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Capital Stock in Latin America: 1950-2000
Marcos Souza (*)
Aumara Feu (**)
The present study calculates the capital stock, according to the perpetual inventory method, of the Latin American countries from 1950 to 2000, at the aggregated level and by type of machines and equipment and construction goods. The series obtained are used as input for analyzing growth in Latin American countries. Additionally, the investment composition and trend of the capital stock in the countries of the region as well as that of the average and marginal productivity of the capital are analyzed. The results show a significant decrease of the average productivity of the capital from 1960 to mid-1980 and show also that this decrease tends to revert if the larger marginal productivity observed in the 90s is maintained.
Key words: capital, investment, productivity, growth and Latin America.
Classification JEL: E22, O54
Capital stock is an explanatory variable in most growth models of economic theory. According to Ferreira, Issler and Pessoa (2003), capital explains 49% of growth when it is considered in the ample sense and 21% when its indirect effect on productivity is not considered.
The weight of this factor on economic growth as well as its relative scarcity in developing countries make the estimate of capital stock, of average and marginal productivity of the capital necessary both for understanding the growth possibilities and for analyzing the growth experience of Latin American countries.
However, there are no series of capital stock that comprise the period and set of the countries analyzed in the present study: 1950-2000 and eighteen Latin American countries. De Gregório (1992), for example, cannot count on these data when he analyzes the economic factors regarding growth of 12 Latin American countries in the 1950-1985 period.
Nevertheless, Hofman (2000) supplies the capital stock for seven Latin American countries from 1950 to 1994 and so does the Penn World Table 5.6 (PWT 5.6,) for a sample of 63 countries, among which 13 are Latin American countries for the 1965-1992 period. However, we point out that the new version of the Penn World Tables, PWT 6.1, Heston et al. (2002) does not present the stock series.
Therefore, the aim of the present work is to estimate the aggregated capital inventory and the capital stock by type of goods: machines and equipment and construction goods by means of the perpetual stock method (PIM) for 18 Latin American countries (from 1950 to 2000).
The PIM consists of summing up the past investments, discounting depreciation and it was used for the first time by Goldsmith (1951). Due to its transparency and simplicity, it continues to be widely used in the literature, for example by Hofman (2000), Morandi and Reis (2004) and Aumara Feu (2003).
As investment is an input for determining the stock, we analyze the behavior and composition of this variable in the period and we also discuss the investment and capital stock effect on the behavior of the marginal and average productivity of the capital.
Preliminarily it should be pointed out that we have found a decrease of the average productivity of the capital in the period as a consequence of a smaller marginal productivity observed from 1960 to mid 1980. This smaller capital productivity would explain part of the poor economic performance in the region in the 1980s and 1990s. However, the good news is that in case the marginal productivity observed in the 1990s persists, we can expect an increase of the average productivity of the capital in the next years.
The present article is divided in four sections, including this introduction and the conclusion. Section 2 describes the methodology used in calculating the capital stock for the Latin American countries from 1950 to 2000 and Section 3 discusses some results such as the composition and behavior of the marginal and average productivity of the capital. The results are presented in the form of tables in the annexes and are analyzed in aggregated form for Latin America and MERCOSUL, emphasizing some relevant behaviors by country, mainly Brazil.
Application of PIM depends on three factors: (i) estimate of the capital lifetime considered as normal; (ii) depreciation function used for calculating capital depreciation along time and (iii) period of investment series available.
Concerning the first two factors, we will use the lifetime (v) estimated by OECD (1999): 19 years for machine and equipment (M&EQP) and 48 years for construction goods (CONST) and a linear depreciation function.
It will be assumed that the period when there is no depreciation, lag. period (m), is equal to 10% of the lifetime (v) of each good. Therefore, for machines and equipment and construction goods for which the considered lifetimes are 19 and 48 years respectively, there will be a lag of two and five years, respectively.
Hulten (1990), Jorgenson and Sullivan (1981) and Hofman (2000) use a one-year lag whereas OECD uses five years. However we have decided to adopt a fixed lifetime percent value.
On the other hand, in what regards the third factor, we describe in the present section the construction of investment series by country for the period before 1950. For the moment, it should be made clear that for treating the capital stock as a function of the past investments (PIM) it is necessary a longer investment series.
As an example, for the year considered as the initial one (t0) and the capital lifetime (v), it is necessary the past investments from v years on before t0 years. That is, this would represent investments made 19 and 48 years before t0 for M&EQP and for CONST, respectively.
Given the capital lifetime (v) and the lag period (m), exogenous to the model, we can calculate the capital depreciation rate (o) as the inverse of the depreciation time (v-m), that is,. In this way, in the year t an investment made in year r will have the age corresponding to and, considering the lag time (m), the depreciation time will be.
Graphic 1 represents the accumulated depreciation function (D), , where and . This function shows the accumulated depreciation year after year and its image, the survival function (S), , shows the capital that has not been depreciated yet. As an example, in Graphic 1 we have fixed m = 2, v = 19 and consequently, .
Graphic 1: Accumulated Depreciation Function (D) and Survival Function (S)
Source: Aumara Feu (2003, p. 9).
We observe that when we adopt a depreciation rate with lag on the invested capital good, that is, zero depreciation in the lagging period and constant depreciation until the end of the capital lifetime, the total capital depreciation rate, d, depends on the investment behavior and on the stock age variation. Therefore, in case of a positive shock on the investment of a country, the capital age of that country would decrease as well as the depreciation rate on that stock.
The behavior described above is due to the considered depreciation function. It would not be that way if the function were linear, without lag and constant depreciation rate on the capital good along the entire lifetime of the good. However, according to the OECD manual (1993) it does not seem plausible to assume that the goods would wear out at the same rate, mainly in the first years of the lifetime.
We also emphasize that d varies by type of good  and d, by type of good and by country. However, in order to simplify notation the formulas presented below do not present the distribution by type of good.
So, the capital stock will be calculated according to the capital movement equation:
where capital K in is given by the sum of past investments (I) still in the scraping process less the depreciation of these investments, according to the depreciation time of each type of good. The number of years on which the depreciation should apply, , is given by the difference between the previous year (t), the lag time (m) and the date when the investment was made (r).
As mentioned before, the stock formula for the capital stock is based on the sum of past investments. So, in order to calculate the capital stock for construction goods in 1950 we need investment data relative to 1902.
These series are available only for six countries of the sample: Argentina, Chile, Colombia, Mexico and Venezuela, from Hofmam (1992), and for Brazil, XX Century Statistic from IBGE.
We emphasize that when dealing with several countries it is difficult to find aggregated time investment series by type of good and most authors like Ferreira, Pessoa and Issler (2003) and Young (1995) use an estimate of the initial capital and apply the PIM for the following years.
Therefore, for the remaining countries, the initial capital stock was calculated using Equation :
where the initial capital stock depends on the investment level in t0, on the depreciation rate on the stock, d, and on the investment growth, gi.
We observe that Equation  assumes that the investment and depreciation rates do not vary with time. However, a constant investment growth rate is not observed in the developing countries that are subject to external shocks most of the time. In the same way, assuming a constant depreciation rate, it does not agree with the estimated rate using PIM with linear depreciation function and lag.
So, by assuming constant rates and fixing the initial year, which can represent an atypical year, Equation  biases the stock calculation result, mainly in the case of developing countries that are more subject to structural shocks.
As an exercise aiming at analyzing these questions, we have calculated the initial capital stock according to the two methods, namely PIM and Equation , for the six countries that had long investment series available. In this exercise, we have observed that the result differs in a significant way in the countries where the investment series present large variations along time.
We point out that the difference persists but it decreases when one considers gi as the average investment growth rate of the period, t0 as the year in which the investment rate (I/Y) approaches the average value in the period and the average rate d as a function of the investment behavior. These variables: gi, t0 e d, differ from country to country and gi, e d, also vary by type of good.
The result described above shows that the initial stock calculation using Equation , as well as its erosion from then on, must consider the investment behavior by country.
Therefore, in order to make a more accurate stock calculation for the countries whose investment series after 1950 are not available: (i) we calculate the initial capital stock according to Equation , and depreciate that stock by means of a constant depreciation that varies according to the country and the type of good (estimated as specified below) and (ii) adding to the surviving initial capital stock the investment made afterwards, depreciated by the PIM.
So, for countries that have investment series from 1950 on available, we have:
where the stock is the sum of the depreciated initial capital stock, according to a constant geometric depreciation rate that varies from country to country and type of good, and the investments made after 1950 depreciated according to PIM.
We still have to describe how the depreciation rates by country and goods applied to the initial capital stock was calculated. We have used the simplified form proposed by Alvim Silva (2004).
This form shows that, considering a linear depreciation rate on the investment and constant parameters in what concerns the lifetime and the investment growth rate, one can calculate a constant depreciation rate on the capital stock.
According to the author, considering the lifetime (v) and the average investment growth rate (gi) in the period from t0 to, the depreciation rate can be calculated using the following equation:
Actually we do not have data regarding investment and consequently data about the respective growth rate (gi) for the period before in the case of the countries for which it was necessary to estimate the initial capital and depreciation rate applied on it. Therefore, for most countries we have used the product growth rate as a proxy of the investment growth rate.
It should be also mentioned that for Bolivia, the Dominican Republic and Panama, for which data regarding the product for the period before t0 were not obtained, we have used the average growth of the other countries, except Venezuela (petroleum-exporting country). So, we are assuming that the depreciation on the initial capital stock in these three countries is equal to the average value of the other countries.
Therefore, we present in the Annex tables relative to the total capital stock series, the machines and equipment stock and construction goods for 18 Latin American economies in the 1950-2000 period, Tables 1, 2 and 3, respectively.
3. Discussing Results
In what follows we will discuss some results of the capital stock obtained according to the methodology presented in the previous section. The capital stock is determinant in what regards long-run economic growth and, from what was deduced in the previous section, it is related in a direct way to the investment rate. Therefore, before presenting the capital stock results we will investigate the investment rate behavior in the 1950-2000 period in the Latin American countries.
It is necessary to mention that until the beginning of the 1980s the largest growth share in Latin America was explained by investment. According to De Gregório (1992, p. 67), in the 1950-1985 period Latin American countries grew at an average rate of 4.2% annually of which 51% are explained by investment, 30% by population growth and 19% by the total productivity growth of factors.
In the case of Brazil, Aumara Feu (2003) finds similar results: in the 1953-1980 period, it is imputed to the Brazilian growth, in the first place – the high investment rates -, and then to the total investment growth of the factors. The author emphasizes that the investment rate effect on growth achieved its potential through the capital productivity in the period.
In Graphic 2 we can see the evolution of the simple average, by decade, of the total investment rate (investment at constant price as a percent of the GDP) of the Latin American countries, of MERCOSUL and of Brazil.
Graphic 2: Total Investment Rate (%): 1950-2000
Latin America Mercosul Brazil
Source: PWT 6.1.
From this graphic we can infer that the total investment rate along the four decades is the same in the three levels, Latin America, MERCOSUL and Brazil: (a) it decrease in the 60s relative to the 50s; (b) it increase in the 70s, presenting the highest average level in the period and (c) it decrease in the 80s and 90s, except for Latin America, that presented a small recovery in the 90s.
We point out the high total investment levels in the region during the 70s, a period of fast growth in the region and the high levels in Brazil vis-à-vis the Latin American average along the period.
It should also be mentioned that, according to the Sachs-Warner (Sachs and Warner, 1995 e Wacziarg and Welch, 2003) liberalization indicator, between 1985 and 1996, sixteen Latin American countries were opened to the world economy. Moguillansky and Bielschowsky (2001) denominated this period the transition period, a phase in which the reforms implemented in the region affected the behavior of the economic agents.
The transition period varies according to the country and, according to Moguillansky and Bielschowsky (2001), it can be divided in two phases: the first one is the rationalization of production and decrease of investment rate and the second one is the modernization of equipment by the enterprises and increase of investment rate.
For most countries of the region, the first phase occurred between mid 1980 and beginning of 1990 and the second one, in the 1990s. In the Latin American case, the behavior concerning investment described by the authors can be observed in Graphic 2.
However, in what concerns Brazil and MERCOSUL, this behavior is not observed in the graphic. This fact can be explained by the delay in the modernization process that, according to Moguillansky and Bielschowsky (2001), started in 1995.
We present in Graphic 3 the behavior of the ratio between investment regarding machines and equipment and total investment. The examination of this ratio is relevant for understanding the stock behavior of this type of good and also because of the empirical evidence of the positive and strong association between investment on equipment and growth.
Graphic 3: Average of the Ratio between Investment in Machines and Equipment and Total Investment (%): 1950-2000
Latin America Mercosul Brazil
Source: PWT 6.1.
As can be observed in the graphic above, except for the 1980s, the Latin American countries have gradually increased the share of total investments for machines and equipment, namely from 38.6% in the 1950s to 45,5% in the 1990s.
In the case of the MERCOSUL countries and Brazil there is no defined trend. The share of total investment for machines and equipment in the MERCOSUL member countries follows the behavior observed in the Latin American countries but has small variation, average of 15.1% and the variation coefficient is 0.1% in the period
In Brazil the percent variation of investment for machines and equipment is larger in the 1960s, increases in the 1970s, reaches its maximum value, and decreases in the two following decades; the variation has average value of 21.0% and the variation coefficient is 0.2% in the period.
Analysis of the two graphics presented above shows that in Brazil the production percent for investment is higher than the Latin American average but the share of this investment for machines and equipment is lower than the average in the region.
This characteristic of the Brazilian investment relative to the Latin American average is reflected in the capital stock composition. Table 1 shows the percent of the capital stock of Latin America, MERCOSUL and Brazil, composed of machines and equipment in 1960 and in 2000 and the GDP growth rate in the 1960s and 1990s.
In this table we point out the reduction of the capital stock share composed of machines and equipment between 1960 and 2000 in Latin America and mainly in MERCOSUL and Brazil. We emphasize that as the share of investment in machines and equipment in Latin America has increased in the last decade, the share of machine and equipment stock should also increase in the next years.
It should be remembered that the change in investment type and consequently in the composition of the capital stock limits the perspectives of growth in the future due to the clear positive correlation with investments in machines and equipment.
The data of the table above support this evidence by showing that from 1960 to 2000 the stock share of machines and equipment has decreased as well as the region’s growth. One can consider that the larger investment in machines and equipment in the last decade in Latin America can be an indication of a larger growth in the region in the next years and also that the investment decreases in this type of good in Brazil is not an optimistic indication for the country.
In what follows , in Graphics 4 and 5, we present, respectively, the marginal product of capital (MPK), the relationship between the annual product variation and the annual capital stock variation , and the average product of capital (APK), the ratio between the product and capital stock (inverse of the capital/product ratio), for Latin America, MERCOSUL and Brazil, for the 1951-2000 period.
Graphic 4: Marginal Product of Capital (MPK): 1950-2000
Source: Estimates calculated by the authors.
In Graphic 4 one can establish three well defined phases of the MPK behavior in Latin America, MERCOSUL and Brazil: (i) increase between 1950 and 1968; (ii) decrease at the beginning of the 70s until mid 80s and (iii) increase in the second half of the 80s until mid 90s. Furthermore, in the second half of the 90s, the MPK starts a new decreasing trend but that seems to stabilize at the end of the period.
In Latin America and Brazil the peak of the marginal product of capital occurs in the second half of the 60s whereas in MERCOSUL the maximum value occurs in 1994. In what concerns the MPK level difference we observe that until the beginning of the 90s, Brazil and Latin America alternated at the highest level. Presently, this value for MERCOSUL is higher than that of Latin America and Brazil.
The peak observed in MERCOSUL in 1994 as well as its marginal productivity increase in the 90s is a result of the MPK increase observed in Argentina between mid 80s and mid 90s. We point out that the weight of Argentina in the MERCOSUL MPK is weighted using the relative income of the country in the region.
Therefore, according to this proxy for the MPK, until the beginning of the 90s the capital revenue was higher in an average Latin American country than in the MERCOSUL countries. As the theory forecasts a higher MPK for countries with lower income, this difference was expected due to the relative poverty of an average Latin American country vis-à-vis the Argentina, Brazil , Paraguay and Uruguay bloc.
However, the argument is not sustained in the 90s, since the marginal product of capital in MERCOSUL is higher than that of Latin America. It should be remembered that the measured MPK is an approximation in the same way that this result for MERCOSUL may be related to the investment rate decrease or to the intensity and characteristics of the liberalization process that occurred in the region in the 90s.
Graphic 5: Average Product of Capital (MPK): 1950-2000
Latin America Mercosul
Source: Estimates calculated by the authors.
The APK, inverse of the capital/product ratio, has a decreasing trend similar in both of its subdivisions: Latin America and MERCOSUL. In the 90s, the APK series seems to be in a stable lower plateau. In MERCOSUL, after reaching the lowest value in the 1989 period, the APK presents a slight increasing trend. This was influenced by the Argentine APK as shown in Graphic 6.
Therefore, Graphic 5 suggests a change in the APK level of the Latin American countries in the last four decades. While the Latin American countries at the beginning of the 60s needed 2 units of the product to generate 1 unit of product, presently they need 2.4 units. The decrease of the average product of capital (16.7%), in spite of the fact that it is foreseen by the theory concerning developing countries, limits the present and future growth when the capital scarcity in the region is taken into account.
Graphic 6: APK of Argentina and Brazil: 1950-2000
MPK Argentina MPK Brazil
Source: Estimates calculated by the authors.
It should be pointed out that, according to Aumara Feu (2003) and Morandi (2004), Argentina and Brazil would have reached the same APK value of the developed countries. So, since Brazil and Argentina have a low relative per capita capital income, a APK value similar to that of developed countries and a capital factor scarcity, the expected growth was hindered in both countries.
However, we clear out that the MPK increase observed in Graphic 4 since the beginning of the second half of the 80s in Latin America, including that of Brazil and Argentina, will be reflected in the APK value along time.
Since the average product of capital is a stock variable whereas the marginal productivity is a flow variable, it also should be remembered that incorporating more productive capital to the stock will increase the aggregated value capacity in a gradual way. So, if it is confirmed the MPK stability in a higher plateau, the perspective of growth in the long term for both countries will have a higher trend.
In the present work we have calculated the capital stock series for 18 Latin American countries. In the methodology adopted, that uses as input the investment by type of goods, machine and equipment and construction goods, we have observed a decrease of investment as a proportion of the GDP in the 80s in Latin America, MERCOSUL and Brazil. In the 90s the decreasing trend persisted, except for Latin America, where it is noticed a small recovery due to a higher investment in some countries like Panama, Chile and Bolivia.
In Brazil we point out the high investment level as a proportion of the GDP as compared with Latin America and MERCOSUL, the decreasing trend of this level as well as the decreasing participation in machines and equipment in the total investment of the country, mainly in the last decade. The investment behavior in Brazil would influence in a negative way the growth perspectives considering the positive correlation between investment and growth according to De Long and Summers (1991) and (1993), if the types of invested goods are machines and equipment.
On the other hand, in Latin America we observe the trend towards increasing investment in machines and equipment as a proportion of total investment as well as the low investment recovery as a proportion of the GDP in the last decade. This trend, even though not confirmed for MERCOSUL and Brazil, is a favorable indicator concerning growth in the region.
We can also infer from the capital stock series calculation that the marginal product capital has decreased between the end of the 60s until mid 80s. This behavior has produced a decrease of the average product of capital that seems to have changed its plateau in the last four decades. The average product of capital decrease (16.7%) would in part explain the weak performance of Latin America in the 80s and 90s.
It should be mentioned, however, that from mid 80s on the marginal product of capital (flow variable) increased. So, in case this result persists as time goes by, soon it will have reflexes on the average capital productivity (stock variable). In this way, should the growth trend be confirmed or even if the marginal product of capital stays in higher plateaus, ceteris paribus, the long term perspectives of growth trend for the region will become higher. It should be mentioned that in parallel studies we are analyzing the influence of the capital stock behavior, as well as the commercial liberalization, on the economic growth of Latin American countries in the 1950-2000 period.
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(*) Marcos Souza: Writing his PhD Economy thesis at the University of Brasília., Universidade de Brasília, Department of Economy, Campus Darcy Ribeiro – ICC Norte. Brasília – DF, CEP 70.910-900.
Fone: (61) 367-3292. Fax: (61) 487-5246.
(**) Aumara Feu: PhD degree in Economy by the University of Brasília and Finance and Control Analyst at the National Treasury Secretariat.
Secretaria do Tesouro Nacional. Esplanada dos Ministérios - Bloco P, Edifício Anexo Ala A – 1º andar, Brasília – DF, CEP: 70.048-900.
Fone: (61) 412-1965. Fax: (61) 487-5246.
 This article is part of Marcos Souza’s PhD Thesis.
 Argentina, Bolivia, Brazil, Chile, Colombia, Costa Rica, El Salvador, Ecuador, Guatemala, Honduras, Mexico, Nicaragua, Panama, Paraguay, Peru, Uruguay and Venezuela.
 The latter describes in details the methodology for calculating the capital stock in Brazil, according to (PSM).
In the present article, each time that we mention MERCOSUL we are considering only Argentina, Brazil, Paraguay and Uruguay. MERCOSUL has developed from an economic approximation process between Brazil and Argentina in mid 1980 to the Assuncion Treaty in 1991 signed by Argentina, Brazil, Paraguay and Uruguay. In the XXVII Meeting of the Common Market Council, held in December 2004 in Belo Horizonte, Colombia, Ecuador and Venezuela became MERCOSUL Associate States.
 The capital depreciation rate (d), in the linear function with lag, is constant from on, and the cumulative rate applied increases d annually until reaching unity.
 The distribution of the investment series by type of good can be obtained from available data banks. In the present work we have considered for Brazil the percent value of investment by type of good supplied by XX Century Statistics of IBGE 2003.For the other countries, we have found data for the years 1950, 1955, 1960, 1965, 1970, 1975 and for the period 1978 - 2002, in several volumes of Statistical Yearbook for Latin America and the Caribbean. Therefore, for most countries we have interpolated the investment participation by type of good in the total investment regarding years without data, except for Argentina, Chile Colombia, Mexico and Venezuela, whose data from 1978 to 2002 were incorporated to those made available by Hofmam (1992).
 For 1950 – 2000 period, the PWT supplies the investment rate and per capita product series at constant 1996 prices, as well as the population of all the countries considered in the present study. Therefore, by multiplying the investment rate by the per capita product and by the population we have the investment series at 1996 prices for the 1950-2000 period for the Latin American countries. The investment series supplied by Hofmam (1992) and by IBGE were associated with those from PWT, according to the corresponding annual variation.
 We remember that in the econometric estimates we use 1960 as initial year when part of the investments before 1950 were already scrapped..
Data regarding product before 1950 were taken from Maddison (1995).
 The investment recovery as a proportion of the GDP in Latin America is due mainly to the positive variation observed, in decreasing order, in Panama (variation of 80.1% between the 90s and the 80s, corresponding to 10.4 percent points of the GDP in the country), in Chile and in Honduras.
 The empirical evidence can be found in contributions from De Long and Summers (1991) and (1993). According to these authors the nations that have contributed to investments in a more intense way in equipment had a faster growth in the 1960-1985 period relative to those that had the same development level and did not invest. Jones (1994) gives evidence of strong and negative relation between machine price and growth.
 The main countries that have influenced the investment behavior for machines and equipment in the region were, Panama, Costa Rica and Honduras (positive effect) and Peru, Venezuela, Ecuador and Brazil (negative effect).
 Both series were fitted using the Hodrik-Prescott filter.
 Calculation of marginal productivity presented: sum of the net investment variation in the region divided by the sum of the product variation, weights the participation of each country according to relative income of this country in the considered sample. So, the marginal product of capital trend reflects the behavior of the countries with highest income like Brazil, Mexico and Argentina.
 Latin America has grown 5.7% annually on the average in the 60s.
Graphic Edition/Edição Gráfica:
Tuesday, 11 November 2008.