Evolution of the Capital/Product Ratio in Brazil and in OECD Countries

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 capital-intensive and that the capital/product ratio is ascending in most of the activities, mainly until the mid eighties. However, precisely in the most capital-intensive 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.

I – Introduction

The 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 capital-intensive 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 Co-operation 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 description

We describe below in two sub-sections 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 Ratio

The 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 bell-shaped function. In Figures 1 and 2 that follow we present the four more usual mortality function – linear, linear with delay, bell-shaped 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 bell-shaped form, both presuppose a smaller depreciation in the first years (linear with delay – zero depreciation in the delay years and bell-shaped form – depreciation increases gradually in the first years). In spite of the fact the the bell-shaped 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 bell-shaped 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- Bell-like 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 – 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 = v-m; as well as its image (1-dx), 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.

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.

Table I – Average Scraping Time (h) by Activity and by Type of Goods

Note: ^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 (1-f) – 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

This estimate does not consider the variation between f and (1-f) 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).

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.

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.

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 Countries

We 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.

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 capital-intensive 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).

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.

	Electricity, gas and water (EGA)	Finance, insurance, ,real estate business services (INF)	Producers of government services (SAP)	Transport, storage and communication (TAC)	Mineral extration industry (MIN)	Mineral extration industry (MIN)
Arithmetic av.(1970)	7,2	5,3	3,8	3,3	2,7	2,6
Arithmetic av.( (1994)	6,9	4,5	3,9	4,0	4,5	4,7
Variation	-4%	-14%	3%	21%	70%	83%
Standard deviation (1970)	3,6	1,0	2,1	0,9	1,5	0,9
Standard deviation (1994)	1,9	1,1	2,6	0,8	1,9	1,3
Weighted av. (1970)	5,4	4,3	3,1	2,9	3,6	2,5
Weighted av. (1994)	5,7	3,7	3,8	3,6	6,1	5,0
Variation	6%	-14%	23%	26%	70%	103%

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 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.

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 Activity

The 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.