DWC-8711 Substitutability of Metals in U.S. Industry Theophilos Priovolos and Tamar Dunietz Division Working Paper No. 1987-1 1 November 1987 International Commodity Markets Division International Economics Department The World Bank Division Working Papers report on work in progress and are circulated to stimulate discussion and comment. SUBSTITUTABILITY OF METALS IN US INDUSTRY Theophilos Priovolos and Tamar Dunietz November 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 con- clusions 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. - ii - TABLE OF CONTENTS Page SUM MARY ................................................................ iv I. INTRODUCTION ................................................... 1 II.' THE TRANSLOG APPROACH . ........ ..................... 3 III. DATA AND SPECIFICATION . ............................... 8 IV. EMPIRICAL RESULTS ............................................. 16 A. Factor Shares .............................................. 16 B. Elasticities of Factor Demand and Substitution ............. 18 C. Factor Efficiency Bias ................ 34 ANNEX 1: STANDARD INDUSTRIAL CLASSIFICATION (SIC) .. 37 ANNEX 2: FACTOR EXPENDITURE SHARES IN TOTAL EXPENDITURES IN SELECTED US INDUSTRIAL SECTORS (1964 AND 1983) ........... 38 ANNEX 3: ALLEN ELASTICITIES OF SUBSTITUTION CORRESPONDING TO ELASTICITIES OF DEMAND OF TABLE 9 ........................ 39 ANNEX 4: ALTERNATIVE METHOD I ..................................... 41 ANNEX 5: ALTERNATIVE METHOD II .. 45 REFERENCES .......................................................... 49 - iii - LIST OF TABLES Page TABLE 1: US BUREAU OF MINES SIC CLASSIFICATION ..................... 11 TABLE 2: INDUSTRY CLASSIFICATION BY METAL .......................... 12 TABLE 3: SIC CODES USED IN CLASSIFYING DEMAND FOR METALS BY INDUSTRIAL SECTOR .. 13 TABLE 4: FACTOR EXPENDITURE SHARES FOR SELECTED US INDUSTRIAL SECTORS, AVERAGE 1964-83 .. 17 TABLE 5: METAL EXPENDITURE SHARES FOR SELECTED US INDUSTRIAL SECTORS, AVERAGE 1964-83 .. 17 TABLE 6: CHANCES IN METAL EXPENDITURE SHARES IN SELECTED US INDUSTRIAL SECTORS .. 19 TABLE 7: DEMAND ELASTICITIES FOR LABOR, CAPITAL, ENERGY AND METALS IN FIVE US INDUSTRIAL SECTORS . . 21 TABLE 8: ALLEN ELASTICITIES OF SUBSTITUTION OF LABOR, CAPITAL, ENERGY AND METALS IN FIVE US INDUSTRIES . . 23 TABLE 9: DEMAND ELASTICITIES FOR ALUMINUM, COPPER, NICKEL, STEEL, TIN, ZINC AND LEAD IN FIVE US INDUSTRIES . . 25 TABLE 10: SUBSTITUTABILITY AND COMPLEMENTARITY AMONG INPUTS IN FIVE US INDUSTRIAL SECTORS .. 27 TABLE 11: MEASUREMENTS OF TECHNOLOGICAL BIAS IN US INDUSTRY ......... 35 - iv - SUMMARY * The study has analyzed the substitutability and technological bias of inputs in the production process of five metal-intensive US industries, namely chemicals, fabricated metals, cans and containers, machinery, electrical equipment and transportation equipment by estimating their cost functions with the use of appropriately constrained translog cost functions and the assumption of separability between factors. Prior comments on substitutability and the impact of technical change in this area have lacked quantitative support as to the sign and magnitude of own and cross elasticities of demand and substitution among the factors we have identified-- labor, capital, energy and aluminum, copper, nickel, tin, zinc, lead and steel. The analysis is based on expenditure data for each of these inputs which was assembled after developing a concordance for industry metal use at the two-digit SIC level. The results of the analysis have corroborated only partly the conventional wisdom. The study has corroborated, for example, conventional understanding of the relationships between labor, capital, energy and metals in general. Labor is seen to be a substitute for capital, energy and metals (except in the chemicals sector) while capital is a complement of energy (except in the chemicals and electrical equipment sectors) and a substitute *x This paper has greatly benefitted from discussions and suggestions from R. Duncan who read, edited and commented on earlier drafts. We acknowledge the intellectual support and comments of B.J. Choe, M. Imran and F. Najmabadi; we also acknowledge with many thanks J. Raulin who proofread and typed the manuscript. for metals in general (except in transportation). Energy and metals in general were found to be complements (except in fabricated metals and machinery). The results indicate that the demand for different metals reacts in a non-uniform way to changes in metal prices and the prices of other inputs. In the fabricated metals, cans and containers sector the use of aluminum is found to be complementary to that of steel, tin and copper--contradicting our expectation of substitutability. The fact that aluminum prices have risen faster than prices of other metals in the period since 1964, and the technical changes favoring use of aluminum, gave rise to the increase in aluminum's expenditure share and to the appearance that aluminum was substituting for other metals. In the machinery, electrical equipment and transportation sectors the substitution of copper with aluminum is corroborated. In the transportation sector and the machinery sector the finding is that steel has not been substituted by aluminum. This finding, though not surprising, is in disagreement with the often-stated view that the sharp growth in aluminum use has reflected increased substitution for steel. Lastly, all industries (except chemicals) exhibit factor-using bias towards aluminum and factor-saving bias towards all other metals. Furthermore, all industries exhibit labor-saving bias and capital-using bias. The results presented here should be seen in the light of the empirical problems described herein. The assembly of the sector-specific metal consumption data involved arbitrary judgements which should not be ignored. The fact that not all constraints were satisfied, in particular that of positive own-elasticities, should also qualify the validity of our results. Perhaps the results could be improved by introducing lags (dynamics) - vi - and additional inputs such as plastics. They could also be improved by disaggregating where possible to the three or four digit SIC level, or validated by extending the analysis to other industrial countries, or extended by considering separately domestic and foreign-produced factors of production. I. INTRODUCTION In the 1980s production capacity did not adjust quickly enough to the slowdown of demand, causing prices of minerals and metals to decline ,sharply. Although the slowdown in the demand for minerals and metals can be partly attributed to the slower growth of output, there is evidence that factors other than the income/output factors adversely affected the demand for minerals and metals in the 1980s. 1/ This study aims at providing some insight to these other factors affecting the demand for minerals and metals by analyzing the substitutability and complementarity among inputs in the production processes of metal-intensive industries. In particular, the analysis focuses on the responsiveness of the demand for minerals and metals to input prices in five US industrial sectors. Within the industrial sector these five use the highest percentage of minerals and metals in their production processes. They are: (1) chemical, (2) fabricated metals, cans and containers, (3) machinery, (4) electrical equipment and (5) transportation. The translog cost approach is used to estimate the elasticities of substitution and the elasticities of demand for ten inputs namely: labor, energy, capital, aluminum, copper, nickel, tin, zinc, lead, and steel. The econometric analysis uses time series 1/ The subject of structural changes in the US demand for minerals and metals has been studied by many analysts. See, for example, The World Bank, "Market Prospects of Raw Materials", Development Committee Paper, 1987, Washington, D.C; International Iron and Steel Institute (IISI) Energy and the Steel Industry, 1982, IISI, Steel Demand Forecasting, 1983, IISI, Steel and the Automotive Sector, 1983, Brussels; Tilton, J. ed., Material Substitution, Lessons from Tin-Using Industries, 1983, Resources for the Future, Washington, D.C. or Tilton, J., "Atrophy in Metal Demand," Earth and Mineral Sciences, 1985 The Pennsylvania State University Park. The evidence assembled by these studies allows limited conclusions to be drawn. - 2 - for the 1964-83 period. The cross-elasticities quantify the responsiveness of the demand for minerals and metals to changes in prices of other inputs in production. The sign of the elasticities indicates substitutability or complementarity among the inputs. The translog cost approach makes possible the evaluation of technological bias in terms of whether it leads to the greater use or saving of the different metals. Section II describes the translog approach. The data and the specification of the model are discussed in Section III. The empirical results are presented in Section IV. - 3 - II. THE TRANSLOC APPROACH The development of the translog function by Christensen, Jorgenson and Lau (1973) initiated the possibility of using flexible functional forms with respect to estimating the elasticities of substitution among factor inputs. Christensen, et al and later Berndt and Wood (1975) and others assumed a homogenous of the first degree translog cost function to derive the demand for factor shares under long-run cost minimization assumptions. The translog cost function is assumed to take the form: n n n In C In a0 + aln i i+ II y 'ij ln Pi ln P n + I Yit ln Pit + y tt + 6t2 (1) subject to: Y = yji for all i.and j, i t j (2) n I a. = 1 (3) i=11 n I y . = 0 for all i (4) j=l I where equation (2) is defined as the symmetry condition and equations (3) and (4) are the conditions for establishing homogeneity of the first degree and C is the cost of production when the cost-minimizing input combination is used; - 4 - Pi, Pj are prices of inputs i, j = 1, ..., n; and t is time Shephard's Lemma and cost-minimization assumptions imply that the optimal expenditures on input i (Yd) relative to total expenditure are given by: Si nc = - 1 = i + ln P + Iitt for i=l.. n (5) where S- is the expenditure share of input i. The system in equation (5) has been used in most empirical studies employing the translog specification. Berndt-Wood show that the Allen Elasticity of Substitution (AES) is given by: y.+S. S. - 1*] + 1 j for i * j (6) a1J S. S. I J y.. + S. - S. a = 11 1 1(7 Yii- (7) S2 1. Similarly, the price elasticities of demand (E ij) for factor inputs follow directly from the AES and cost shares Eij = Sj aij (8) As can be seen from equations (6) and (7), AES are not constant. The translog cost function is not necessarily a concave function for the whole range of positive factor shares. The range of concavity depends on the parameters Yii. In other words, concavity (or economical range) implies that - 5 - the own-price elasticities (Eii) must be negative. According to equation (8) it implies that aii <0. By using this condition and equation (7) it is implied that yii <0.25. Any empirical study resulting in yii >0.25 implies a non-concave translog cost function. The parameter yii can also be used to determine the maximum range of Si. If the actual Si is not within that range, concavity may not be expected. From (5) changes in the factor share due to factor efficiency bias can thus be expressed in terms of time as: as. at= Yit (holding all P constant) atit In this paper separability is assumed with respect to metals as a factor in a translog cost function. On this basis we derive estimating equations to measure efficiency bias for seven major metals--namely steel, aluminum, copper, nickel, lead, zinc and tin. So if n, i.e., the separable factor, is further decomposed and if Pn is further decomposed to: In Pn = Vo + I Vr lnbr + ½X X Vrk lnbr lnbk + I Vrt lnbrt (9) r r k r where br, bk are the rth and kth metal prices and r, k = 1..., m. Based on (5) 3lnC 3lnC aIG = s and aln alnP n alnb r n r where Sn is the share of the separable factor and Sr is the share of the rth component of the separable factor in total expenditure. - 6 - If separability exists, the share of the rth metal input in the total metal share can be expressed as follows: s alnP r = S = aln b + V t (10) S rn alnb r rk k rt n r k This is derived from the general case by using the Chain rule. 1/ The elasticities of substitution, a , and factor demand, Erk, for rkrk any rth metal input are calculated from the cost function as follows: ark = + YnnSn + Vrk /sk S for Yr, k: r * k (11) a = 1 - i/S + y /S 2 + v /S s for Yr (12) rr r nn n rr r rn E = S + 1/S y S S + V /S for Yr, k: r * k (13) rk k r nn kn rn rk rn E = S- I + 1/S y S2 + V /S for Yr (14) rr r r nn rn rr rn For a proof of equations (11) to (14) see Duncan and Binswanger. The estimated coefficient of Vrt in (9) is one measure of the constant rate of factor efficiency bias of the individual metal source. For example, if Vrt is positive the share of factor r would rise at constant factor prices (factor r- using). A measure of bias that takes into account both the changes in the 1/ See Duncan and Binswanger (1976) for a derivation of this equation and an analysis of separability in the energy sector. - 7 - share of metals and the changes in the share of each metal has been found by Duncan and Binswanger to be equal to: as r= y S + V S (15) at nt rn rt n Clearly, the estimation of (15) requires the estimation of coefficients of both models, i.e. the full cost function model and the metal sub-model. In the fourth section of this paper the estimates of elasticities of substitution, elasticities of demand and technological bias for the full model and the sub-model are presented. - 8 - III. DATA AND SPECIFICATION The analysis is based on US data for the 1964-83 period. Due to lack of disaggregated data, the analysis was limited to the two-digit SIC level. Fi-ve' industrial sectors were selected: chemicals (SIC 28), fabricated metals, cans and containers (SIC 34), machinery (SIC 35), electricity (SIC 36) and transportation (SIC 37). Together, these sectors consume 83% to 95% of total industrial demand for major metals: aluminum (83%), copper (95%), nickel (84%), steel (86%), tin (95%), zinc (86%) and lead (87%). The main source for data, in particular for value added, wage rates and payroll expenditures data was the US Department of Commerce, Annual Survey of Manufactures: Statistics for Industry Groups and Industries. Energy expenditures in nominal terms were calculated on the basis of data provided by the US Department of Commerce, Annual Survey of Manufactures: Fuels and Electric Energy Consumed. Energy-related price deflators by industrial sector' were drawn from data supplied by Wharton Econometrics Forecasting Associates (WEFA). Capital stock data in nominal terms were estimated by subtracting payroll expenditures from value added. Estimates of capital stock in real terms were taken from WEFA data. Capital stock deflators were derived from these two sets of data. Two other approaches for the estimation of capital stock were also used. The first approach uses data on net investment from the Annual Survey of Manufactures: Statistics for Industry Groups and Industries. On the basis of assumptions regarding depreciation rates and initial values of capital stock (equal to those estimated by subtracting payroll expenses from value added), capital stock in nominal terms was estimated. With a similar procedure and investment price deflators supplied - 9 - by WEFA, capital stock in real terms and capital stock price deflators were estimated. For convenience purposes, we name the capital stock data and the translog cost estimates derived from these data "Alternative Method I". The second approach uses capital stock- data in current terms as calculated in "Alternative Method I" and capital stock data in real terms from WEFA files as in the base run scenario. The derived capital stock price deflators and the translog cost estimates derived from these data are denoted under "Alternative Method II". The translog cost function parameter estimates for Alternative Methods I and II are presented in the Annex (see Annexes 4 and 5). The estimates of expenditures on metals were based on volume and price data from the publication by the US Bureau of Mines, Mineral Facts and Problems. Within a given industry not all metals received the same classification. Moreover, two-digit SIC level subgroups were not always available. Where possible, we aggregated three and four-digit SIC subgroups under a particular two-digit code. For example, codes 343, 344 (classified under construction by the US Bureau of Mines) and 348 (classified under ordinance by the US Bureau of Mines) were aggregated and reclassified under the two-digit SIC industry level of Fabricated Metals (34). In other cases, we have disaggregated or reclassified two or more sets of two-digit level industries into their respective subsectors or into a new sector. For example, in the case of aluminum, the US Bureau of Mines classifies 34 and 36 under "electricity". We classified these two sectors under SIC 36, as we are unable to subtract the SIC 34 part from the total due to lack of data. As a results, we overestimate SIC 36. - 10 - Table I shows the first step in the classification process. In view of the problems identified in the previous paragraph and in view of the fact that construction cannot be considered as part of fabricated metals and containers, we decided to omit "construction" from this analysis (see Tables 2 and 3). Most of the metal prices used in this study are published by the US Bureau of Mines. Most of these prices are producer prices. However, the steel price is a weighted index of steel bars, shapes, plates, wire, rails, black pipe, hot and cold rolled sheets and strip. The weights are the shares of output of each product to total tonnage in crude steel equivalent terms. The tin price is the New York market price for the 1963-75 period and the composite price thereafter. Lastly, the zinc price is the Western price up to 1981 and the US high grade price thereafter. The metal price deflator was calculated as a weighted index of the seven metal prices (aluminum, nickel, copper, steel, lead, zinc and tin). The weights are the shares of individual metal expenditures in total metal expenditures. The expenditure shares were calculated by multiplying the above price and quantity series (whenever expenditures were not available). (Expenditure shares are theoretically correct for estimating the translog cost function but not the translog production function). 1/ 1/ See Duncan and Binswanger. TABLE 1: US BUREAU OF HINES SIC CLASSIFICATION O(E D4N1RY NAME AUINIIJ4M O2P1R NICtEL STDL TIN ZN LD (1964-72) (1973-83) (1964-72) (1973-63) (1964-72) (1973-63) (1964-72) (1973-83) (1964-72) (1973-83) (1964-72) (1973-63) (1964-72) (1973-83) CO aW[RUCTION 344,379, 344 344 344 344 344 344 15,16, 343 343 343,344 343,344 344 344,15, 245 344 3693 CO CAI GE & O INES 341,349, 341 341 3411 3411 335 CP CANS & PA.KALES 341,349 AP APLNCS & ETR 25,33,35 363 342,363 36 d) aO&iiR ItJWABIUS 25,33,34, 35,36 HA MAQIHRY 35 35 35 35 35 35 35 35,361, 35 35 35 35 362 IR TRAfl PRTATIG 37 37 37 37 37 37 37 37 37 37 37 37 3691,37 3691,371, 37 EL ELE3RICAL 3441,36 34,36 36 36 362 362 36 36 363 363 3356,3357, 3356,3357 3691 3691 CH CHEMICAL 281 281 28 28 2821 2821 281,3861 281,3861 OJUIE CHtICAIS 28,32 CR CRINAN&E 348 348 AHtNTU0N 348 3482 FE PIETR0LEtI 2911 2911 GASOLI1f AMDITIVES 2911 2911 CP FABRICATED MLTAIS 34 34 HA HIOXiB3D APYLIANCES 363 363 OG OIL & GS 13,461 13,461 IN111IES 492 492 PA PAINTh 2851 2851 2851 RB RIJBBER FRW 1S 30 30 RF RERACItRUES 3297 3297 AB ABRASIVES 3291 3291 S)UAS: IUE tS BEREAI) OF MINES AND 1E IWI BAMK. TARTF.-2-: INDUSTRY CLASSIFICATION BY METAL A/ ------------------------------------------------------------------------__---__--------- CHEMICALS FABRICATED METALS MACHINERY ELECTRICITY TRANSPORTATION (28) (34) (35) (36) (37) ALUMINUM CP MA EL TR cc COPPER OR MA EL TR NICKEL CH CP MA EL TR HA STEEL CC MA AP TR TIN CH CC MA EL TR ZINC MA EL TR LEAD CH OR EL TR PA A/ SEE TABLE 1 FOR CODES. TARLF 3: SIC CODES USED IN CLASSIFYING DEMAND FOR METALS BY INDUSTRIAL SECTOR A/ -------------------------------------------------------------------__--------__------------------------------------------------------------ CHEMICALS FABRICATED METALS MACHINERY ELECTRICITY TRANSPORTATION (1964-72) (1973-83) (1964-72) (1973-83) (1964-72) (1973-83) (1964-72) (1973-83) (1964-72) (1973-83) ---------------------------------------------------------__------------------__--------------------------------------------------------__-- ALUMINUM 341,349 341,349 35 35 3441,36 34,36 37 37 335 COPPER 348 348 35 35 36 36 37 37 NICKEL 28 28 34 34 35 35 362 362 37 37 363 363 TIN 2821 2821 3411 3411 35 35 36 36 37 37 ZINC 35 35 363 363 37 37 LEAD 2851 28,32 348 3482 3356,3357 3356,3357 3691,37 3691,371 3691 3691 37 STEEL 341 341 35 35,361 363 342,363 37 37 362 A/ DERIVED FROM TABLES 1 AND 2. - 14 - Before turning to the discussion of the empirical results, it is worth noting that translog cost functions are homogeneous of degree one in prices. With separability the constraints (2) to (4) are written as follows: Vrk = Vk for all r and k, r * k (16) I V = 1 (17) r X Vrk = ° Vr 0 (18) r k The equation (16) is the symmetry constraint and the equations (17) and (18) are the homogeneity constraints. 1/ Imposition of the symmetry condition in a simultaneously estimated system means that one share equation of the set of four share equations of the full cost function model (labor, energy, capital and metals) and one share equation of the set of seven share equations of the metal sub-models (aluminum, copper, nickel, steel, lead, zinc and tin) should be dropped. The "energy" share equation was dropped from the first system of equations and the "lead" share equation was dropped from the second set of equations. 2/ The 1/ The symmetry condition was tested with the help of the likelihood ratio for the case that assumed metals were not separable. The x2 test rejected the hypothesis most of the time, most likely due to the heterogenous sources of data. 2/ For the set of equations of the machinery sector the zinc share equation was dropped. - 15 - complete model was estimated using a constrained maximum likelihood package 1/ and with homogeneity and symmetry constraints imposed. Maximum likelihood estimators are invariant to the choice of which equation to drop. To be judged as well-behaved, the translog cost function must satisfy monotonicity and concavity conditions. 2/ The monotonicity was satisfied as all fitted cost shares were positive at each observation. Concavity was satisfied in most cases so that the estimated functions can be judged as providing a good representation of relevant production possibilities. 3/ The fact that concavity was not always satisfied negatively qualifies some of the results which are presented in the next section. 1/ The TSP package of the University of Harvard. 2/ See Pollak and Wales (1969). 3/ See also next section. - 16 - IV. EMPIRICAL RESULTS A. Factor Shares Table 4 shows the expenditure shares of ten inputs for the five US industrial sectors selected. On the average, over the -sample period, labor accounted for close to one-third of all expenditures in all industrial sectors except chemicals. Capital expenditure accounted for between 49% and 57% in all sectors except chemicals (77%). The share of energy expenditures ranged between 2 and 3% in all sectors except chemicals. The chemicals sector had the highest energy expenditure share (9%) and the lowest minerals and metals expenditure share (0.4%). 1/ The minerals and metals share of the other four sectors (i.e., fabricated metals, machinery, electricity and transportation sectors) ranged between 9% for the fabricated metals sector and 18% for the transportation sector. Aluminum expenditure was particularly important in the fabricated metals, cans and containers sector, accounting for some 24% of total expenditures on minerals and metals (see Table 5). Copper was important in the electricity sector, accounting for 38% of total minerals and metals expenditures. Nickel expenditure was only important in the chemical sector and in this sector it was much more important than other metals. Tin and lead expenditures were only important in the chemical sector. Steel has been the most important metal cost element in all industrial sectors except chemicals. 1/ Energy expenditure might be underestimated as self-generated energy is not included. - 17 - TABLE 4: FACTOR EXPENDITURE SHARES FOR SELECTED US INDUSTRIAL SECTORS, AVERAGE 1964-1983 (in %) INDUSTRY FABRICATED FACTOR CHEMICALS METALS MACHINERY ELECTRICITY TRANSPORT. LABOR 14 35 31 31 31 ENERGY 9 3 2 2 2 CAPITAL 77 53 54 57 49 METALS 0.4 9 13 11 18 ALUMINUM 2 1 1 1 COPPER - 0.3 1 4 0.5 NICKEL 0.2 0.2 0.1 0.4 0.4 STEEL - 6 11 4 15 TIN 0.1 0.5 - 0.2 0.1 ZINC - 0.0 0.1 0.2 0.3 LEAD 0.1 0.1 - 0.1 0.6 TOTAL/A 100 100 100 100 100 /A MAY NOT ADD UP TO 100 DUE TO ROUNDING ERROR SOURCE: THE WORLD BANK, INTERNATIONAL ECONOMICS DEPARTMENT. TABLE 5: METAL EXPENDITURE SHARES FOR SELECTED US INDUSTRIAL SECTORS, AVERAGE, 1964-83 (in %) INDUSTRY FABRICATED METAL CHEMICALS METALS MACHINERY ELECTRICITY TRANSPORT. ALUMINUM 0 24 4 12 8 COPPER 0 3 5 38 3 NICKEL 55 3 1 4 2 STEEL 0 63 88 41 82 TIN 19 5 1 2 1 ZINC 0 0 1 2 2 LEAD 26 1 0 1 3 TOTAL /A 100 100 100 100 100 A/ MAY NOT ADD UP TO .100 DUE TO ROUNDING ERROR SOURCE: THE WORLD BANK, INTERNATIONAL ECONOMICS DEPARTMENT. - 18 - Steel expenditure shares in these industries ranged between 41% in the electricity sector and 88% in the machinery sector. Expenditures on zinc have been small in all sectors. A. comparison of me-tal expenditure shares in 1964 and 1983- (Table 6) shows that the share of steel has declined sharply in the fabricated metals, cans and containers sector (from 75% to 50%) during that period, while it has remained unchanged in the transportation sector and increased in the machinery and electricity sectors. 1/ The aluminum share has increased in all industries but most sharply in fabricated metals, cans and containers sectors (from 10% to 45%). The copper share has been reduced in all sectors. The most important decline was in the electricity sector (from 37% to 30%). Nickel shows increases in all sectors, in particular the chemicals sector (from 30% to 57%). Lead also declined sharply in the chemicals sector (from 51% to 13Z). Lastly, tin's share increased in the chemicals sector (from 18% to 29%) but declined in all other sectors, in particular in the fabricated metals, cans and containers sector. B. Elasticities of Factor Demand and Substitution Equations (6), (7), and (8) of Section II are used to calculate the elasticities of demand and substitution based on coefficients estimated from equation (5) for the four factors, labor, capital, energy and metals. On the basis of estimated coefficients from this first step and equations (10), (13) and (14), elasticities of demand and of substitution are calculated for the seven metals. We do not report the estimates of coefficients of equations (5) 1/ See also Annex 2. - 19 - TABLE 6: CHANGES IN METAL EXPENDITURE SHARES IN SELECTED US INDUSTRIAL SECTORS, 1964 AND 1983 1964 -------------------------------------------------------------------__--------__ FABRICATED CHEMICALS METALS MACHINERY ELECTRICITY TRANSPORTATION --------------------------------------------------------------__-------------__ ALUMINUM - 10 3 10 7 COPPER - 2 7 37 3 NICKEL 30 2 1 3 1 TIN 18 8 0.8 2 0.6 ZINC - - 0.9 2 2 LEAD 51 1 - 1 2 STEEL - 76 86 44 84 TOTAL A/ 100 100 100 100 100 1983 FABRICATED CHEMICALS METALS MACHINERY ELECTRICITY TRANSPORTATION -------------------------------------------------------------__--------------__ ALUMINUM - 45 5 13 10 COPPER - 0.6 3 30 1 NICKEL 57 1 0.6 2 1 TIN 29 2 0.6 1 0.4 ZINC - - 0.8 1 1 LEAD 13 0.4 - 0.5 2 STEEL - 50 89 50 83 TOTAL /A 100 100 100 100 100 A/ DUE TO ROUNDING THE FIGURES MAY NOT ADD UP TO 100%. SOURCE: THE WORLD BANK, INTERNATIONAL ECONOMICS DEPARTMENT. - 20 - and (10). The estimated elasticities of demand and substitution of the first stage of estimation are presented in Tables 7 and 8. The demand elasticities for the seven metals are presented in Table 9. The results expressed in terms of the substitutability and complementarity among inputs in the five US industrial sectors are summarized in Table 10. 1/ An analysis of the estimated elasticities suggests the following conclusions: (1) Own-elasticities of input demand are in general inelastic. A 1% increase (decrease) in the price of the input will decrease (increase) the demand for that input by less than 1%. Although all own-elasticities of demand are negative for the four major factors, i.e., labor, capital, energy and metals, this is not always the case with the own-elasticities for the individual metals (see Tables 7 and 9). Eight out of 35 cases show positive own-elasticities. They are nickel in chemicals, aluminum, copper and tin in fabricated metals, cans and containers, nickel and zinc in electrical equipment and copper and zinc in transportation equipment. These positive own elasticities indicate the existence of local non-concavities. 21 1/ The elasticities of substitution for the seven metals are presented in Annex 3. It should be noted that in the case of more than two factors their interpretation is not always clear. 2/ Non-concavities exist when the coefficients Vi or yii 0.25 or better, when ii . Technological reasons may also lie behind the positive own-elasticities. The results involving these industries and metals should be treated with caution. - 21 - TABLE 7: DEMAND ELASTICITIES FOR LABOR, CAPITAL, ENERGY AND METALS IN FIVE US INDUSTRIAL SECTORS CHEMICALS -----------------------------------------------------------__----- LABOR CAPITAL ENERGY METALS ---------------------------------------------------------------__- LABOR -0.131 0.149 0.009 -0.028 CAPITAL 0.028 -0.077 0.040 0.009 ENERGY 0.016 0.357 -0.348 -0.026 METALS -0.908 1.580 -0.495 -0.179 FABRICATED METALS, CANS & CONT. ------------------------------------------------------------------ LABOR CAPITAL ENERGY METALS ---------------------------------------------------------------__- LABOR -0.402 0.305 0.032 0.065 CAPITAL 0.203 -0.277 -0.007 0.081 ENERGY 0.421 -0.129 -0.378 0.086 METALS 0.249 0.465 0.025 -0.739 MACHINERY LABOR CAPITAL ENERGY METALS LABOR -0.460 0.354 0.036 0.070 CAPITAL 0.202 -0.333 -0.005 0.135 ENERGY 0.637 -0.141 -0.537 0.041 METALS 0.167 0.565 0.005 -0.737 - 22 - . . . / ELECTRICAL EQUIPMENT LABOR CAPITAL ENERGY METALS ---------------------------------------------------------------__- LABOR -0.576 0.461 0.021 0.094 CAPITAL 0.249 -0.267 0.002 0.016 ENERGY 0.356 0.061 -0.377 -0.040 METALS 0.271 0.084 -0.007 -0.348 TRANSPORTATION EQUIPMENT LABOR CAPITAL ENERGY METALS ---------------------------------------------------------------__- LABOR -0.761 0.403 0.023 0.335 CAPITAL 0.259 -0.243 -0.005 -0.011 ENERGY 0.403 -0.138 -0.202 -0.064 METALS 0.570 -0.029 -0.006 -0.535 SOURCE: THE WORLD BANK, INTERNATIONAL ECONOMICS DEPARTMENT. - 23 - TABLE 8: ALLEN ELASTICITIES OF SUBSTITUTION OF LABOR, CAPITAL, ENERGY AND METALS IN FIVE US INDUSTRIES CHEMICALS ---------------------------------------------------------------__- LABOR CAPITAL ENERGY METALS ---------------------------------------------------------------__- LABOR -0.905 0.195 0.111 -6.273 CAPITAL 0.195 -0.100 0.466 2.063 ENERGY 0.111 0.466 -4.085 -5.817 METALS -6.273 2.063 -5.817 -40.721 FABRICATED METALS, CANS & CONT. ------------------------------------------------------------------ LABOR CAPITAL ENERGY METALS ---------------------------------------------------------------__- LABOR -1.143 0.576 1.197 0.707 CAPITAL 0.576 -0.525 -0.245 0.879 ENERGY 1.197 -0.245 -13.920 0.928 METALS 0.707 0.879 0.928 -7.994 MACHINERY LABOR CAPITAL ENERGY METALS LABOR -1.485 0.652 2.056 0.540 CAPITAL 0.652 -0.614 -0.259 1.041 ENERGY 2.056 -0.259 -30.746 0.314 METALS 0.540 1.041 0.314 -5.666 - 24 - *. . ./ ELECTRICAL EQUIPMENT LABOR -.CAPITAL ENERGY METALS ---------------------------------------------------------------__- LABOR -1.874 0.811 1.157 0.883 CAPITAL 0.811 -0.470 0.108 0.148 ENERGY 1.157 0.108 -20.444 -0.377 METALS 0.883 0.148 -0.377 -3.288 TRANSPORTATION EQUIPMENT LABOR CAPITAL ENERGY METALS LABOR -2.433 0.830 1.290 1.822 CAPITAL 0.830 -0.501 -0.284 -0.060 ENERGY 1.290 -0.284 -11.380 -0.346 METALS 1.822 -0.060 -0.346 -2.909 SOURCE: THE WORLD BANK, INTERNATIONAL ECONOMICS DEPARTMENT. - 25 - TABLE 9: DEMAND ELASTICITIES FOR ALUMINUM, COPPER, NICKEL, STEEL, TIN, ZINC AND LEAD IN FIVE US INDUSTRIES CHEMICALS -----------------------------------------------------------------__--------- ALUMINUM COPPER NICKEL STEEL TIN ZINC LEAD ALUMINUM____0__00_ 0.000-----0.000----- 0.000-----0--- 000- 0.00_______ 0.000__ ALUMINUM 0.000 0.000 0.000 0.000 0.000 0.000 0.000 COPPER 0.000 0.000 0.000 0.000 0.000 0.000 0.000 NICKEL 0.000 0.000 0.243 0.000 -0.014 0.000 -0.282 STEEL 0.000 0.000 0.000 0.000 0.000 0.000 0.000 TIN 0.000 0.000 -0.392 0.000 -0.350 0.000 0.563 ZINC 0.000 0.000 0.000 0.000 0.000 0.000 0.000 LEAD 0.000 0.000 -0.589 0.000 0.428 0.000 -0.018 FABRICATED METALS, CANS & CONT. ---------------------------------------------------------------------__----- ALUMINUM COPPER NICKEL STEEL TIN ZINC LEAD -------------------------------------------------------------------------__- ALUMINUM 0.099 -0.029 -0.206 -0.505 -0.060 0.000 -0.038 COPPER -0.202 0.186 -0.342 0.014 -0.378 0.000 -0.016 NICKEL -1.867 -0.447 -0.170 1.535 0.171 0.000 0.040 STEEL -0.190 0.001 0.064 -0.595 -0.028 0.000 0.011 TIN -0.267 -0.244 0.084 -0.340 0.092 0.000 -0.064 ZINC 0.000 0.000 0.000 0.000 0.000 0.000 0.000 LEAD -0.834 -0.050 0.095 0.620 -0.312 0.000 -0.258 MACHINERY ALUMINUM COPPER NICKEL STEEL TIN ZINC LEAD -------------------------------------------------------------------__------- ALUMINUM -0.377 0.021 -0.001 -0.297 0.003 -0.087 0.000 COPPER 0.016 -0.081 -0.212 -0.334 -0.026 -0.101 0.000 NICKEL -0.006 -1.109 -0.146 -0.217 0.291 0.448 0.000 STEEL -0.014 -0.020 -0.002 -0.705 -0.006 0.010 0.000 TIN 0.019 -0.183 0.396 -0.713 -0.178 -0.079 0.000 ZINC -0.461 -0.684 0.582 1.165 -0.075 -1.264 0.000 LEAD 0.000 0.000 0.000 0.000 0.000 0.000 0.000 - 26 - ELECTRICAL EQUIPMENT --------------------------------------------------------__------------------ ALUMINUM COPPER NICKEL STEEL TIN ZINC LEAD -------------------------------------------------------------------__------- ALUMINUM -0.356 0.436 -0.154 -0.272 0.016 0.090 -0.108 COPPER 0.137 -0.204 -0.047 -0.191 -0.017 -0.039 0.012 NICKEL -0.486 -0.466 0.170 0.028 0.244 0.276 -0.115 STEEL -0.081 -0.175 0.003 -0.099 -0.009 -0.029 0.042 TIN 0.103 -0.355 0.504 -0.194 -0.056 -0.321 -0.030 ZINC 0.551 -0.744 0.540 -0.608 -0.303 0.357 -0.142 LEAD -1.213 0.426 -0.409 1.562 -0.052 -0.259 -0.404 TRANSPORTATION EQUIPMENT ALUMINUM COPPER NICKEL STEEL TIN ZINC LEAD -------------------------------------------------------------------__------- ALUMINUM -0.280 0.005 0.010 -0.148 -0.007 -0.035 -0.080 COPPER 0.015 0.049 -0.317 -0.009 0.014 -0.304 0.018 NICKEL 0.043 -0.414 -0.289 -0.218 0.029 0.385 -0.071 STEEL -0.015 0.000 -0.005 -0.514 -0.001 -0.001 0.002 TIN -0.097 0.060 0.098 -0.180 -0.170 -0.231 -0.015 ZINC -0.174 -0.469 0.455 -0.039 -0.081 0.182 -0.407 LEAD -0.210 0.015 -0.045 0.038 -0.003 -0.218 -0.110 SOURCE: THE WORLD BANK, INTERNATIONAL ECONOMICS DEPARTMENT. - 27 - TABLE 10: SUBSTITUTABILITY AND COMPLEMENTARITY AMONG INPUTS IN FIVE US INDUSTRIAL SECTORS A/ LABOR CAPITAL ENERGY ALUMINUM COPPER NICKEL STEEL TIN ZINC CAPITAL + ENERGY + C,E METALS + + C T F,M COPPER + F NICKEL T STEEL + F M,T TIN + - + F,T T C ZINC + E M LEAD _ + o F F C A/ + SUBSTITUTES - COMPLEMENTS C CHEMICALS F FABRICATED METALS, CANS AND CONTAINERS M MACHINERY E ELECTRICAL T TRANSPORTATION NOTE: LETTERS BELOW SIGN INDICATE INDUSTRY EXCEPTIONS. SOURCE: TABLES 7 AND 9 - 28 - (2) Labor and capital are substitutes. However, their cross elasticities of substitution are less than one, indicating weak substitutability. (3) Labor and energy are also substitutes. Here the elasticities of substitution are mostly greater than one, indicating strong substitutability. The cross elasticities of demand are inelastic, however. The cross elasticities of labor demand with respect to energy prices range between 0.009 in chemicals and 0.036 in machinery while the cross elasticities of energy demand with respect to labor price range between 0.016 for chemicals and 0.637 for machinery. The latter elasticities are generally greater than the former. (4) Labor and metals are substitutes in all industries except for chemicals. As in the case of labor and energy, the relationship between labor and metals needs to be interpreted with care, as the meaning of substitution is not straightforward. The magnitude of elasticities of substitution varies with the industries; in some the elasticity is greater than one and in some others less than one. However, the cross elasticities of demand are all less than one in absolute terms. The cross elasticities of metal demand with respect to labor costs are larger than the cross elasticities of labor demand with respect to metal prices (in absolute terms). (5) Capital and energy are complements in all sectors except for chemicals and electrical equipment. The elasticities of substitution and demand are less than one in absolute terms. The cross elasticities of capital demand vis-a-vis energy prices are significantly smaLler than the cross elasticities of energy demand with respect to capital costs. In the case of the chemicals and - 29 - electrical equipment sectors, however, the relationship between capital and energy is one of substitution. 1/ (6) Capital and metals are substitutes except in the transportation equipment sector. The cross elasticities of demand are smaller than one except for metal demand with respect to capital costs in the chemical sector. In contrast, the cross elasticity of capital demand with respect to the metal price is close to zero. (7) Energy and metals are complements in the chemicals, electrical equipment and transportation equipment sectors and substitutes in fabricated metals and machinery sectors. With the exception of the chemicals sector, all other cross elasticities of demand and of substitution are very small (less than 0.1). In the chemicals sector the cross elasticity is -0.5. In evaluating the importance of these results, it is noteworthy that the share of metal expenditures to total expenditures is very small in the chemicals sector (only 0.4). (8) Between 1964 and 1983 the labor expenditure share declined while energy and capital stock share increased in most metal-using industries. During the same period the share of metal expenditures declined or remained constant. Within the group of seven metals the share of aluminum increased significantly while that of other metals decreased during the 1964 to 1983 period. In the fabricated metals, cans and containers sector the share of aluminum increased four times while that of copper, steel and other metals declined during the / Our findings coincide with those from earlier literature in this area; namely that capital and energy are complements in the short run and substitutes in the long run. See Najmabadi and Imran (1987). - 30 - 1964-83 period. Surprisingly the findings of Table 9 indicate that aluminum has been complementary to all other metals. This result leads us to believe that the substitutability that we expected to see (between aluminum and steel in the fabricated metals, cans and containers industry, for example) did not really exist. The changes in the shares have apparently been caused by the relatively faster rise of aluminum prices than those of other metals in the 1964-83 period. 1/ (9) In the machinery sector the share of metal expenditures declined from 15% in 1964 to 12% in 1983. Among metals the share of aluminum and steel increased at the expense of copper and to a lesser degree of nickel, tin and zinc. The results of Table 9 indicate that steel is complementary with all other metals except zinc. Since durability and cost are the primary characteristics of the goods produced in the machinery end-use sector, carbon steel is the preferred material in most uses and has no major competition in this market. The steel share of total metal expenditures average 88% through the 1964-83 period. The dominant role of steel in the machinery sector is supported from the sign of the cross elasticities of demand of Table 9 indicating complementarity between steel and all other metals except zinc. Substitution between carbon steel and zinc very likely occurred in view of the increased quality of today's carbon steel. In the machinery sector the aluminum share increased at the expense of copper. The results of Table 9 support the conventional wisdom / Substitution with plastics was not examined. - 31 - that substitution took place between copper and aluminum in the machinery sector between 1964 and 1983. The cross elasticities of demand between copper and aluminum are small and almost symmetrical in response to changes in prices or *quantities. Their magnitude indicates weak substitution between copper and aluminum. (10) In the electrical equipment sector the shares of capital and energy increased sharply over time at the expense of other expenditures including that of metals. The share of metals declined from 11% to 8% of total expenditures. Among the metals the share of aluminum and steel increased at the expense of copper and other metals. The results of Table 9 support the implications of these trends in shares. Aluminum has been used as substitute to copper (and tin and zinc) while steel has been used to replace lead (and to a minor degree nickel) in the electrical equipment sector. This study did not consider fiber optics that has reduced demand for copper in wiring nor plastics that has reduced demand for steel in electrical appliances. Cost reductions, increases in productivity and quality improvements have been some of the reasons for introducing materials such as fiber optics and plastics into the electrical equipment market. Energy conservation has also become an important factor. Energy consumption was reduced in refrigeration by adding more insulation and using one-piece plastic linens. Steel has been displaced by plastics in air-conditioning for housing and even in electric irons. Aluminum is now used more intensively for freezer doors, interior support posts and trim components in refrigerators and other appliances, thus displacing steel. However, steel use has - 32 - increased in other areas. For example, more precoated and enameled sheets are now being used. The embossed or textured sheet introduced in the 1980s has been readily accepted by appliance manufacturers because it reduces plant handling and refinishing costs and is demanded by consumers. From the results aluminum and steel are found to be complements, indicating either that relative price changes have caused any displacement of steel by aluminum or that any displacement in some areas has been counterbalanced by displacements in the opposite direction in other areas. (11) Metals comprise a small share in the chemicals sector (0.3%) and their share in total expenditures has remained the same in 1983 as in 1964; in contrast to the share of energy expenditures that increased sharply at the expense of labor expenditures. Among the metals, nickel and tin increased their share at the expense of lead. The results of Table 9 reveal that tin has been actively used as a substitute to lead; there is no indication, however, that nickel is a substitute to lead. (12) Steel is by far the dominant metal in the transportation equipment sector. In 1983 it accounted for an average of 83% of total metal expenditures--almost as much as in 1964. During the 1964-83 period, however, the share of aluminum increased (from 7% to 10%), mostly at the expense of copper (from 3% to 1%). The results of Table 9 show that although copper was indeed substituted by aluminum, this was not the case for steel. The decrease in the average consumption of carbon steel in automobiles, rails and other transportation-related output did not result in an equivalent increase in the use of - 33 - aluminum. In the automobile area, changes have been primarily a function of consumer preference for smaller and more fuel-efficient cars and have been influenced by US Federal Government mandate under the Energy Policy and Conservation Act for-improved fuel economy. The mandates establish standards and require that the sales weighted city/highway average fuel economy increases every year. As a result, US cars have been made increasingly smaller and lighter and with more aerodynamic designs and more efficient power trains. In 1976 the average automobile weighed 3,760 lb and was composed of approximately 2,320 lb of steel, 90 lb of aluminum, 160 lb of plastics and 1,190 lb of other materials. In 1985 the average automobile weighed 2,500 lb and was composed of 1,300 lb of steel, 400 lb of aluminum, 300 lb of plastics and 500 lb of other materials. It is noteworthy, however, that despite the increase of aluminum and the decrease of carbon steel in the construction of an automobile, the use of high strength steel (HSLA) has increased much faster than any other metal. Aluminum, plastics and high strength steels will continue competing with carbon steel in the motor vehicle market. A group of materials that may replace more carbon steel is graphite composites. Because of their high costs to date, their application has been limited to air conditioner mounting brackets. Another composite material, a plastic core sandwiched between sheets of either aluminum or steel, is increasingly used for body panels. So far, however, the high-cost and problems of availability with aluminum and production problems with HSLA and dual phase sheets have helped carbon steel maintain its markets. The need to improve corrosion resistance has led to the - 34 - increased use of one carbon steel shape group, that is, galvanized and coated sheet and strip. New galvanizing techniques have led to many new uses for this material. The rail transportation sector has -witnessed. similar changes to those of the motor vehicle sector. Safety mandates and cost considerations were behind the increased use of alloy steels and aluminum and the partial displacement of carbon steel in this sector. To sum up, while the fast growth in aluminum consumption reflects substitution for copper, aluminum remains complementary to steel. C. Factor Efficiency Bias Duncan and Binswanger describe two measures of factor efficiency bias for the case of the components of a separable factor. The "first step" measure (as we will call it) takes account of the specific factor (metal) share to total expenditures ( as rnat ) without also accounting for the share of each metal in total metal expenditures. The "second stage" measure considers both sources of bias. The measure as /at = ynt S + V t S is thus more comprehensive. The "first stage" and the "second stage" factor efficiency bias coefficients are reported in Table 11. If the factor efficiency bias coefficient is positive, it implies factor-using bias; if it is negative, it is interpreted as factor-saving bias. In all five industries technological bias in respect of labor is seen to be factor-saving and for capital it is factor-using. The factor efficiency of metals is estimated to be factor-saving in all industries except chemicals (where the share of metals is very small, 0.4% of total expenditures). - 35 - TABLE 11: MEASUREMENTS OF TECHNOLOGICAL BIAS IN US INDUSTRY FABRICATED CHEMICALS METALS MACHINERY ELECTRICITY TRANSPORTATION FIRST STAGE ESTIMATES -------------------------------------------------------------__--------------__--- LABOR -0.00421 -0.00468 -0.00617 -0.00647 -0.00421 CAPITAL 0.00197 0.00410 0.00675 0.00744 0.00414 METALS 0.00008 -0.00009 -0.00083 -0.00215 -0.00022 -----------------------------------------------------------__----------------__--- FIRST STAGE ESTIMATES ALUMINUM 0.00000 0.02163 0.00081 0.00157 0.00141 COPPER 0.00000 -0.00267 -0.00054 0.00240 -0.00047 NICKEL 0.00607 -0.00175 -0.00060 -0.00121 -0.00034 STEEL 0.00000 -0.01306 0.00115 -0.00106 -0.00097 TIN 0.00848 -0.00382 -0.00026 -0.00082 -0.00016 ZINC 0.00000 0.00000 0.00000 -0.00043 -0.00070 SECOND STAGE ESTIMATES /A ALUMINUM 0.00000 0.00198 0.00007 0.00001 0.00024 COPPER 0.00000 -0.00025 -0.00011 -0.00022 -0.00009 NICKEL 0.00007 -0.00016 -0.00009 -0.00018 -0.00007 STEEL 0.00000 -0.00126 -0.00058 -0.00062 -0.00036 TIN 0.00005 -0.00036 -0.00004 -0.00011 -0.00003 ZINC 0.00000 0.00000 0.00000 -0.00007 -0.00013 LEAD 0.00000 0.00000 0.00000 0.00000 0.00000 /A BASED ON EQUATION (15). SOURCE: THE WORLD BANK, INTERNATIONAL ECONOMICS DEPARTMENT. - 36 - Except for two cases the signs of the "first stage" and "second stage" coefficients for the six metals are the same in all five industries. (Energy and lead equations were dropped to satisfy the homogeneity condit-ion.) The results of. the "second stage"-estimations clearly indicate that technical change occurring in the 1964-83 period had a factor-using bias in favor of aluminum. In the second stage results, aluminum is the only metal that exhibits factor-using bias in all industries. All the other metals exhibit factor-saving bias in all industries, except chemicals. In chemicals, nickel and tin exhibit factor-using bias. 37 ANNEX 1 STANDARD INDUSTRIAL CLASSIFICATION (SIC) --------------------------------------------------------__------------------ NO. DESCRIPTION -------------------------------------------------------------__------------- 13 Oil and Gas Extraction 15 Building Construction - General Contractors and Operative Builders 16 Construction Other Than Building - General Contractors 245 Wood Buildings and Mobile Homes 25 Furniture and Fixtures 281 Industrial Inorganic Chemicals 2821 Plastic Materials 2851 Paints, Lacquers, Enamels 2911 Petroleum Refining 30 Rubber & Miscellaneous Plastic Products 3291 Abrasive Products 3297 Non-clay Refractories 335 Rolling, Drawing and Extruding of Nonferrous Metals 3356 Except Copper and Aluminum 3357 Drawing and Insulating of Nonferrous Wire 341 Metal Cans and Shipping Container 3411 Metal Cans 342 Cutlery, Hand Tools, and General Hardware 343 Heating Equipment 344 Fabricated Structural Metal Products 3441 Fabricated Structural Metal Products 348 Ordinance and Accessories 3482 Small Arms Ammunition 349 Miscellaneous Fabricated Metal Products 35 Machinery Except Electrical 361 Electric Transmission and Distribution Equipment 362 Electrical Industrial Apparatus 363 Household Appliances 367 Electronic Components and Accessories 3691 Storage Batteries 3693 X-Rays 371 Motor Vehicles 3861 Photographic Equipment and Supplies 461 Pipeline Except Natural Gas 492 Gas Production and Distribution SOURCE: EXECUTIVE OFFICE OF THE PRESIDENT, OFFICE OF MANAGEMENT AND BUDGET, STANDARD INDUSTRIAL CLASSIFICATION MANUAL, 1972, WASHINGTON, D.C. - 38 - ANNEX 2 FACTOR EXPENDITURE SHARES IN TOTAL EXPENDITURES IN SELECTED US INDUSTRIAL SECTORS: 1964 AND 1983 1964 FABRICATED CHEMICAL METAL MACHINERY ELECTRICITY TRANSPORTATION LABOR 16 40 35 35 33 ENERGY 6 2 1 1 1 CAPITAL 78 48 48 53 47 METALS 0.3 10 15 11 18 ALUMINUM - 1 0.5 1 1 COPPER - 0.2 1 4 0.6 NICKEL 0.09 0.2 0.2 0.3 0.3 TIN 0.06 0.8 0.1 0.2 1 ZINC - - 0.1 0.2 0.3 LEAD 0.16 0.1 - 0.1 0.4 STEEL - 8 13 5 16 TOTAL A/ 100 100 100 100 100 1983 FABRICATED CHEMICAL METAL MACHINERY ELECTRICITY TRANSPORTATION LABOR 13 32 27 25 26 ENERGY 12 4 3 3 3 CAPITAL 75 54 57 64 55 METALS 0.3 10 12 8 16 ALUMINUM - 4 0.6 1 2 COPPER - 0.1 0.1 2 0.2 NICKEL 0.16 0.1 0.1 0.2 0.2 TIN 0.08 0.2 0.07 0.1 0.06 ZINC - - 0.1 0.1 0.2 LEAD 0.03 0.03 - 0.03 0.3 STEEL - 5 11 4 13 TOTAL A/ 100 100 100 100 100 A/ DUE TO ROUNDING THE FIGURES MAY NOT ADD UP TO 100%. SOURCE: THE WORLD BANK, INTERNATIONAL ECONOMICS DEPARTMENT. - 39 - ANNEX 3 ALLEN ELASTICITIES OF SUBSTITUTION CORRESPONDING TO ELASTICITIES OF DEMAND OF TABLE 9 CHEMICALS …--- - - - - -- - - -- -- -- -- -- - - -- -- -- - - -- -- -- -- -- - - -- - - -- --_ - - - - -- - - - - -- -_ _ _ _ _ ALUMINUM COPPER NICKEL STEEL TIN ZINC LEAD ALUMINUM--------.000----0.000----0.000-----0.000----0.000----0.000-__--0.000-_ ALUMINUM 0.000 0.000 0.000 0.000 0.000 0.000 0.000 COPPER 0.000 0.000 0.000 0.000 0.000 0.000 0.000 NICKEL 0.000 0.000 98.766 0.000 -165.662 0.000 -258.043 STEEL 0.000 0.000 0.000 0.000 0.000 0.000 0.000 TIN 0.000 0.000 -159.431 0.000 -414.425 0.000 514.981 ZINC 0.000 0.000 0.000 0.000 0.000 0.000 0.000 LEAD 0.000 0.000 -239.545 0.000 506.992 0.000 -16.429 FABRICATED METALS, CANS & CONT. ---------------------------------------------------------------------__------_ ALUMINUM COPPER NICKEL STEEL TIN ZINC LEAD -------------------------------------------------------------------__--------_ ALUMINUM 4.447 -9.337 -85.446 -8.619 -12.054 0.000 -37.976 COPPER -9.060 59.171 -142.078 0.231 -76.211 0.000 -15.873 NICKEL -83.677 -142.480 -70.751 26.211 34.585 0.000 39.333 STEEL -8.504 0.197 26.449 -10.164 -5.751 0.000 10.626 TIN -11.984 -77.670 35.082 -5.797 18.504 0.000 -63.628 ZINC 0.000 0.000 0.000 0.000 0.000 0.000 0.000 LEAD -37.390 -16.033 39.544 10.592 -62.984 0.000 -256.302 MACHINERY ALUMINUM COPPER NICKEL STEEL TIN ZINC LEAD ALUMINUM -69.477 3.003 -0.980 -2.600 3.466 -84.759 0.000 COPPER 3.017 -11.563 -157.321 -2.917 -26.063 -98.991 0.000 NICKEL -1.042 -158.282 -108.034 -1.901 295.057 439.162 0.000 STEEL -2.635 -2.882 -1.850 -6.163 -6.174 10.232 0.000 TIN 3.488 -26.078 293.464 -6.238 -180.079 -77.449 0.000 ZINC -84.926 -97.721 431.079 10.188 -76.405 -1238.561 0.000 LEAD 0.000 0.000 0.000 0.000 0.000 0.000 0.000 - 40 - ELECTRICAL EQUIPMENT --------------------------------------------------------__-------------------_ ALUMINUM COPPER NICKEL STEEL TIN ZINC LEAD ALUMINUM -27.899 10.703 -37.203 -6.313 8.058 42.748 -92.810 COPPER 10.766 -5.005 -11.342 -4.435 -8.764 -18.318 10.432 NICKEL -38.069 -11.447 40.963 0.652 122.458 130.989 -98.180 STEEL -6.329 -4.304 0.753 -2.299 -4.414 -13.924 35.669 TIN 8.078 -8.712 121.363 -4.509 -27.939 -151.949 -25.828 ZINC 43.181 -18.268 129.992 -14.134 -152.178 169.363 -121.109 LEAD -95.099 10.471 -98.502 36.311, -26.232 -122.529 -345.394 TRANSPORTATION EQUIPMENT ALUMINUM COPPER NICKEL STEEL TIN ZINC LEAD ALUMINUM -19.092 1.002 2.957 -0.978 -6.519 -11.899 -14.000 COPPER 1.017 10.666 -89.812 -0.061 12.987 -101.894 3.160 NICKEL 2.956 -90.577 -81.827 -1.440 27.384 128.939 -12.484 STEEL -1.000 -0.103 -1.471 -3.396 -1.178 -0.279 0.280 TIN -6.608 13.194 27.668 -1.191 -159.884 -77.320 -2.668 ZINC -11.878 -102.770 128.951 -0.258 -76.426 61.056 -71.631 LEAD -14.334 3.179 -12.811 0.249 -2.722 -73.242 -19.417 SOURCE: THE WORLD BANK, INTERNATIONAL ECONOMICS DEPARTMENT. 41- ~~~~ANNEX 4 - 41-- ALTERNATIVE METHOD I - DE D ELASTICITIES LABOR CWITAL EDER6Y METALS INJSTRY - CIMICALS LABOR -1.446 1.406 .017 .023 CAPITAL .212 -.209 .001 -.003 EDERBY .030 .006 -.043 .007 MTALS .756 -.655 .127 -.225 DE0{ND ELASTICITIES LABOR CWITAL EKR6Y ETALS INUJSTRY - FABRICATED METALS,CANS.CONT. LABOR -.021 -.155 .0O0 . 0X CAITAIL -. IOS . 124 -. 047 .031 EER6Y 1.035 -.875 -.149 -.011 METALS .366 .168 -.003 -.531 DOM ELASTICITIES LABOR CAPITAL E\ER6Y METAS INDUSTRY - NINERY LABOR -.422 .082 .031 .309 CWITAL .047 .103 -.005 -.145 ENER6Y .558 -.142 -.343 -.073 METALS .731 -.603 -.010 -.118 DEPIRD ELASTICITIES LABOR CWITAL EOR6Y ETAS INWSTRY - ELECTRICAL EUIPIMNT LABOR -.902 .741 .017 .144 CWITAL .395 -.411 -.002 .018 E)ER6Y .285 -.063 -.121 -.100 METAS .417 .097 -.017 -.497 DW ELASTICITIES LABOR CWITAL EDERBY META INDUSTRY - TRANSPORTATION EWUIP LABOR -.572 .303 .027 .242 CWITAL .169 -.059 -.007 -.103 ENERMY .485 -.224 -.207 -.053 METALS .411 -.315 -.005 -.091 SOURCE: THE WORLD BANK. . . . . .i . . . S . . . . | M 8 & z ~*_ | | g * | 'I * | b = t | _ |B || S g I I_ I { | R || X R § p2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~r SIll C S~~~~~~~~~~~~~~~~~~~~~a - La S * g 0 | - 43 - ALTERNATIVE METHOD I ALLEN ELASTICITIES OF SUBSTITUTION LABOR CAPITAL ENERGY METALS INDUSTRY - CQENICALS LABOR -11.924 1.746 .249 6.233 CAPITAL 1.746 -.260 .007 -.814 ENERSY .249 .007 -.613 1.818 METALS 6.233 -.814 1.818 -61.403 ALLEN ELASTICITIES OF SUBSTITUTION LABOR CAPITAL EERGSY METALS INDUSTRY - FABRICATED METALS,CANS+CONT. LABOR -.058 -.299 2.871 1.016 CAPITAL -.299 .240 -1.691 .325 EDERBY 2.871 -1.691 -5.377 -.118 METALS 1.016 .325 -.118 -5.617 ALLEN ELASTICITIES OF SUBSTITUTION LABOR CAPITAL ENERSY METALS INDUSTRY - NAIINERY LABOR -1.366 .151 1.806 2.367 CAPITAL .151 .189 -.262 -1.110 EWEJrY 1.806 -.262 -19.762 -.556 METALS 2.367 -1.110 -.556 -.905 ALLEN ELASTICITIES OF SUBSTITUTION LABOR CAPITAL ENERSY METALS INDWSTRY - ELECTRICAL EGUIPMENT LABOR -2.958 1.296 .934 1.368 CAPITAL 1.296 -.719 -.111 .170 ENERGY .934 -.111 -6.594 -.955 METALS 1.368 .170 -.955 -4.719 ALLEN ELASTICITIES OF SUBSTITUTION LABOR CAPITAL ENER6Y METALS INDUSTRY - TRANSPORTATION ECtJIP LABOR -1.965 .582 1.664 1.410 CAPITAL .582 -.113 -.430 -.604 ENERSY 1.664 -.430 -12.712 -.311 METALS 1.410 -.604 -.311 -.531 SOTURC'E: THE %OPT,TD BANK. - 44 - ALTERNATIVE METHOD I SU8TTITUTION ELASTICITIES .AI. aWR NIo(EL STEEL TIN ZINC LEAD INDUSTRY - DENICALS ALHNIMM .000 .000 .000 .000 .000 .000 .000 CPER .000 .000 .000 .000 .000 .000 .000 NICKEL .000 .000 104.800 .000 -213.828 .000 -85.745 STEEL .000 .000 .000 .000 .000 .000 .000 TIN .000 .000 -206.923 .000 -513.724 .000 430.007 ZINC .000 .000 .000 .000 .000 .000 .000 LEAD .000 .000 -303.645 .000 597.090 .000 75.458 SUBSTITUTIDN ELASTICITIES cLIJq COPPER NICKEL STEEL TIN ZINC LEAD INDUSTRY - FABRICATED METALS,CANSCONT. ALUNIMN 6.540 -7.002 -80.823 -6.216 -9.485 .000 -17.339 CDPPR 4-6.708 60.314 -135.851 2.418 -71.718 .000 -5.264 NIOCEL -79.890 -137.828 -66.544 27.764 35.757 .000 24.895 STEEL -6.162 2.366 27.903 -7.724 -3.370 .000 9.213 TIN -9.576 -74.146 36.292 -3.463 20.158 .000 -31.353 ZINC .0 .000 .000 .000 .000 .000 .000 LEAD -34.493 -13.581 40.628 12.527 -58 888 .000 -13. 612 SU5TUTIMN ELASTICITIES PJlt CPPER NICKEL STEE TIN ZINC LEAD INDUSTRY - W1INERY ALLIMIMM -64.806 7.751 3.789 2.157 8.205 -80.801 .000 COPPER 7.767 -6.802 -151.471 1.841 -21.138 -95.163 .000 NICKEL 3.703 -153.388 -102.25 2.855 297.973 447.894 .000 STEEL 2.109 1.871 2.926 -1.399 -1.374 15.056 .000 TIN 8.228 -21.304 296.198 -1.474 -174.191 -73.424 .000 ZINC -80.271 -92.88 432.861 14.922 -71.166 -1245.117 .000 LEAD .000 .000 .000 .000 .000 .000 .000 QUBSTITUTION ELRSTICITIES mix COWPER NICKEL STEEL TIN ZINC LEAD INDISTRY - ELECTRICAL EQUIPENT ALUIN -29.506 9.374 -38.920 -7.740 6.690 41.831 -51.636 COPPER 9.430 -6.469 -12.851 -5.853 -10.132 -19.988 7.224 NICKEL -39.747 -12.966 39.875 -.742 121.087 131.162 -54.698 STEEL -7.785 -5.762 -.659 -3.707 -5.782 -15.540 21.613 TIN 6.724 -10.208 120.922 -5.928 -29. 307 -155.270 -13.448 ZINC 42.072 -19.846 129.621 -15.599 -153.543 170.010 -67.770 LEAD -97.175 9.139 -100.713 35.085 -27.599 -125.486 -195.640 SU9STIMIDN ELASTICITIES mmA COPPER NICKEL STEm TIN ZIINC LEAD IISEIRY - TR RTATIDN EWUIP ALLNIMN -17.950 3.674 5.759 1.540 -4.398 -10.117 -4.574 CPER 3.675 13.970 -93.629 2.524 16.509 -106.281 5.679 NIOCEL 5.760 -93.901 -85.074 1.045 31.940 140.376 -3.668 STEE 1.505 2.496 1.015 -1.052 1.327 2.300 3.958 TIN -4.526 16.663 32.233 1.312 -168.774 -80.023 2.197 ZINC -10.192 -106.891 140.742 2.313 -79.323 67.839 -39.007 LEAD -12.833 5.993 -11.135 2.856 -.327 -75.664 -7.810 SOURCE: THE WORLD BANK. - 45 - ANNEX 5 ALTERNATIVE METHOD II DEWI EATICITIES LAJBOR CWITAL DERBY ETALS INDUSTRY - OfnICRLS LABOR .076 -.152 .050 .026 CAITAL -.023 .002 .023 -.002 ENERGY .087 .265 -.330 -.022 NETALS .873 -.502 -.418 .047 DEOW ELASTICITIES LABOR CAPITAL ER6Y METALS INDISTRY - FABRICRTED ETALS,CANS4CONT. LABOR -.124 -.089 .121 .092 CAPITAL -.062 .090 -.064 .035 E)ERW Y 1.576 -1. 186 -.422 .033 METALS .351 .194 .010 -.554 DEOW EaSTICITIES LABOR CWITL ENERGY METALS INDlSTRY - IAOCINERY LABOR -1.026 .529 .048 .449 CAPITAL .301 -.016 -.010 -.275 ENER6Y .857 -.307 -.553 .004 METALS 1.063 -1.145 .000 .082 DEIUND aASTICITIES LABOR CAITAL EDER6Y METALS INIUSTRY - ELECTRICPL EGIIPMiT LABOR -1.550 1.287 .065 .198 CAPITAL .687 -.613 -.022 -.052 EDERSY 1.082 -.685 -.357 -.039 PETALS .573 -.282 -.007 -.285 DEIW4D ELASTICITIES LABOR CWITAL ENERGY ETALS INDUSTRY - TRANWORTATIN EQUIP LABOR -.599 .301 .015 .283 CAPITAL .168 .002 .003 -.172 ENERGY .269 .083 -.343 -.010 METALS .480 -.524 -.001 .045 SOURCE: THE WORLD BANK. w ztas|| g35S ;[ 0YSg[1l |Oggl0| |sOsl4 H I~ ~ ~ ~ ~ ~~~~~ . a . . . . . .. = . : 1 I I -. - 2 ~~~~ 8 2 I t -J-.J o .... . . . . . . . . . . . . . . ..A < 4 t3lC G~~~~; . . . . . . . . . . .f "i;1 OZ - M O ....... ... ~ ~ ~ ~ ~~~~. .. .. -... . .. ff ie fi a °9 R a a I I*1 a 8 a° I SI °o 8 a 0° 8 8 8 | Ri 80 g °s ;Ni o kB b x o N o o o o - 47 - ALTERNATIVE METHOD II ALLEN ELASTICITIES OF SU8STIIUTION LAWR CAPITAL ENERGY METALS INDUSTRY - CHEICALS LABaR .626 -.189 .716 7.199 CAPITAL -.189 .003 .329 -.624 ENERSY .716 .329 -4.715 -5.969 METALS 7.199 -.624 -5.969 12. 805 ALLEN ELASTICITIES OF SJ ITUTItN LAOR AITAL EIERGY METALS INDUSTRY - FABRICATED ETALS,CANS4CONT. LABOR -.344 -.173. 4.373 .974 CAPITAL -.173 .174 -2.293 .375 EIERGY 4.373 -2.293 -15.240 .344 METALS .974 .375 .344 -5. 81 ALLEN ELASTICITIES OF SUBSTITUTION LABOR CAPITAL ENERGY METALS INSTRY - OINERY LABOR -3.323 .974 2.775 3.442 CAPITAL .974 -.030 -.565 -2.108 EDERBY 2.775 -.565 -31.888 .027 ETALS 3.442 -2.108 .027 .628 ALN ELASTICITIES OF BSITUTION LABOR CITAL ENER6Y METALS INDUSTRY - ELECTRICAL EUUIPIENT LABOR -5.082 2.252 3.547 1. 88 CAPITAL 2.252 -1.072 -1.198 -.493 EYR6Y 3.547 -1.198 -19.478 -.374 METALS 1.880 -.493 -.374 -2.708 ALLEN ELASTICITIES OF SU ITUTION LABOR CAPITAL ENER6Y ETALS INDlSTRY - TRORTATION EUIP LABOR -2.056 .578 .924 1.649 CAPITAL .578 .003 .160 -1.006 EBERGY .924 .160 -21.042 -.057 ETALS 1.649 -1.006 -.057 .264 SOURCE: THE WORLD BANK. - 48- ALTERNATIVE METHOD II SUBSTITUTION ELASTICITIES mm CWER NICKEL STEEL TIN ZINC LEAD INDUSTRY - DENICRLS ALUNINSM .000 .000 .000 .000 .000 .000 .000 COPPER .000 .000 .000 .000 .000 .000 O00 NICKQ .000 .000 179.007 .000 -139.620 .000 -11.537 STEEL .000 .000 .000 .000 .000 .000 .000 TIN .000 .000 -132.715 .000 -439.517 .000 504.215 ZINC .000 .000 .000 .000 .000 .000 .0O0 LEAD .000 .000 -22. 437 .000 671.296 .000 149.665 SU85TITUTION ELaSTICITIES 1I. caPER NICKEL S5EEL TIN ZINC LERD INDUSTRY - FABRICATED MTALS, CANS+COMT. ALUINFU 6.296 -7.245 -81.066 -6.460 -9.728 .000 -17.583 COPR -6.952 60.071 -136.094 2.174 -71.962 .000 -5.507 NICKEL -80.133 -13L072 -66.786 27.520 35.513 .000 24.652 STEEL -6. 06 2.123 27.660 -7.968 -3.614 .000 8.969 TIN -9.819 -74.390 36.048 -3.707 19.914 .000 -31.597 Z INC .000 .000 .000 .000 .000 .000 .000 LEAD -34.736 -13.2 40.385 12.2U3 -59.131 .000 -136.855 SL8STITUTION ELASTICITIES FLIP. CWER NICKEL STEEL TIN ZINC LEAD INDSTRY - 4INWERY LUIINI( -63.274 9.283 5.322 3.689 9.738 -79.269 .000 9.299 -5.270 -149.939 3.373 -19.606 -93.631 .000 NICKEL 5.235 -151.856 -100.903 4.387 299.505 449.426 .000 STEEL 3.641 3.403 4.458 .133 .158 16.588 .000 TIN 9.770 -19.772 297.730 .058 -172.659 -71.802 .000 ZINC -7L.739 -91.350 434.393 16.44 -69.634 -1243.585 .000 LERD .000 .000 .000 .000 .000 .000 .000 9A9STITJTION ELRSTICITIES LUL CW.ER NICKEL STEEL TIN ZINC LEAD INDUSTRY - ELECTRICAL EUIPWNT (LUNIN -27.494 11.385 -36.909 -5.728 8.702 43.843 -49.625 11.442 -4.457 -10.839 -3.842 -120 -17.977 9.236 NICKEL -37.735 -10.954 41.886 1.270 123.099 133.174 -2.686 STEEL -5.7m -3.750 1.353 -1.696 -3.770 -13528 23.624 TIN 8.735 -.196 122.934 -3.916 -27.295 -153.259 -11.437 ZINC 44.083 -17. 834 131.633 -13. 587 -151.531 172.022 -5.758 LEA -95.164 11.151 -96.701 37.097 -25.588 -123.474 -193.628 9USTITUTION ELASTICITIES RLUL WER NICKEL STEEL TIN ZINC LEAD - INSTRY - TRI0RTATION EIUIP LUMINUM -17.155 4.468 6.553 2.335 -3.603 -9.322 -3.779 4.469 14.765 -92.834 3.318 17.303 -105.487 6.474 NICKEL 6.554 -03.106 -84.280 1.840 32.734 141.170 -2.873 STEEL 2.300 3.291 1.800 -.257 2.122 3.094 4.753 TIN -3.731 17.458 33.028 2.107 -167. 70 -79.228 2.991 ZINC -9.398 -106.097 141.537 3.108 -78.528 68.634 -38.212 LEAD -12. 039 6.788 -0o.340 3.651 .467 -74. 870 -7.016 SOURlCE: THE WORLD BANK. - 49 - REFERENCES Berndt, E.R. and D.O. Wood, "Technology Prices and the Derived Demand for Energy", The Review of Economics and Statistics, pp. 259-262, 1975. Christensen, L.R., D.W. Jorgenson and J. Lau, "Translogarithmic Production Frontiers", The Review of Economics and Statistics, pp. 255-266, 1973. Diewert, W.E., "An Application of the Shephard Duality Theorem. A Generalized Leontief Production Function", The Journal of Political Economy, vol. 79, 1971. Duncan, R. and H.P. Binswanger, "Energy Sources: Substitutability and Biases in Australia", Australian Economic Papers, Australia, 1976. Najmabadi, F. and M. Imran, Energy Demand in the US Manufacturing Sector, World Bank, Commodity Studies and Projections Division, Working Paper No. 1987-5, May 1987. Pollak, R.A. and T.J. Wales, "Estimation of a Linear Expenditure System", Econometrica, vol. 37, 1969. Shephard, R.W., Cost and Production Functions, Princeton, 1953. Theil, H., Principles of Econometrics, New York, 1971. US Bureau of Mines, Mineral Facts and Problems, Washington, DC., various issues (1965 to 1985 years). US Department of Commerce, Annual Survey of Manufacturers: Fuels and Electric Energy Consumed, Washington, DC., various issues (1964 to 1983), US Department of Commerce, Annual Survey of Manufacturers: Statistics for Industry Groups and Industries, Washington, DC., various years (1964 to 1984), Zellner, A., "An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias", Journal of the American Statistical Association, vol. 57, 1962.