DWC-8702 Investment Policies for Steel-Producing Countries An Empirical Analysis of the Use of Iron Ore by Major Steel-Producing Countries Theophilos Priovolos Division Working Paper No. 1987-2 March 1987 Commodity Studies and Projections Division Economic Analysis and Projections Department Economics and Research Staff The World Bank Division Working Papers report on work in progress and are circulated to stimulate discussion and comment. INVESTMENT POLICIES FOR STEEL-PRODUCING COUNTRIES AN EMPIRICAL ANALYSIS OF THE USE OF IRON ORE BY MAJOR STEEL-PRODUCING COUNTRIES Theophilos Priovolos March 1987 The World Bank does not accept responsibility for the views expressed herein which are those of the author and should not be attributed to the World Bank or its affiliated organizations. The findings, interpretations, and conclusions are the results of research supported by the Bank; they do not necessarily represent official policy of the Bank. The designations employed and the presentation of material used in this document are solely for the convenience of the reader and do not imply the expression of any opinion whatsoever on the part of the World Bank or its affiliates concerning the legal status of any country, territory, city, area, or of its authorities, or concerning the delimitation of its boundaries, or national affiliations. TABLE OF CONTENTS Page SUMMARYS ....... ..*0-.0.0........ ....................................... iv I. INTRODUCTION ................................................................ 1 II. THE MODEL .... ........................................................ 3 III. EMPIRICAL ANALYSIS . ... .............................................. 11 A. Cobb-Douglas Production Function Estimates . . 12 B. Steady States . . ................. .... 19 IV. POLICY CONCLUSIONS ... ...... .............................. . 24 ANNEX 1: DATA BANK SOURCES ......... . . 33 ANNEX 2: NON-MONOTONIC EQUILIBRIUM PATHS .. ...... .. ................. 34 ANNEX 3: ESTIMATING THE ELASTICITY OF SUBSTITUTION BETWEEN IRON ORE AND OTHER FACTORS OF PRODUCTION .................. 36 REFERENCES ......................o........ 45 !~~~~~~~~~~~ -iii - LIST OF TABLES Page TABLE 1: ESTIMATES OF PARAMETERS OF COBB-DOUGLAS PRODUCTION FUNCTIONS FOR STEEL WITH VARIABLE RETURNS TO SCALE .... 15 TABLE 2: ESTIMATES OF PARAMETERS OF COBB-DOUGLAS PRODUCTION FUNCTIONS FOR STEEL WITH CONSTANT RETURNS TO SCALE .... 18 TABLE 3: STEADY STATES OF STEEL OUTPUT/CAPITAL STOCK RATIO (Z) AND IRON ORE CONSUMPTION/RESERVES RATIO (d) ...................... 20 TABLE 4: ASSUMPTIONS FOR DIFFERENT PRICE PATHS ............................ 23 TABLE 5: GROWTH RATES FOR IRON ORE CONSUMPTION/RESERVES RATIO: 1972-83 .. ............................ 24 TABLE 6: RELATIVE IMPORTANCE OF FACTORS OF PRODUCTION IN THE STEEL PRODUCTION PROCESS: AN INTERNATIONAL COMPARISON ............ 26 ANNEX TABLE 3.1: ELASTICITIES OF SUBSTITUTION BETWEEN INPUTS IN THE STEEL PRODUCTION PROCESS .......................... 39 LIST OF FIGURES FIGURE 1: PHASE DIAGRAM OF d AND Z ....... 7 FIGURE 2: PRICE PATHS BASED ON DIFFERENT VALUES FOR Z* AND d* . . 22 FIGURE 3: WORLD DEPLETION RATE (DSWW) AND INTERNATIONAL IRON ORE PRICE (IOP) ............................. 25 FIGURE 4: STEEL OUTPUT TO CAPITAL RATIO, SELECTED COUNTRIES .............. 28 FIGURE 5: IRON ORE CONSUMPTION TO WORLD RESERVES, SELECTED COUNTRIES ..... 30 - iv - SUMMARY * Based on the analysis by Stiglitz (1974) and Dixit (1976) on natural resources dynamics this study shows that steel industries with high capital stock shares relative to labor or other raw material inputs should seek to increase their steel output/capital ratio and their consumption of iron ore to world iron ore reserves ratio in order to approach efficiency. The opposite policies should be adopted if the capital stock share is low relative to labor and other raw materials. The analysis also notes that constant monitoring of iron ore depletion plans is necessary in order to minimize error from choosing inappropriate initial conditions. The study analyses empirically the operations of nine major steel producing countries namely: the United States, the Federal Republic of Germany, France, the United Kingdom, Italy, Japan, India, Brazil and the Republic of Korea. It shows that during the 1973-83 period most steel producers tended to use iron ore efficiently in their production process. The study shows that the investment policies of the steel industries in the United States, the Federal Republic of Germany, France and India should aim at further decreasing their output/capital ratio and their consumption of iron ore to world reserves ratio to achieve efficiency. On the contrary, the investment policies of the Republic of Korea should aim at increasing the steel industry's output/capital ratio and the consumption of iron ore to world reserves ratio to achieve efficiency. The efficient investment strategies of Japan, Italy and Brazil are not as clear. Very likely, Japan should follow policies similar to those in the United States or the Federal Republic of Germany. Italy should try to increase its output/capital ratio while decreasing its consumption of iron ore to world reserves ratio. Lastly, drawing conclusions for Brazil's strategy to achieve efficiency was found to be difficult due to data problems. * This paper has greatly benefitted from discussions and suggestions from R.C. Duncan, D. Tarr and M. Imran, who read and commented on earlier drafts. Tamar Dunietz and Moshe Buchinsky provided excellent research assistance. I. INTRODUCTION 1. During the 1960-84 period, iron ore prices increased a mere 1.2% p.a. while steel merchant bars and the manufacturing unit value (MUV) increased by 5% p.a. and 4.9% p.a. respectively.l/ In view of the decline of iron ore prices in real terms, several questions are raised: Have the major steel producing countries of the world adjusted to declining real iron ore prices? Are their production methods still efficient? What should their policies be in order to achieve efficiency? This paper aims at providing some answers to these questions by an empirical analysis of the operations of nine major steel producing countries namely: the United States, the Federal Republic of Cermany, France, the United Kingdom, Italy, Japan, India, Brazil and the Republic of Korea. 2. Iron ore is used almost exclusively for the production of pig iron and sponge iron. In the steel making process per se iron ore is a minor input compared with pig iron and scrap. Ninety-eight percent of iron ore goes into pig iron and sponge iron production, 1% of iron ore is consumed directly in the steel making process itself and 1% is consumed in other industries such as the cement industry. Annual world iron ore production exceeds 450 million tons in Fe content of which about 90% is produced by 12 countries. 3. According to the US Bureau of Mines, world iron ore resources were estimated to contain some 235 billion tons of iron in 1984. Of these resources about 89 billion tons were considered to be reserves and of these 63 billion 1/ See Commodity Trade and Price Trends, The World Bank, Economic Analysis and Projections Department, 1986 Edition, Washington, D.C. -2- tons were located in industrial and developing countries. At 1984 steel and iron ore consumption levels, iron ore reserves could satisfy steel demand for 194 years. The percentage of world iron ore produced that is traded inter- nationally has risen from 30% in 1961 to 48% in 1984. Six countries, of which one is industrial, accounted for more than 75% of the iron ore exports. Three groups: Japan, the European Economic Community (EEC) and the United States, accounted for 70% of total imports in 1984. Nine countries, the United States, the Federal Republic of Germany, France, the United Kingdom, Italy, Japan, the Republic of Korea, India and Brazil produced 42% of world crude steel production (or 59% of industrial and developing countries world crude steel production) in 1984. Iron ore price growth prospects remain bleak. In addition to the declining demand for steel, the oversupply of iron ore persisting from the last decade and the relative simplicity of replacing one source of supply with another have made the iron ore market quite competitive. In the last four years, international iron ore prices have been declining continuously in real terms, and for 1987 price prospects are equally gloomy because of the abun- dance of iron ore capacity and the slackness in steel demand. 4. The following three sections of this study will present: (a) the model from which the equilibrium and efficiency conditions and relevant steady state paths are derived; (b) the empirical results of the analysis; and (c) policy conclusions. A Cobb-Douglas production technology is used to estimate the parameters that determine steady states and equilibrium price and depletion paths. The production technologies and iron ore needs of the nine largest steel-producing nations are compared. Policy conclusions are derived as to the optimal strategy for steel producers to reach equilibrium production paths. -3- II. THE MODEL 5. The analysis focusses on the special but useful case of an economy in which the steel industry is characterized by a Cobb-Douglas technology of the form Y = A eXt Ka L MY R6 (1) where Y = aggregate steel output A = constant x rate of output-augmenting technological progress (assumed to be constant) R = utilization of iron ore L = supply of labor K = capital stock M = utilization of other raw materials and inputs a, 8, y, 6 > 0 For the purposes of this section of the study nothing is gained by assuming different production functions for different countries and different stages of steel production. We may also write Y = C +K where C = consumption -4- K = net investment Y may be thought of as net output or a depreciation rate can explicitly be assumed.l/ It is also assumed that labor grows at a constant rate n, i.e., L/L = n. The labor supply at time t being L = L ent 0 Raw materials (M) other than iron ore are assumed to grow at a constant rate as well, i.e., M/M = m. The supply of these raw materials at time t is mt M = Me e. In addition it is assumed that R is subject to the stock 0 constraint f R(t) dt S t=O0 where SO is iron ore stock at time o In this model it is also assumed that there is no deterioration of capital and the equation for the accumulation of capital takes the form K = sY or K/K = sY/K (2) The propensity to save (s) is assumed constant. From (1), by taking growth 1/ For simplicity purposes, the analysis here deals with one sector model only. Modification of this assumption has not been attempted successfully due to the complexities involved in deriving steady state paths. -5- rates we have: (Y/Y) = x + a(K/K) + Bn + ym + 6(R/R) The condition for efficient asset allocation is: 1/ Cs(Y/K) = (Y/Y) - (R/R) (3) If Z = Y/K, x= 1 - s and (4) d = R/S (5) From (1) to (5) the following differential equations are obtained: 2/ Y/Y = {(8n + ym + X - axZ)/(l - d)} + aZ (6) R/R = {(Bn + ym + X - axZ)/(l - 0)} (7) Z/Z = Y/Y - K/K = {(8n + ym + X - axZ)/ (1 - d)} + (a - 1 + x) Z (8) 1/ See Dixit (1976) and Stiglitz (1974). Efficient asset use requires the marginal products of capital and of the resource (R) to grow at equal rates. 2/ These are the same equations as in Stiglitz (1974), Solow (1974b) and Dixit (1976). d/d = R/R + d = {(Bn + ym + X - axZ)/(l - d)} + d (9) The two lines with Z = 0 and d = 0 intersect at the point (Z , d ) given by Z = {(Bn + ym + X)/(s (1-a) + 6(a-s))} (10) d = Z (a - s) (11) These two points are the efficient steady state. 1/ 6. The phase diagram, Figure 1, shows the solutions of the differential equations. The steady state is a saddle-point. As Z goes to Z it goes to 0 or - on all but the two stable paths. Efficiency in use requires also that the relative price of iron ore to steel is equal to the marginal product of iron ore, i.e., P = 6Y/R = 6 eXt Ka Li MY/R1-6 (12) where P = relative iron ore price (with the denominator the steel price). 1/ For proof and for stability/Jacobian conditions see Stiglitz (1974) or Dixit (1976). Identical notation as that of Dixit has been used here to show that the problem and its solution are the same as that presented in Dixit's (1976) discussion on natural resources dynamics. -7- FIGURE 1: Phase Diagram of d and Z Z z SOURCES: DIXIT (1976) AND WORLD BANK, ECONOMIC ANALYSIS AND PROJECTIONS DEPARTMENT. ,~~~~~~~ , -8- The rate of change of the price would then be P = a-, = aZ (13) which makes it endogenous to Z. Equation (12) shows that price is inversely related to the depletion rate. The choice of too high a depletion rate is equivalent to the choice of too low a price. 7. The phase diagram show that the depletion rate will continue to remain high while the price will continue to remain low. As Z goes to Z and d goes to -, d/d goes to 1 (see equation (11)). Nordhaus and Tobinl/ show that by integrating equation (11) a finite amount of time is necessary for d to go to -. If the initial choice of the depletion rate is too low, the price will be high and the reserves of iron ore will never be used up. The solution of the differential equation (9) will be a function of Z and thus of its initial conditions from the solution of equation (8). Taking KO, Lo, Mo and Ro as given, equation (1) gives the following relation: Z( = {A La MY Ro }i do This is a relation that can be represented in the diagram of (d,Z) space. Two curves are presented, curve C1 is generated with a ZO smaller than curve C2. Ko is large relative to Lo and Ro in Cl curve. The opposite is true in curve C2. The appropriate initial conditions should then be those that correspond to the curve that meets one of the stable paths into the saddle-point. The important conclusion is that stable paths are the only desirable ones but the ability of an economy to select them is very doubtful. Even with perfect 1/ For proof see Nordhaus and Tobin (1972). -9- foresight over a finite or an infinite horizon,l/ the error of choosing the wrong initial conditions and thus, for example, setting the price too high or too low and discouraging or encouraging iron ore utilization is difficult to avoid. 8. If the steel industry's Ko is large relative to Lo, Mo and Ro the initial values of Z (Z0) and d (do) should be made low relative to steady state values (Z* and d*) and they should increase steadily through time. The opposite should happen if the initial capital stock is relatively low. Undue compliance with the observation that current iron ore reserves at current rates of consumption will last 194 years is not desirable as the wrong initial depletion plans or rates of consumption will lead to ever-increasing error if followed relentlessly. 9. Dixit2/ shows that removal of some of the restrictions of the Cobb- Douglas production'function is possible. However, he shows that increasing the number of factors, resources and capital goods does not yield many general qualitative results. He also shows that making endogenous the consumption growth path of steel or allowing for an elasticity of substitution different from one or a variable elasticity increases the possibilities for non- monotonic paths; for example, the iron ore consumption per capita can fall then rise and 1/ For proof, Stiglitz (1974). 2/ See Dixit (1976) for an analysis of equilibrium conditions and paths of a two-factor production function with constant returns to scale, Y=F(K, R) and a maximization problem of the following iso-elastic utility function: rO u (c) e Ptdt where p = interest rate in utility terms. Annex 2 demonstrates some of the characteristics of non-monotonic equilibrium paths, given the removal of some of the restrictions of the Cobb-Douglas production function. - 10 - finally fall again along an optimum path. In the long run, if the elasticity of substitution (a) between iron ore (R) and capital stock (K) is smaller or equal to one, i.e., a 5 1 and the limit of the marginal product of capital is zero then: R = K = C _ p (14) R K C E where p = interest rate in utility terms E = elasticity of marginal utility, i.e., the relative rate at which undiscounted marginal utility falls as consumption per head increases. If p is positive the growth rate of consumption for iron ore should decline with time. If a > 1 then R.= p + n . (1-E) _ (a - l)n = P + n - can (15) where n = limit of marginal product of capital (if a > 1 then n > 0) Relation (15) indicates that growth of iron ore consumption may be sustained if n is large enough. Thus the elasticity of substitution between iron ore and the other inputs into the production technology govern the possibility of sustaining growth of iron ore consumption and depletion growth rates.1/ 1/ The model presented here does not consider uncertainty. This is quite difficult to handle. In the literature of natural resources, Dasgupta and Heal (1974) have studied a simple kind of uncertainty, namely about the date at which a new technology will enable us to do without the resource altogether. It was found that uncertainty has the effect of raising the discount rate. - 11 - III. EMPIRICAL ANALYSIS 10. This section estimates and carries out an analysis of the production functions of the nine most important steel-producing countries of the western world namely, the United States, Japan, the Federal Republic of Germany, France, the United Kingdom, Italy, Brazil, India and the Republic of Korea. The following results are presented: (a) estimates of the coefficients of Cobb-Douglas production functions under constant and variable returns to scale; (b) steady states of steel output capital ratio (Z) and of the iron ore depletion rate (d); and (c) the iron ore equilibrium prices and consumption under alternative initial conditions. The estimates elasticities of substitution between iron ore and the other factors of production (based on a CES production function) are presented in Annex 3. These estimates have been made to test the elasticity of substitution implicit in assuming a Cobb- Douglas production function. 11. The primary sources for the data are World Steel Dynamics (WSD),1/ International Iron and Steel Institute (IISI)2/ and UNCTAD.3/ The World Bank's data banks have been used to double check the consistency of the primary data. All assumptions regarding future employment growth and output growth rates are consistent with World Bank forecasts as of January 1986. Annex 1 gives a list of all variables used in the empirical analysis, their source, units and sample period. 1/ See World Steel Dynamics (1985) for company steel data. 2/ See IISI (1985) for country steel data. 3/ See UNCTAD (1984) for country iron ore data. - 12 - A. Cobb-Douglas Production Function Estimates 12. The coefficients of equation (1) Y = A Ka La MY R6 ext are estimated with variable returns to scale (v * 1) and constant returns to scale (v = 1). The analysis of Klein (1953) for railroad operations is the basis of analysis with variable returns to scale. Equation (1) is rearranged so that endogenous variables are on the left hand side (lhs) and predetermined or exogenous variables are on the right hand side (rhs) of the equation, i.e., Ka L8 MY R6 = YA e xt eu = C (16) where u is a disturbance term The production unit is assumed to minimize costs by varying the four endogen- ous inputs K, L, M and R subject to the condition that it must meet given steel output demand. The first order conditions from the cost minimization problem using production function (16) are: a C/K = (P /9) e K w 3 C/L = (P /L1) e y C/M = (P I9) e M 6 C/R = (P It) e R - 13 - Ka La MY R6 - C = 0 Where PX' PL' PM, and PR are the prices of capital, labor, raw materials, and iron ore and Q is a Langrangean multiplier and V, W, X and Z are disturbance terms. The first four equations can be rearranged to yield K = a (X-V) PRR 6 L a 8 (X-W) --e PRR 6 MM=y e(X~Z PRR 6 Upon further rearrangement and taking logarithms this is equivalent to: ln (a/6) = ln(PK K/PRR) + (V-X) ln(0/6) - ln(P LL/PRR) + (W-X) ln(Y16) ln(P MM/PR R) + (Z-X) The unknown parameters on the lhs of these expressions can simply be estimated by taking the sample means of the rhs by equating a/6, 8/6 and y/d, respect- ively, to the (geometric) sample average of the ratio of the corresponding production factor rewards or In( 1)= 1 Zln( R - 14 - and similarly for the other expressions. The main advantage of this method is that the dependent variables and the disturbance term enter additionally in the estimators. The estimates are unbiased and consistent even though the terms involved are not independent. To obtain the remaining parameters of the production function (16), the equation can be rewritten upon taking logarithms as: lnR + a lnK + lnL + Yt lnM = - lnA + tlnY - Xt + u The lhs can be constructed now in the manner of two stage least squares by substituting the estimates of a/6, 8/6, and y/t for the corresponding para- meters. The lhs variable is then used as the dependent variable in a least- squares regression on the predetermined variables Y and t, yielding estimates of parameter ratios from which the original parameters are readily identified. The sum of coefficients a, B, y, and 6 provides an estimate of the returns to scale. The results of this estimation method are presented in Table 1. 13. A second method has been used to estimate the parameters of equation (1), i.e., by imposing the assumption of constant returns to scale. From the equations to be estimated the marginal productivity conditions are derived from the profit maximization problem under perfect competition as follows:l/ a Y/K = (P /P) e K 1/ Wallis (1973) shows that the marginal productivity conditions are identified. - 15 - TABLE 1: ESTIMATES OF PARAMETERS OF COBB-DOUGLAS PRODUCTION FUNCTIONS FOR STEEL WITH VARIABLE RETURNS TO SCALE PARAMETERS/A/B WW U J D F C I B N K A 0.01 0.01 0.001 0.01 0.00 *** 0.00 **i 0.002 0.00 aL 0.22 0.13 0.26 0.18 0.53 *** 0.53 *** 0.23 0.37 8 0.54 0.90 0.21 0.49 0.91 *** 0.32 * 0.53 0.10 y 0.31 0.19 0.68 0.38 1.12 *** 0.62 - 0.67 1.13 6 0.16 0.15 0.14 0.14 0.35 *** 0.11 *** 0.22 0.12 X -0.001* 0.02 -0.02 0.001* 0.02* *** 0.03 *** -0.03 -0.20 v 1.23 1.37 1.29 1.19 2.91 *** 1.58 *** 1.65 1.72 R2 0.82 0.92 0.42 0.72 0.24 0.80 0.83 0.22 0.56 0.98 DW 1.18 1.64 2.39 1.54 2.22 0.49 1.59 1.23 0.92 1.40 /A COUNTRY CODES: WW INDUSTRIAL AND DEVELOPING COUNTRIES U UNITED STATES J JAPAN D GERMANY, F.R. F FRANCE G UNITED KINGDOM I ITALY B BRAZIL N INDIA K KOREA, R. OF /B * T TEST INSIGNIFICANT. *** WRONG SIGN. SOURCE: WORLD BANK, ECONOMIC ANALYSIS AND PROJECTIONS DEPARTMENT. - 16 - 3 Y/L = (P /P) e L x y Y/M = (P m/P) e 6 Y/R = (P /P) e R where P is the price of steel output. These equations can be alternatively written in the form: Ina = ln(P K/PY) + V K and similarly for the other equation. If E(V) = 0 then the estimates of ln a = n Zln( py ) etc. are unbiased and consistent. The disturbance term also enters additionally here. The unbiasedness property disappears but consistency remains when we unscramble an estimate of a as exp (lna). The resulting estimate is the sample geometric mean of the input's (capital) share in total output. n | - K a =p etc. Py The estimates a, 3, y, 6 will tend to have a sum close to 1 as long as the data obey the identityl!/ 1/ Some errors due to aggregation may occur as the country data are derived from company balance sheets in current US$; subsequently they are deflated into real US$. - 17 - PY = PKK + P LL + PMm + PRR In that case the arithmetic mean of factor shares has a + 8 + y + & = 1 (variations in prices might give slight departures from 1). Estimates of a, 8, y, and 6 using this method are presented in Table 2. 14. Tables 1 and 2 indicate the following: (i) Returns to scale are not constant but increasing. The results of Table 1 are generally statistically superior to those of Table 2. The R2 of the equations of Table 1 are higher than those of Table 2 (with the exception of the R2 for Japan and France);l/ (ii) The results of Table 1 show that in most cases 6 > y > a > S. That is the elasticities of labor with respect to steel output are higher than those of raw materials (other than iron ore), capital and iron ore. (With constant returns to scale, the elasticities of raw materials other than iron ore become more important than those of labor.) In Japan and in the Republic of Korea the elasticities of raw material (other than iron ore) and of capital become more important than those of labor. The labor elasticity of steel production in the United States (and in France2/) is the highest among all the countries considered in Table 1. India seems to have a relatively high labor elasticity; India also has the highest iron ore elasticity among the I/ The Durbin-Watson test for India's and the western world's equations indicate some serial correlation. 2/ Statistically, France's elasticity coefficient is less reliable. - 18 - TABLE 2: ESTIMATES OF PARAMETERS OF COBB-DOUGLAS PRODUCTION FUNCTIONS FOR STEEL WITH CONSTANT RETURNS TO SCALE PARAMETERS/A/B WW U J D F c I B N K A 0.03 0.04 0.02 0.02 0.01 0.01 0.004 0.003 0.02 0.01 a 0.11 0.06 0.15 0.08 0.12 0.09 0.25 0.13 0.00 0.21 a 0.26 0.39 0.12 0.23 0.21 0.32 0.22 0.12 0.19 0.05 Y 0.51 0.48 0.60 0.60 1.68 0.60 0.60 0.74 0.58 0.57 6 0.08 0.07 0.08 0.07 0.08 0.07 0.05 0.05 0.08 0.06 x -0.014 -0.019 -0.02 -0.003* -0.022 -0.009* -0.008 0.043 -0.022 0.091 v 0.96 0.99 0.96 0.98 1.10 1.08 1.11 1.04 0.93 0.89 R2 0.61 0.40 0.66 0.08 0.36 0.07 0.09 0.24 0.37 0.75 DW 1.82 2.46 2.59 1.31 2.19 0.96 2.12 0.83 1.00 1.61 /A COUNTRY CODES: WW INDUSTRIAL AND DEVELOPING COUNTRIES U UNITED STATES J JAPAN D GERMANY, F.R. F FRANCE C UNITED KINGDOM I ITALY B BRAZIL N INDIA K KOREA, R. OF /B * T TEST INSIGNIFICANT. *** WRONG SIGN. SOURCE: WORLD BANK, ECONOMIC ANALYSIS AND PROJECTIONS DEPARTMENT. - 19 - countries considered.l/ Italy has the highest capital elasticity; and, (iii) The parameter X (the rate of output-augmenting technical progress) takes values that in most cases are either insignificant statistically or negative. Only for the United States and Italy is X significant and positive,2/ and varies between 0.02 and 0.03 for the 1972-1983 period. B. Steady States 15. Equations (10) and (11) of Section II identify the steady state values of Z (the steel output to capital ratio) and d (the iron ore consumption to iron ore reserves ratio). Based on values of Z a set of price paths may be determined as follows: * p p e (17) where p is the iron ore/steel price ratio. 16. The equilibrium price path may also be estimated by equation (17) if Z values are replaced by Z equilibrium values, i.e., the solution of equation (8). Table 3 presents the Z and d values for four different cases. From the foregoing results, the most reliable results from the statistical and economic point of view are those of Case 1, i.e., for the Cobb-Douglas production function with variable returns to scale and no technical progress. For the United States, the Federal Republic of Cermany, France and Italy, however, the results of Case 3 would be preferred to those of Case 1 as the Cobb-Douglas production function includes technical progress coefficients. 1/ France's iron elasticity seems excessively high and the R2 indicates that it should be viewed with caution. Table 2 gives a very different picture than that of Table 1 for France. 2/ In Table 2 X is positive and significant only for Brazil. - 20 - TABLE 3: STEADY STATES OF STEEL OUTPUT/CAPITAL STOCK RATIO (Z) AND IRON ORE CONSUMPTION/RESERVES RATIO (d) PARAMETERS/A WW U J D F G I B N K CASE 1 /B Z 0.11 0.07 0.12 0.05 0.09 0.12 0.17 0.31 d 0.02 0.10 0.03 0.01 0.05 0.06 0.03 0.10 CASE 2 IC Z 0.18 0.21 0.15 0.12 0.19 0.13 0.18 0.46 0.28 0.23 d 0.01 0.01 0.02 0.00 0.02 0.01 0.04 0.03 0.01 0.03 CASE 3 /D Z 0.10 0.21 0.00 0.05 0.14 0.36 0.04 d 0.02 0.03 0.00 0.01 0.01 0.17 0.01 CASE 4 /E Z 0.07 0.09 0.03 0.09 0.89 0.09 d 0.00 0.00 0.00 0.02 0.06 0.00 / IF 6.1 0.0 5.1 4.4 1.1 2.7 4.8 6.1 4.2 6.1 n IF 2.0 0.7 0.4 -0.1 0.4 0.1 0.1 2.0 1.9 1.4 m IF 3.4 2.5 2.9 2.2 2.4 1.9 2.5 5.9 5.0 4.0 /A COUNTRY CODES: VW INDUSTRIAL AND DEVELOPING COUNTRIES U UNITED STATES J JAPAN D GERMANY, F.R. P FRANCE G UNITED KINGDOM I ITALY B BRAZIL N INDIA K KOREA, R. OF /B CASE 1 USES ESTIMATES OF PARAMETERS OF THE COBB-DOUGLAS PRODUCTION FUNC- TION WITH VARIABLE RETURNS TO SCALE AND WITHOUT TECHNOLOCICAL PROGRESS, i.e., x - 0 . IC CASE 2 USES ESTIMATES OF PARAMETERS OF THE COBB-DOUGLAS PRODUCTION FUNC- TION WITH CONSTANT RETURNS TO SCALE AND WITHOUT TECHNOLOGICAL PROGRESS, i.e., )x - 0 /D CASE 3 IS AS CASE 1 BUT WITH TECHNOLOGICAL PROGRESS, i.e., x * 0. /e CASE 4 IS AS CASE 2 BUT WITH TECHNOLOCICAL PROGRESS, i.e., x . 0. IF . - SAVINCS RATIO (IN Z); THIS RATIO HAS BEEN CALCULATED BY REGRESSINC THE CHANCE OF NET WORTH IN REAL TERMS OF STEEL PRODUCING COMPANIES IN THE COUNTRIES CONSIDERED HERE TO THE STEEL OUTPUT OF THESE COMPANIES. n * GROWTH OF LABOR EMPLOYED (IN 1); IT HAS BEEN ASSUMED THAT THIS GROWTH RATE IS EQUAL TO THAT OF THE POPULATION OF THE COUNTRY IN QUESTION. WORLD BANK POPULATION FORECASTS HAVE BEEN USED; THE CROWTH RATES ARE THOSE OF THE 1985-90 PERIOD. m s CROWTH RATE OF RAW MATERIAL SUPPLY OTHER THAN THAT OF IRON ORE (IN Z); IT IS ASSUMED THAT THIS CROWTH RATE WILL BE EQUAL TO THAT OF CDP; WORLD 8ANK JANUARY 1986 FORECASTS HAVE BEEN USED; THE GROWTH RATES ARE THOSE OF THE 1985-90 PERIOD. - 21 - 17. Based on Case 1 of Table 3 the following points may be made: (i) the steady state consumption level of iron ore of the United States and the Republic of Korea are the highest; they are followed by the steady state values of Italy and France. The lowest steady state levels of consumption are those of the Federal Republic of Germany, Japan and India.l/ The only country, among the nine examined here, that has a steady state consumption level below that of the western world as a whole is that of the Federal Republic of Germany; and, (ii) the countries that have a steady state output/capital value higher than that of the western world are the Republic of Korea, Japan, Italy and India.2/ The countries that have the lowest output/capital value are the Federal Republic of Germany, the United States and France. 18. Equation (17) for the western world, based on the assumptions of Table 3, could take the form: * 0.024t p = pOe The paths of the iron ore/steel price ratio are presented in Figure 2. This price ratio is dependent on the initial price (po)--1983 has been used as the initial year--and the value of the steady state Z^ (which depends inter alia on the long-term growth rates of employment and the supplies of iron ore raw materials, n and m). By changing the assumptions about the long-term growth of 1/ The results regarding India have to be regarded with caution as the Durbin-Watson of the production function in Table 2 indicates the existence of serial correlation. 2/ See footnote 1/. - 22 - Figure 2: Price Paths Based on Different Values For Z' and d*: 1972-2000 (Iron Ore Price Deflated by Steel Price) Ratio 0.096 i P J-. JJ 0.056 (3 I~~~~~~P 0.036 1972 1992 2012 SOURCE: SEE TABLES 3 AND 4. - 23 - employment and other raw materials, different Z steady states and price paths p are derived. Four such paths are shown in Figure 2. The assumptions behind these four paths p , P(1)' p (2) and p(3) are presented in Table 4. As pointed out TABLE 4: ASSUMPTIONS FOR DIFFERENT PRICE PATHS PRICE PATH GROWTH RATES /A p P(l) P(2) P(3) n (Z) 2.0 -3.53 -3.53 0 m (Z) 3.4 3.40 -14.96 0 /A FOR DEFINITIONS OF n AND m SEE TABLE 3. in Section II, the steady state Z is a saddle point and only the solutions of equations (8) and (9) may lead to it. At any other point of Figure 1 policy should be induced to reach the steady state or the path of the solution of equations (8) and (9). As the solution of equations (8) and (9) is unknownl/ it cannot be asserted with absolute certainty that the actual iron ore/steel price or the actual steel output/capital ratio or the actual iron ore depletion rate is on the efficient path or not. The movement of the Z and d variables over time towards their steady state values or away from them may provide an indication as to whether steel producers are moving on their efficient path or whether some policy changes are needed.2/ 1/ The solution of these differential equations is difficult. 2/ As p, Z and d depend on "exogenous" long-term values of m and n, any policy conclusions depend as well on the values of these parameters. -24- IV. POLICY CONCLUSIONS 19. As expected, the depletion of iron ore, i.e., the ratio of iron ore consumption to world iron ore reserves is negatively related to iron ore prices (see Figure 3).1/ The growth rates of the iron ore consumption to reserves ratio for the nine countries examined in this study and the western world are presented in Table 5. Only Italy and the Republic of Korea showed positive average growth rates for the 1972-1983 period. Iron ore prices increased by an annual average rate of 5.4% during the same period. For the United States, France, United Kingdom and Brazil their consumption to reserves ratio declined on average far more than the western world as a whole. The western world's iron ore consumption to reserves ratio declined by an average of 3.4% during the 1972-1983 period. TABLE 5: GROWTH RATES FOR IRON ORE CONSUMPTION/RESERVES RATIO: 1972-83 COUNTRY (Z) WESTERN WORLD -3.40 UNITED STATES -7.77 JAPAN -1.38 GERMANY, F.R. -0.23 FRANCE -4.72 UNITED KINGDOM -4.71 ITALY 0.92 BRAZIL -3.88 INDIA -1.41 KOREA, R. OF 36.77 1/ The Rotterdam CIF price of Brazilian iron ore sinter shipment is used as the international iron ore price. - 25 - FIGURE 3: WORLD DEPLETION RATE (DSW) AND INTERNATIONAL IRON ORE PRICE (IOP) (DSWW) 0.004- 0.0039 0.0038 0.0037 0.0036 0.0035 0.0034 0.0033 0.0032 0.0031 0.003 0.0029 0.0028 0.0027 0.0026 0.0025 0.0024 0.0023 0.0022 0.0021 - 0.002- 1972 1975 1978 1981 (lOP) 29- 28 - 27 - 25- 25 - 24- 23 - 22 - 21- (L 20- 19 1 i8 17 16 1s 14 13 12 11 1972 1975 1978 1981 1984 YEARS SOURCE: WORLD BANK, ECONOMIC ANALYSIS AND PROJECTIONS DEPARTMENT - 26 - 20. Table 6 shows the relative importance of different factors of production in the steel production process. In nearly all countries the share of capital stock in the production process is small relative to the share of all other factors of production, with the exception of the share of iron ore. In the case of the Republic of Korea, the share of labor is smaller than that of capital. The country with the smallest share of capital in its production process is the United States followed by the Federal Republic of Germany, France and India. Japan, the Republic of Korea and Italy have larger shares of capital in their production process than the other countries. TABLE 6: RELATIVE IMPORTANCE OF FACTORS OF PRODUCTION IN THE STEEL PRODUCTION PROCESS: AN INTERNATIONAL COMPARISON (Z) FACTORS OF PRODUCTION U J D F G I B N K CAPITAL (K) 0.7 2.0 1.3 1.3 - 3.3 - 1.3 2.3 LABOR (L) 11.6 4.0 8.5 7.1 - 4.9 - 7.0 1.5 RAW MATERIALS (M) 1.4 7.5 3.8 5.0 - 5.5 - 5.1 9.9 IRON ORE (R) 0.6 0.8 0.7 0.8 - 0.5 - 0.9 0.5 /A COUNTRY CODES: WW INDUSTRIAL AND DEVELOPING COUNTRIES U UNITED STATES J JAPAN D GERMANY, F.R. F FRANCE G UNITED KINGDOM I ITALY B BRAZIL N INDIA K KOREA, R. OF SOURCE: SEE TABLE 1. - 27 - 21. Based on the analysis of Section II, countries with a small initial capital share relative to other factors of production should choose as high as possible initial steel output-to-capital ratio and as high as possible iron ore consumption-to-reserves share relative to their steady state values and aim at decreasing them over time in order to reach either their efficient path or their.steady state. The opposite should be true for countries with large initial capital shares. The results of Table 6 indicate that the United States, the Federal Republic of Germany, France and India should follow the first pattern in order to reach their steady state. The Republic of Korea should follow the second pattern. Japan and Italy are less clear cases and they could follow either pattern. 22. Figures 4 and 5 plot the historical path of steel output to capital ratio divided by the appropriate steady state and the historical path of iron ore consumption-to-reserves ratio divided by the appropriate steady state, respectively. 23. From these graphs, the following points are noteworthy:l/ (i) The United States started to operate "optimally" sometime after 1979 as far as the steel output-to-capital share (Z) is concerned, and sometime after 1975 as far as the iron ore consumption-to-reserves ratio (d) is concerned. In order to reach its steady state, the United States will have to continue decreasing its steel output-to-capital ratio and its iron ore consumption-to-reserves ratio; (ii) The Federal Republic of Germany did not operate "optimally" for the 1975- 81 period, as far as the steel output-to-capital share (Z) is concerned. Since 1981, its policies regarding Z have been "optimal". Germany's policies l/ The word "optimal" is used here to describe desirable behavior, consistent with the previously described expectations for reaching steady states. FIGURE 4: STEEL OUTPUT TO CAPITAL RATIO, SELECTED COUNTRIES GERMANY U.S.A. (DELATED BY 15 STEADY STATE VALUE_DEFLATED eV ITS STEADY STAIE VAE) 0.069 0.047 O.OU9 - 0.047 - 0.058-8 0.044- 0.057- 0.045-\ 0.046- 0.044 - 0.05- 0.043 - 0.054- 0.042- 0.053 - 0.041 - 0.052 -0.04 0 0.081 0.039 0.08 F 0.036 0.049- 0.0/37- 0.042- 0.036 - 0.047- 0.032-/ 0.048- 0.034 - 0.041 - 0.0133 0.04.4 -0.032 0.043 - 0.031 - 0.042 -0.03 0.041 0.029 0.04 - T 1972 1975 1978 1981 1972 1975 1971 1961 YEARS YEARS FRANCE JAPAN DEFLA.MD sy rrs SEAuy sTATE vAwE) (DEFLATED BY ITS STEADrY STATE VALUE) 0.026 .1 0.026 - ~~~~~~~~~~~~~~~~~~~~~~0.017 0.024- / ~~~~~~~~~~~~~~~~~~~~~0.018 0.022- 0.02- 0.018 0.014- 0 0 F- 0.016 F: 0.013- 0.014-001- 0.012 -~~~~~~~~~~~~~~~~~~~~~~~.1 0.011 0.01 0.01 0.008 0.006 0.000 0.004 - - 0.006 -l . I* 1972 1975 1976 1961 1972 1975 1767 1961 YEARS YEARS FIGURE 4 (CONTINUED): STEEL OUTPUT TO CAPITAL RATIO, SELECTED COUNTRIES ITALY KOREA (DELATED BY FM S1EADY STATE VALUE) _ _( AUt Of SI EADY UTAIE VMJE) 0.011 - _ _ _ _ .0_ _0 ,___-_-_-.-- - 0.014 0.013 0.002 0.012- 0.011 W GAN ~~~~~~~~~~~o.om __ __ 0.01 - O.000 - O.Ot~~~~~~~~~~~~~.0 - 0.008 - 0.007- 0.006 ~~~~~~~~~~~~~~~~~~~~~~~~0.004 0o.. 000 0~~~~~~~~~~~.0oo - s . 003 --r---_--r---- 0.003 0.002 -0.002- 0.001 1672 1171 1173 l"I 1372 177 173 ins '0 INDIA SOURACE W MB EIO I A START VALIET 0.011 - 0.013 0.017- 0.016 0.013 80.014- 0.013- 0.012- 0.011 0.01 1172 1375 1371 lilt SOURCE: WORLD BANK, ECONOMIC ANALYSIS AND PROJECTIONS DEPARTMENT FIGURE 5: IRON ORE CONSUMPTION TO WORLD RESERVES, SELECTED COUNTRIES GERMANY U.S.A. 0.0 62 - -0 .__ - _ _ _ _ _- _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 0.06 0.1 0.0C X 0.066- 0.06 0.064- 0.062- 0.06 0.06 007i 0.046~~~~~~~~~~~~~~~~~~~~~~~~~00 OA"4 0.06 0.044 0.042 -.oj 0.04~~~~~~~~~~~~~~~~~~~~~~~~~00 0.0m~~~~~~~~~~~~~~~~~~~~~~~~~~00 0.036.0 0.002 . .6 . . , . 0---. . . . . 1072 1675 1676 151 1672 1671 157 1461 w FRANCE JAPAN O .004 - - _ _ _ _ _ _ . 4 0.0042 0.042 0.004 0.041- 0.04- 0.0m 6 0.0036- 0.036 0.0034 -0 F- 0.037- 0.0032- 0.0m 6 0.003- 0.0m 6 0.0025 0.034- 0.0026 0.033- 0.0024 0.032- 0.0022 0.031 0.002 0.03 1672 1175 1176 61" 1672 1076 l56 66 FIGURE 5 (CONTINUED): IRON ORE CONSUMPTION TO WORLD RESERVES, SELECTED COUNTRIES ITALY KOREA 0.0014 - _ _ __0.0009 -_ _ __ _ _ __ 0.0006 0.0007- 0.0012 - 0.0000 0.0011 -000 0.001 0.0004- 0.0003- 0.00090 0.0002- 0.0006 -000 0.0007 - _ , , , , , , . , W , 0-,,,, 172 1976 176 1971 1972 1976 1971 1361 YEAS YFAMWA INDIA 0.00116 0.0011- 0.00106 0.001- 0.00066- 0. 0.0006 0.00076 0.00076 1972 1976 1978 1901 ECRS SOURCE: WORLD BANK, ECONOMIC ANALYSIS AND PROJECTIONS DEPARTMENT - 32 - regarding its iron ore consumption-to-reserves ratio have been "optimal" for the whole period with the exception of 1974 and 1980. Germany should continue to aim at decreasing Z and d; (iii) France was following "optimal" policies regarding Z up to 1978 (with the exception of 1974 and 1976). Since then (with the exception of 1982) policies regarding Z have tended to be opposite to those expected in order to reach the steady state or an "optimal" production path. France's policies regarding d have been "optimal" for the whole period under investigation. The 1974 and 1980 years were the only exceptional ones. France's policies should continue aiming at decreasing Z and d; (iv) India has been following policies that were not "optimal" as far as Z is concerned up to 1977 (with the exception of 1975). Since then Z has been declining as "optimal" policies would have demanded. India's policies regarding d seem to be less clear. The iron ore consumption-to-reserves ratio has been declining for the 1972-73, 1975-76, 1977-80 and 1981-82 periods. In order to reach its "optimal" steady state, India should aim at reducing Z and d; (v) The Republic of Korea is characterized by an increasing Z and an increasing d. The years for which this pattern is reversed are very few (1976, 1977, 1978 and 1982 for Z and 1982 and 1983 for d). This is the expected "optimal" path for Korean steel producers who will have to continue aiming at increasing Z and d until the steady state is reached; (vi) Japan's graphs seem to indicate that "optimal" policies are similar to those for the United States, the Federal Republic of Germany, France and India, i.e., declining Z and d. In 1973, 1974 and 1979 Z increased, and in 1973 and 1979 d increased. Japan may be on an "optimal" path tending to reach its steady state; and, (vii) Italy's steel industry is characterized by a constantly increasing Z and a decreasing d. As was earlier noted, Italy's policies may not be contrary to "optimal" behavior. - 33 - ANNEX I DATA BANK SOURCES Variable/ Name Description Period Unit Source YC Steel Revenues 1972-1983 Mill US$ WSD LC Labor Cost 1972-1983 Mill US$ WSD IC Interest and Depreciation Cost 1972-1983 Mill US$ WSD CC Iron Ore Consumption Cost 1972-1983 Mill US$ WB MC Other Raw Material Cost 1972-1983 Mill US$ WB PROFIT Profit/Loss Steel Industry 1972-1983 Mill US$ WSD Y Steel Production 1972-1983 Mill T WSD, IISI L Labor Employed 1972-1983 Thousand WSD ARI Capital Stock 1972-1983 Mill 1980 US$ WSD, WB C Iron Ore Consumption 1972-1984 Mill T(Fe cont) WB MR Other Material Cost 1972-1983 Mill 1980 US$ WB P80 Wholesale Price Index Steel 1972-1984 1980=100 WSD PMUV MUV Index 1972-1984 1980=100 WB PC Import Unit Value 1972-1984 $/T (Fe cont) WB PY Steel Deflator 1972-1983 $/T WB IOP Brazilian North Sea CIF Iron Ore Price 1972-1985 $/T WB RES Iron Ore Reserves 1972-1985 Mill T B. of M. L* Wage Rate Steel Industry 1972-1983 $/Year WSD JC Interest Rate 1972-1983 % IMF/IFS SOURCES: WSD - WORLD STEEL DYNAMICS; WB - WORLD BANK; IISI - INTERNATIONAL IRON AND STEEL INSTITUTE; B. OF M. - U.S. BUREAU OF MINES; IMF/IFS - INTERNATIONAL MONETARY FUND, INTERNATIONAL FINANCIAL STATISTICS. -34- ANNEX 2 NON-MONOTONIC EQUILIBRIUM PATHS 1. Dixit (1976) shows that removal of some of the restrictions of the Cobb-Douglas production function is possible. He shows that increasing the number of factors, as in this case, or endogenizing steel consumption increases the possibilities for non-monotonic paths. The resource use per capita can then fall, rise and fall again along an optimal path. 2. Ingham and Simmons (1975) have also shown that the elasticity of substitution can govern the possibility of sustaining growth in the long run. Using a two-factor production function with constant returns to scale (F (K, R) where K is capital stock and R resource use) and a maximization problem of an iso-elastic utility function (IF u(c) e ptdt where 0 c = steel consumption and p = interest rate in utility terms) proves that the equilibrium path of the depletion rate may be represented as: d = d + {f(k) - h} - a f(k) (2.1) d ~~k k where h = consumption of steel to capital stock ratio (= C/K) k = capital stock to iron ore consumption ratio (=K/R) f(k) = F(K, 1) a - elasticity of substitution between K and R 3. The growth pattern for h is shown to be: * h t f (k) -p } _ {f(k) - h} (2.2) - 35 - ANNEX 2 where p = interest rate in utility terms ("rate of impatience"). £ = elasticity of marginal utility, i.e., the relative rate at which undiscounted marginal utility falls as consumption per head increases. In the long-run h must ultimately equal to the following expression: h = {p - n . (l-E)}/£ (2.3) where n = lim f (k) = lim f(k) (2.4) k It is noteworthy that if a-S 1 then n = 0 while, if a > 1 then n > 0. The asymptotic value for d would then be: d = h + (a - 1) * n (2.5) and the following expressions can be derived k = n -h = C = (n - p)/e (2.6) k = a . n (2.7) R = -d (2.8) Expressions (2.3) to (2.8) indicate that as capital accumulates relative to resource flow (k) the resource flow must decline (see (2.5), (2.7) and (2.8). Ultimately, whether this will enable sustained growth of consumption (2.6) depends on whether n will exceed p. -36 - ANNEX 3 ESTIMATING THE ELASTICITY OF SUBSTITUTION BETNEEN IRON ORE AND OTHER FACTORS OF PRODUCTION 4. As noted in Section II, the elasticity of substitution between iron ore and capital (a) in a two-factor production technology governs the possibility of sustaining growth of iron ore consumption. It was found there that such growth may be sustained if the elasticity of substitution is greater than one and if the limit of the marginal product of capital is large enough to make the numerator of the rhs of equation (15) positive. Otherwise, and in particular if a < 1, the growth of iron ore consumption may not be sustained. 5. In the Cobb-Douglas production function the elasticity of substi- tution between inputs is constant and equal to one, which implies that optimal growth of iron ore consumption may not imply sustained growth over time. It is thus important to test the implied assumptions of the Cobb-Douglas production function, i.e., to find out whether or not the elasticity of substitution between iron ore and the other inputs in the steel production process is greater than one. 6. From the pure profit maximization problem of the CES production function of the form: Y = y{6 N-0 + (1 - 6) N-0}-v/P where Y = output N1, N2 = two inputs 1-a 0 o a a = elasticity of substitution v - returns to scale -37- ANNEX 3 we get the input marginal productivity conditions P1a V (L.~ PPV= -(3.1) ey = -p/v( Y )l+p Y-p+p/v = 31 -N = v (1-6) Y p/v Y Yl+ =~+/v (3.2) ON2 N2 y 32 where n1, n2 = input prices y = output price From any of these two equations the following equation is derived and used to estimate the elasticity of substitution between N1 and N2 and the returns to scale v. Y ~~~~N2 1 m 33 ln- N = constant + oln-T-- + p a(l- V ) lnY (3.3) The second term of the rhs part of the equation provides an estimate of (a) and the third term provides an estimate for v. If we also allow neutral technical progress to occur via changes in the parameters y, i.e., pxt y = y where X is some constant rate, equation (3.3) may be rewritten as follows: y 1 1 In- constant + X pa - t + pa (1- -) ln Y + aln - (3.4) N2 v v y Equation (3.4) allows for the estimation of X. Alternatively, equation (3.1) or (3.2) may be rewritten as follows: -38- ANNEX 3 n2N2 2 (- ~ +( ln y = ln v(l - 6) y - p(l- v) ln Y + (-a)ln- (3.5) yY o v v Y Estimates for a, v and X for the nine most important steel-producing countries and the world (excluding the Eastern European countries) are presented in Annex Table 3.1. Data are available for four different inputs (capital, labor, iron ore and other raw materials), therefore elasticities of substitution have been estimated between each of these inputs and all the other inputs as a whole. ANNEX TABLE 3.1: ELASTICITIES OF SUBSTITUTION BETWEEN INPUTS IN THE STEEL PRODUCTION PROCESS /A/B PARAMETERS WW U J D F c I B N K 1. IRON ORE AND ALL OTHER INPUTS METHOD 1 /C s 0.48 0.31 0.06 0.076 p *** 1.08 *** 2.23 *** *** *** 15.67 *** 12.160 v *** 0.59 0.75 *** *** *** 1.15 *** 0.790 R2 0.19 0.54 0.02 0.71 0.04 0.04 0.13 0.54 0.73 0.600 DW 1.53 1.56 1.70 1.69 2.05 3.00 1.69 2.36 3.00 2.610 METHOD 2 /C s *** 0.42* *** 0.33 *** 0.19* 0.16* 0.31* *** 0.082* p *** 1.38* *** 2.03 *** 8.09* 5.25* 2.23* *** 11.200 v *** 0.67* *** 0.76 *** 0.71* 0.73* 1.46* *** 0.690* g *** 0.009* *** 0.001* * -0.013* 0.01* 0.27* *** 0.040* R2 0.16 0.49 0.13 0.68 0.16 0.03 0.13 0.60 0.74 0.570 DW 1.19 1.46 1.69 1.78 2.00 2.52 2.26 2.62 3.16 2.830 METHOD 3 /C s 0.43* 0.34 0.11 0.16 0.31* *** 0.08 R2 0.76 0.08 0.89 0.87 0.73 0.93 0.65 0.34 0.96 0.87 DW 1.19 1.46 1.69 1.78 2.00 2.52 2.26 2.62 3.16 2.83 *. . Il PARAMETERS WW U J D F C I B N K 2. LABOR AND ALL OTHER INPUTS METHOD 1 /C s 0.65* 0.87 0.39 0.40 1.21 1.40 *** 0.01* 0.90 0.13* p 0.53* 0.16 1.59 1.53 -0.17 -0.29 *** 90.03* 0.11 6.81* v 0.75* 4.47* 12.78 28.59 0.29 0.81* *** 1.05* *** 2.01* R2 0.08 0.38 0.79 0.80 0.54 0.94 0.49 0.14 0.89 0.95 DW 1.72 2.13 1.20 1.66 1.41 2.35 1.56 1.39 1.88 1.62 METHOD 2 /C s 0.68 0.82 *** 0.26 0.60* 1.19 *** *** 0.98 0.12* p 0.47 0.22 *** 2.85 0.07* -0.16 *** * 0.02 7.33* v 4.57 *** *** 9.77 *** *** *** *** *** 2.02 g 0.24 *** *** 0.09 *** *** *** *** *** -0.003 R2 0.53 0.60 0.93 0.87 0.58 0.96 0.66 0.79 0.89 0.94 DW 1.38 1.21 0.67 2.66 0.81 2.58 1.30 3.18 2.09 1.60 3. CAPITAL STOCK AND ALL OTHER INPUTS METHOD 1 /C s 5.20* 0.27* 1.41 0.61 0.94 1.61 0.84* 0.43 0.75 p -0.81* 2.76* -0.29 0.64 0.06 *** -0.38 0.19 1.31 0.34 v 4.17* 1.44 0.28 2.40* *** *** *** *** 3.90 R2 0.72 0.00 0.74 0.14 0.80 0.10 0.78 0.85 0.50 0.88 DW 1.60 1.33 1.01 0.22 1.35 0.84 1.56 0.34 1.43 0.88 PARAMETERS WW U J D F C I B N K METHOD 2A /C s 0.64 0.03* 1.07 0.33 0.86 0.99 0.01 0.53 0.65 p 0.56 32.33* -0.07 2.03 0.16 0.11 99.00 *** 0.89 0.54 v *** 11.02* 0.10 3.09 *-* *** 5.69* ** 2.53* 1.67* g 0.009* 0.59* -0.09* 0.03 0.08* -0.11* 0.30* -^* 0.02* -0.13* R2 0.74 0.85 0.76 0.88 0.80 0.22 0.89 0.92 0.100 0.81 DW 1.42 1.73 1.21 2.29 1.88 0.65 1.94 2.54 0.56 1.01 METHOD 2b /C s 0.97 0.23 0.89 0.54 0.80 0.61 0.83 0.59 0.32 0.72 a p 0.03 3.35 0.12 0.85 0.25 0.64 0.21 0.70 2.13 0.39 . v 2.04 0.26* *** 0.96 *** 3.97 *** g *** *** *** -0.04 -0.05 0.02 *** 0.21 *** R2 0.99 0.91 0.95 0.93 0.96 0.46 0.90 0.98 0.78 0.95 DW 1.41 1.56 1.10 1.31 1.57 1.51 2.17 1.02 1.23 1.18 4. "OTHER MATERIALS" AND ALL OTHER INPUTS (i.e., CAPITAL STOCK, LABOR AND IRON ORE) METHOD 1 /C s 1.90 1.22 0.94 1.29 0.91 1.04 *** 1.25 1.23 0.98 p -0.47 -0.18 0.06 -0.22 0.10 -0.04 *** -0.20 -0.19 0.02 v 0.74 0.32 0.59* 1.51 *i- 0.07 *** 2.04* *** ** R2 0.90 0.82 0.89 0.96 0.77 0.93 0.00 0.65 0.98 0.81 DW 1.42 1.08 1.31 1.86 1.01 1.36 0.55 1.82 2.28 2.51 ;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~... * . . PARAMETERS WW U J D F C I B N K METHOD 2 /C s 1.30 1.30 1.04 1.26 0.60 1.20 0.77 1.62 1.32 0.73 p -0.23 -0.23 -0.04 -0.21 0.49 -0.17 0.30 -0.38 -0.24 0.37 v 0.82* 0.68 0.44* 2.50 *** 0.93* 0.53 *-k* *** *** g 0.05* 0.06 -0.p6* 0.04 0.05* 0.11 R2 0.96 0.94 0.88 0.98 0.87 0.92 0.85 0.70 0.99 0.83 DW 1.67 1.87 1.05 3.16 1.88 1.94 2.07 2.28 2.69 1.74 /A COUNTRY CODES: WW INDUSTRIAL AND DEVELOPING COUNTRIES U UNITED STATES J JAPAN D GERMANY, F.R. F FRANCE G UNITED KINGDOM I ITALY B BRAZIL N INDIA K KOREA, R. OF lB * T TEST INSIGNIFICANT. *** WRONG SIGN. /C THE PARAMETERS OF METHOD 1 ARE DERIVED FROM EQUATION (3.4) BUT WITHOUT THE TREND VARIABLE. THE PARAMETERS OF METHOD 2 ARE DERIVED FROM EQUATION (3.4). THE PARAMETERS OF METHOD 3 ARE DERIVED FROM EQUATION (3.5). TWO DIFFERENT SOURCES FOR CAPITAL HAVE BEEN USED TO ESTIMATE THE "ELASTICITY" OF SUBSTITUTION OF CAPITAL AND ALL OTHER INPUTS. METHODS 1 AND 2a USE EQUATION (3.4) AND CAPITAL DATA THAT RELATE TO REAL ASSETS. METHOD 2b USES EQUATION (3.4) AND CAPITAL DATA THAT RELATE REAL NET WORTH OF STEEL COMPANIES IN THE COUNTRIES UNDER CONSIDERATION. ALL EQUATIONS HAVE BEEN RUN FOR THE 1972-1983 PERIOD. SOURCE: WORLD BANK, ECONOMIC ANALYSIS AND PROJECTIONS DEPARTMENT. -43- ANNEX 3 7. The empirical results presented in Annex Table 3.1 indicate the following: (i) The elasticity of substitution of iron ore is less than one whenever the coefficients of the estimated equations are statistically significant. In the majority of cases, the elasticity of substitution of iron ore is not statistically significant. It is significant and less than one for the United States, the Federal Republic of Germany, Brazil and the Republic of Korea. For these countries, their optimal steady state will be reached by increasing consumption of iron ore at a decreasing rate. During the 1972-83 period, substitution between iron ore and other raw materials, labor and capital was not significant for all the other countries; (ii) In three of the four cases when the elasticity of substitution of iron ore was significant, returns to scale were found to be decreasing (v < 1). This is a surprising result given the results of Section III-B. The technological progress parameter X was statistically insignificant in almost all cases; (iii) The elasticity of substitution between labor and all other inputs was found to be less than one in most cases (with the exception of France and the United Kingdom). For several countries, the statistics R2 and DW lent no credence to the estimates; (iv) The elasticity of substitution between capital stock and all other inputs is also estimated to be less than one (in all cases but that of Japan and India) independently of the data basis of the capital stock. (v) The elasticity of substitution between other materials and all other inputs was greater than one in all cases but France and the Republic of Korea. 8. To summarize, using a CES production function approach, the elasticity of substitution between iron ore and otherinputs in the steel production process was found to be either insignificant statistically or, if significant, less than one. Data were not available for all countries prior to -44- ANNEX 3 1972. Although the results presented here (i.e., for some countries the elasticity of substitution is less than one) do not alter the results of the previous analysis, much important and useful empirical work remains to be done when longer historical data series become available. Such empirical work could, for example, trace the possible non-monotonic equilibrium path of iron ore consumption and prices.l/ 1/ See Annex 2 for a brief discussion of the possible removal of some restrictions of the Cobb-Douglas production function. - 45 - REPERRNCES Dasgupta, P.S. and G.M. Heal, (1974) "The Optimal Depletion of Exhaustible Resources", Review of Economic Studies 41, Symposium, 3-28. Dixit, A.K., (1976), The Theory of Equilibrium Growth, Oxford University Press, London. Ingham, A. and P. Simmons, (1975), "Natural Resources and Growing Population" Review of Economic Studies 42, 101-206. International Iron and Steel Institute, (1985), Steel Statistical Yearbook, Committee on Statistics, Brussels. 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