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Energy and Emissions Matrix: Agriculture and Husbandry Sector Capital/Product Ratio in Brazil and in OECD Countries Under Translation links e&e 
Evolution of the Capital/Product Ratio in Brazil and in OECD CountriesAumara FeuAbstract:The aim of our article is to calculate and analyze the trend in historical series of the capital/product ratio at the aggregated level in Brazil and in the OECD countries as well as to estimate the capital/product ratio per activity series in OECD countries. Furthermore, we intend to contribute to the verification of the influence of variation on the capital/product ratio by activity along the period studied (content effect) and that of the reallocation of product in the activities (structure effect) on the variation of the aggregated capital/product ratio. We show that the capital/product ratio has an ascending trend from 1970 to 1996 with reduction of the trend’s slope from the eighties on in most of the countries. We evaluate the capital/product ratios by activity where the large influence of the petroleum and interest shocks become evident. We conclude that the reallocation in the developed countries occurs in the sense of increasing the participation in the product of activities that are more capitalintensive and that the capital/product ratio is ascending in most of the activities, mainly until the mid eighties. However, precisely in the most capitalintensive activities we observe a decreasing trend of the capital/product ratio in most countries. The large and growing participation of these activities and the decrease of their ratio is one of the observed reasons to explain the decrease of the content effect and consequently the diminishing of the growing trend in the capital/product ratio after the mid eighties. In Brazil there occurred a significant variation of the capital/product ratio in the period, which doubled its value from 1.5 in the seventies to 3 in the nineties, coming close to the level observed in most of the developed countries. Since the capital/product ratio is the inverse of the capital productivity, the rapid growth of this ratio is one important cause in the reduction of the growth pace.Key Words: Capital/Product Ratio, Capital Productivity and Economic Growth I – IntroductionThe capital/product ratio (K/Y), i.e., the inverse of capital productivity, indicates the amount of capital necessary to generate one unit of gross domestic product. Therefore, the larger this ratio the larger the stock of capital goods the country must have in order to obtain the same amount of product. The growing rate of a country , given the investment level, is limited by an inverse function of the capital/product ratio. Therefore, the behavior of this ratio and that of the factors that determine it are extremely important in order to know the growing capacity and limitations of an economy. This importance is emphasized when it concerns developing economies where among the traditional production factors – labor, capital and natural resources – capital is the scarcest and it also seems to be the largest limiting factor to economic growth. Therefore, apart from the scarce periods when the external capital flux is abundant, as for example the seventies, growth depends on the internal saving which will have to be larger the larger the capital/product ratio will be. According to Jones (1999), one can infer from Kaldor’s[1] stylized facts that the capital/product ratio is approximately constant. However, according to Foley e Michl (1999), the capital productivity ratio of six countries (United States, France, Germany, the Netherlands, England and Japan) have been dropping since 1973. The authors also emphasize the estimates of the Extended Penn World Tables with a data base of 49 countries that demonstrate a trend in the economic development to save labor and at the same time to decrease the capital productivity. This productivity decrease would be explained by the use of more capitalintensive production methods for development. Consequently, the workers became more productive but the amount of capital they use grows more that their productivity so that presently the capital productivity tends to drop. Both the economic theory and the economic policy planners have emphasized the labor productivity and the productivity of some natural resources such as land and energy. Foley e Michl (1999) call attention to the fact that many economists neglect this strong (even though not uniform) evidence of capital productivity decline. According to these authors, when they show that economic growth tends to increase the capital stock and concurrently product growth, the positive relationship between capital and per capita product leads some economists to think that a production function establishes an uniform behavior between capital stock and product. Data from the International Sectorial Data Base (ISDB) of the Organization for Economic Cooperation and Development (OECD, 1999) indicate an increasing trend in capital/product ratio from the sixties on for most of its member countries. The same growing behavior was verified by Alvim et alii.(1996) for Brazil. According to these authors: The capital/product ratio has grown from its initial value, close to 1.2 in the fifties, to reach about 2.7 in 1992. The capital/product ratio growth means that production in Brazil became more demanding regarding capital inflow. This would be one of the main reasons of the economic growth reduction in the last decades. The growing behavior of the capital/product ratio for Brazil was also verified by Hofman (1992), Carvalho(1996) and Morandi(2001) while Carvalho (1996) points out in the last years of its series a slow down of the series’ growing trend when the K/Y ratio becomes constant. Among the possible causes listed by Pinheiro and Matesco (1989) concerning the growth of the capital/product ratio – “a) rise in the relative price of investment goods; b) growing importance of capital as a source of potential product expansion; c) changes that occurred in investment composition and d) sectorial allocation of investments and production” – we will try to give a contribution to the second and fourth causes. The analysis of the capital/product ratio by activity will seek to verify if the growing trend at the aggregated level is due to the increase of the ratio in each activity or in some specific activities (second cause) or to the reallocation of product by activity (fourth cause). In the present work we will analyze the capital/product ratio series at the aggregated level for OECD member countries and for Brazil and we will seek to verify if their trends have an uniform evolution. Then, using a methodology described in the article, we will try by means of analysis by activity to verify the influence of the K/Y ratio by activity along the period studied (content effect) and that of the reallocation of product in the activities (structure effect) on the variation of the aggregated K/Y ratio. The present work is organized as follows: Section II describes the methodology to be adopted. Section III discriminates the results regarding the trends of the capital/product ratio by country and for OECD. Section IV indicates the results found concerning the capital/product ratios by activity. Section V analyzes the structure and content effects (described in Section II) and finally, Section VI presents the main conclusions.
II – Methodology descriptionWe describe below in two subsections the methodology to be used in the present work. The first one describes the steps to be followed in the calculation of the capital/product ratio for Brazil and the aggregated and per activity capital/product ratios for OECD countries. Due to lack of data, we will not calculate the ratios by activity for Brazil. The second one describes the effects – structure and content – to be used in the analysis of the factors that affect the K/Y ratio. II.1 – Calculation of the Aggregated and Per Activity Capital/Product RatioThe first step to determine the capital/product ratio is to calculate the capital stock and the second one is to divide it by the product. The capital stock will be estimated by the same method used by OECD as well as by several authors such as Alvim et alii(1996), Hofman(1992) and Morandi(2001). This method is called “Perpetual Stock Method” that consist in adding up past investments, that still are in the scraping stage, subtracting the depreciation generated by normal wear away, be it physical, accidental or due to obsolescence. Therefore, we will use the “net” capital stock, i. e., the “gross” capital stock discounting the fixed capital consumption – the depreciation. Application of the method depends on the period available concerning the investment data, on the function used to calculate the wear away of investment in time as well as the estimation of wear away that is considered normal. In what concerns the mortality function, we will use the linear function with delay, following again the OECD methodology that in its turn follows closely the functions officially adopted by its member states. We point out that Hofman and Morandi use linear functions without delay while Alvim et alii use a bellshaped function. In Figures 1 and 2 that follow we present the four more usual mortality function – linear, linear with delay, bellshaped form and sudden death – and their corresponding scraping functions for an average life of 24 years. According to the OECD manual (1993), of these four forms, two do not reflect the reality, namely the linear and sudden death functions. Actually, it does not seem plausible either that all goods of a determined group should be discarded at the same time (sudden death function) or that during the whole period these goods wear away at the same rate (linear function), mainly in the first years of life when, by definition, it is expected that the good has full capacity to aggregate value. Of the two remaining forms, linear with delay and bellshaped form, both presuppose a smaller depreciation in the first years (linear with delay – zero depreciation in the delay years and bellshaped form – depreciation increases gradually in the first years). In spite of the fact the the bellshaped form is the one that conforms more to reality, with smaller discarding in the first and last years, our choice of the linear depreciation with delay is justified by its simplicity and by the smaller number of parameters to be estimated, therefore avoiding spurious assumptions. In the linear function with delay it is necessary to have the average life and delay times, in the bellshaped form one needs the average life time and the discarding parameters in order to determine the curtose and the skewness – the velocity in which the discarding gradual variation occurs. Mortality Function– Linear
Mortality Function  Linear with Delay
Mortality Function Belllike Shape
Mortality Function – Sudden Death
Figure 2 –Mortality Functions Show depreciation rate in time for a capital with average life time of 24 years for this type of good (machines and equipment). It is a probabilistic density function with area equal to unit. Survival Function– Linear
Survival Function Linear with Delay
Survival Function Belllike Shape
Survival Function – Sudden Death
Figure 3 –The survival function indicates which proportion of a capital that continues to aggregate value during the average life time for this type of good. The linear mortality function with delay generates a scraping function equal to zero in the first years after the investment (delay period) and ascending linear in the years the follow. The straight line slope, a consequence of the average scraping time (h)[1] of the goods will vary according to the type of good, whether machine and equipment or construction, and according to the activity (see Table I). Assuming the delay years to be five, m=5, that is, the capital‘s capacity of aggregating value remains constant during the first five years, we will have a growing linear scraping function with time that stars in year m+1 and ends in the final period of the average life (v) of the good (see Figure III). The scraping function of investment in time is represented by dx, where x is the difference between the years t and m, i. e., is the amount of years in which depreciation is to be applied[1], and d is the additional depreciation rate[2] determined by the inverse of the average scraping time (d= 1/h). Therefore, the accumulated depreciation is equal to zero in year m, equal to d in year m+1, equal do 2d in year m+2 and so on until the year (h+m)[3] when it is equal to hd and, consequently equal to one.
Figure III  Representation, similar to that used by OECD (1999) [1], of the mortality function (dx), showing the accumulated depreciation year by year with m = 5, v = 24, and, consequently, h = 19 = vm; as well as its image (1dx), that gives the capital that has not been scraped, that is, the capital survival.
Therefore we will calculate the capital stock for each year subtracting the sum of investments[2],that still are in the scraping stage, the depreciation corresponding to its age, that is, we will add up the surviving investments. (1)_{ } The capital in t+1 is given by the sum of previous investments, still in the scraping stage , less the depreciation of these investments, according to the scraping[1] of each one. The number of years in which depreciation is to be applied (x= tmr) is given by the difference between the previous year (t), the delay time (m) and the date when the investment was made (r), while the additional depreciation rate for each investment is calculated by multiplying the additional depreciation rate (d) by x. Since m=5, we point out that x corresponds to the age of the capital asset less five.It should be pointed out that there are no official data concerning capital stock in Brazil while they are available for OECD countries. This organization supplies the aggregated capital stock and its value by activity, most of them obtained from the national systems of each country and in cases when they are not comparable , they are given by the sum of past investments which are depreciated according to distinct depreciation rates for each activity and for each country. The OECD International Sectorial Database (ISDB) user’s guide clarifies that the scraping rates used by the different national bodies are quite different. According to the guide: This difference is due much more to distinct estimation methods that to fundamental differences in the nature of the capital goods or their use. As an example, we could mention the average scraping time of constructions that is considered to be 42 years in Filand and 70 years in Sweden. OECD compares the stock capital calculations using the average scraping time (h) according to estimations[1] of each country and according to the average of these estimations and concludes that the results are significantly distinct in what concerns the stock level but relatively similar when compared to trends of the K/Y ratio. This organization concludes that in general the K/Y ratios using the average of h by activity tend to be more similar among the member states than would be expected but it does not give the reason of this expected discrepancies among the ratios. Our opinion is that it would be easier to justify the large similarity among the ratios due to the similarities among the considered countries, among the type of goods produced, including in what concerns the technological level which, due to the commercial liberalization, has been easily and rapidly disseminated, than to find reasons that explain such large discrepancies among the scraping times of the countries. Keeping in mind what was explained above and taking into account that we intend to compare the results of the aggregated and per activity K/Y ratio among the countries, we have opted to recalculate the capital stock using the average of h by activity for the different countries. These averages are available in the ISDB data base and are presented in Table I – Average Scraping Time[2] by Activity and by Type of Good below. The classification criterion uses the first specification level by activity of OECD[1] and comprises nine industrial activities, two nonmercantile service activities and the total. Therefore, we have eleven activities and the total that in turn are subdivided by type of goods: machines and equipment (M&EQP) and construction goods (CONST).Table I – Average Scraping Time (h) by Activity and by Type of GoodsNote: ^{a} Since h of the SAP activity for all countries is supplied by ISDB, we assume that it is the average value of h of this activity for the countries where they are known. ^{b} Since h of OUT is not supplied by ISDB, we assume that its is h of TOT.Actually , only Finland has full data concerning this activity.
Once the capital stock is calculated, it should be divided by the corresponding product in order to determine the capital/product ratio. In what follows we describe step by step the procedure used to calculate the total K/Y ratio, aggregated and by activity, pointing out the difficulties encountered in what concerns the lack of data and the solutions found. We should remember that for Brazil only the total K/Y ratio will be calculated. a) we will obtain the additional depreciation rate (d=1/h) for each of the activities (a) and by type of good (i) as the inverse of the average scraping time (h) according to Table I; b) we will divide the investment – FBKF current prices[1]  by the domestic gross product at current prices (GDP)[2] , and obtain the portion of investment by activity in the product (FBKF/PIB). According to what Equation (1) above shows, the capital stock calculation is a function of the historical past investments, therefore it is necessary an older investments series for the calculation of the capital stock of the initial years. It should be clarified that we consider as the initial year the first year of the FBKF and of the GDP series supplied by the International Sectorial Database (ISDB) of OCDE for each country. For example, for the year considered as t(0) in the calculation of the capital/product ratio, we will need the history of the past investments, from v years before the initial t on, that is, it would represent on the average, for machines and equipment, investments made 24 years before t[1]; and, construction, investments made 53 years before t. We will close the preceding total investment fraction series of the GDP with growth rates supplied by the International Monetary Fund  IMF (for OECD countries, except the United States), by the Bureau of Economic Analysis (NBER) of the United States (for the United States) and by Hofman (1992) for Brazil, considering constant and equal to the average of the three first years (average from t(0) to t(2)) the specification by activity of the total investment fraction in the GDP. Depending on the series and on the type of good considered, whenever data supplied by these additional sources concerning data previous to the first year[2] are necessary, we will also assume the total investment fraction in the GDP to be constant and equal to the average of the first three known years. We point out that errors in the capital stock concerning the past investment estimates are progressively smaller as the investment capital ages, since the portion of this capital in the stock decreases with time, that is, with depreciation[3]..
c) then we will multiply the %FBKF by the GDP at the 1990[4] market prices and we will find the investment by activity at the 1990 market price (FBKF(1990)). d) we will determine, as described below, the fraction of machines and equipment (f) by activity for each country as well as , by difference, its complement (1f) – the fraction of construction goods. Considering that OECD does not supply these fractions in the investment of each activity, we will base our calculations in each country on the average scraping time (h) by activity and by type of good as well as on the the total average scraping time (ha). It should be pointed out that each country will have its fraction of machines and equipment for each activity[5]. Therefore we will have Þ where: fraction of machines and equipment in activity 1 average scraping time of machines and equipment in activity 1 average scraping time of construction goods in activity 1 total average scraping time of the activity This estimate does not consider the variation between f and (1f) during the considered period because it is calculated based on the supplied scraping time that do not vary with time. This procedure is not necessary for Brazil because the investment series (FBKF[1]) published in the National Accounts (NA) by the Brazilian Institute of Geography and Statistics (IBGE) supplies the portion of investment by type of good for the 1947 to 1999 period. e) we have estimated the capital stock for each year (Equation 1) based on investment by activity and by type of good and on their respective depreciation rate determined in item a). We remember that the capital stock by activity is obtained by summing the capital stock for machines and equipment and for construction goods in each activity. f) we will calculate the percent of GDP for each activity in current values and will multiply by the total GDP (at 1990 prices) and will find the GDP by activity (at 1990 prices), the same way that was used to calculate the investment by activity (at 1990 prices) in items b) and c); and, g) finally, we will estimate the K/Y ratio by activity dividing the stock of each activity (at 1990 prices, item e), by its GDP (at 1990 prices), item f); and, the aggregated K/Y ratio that corresponds to the sum of stocks per activity divided by the sum of the GDP by activity. For Brazil the only ratio calculated is the total one which is the sum of the estimated stocks for machines and equipment and for construction goods divided by the GDP (at 1990 prices).
II.2 – Calculation of the Content and Structure Effects In Section IV the capital/product ratio variation by country will be examined through the analysis of the weight of structure and content changes according to the description and procedure described below. A change in the behavior of the K/Y ratio can be divided in two effects : a) the “structure” effect that is due to the reallocation of resources among activities, modifying the total K/Y ratio by concentrating the product in activities with different levels of capital intensity; and b) the “content” effect, a result of the capital/product ratio evolution in each activity. Therefore, starting with:
where: K_{at} = capital stock of activity a in period t_{ } We can write the aggregated capital/product ratio as the weighted average of the capital/product ratios by activity, where the weights are given by the participation of each activity in the total product.
Considering :
we have:
Calculating the variation of each given term, we have: _{ }
Since we find: ^{ } The above expression permits finally to decompose the aggregated capital/product ratio variation in three parts :
This methodology permits to verify the contribution of the K/Y ratio variation by activity and of the reallocation of resources in the determination of the aggregated K/Y ratio behavior. We will be able to verify for example if the intensity and evolution of capital for each activity confirm or not the hypothesis that development saves labor and intensifies the need of capital. It should be mentioned that the structure and content effects will be calculated on the v and e series fitted by a mobile average process centered in five years. The equation below, exemplifies this process for v, where the capital/product ratio in year t(vt) is equal to the average of the ratios in the period that comprises two years before t and two years after t.
^{ } The fitting was necessary to smooth in the originally calculated series the conjuncture variation due for example to retractions and expansions of the product along its trends.
III –Capital/Product Ratio in Brazil and OECD CountriesWe have analyzed the K/Y ratios of twelve countries whose data are supplied by the International Sectorial Data Base (ISDB) [1] of OECD: Australia, Belgium, Canada, Denmark, United States, Finland, France, England, Italy, Japan, Norway and Sweden. It should be mentioned that ISDB has excluded some countries such as Spain and Austria because these countries do not have a detailed data base. According to the proposal for the present study that was presented above, we have calculated the capital/product ratio for Brazil as a whole. As an exercise, as well as for a better perception of the weighted average behavior, we have determined the K/Y ratio of OECD countries as the sum (after conversion of the series for the same currency [2]) of the capital stock of each country divided by their respective product[3]. Therefore, we have estimated the aggregated capital/product ratio of the total (TOT) for each country. The series differ in the way they are calculated: the aggregated ratio, because it is the result of the sum of the capital stocks by activity divided by the sum of products by activity, it uses different scraping times by activity while the total ratio, obtained by dividing the total capital stock by the total product, uses only the average scraping time of the total. The aggregated K/Y ratios and that of the total are similar in level in what concerns trends and cycles, therefore we have opted for presenting below the K/Y ratio of the total (TOT) as well as the logarithmic trend fitted to the latter.
We can verify a capital/product ratio with ascending trend with different slopes in all analyzed countries. Of the countries with ascending trend, we point out Brazil, Denmark, England, Italy and Japan. We notice that in the seventies all of them have a ratio smaller or equal to 2.5. Among the countries with less stressed growing trends are Australia, Belgium, Canada, USA, France, Norway and Sweden. It is interesting to observe that the USA and Belgium are singularly at a level lower than 2.5. in 1970. As to the other countries, we have Norway and Sweden with ratios equal or higher than 3 and Australia, Canada and France with close ratios values between 2.5 and 3. Besides the growing trend of the capital/product ratio, the data indicate that those countries with lower ratios tend to have a more accelerated growth, while those with higher ratios tend to have a slower growth. The relationship between the initial ratio level and its growing rate – see Figure below – has shown to be negative with a statistically significant coefficient of 0.31 (the determination coefficient grows from 0.42 to 0.57 when the US is excluded). The convergent behavior between the capital/product ratios occurs around the average level, three (see Table II).
This convergence could be explained by the technological dissemination, direct function of the commercial liberalization, that increases the access to capitalintensive technologies generated in countries where this factor is abundant – developed countries. Particularly for OECD countries, with the formation of regional blocks, the convergence could occur due to the increase of similarities existing among these economies and consequently among the goods and services produced. We notice that most (ten) of the analyzed countries had a K/Y ratio between 2.5 and 3.5 in 1996, while Norway and Italy had ratios between 3.5 and 4 and the USA had ratios below 2.5. Furthermore, we observe a retraction in the slope of the K/Y ratio in most of the countries in the eighties, stressed at the first half of the nineties. The higher ratio decrease after the 1992 recession coincides with a product growth acceleration period in the economy as a whole. According to what was previously mentioned, in Brazil we can verify a strongly increasing trend in the K/Y ratio. However, this ascending behavior presents stagnation periods. The first decrease in the ratio rise, when it remains practically constant, occurred in the period after the military coup d’état until the first petroleum crisis. From 1974 until 1982 the ratio trend became again strongly increasing, experimenting a new break in the period after the interest rate shock, when it even decreased. It rises again in 1987 until the beginning of the nineties, period of the world retraction, when it returns to a constant behavior, and it increases again after the mid nineties. In what concerns the K/Y ratio in the OECD countries, its behavior confirms the rising trend as well as the slow down of this trend from the eighties on. Since the ratio in the United States (with a rising level and trend relatively lower than those of most countries) has a higher weight (approximately 40%) in the OECD’s K/Y ratio calculation we notice consequently that the ratio level of OECD is smaller than the arithmetic average and similar to the weighted average (see Table II). IV –Capital/Product Ratio by Activity In Table Ii that follows we show for the 1970 and 1994[1], the arithmetic average[2] od the K/Y ratios by activity, the standard deviation of the ratio in each country relative to the arithmetic average by activity, the average weighted by the participation of the activity in the OECD product and also the percent variations of the averages between these two years. We present the activities by decreasing order of the K/Y ratios arithmetic average in 1970, besides the total and aggregated ratios that are in the two last columns. We notice that the variables with larger average in this year: electricity, gas and water (EGA), finance, insurance, real estate and business services (INF) and producers of government services (SAP) were exactly those that presented the smaller variations. Two of them, EGA and INF were the only ones that decreased in time.Table II –Averages of the Capital/Product Ratio by Activity[26]
The averages of the K/Y ratio that have the highest growth rate were in decreasing order those of agriculture, hunting, forestry and fishing (AGR), mining and quarrying and construction activities. This last activity is the one that presents the smallest average, both weighted and arithmetic. When one analyzes the standard deviation relative to the average by activity for each country, the ratios with largest deviation were the mining and quarrying (MIN), electricity, gas and water (EGA) and producers of government services (SAP) activities. The large deviation of the SAP activity can be explained by the Australia and Japan series. In 1970, Australia stands out by the high ratio level, 9.7, compared to an arithmetic average of 3.8, while in 1994 there are two countries with a level much above the 3.9 average, Australia and Japan, both with a 9.4 ratio. It should be emphasized that the high value of this ratio in Australia is due to the fact that this activity, distinct from what occurs in other countries, incorporates only public administration services, not including for example health, education, culture and others.The capital/product ratio by activity present different levels and trends among the countries. However, we can verify some similar characteristics as for example the ratio trends concerning agriculture, hunting, forestry and fishing (AGR), manufacturing (MAN), construction (CST) and wholesale and retail trade, restaurants and hotels (CRH) that are ascendant in all countries. Particularly in AGR, where the ascendant trend is more marked, we notice at the end of the period the high level of the ratio in two countries, Italy and Japan. In CST, three countries show up due to their high ratios, Denmark, France and Italy, and we have in almost all countries a positive cycle that begins in the eighties when the drop of the interests rate occurs. In the CRH activity we point out the ratio’s high level in Finland and Denmark. In the graphics below we confirm the growing trend of the ratio in the AGR, MAN, CST and CRH activities in the OECD countries.Capital/Product Ratio by Activity in OECD
According to what was show above, the K/Y ratio in the mining and quarrying (MIN) has large positive variations and large spread among the countries. The ascending trend of this series is not behaved. We point out as characteristic of most countries the rise above the ratio trend in the mid eighties and a small decrease in the last years. We point out as well large cycles from the beginning of the seventies until the beginning of the eighties (Denmark, Sweden and England – positive cycles, and Australia and Norway – negative cycles). The ratio in France is singularly low. Since this activity includes petroleum extraction, the data seem to indicate that the petroleum shocks in 1973 and 1979 have caused an alteration in the ratio normal behavior in some countries. It is still interesting to observe, at the time of the petroleum price drop in 1986, that the ratio seems to have grown in several countries as a consequence of the drop of the product value of this activity (denominator of the capital/product ratio). It is convenient to remember that we are taking the activity participation in the product and in investment at current prices. The K/Y ratio series in the MIN activity in OECD countries closely follows the series behavior in the USA, as the weight of the capital stock and of the product of this country relative to the set of analyzed countries[1] is huge, more than 48%. The finance, insurance, real estate and business services (INF) and electricity, gas and water (EGA) activities have K/Y ratios with non rising trends. In EGA we point out the decreasing trend in England, Norway and Sweden and as exceptions the rising behavior in Japan and Denmark. In INF, we point out the existence of a positive cycle in most countries from the mid seventies until the mid eighties when the drop of interests rate occurred in 1986. The ratio behavior in the OECD countries is similar for the INF activity and practically constant for the EGA activity where the rising trends (in Japan and Norway) contributed to decrease the weight in the more marked declining behavior in the above mentioned countries. In the K/Y ratio series of the transport, storage and communication activities (TAC) the behavior for most countries is ascending with positive cycle above the trend after the petroleum shock until the mid eighties, becoming practically constant in the rest of the period. We point out the decreasing trend in Finland. The OECD series follows the behavior of most countries in this activity. On the other hand, the services rendered to the community, social services and personal services (SSO) have ratios with no defined trend. We point out the rising behavior of the ratio in Denmark and Japan, decreasing in Finland, Canada and USA and ascending until 1987 and decreasing until the end of the period in England. According to what was previously mentioned (footnote 15), this activity in Belgium and Italy includes the INF activity, more specifically the real estate business and services rendered to companies, which corresponds to ninety percent of the capital invested in INF. Since the largest capital/product ratio and the largest participation in the product (see Table III in Section V) occur precisely to the INF activity, this fact changes significantly the ratio and the behavior of the SSO activity in these countries and for that reason the rising behavior of the ratio in OECD countries was calculated excluding Belgium and Italy. Finally, the ratio behavior in the non mercantile public administration activity (SAP) is decreasing in most countries, except France and Japan where it has a trend with positive slope. We remember that in Australia and Japan the level is high relative to the average of this activity. V – Structure and Content Effects by ActivityThe graphics below represent the structure and content effects and the accumulated residue year by year and the variation of the K/Y ratio (sum of the two effects and the residue):
The accumulated structure effect is positive in nine countries (Australia, Belgium, Canada, Denmark, USA, Finland, France, Italy and Sweden) and oscillates between positive and negative values in three countries (England, Japan and Norway). The accumulated content effect is positive in nine countries and oscillating in three countries (Denmark, Norway and Sweden), however the positive trend of the content effect becomes negative after the start of the of the eighties with small positive cycle at the start of the nineties in most countries. In the OECD countries we notice as a whole that the two accumulated effects are positive, increasing until 1984 and after that it is practically constant (the structure effect with small decreasing slope and the content effect oscillating between increasing and decreasing values). The K/Y ratio variation is ascending until the mid eighties when its positive slope drops, becomes negative and increases again at the end of the eighties and remains practically constant from the start of the nineties until the end of the period. These changes in the K/Y ratio variation closely follow the accumulated content effect which has a weight larger than the structure effect. Since the accumulated structure and content effects are positive in most countries and in OECD as a whole, the increasing behavior of the capital/product ratio is determined by the combination of the reallocation of product in activities more capitalintensive and by the increase of the K/Y ratio in some activities. In order to allow for a more detailed analysis of these effects we present in Table III below the participation of the product of each activity[1] in the GDP and the weight of the ratio of each activity, weighted by its participation, in the total K/Y ratio.Table III – GDP Participation by Activity ( e_{a }) and Weight of each Activity in the K/Y ( ) ratio[29] in OECD
In the table above the weight of the capital/product ratio of each activity in the total ratio clearly demonstrates the importance of the INF activity, more than 30%, of the activities MAN and SAP, both with more than 15%. In order to analyze the structure effect we will concentrate on the activities with larger participation in the GDP (INF, MAN, SSO and AGR). The positive variation in the participation of the product of the INF activity and the negative variation of MAN have had almost the same similar absolute value, namely 7.5% and 6% respectively. We observe that from 1970 until 1994 the INF activity has changed place with the MAN activity, instead of representing the second largest participation in the GDP, it is now the first one which previously belonged to MAN. Since the weight of the structural change is given by the capital/product ratio (see Equation (3) in Subsection II.2), the positive structural modification supersedes the negative one since the weighted average[1] of the K/Y ratio of the INF activity is more than twice the average of the MAN ratio (see Table II in Subsection IV). To this positive structural model is added the increase of 3% in the participation of the SSO activity in the GDP, while the drop of participation of the AGR activity, 2%, smoothens the increase of the accumulated structural effect as the increase in the ratio of this activity correspondingly increases the weight of the structural effect in this activity. Differentiating now the effects by country, we clarify that in principle the sense of variations in the participation in the GDP of the AGR, MAN, INF and SSO activities is equal in all countries[2]. In what concerns the similar absolute values of the changes in MAN and INF activities , the positive variation in INF was significantly larger in Denmark, Finland and Japan and smaller in Norway. Besides those four activities, the CST one has also a variation in the participation in the GDP, with the same sense (negative) in all countries, mainly in Denmark, Finland and Italy. However, since this is the activity with smaller weight it does not much affect the total structure effect. As to the differences among countries in the reallocation of product by activity we mention Denmark, Finland, France, Norway and Sweden which present increase in the SAP activity, whose weight (K/Y ratio) is smaller only than the values of the EGA e INF activities. The increase of participation in the product of the SAP activity has a positive effect on the accumulated structure effect in these countries (in spite of the fact that the reallocation of the product in other activities makes the negative the structure effect in Norway) In Japan, Canada and Norway we point out the drop in participation of the TAC activity and specifically for Japan the drop in the SAP activity. The effect of these reallocation changes decreases the structure effect in Canada, Norway and Japan. In these two last ones, the accumulated structure effect turns negative in spite of the fact that it is small compared to the content effect. These changes in sense of the structure effect are due mostly to the drop of participation of the SAP and TAC activities whose capital/product ratios have high levels. In what concerns the accumulated content effect in OECD, we will analyze the activities that had positive modifications in the weighted average of the K/Y ratio (see Table II of Subsection III), namely AGR, MIN, MAN as well as the INF activity that had the largest negative variation. The weight of change in content is given, according to Equation (4) in Subsection II.2, by the participation of the activity in the GDP. Therefore, we notice that the positive variations in the K/Y ratio averages of AGR and MAN activities are softened as the participation drops along the period from 4.1% to 2.1% in AGR and from 26% to 20.1% in MAN. The MIM activity on the other hand has a low participation in the GDP, so the variation of its ratio, in spite of being significant, has a limited effect on the total K/Y ratio, weight of 3% in 1970 and 3,9% in 1994. We remember that the K/Y ratio has a break in trend in mid eighties when it practically duplicates its value. We point out that even though the construction activity (CST) has a high ratio variation, 70%, we will not analyze it in detail taking into account the small absolute value of its ratio variation, 0.3, since it has the smallest capital/product ratio average among the activities. The weight of this activity in the determination of the aggregated capital/product ratio is not only smaller but it also dropped from 2% to 1.8%, see Table III. In what concerns the drop in the capital/product ratio of the INF activity (14% on the average), we point out that since the weight in the content effect, given by the participation of this activity in the product, is large, 15,8% in 1970 and 23.3% in 1994, and that the absolute value of the variation is large as well, 0.8, this activity will significantly alter downward the content effect mainly after the fall of interest rates in 1986. We remember the positive shock on the K/Y ratio of this activity in the mid seventies until 1986 when the content effect, contrary to the trend, becomes positive in several countries. The content effect seeks to show the weight of variation in the capital/product ratios by activity on the calculation of the total capital/product ratio. In the countries with positive aggregated content effect (Australia, Belgium, Canada, Denmark, USA, France, Finland, England, Italy and Japan) it is confirmed the increase of the positive capital/product ratio of the AGR, MAN and MIN[1] activities, restricted by the drop of weight on the content effect, given by the drop in the participation of the MIN activity in the GDP, as well as the negative content effect and high weight of the INF activity (except Japan that a slightly ascending trend in this activity) but with positive cycle in mid seventies and ending in 1986. Italy together with Japan are noticeable for the high accumulated content effect , and that of Japan is always ascending. The content effect is reinforced in Italy by the rise of the capital/product ratio in the TAC activity and in Japan by the growth in the ratios of the EGA, TAC, SSO ans SAP activities. We remember that in spite of the drop of participation in product of the SAP activity in Japan, the capital/product ratio remained well above the average at the end of the period so that the weight of this activity in the determination of the capital/product ratio rose from 19% to 21% in Japan. Of the countries with oscillating accumulated content effect (Denmark, Norway and Sweden), we notice that the content effect is ascending from 1973 on until mid eighties when it becomes descending. In Norway the capital/product ratios present a positive cycle in this period, TAC, INF and MAN that supersede the negative cycle that occurs in this country in the same period in the MIN activity. At the end of the period, the TAC and MAN activities change weight in the determination of the capital/product ratio, with similar ratios but with ascending participation of the MIN activity and descending participation of the TAC one. Finally, in Sweden we observe an elevated positive cycle in the MIN activity in the period and a drop in the K/Y ratio of the EGA activity, from 13.6 to 8.6. VI – Conclusions The capital/product ratios of the OECD member countries as well that of Brazil show a positive trend. The inverse relationship between the initial level and the growth of the ratio suggests a convergent behavior that would be around the average level 3. We notice also a slowdown of the ascending trend from the eighties on in most countries and a larger drop of the ratio after the 1992 recession, coinciding with the acceleration of the product growth. Of the capital/product ratios by activity, those with higher initial level, electricity, gas and water (EGA) and finance, insurance institutions, real estate and business services rendered to companies (INF) present a descending behavior while all the others show an average ascending behavior among the countries. The evolution of the the K/Y ratios by activity naturally has shown to be more vulnerable to shocks. We point out the ascending trends presented in the agriculture, hunting, forestry and fishing (AGR) activities mining and quarrying (MIN), manufacturing (MAN) and construction (CST). The ratio series show : a) higher positive slope in AGR; b) large cycles (determined by the petroleum shocks and by the price drop of this product in 1986) in the MIN activity as well as in transport, storage and communication (TAC) and c) lower level in CST. We also point out that the INF activity, in spite of the descending trend of the capital/product ratio, is marked by a positive cycle that starts in mid seventies and ends around 1986 when occurs the interests rate drop around the world. The capital/product ratios of the INF, SAP and manufacturing (MAN) activities are responsible for more than 50% of the capital/product ratio determination not only due to the large participation of these activities in the product but also due to the level of their ratio. We verify that the participation of the MAN activity in the product has been dropping and the product is being allocated to a more capital intensive activity, namely INF. The structure effect – reallocation of the product in sectors that are more or are less capitalintensive – accumulated in the period has shown to be predominantly positive with large growth until the eighties, remaining practically constant from that decade on. This effect, whose series is well behaved, helps to determine the trend of the capital/product ratio. The content effect – increase of the capital/product ratio by activity – accumulated year by year in most activities adds up to the positive structure effect. The significance of this effect is larger in the countries where it is positive, and where sometimes it determines its trend, and smaller when it oscillates, where, besides decreasing the positive structure effect in determined periods, it appears with larger volatility, determining in most cases variations around the capital/product ratio trend. Therefore, the developed countries, OECD members, have invested in capital intensive activities and have as well adopted, in most cases, more capital intensive techniques. However, the adoption of less intensive techniques in the finance, insurance, real estate and business services and, in some countries, in the electricity, gas and water activities, the end of positive cycles in some activities that coincided with the petroleum and interest rates shocks, as well as the drop of participation of sectors with growing capital/product ratios, AGR and MAN, tend to slowdown the trend of high total K/Y ratio in the eighties in most OECD countries. In Brazil we did not carry out the analysis by activity due to the absence of specified data regarding investment. However, we should highlight its behavior that was markedly ascending, as well as the level reached by the ratio (using average life times equal to those of OECD). The K/Y ratio for the country was duplicated in the 1979/1980 period, from 1.5 to 3, indicating that the country needs today twice as much capital that was necessary in the seventies to generate one unity of product. Less developed countries, where capital is the scarce factor, should take into account the need of contribution of this factor when they plan the reallocation of resources in the product and when they absorb or even develop technologies, in order to prevent blocking points in their growth. This situation is aggravated when the country, besides not considering this growth limiting factor in its development strategies, is not concerned with long term planning and pays attention only to the short term.
Bibliography Agénor, PierreRichard e Peter J. Montiel. Development Macroeconomics. Princeton University Press. New Jersey, 1996. Alvim, Carlos Feu et alii. Brasil: O Crescimento Possível. Bertrand. São Paulo, 1996. Barro, Robert J. e Xavier SalaiMartin. Economic Growth. McGrawHill. New York, 1995. Carvalho, José Carlos., “Estimativas do Produto Potencial, Relação Capital/Produto e Depreciação do Estoque de Capital”, Textos para Discussão 44, Área de Planejamento do Departamento Econômico do BNDES, Rio de Janeiro, (1996). De Long, J., Bradford, and Lawrence H. Summers. “Equipment Investment and Economic Ghrowth”, Quartely Journal of Economics, CVI, 445502, (1991). ___________. “How Strongly do Developing Economies Benefit from Equipment Investment?”, Journal of Monetary Economics, 32, 395415, (1993). Feu, Aumara. Projeto de Pesquisa para seleção do Doutorado na Universidade de Brasília: A Produtividade do Capital, a Transferência de Recursos do Exterior e o Crescimento Econômico. Brasília, (1999). ___________. “A Influência na Dinâmica do Crescimento da Taxa de Depreciação Variando de Acordo com a Idade do Capital,” XXVIII Encontro nacional de Economia, Campinas, (2000). Foley, Ducan K. e Thomas R. Michl. Growth and Distribution. Harvard University Press, Canbridge, 1999. Hofman, André A. "Capital Accumulation in Latin America: A Six Country Comparison for 19501989," The Review of Income and Wealth, 38 (1992): 365401.
Instituto Brasileiro de Geografia e Estatística. Produto Industrial Bruto Trimestral, Série de Relatórios Metodológicos, 19, Rio de Janeiro, (1999). Jones, Charles I. Introduction of Economic Growth Theory. W.W. Norton & Company. New York., 1998. Jones, Charkes I. “Time Series Tests of Endogenous Growth Models”. Quartely Journal of Economics, CX (2) (maio, 1995): 495525. Morandi, Lucilene, “Metodologia de Cálculo do Estoque de Capital Fixo – Estruturas NãoResidenciais e Máquinas e equipamentos, Brasil 1940/2000.” In Bacha, Edmar L. e Bonnelli, Regis.”Crescimento e Produtividade no Brasil: o que nos diz o Registro de Longo Prazo”, Seminários da Diretoria de Estudos Macroeconômicos n°52do IPEA, Rio de Janeiro, (2001). Organisation for Economic CoOperation and Development. Methods used by OCDE Countries to measure Stoks of Fixed Capital  OECD. Paris, 1993. ___________. Monitoring the world Economy 18201992, por Angus Maddison. Paris, 1995. ___________. International Sectoral Data Base. Paris, 1999. ___________. National Accounts of OECD Countries –main aggregates. Paris, 2001. Pinheiro, A. Matesco, V. “Relação capital/produto incremental: estimativas para o período 1948/87”. Pesquisa e Planejamento Econômico, Rio de Janeiro, V. 19, n. 3, (1989). Romer, Paul. “Capital Accumulation in the Theory of Long Run Growth.” Modern Business Cycle Theory, Robert J. Barro. ed (Cambridge, MA: Harvard University Press, 1989): 55127. Summers, Robert, and Alan, Heston. “A New Set of International Comparisons of Real Product and Price Levels Estimates for 130 Countries, 195085.” Review of Income and Wealth, XXXIV (1988): 126. System of National Accounts. Rev. 4. Brussels: Commission of the European Comunities; Washington, D.C.: International Monetary Fund; Paris: Organization for Economic Cooperation and Development ; New York: United Nations; Washington, D.C. World Bank, 1993.
[1] PhD student of Economy at the Brasilia University and finance and control analyst of the National Treasure Secretariat – SNT of the Ministry of Finance. Started the development of the present work to be presented at the closing of the “Special Topics of the Economic Analysis Methods 2” discipline under the responsibility of Professor Dr. Joaquim Pinto de Andrade, that had assistance from Professor Dr. Maurício Barata de Paula Pinto adviser to her Ph D thesis of which the present work will be part of. [2] The rate of return on capital does not show either an increasing or a decreasing trend and the capital and labor participation in the per capita income do not present trends. [3] The average scraping time (h) is the time after which, on the average, the good looses its capacity of aggregating value, not including the delay period.Therefore, h determines the wearing away that is considered as normal for each good. [4] In Equation (1) that follows, x will be given by the difference between tmr, where r is the year in which the investment was made. Here, r is absent because it is taken to be zero, that is, the investiment was made in year zero. [5] We consider de additional depreciation rate (d) the rate value that is applied in the first year of scraping of investment, and from this moment on, until it reaches unity, the rate applied to the initial investment is cummulative and increases d annually. [6] Adding h + m we obtain the final period of the good’s average life, v, that is, after the m periods when the good’s depreciation is zero, and the h periods in which the capital depreciates at an additional d rate. In the year v, the capacity to aggregate value to the good is zero. [7] The values of m=5 and v=24 correspond to the delay period and to the average life time for machines and equipament, supplied by OECD. [8] For investiment, we will take the series of Gross Formation of Fixed Capital (FBKF). [9] This procedure is similar to that used by Solow (1959) in Generation Model for capital, where investiment is treated according to its generation (its age). In the theoretical models it is usual to use geometric depreciation, which allows for aggregating different generation of assets but it has the disadvantage of never using up the assets and of not permitting tovisualize the effect of investment behavior changes on the growth dynamics. Since one of the objectives of the present work is to verify the evolution of the quantity of investment necessary for growth, one must calculate the aging of the capital stock, its depreciation rate and the quantity of investment necessary to replace the wear away of capital. It should be clarified that with the recessive periods that occurred in Brazil in the last decades its capital stock has aged and consequently its depreciation has increased ( see Chapter IV). [10] The active life of a good – delay time plus scraping time, i. e., time in which an asset remains in the stock capital – is estimated by different sources. Those usually used are the taxing authorities, the companies’ accounting, statistical research, administrative recording, studies of specialists and estimates of other countries. Most countries use a fixed life time for stock capital calculation, in spite of the fact that actually in most activities the life time is decreasing what would be explained either by the reduction of the assets’ life time or by the increase of the portion of the assets with smaller life time in the stock of the activity. As example of goods with smaller life we could mention components containing microchips and as exceptions OECD (1993) mentions highways and airplanes. [11] In what concerns the average scraping time of capital (h), it is important to mention that, according to exercices in which we have changed its value, the larger the value of h used the larger the growing trend and the K/Y ratio and the smaller this ratio’s volatility will be. The increase of level and of the trend’s positive inclination is explained by the larger evolution of the capital stock, since when h increases depreciation diminishes. Therefore, a capital stock that has a higher level and that is growing more rapidly for a specific product determines a larger K/Y ratio with more accelerated positive behavior. On the other hand, the smaller volatility of the ratio is explained by its smaller sensitivity to conjuncture changes due to larger permanence of these investments in the series. Therefore, the higher the value of h, the less sensitive is depeciation to temporary variations in the behavior of the investment. [12] For more informations about the activities, see OCDE(1999). [13] Between the constant and current prices series, we have chosen the current prices series. First of all because this series comprises a longer time period and second because it prevents problems that would arise if we would chose constant prices with fixed base. The constant prices series with fixed base has consistency problems generated when the base year is changed and, since it is a quantum index, it ignores price changes that reflect changes in the productivity of assets. However, the procedure that we have adopted ignores investment prices variation relative to price variations in the GDP as well as differences in prices variations among activities. [14] It should be clarified that the total (TOT) and the sum of its components sometimes don’t agree. According to ISDB of OCDE this is due to the different sources used for the same country and particularly in what concerns series with constant prices by change of base.Therefore we have normalized the series’ data. [15] v = m + h = 19 + 5 [16] We remind that the first year supplied are: 1900 (Brazil); 1947 (US); 1948 (Canada and England); 1949(Australia and Norway); 1950(Denmark, Finland and Sweden); 1952 (France and Italy); 1953(Belgian) and 1955(Japan). [17] Of the investiments made in 1950 (year in which total investments data are available for most of the countries, see Footnote14), 35,8% would remain in1970 and 8,4% in 1990. As an exercise we have calculated for Australia the weight of investimentos prior to 1951 in the capital stock of 1970 and 1990, and we found 9% and 0,6%, respectively. [18] The GDP series at market prices of 1990 for each country were completed using the GDP growth index supplied by OECD (1995). [19] As a exception, Denmark, since ISDB has not supplied the average lifes for this country, it was considered the proportion of machines and equipment, calculated using the average of the average lifes of other countries. It should be menntioned that the standard deviation for the proportion of machines and equipment by activity in other countries, except Denmark, is very small, below 0.03 in all activities, except the activity of nonmercantile public administration services where it is 0.098. [20] We point out that this series is divided in three types of goods: construction goods, machines and equipment and others. As in Alvim et alii (1996), Hofman (1992) and Morand i(2001), the item others will be incorporated to the machine and equipment item , because it represents at most 6,3% of the FBKF total during the period analysed.
[21] Except for the Netherlands (since the data by activity, which are incomplete, are very different from the sum) and Germany (due to the discontinuity of its series resulting from the unification of West and East Germany) . The periods supplied by ISDB are discriminated by country and by activity in OECD (1999). [22] The series in national currency, at 1990 prices, were converted to US dollars by the exchange rate supplied by ISDB. [24] Years included by all countries in their data series. [25], Belgium and Italy do not have data concerning the product in the INF activity, mostly incorporated (90%) in the SSO activity, and the product of the FBKF in the MIN activity, incorporated in the MAN activity. This difference is due to differences in the desaggregation system by acivity used by these countries– Nomenclature des Activités dans les Communautés Européennes (NACE) –relative to the system used by most countries – International Standard Industrial Classification (ISIC).Therefore we have not included Belgium and Italy in the average calculation of the SSO and INF activities and in the calculation of the K/Y ratio in OCDE. The treatment given to the calculation of the ratio of the SSO activity in these countries will be shown below. [26] The OUT activity is not mentioned because there are complete data only for Finland. The calculated ratio for this activity in Finland was 1.4 in 1970 and 2.3 in 1994.[27] The data relative to the MIN activity in Belgium and Italy are incorporated in the MAN activity. [28] In the calculation of the participation of the product of the activity in the product of the total, we have excluded two countries, Belgium and Italy. [29] The weight of each activity in the total K/Y ratio corresponds to the terms of Equation (2), after its division by capital/product ratio (v). [30] We have used the weighted average because we are dealing with the K/Y ratio for OECD, where the stock and the product of each country has different weights in the ratio calculation. [31] We remember the particular case of Belgium and Italy where the positive variation in participation in the GDP in the INF activity is sensed in the SSO activity, since the latter incorporates most part of the INF activity (see footnote 24). [32] We distinguish in these countries, Belgium and Italy, because the disagregation of their data is different from that of other countries, a larger positive variation of the K/Y ratio in the MAN (MAN + MIN) activity, and a larger negative variation, with positive cycle in the SSO (SSO + INF) activity, that closely follows the behavior of the INF activity.

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