. During the military regime there has been two huge capital productivity decreases, about 20% in a single year. The first one was in 1975 and the second one in 1982. The income level in 1970 was re-established in 1989 when the military regime was over. The policy established in the last years of the military regime was maintained by the civil governments that followed. To this policy is credited the growth observed in the nineties.

Chile has made a clear option for becoming specialized in activities in which it can compete internationally. It has abandoned the strategy of generating an autonomous economy or even directed to the regional trade of South America. It has adopted a policy of de-industrialization, renouncing to the so considered previous advancements via substitution of imports and it became specialized in products of the agriculture industry, profiting from its access to the Pacific.

In spite of a successful privatization policy, the policy that emerged at the end of the military regime had consolidated and maintained the copper under the control of the state. In 2002 and 2003 this product corresponded to about 35% of the Chilean exports[13].

Chile’s strategy has been pointed out as a success of the globalization policy. Its defenders maintain that specialization of countries in fields where they are more competitive would improve the global efficiency, benefiting all countries. In the graphic one can observe that there has been an expressive recovery of the capital productivity of that country and a considerable advance of the per capita product in the last years.

As shown in Figure 7, in spite of the fact that for more than two decades the per capita GDP has oscillated around the same value, Chile has resumed the “fitted” path of Korea, Japan and Italy and has succeeded in increasing the annual investment rate almost eight percent points.[14]

India is another country that has presented high and constant growth indexes. However, the per capita income continues to be very low and there are big problems of social mobility[15].

Nevertheless, some aspects of its development model have attracted attention such as: (i) priority given to the use of manpower in civil construction, agriculture, where modern and traditional forms coexist; (ii) specialization in the chemical industry, generic medicine, reproducing medicine formulas with expired patents; (iii) priority given to small vehicles in the individual transport system; (iv) directing the cinema industry to the local market; (v) expressive participation in the generation and exports of software; (vi) independent technological policy and (vii) economic policy far apart from the recipes of the Washington Consensus.

Some of these aspects aim at stopping the capital productivity decrease. This has actually occurred as can be observed in Figure 7. This must have contributed in the eighties and nineties, lost decades in what concerns Brazil, for increasing 5.6% the GDP and 3.6% the per capita GDP in India. The gross domestic product of India has more than doubled in this period.

South Korea is another remarkable example of growth. In the fifties its per capita product was lower than that of Brazil and in the last years it reached the level of some OECD countries and now its per capita product is almost three times that of Brazil.

South Korea has certainly benefited, mainly in the fifties, from the massive external aid that aimed at creating a positive example of success of the capitalist economy in an area of the world where a strong communist advance was feared. However, the success obtained can hardly be credited to external aid. It should be remembered that Korea has maintained during decades an investment rate of 30% annually, essentially from internal saving[16].

A good fitting of a straight line in the log x log graphic implies that it is possible to describe the evolution of the capital and labor productivities behavior by considering a zero technology growth. Actually in the three countries for which the graphic of Figure 5 has been fitted (Italy, Japan and South Korea) it is not observed a shift in the direction of larger labor productivity (bending to the right in the graphic) that is expected when there is incorporation of technology. In the situation expected for this type of growth path, Korea presents today low capital productivity what hinders its future development. According to the model, this would only be possible if the component ascribed to technology[17] would growth with time[18].

The Cobb-Douglas function aims at describing the competition between the labor and capital inputs that operate inside an economic logic that aims at the best use of the inputs. In the present paper we are formulating the hypothesis that in peripheral countries this competition is hindered by the external choice of the technology used.

An interesting characteristic of the South Korean economy is that its big enterprises have predominantly national capital and their own trade marks known all over the world. This might have made easier a more rational choice in the use of production means. It is interesting to notice that Korea has directed its efforts in the seventies to exporting labor-intensive sectors products. From 1970 on the emphasis has changed to chemical products, cars and appliances. The manufacture sector, that includes the two latter categories, is a sector where the capital/product ratio is 31% lower than that of the total of the economy in the OECD countries[19]. This re-allocation of resources for less capital-intensive sectors could, therefore, explain how Korea has prevented the premature capital productivity drop observed in other developing countries [20].

From the analysis of Korea’s development path, lessons can be learned regarding a growth path that has optimized the use of capital and labor inputs. Chile has undergone a traumatic course change and made choices that seem adequate for the characteristics of its economy but that could hardly be applied to Brazil whose economy has another dimension. India has developed a system that assigns priority to the labor input and that adopts production forms that are adequate to its development grade. This might have contributed for resuming the development process without decreasing the capital productivity.

Conclusions and Notice of the Next Article 

As described above, the low capital productivity in Brazil, similar to that of developed countries, is a hinder to the growth of the country. It was also observed that this low level of capital productivity in developing countries with per capita income relatively well lower could be explained by the incorporation of capital-intensive technologies developed in frontier countries where the factors’ property is different.

The main problem examined here is not only the low capital productivity in Brazil but the fact that we have reached this value with a per capita product much lower than that of the developed countries.

Therefore, a country with a small level of capital and labor productivities is in a poverty trap and it needs large allotments of both factors in order to generate a positive variation in the per capita product. However, it was observed that Chile, that has undergone a similar situation, has managed to change it. On the other hand, Korea has allocated in a balanced way the capital and labor inputs during forty decades, what in part explains its accelerated growth.

In a country with continental dimensions like Brazil and with a diversified economy it is difficult to transplant solutions either from a country as big and complex as India or Chile, that has opted for simplifying its economy. Countries like Korea, Chile and India, however, could suggest approaches that could lead the country to solve this knotty question. 

There are countries that are approaching seriously the capital productivity problem that also is monitored by the parliament. Australia, New Zealand and the United Kingdom itself have already presented visible results for reverting or limiting the decrease trend.

In the next issue we intend to present some suggestions concerning the paths for increasing the capital productivity in Brazil and breaking the stagnation in the per capita growth.


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  [1] Capital productivity was 0.39 and 0.36, respectively, in the OECD countries and in  Brazil.

  [2] Barro (1991), Barro and Sala-i-Martin, (1991) and Barro and Sala-i-Martin (1992).

  [3] We are considering the average productivity and not the marginal one.

  [4] Investments (gross formation of  fixed capital ) are composed of residential and non-residential construction and of machines and equipment. Therefore, we are considering as component of the capital stock the investment in residential buildings whose product in the rental form (real or presumed) is part of the GDP.

  [5] Among them one should mention  Alvim (1996), Hofman (1992) and (2000), Morandi, Zygielszyper and Reis (2000), IBGE (2003) and Aumara Feu (2004).

  [6] Investment and product data were transformed into international currency considering the purchase power parity relative to the international dollar, corresponding to investment and product, supplied by Heston et al. (2002).

  [7] In the case of constant  technology (A) along time, we have considered the Solow model, with Cobb-Douglas production function and Hicks-Neutra technology, .Concerning the cases with technology growth different from zero, we have used the Solow model, with Cobb-Douglas function and Harrod-Neutra technology, that is, with labor-saving technology. In the simulation it was further assumed  a growth of 2% in the workforce, investment rate (investment as a proportion of the GDP) of 20% annually, a depreciation of 4% and a 0.4 participation of the capital in the product (α). It should be emphasized that the form one puts A(t) in the equation, as an isolated factor or under the exponent (1- α ), associated with the labor, or under α, associated with the capital - respectively Hicks, Harrod or Solow-Neutra technology – alters the distribution between the growth rate factors of the economy (Y) and not the shape of the curves represented in Figure 2.

 [8] To compose the example we have used the function and it was assumed  a workforce growth of 2% annually, investment rate (investment as a proportion of the GDP) of 20%, 4% depreciation and α = 0.4. The example would simulate (in thousand dollars per inhabitant)  the expected evolution in Brazil from the middle of the XX century on, with the assumed conditions.

 [9] The labor here is represented by the economically active population in Brazil, calculated in the mentioned paper and by the total employed workers of the OECD members supplied by OECD.

  [10] In constant values, the productivity stopped decreasing at the start of the eighties - Aumara Feu (2003)

  [11] As mentioned previously, in this section  the population was used as a proxy of labor.

  [12] The straight line’s slope gives the value of   . since      one has     and


  [13] The Chilean military government created in 1976 the CODELCO state company. This is the biggest Chilean enterprise that consolidated the copper nationalization decreed by the Allende administration (ousted by the military).

  [14] Average from 1989 to 2001 relative to the average from 1974 to 1987 (military regime), according to data from the Chilean Central Bank.

  [15] In spite of all castes and its “untouchable”renegates, Índia has a better income distribution than Brazil, respectively the worst  35o and  3o  of the world, according to

 [16] Korea presented an average investment rate of 31.5% from 1975 to 2001 (data at current prices  from the IMF). The contribution from external transfer was almost zero (º2% of the GDP) on the average of this period.

  [17]  A(t) function.

  [18] Japan also presents low capital productivity relative to the other developed countries. Anyway, it is disturbing to credit  zero growth to the technologic component  in the period in countries like Japan, Korea and Italy.

  [19] Aumara Feu (2003).

  [20] Until the Asian crisis, Korea has practiced a central planning policy. Only after the agreement with the IMF in 1998 there has been a move towards a larger emphasis to the market economy. Even though central planning may induce equivocal economic choices, it can also constitute a mechanism to protect the internal economy against production standards imposed from abroad.



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