Economy & Energy
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Productivity factor in selected countries
Carlos Feu Alvim
The importance of capital productivity to economical growth is emphasized. The Brazilian case is analyzed and comparisons are made regarding the historical behavior of this parameter in developed countries, showing that those that did not control the capital productivity decrease are in a disadvantageous situation.
Keywords: Brazil, capital productivity, total factors productivity, development, economic growth
Capital productivity and economic growth
This article aims at drawing attention to the importance of capital productivity in economic growth. For this purpose the historical behavior of capital and labor productivities has been examined for some developed countries and "emerging" ones. To allow inter-comparisons among countries, the data were treated in a uniform and explicit way.
The article shows that the countries that are emerging from underdevelopment present a performance of the capital and labor productivities rather different from those historically observed in developed countries. Moreover, developed countries also have growth paths very different from each other and they are analyzed here in two groups. The first one consists of countries that have developed in the post-war period and the second one, of some countries that managed to halt the decline of capital productivity. However, until the recent financial crisis, the first group was in a disadvantageous position.
By analyzing the Brazilian case and its comparison with the trajectory of other countries, we can find indications for the Brazilian development policy.
GDP growth and the capital and labor production factors
In general, the growth models assume that the substitution of labor and capital inputs takes place according to their relative cost. This relationship between the two production factors is mediated by the technology used that can also be seen as a third production factor. An increasingly important role has been assigned to the so-called human capital that would influence the adoption of new technologies and efficiency of the production process. However, the relationship between the capital and labor production factors constitutes the basis of growth models.
When the Cobb-Douglas formula [Y = A (t) K α L (1 - α)]  is used to express in a logarithmic X logarithmic scale the capital productivity against labor productivity, the result is a straight line if the technology (A) is a constant. This feature has been used in the Economy and Energy N ° 44 periodical to examine the historical development process of some countries. In order to increase technological content, there is a change in the curve behavior in order to achieve higher productivity per worker for the same stock of capital. When this happens there is a major increase in the GDP per capita for this country for the same annual investment. Figure 1, from that reference, shows examples of the expected path of capital productivity and  labor productivity for unchanged technology (A) and for annual rates of technological growth (g) of 1% and 2%.
Capital Productivity x Labor productivity
Figure 1: Capital and labor productivity with and without technology growth.
This article is intended to provide support for the capital productivity projection to estimate economic growth. In particular, it is useful to discuss the temporal behavior of this variable in Brazil to be used in the projetar_e software developed by Economy and Energy to make macroeconomic projections. Many of the choices in the treatment of variables adopted in this work are related to the purpose of supporting the use of that software.
The projetar_e program is based on the extrapolation of some variables that were chose following the principles:
In the program the value of independent variables is extrapolated with the help of experts group. The group’s evaluation capacity is guided by studies of historical behavior of the variables in Brazil and in other countries of the world. This study is intended to better understand the behavior of the capital productivity to anchor the model projections.
An important aspect when considering the use of a variable for a projection program is its easy extrapolation. This is a reason that justifies, for example, the quantification of all variables referred to GDP in the program. As the real value of GDP referred to one year is used, this implies using the implicit deflator of GDP as the only price index for all economy sectors and, in this case, for the values associated with the production factors under study: capital and labor. Using different price indexes for both production factors implies the need of projecting them for the future for the program operation. Furthermore, the price index for capital and salaries have different time behavior. If the capital X labor relationship is studied by using different price indexes, the phenomenon under study is missing an important information for understanding the phenomenon, with an additional inconvenient regarding the program, namely, this relationship between the indexes must be projected.
Another factor to be considered is that the program is based on the national accounts and its characteristics of a coherent accountability system. By introducing different indexes for the several sectors or production factors, the national accountability misses the best characteristic of an accountability system: the ability to even out the accounts. This was, by the way, the main reason, or at least one of the main reasons for abandoning the fixed base system in the national accounts.
Adoption of the same price index for the capital stock evaluation, necessary to quantify the capital productivity, means that the value of its replacement is not being assessed, but rather its historical value relative to other production factors.
Capital and labor productivities on a national scale
In this article the productivity issue is treated at each country’s level. When considering the capital and labor productivities on a national scale, boundaries are naturally set in a different way than those for a production unit (industrial, agricultural or services). The main one is the slow variation of the potential workforce subject, fundamentally, to demographic factors. Naturally, there is the manpower mobility among the countries that may be important in some cases. There is a fundamental restriction in Brazil because of its continental size, which reduces the international manpower mobility. Anyway, all over the world there are important economic and cultural restrictions for workers moving to other countries. In this article, it is considered as a country’s workforce the population from 15 to 64 years old.
This choice simplifies the problem treatment as a local increase of labor productivity will only make sense when followed by a real increase of national productivity that compensates the adoption of a new productive process. While a company reduces or increases its workforce by fire and hire, a country can generate an increase in the labor productivity of the potentially active population only if the national product has a higher increase rate than that of the manpower.
What could be considered a limitation of this approach in fact correspond, in the real economy, to a concern that should always be included in the national and sectorial policies. In fact, an isolated labor productivity increase might mean just a higher unemployment rate without a really positive result in the national product. Frequently, it is expected that the market will solve a distortion induced by a technology replacement mechanism that, in the peripheral countries, often does not consider the factors cost in the local market because the production form and the technology are determined abroad and, as a consequence, the use of production factors.
Another important aspect concerning the purposes of the data exposed here is the non separation of the residential construction capital stock from the civil work. In order to make a coherent calculation, it would be necessary to know the percentage of the Gross Fixed Capital Formation for residential buildings (not included in the National Accounts) and subtract from the GDP the product generated by the real and presumed rentals. Furthermore, it would be necessary to project these variables.
In this article, the capital and labor productivities behavior was studied for several countries and they have a very distinct type, which is indicative of the development process.
Twelve countries were studied and grouped in the following way:
In the productivities calculation it was used annual values of real GDP growth and relative GDP values of gross fixed capital formation (investments). For the comparisons among the countries, the capital and product values were referred to each country’s GDP in the year 2000 in purchasing parity power (PPP). To estimate the income per worker, the workforce considered was the population from 15 to 64 years old.
Figures 2 and 3 show the capital productivity behavior as a function of labor for countries that achieved the full development in the second half of the past century (South Korea, Japan, Spain and Italy).
In Figure 2 the data are shown in natural scale. The product per worker, which usually has a direct effect on the compensation per worker, is, for this reason, taken as a proxy of worker payment. The capital productivity decreases as the capital productivity increases.
Capital productivity (Y / K) and
Labor productivity (Y / L)
Figure 2: The capital productivity decreases as the product per worker increases and, hence, the cost per worker.
The behavior shown in Figure 2 is basically the expected one when there is a factor replacement (in case labor) for another (capital). Note that this replacement already implies a technology change. For example, whenever a manual harvesting is replaced by the mechanical one in a farm there is a technological change that was adopted because the market decided that it was a more profitable production form. That is, the technology was available for the business owner who chose the best production form. It is assumed that this decision has been made because it is the one that maximizes the profit. The simple exchange of inputs may or may not mean a total productivity gain, which is assessed by the global production cost. In the economical logic, the decision is taken by assessing the production increasing cost using one or other factor.
The real decision takes into account other factors such as the modernity of the production method, environmental and human factors, but it is assumed, in general, that the economic logic is respected.
The production technology depends, therefore, on the available equipment, that is defined in the dominant market. Actually, the fundamental decision on the production factors proportion to be used is taken at this level. A real capacity for choosing equipment in the peripheral countries does not always exist, since it was made for other markets. Moreover, the decision is not always local; global companies are used to standardize their decisions. In this case, the countries shown in Figures 2 and 3 have economies of sufficient scale and policy decision capacity to influence this type of decision.
In Figure 3, the capital productivity evolutions are represented as a function of labor for these four economies in log X log scale.
Capital Productivity and
(log x log scale)
Figure 3: The capital productivity as a function of labor for Italy, Japan, South Korea and Spain can be described in an approximate manner by one same function.
It may be observed in Figure 3 that the same function satisfactorily describes the behavior of the four economies. The observed inclination for the several countries has a mean value of -0.511 + / - 0.022 with a standard deviation, therefore, of 4%. The adjustment that permits to determine the inclination also permits to deduct the constant α = 0.66 from the function shown in footnote . This parameter determination allows assessing the total factors productivity (PTF) behavior.  In the capital productivity calculation of the different countries, the constant α = 0.66 that weights the average productivities in the total factors productivity calculation was kept constant, so that the different groups of countries could be compared.
The good fit by a straight line when a log X log scale is used means that the technological parameter value (A in the Cobb-Douglas function) may be taken as constant. Since this factor is usually associated with technology, it seems surprising that countries like Japan and South Korea and even Spain and Italy may be included in this case.
By the other hand, decreasing capital productivity means that a higher GDP share has to be destined to the investment in order to maintain a desired growth rate. This path slows down development because it implies a higher share of the invested GDP for the same growth rate.
Therefore it does not seem surprising that these four countries were already facing difficulties to maintain the growth rate although, in Japan’s and Korea’s case, they continued investing a significant GDP fraction.
The Total Factors Productivity evolution – TFP, for these four countries is shown in Figure 4 relative to the USA TFP in 1960. It is also shown the evolution of their average productivity value and that their values oscillate around a mean value of 107. The general factors productivity is a weighted average of capital and labor productivities.
Total Factors Productivity
Figure 4: Total factors productivity for Italy, Japan, South Korea and Spain (IJKS).
Capital productivity of developed countries that interrupted their decreasing trend
The evolution of capital productivity as a function of labor productivity showed significant changes in some countries as shown in Figure 5. It also indicates the average path of the four countries shown in Figure 3 (South Korea, Spain, Japan and Italy).
It should be pointed out in Figure 5 what happened in the USA where the capital productivity has an ascendant path along the period and at the same time, an increase in the product per worker (labor productivity). This path, in which it has been possible to combine both productivities growth, highlights the special performance of the post-war USA economy where the “soft” technologies and services have been important. Naturally, the constant deficits in the trade balance contribute to aggregate value in that country in investments made outside its territory. The services sector has a high participation in the GDP and, as the current crisis showed, including the financial sector, which has a minor dependence on the existing fixed capital.
Capital and Labor productivities -
Developing countries with behavior change
Figure 5: Capital and labor productivities path of countries that managed to increase the labor productivity without a capital productivity decrease
The special behavior of the American economy, even with a relatively modest investment rate (average of 18% of GDP), has permitted the USA to maintain an average growth rate of 3.3% in the nineties, while Japan invested 29% of GDP to grow 1.2% in the same decade.
In Australia, United Kingdom and France it can be noticed a behavior that has changed from loss in capital productivity (parallel to the observed trend for the countries in Figure 3) to a constant value or rather a small growth in capital productivity. These countries (and the USA) had a better result regarding GDP growth with a lower investment rate. By contrast, the countries of the first group entered an adverse period where growth demanded higher investment rates each year.
Examining in Figure 6 the capital productivity behavior as a function of time, we can observe that it was decreasing until the beginning of the eighties and that it stabilized and even recovered in the subsequent years. For the USA, this value slightly rises along the period.
USA, United Kingdom, France and Australia
Figure 6: United Kingdom, France and Australia have managed to interrupt the decrease of capital productivity in the eighties and the USA experienced a constant growth in the period shown
The most notable change is that of the United Kingdom, whose capital productivity has systematically decreased during the seventies and eighties and was interrupted in the eighties. It is true that the United Kingdom’s capital productivity was much higher than that of other countries and the decrease has been interrupted when it reached the American productivity level. The behavior change coincided with two important events for the United Kingdom: the oil and gas production in the North Sea (and the decrease of coal production) and the beginning of the Thatcher era.
The productivity path for the countries of this group shows a rising value of the A (t) parameter, taken as TPF, as shown in Figure 7.
Total Factors Productivity
USA, United Kingdom, France and Australia
Figure 7: Total factors productivity in the United Kingdom, France, Australia and USA with ascendant paths compared to the average for Italy, Japan, Korea and Spain (IJKS).
In the productivities graph and economic life Brazil followed a particularly unfortunate path concerning its development over the last two decades of the twentieth century, with considerable decrease in its capital productivity and basically stagnation in its product per worker (and product per capita). This behavior may be seen in Figure 8. This phenomenon dominated the eighties and nineties, but there are recovery evidences at the beginning of this century. It should be noticed that the recovery in recent years is still insufficient to significantly reverse the situation and reach the "normal" curve of countries that have developed in the second half of the past century.
Capital and Labor Productivities-
Developing Countries with Behavior Change
(log x log scale)
Figure 8: The productivity curves behavior show that developing countries generally present lower productivities than would be expected from their development level; in Brazil’s history there was a long declining period with a slight recovery in recent years.
It is important for Brazil to increase its capital productivity in its future path choice. Traditionally, it was believed that the high capital productivity was a competitive advantage of underdeveloped countries that eventually would lead them to development. In the nineties, after the end of the military regime, Chile experienced a period in which it was nearing the normal development path. In the first years of this century, the Chilean economy experienced again the capital productivity decrease without a GDP increment per worker. India and China are in a period of rapid growth based on high investment rates (over 35%). As Brazil’s productivity is between those of India and China, only significant gains in capital productivity and investment rate can approach Brazil to those countries’ growth rate.
Figure 9 compares the total factors productivity for the four emerging countries. Relative to China and India, Brazil has a higher total factors productivity, which means a greater productivity relative to the income level of its population. This means a comparative advantage relative to those countries. However, China stands out among the three countries because of the constant growth of its TFP. All three countries are currently still far from the capital productivity of a "normal" development path. Chile would be closer to this standard.
Total Factors Productivity
Brazil, Chile, China and India
Figure 9: Total factors productivity evolution in developing countries compared to the average of Italy, Japan, South Korea and Spain (IJKS).
Figure 10 shows the capital productivity in 1970, 1990 and 2004 for the studied countries. In the figure, the countries are ordered by group, which facilitates summarizing what was discussed here. In the first four countries there was a considerable decrease in capital productivity. In Japan this low productivity already constitutes a negative handicap for the country. All of them reached a capital productivity level lower than that of the USA. An interesting fact is that Australia and the United Kingdom, which maintained explicit increasing or attenuating programs of capital productivity decrease, managed to increase it between 1990 and 2004. Brazil has capital productivity higher than those of most developed countries, but lower than that of the USA and theoretically incompatible with its development stage. India and Chile have capital productivity higher than that of Brazil, but are in very different stages regarding per capita GDP, and it seems that China has chosen to maintain high investment level and low capital productivity level in order to achieve development.
Capital productivity in 1970, 1990 and 2004
Figure 10: Capital productivity for different countries in three selected years.
One of the problems faced by the underdeveloped countries during the last decades of the last century was the urbanization growth due to migration of rural population, which required and will require high investment rates in infrastructure. It is interesting to note that the phenomenon occurred in Brazil, despite a marked growth in the agribusiness in which there was a drastic manpower shift because of the change or simply the adoption of new (or already old, in global terms) technologies.
The lack of urban planning leads to greater a posteriori investments or even wasted investments such as buildings in slums that later on would have to be rebuilt or restored.
The impasse to get out of underdevelopment is that it requires high investment rates. This can be minimized by capital productivity increase which should be priority in economic policy. It is should be said that for a specified GDP value there is a choice between consumption and investment, which is not obvious. Investment requires consumption postponement, which is not easy to do in a consuming society. Brazil managed to grow in recent years only because it interrupted the decreasing cycle in capital productivity. To accept investment levels as the ones made by Japan, Korea, and China presumes a social choice that is not compliant with the illusions often sold to the population.
One reason for the low capital productivity in Brazil is the "commodity trend" option, which was previously mentioned (Economy and Energy periodical № 67 issue). The solution for development would be to look for a mix of investments rate increase and improvement of capital productivity. Brazil has a great opportunity in the next years that poses, however, important challenges. In fact, despite being intensive in investments, even in the current oil prices already reduced by the crisis, oil has high capital productivity. This effort may be lost either in the hypothesis of choosing the lower investment like buying the equipments abroad or in the hypothesis of excessive expenditure in the national industry, which would reduce the capital productivity. It should be also considered the existing delay in the petroleum and energy industries in general (it is more serious in hydroelectric generation), namely from investment to its contribution to production.
A capital productivity program or, even better, general factors productivity is an essential condition for taking advantage of the opportunities of the pre-salt and those that exist in all crises, at the same time.
The function used was: Y = A (t) K α L (1 - α), where Y is the product, K the capital stock and L the measured labor, in this article, by the potential manpower (as proxy of the available manpower), but it can also be measured in people.year or worked hours in the year. A (t) is a coefficient that may vary over time and it is linked to the adopted technology.
 A (t) = A 0. (1 + t) g where A0 corresponds to the value of the initial year and t is the time in years.
 The inclusion of new variables often improves the past description and deteriorates the future one. In a projection model each new independent variable introduced implies a new projection process.
 It is common to leave the market in charge of solving problems induced by sectorial policies. A recent example is the cane harvesting mechanization, induced because of environmental restrictions and credit incentives, without finding a solution for employment which, although considered by policy makers as of poor quality, was approved by the work market for filling a seasonal void of agricultural occupation (the sugar cane harvesting is in the dry season when the demand for manpower in other agriculture type is lower). By not creating an alternative to manpower, it is generated a problem bigger than the poor quality work, namely the lack of work. A solution to improve the work conditions in the manual process is not proposed, and the solution often mentioned regarding manpower re-training for functions in cane harvesting is not a quantitatively valid solution, given the limited number of employment generate by new technology.
 This corresponds, as noticed above, to adopt for the GDP and capital stock the GDP implicit deflator provided by the National Accounts.
 TFP = A (t) = (K / Y) α (L / Y) (1 - α)
 It should be noticed the fact that the constant determination (by adjusting the curve log x log behavior of both capital and labor productivities) and the fact that this curve can be adjusted by a straight line determine that A(t) or the attributed value to TFP are approximately constant.
Graphic Edition/Edição Gráfica:
Friday, 13 January 2012.