For Staff Use Only cwc-g7o G Modelling Global Demand for Fertilizer Moshe Buchinsky Division Working Paper No. 1987-6 June 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. Modelling Global Demand for Fertilizer June 1987 Prepared by: Moshe Buchinsky Commodity Studies and Projections Division Economic Analysis and Projections Department - 1/ - 1 Z - IHIS PAGE ISBLNK TABLE OJF CONTENTS I. SUMMARY AND INTRODUCTION ............................................... 1 II. DEMAND FOR FERTILIZER .......................................... 3 III. FERTILIZER SUPPLY SPECIFICATION............................. 9 IV. SPECIFICATION OF PRICEFORMATION..S *...................,..,.,,...17 World Price Specification........................ .......17 Domestic Price Linkages .............................................. 20 V. ESTIMATED EQUATIONS .............................................. 23 Consumption Equations..................................................23 Variables and Country Codes for Demand Equations......................33 Capacity and Production Equations .................................... 34 Codes for the Capacity and Production Equations ...............40 Price Equations...................................................... 40 VI. AN EX-POST MODEL SIMULATION....................... ..... 43 VII. MODEL PROJECTIONS FOR THE PERIOD 1985-2000.......................... 73 VIII. CONCLUSIONS AND SUGGESTIONS FOR FURTHER WORK .......................... 81 APPENDIX A ....................*. 0........................................ 83 AP PENDIX B ....................... ....................... O..87 REFERENCES .................................... o .................... .. . . o88 TABLE NO. PAGE NO. TABLE 2.1: MODEL REGIONS................ ................................. 7 TABLE 6.1: SUMMARY STATISTICS FOR EX-POST SIMULATION OF NITROGEN CONSUMPTION...................................... *e *Q * ** ** C *e ** 4 TABLE 6.2: SUMMARY STATISTICS FOR EX-POST SIMULATION OF PHOSPHATE CONSUMPTION--..- ................................... 47 TABLE 6.3: SUMMARY STATISTICS FOR EX-POST SIMULATION OF POTASH CONSUMPTION ............................................. 48 TABLE 6.4: SUMMARY STATISTICS FOR EXPOST SIMULATION OF NITROGEN CAPACITY AND PRODUCTION............... . . .49 TABLE 6.5: SUMMARY STATISTICS FOR EX-POST SIMULATION OF PHOSPHATE CAPACITY AND PRODUCTION ........................... . . . . . . . . . . . . e50 i v - TABLE 6.6: SUMMARY STATI STICS FOR EX-POST SIMULATION OF POTASH CAPACITY AND PRODUCTION ......................................... 51 TABLE 6.7: SUMMARY STATISTICS FOR EX-POSNT SIMULATION OR WORLD FERTILIZER PRICES ..........................................................51 FIGURE NO. PAGE NO. 6.1 NITROGEN CONSUMPTION: DYNAMIC SOLUTION TRACKING, BRAZIL...........e...52 6.2 NITROGEN CONSUMPTION: DYNAMIC SOLUTION TRACKING, MEXICO . 52 6.3 NITROGEN CONSUMPTION: DYNAMIC SOLUTION TRACKING, LATIN AMERICA AND 6.4 NITROGEN CONSUMPTION: DYNAMIC SOLUTION TRACKING, NORTH AFRICA AN] MIDDLE EAST .................................... . ..........0.0........ 52 6.5 NITROGEN CONSUMPTION: DYNAMIC SOLUTION TRACKING, EAST ASIA ............ 53 6.6 NITROGEN CONSUMPTION: DYNAMIC SOLUTION TRACKING, INDIA ................ 53 6.7 NITROGEN CONSUMPTION: DYNAMIC SOLUTION TRACKING, CHINA ................ 53 6.8 NITROGEN CONSUMPTION: DYNAMIC SOLUTION TRACKING, EEC-10.............o 53 6.9 NITROGEN CONSUMPTION: DYNAMIC SOLUTION TRACKING, JAPANe............ ..54 6.10 NITROGEN CONSUMPTION: DYNAMIC SOLUTION TRACKING, UNITED STATES ....o... 54 6.11 NITROGEN CONSUMPTION: DYNAMIC SOLUTION TRACKING, OTHER INDUSTRIAL COUNTRIES ........................................ ................... 54 6.12 NITROGEN CONSUMPTION: DYNAMIC SOLUTION TRACKING, USSR...........e.. o54 6.13 NITROGEN CONSUMPTION: DYNAMIC SOLUTION TRACKING, DEVELOPING COUNTRIES.55 6.14 NITROGEN CONSUMPTION: DYNAMIC SOLUTION TRACKING, INDUSTRIAL COUNTRIES .55 6.15 NITROGEN CONSUMPTION: DYNAMIC SOLUTION TRACKING, CENTRALLY PLANNED ECONOMIES .................................................*o * ........ 55 6.16 NITROGEN CONSUMPTION: DYNAMIC SOLUTION TRACKING, WORLD ................ 55 6.17 PHOSPHATE CONSUMPTION: DYNAMIC SOLUTION TRACKING, BRAZIL ............. 56 6.18 PHOSPHATE CONSUMPTION: DYNAMIC SOLUTION TRACKING, MEXICO.............. 56 6.19 PHOSPHATE CONSUMPTION: DYNAMIC SOLUTION TRACKING, LATIN AMERICA AND CARIBBEAN .......................... ..... * . . e . e . e . a..... . . . . . . . .56 6.20 PHOSPHATE CONSUMPTION: DYNAMIC SOLUTION TRACKING, EAST ASIA ........... 56 6.21 PHOSPHATE CONSUMPTION: DYNAMIC SOLUTION TRACKING, INDIA ............... 57 6.22 PHOSPHATE CONSUMPTION: DYNAMIC SOLUTION TRACKING, CHINA ............... 57 6.23 PHOSPHATE CONSUMPTION: DYNAMIC SOLUTION TRACKING, NORTH AFRICA & MIDDLE EAST ..........................................................5 7 6.24 PHOSPHATE CONSUMPTION: DYNAMIC SOLUTION TRACKING, SOUTH AFRICA ........ 57 6.25 PHOSPHATE CONSUMPTION: DYNAMIC SOLUTION TRACKING, AUSTRALIA..4........58 6.26 PHOSPHATE CONSUMPTION: DYNAMIC SOLUTION TRACKING, EEC-10............. . 8 6.27 PHOSPHATE CONSUMPTION: DYNAMIC SOLUTION TRACKING, JAPANee...........,.58 6.28 PHOSPHATE CONSUMPTION: DYNAMIC SOLUTION TRACKING, UNITED STATES ....... 58 6.29 PHOSPHATE CONSUMPTION: DYNAMIC SOLUTION TRACKING, USSR ................ 59 6.30 PHOSPHATE CONSUMPTION: DYNAMIC SOLUTION TRACKING, DEVELOPING COUNTRIES ........................... *. o ................. o..........60 6.31 PHOSPHATE CONSUMPTION: DYNAMIC SOLUTION TRACKING, INDUSTRIAL C ONTR ES.................................................6 6.32 PHOSPHATE CONSUMPTION: DYNAMIC SOLUTION TRACKING, CENTRALLY PLANNED ECONOMIES ............................................................. 60 6.33 PHOSPHATE CONSUMPTION: DYNAMIC SOLUTION TRACKING, WORLD......... .60 6.34 POTASH CONSUMPTION: DYNAMIC SOLUTION TRACKING, BRAZIL ................. 61 6.35 POTASH CONSUMPTION: DYNAMIC SOLUTION TRACKING, LATIN AMERICA AND CAIBBEAN....*.................o ............ . * .... ............ O..61 6.36 POTASH CONSUMPTION: DYNAMIC SOLUTION TRACKING, EAST ASIA .............. 61 6.37 POTASH CONSUMPTION: DYNAMIC SOLUTION TRACKING, INDIA ................ 61 6.38 POTASH CONSUMPTION: DYNAMIC SOLUTION TRACKING, CHINA ................. 62 6.39 POTASH CONSUMPTION: DYNAMIC SOLUTION TRACKING, SOUTH AFRICA..........62 6.40 POTASH CONSUMPTION: DYNAMIC SOLUTION TRACKING, EEC-10e................62 6.41 POTASH CONSUMPTION: DYNAMIC SOLUTION TRACKING, JAPAN................62 6.42 POTASH CONSUMPTION: DYNAMIC SOLUTION TRACKING, UNITED STATES....e.h...63 - vi - 6.43 POTASH CONSUMPTION: DYNAfMIC SOLUTION TRACKING, OTHER INDUSTRIAL COUNTRIES .............................................................. 63 6.44 POTASH CONSUMPTION: DYNAMIC SOLUTION TRACKING, USSR ................... 63 6.45 POTASH CONSUMPTION: DYNAMIC SOLUTION TRACKING, DEVELOPING COUNTRIES...64 6.46 POTASH CONSUMPTION: DYNAMIC SOLUTION TRACKING, INDUSTRIAL COUNTRIES...64 6.47 POTASH CONSUMPTION: DYNAMIC SOLUTION TRACKING, CE1TRALLY CENTRALLY PLANNED ECONOMIES .......................................... 64 6.48 POTASH CONSUMPTION: DYNAMIC SOLUTION TRACKING, WORLD .................64 6.49 NITROGEN PRODUCTION CAPACITY: DYNAMIC SOLUTION TRACKING, EUROPE & JAPAN ....................................................... 65 6.50 NITROGEN PRODUCTION CAPACITY: DYNAMIC SOLUTION TRACKING, NORTH AMERICA ................. 6 .................... 65 6.51 NITROGEN PRODUCTION CAPACITY: DYNAMIC SOLUTION TRACKING, DEVELOPING COUNTRIES .................................................. .65 6.52 NITROGEN PRODUCTION CAPACITY: DYNAMIC SOLUTION TRACKING, CENTRALLY PLANNED ECONOMIES ............................. . ......... . 65 6.53 PHOSPHATE PRODUCTION CAPACITY: DYNAMIC SOLUTION TRACKINC, EUROPE & JAPAN........... ........... . . . . . . . . . . ......... . 66 6.54 PHOSPHATE PRODUCTION CAPACITY: DYNAMIC SOLUTION TRACKING, NORTH AMERICA ......................................................... 66 6.55 PHOSPHATE PRODUCTION CAPACITY: DYNAMIC SOLUTION TRACKING, DEVELOPING COUNTRIES ..................................... . . . . . . . . . . . .66 6.56 PHOSPHATE PRODUCTION CAPACITY: DYNAMIC SOLUTION TRACKING, CENTRALLY PLANNED ECONOMIES ....................... .. . . ........ * .66 6.57 WORLD NITROGEN PRODUCTION CAPACITY.................................... .67 6.58 WORLD PHOSPHATE PRODUCTION CAPACITY....................... 67 6.59 WORLD POTASH PRODUCTIONCAPACITY..............................67 6.60 NITROGEN PRODUCTION: DYNAMIC SOLUTION TRACKING, EUROPE & JAPAN........68 6.61 NITROGEN PRODUCTION. DYNAMIC SOLUTION TRACKING, NORTH AMERICA......... 68 6.62 NITROGEN PRODUCTION: DYNAMIC SOLUTION TRACKING, DEVELOPING COUNTRIES.68 - vii - 6.63 NITROGEN PRODUCTION: DYNAMIC SOLUTION TRACKING, CENTRALLY PLANNED ECONOMIES ...................................... ....................... 68 6.64 PHOSPHATE PRODUCTION: DYNAMIC SOLUTION TRACKING, EUROPE & JAPAN.......69 6.65 PHOSPHATE PRODUCTION: DYNAMIC SOLUTION TRACKING, NORTH AMERICA........69 6.66 PHOSPHATE PRODUCTION: DYNAMIC SOLUTION TRACKING, DEVELOPING COUNTRI ES ..............5.*.....*...-.- #.......69 6.67 PHOSPHATE PRODUCTION: DYNAMIC SOLUTION TRACKING, CENTRALLY PLANNED ECONOMIES ......................................................... *...69 6o68 WORLD NITROGEN PRODUCTION.*.* .*O............... . ...... 6.69 WORLD PHOSPHATE PRODUCTION ......................................... 70 6.70 WORLD POTASH PRODUCTION ............................. .70 6.71 NITROGEN WORLD PRICE, DYNAMIC SOLUTION TRACKING.......................71 6.72 PHOSPHATE WORLD PRICE, DYNAMIC SOLUTION TRACKING............. .......71 6.73 POTASH WORLD PRICE, DYNAMIC SOLUTION TRACKING ......................... 72 7.1 NITROGEN CONSUMPTION SHARE OF WORLD TOTAL BY MAIN ECONOMIC REGIONS, 1962-2000 ........................................... O.. ........ 75 7.22 PHOSPHATE CONSUMPTION SHARE OF WORLD TOTAL BY MAIN ECONOMIC REGIONS, 1962-2000 ........................................0.................... 75 7.3 POTASH CONSUMPTION SHARE OF WORLD TOTAL BY MAIN ECONOMIC REGIONS, 1962-2000 .....................................................76 7.4 NITROGEN PRODUCTION SHARE OF WORLD TOTAL BY MAIN ECONOMIC RECIONS 196 2-20 00................................................................77 ** ** *e e* *Z Z Z * * 7 7.5 PHOSPHATE PRODUCTION SHARE OF WORLD TOTAL BY MAIN ECONOMIC REGIONS, 1962-2000 ....................................................... * . 77 7.6 NITROGEN PRICE FORECAST (ACTUAL: 1960-85; FORECAST: 1986-2000)........78 7.7 PHOSPHATE PRICE FORECAST (ACTUAL: 1960-85; FORECAST: 1986-2000)......e78 7.8 POTitSH PRICE FORECAST (ACTUAL: 1960-85; FORECAST: 1986-2000) ..........79 I. SUMMARY AND INTRODUCTION 1. This paper describes the recently-completed fertilizer model which is used by the Commodity Studies and Projections Division. The fertilizers included in the model are nitrogen, phosphate and potash. The model is a partial equilibrium model of production and consumption. A separate module was built for each of the three fertilizers, but cross linkages between the different types of fertilizers within a country or a region were established. On the demand side 24 regions are distinguished; 16 of these are individual countries while the remaining countries are modeled as 8 regions based on the geographic location of the countries. 2. The fertilizer supply model was built in a more aggregated way. For nitrogen and phosphate there are four country groups--Europe and Japan, North America, Developing Countries and Centrally Planned Economies (CPEs). The production of potash is specified only on a world basis. 3. The fertilizer demand model is linked to the Division's grains and soybean model in the sense that the two models are solved iterative±y, i.e., the solutions from the grains model are entered into the fertilizer model, the results of which are then entered into the grains model. Model simulations are continued until the results become stable. 11 Therefore, the production and prices of the four major commodities (wheat, rice, coarse grain and soybeans) in the grains and soybeans model are endogenous to the fertilizer modEl. 4. Major changes have occurred in the last 20 years in agricultural production. These changes have also changed the nature of the demand for L/ See Mitchell (1985). -2- fertilizers. Growth in fertilizer consumption is especially evident in the developing countries where there is generally a rapidly-increasing demand for farm inputs. But major macroeconomic changes, fiscal and monetary, have also taken place and these have strongly influenced the fertilizer market. In this study we have tried to capture the most important of these historical changes and to give an idea of what to expect in the next decade or so. 5. The format of the paper is as follows. The specification of the demand side of the model is introduced in Section II followed by the specifi- cation of the supply side in Section III. Section IV is devoted to the price equation specification while Section V presents some results of the estimated equations. An ex-post simulation of the model carried out over the historical period is presented in Section VI with summary statistics as well as graphical representation of the behavior of some of the major variables in the model. Short- and long-term projections for both production and consumption, run over the 1985-2000 period, are presented in Section VII. Section VIII contains the conclusions and suggestions for further work. -3- II. DEMAND FOR FERTILIZER 6. The demand for fertilizers is derived from the demand for agricul- tural products. In turn, the demand for products such as food and fiber are partially determined by the growth in income and population. In this study these macro-variables are assumed to influence the demand for fertilizers only through the demand for crops and other agricultural products. 7. Several approaches to modeling fertilizer demand have been used in the past and each has its advantages and disadvantages. The most popular approach has been the pure maximization approach as applied to an agronomic fertilizer response function. Although the calculus is straightforward it involves two critical eltments, as has been mentioned by Timmer (1974). First, there is the necessity to assume some form of maximizing behavior on the part of the farmers and second, knowledge of the relevant agronomic function is required. One concern with this approach is the difficulty of accepting the underlying assumption of profit maximization by farmers the world over. Very few farmers equate marginal costs with marginal revenues for an input without regard to risk, uncertainty, knowledge and other constraints. Timmer has esti- mated that during the period 1960-80 the marginal return for the last dollar spent on fertilizer varie1 throughout the United States over the range $1.6 to $7.3. For developing countries, even higher marginal returns could be expected because of the widespread constraints on supplies. 8. Timmer mentions the additional problem of the difference in the use of fertilizer per hectare in various places in the world at the same price level (implying a different agronomic response function with respect to fertilizer use). The optimal level of fertilizer use varies significantly even within a country, depending on the location, the crop for which it is used, -4- the degree of water control, the availability of fertilizer, and other factors. 9. A second approach to analyzing fertilizer demand is the prescriptive approach; but although it is useful in understanding the nature of fertilizer use, it is somewhat irrelevant to our study. As noted by Barker (1972) "The analysis of fertilizer response can be useful. But the major problem is nrot necessarily one of determining the optimum level of fertilizer input, but rather of identifying the factors that constrain yield response on farmers' fields..." In short, neither the indirect demand functions derived from agronouiic response functions nor the prescriptive approach to fertilizer der.,and give any idea of the impact of the different factors which affect fertilizer demand. 10.) This paper adopts the direct approach following the work done by Griliches (1958, 1959), Timmer (1974) and others. The approach is a simple version of Nerlove's distributed lag technique, where the demand for fertilizer i.s specified and estimated directly. 11. The specification consists of two parts: a long-run demand function and an adjustment equation. The demand function assumes that the use of fe.tilizer is a function of the relevant product and input prices. Prices of agricultural products and fertilizers are affected by the aggregate response of both fertilizer consumption and product production, as well as other factors. The functional form of the dernand equation is assumed to be linear in the variables, or in some cases, especially in the developing countries, linear in the logarithms of the variables. 12. The adjustment equation is based on the idea that changes in prices (both input and output) and other independent variables take time to be fully reflected in demand. It is very clear, especially in the case where lower prices make fertilizer available to new users, that it takes time to introduce a new factor into the production process. 13. The partial adjustment method which was introduced by Griliches and others, consiste basically of distinguishing between actual and "desired" levels of use. The demand function determines the long-run "desired" level of use. However, in the short run, the desired level may not be fulfilled and the actual level changes only by some fraction of the difference between the desired use and the current use. The adjustment equation takes into account the direction of the "desired" level but does not permit an instantaneous change. The structural form of the adjustment equation is a function of the difference between the "desired" and actual use of the fertilizer. 14. If we let lower case letters denote the logarithms of the variables, then: * * (1) it l01 +Lpit +2 hag + 3 Pjt + 't represents the demand for fertilizer, where tcit is the desired fertilizer consumption of fertilizer i at time t. pit is the real price of fertilizer (deflated by the CPI). A vector, hat is harvested areas of various crops planted. A vector, pjt consists of all other relevant prices in the production process such as other ferti `zers and agricultural products. The adjustment equation is: (2) tc. tc Y(tC- - tci t 1 it it = i(tc -tc where y is the adjustment coefficient. In original units we would then have itc- tci .. . . ...- - 6 - The percentage change in actual consumption is a power function of the percentage difference between the "desired"' and actual consumption. Substituting (1) into (2) and solving for tcit gives: (3) tcit = ya0 + YS pit + Y2 ha + y3 pjt + (1-Y)tcit- yet This is the basic equation estimated in the model and the results are given in the following section. 15. Since the variables are in logarithms, the short-run elasticity of fertilizer demand with respect to its own price is given as ya and the long aly run elasticity is given as i*(1 ) . Some estimates of these long- and short- run elasticities are given in the discussion of the model results. Although such a model usually performs quite well in the sen'se of tracking historical observations, this good performance is partially due to the fact that a lagged dependent variable is included (although with good reason). The interpretation of the size of y may be disputed because the lagged variable captures some of the effects of excluded variables which therefore biases the estimation of (l-y) upward. 16. The demand side as a whole was constructed in a way that allows every region to change its demand, while the demand for the world is the sum of its 24 regions. The list of the regions and countries in each is shown in Table 2.1. -7- TABLE 2.1: MODEL REGIONS ------------------------------------------------------------------------------ Coun try/Region Countries -------------------------------------------w---------------------------------- Industrial Countries Australia Austral" ia Canada Canada EC-10 Belgium, France, Italy, Luxembourg, Netherlands, W. Germany, United Kingdom, Ireland, Denmark, Greece Japan Japan Other Industrial Countries Austria, Finland, Iceland, Malta, Norway, Portugal, Spain, Sweden Switzerland, New Zealand United States United States Centrally Planned Economies Eastern Europe Albania, Bulgaria, Czechoslovakia, East Germany, Hungary, Poland, Romania, Yugoslavia U.S.S.R. Union of Soviet Socialist Republic Developing Countries Argentina Argentina Brazil Brazil Central Africa Botswana, Lesotho, Namibia, Swaziland, Kenya, Malagasy Republic, Malawi, Mozambique, Tanzania, Uganda, Zambia, Angola, Burundi, Cameroon, Central Arrican Republic, Chad, Congo, Ethiopia, Djibouti, Benin, Gabon, Gambia, Ghana, Guinea, Equatorial Guinea, Guinea-Bissau, Ivory Coast, Liberia, Mali, Mauritania, Mauritius, Niger, Reunion, Rwanda, Senegal, Sierra Leone, Somalia, Sudan, Togo, Upper Volta, Zaire, Zimbabwe ... /continued .../Table 2.1 continued China China East Asia Burma, Kampuchea, Laos, Vietnam, Hong Kong, Singapore, South Korea, Brunei, Malaysia, Philippines, North Korea, Mongolia,Pacific Islands, Papua New Guinea, Fiji Islands Egypt Egypt India India Indonesia Indonesia Latin America and Caribbean Bahamas, Barbados, Bermuda, Belize, Other Caribbean Islands, Cuba, Dominica, Dominican Republic, Jamaica, Trinidad and Tobago, Honduras, Nicaragua, Panama, Costa Rice, El Salvador, Guatemala, Haiti, Bolivia, Chile, Colombia, Ecuador, French Guiana, Guyana, Paraguay, Peru, Surinam, Uruguay, Venezuela Mexico Mexico Nigeria Nigeria North Africa & Middle East Algeria, Bahrain, Cyprus, Iran, Iraq, Israel, Kuwait, Libya, Oman, Qatar, Saudi Arabia, United Arab Emirates, Jordan, Lebanon, Morocco, Syria, Tunisia, Turkey, Yemen A.R., Yemen D.M. Paki stan Pakistan South Asia Afghanistan, Bangladesh, Bhutan, Nepal, Sri Lanka Thailand Thai land -9- III. FERTILIZE!R SUPPLY SPECIFICATION 17. The fertilizer supply model is based on work done by Choe (1986). It is presented here for completeness, though it was not part of this study. 18. The fertilizer industry is assumed to be competitive and is repre- sented by a risk-neutral profit-maximizing firm. Further, fertilizer produc- tion is assumed to require two factors of production, a variable factor called material (M) and a quasi-fixed factor capital (K) or production capacity. 1/ It is assumed that fertilizer production technology is represented by the following quadratic production function: Qt =F(Mt, Kt ; t) =a at +aK Kt +M + 1/2 K2 +1/2 a MN +c K M(1 MM t KM t t The first- and second-order conditions for profit maximization require: > ° ¶ a > 0, acK < 0, and a a a- > K K mKKKK MM KM 1/ The labor input is ignored because it is a relatively small part of the cost of fertilizer production. The most important material input for ammonia production is natural gas. Phosphate rock is the main raw material for phosphate fertilizers. Relatively simple processing is required to transform run-of-mine potash into potash fertilizers, involving little material input. - 10 - 19. Under uncertainties of future output and input prices, the firm's problem is to choose a contingency plan for inputs that maximizes the present value of expected future profits: co Max E T P [F(Kty Mt ; t) - wtMt vtKt- 1/2 a I2], (2) subject to given initial capacity, KT, and It = Kt - (1-6)K t-(3) where ET is the mathematical expectation operator conditional on information available at time T; the term p = (l+r) is the discount factor where p is the interest rate; w. is the price of material input and vt is the service price of capital, each normalized by the output price; It is the gross investment, and 6 is the constant depreciation rate. 20. The last term in the objective function (1/2 0 I) reflects the costs t of adjusting the quasi-fixed factor. There are two ways of interpreting the adjustment cost term. One is to consider it as an expenditure, i.e., as a factor cost. The other is to consider it in the form of foregone output. In the latter case, the adjustment cost term can be included as an argument of t-he production function. The implications of this different treatment for the derivation of the model will be seen later. 21. It has been shown by Sargent (1979) that the fir,7-order necessary conditions for the stochastic optimization problem can be derived by substitu- ting (1) and (3) into (2) with respect to Mt and Kt for t=T, T+1, ...m aM + aMmmt+ a KM Kt Wt 0, (4) aK + a K + acMM - vt - 0 [Kt (1-S)K KtK t M lt + Et {pO(l-6)[K t+l- (l-S)K ]= 0, (5) where the certainty equivalence property of the quadratic specification is used. The condition (4) states that the marginal value product of material input should equal its price. The condition (5) is the "Euler equation" which states that the marginal value product of capital plus the expected future savings in adjustment cost by investing now rather than later should equal the service price of capital plus the current adjustment cost. Equation (4) yields the familiar demand equation for the variable factor; demand for the variable factor depends only on the current period values of the relevant variables. 22. Equation (5) is a second-order stochastic difference equation, the solution of which requires two boundary conditions. One of them is provided by the initial capacity, Kt, and the other is the transversality (terminal) condition: lim t-T-1 (a + a K a M v - Kt - (l-6)K 1 ]}= 0, (6) 1 im PtT1{K + KKK t + aKMMt Yt v t ( t -1 t +c which states that the adjustment cost should not affect the optimal capacity level in the very long run. To solve the difference equation, substitute (4) into (5) and rearrange terms to get: P ET Kt+ + d Kt + Kt B + C wt + D v (7) where - 12 - D, 1) {A - s[l + p(1-6) ]}, (8a) A =(a a -a2 )Iam (8b) KK MM KM ¶4M( D = 1-) s(8c) CD(a KM/a M (8d) B = (aMaKM -aK aMM) aMM (8e) Sargent (1979) showed that the stochastic difference equation (7) has two characteristic roots, X and (1/pX), such that X < 1 < I/pX. To satisfy the transversality condition (6), the difference equation should be solved backward with the stable root (X) and forward with the unstable root (1/pX), to get: K XtK A X (px) E (B + C w + D v (9) t ti1 i=0 t+l tD where X - [-4, + ,2 4p) 11/(2p)e (10) 23. It is postulated that the firm's expectations about future prices are formed according to the following two univariate autoregressive processes: 1/ m Et-1 wt i 1li wt-i ult' (11a) m t-l t 02i v-i u2t (llb) where uit and u2t are independently distributed white noise. The exponential order of the above processes are assumed to be less than p d in order to 1/ This formulation is chosen instead of the more general vector auto- regressive representation to avoid unnecessary complication. The markets for the capital and raw material inputs for fertilizers are quite separate and one is not expected to have significant influence on the other. - 13 - ensure their stability. It has been shown by Hansen and Sargent (1980) that if (11) is the expectations formation process, then the dynamics of investment is as folLows. rnm- i(px E t wt+l IO I'li wt-l ' (12a) i=0 i=0 co. m-1 i-O ti i=O 2it-( where II - pX and (i - 111 - 012 Il -m 8IIn ) l = 0 (012 11 +813 12 + n*+ 8m11 )s .l 2 =110 (813II 014 2 + e..8m I2 IVlm-l = 10 (alt II ), (13) and likewise f(4r p2i. Substituting (12) into (9), leads to pBX2 mr- mr- K X K _- + I C pli wt -I D I t t-1 l-pX 21 t- 24. Following the suggestion of Epstein and Yatchew (1985), the following set of equations are estimated: - 14 - Qt 0 Ot t t aMMa + 1i2 KK t +/2MM!2 + aK Mt t lt' (14) t Kt- p t-i i mn-i i-O i- wt __ li wt-1 + '3t' (16) m vt il 2i vt- + 4t' (17) -where the parameters satisfy the restrictions in (8), (10) and (13), and sit's are random variables assumed to be jointly normally distributed with zero mean and constant non-singular covariance matrix, and are serially inde- pendent. The inclusion of the production function in the specification has the advantage of permitting identification of both technology and expectations, as suggested by Epstein and Yatchew. The system of equations yields closed-form solutions for all the parameters of the model (aOt' K ' aKK' aMM, aKM9 0 p' ', 0li' 62i' lil 02i), i=l, 2, ..., im), If p is treated as a variable, then equation (15) becomes the flexible accelerator investment equation. 25. The autoregressive structure in (11) postulated for the firm's expec- tations formation and embedded in equation (15) is more general than the rational expectations hypothesis. The equations (16) and (17) describe the evolution of actual prices. If expectations are rational, the actual prices will evolve as expected and the equations (11) and (16)-(17) will be identical - 15 - 6. 9s = 1L 2; i=l, 2, ..., m). If the rational expectations hypothesis holds, the parameter restrictions in (13) will apply with 0li and 02i replaced by 0li and 02i* One can also experiment with the static expectations hypothesis adopted in earlier dynamic factor demand studies such as BerndL, Fuss and Waverman (1979). In the case of static expectations, 011=012=l and ili0 2i =0, for i=2, *.., m, which greatly simplifies the restrictions in (13). 26. The hypotheses associated with the restrictions can be tested by progressively imposing restrictions on the parameters. Three different versiors of the model have been estimated--the unrestricted model and the rational and static expectations models; they differ only in the way the investment equation (15) is parameterized. It is useful at this point to set out the investment equations for the three cases. Unrestricted Model Kt =0 + X Kt-1 + y +wt Y2 + 2t (18) Rational Expectations Model -t t-l p Icwt/(-)pX) - tDvt/--621 p-) + £2t (19) Static Expectations Model K -pBX /(l-pX) + XKt + XCw I(l-pX) - XDv M(P) + e (20) t: t- t t PX+2t (0 Note that the "unrestricted" model is equivalent to the general autoregressive model in equation (15), except that the intercept term is free rather than constrained to take on a certain value implied by the adjustment cost and the autoregressive expectations. Rational and static expectations models are self explanatory. - 16 - 27 The three models are estimated. with and without the adjustment cost term (1/2a I ) in the production function (14). This corresponds to the alternative interpretations of the adjustment cost mentioned earlier. ,,, , ,,-, ,,-,.,-,,, ..... .,,,,^,,,<.v.M........1.- .~~- .^o:...+ A< ....eSis.--....... .:NltA.-u..ss :*-bN ................ v euDJoQ - 17 IV. SPECIFICATION OF PRICE FORMATION World Price Specification 28. The model is solved for the "world price" which equates world demand with the world supply. How the price is determined is a complex problem that involves questions about the structure of the market in which the commodity is traded. In the fertilizer market it would not be too extreme to assume that the market is competitive and therefore the "world price" equation is such that it corresponds to the law of supply and demand 29. Following this idea it is straightforward to assume that three variables are to be determined by the model: supply, demand and the market- clearing price. The equilibrium condition of demand being equal to supply is achieved by a price that will determine such a condition and will take the short-term differences between demand and supply into account. However, in such a case it must be assumed that any excess of production over supply would be willingly held. Therefore, the price equation was constructed to give weight to the level of production (or capacity), the level of consumption and the desire to hold inventories. It still remains to be determined what path prices will take from one equilibrium situation to another and this relates to what one is willing to assume about the expected behavior of the participants in the market. 30. In order to simplify the price determination as well as the formula of the reduced form for the estimated price equation, rational expectations in price behavior is assumed. Under this assumption, a simple linear model of world demand and supply consists of the following equations: - 18 - (1) qt =0 1 Pt +a2 Pt + Xt +ust (supply) (2) qd = ao - a1 at + +d udt dt (demand) (3) Pt E(ptt) (expectations) s d (4 ) qt= qd (market clearing conditions) where qd quantity desired for consumption and inventories qt quantity supplied Pt price vector Xst Xdt exogenous variables of supply and demand respectively Q t 1 the set of information available at time t-l and u t udt coming from a joint normal distribution. 31. Substituting (1) - (3) into (4) and solving for Pt will give p (a a - ~Xd x4 X - e + (u -u) ( 1 1 1 (d dt s St 2 t dt st (00 io) 1 pt ++ aF +a ) B) d xdt 4 5sd a_2 e 1 (c1 - t (a+ + (udt - Lst) - 19 - 32. The set of equations (I)-(4) is consistent with the world production and consumption equations which have been previously discussed. Nevertheless, to ensure the homogeneity property of demand and supply, the relevant deflators such as the world price level and the exchange rate should be used to deflate the price wherever the price is used in both the supply and demand equations. That is to say, the price used should be the "real" price. Rewriting (5) gives: (5 ) - Pt J l2Xdt 3 Xst 4 Pt t where Iii, i2 , 1P39 P4 are defined as: $0 0 U1 A ~d 'P2 A s ½3 = A 3 A a2 Aa + it dt ust However, (5') is not an estimable equation since the expected price formation, pe, should be estimated first. If the expected price formation has the following simple rule - 20 - pt-i Pt P pt-2 t where Utis white noise, e E(~~i tipt-1 then p t / p - + E(u / ) p- without dependency on the future values of the exogenous variables. It can now be introduced into equation (5') without further complication, obtaining: (6) Pt 0 1 t 62TC + 63 t + 4 EXRt + 65 INTRt where Kt is the capacity and represents all the exogenous variables determining the potential production at a given year t. TC represents the exogenous and endogenous variables determining the consumption and is estimated as a behavioral equation at a first-stage estimation. EXRt is the effective exchange rate index, reflecting strength of the iollar relative to other currencies since the price is in US$ per metric ton. INTR is the real short-term interest rate representing the cost of inventory holding since implicitly it was assumed that the demand qd is both for inventories as well as for actual consumption at time t. Domestic Price Linkages 33. It is necessary to use domestic prices, or prices at the farmgate, in order to measure the correct price effect on fertilizer consumption. However, it is not always easy, and sometimes impossible, to obtain the relevant data. In cases where fertilizer prices paid by farmers were available, this price was linked to the world price through a simple equation as follows. If the - 21 - world price at time t be pt expressed in US$ per metric ton, pit is domestic prices in local currency per metric ton in region i at time t, and XRTit is the exchange rate of region i at time t expressed in local currency per one dollar. Then pt p. /XRT. it Pit it and Pit f(P t p) The error term of this equation is assumed to be autoregressive of order 1, i.e. = t-l twhere Ct is white noise. 34. In cases where we did not have domestic prices the international price (the so-called world price) was used as a border price, i.e., the deflated price in region i at time t, defined as: Pit = Pt * XRTit/cPiit This is a good approximation in a situation where the extent of subsidies is low. It is not a very good approximation where taxes and/or subsidies are high and therefore it does not reflect the prices farmers are facing. Nevertheless, it is often the only measure for fertilizer prices obtainable. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - IS BLANK I- - 23 - V. ESTIMATED EQUATIONS Consumption Equations 35. Demand equations were estimated for each of the fertilizers and for each of the regions included in the model. A sample of equations are presented below. NITROGEN CONSUMPTION BRAZIL NTTCBRA - - 13841.2695 DFNTPFBRA2 + 0.2817 NTTCBRA(-1) (-1.3904) (1.3258) + 0.0537 SBHABRA(-1) + 0.0074 CRHABRA(-1) (3.0789) (1.9308) R-SQUARED(CORR.): 0.914 SEE: 77.707 DW: 2.50 PERIOD OF FIT: 1966 1982 F( 4, 13): 43.012 MEXICO NTTCMEX = -186.3516 - 1573.0941 DFNTPFMEX + 0.9041 NTTCMEX(-1) (-1.7955) (-2.3193) (14.5988) + 0.4632 WHHAMEX (3.6758) R-SQUARED(CORR.): 0.981 SEE: 33.877 DW: 2.75 PERIOD OF FIT: 1963 1981 F( 3, 15): 304.630 LATIN AMERICA NTTCLAC = -875.3987 - 0.3399 DFNTPFLAC + 0.4876 NTTCLAC(-1) (-1.7955) (-2.2754) (2.6188) + 0.1141 CGHALAC + 0.4619 RPHALAC (1.4579) (2.6498) R-SQUARED(CORR.): 0.961 SEE: 46.552 DW: 1.86 PERIOD OF FIT: 1963 1981 Ft 4, 14): 110,788 - 24 - NORTH AFRICA NTTCNAF - 0.5514 DFNTPFNAF + 1.0202 NTTCNAF(-1) + 0.0090 WHHANAF(-1) (-3.6210) (28.5250) (3.9674) R-SQUARED(CORR.): 0.981 SEE: 69.933 DW: 2.27 PERIOD OF FIT: 1963 1982 F( 3, 17): 335.732 EAST ASIA NTTCEAS = - 699.0209 - 0.4754 DFNTPFEAS + 0.8492 NTTCEAS(-1) (-1.7633) (-2.0930) (9.5204) + 0.2162 CGHAEAS (2.0118) R-SQUARED(CORR.): 0.979 SEE: 64.051 DW: 2.26 PERIOD OF FIT: 1963 1981 F( 3, 15): 278.050 INDIA NTTCIND - 4494.4146 - 54.2922 DFNTPFIND + 0.7916 NTTCIND(-1) (-2.5018) (-2.0202) (7.7784) + 0.1469 RPHAIND (2.7202) R-SQUARED(CORR.): 0.975 SEE: 158.88 DW: 1.85 PERIOD OF FIT: 1963 1981 F( 3, 15): 230.459 CHINA NTTCPRC = - 9484.2725 - 238.7235 DFNTPFPRC2 + 1.0598 NTTCPRC(-1) (-2.7834) (-2.5707) (13.5603) + 0.3927 WHHAPRC (2 .8177) R-SQUARED(CORR.): 0.965 SEE: 625.36 DW: 2.26 RHO(1):--0.388 PERIOD OF FIT: 1968 1981 F( 3, 9): 111.938 - 25 - EEC - 10 NTTCEEC = - 1335.2217 + 1.0898 NTTCEEC(-1) - 0.7083 DFNTPFEEC2 (-0.6214) (8.0771) (-1.7949) + 654.3002 DFWHPFEEC (0.8960) R-SQUARED(CORR.): 0.986 SEE: 189.80 DW: 1.95 RHO(1): -0.078 PERIOD OF FIT: 1963 1983 F( 3, 16): 446.935 JAPAN NTTCJPN - 306.5961 - 346.5631 DFNTPFJPN + 0.2306 NTTCJPN(-l) (3.2033) (-4.1251) (1.5600) + 0.2224 TCHAJPN(-1) - 118.5227 D76 (5.1712) (-2.2892) R-SQUARED(CORR.): 0.761 SEE: 47.977 DW: 1.93 RHO(l): -0.263 PERIOD OF FIT: 1965 1982 F( 4, 12): 13.767 UNITED STATES NTTCUSA - 2718.2876 - 71336.3594 DFNTPFUSA + 0.7461 NTTCUSA(-1) (-2.1586) (-4.2600) (11.4621) + 1374.0574 DFWHPFUSA(-1) + 0.0972 WHCGHAUSA (3.0336) (3.5109) R-SQUARED(CORR.): 0.976 SEE: 325.18 DW: 2.15 PERIOD OF FIT: 1964 1981 F( 4, 13): 171.974 OTHER DEVELOPED NTTCODC = - 0.2455 DFNTPFODC + 0.8334 NTTCODC(-1) + 0.0432 CGHAODC (-2.4411) (14.8798) (3.7322) R-SQUARED(CORR.): 0.982 SEE: 50.037 DW: 2.58 PERIOD OF FIT: 1963 1981 F 3, 16): 331.550 - 26 - SOVIET UNION NTTCUSR -1266.5438 + 1.0020 NTTCUSR(-1) + 0.0258 WHHAUSR(-1) (-0.6161) (21.6761) (0.8819) R-SQUARED(CORR.): 0.988 SEE: 260.35 DW: 1.95 PERIOD OF FIT: 1964 1982 F( 2, 16): 726.317 PHOSPHATE CONSUMPTION BRAZIL POTCBRA - 16538.3965 DFPOPFBRA2 + 0.8707 POTCBRA(-1) (-1.4680) (6.9253) + 0.0059 CGHABRA + 0.0420 SBHABRA (1.2927) (1.8473) R-SQUARED(CORR.): 0.981 SEE: 86.454 DW: 2.10 PERIOD OF FIT: 1964 1981 F( 4, 14): 220.226 MEXICO POTCMEX = - 680.0370 + 0.7097 POTCMEX(-l) + 0.0678 CGHAMEX(-l) (-4.4882) (4.9484) (4.0144) + 0.1613 CRHAMEX(-1) (2.7782) R-SQUARED(CORR,): 0.912 SEE: 25.872 DW: 2.51 PERIOD OF FIT: 1965 1982 F( 3, 14): 59.961 LATIN AMERICA POTCLAC - 537.5496 - 0.0956 DFPOPFLAC + 0.5800 POTCLAC(-1) (-2.1729) (-1.1809) (3.4754) + 0.1130 CGHALAC + 0.0572 RPHALAC(-1) (2.4313) (1.1726) R-SQUARED(CORRo) 0.862 SEE. 28.562 DW: 2.23 PERIOD OF FIT: 1963 1981 F( 4, 14): 29,160 - 27 - EAST ASIA POTCEAS = 1363.8975 + 0.4404 POTCEAS(-l) + 0.2141 CGHAEAS(-1) (2.4859) (2.6501) (2.9932) - 0.1046 CRHAEAS(-1) (-3.2853) R-SQUARED(CORR.): 0.840 SEE: 50.477 DW: 1.70 PERIOD OF FIT: 1966 1982 F( 3, 13): 28.931 INDIA POTCIND - 2040.3231 - 12.8347 DFPOPFIND + 0.6659 POTCIND(-1) (-2.2091) (-2.0693) (4.0522) + 0.0631 RPHAIND (2.3660) R-SQUARED(CORR.): 0.906 SEE: 94.627 DW: 1.77 PERIOD OF FIT: 1963 1981 F( 3, 15): 58.769 CHINA POTCPRC - 2283.5125 + 0.4789 POTCPRC(-1) + 0.1990 WHHAPRC(-1) (-0.4841) (1.2484) (1.6929) - 0.0206 TCHAPRC(-1) - 932.9116 D79 (-0.7458) (-2.5857) R-SQUARED(CORR.): 0.734 SEE: 311.51 DW: 1.74 PERIOD OF FIT: 1967 1981 F( 4, 10): 10.669 NORTH AFRICA POTCNAF = - 1006.3026 + 0.8673 POTCNAF(-1) + 0.0536 WHHANAF(-1) (-2.5444) (12.9925) (2.6840) R-SQUARED(CORR.): 0.964 SEE: 75.153 DW: 2.61 PERIOD OF FIT: 1963 1982 F( 2, 17): 256.973 - 28 - SOUTH AFRICA POTCSAF + 0.9867 POTCSAF(-1) + 0.0039 CGHASAF (29.6900) (2.1106) R-SQUARED(CORR.): 0.978 SEE: 13.278 DW: 2.26 PERIOD OF FIT: 1963 1981 F( 2, 17): 397.888 AUSTRALIA POTCAUS = 361.7017 - 346.5064 DFPOPFAUS + 0.0833 WHHAAUS (2.4417) (-11.9181) (9.7422) - 0.0107 CRHAAUS + 365.1413 DFWHPFAUS(-1) (-0.4126) (5.1420) R-SQUARED(CORR.): 0.903 SEE: 50.468 DW: 2.48 RHO(1): -0494 PERIOD OF FIT: 1968 1981 F( 4, 8): 28.841 EEC - 10 POTCEEC = - 2824.4636 - 1.9086 DFPOPFEEC2 + 0.5923 POTCEEC(-1) (-2.2849) (-7.7600') (6.8121) + 10.2253 RPHAEEC(-1) + 0.1773 CRHAEEC2(-1) (3.1205) (1.9750) R-SQUARED(CORR.): 0.932 SEE: 108.51 DW: l1.94 PERIOD OF FIT: 1966 1982 F( 4, 12): 56.031 JAPAN POTCJPN = 379.3159 - 146.7041 DFPOPFJPN + 0.4396 POTCJPN(-1) (2.7608) (-2.7613) (3.4093) + 143.0723 DFRIPFJPN(-1) (2.7370) R-SQUARED(CORR.): 0.813 SEE: 42.387 DW: 2.03 PERIOD OF FIT: 1963 1983 F( 3, 17): 29.935 - 29 - UNITED STATES POTCUSA - 20750.6699 DFPOPFUSA + 0.8018 POTCUSA(-1) (-2.1707) (8.4024) + 0.0185 CGHAUSA + 0.0478 WHHAUSA (2.0024) (2.0648) R-SQUARED(CORR.): 0.874 SEE: 244.85 DW: 2.55 PERIOD OF FIT: 1963 1981 F( 4, 15): 31.825 SOVIET UNION POTCUSR - + 0.9895 POTCUSR(-1) + 0.0024 WHCGHAUSR\-1) (31.7278) (2.5487) R-SQUARED(CORR.): 0.982 SEE: 217.18 DW: 1.98 PERIOD OF FIT' 1963 1982 F( 2, 18): 519.137 POTASH CONSUMPTION BRAZIL KOTCBRA = - 59.6716 - 50557.2891 DFKOPFBRA2 + 1.1130 KOTCBRA(-1) (-0.2668) (-1.5536) (10.8048) + 0.0157 CGHABRA (0.6999) R-SQUARED(CORR.): 0.978 SEE: 57.339 DW: 2.39 PERIOD OF FIT: 1963 1981 F( 3, 15): 272.733 LATIN AMERICA KOTCLAC = - 591.4120 + 0.4049 KOTCLAC(-1) + 0.0884 CGHALAC (-2.7673) (2.9938) (2.2461) + 0.2328 RPHALAC - 0.7364 DFKOPFLAC(-1) (4.0846) (-1.7081) R-SQUARED(CORR.): 0.925 SEE: 27.094 DW: 1.99 PERIOD OF FIT: 1963 1981 F( 4, 14): 56.238 - 30 - EAST ASIA KOTCEAS = - 0.7448 DFKOPFEAS + 0.8292 KOTCEAS(-1) (-1.2163) (7.6451) + 0.1033 CCHAEAS - 0.0172 CRHAEAS (1.9167) (-1.4081) R-SQUARED(CORR.): 0.945 SEE: 37.753 DW: 2e68 PERIOD OF FIT: 1965 1981 F( 4, 13): 69.186 INDIA KOTCIND = - 699.1591 + 0.6560 KOTCIND(-1) - 60.7125 DFKOPFIRD (-3.0497) (11.8951) (-11;0945) + 0.0211 RPHAIND + 0.0164 WHHAIND + 142.1651 D68 (2.8522) (4.7196) (6.0442) R-SQUARED(CORR.): 0.984 SEE: 23.695 DW: 2.28 RHO(1): -0.595 PERIOD OF FIT: 1963 1981 F( 5, 12): 207.012 CHINA KOTCPRC - 96.1513 - 87.7067 DFKOPFPRC2 + 1.3255 KOTCPRC(-l) (-0.1618) (-1.0436) (4.0079) + 180.9829 RWHHAPRC + 161e2131 D74 (0.3002) (3.2311) R-SQUARED(CORR.): 0.853 SEE: 50.338 DW: 1.63 RHO(1): 0.387 PERIOD OF FIT: 1967 1981 F( 4, 9): 194870 SOUTH AFRICA OTCSAF = 1.1384 - 40.2878 DFKOPFSAF2 + 0.6829 KOTCSAF(-1) (0.1036) (-1.1015) (5.9301) + 0.0116 WHHASAF + 47.0672 DFWHPFSAF(-1) (1.7826) (3.0767) R-SQUARED(CORR.): 0.941 SEE: 5.1252 DW: 2.22 PERIOD OF FIT: 1966 1981 F( 4, 11): 61.294 - 31 - EEC - 10 KOTCEEC - 1731.2428 - 6.1897 DFKOPFEEC2 + 0.6652 KOTCEEC(-l) (-0.8629) (-2.1381) (5.8578) + 8.2492 RPHAEEC + 0.1659 WHHAEEC (1.8124) (1.5372) R-SQUARED(CORR.): 0.819 SEE: 181.33 DW: 1.96 PERIOD OF FIT: 1964 1981 F( 4, 13):* 20.290 JAPAN KOTCJPN = 1060.8259 - 669.9056 DFKOPFJPN - 0.2224 KOTCJPN(-1) (8.1666) (-8.3149) (-1.7281) + 0.0676 RPHAJPN (3.9068) R-SQUARED(CORR.): 0.798 SEE: 27.968 DW: 2.14 RHO1i): -0.591 PERIOD OF FIT: 1963 1981 F( 3, 14): 23.326 UNITED STATES KOTCUSA = - 90627.1797 DFKOPFUSA + 0.7780 KOTCUSA(-l) (-1.9009) (7.4630) + 0.0636 WHHAUSA + 0.0261 CGHAUSA (2.0077) (1.6687) R-SQUARED(CORR.): 0.936 SEE: 278.92 DW: 2.56 PERIOD OF FIT: 1963 1981 F( 4, 15): 66.380 OTHER DEVELOPED --#------------- KOTCODC = - 0.5512 DFKOPFODC(-1) + 0.6538 KOTCODC(-1) + 0.0461 CCHAODC (-1.1200) (4.0962) (2.1613) R-SQUARED(CORR.): 0.899 SEE: 54.490 DW: 1.82 PERIOD OF FIT: 1 963 1981 F( 3, 16): 53.995 - 32 - SOVIET UNION KOTCUSR = - 11674.7217 + 0.2489 KOTCUSR(-1) + 0.1004 WHCGHAUSR(-1) (-3.0529) (1.2016) (3.0984) - 19.8792 KOPRWRD + 253.3810 TIME (-3.1345) (3.5287) R-SQUARED(CORR.): 0.948 SEE: 326,43 DW: 1.46 PERIOD OF FIT: 1965 1982 F( 4, 13): 79.176 -33 - Variables and Country Codes for Demand Equations 36. Every region, whether it is an individual country or a set of countries, was given a name consisting of three letters. The regions and their abbreviations are listed below. Australia AUS Canada CAN EEC 10 EEC Japan JPN United States USA Other Industrial Countries ODC Eastern Europe EEU. Union of Soviet Socialist Republics USR People's Republic of China PRC Argentina ARG Brazil BRA Central Africa CAF East Asia EAS Egypt EGY India IND Indonesia INO Latin America LA- Mexico MEX Nigeria NIG North Africa NAF Pakistan PAK South Africa SAF South Asia SAS Thailand THA Two letters were used to identify each of the commodities used in the model: wheat-WH; coarse grains-CG; rice paddy-RP; rice-RI; total crop-TC; soybean-SB; nitrogen-NT; phosphate-PO; potash-KO. The type of variable is also indicated by two letters: total consumption-TC; production-PD; price Daid by farmers-PF; harvested area-HA. If a variable is a price variable deflated by the consumer price index it is preceded by DF. For example, WHHATHA = harvested area of wheat in Thailand and DFNTPFNAF = deflated price of nitrogen paid by farmers in North Africa. The macro variables i.e. population, exchange rate and consumer price index are indicated by the letters XaT-exchange rate; CPI- consumer price index; and POP-population. - 34 - Capacity and Production Equations 37. Capacity equations were estimated fQr nitrogen and phosphate in Europe & Japan, North America, Developing Countries and Centrally Planned Economies. For those same fertilizers a production function was estimated which takes into account the potential capacity available and other factors (as explained in Section III). The capacity and production of potash were estimated only on a world basis. The capacity equation and the production equation are presented below for each of the fertilizers. NITROGEN EUROPE AND JAPAN CAPACITY NKEJ = 1092.7333 + 0.9444 NKEJ(-1) - 851.9091 PMNEJ(-2) + 98.5891 PMNEJ(-3) (0.9701) (16.8222) (-1.8262) (0.1520) + 605.5921 PMNEJ(-4) + 5132.2632 PKN(-2) - 4455.6479 PKN(-3) (1.3453) (2.6953) (-1.9352) R-SQUARED(CORR.): 0.971 SEE: 665.12 DW: 1.67 PERIOD OF FIT: 1964 1984 F( 6, 14): 113.276 PRODUCTION t NQEJ 1651.7440 + 305.1215 TIME + 1.0929 NKEJ - 0.0001 NKEJ2 (1.2979) (4.1638) (4.0492) (-3.9179) - 159.5117 PMNEJ2 (-3.3772) R-SQUARED(CORR.): 0.900 SEE: 510.76 DW: 1.84 PERIOD OF FIT: 1964 1984 F( 4, 16): 45.986 - 35 - NORTH AMERICA CAPACITY NKNA - 9107.6074 + 0.1905 NKNA(-1) - 1472.6921 PMNNA(-2) (-2.8662) (0.9268) (-1.1750) - 1334.7931 PMNNA(-3) + 2991.6907 PKN(-2) (-0.7784) (1.1870) - 2703.5776 PKN(-3) + 8412.0430 LOCTIME (-0.9423) (3.7616) R-SQUARED(CORR.): 0.974 SEE: 657.14 DW: 2.26 PERIOD OF FIT: 1964 1984 F( 6, 14): 127.323 PRODUCTION NQ4A = 806.4847 + 477.1568 TIME + 0.2891 NKNA ° 0.0000 NKNA2 (0.7828) (5.5900) (1.6130) (-1.0864) 372.6502 PMNNA2 (-4.1807) R-SQUARED(CORR.): 0.958 SEE: 541.93 DW: 1.12 PERIOD OF FIT: 1964 1984 F( 4, 16): 115.808 CENTRALLY PLANNED COUNTRIES (EUROPE) CAPACITY : NKCP - 3873.6460 + 1.0764 NKCP(-1) - 535.5579 PMNAVG(*-2) (4.3202) (53.1602) (-0.5565) + 2303.0950 PMNAVG(-3) - 4099.2563 PMNAVG(-4) (1.8900) (-5.3783) 3333.0867 PKN(-2) + 2480.0168 PKN(-3) (-1.2685) (0.8624) R-SQUARED(CORR.): 0.997 SEE: 772.73 DW: 2.87 PERIOD OF FIT: 1964 1984 F( 6, 14): 956.701 - 36 - PRODUCTION NQCP - 2010.2239 + 800.0512 TIME + 0.2156 NKCP + 0.0000 NKCP2 (-4.9521) (5.9929) (1.6269) (1.4277) - 129.5176 PMNAVG2 (-2.3784) R-SQUARED(CORR.): 0.998 SEE: 392.18 DW: 2.27 PERIOD OF FIT: 1964 1984 F( 4, 16): 2579e396 DEVELOPING COUNTRIES CAPACITY NKDC = 1871.8712 + 1.0828 NKDC(-1) + 523.7126 PMNAVC(-2) (2.5632) (33.2701) (0.7547). 1658.8002 PMNAVG(-3) + 372.4431 PMNAVG(-4) (-1.3297) (0.3870) - 3266.5479 PKN(-2) + 6106.0317 PKN(-3) - 4161.8843 PKN(-4) (-1.5149) (1.6976) (-1.4882) R-SQUARED(CORR.): 0.994 SEE: 554021 DW: 2.40 PERIOD OF FIT: 1964 1984 F( 7, 13): 440.768 PRODUCTION: NQDC = - 1158.9550 + 476.2791 TIME - 0.2157 NKDC + 000000 NKDC2 (-2.2905) (3.6606) (-1.1917) (4.8512) - 385176.9063 PUREA-1-2 (-0 .8410) R-SQUARED(CORR.): 0.996 SEE: 234.21 DW: 1.63 PERIOD OF FIT: 1964 1984 F( 4, 16): 1315.560 - 37 - PHOSPHATE EUROPE AND JAPAN ---------------- CAPACITY PKEJ = 1864.7880 + 0.8114 PKEJ(-1) - 2626.2107 PMP(-2) (2.7224) (6.5994) (-1.5258) - 752.3315 PMP(-3) + 444.9250 PKP(-2) - 82.6618 PKP(-3) (-0.3918) (0.8768) (-0.1200) - 409.5767 PMP(-4) - 320.0896 PKP(-4) + 282.6097 RPKPQEJ (-0.3596) (-0.6041) (0.3592) R-SQUARED(CORR.): 0.981 SEE: 146.22 DW: 2.13 PERIOD OF FIT: 1965 1984 F( 8, 11): 121.050 PRODUCTION: PQEJ = 2890.5840 - 131.9156 TIME + 2.4341 PKEJ (3.8594) (-4.2505) (6.7581) - 0.0004 PKEJ2 - 11792.9004 PMP2 (-3.6958) (-4.5292) R-SQUARED(CORR.): 0.903 SEE: 318.38 DW: 1.94 PERIOD OF FIT: 1960 1984 F( 4, 20): 56.882 NORTH AMERICA CAPACITY : PKNA = 1723.0560 + 0.9122 PKNA(-1) - 5093.8765 PMP(-2) (0.9182) (16.2011) (-1.1255) - 533.9583 PMP(-3) + 1791.9712 PKP(-2) - 2181.9109 PKP(-3) (-0.1385) (1.1500) (-1.3106) + 1303.3057 RPKPQNA (0.8942) R-SQUARED(CORR.): 0.976 SEE: 511.74 DW: 2.73 PERIOD OF FIT: 1963 1984 F( 6, 15): 142.926 - 38 - PRODUCTION PQNA = 3900.0164 - 204.3221 TIME + 0.6859 PKNA + 0.0000 PKNA2 (4.1158) (-1.4101) (2.5568) (1.2218) - 9637.8809 PMP2 (-2.1383) R-SQUARED(CORR.): 0.926 SEE: 537.57 DW: 1.66 PERIOD OF FIT: 1963 1984 F( 4, 17): 66.914 CENTRALLY PLANNED COUNTRIES CAPACITY.: PKCP = - 705.5914 + 0.7881 PKCP(-1) - 978.4176 PMP(-2) (-0.7353) (8.8050) (-0.3588) - 451.1628 PMP(-3) + 2417.7961 PMP(-4) + 130.2768 PKP(-2) (-0.2383) (1.5051) (0.1628) - 304.9286 PKP(-3) + 3769.4492 RPKPQCP (-0.3178) (2.7382) R-SQUARED(CORR.): 0.992 SEE: 248.89 DW: 2.11 PERIOD OF FIT: 1964 1984 F( 7, 13): 365.032 PRODUCTION : PQCP = 953.1170 + 339.4733 TIME + 0.7812 PKCP - 0.0001 PKCP2 (1.7337) (3.8371) (2.4829) (-3.0594) - 2484.3335 PMP2 (-0. 75 78) R-SQUARED(CORR.): 0.990 SEE: 376.94 DW: 2.03 PERIOD OF FIT: 1960 1984 F( 4, 20): 577.122 - 39 - DEVELOPING COUNTRIES --- ---- ----- ---- -- - CAPACITY: PKDC 524.4303 + 1.0669 PKDC(-1) + 874.6616 PMP(-2) (0.5674) (46.1274) (0.3483) - 2506.5728 PMP(-3) + 1929.1949 PMP(-4) - 505.3241 PKP(-2) (-0.9386) (0.8486) (-0.4841) + 148.0381 PKP(-3) - 119.5401 RPKPQDC (0.1346) (-0.2125) R-SQUARED(CORR.): 0.988 SEE: 367.74 DW: 2.16 RHO(l): -0.590 PERIOD OF FIT: 1964 1984 F( 7, 12): 233.153 PRODUCTION : PQDC = 221.1357 + 114.6447 TIME + 0.3252 PKDC + 0.0000 PKDC2 (0.4170) (1.1738) (1.0382) (0.1952) - 830.7317 PMP2 (-0.4069) R-SQUARED(CORR.): 0.985 SEE: 238.70 DW: 2.15 PERIOD OF FIT: 1963 1984 F( 4, 17): 341.358 POTASH WORLD CAPACITY AND PRODUCTION ----------------------*-------------- CAPACITY : KKWD = 1208.8502 + 0.8716 KKWD(-l) + 100.5937 PPOT(-2) (0.4275) (9.1955) (2.0775) - 73.3431 PPOT(-3) + 3164.8545 PKK(-2) - 1784.6998 PKK(-3) (-1.4199) (0.8557) (-0.4504) R-SQUARED(CORR.): 0.952 SEE: 1552.9 DW: 1.90 PERIOD OF FIT: 1963 1984 F( 5, 16): 85.216 PRODUCTION: KQWD - 504.9231 + 818.6190 TIME + 0.6357 KKWD - 0.0000 KKWD2 + 14.7639 PPOT (0.1158) (3.1746) (1.6762) (-2.1525) (0.6578) R-SQUARED(CORR.): 0.980 SEE: 953.33 DW: 1.75 RHO(1): 0.570 PERIOD OF FIT: 1960 1984 F( 4, 19): 278.578 - 40 - Codes for the Capacity and Production Equations 38. Four regions are differentiated for the supply side of the model. These regions are denoted by two letters. Europe and Japan and other industrial countries EJ North America NA Developing Countries DC Centrally Planned Economies CP Capacity is denoted by the letter K and production by the letter Q. Other variables appear in the capacity and production equations and are defined as follows, PKN = MUV/Nitrogen price where MUV is the manufacturing unit value index PMNNA = natural gas price in North America/ nitrogen price) *100.0 PMNAVG = (PMNNA + PMNEJ)/2.0 PUREA-1-2 = [nitrogen price]2 PMP = (phosphate rock price/phosphate price) PKP = MUV/phosphate price RPKPQ is the ratio of capacity to production that was added to the phosphate proauction equations in order to adjust for the different process that had been used throughout the period of the sample. It is a predetermined exogenous variable. PKK = MUV/potash price PPOT = potash price Price Equations 39. Nitrogen and phosphate prices are estimated as a ratio of the price of the fertilizer and its most important input. Therefore the estimated equations for prices these two fertilizers' are: - - 41 - Natural_&as 2rice - f( Nitrogen price 1' and Phosphate rock price = f ( x Phosphate price -2' Y2 where x1, x2 are vectors of variables exogenous to the model, and l 2 are vectors of variables endogenous to the model. The potash price is estimated directly i.e., potash price = f (x3, Y3) where x3 and X4 are defined similarly to the equations above. 40. Regression estimates of the fertilizer price equations are shown below. NITROGEN WORLD PRICE -------------- s------ PMNAVG -2.1948 + 0.0000525 NKWD - 0.0000636 FNTTCWRD + 0.1084 INTR (-3.6691) (2.7977) (-2.0598) (4.3768) + 0.0227 EXR + 0.1840 PMNAVGRISK - 1.0418 D7483 (4.8804) (1.7224) (-5.4594) R-SQUARED(CORR.): 0.939 SEE: 0.19741 DW: 2.47 PERIOD OF FIT: 1962 1984 F( 6, 16): 57e501 PHOSPHATE WORLD PRICE PMP 0.3780 + 0.0000123 PKWD - 0.0000203 FPOTCWRD + 0.0027 DINTR (4.7683) (2.8185) '(-2.9676) (0.6873) + 0.1200 PMPRISK - 0.0995 D72 (4.5439) (-3.5759) R-SQUARED(CORR.): 0.796 SEE: 0.26303E-01 DW: 2.22 PERIOD OF FIT: 1963 1984 F( 6, 15): 14.671 POTASH WORLD PRICE PPOT = 1.3275 - 0.0057 KKWD + 0.0096 FKOTCWRD + 0.6153 PPOT(-1) (0.1796) (-5.0617) (5.9448) (5.5601) - 3.6374 DINTR - 20.6276 D77 (-2.4745) (-2.1589) R-SQUARED(CORR.): 0.903 SEE: 8.8564 DW: 1.59 PERIOD OF FIT: 1962 1984 F( 5, 17): 41.854 0I z Hi I '¢ r- r *lt, - I -. w m - 43 - VI. AN EX-POST MODEL SIMULATION 41. In order to validate the specification of the equations as well as the overall performance of the model an ex-post simiulation was run dynamically, i.e., where the lagged variables in any equation are the simulated values, except for the first year for which the model is solved. 42. The ex-post simulation was carried out for the period 1970-1984 and the simulated series were compared with the actual series to derive statistics to evaluate the performance of each variable. The summary statistics for simulations of nitrogen, phosphate and potash consumption are shown in Tables 6.1, through 6.3, respectively. 1/ 43. As Tables 6.1 and 6.2 show, the overall performance of the model is quite good; the RMSPE 2/ are low for almost all of the variables. For the major economic regions it can be seen that the RMSPE for nitrogen consumption does not exceed 7.403 (for the developing countries), and it is even lower for phosphate consumption. 44. The fluctuations in potash consumption through the period of this simulation were much greater than for nitrogen and phosphate. Even so, the diagnostics of the potash consumption variables are satisfactory (Table 6.3). The RMSPE for the world is slightly higher than 4.2, which is not as low as for nitrogen and phosphate but is still creditable. Special attention should be given to the inequality proportions. For nitrogen the covariance proportion is very close to 1.0 for all of the major economic regions. The covariance proportion factor for the centrally planned economies is slightly lower, 1/ The definitions of each of the statistics used in the following tables are provided in Appendix A. 2/ Root mein square percentage error. 44 - 0.569, but in the other regions the proportions are very high (developing 0.986, industrial 0.992 and for the world 0.999). The results for phosphate and potash are generally not as good as those for nitrogen. Graphic displays of the tracking performance for the consumption variables can be found in Figures 6.1 through 6.16 for nitrogen, 6.17 through 6,33 for phosphates and 6.34 through 6.48 for potash. 45. Tables 6.4 through 6.6 summarize the tracking statistics for the ex- post simulation of capacity and production. As can be seen, the performance of the supply side of the model is at least as good as the demand side. For nitrogen the highest RMSPE is about 6.6%, which was for capacity in developing countries, but even so the RMSPE for production of the developing countries is less than 2%. The fact that the covariance inequality proportion for capacity in the developing countries is 0.998 and the inequality proportion for produc- tion in that region is 0.673--which is the lowest among all the nitrogen capacity and production equations--is indicative of the good performance. There are mixed results concerning phosphate. Generally, the results are not nearly as good as for nitrogen. However, in absolute terms the results are reasonably good. The bias inequality proportions are very small for all of the regions for both fertilizers and the covariance inequality proportions are relatively high in most cases. 46. Equations for potash world capacity and production have been esti- mated, as previously mentioned, on a world basis. Given the difficulties of estimating a "world equation" the results are encouraging. The RMSPE of the capacity equation is 6.5 and the bias inequality proportion is almost zero. The production equation produced a RMSPE which is only 4.7 with a bias inequality proportions which is effectively zero. For both of these variables, the covariance inequality proportion is reasonably high--0.531 for capacities - 45 - and 0.548 for production. Graphical displays of the tracking performance of production by the model are presented in Figures 6.49-6.70. 47. Finally, we illustrate the performance of the most important variables in the model--prices. It should be remembered that this is a dynamic ex-post simulation; only the first year simulated uses actual lagged variables. The lagged values for periods thereafter are the simulated values. A forecast error of up to 15% can therefore be considered a reasonably good result. 48. As can be seen from Table 6.7 the RMSPE for nitrogen prices is 15.29. A large part of the reason for this result is because the model overshot in predicting the price level in 1974--the highest price peak during the simulation period. The contribution of this single year to the RMSPE statistic is very high (25%). Otherwise, the RMSPE would be no more than (9%). The same problem occurs with the phosphate price. The RMSPE for this equation is 13.18, but if the unusual case of 1974 is taken into consideration it would be less than 8% on the average. 49. It appears from our experience in estimating the potash price that the variables we were using did not fully explain the events of 1980-84 at all well. Even so, the RMSPE is only 15.86. 50. Clearly the simulated series of all three world prices do closely follow the actual series, especially in the cases of nitrogen and phosphate. The covariance inequality proportions prove this point. They are 0.69 for both nitrogen and phosphate while the bias inequality proportions are very close to zero. The coefficients for these two statistics can make the argument that there is no syttematic deviation from the actual series for any of these prices and that the equations used do have the capability of duplicating the degree of variability of any of the world fertilizer prices. 51. Figures 6.71-6.73 provide the visual backup to the above discussion. TABLE 6.1: SUMMARY STATISTICS FOR EX-POST SIMULATION OF NITROGEN CONSUMPTION ----------------------------------~--------------------------------------------------------------------------------------------- REGION MEAN OF MEAN ROOT MEAN MEAN % ROOT MEAN THEIL BIAS VARIANCE COVARIANCE NAME ACTUAL ERROR SQUARFD ERROR ERROR SQUARED % ERROR ERROR --INEQUALITY PROPORTIONS-- ARGENTINA 46.870 4.471 5.499 9.438 11.170 0.523 0.047 0.121 0.832 BRAZIL 515.694 55.576 70.260 11.498 16.073 0.566 0.015 0.291 0.694 CENTRAL AFRICA 330.826 29.313 33.026 8.994 10.081 0.908 0.000 0.283 0.717 EAST ASIA 1310.141 107.485 119.488 8.810 9.994 0.912 0.011 0.001 0.987 EGYPT 457.749 43.990 49.303 9.918 11.484 0.710 0.011 0.365 0.624 INDIA 2586.100 147,726 173,061 8,246 11.875 0.538 0.082 0.345 0.572 INDONESIA 523.546 71.942 103.314 12.080 14.915 0.549 0.004 0.096 0.900 LATIN AMERICA 833.914 46.286 58.506 5.640 7.M(X 0.650 0.000 0.197 0.802 MEXICO 739,433 55.868 74.977 7.246 8.420 0.771 0,001 0.077 0,922 NORTH AFRICA 1167,168 57.501 74.969 5,755 7.766 0.755 0.003 0.313 0.684 NIGERIA 42.562 6.524 7.427 71.927 125.495 0.732 0.037 0.413 0.551 PAKISTAN 564.727 61.605 78.146 10.800 13,078 0.814 0.001 0.407 0.593 PEOPLE'S REP. OF CHINA 7190.067 478.105 585.850 8.146 10.361 0.716 0.004 0.002 0.994 SOUTH AFRICA 321.048 82.421 103.688 22.731 24.936 0.740 0.057 0.052 0.891 SOUTH ASIA 290.626 41.273 45.179 17.739 21.863 0.735 0.016 0.360 0.624 THAILAND 121.294 20.457 23.862 22.479 27.790 0.845 0.008 0.467 0.525 ON TOTAL DEVELOPING 17041.764 581.460 777.922 3.073 3.663 0.326 0.005 0.010 0.986 AUSTRALIA 197,382 11.827 14.448 6.702 8.505 0.718 0.006 0.467 0.527 CANADA 665.471 39,474 47.735 7.294 9.073 0.522 0,002 0.055 0.943 EEC-10 6500.139 221.564 271.979 3.403 4.060 0.531 0.027 0.132 0.841 JAPAN 726.540 90.895 103.118 12.703 14.544 0.547 0.011 0.001 0.988 OTHER INDUSTRIAL 2032.683 66.982 79.431 3.291 3.840 0.818 0.020 0.065 0.915 UNITED STATES 8826.339 * 11.626 14.852 1.017 0.004 0.002 0.995 TOTAL INDUSTRIAL 18948.555 * 5.909 7.403 0.874 0.002 0.006 0.992 EASTERN EUROPE 3961.564 129.067 144.975 3.410 3.870 0.625 0.000 0.162 0.837 USSR 70210600 426.632 486.031 6.096 6,783 0.543 0,007 0,589 0.404 TOTAL CENTRALLY PLANNED 10983.165 400.928 498.424 3.504 4.176 0.476 0.006 0.425 0.569 TOTAL WORLD 46973.488 ******* 2.910 3.869 0.458 0.000 0.000 0.999 SOURCE: WORLD BANK, ECONOMIC ANALYSIS AND PROJECTIONS DEPARTMENT. TABLE 6.2: SUMMARY STATISTICS FOR EX-POST SIMULATION OF PHOSPHATE C-ONSUMPTION --------------------------------------------------.- ----------------------------------------------------------------------------- REGION MEAN OF MEAN ROOT MEAN MEAN % ROOT MEAN THEIL BIAS VARIANCE COVARIANCE NAME ACTUAL ERROR SQUARED ERROR ERROR SQUARED % ERROR ERROR --INEQUALITY PROPORTIONS -- -------------------------------------------------------------------------------------------------------------------------------- ARGENTINA 38.185 3,648 4.915 9,545 12.042 0.698 0.006 0.294 0.699 BRAZIL 1082.971 181.086 237.104 18.653 24.821 0.605 0.001 0.508 0.491 CENTRAL AFRICA 173.774 12.792 15.744 7.232 8.810 0.875 0.003 0.173 0.824 EAST ASIA 523.030 550321 66.246 10.653 12.596 0.970 0.011 0.375 0.614 EGYPT 81.569 13.038 15.373 19.358 24.877 0.921 0.018 0.250 0.732 INDIA 746.600 69.904 89.973 15.930 25,947 0.843 0.032 0.550 0.418 INDONESIA 154.614 19.609 23.947 28.905 54.185 1.024 0.003 0.276 0.721 LATIN AMERICA 429.648 14.630 18.163 3.458 4.292 0.684 0.001 0.070 0.930 MEXICO 248.314 20.341 24.416 8.755 10.399 0.813 0.000 0.076 0.924 NORTH AFR'CA 887.036 69.002 86.638 9.844 12.680 0.726 0.009 0,428 0.563 NIGERIA 30.474 6.198 7.579 41.223 59.178 0.946 0.000 0.429 0.571 PAKISTAN 134.477 6.631 8.356 8.147 12.320 0.786 0.000 0.156 0.844 PEOPLE'S REP. OF CHINA 1891.240 153.617 206.250 8.908 12.202 0.480 0.002 0.055 0.942. SOUTS AFRICA 382.458 17.446 29.406 4.289 7.311 O.9t> 0.029 0.001 0.970 SOUTH ASIA 115.707 17.071 18.747 19.336 23.031 0.732 0.024 0,410 0.566 THAILAND 82.763 5.543 7.136 8.281 10.832 0.597 0.000 0.439 0.561 TOTAL DEVELOPING 7002.860 287.521 324.785 4.583 5.565 0.449 0.006 0.081 0.913 AUSTRALIA 786.786 56.036 74.550 7.974 11.285 0.402 0.000 0.526 0.474 CANADA 523.420 32e456 42.435 6.468 8.163 0.692 0.015 0.454 0.532 EEC-10 4400.975 113.026 150.904 2.615 3.578 0.544 0.000 0.450 0.550 JAPAN 721.720 58.544 69.861 8,484 10.332 0.941 0.004 0.334 0,662 OTHER INDUSTRIAL 1609.107 74.892 81.634 4.691 5.161 0.778 0.031 0.262 0.707 UNITED STATES 4547.938 255.723 318.356 5.740 7.417 0.874 0.005 0.125 0.869 TOTAL INDUSTRIAL 12589.946 409.947 511.737 3,314 4.234 0.657 0.003 0.506 0.491 EASTERN EUROPE 2713.859 171.544 203.762 6.246 7.211 0.863 0.004 0.770 0.225 USSR 4679.733 113.036 128.914 2,465 2.765 0.385 0.002 0.505 0.493 TOTAL CENTRALLY PLANNED 7393.592 242.846 298.696 3.221 3.867 0.511 0.006 0.526 0.468 TOTAL WORLD 26986.400 632.366 799.498 2.308 2.836 0.527 0.000 0.395 0.605 SOURCE: WORLD BANK, ECONOMIC ANALYSIS AND PROJECTIONS DEPARTMENT. TABLE 6.3: SUMMARY STATISTICS FOR EX-POST SIMULATION OF POTASH CONSUMPTION -------------------.------------------------------------------------- -------------------.--------------------------------------- REGION MEAN OF MEAN ROOT MEAN MEAN % ROOT MEAN THEIL BIAS VARIANCE COVARIANCE NAME ACTUAL ERROR SQUARED ERROR ERROR SQUARED % ERROR ERROR --INEQUALITY PROPORTIONS -- ARGENTINA 7.446 3.438 4.085 59.301 79.611 0.841 0.004 0.323 0.673 BRAZIL 691,582 102.806 122.357 17.367 23.538 0.693 0.019 0.106 0.875 CENTRAL AFRICA 127.568 10.353 12.842 8.225 10.433 1.028 0.000 0.140 0,860 EAST ASIA 420.698 44.542 55.631 9.898 11.634 0.916 0,001 0.271 0,728 EGYPT 4.720 1.037 1.637 19,354 25,725 0.977 0.000 0.002 0.998 INDIA 421.747 48.801 55.868 12,810 14.572 0.679 0,009 0.211 0.780 INDONESIA 52.828 8.706 10.483 50.295 86.910 0.733 0.007 0.573 0.419 LATIN AMERICA 366.453 18.695 21 .793 5.122 50959 0.771 0.019 0.007 0.973. MEXICO 50.114 7.401 8.613 17.503 22.280 0.826, 0.008 0.161 0.831 NORTH AFRICA 117.192 16.001 18,501 14.555 17.122 0.889 0.015 0.124 0.860 NIGERIA 15.624 2.660 3.736 40.956 67.206 0.631 0.093 0.452 0.455 PAKISTAN 8.156 2.355 2.978 86.692 112.490 0.737 0.040 0.266 0.694 PEOPLE'S REP, OF CHiNA 305.533 73.255 90.265 46.767 65.438 0.873 0.010 0.635 0.355 SOUTH AFRICA 125.806 9.961 11.314 7.882 8.867 0.992 0.001 0.082 0.917 SOUTH ASIA 54.444 5.562 7.155 11.512 16.430 0.922 0.002 0.399 0.599 THAILAND 36.048 12.679 14.843 42.247 51.373 N.A. N.A. N.A. N.A. TOTAL DEVELOPING 2805.959 156.899 181.810 6,044 7,266 0,621 0.008 0.178 0.813 AUSTRALIA 107.223 8.577 11.181 8.402 11.281 0.699 0.010 0.599 0.392 CANADA 267.203 11.617 13.602 4.172 4.791 0.721 0.004 0.055 0.942 EEC-10 4148.763 157.626 202.107 3.734 4,746 0.759 0.004 0.235 0.761 JAPAN 620.420 47.979 65.465 8,149 11.556 0.905 0.000 0.105 0.894 OTHER INDUSTRIAL 1156,871 57.086 78.935 4.968 6.759 0.849 0.004 0.646 0.351 UNITED STATES 4740.339 240.141 288.765 5.105 6.305 0.810 0.000 0.213 0.787 TOTAL INDUSTRIAL 11040.819 435.839 510.520 3.904 4,521 0.839 0.001 0.296 0.703 EASTERN EUROPE 3065.786 162.299 206,787 5,054 6,232 0.888 0.009 0c459 0.532 USSR 4357.733 460.552 553,433 9.830 11,436 0.925 0.003 0,112 0.885 TOTAL CENTRALLY PLANNED 7423,520 499.293 639.466 6.320 7.768 0.860 0.001 0.198 0,801 TOTAL WORLD '21270.301 724.013 .p37.516 3,342 4.232 0.726 0.002 0.269 0.729 ------------------------------------------------------------------------------------------------------------------- N.A.: NOT APPLICABLE, SOURCE: WORLD BANK, ECONOMIC ANALYSIS AND PROJECTIONS DEPARTMENT. 7 'I TABLE 6.4: SUMMARY STATISTICS FOR EX-POST SIMULATION OF NITROGEN CAPACITY AND PRODUCTION --------------------------------------- -------------------------------- ------------------------------------------------------- REGION MEAN OF MEAN ROOT MEAN MEAN % ROOT MEAN THEIL BIAS VARIANCE COVARIANCE NAME ACTUAL ERROR SQUARED ERROR ERROR SQUARED % ERROR ERROR --INEQUALITY PROPORTIONS -- ,- -- --------------- ----- --- --- ---- ->o--.- - ----.-----~--- ----- -- ----------------*------ ----~---- - ------- ~-~ ~- -~- ---------------------- CAPACITY: DEVELOPING COUNTRIES 13698.667 651,101 723.844 5.591 6.656 0.465 0.010 0.002 0.988 EUROPE & JAPAN 14494.333 700,830 806.388 4.780 5.492 0.684 0.000 0.014 0.986 NORTH AMERICA 15556.733 537.054 704.891 3.298 4.226 1.058 0.000 0.032 0.967 CENTRALLY PLANNED 26922.400 858.964 974.346 3e930 4.868 0.434 0.011 0.097 0.893 WORLD 70672.133 N.A. N.A. 3.112 3.683 0.401 0.005 0.140 0.855 PRODUCTION: DEVELOPING COUNTRIES 7452.000 145,955 210.052 1.886 2.643 0.306 0.000 0.327 0.673 EUROPE & JAPAN 11035,733 509.074 580.708 4.662 5.368 1.069 0.003 0.007 0.990 NORTH AMERICA 10654.000 421.473 578.665 3.894 5.223 0.802 0.023 0.021 0,957 CENTRALLY PLANNED 19703.066 371.926 499,543 2,155 2.787 0.380 0.008 0.141 0.852 WORLD 48934.801 792.745 N.A. 1,417 2.037 0.433 0.003 0.007 0.990 ------------------- --------------- ------------------ -------- --------------------------------------- --------.------------------ N.A. - NOT APPLICABLE. SOURCE: WORLD BANK, ECONOMIC ANALYSIS AND PROJECTIONS DEPARTMENT. TABLE 6.5: SUMMARY STATISTICS FOR EX-POST SIMULATION OF PHOSPHATE CAPACITY AND PRODUCTION ---------------------------------------------------------------------------------------------------------------- REGION MEAN OF MEAN ROOT MEAN MEAN % ROOT MEAN THEIL BIAS VARIANCE COVARIANCE NAME ACTUAL ERROR SQUARED ERROR ERROR SQUARED % ERROR ERROR --INEQUALITY PROPORTIONS -- -- --- .--------- - ------ ------------------------- ---- --------------- ---------------- -------- ------------------- --- -- ---------- ------ CAPACITY: DEVELOPING COUNTRIES 6034.200 198.236 224.057 4.543 6.562 0.565 0.031 0.322 0.647 EUROPE & JAPAN 5271.000 107.859 136.518 2.076 2,621 0.659 0.018 0.036 0.946 NIORTH AMERICA 9381.200 351.527 434.322 4.187 5.464 0.646 0.OOQ 0,190 0.810 CENTRALLY PLANNED 5492.533 193.958 243.179 5.419 8,269 0.395 0.031 0.333 0.636 WORLD 26178.934 512.034 598.251 2.413 3.131 0.245 0.025 0.171 0.804 o PRODUCT ION: DEVELOPING COUNTRIES 4274.267 170.463 227.677 4.473 5.786 0.576 0.013 0.591 0.396 EUROPE & JAPAN 7191.000 347.752 447.150 4.832 6.245 0.935 0.001 0.355 0.644 NORTH AMERICA 7720.667 583.506 630.664 7.631 8.193 0.812 0.006 0.416 0.578 CENTRAl.LY PLANNED 9526.400 252.610 330.226 3,038 4.261 0.735 0.015 0.545 0.440 WORLD 28712.334 866.467 N.A. 3.132 3.736 0.639 0.017 0.428 0.555 _. -- -------------------------------------------- ---------------- ---------- - --------- --------- ----- ------ -------------------- --- N.A. - NOT APPLICABLE. SOURCE: WORLD BANK, ECONOMIC ANALYSIS AND PROJECTIONS DEPARTMENT. TABLE 6.6: SUMMARY STATISTICS FOR EX-POST SIMULATION OF POTASH CAPACITY AND PRODUCTION -------------------------------------------------------------------------------------------------------------------------------- REGION MEAN OF MEAN ROOT MEAN * MEAN % ROOT MEAN THEIL BIAS VARIANCE COVARIANCE NAME ACTUAL ERROR SQUARED ERROR ERROR SQUARED % ERROR ERROR --INEQUALITY PROPORTIONS -- ----- -------------------------------------------------------------------------------------------------------------------------- CAPACITY: WORLD 30838.045 N.A. N.A. 5,320 6.487 0.858 0.001 0.468 0.531 PRODUCTION: WORLD 23317.400 855.499 N.A. 3,536 4.679 0.792 0.000 0.452 0.548 --------------------------------------------------------------------- ---------------------------------------------------------- N.A. - NOT APPLICABLE. SOURCE: WORLD BANKp ECONOMIC ANALYSIS AND PROJECTIONS DEPARTMENT. Un TABLE 6.7: SUMMARY STATISTICS FOR EX-POST SIMULATION OF WORLD FERTILIZER PRICES ----- -------------------------------------------------------------------------------------------------------------------------- REGION MEAN OF MEAN ROOT MEAN MEAN % ROOT MEAN THEIL BIAS VARIANCE COVARIANCE NAME ACTUAL ERROR SQUARED ERROR ERROR SQUARED % ERROR ERROR --INEQUALITY PROPORTIONS -- ------ -------------------------------------------------------------------------------r---------------------------------- NITROGEN 148.127 18.234 32.926 11,564 15.286 0.470 0,002 0.305 0.693 PHOSPHATE 128.920 16.687 26.192 11.212 13.184 0,397 0,001 0,312 0.687 POTASH 65.987 9.344 12.508 13.765 15.863 0.824 0.002 0,014 0.983 ------ --W------ -- ---------------------------------------------------------------------------- -------------------N---------- SOURCE: WORLD BANK, ECONOMIC ANALYSIS AND PROJECTIONS DEPARTMENT. NITROGEN CONSUMPTION: DYNAMIC SOLUTION TRACKING FI-GURE 6.1: BRAZIL FIGURE 6.2: MEXICO 1100 1400 1000 ACTUAL ACTUAL C 0D 80 C 1000 12Dr 800 SIM1M LRTD D 1r80[- \| 133- L SI.MULATED 2 ' UACTED C3 C22001 I 400 c n 1 300 4001 200 1800 SIUAE C o -*,- - o 1 14001400 3.- LU80SIUA E LU CfCD 400 1970 197 1974 1975 1978 1980 182 198 1970 1972 1974 1976 1978 1980 1982 1984 NITROGFN CONSUMPTION: DYNnMIC SOLUTION TRRCKING (CONTINUED) FIGURE B.5: EAST ASIA FIGURE 6.8: INDIA 460 4200 o RCTURL J1400 u3400 AICTUAL SMULRTED .| z.. c32 SI[MULATEO 0CIWO scc cn= -2 1970 1972 1974 1978 1978 1980 1982 1984 19 1972 19G4 1976 1978 1980 12 184 FIGURE 5.7: CHINA FIGURE 5.8: EEC-10 14000 9000 13000 amo 12000 - RCTURL , - 110 . X . GooRCTURL f - 11000 CD75 - g0m 70lUD 8000 sQ0 4:2000 4500 - . 14000 2000 S3ULTE Ic 1000 1970 1972 1974 1976 1976 1 980 1982 1984 1970 1972 1974 1978 1978 1 980 1982 1984 NITROGEN CONSUMPTION: DYNAMMIC SOLUTION TRFCKING (CONTINUED) FIGURE 6.9: JAPAN FIGURE 6.10: UNITED STATES 1100 12000 100D . 110001O zn 90o RCTUA10000L G 900 z 70 8SIMULATED 6ooo 500 600 ACTUAL ~6000 SIUAE 700 000 40000 1970 1972 1974 1978 1978 1980 198 1984 1970 1972 1974 1975 1978 1980 1982 1984 FIGURE 6.11: OTHER INDUSTRIAL COUNTRIES FIGURE 6.12: U.S.S.R. 2500 . ,,1 1000 2400 ACTUAL10000 2300 cn200> < . 9000t IU 5 8000 400 4000 1970 1972 1974 1975 1978 1980 1982 1984 1970 1972 1974 1976 1978 1980 1982 1984 NITROGEN CONSUMPTION: DYNAMIC SOLUTION TRFCKING (CONTINUED) FIGURE 8.13: DEVELOPING COUNTRIES FIGURE 5.14: INDUSTRIAL COUNTRIES 30000 24500- Z7500 ACTUfAL 25000 cn co c 22500 c 2SMUL0TED C F-SIMULTE 17500 IL 0 s12000 1g71 1972 1974 197B 1978 1980 1982 I984 1970 1972 1974 1970 1978 1980 198 194 FIGURE 0.15: CETRALLY PLANNED ECONOMIES FIGURE 6.16: WORLD 14000 -- SIMULATEo --. e cD Co , 1300 . . I a 1100l0 Al RCTUAL SIMULfTEO a: cc CO mo 700 3 0000 1970m 9 7 8 .- t 7 7 7 1 1970 1n 1i74 1976 1978 198 1WK 18 1970 1972 1974 1978 1978 1g0o 1 198 PHOSPHnTE CONSUMPTION: DYNnMIC SOLUTION TRACKING FIGURE 6.17: BRAZIL FIGURE 6.18: MEXICO 2200 550 2000 ./ CTU\ 500 1800 450 00 ; --4200 SIMULATED 1400 ' 350 1200 CTA C3 100 C3250 :2 o ci c 1970 1972 1874 1976 1Q78 1980 198 198 1970 197 1974 1975 1978 1980 198 1984 FIfGURE 6 . 19: LAT IN AMERI CA 8 CAR IBBEAN FIfGURE S6.20: EAST ASIA 800 700 00 .C50 50 1970 197 1974 1970 1978 1880 198 198 1970 1a72 1974 1978 1978 lgo0 18 1iQ4 700 ACTUALUA ,-~ 500 * 3-3-35 1970 1972 1974 1975 1978 1980 1 982 1 984 1970 1972 1974 1975 1978 1980 1982 1984 PHOSPHATE CONSUMPTION: DYNAMIC SOLUTION TRACKING (CONTINUED) FIGURE 8.21: INDIA FIGURE 6.22: CHINA 14100 4000 1300 t - X 35cn 1200 c00 1- 1000 1 -- 900 SIMULATE0 f 2s SIMULATED wi w z 700 MO o kTCTUAL 300 200 50_ _ _ _ _ _ _ _ __0 19r70 197 1974 1978 1978 1980 1Q82 1984 iev 1w 1e74 1ts two im t8 I FIGURE 6.23: NORTH AFRICA MIDDLE EAST FIGURE 6.24: SOUTH AFRICA 1500 1400 5 1300 z 100ACTUAL 02 '-J100 ACTUAL 5R L SIMULATED 200 0 400 - n700- Iao- 400 3000 1970 1972 1974 1976 1978 1980 1982 1084 1970 1972 1974 197B 1978 1980 1Q8 1984 PHOSPHATE CONSUMPTION: DYNAMIC SOLUTION TRACKING (CONTINUED) FIGURE 6.25: AUSTRALIA FIGURE 6.26: EEC-10 14200 b. G1T00 5C4100; 1g71 1g72 iE17 1g H 1 E 1 R 141M s 9 X -10OO .*62 SX3. SIMULATED - 4SIMULATED LU am. - ' A - , f ' w01 ,' ACTUAL .4aoo - 44// to cn 4200 4000 ACTUAL 4000 3003400 190 1g9 1274 1W7 1 low 1S 1W 1 Io 1974 1970 1978 198D 1982 184c FIGURE 6.27: JAPAN FIGURE 6.28 UNITED STATES 1000 60 SIMULATED a, SIMULATED cn 5400 cc 0 W tu 4800 4000CTULCTUAL6 m -3400 970 1972 1974 19B 197 1980 1982 1984 197 1972 1974 1070 1078 1980 1982 196 PHOSPHnTE CONSUMPTION: DYNAMWC SOLUTION TRACKING (CONTINUED) FIG3URE 6.29: U.S.S.R. 7000 6500 SIMULATED 6000 C3 a 5500 ,-5000 flCTURAL Ci 50 4500 4o 000 C3 3000 ?boo. . . , ,.I 1970 1972 1Q74 197B 178 1980 1982 1Q84 PHOSPHATE CONSUMPTION: DYNAMIC SOLUTION TRACKING (CONTINUED) FIGURE 6.30: DEVELOPING COUNTRIES FIGURE 5.31: INDUSTRIAL COUNTRIES 13000 IBM0 F SIMULATED 14500 11000 14000 SIMULATED 000 RUACTUAL S i 22[150 -o 40M 11000D 10000 0 19m 1972 174 17e 1978 10 19. 184 1970 1972 1974 1978 1978 1980 182 940 FIGURE 6.32: CENTRALLY PLANNED ECONOMIES 3400 cn RCTAL. ,31000 w 7r00 -ACTUAL o 3 SIMULATED cn o 2200 1970 I972 1974 1970 1978 1980 982 1984 1970 1972 1974 1975 1978 1980 1982 1984 -4 POTASH CONSUMPTION: OYNRMIC SOLUTION TRACKING FIGURE 5.34: BRAZIL FIGURE 6.35: LATIN AMERICA CARIBBEAN 1400 500 1300 - ACTUAL 1200 450 2 1100 *0 . CI) iD 2 | 0 .;00*M @ 0 SIMULRTED L2700 .T- Lu 350 I CTUAL Cc 300. 300 250 2000 1970 1 972 1974 197B 1978 1 980 1Q82 1Q84 1970 1972 1974 1976 1978 1 980 f982 I1984 FIGURE .5.35: EAST ASIA FIGURE 5.37: INUIA 600- 800 550 -700~ ACTUAL Co BUD 600 c. 450 500 Lu 400 u 400 X 350 .n ~ 300SIMULATED 30 260 2 0 0 -a__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _I__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _I__ _ _ _ _ _ _ 1 970 1972 1Q74 1976 1978 1980 1982 1Q84 1970 1972 1974 1976 1978 1980 1Q82 1984 POTASH CONSUMPTION: DYNAMIC SOLlUTION TRACKING (CONTINUED) FIGURE 6E.38: CHINA FIGURE 6 .39: SOUTH AFRICA 900 180 800 160 7M- 7n cn ISIMULATED I- F- 1I40 500 ~120 CUL 400 SIMULATED.. a:UR a:4:ECI IUR 4:JRR Ca ca 000 - 100 ;4tOO .. c |SEI . \ / Z00 ACTUA'| 100 0 453 . 1g70 I972 1Q74 1970 1978 198 lE 1984 170 1972 1974 1970 1978 190 1982 1984 FIGURE 6.40: EEC-10 FIGURE 6.41: JAPAN m00 800 4800 4800 Ca RCTUJAL ca 0 C= 4400 c CU Lu 42000 C3 SIMULATED ... ~3800 cc 3400 SIMULATED 3000 400 1970 1972 1974 1976 1978 1980 1962 1984 1970 197 1974 1970 1078 1980 1982 1084 POTASH CONSUMPTION: DYNAMIC SOLUTION TRRCKING (CONTINUED) FIGURE 6.42: UNITED STATES FIGURE 8.43: OTHER INDUSTRIAL COUNTRIES 0500 1400 S IMULATED 000 .1300 1E50 0 a 4EOO z - X/V~~~~RCTUAL D10 URE LU L 1100 4500 - ccCUR ACUL/ en enSIUAE 50a -' 0500 6000. 00 Z5000 4000 1n 19750 17 Q4 196 17 98 92 1 POTASH CONSUMPTION: DYNAIMIC SOLUTION TRAICKING (CONTINUED) FIGURE 5.45: OEVELOPING COUNTRIES FIGURE 6.46: INDUSTRIRL COUNTRIES 4600 14M 4000 o ACTUAL 3600 -c 3 aiao RCTURL uJ /21X4 /.- I ULFITED e ./ ~SIM LRTED 1000 80 10 0 1970 1W2 i 974 197B 1 G78 1S80 1Rz 1984 790 1972 1974 1978 1978 1980 1 W 198 FI GURE 6.47: CENTRALLY PLANNED ECONOM IESFlGR6.48WOL U2m Z7000 TDSIMULATE A8C[g/t"20O CTURL mo/o =8CCC jt IMLTE 2mCC , 1600 91000 n 7000 | 000 7 17000 15000- r32400Q* , . . . 20 .,,. 0g7 ci3 174 1W7 1W7 1@0 l l 170 00 1974 1W7 197 l W2 I- NITROGEN PRODUCTION CAPACITY: DYNRMIC SOLUTION TRRCKING FIGURE 6.49: EUROPE 8 JAPAN FIGURE 6.50: NORTH AMERICA 18000 20000 17o00 1-0 Xtatt , - F tACTUAL o W000 1C000 c100 c= 7000 LI100 I-1 m ul 13Mcs I= / - ~ = SIMULATED SIMULRTED c_12000 - 140M 19t7 s7 s7 t7 b8 tbt X Es 70 1972 1974 1978 (978 198 1982 (984 0, FIGURE 6.51: DEVELOPING COUNTRIES FIGURE 6.52: CENTRALLY PLANNED ECONOMIES 24 0 lam , 1 1000 im 20000-la I0000 C !mO CO/< zisoint z t< 2 14000 /000 o100 ACUA /.x : SIMULATED 212000 4000 c2O tO A ,2\ CTUAL tmo .o SIMULRTED | 8000M eDo to,,,,,l< 400 10000 1 97 0 1 97 (9 74 1 9 7 8 (9 7 8 1 98 0 (9 8 1 98 197 1 9 7 1 9 7 4 1 7 8 (9 7 8 1 9 8 0 1 9 8 1 98 =' PHOSPHnTE PRODUCTION CRPACCITY: DYNFAMIC SOLUTION TRACKING FIGURE 6.53: EUROPE 8 JAPAN FIGURE 6.54: NORTH AMERICA woo . .o. o Ei8O0 ACTUAL 1 600 cn 54000 4O,1 ...- - ! C-,TU-F, - i,-LS- -*t .u 51W00 SIMULATED SIMULATED 0 !I0gm / C3 C 48 - '7 am* 1970 197 1974 1976 1978 1980 1982 1984 1970 1972 1974 1976 1978 1980 1982 1084 a FIUR .5 44000__ 4000 1970 I972 1974 1976 1978 1 980 1982 1Q84 1970 1972 1974 1976 1978 1980 1982 1984 FIUE65:CETALYPANE CNME FIGURE 6.57: WORLD NITROGEN PRODUCTION CRPRCITY FIGURE 6.58: WORLD PHOSPHATE PRODUCTION CAPACITY 1,0000 40=0 0 - 0 7 030000e W - 1 ass W 4 z 18 tm 1 w ACUA p CTRz LiM7= ACULSIMULATED z SI LRTEDULTE cn 2 I-15000 40000ATUA am00000 10 172 1974 197 1978 1980 1982 1984 1970 1971 1974 17 1978 198 198 1984 FIGURE 6.59: WORLD POTASH PRODUCTION CAPACITY 35000 tu"i4 3= ACTUAL a:SILTE 200 2000 1970 1972 1974 1 975 1 978 1 980 I982 1984 NITROGEN PRODUCTION: DYNnMIC SOLUTION TRACKING FIGURE 6.60: EUROPE 8 JAPAN FIGURE 6.61: NORTH AMERICA 14000 14000 ACTURL 11300 C0a F R . SIMULATED FISIMULATED 1r 1 .1000 3:3 120oo. , 20o0A,TUALU o~~~ 10000RTE X 2o 7 =llX 1g70 1o 1074 1078 1978 1080 1082 184 1970 1i7 1074 1076 1078 180 1082 10W4 FIGURE 6.62: DEVELOPING COUNTRIES FIGURE: 6.63: CENTRALLY PLANNED ECONOMIES 1400 3=E ACTUAL 11000 loa 100 0-2400 70 0,18000 0n 0 '-[1400 * SIMULATED 1070194 17 17 08 8 i9 o 1970774 0 1078 1080 1082 108.4 PHOSPHATE PRODUCTION: DYNAMIC SOLUTION TRACKING FIGURE 6.64: EUROPE 8 JAPRN FIGURE 6.65: NORTH AMERICA sooo ,... .. 1200- libm 650 1100 z C / ACTURL 0 ACTUAL 6EK~~ .9000: emI- 7= - MW cs W .n 7. ..UL TE ,,...../ mm -0 17 1272 1974 1278 lQ8 198 l98 1984 197 172 1974 1976 197 10 198 1W4 FIGURE 6.66: DEVELOPING COUNTRIES FIGURE 6.67: CENTRALLY PLANNED ECONOMIES 75-14000 W0 ACTUAL z \ /' S IMULATED 5500 . p1000 5-4 5000-loom o E 4500 SIMULATED C cRCTU C3 40 00 a: c cn 1000 L0- 119 172 1974 770 H 10 1 1 4 1972 1974 1975 1978 1080 1082 1984 FIGURE 6.68: WORLD NITROGEN PRODUCTION FIGURE 6.69: WORLD PHOSPHATE PRODUCTION 70000 _ B ACTUAL CTU n:lIOOm/ S IMULATED,-/ 350000 4000 M30T00 w 28000 Zo 1970 1972 1974 1978 1978 1980 1982 1984 1970 17 1974 1976 1978 1980 1982 1984 FIGURE 6.70: WORLD POTASH PRODUCTION 30000 z SIM ATED 18000 1C7 24000 * t . ' 1 1970 1972 1974 1976 1978 1980 198 198 - 71 - FIGURE 6.71: NITROGEN WORLD PRICE DYNAMIC SOLUTION TRACKING 500 450 400 :'-SIMULATED a 350 ACTUAL: 300- Li 250- 200 lo 150 - 100 - 50 0 1970 1972 1974 1978 1978 1980 1982 1984 FIGURE 6.72: PHOSPHATE WORLD PRICE DYNAMIC SOLUTION TRACKING 350 300 - ACTUAL 250 SIMULATED 2 00 " I- 150 % 50- 0 1970 1972 1974 1978 1978 1980 1982 1984 - 72 - FIGURE 6.,73: POTASH WORLD PRICE DYNAMIC SOLUTION TRACKING 120 ACTUAL 100 SIMULATED 1-- C-, - 40... 20 0 - - I- . . I 1970 1972 1974 1978 1978 190 1982 f984 - 73 - VII. MODEL PROJECTIONS FOR THE PERIOD 1985-2000 49. The ex-ante simulation was carried out for the period 1985-2000. Most variables were solved endogenously except for the macro-economic variables i.e., GDP, exchange rates and consumer price index. Assumptions for these macro-economic variables were taken from forecasts provided by the World Bank and Wharton Econometric Forecasting Associates. The projections for grains prices, planted area and yields were generated by the Division's grains model to which the fertilizer model is linked. 50. -he projections of fertilizer production, consumption and price are in line with those reported recently in the Division's Report No. 814/86, Price Prospects for Major Primary Commodities. Graphs showing forecast changes in the market shares held by the industrial, developing and centrally planned country groups are presented in Figures 7.1 through 7.8. 51. The share of nitrogen consumption held by the industrial countries constantly declined throughout the 1960s and 1970s--from about 68Z in 1962 to 51% in 1970 and 39% in 1980. This decline was mainly due to the "green revolution" which significantly increased fertilizer use in the developing countries. The developing countries went from a nitrogen consumption share of 16% in 1962 to 40% in 1980. It appears that the trend will continue in the next decade with projected shares of 48% in 1990 and 52% in 2000 for the developing countries. Much the same applies to phosphate and potash consump- tion, with the share of the developing countries in the phosphate market projected to increase gradually to about 39% by the year 2000, and to grow to 18% of total potash consumption. 52. The centrally planned economies of Europe increased sharply their consumption of fertilizers during the 1960s and 1970s. As a result their world - 74 - shares also increased sharply. However, due to the expected slowdown in their agricultural production, their share of world consumption is forecast to decline somewhat over the 1985-2000 period. 53. Nitrogen was produced almost exclusively in the industrial countries only 20 years ago. In 1962, they accounted for a market share of 74%. Their current share of the market has decreased to only 34% and is projected to decrease to less than 25% by the year 2000. The same appears to be happening in the phosphate market. The industrial countries' share of the market fell from 77% in 1962 to 43% in 1985 and is projected to decline to about 26% by the year 2000. The share of the developing countries in the production of these fertilizers increased sharply from about 8% in 1962 to about 20% in 1985. According to the projections, by the year 2000 they will produce about 35% of world nitrogen output and about 40% of world phosphate output. - 75 - FIGURE 7/".1: NITROGEN CONSUMPTION SHARE OF WORLD TOTAL BY MAIN ECONOMIC REGIONS, 1962-2000 30 75 70 INDUSTRIAL COUNTRIES 65 5 60 t0/EVEI-lPING COUNTRIES 55 so LU 0r 45 - ..= = 40 ke 35 30,..... .. . .. .. . .. ...... t........... 30 25 - 15 10 CENTRALLY PLANNED ECON. 5 1962 1956 1970 1974 1978 1982 1986 1990 1994 1998 FIGURE 7.2: PHOSPHATE CONSUMPTION SHARE OF WORLD TOTAL BY MAIN ECONOMIC REGIONS, 1962-2000 80 75 .INDUSTRIRAL COUNTRIES 70- 155 55 DEVELOPING COUNTRIES 50 LU cr 45 a: 40 o@ 35 ------------- ----- -------------- 25 - / 20 15 CENTRALLY PLANNED ECON. 10 4 5- 0 - I I 1962 1 966 1 970 19 74 1978 1982 1986 1990 1994 1998 - 76 - FIGURE 7.3: POTASH CONSUMPTION SHARE OF WORLO TOTAL BY MRIN ECONOMIC REGIONS. 1962-2000 9o 85 80- INOUSTRIAL COUNTRIES 75 70 - e5 - ..CENTRALLY PLANNED ECON. 55- cr: 5 r 45 - ci, 40- 35 - 35 - - - 25 oz 20 15 10 5 DEVELOPING COUNTRIES 0 , 8 l I70 I t I I - ^ t 19682 1 ae6 1970 1974 1978 1 982 1986 1990o 1 994 1 998 - 77 - FIGURE 7,4 : NITPOGEN PRODUCTION SHARE OF WORLD TOTAL 80 BY MRIN ECONOMIC REGIONS, 1962-2000 75- 70 INDUSTRIAL COUNTRIES 60 . 55 - /CENTRALLY PLANNED ECON- 20 - 5 .. . . t .g.*.*. - g--*. r40- U) 35 -3 30 20 15 70 DEEOPN COUNTRIESR CUNR E 5- 0 . I 1962 166B 1970 1974 1978 1982 1986 1990 1994 1998 FIGURE 7.5: PHOSPHATE PRODUCTION SHARE OF WORLD TOTAL BY MAIN ECONOMIC REGIONS, 1982-2000 80 70 .INOUSTRIAL COUNTRIES 60 CENTRALLY PLANNED ECON. 50 Lu cn 40 30 410 DEVELOPING COUNTRIES 0 I 1962 1966o 1970 1974 1978 1982 1 986 1 990 1994 1998 - 78 - FIGURE 7.6:6 NITROGEN PRICE FORECAST (ACTUAL: 1960-85, FORECAST: 1986-2000) 350 300 - C3 o 250 * 200 20 150 - ennL cj, 100 50- 0 I 1960 1965 1970 1975 1980 1985 1990 1995 2000 FIGURE 7.7: PHOSPHATE PRICE FORECFAST (ACTUAL:. 1960-85, FORECAST: 1986-2000) 350 300- 250- H-3 c-:i t= 200 H-- LU 150 100 50 1960 1965 1970 1975 1980 1985 1Q90 1995 20600 - 79 - FIGURE 7.8: POTRSH PRICE FORECAST CACTUAL: 1960-85. FORECAST: 1985-2000) 200 175 - : 150 - C3 cL 125 - L.L 100 75 X,> rn50 / 25- 1960 1965 1970 197E i980 1985 1990 1995 2000 THIS PAGE IS BLANK - 81 - VIII. CONCLUSIONS AND SUGGESTIONS FOR FURTHER WORK 57. This paper summarizes the work that has been done to date on the global fertilizer model. It describes the structure of the model and thle estimated equations, as well as providing statistical measures which allows evaluation of the performance of each equation individually and the model as a whole. 58. The model performs well. However, additional work would provide improved analysis of the nature and characteristics of the fertilizer markets. For example, one improvement would be to estimate the consumption equations on a per acre basis and allow the yield and price of both fertilizers and commo- dities produced determine the level of fertilizer use per acre. 59. Another refinement would be to disaggregate the supply side further and with greater detail for individual countries, especially for the large producers. The model could also be expanded to include trade, and perhaps also stocks in addition to consumption and production. The degree of expansion will be largely determined by data availability. 60. Much additional work would be needed to reach a stage where the fertilizer model could be solved simultaneously with the grains model. Such a model would enable us to examine the interaction between products and ferti- lizers in a more comprehensive way. This exercise would be very difficult to carry out due to its size, however. TIS PG ISBLAZNK - 83 - APPENDIX A ORECAST ERROR STATISTICS 1. Root mean squared error (RMSE) Let Yt be the actual value of variable Y at time t, and let Ybe the simulated value of that same variable at time t, then T T 2 1(y-Yt) (1) RMSE [tl T 2. Average absolute percentage error (AAPE): Under the same definition of Y and Y t T X (Yt- Yd/lYt (2) AAPE =t- and 3. Root mean squared percentage error (RMSPE): will be defined as: T 2 I [(t- Yt )/Yt ] (3) RMSPE = {t=l T , 100 A very useful statistic related to the root mean square (RMS) simulation error and applied to the evaluation of historical simulations (ex-post forecasts) is Theilts inequality coefficient defined as. - 84 - T E~l I Y- [T tE (t ~ t) U T T [ TZ (t) ] + E l ( 2)2] the numerator is exactly RMSE but it is scaled by such a denominator that allows U to always fall between zero and one. As U approaches one the forecast may be considered better. This Theil inequality coefficient can be decomposed into three different elements. It can be shown that the following identity holds (S) (T I (Y^ -y )2 = (Y-Y) + (a -a ) - 2(l-p) a a T s a s a where a and a are the standard deviation of the simulated variable and the s a actual variable respectively, and p is their correlation coefficient. The proportions of inequality can then be defined as: - 2 P (Y-y) The bias proportion u1'- T 2 t=l (a - a )2 The variance proportion T a 2 T IE (Yt t: 2(1-p) a a and the covariance proportion Uc sa T t t t=(l Y - 85 - These three statistics are essential in determining the source of a problem if there is one. um gives an indication of a systematic error since it measures the extent to which the average values of the simulated and actual series deviate from each other. Us indicates the ability of the model to replicate the degree of variability in the variable simulated. Therefore, a large Us indicates that the variability of the actual series is different from the variability of the simulated series, Uc measures the degree of correlation between the actual and simulated series. It represents the remaining error after, deviations from average value and average variabilities have been accounted for. In the case of this model the inequality Theil statistic is calculated based on log-relative changes, which can be explained as follows. Let yt be defined as Y = ln (Y /Y and similarly let Yt be yt = ln (Yt/Yt-). Let Sa and S be the standard deviation of the series Yt and Yt respectively, and let p be the correlation coefficient of these two series; then the ap inequality coefficient U* will be determined by: T U-- [~T-1 t-2 (yt Yt - 1 T T2 T TI 1(Y2 )2] + t I ( t)2) Henc ti 2 of T U t-2 Hence the proportions of inequal.ity U Us and UC will be defined as: - 86 - T whpre Y 3 - Yt - T 1 rt t-2 m T A 2 T T 1 t t t an __a Yt (S2 Whe a aribp cane sinfo po'tv tongtv (rvce esa th rai y t/y is 2eaieadtee'r t(n/o sntdfnd hti wha hs hppne -hnwye)h ube 9.9 ntetal.I hscs When aTvaisabletichange signcefrom poiniequlto pegrieporto vice versa)ethel irrelevant. - 87 - APPENDIX B DATA SOURCES AND DEFINITIONS The primary historical data sources are the World Bank, FAQ and the International Monetary Fund. The world prices that are used are as follows: Nitrogen - Urea, fob Europe bagged. Phosphate - Triple superphosphate, fob US Gulf ports. Potash - Muriate of potash (potassium chloride) fob Vancouver. Phosphate Rock - 72%, fas Casablanca. Rice - US No. 2 long-grained, milled, fob Houston, Aug-July year. Corn - (proxy for all coarse grains) US No. 2 yellow, fob Gulf ports, Oct- Sept year. Wheat - US No. 1. HRW, ordinary protein, fob Culf ports, July-June year. The macro economic data is taken from the World Bank and International Financial Statistics (International Monetary Fund). Income is defined in terms of gross domestic product measured in billions of local currency. The exchange rate is measured in units of local currency per US dollar and the consumer price index (CPI) is expressed as an index with the base year in 1980. The data for the regions was created in a special way. It was aggre- gated from the country data for those variables with common units (hectares, tons, etc.). GDP for a region was obtained by first converting the GDP of all of the countries in a region into dollars using the average exchange rate of 1971-80, and then aggregating it across countries in a region. The regional exchange rate and CPI were obtained also in a two-stage process. First, every exchange rate was converted to an index and then the regional exchange rate was created as a weighted average where the weight was the GDP share of a country of the regional total. - 88 - REFERENCES Barker, R., "The Place of Agriculture in the Developing Countries of Southeast Asia with Special Reference to Fertilizer Use," prepared for the Conference on Economics of Fertilizer Use, Asian and Pacific Council, Food and Technology Center, Taipei, Taiwan, June 1972. Berndt, E.R., M.A. Fuss and L. Waverman, "A Dynamic Model of Costs of Adjustment and Interrelated Factor Demands, with Empirical Applicaition to Energy Demand in U.S. Manufacturing," Discussion Paper 79w30, Univercity of British Colombia, 1979. Boyle, C., "Modeling Fertilizer Demand in the Republic of Ireland: A Cost Function Approach," Journal of Agriculture Economics, May 1982, Vol. 33, pp. 181-192. Choe, B.J., "Estimating a Model of Fertilizer Supply and Price Determination," mimeo, Commodity Studies and Projections Division, Economic Analysis and Projections Department, World Bank, 1986. Epstein, L.G., and A.J. Yatchew, "The Empirical Determination of Technology and Expectations: A Simplified Procedure," Journal of Econornetrics, 1985, pp. 235-258. Griliches, Z., "Distributed Lags, Diasaggregation, and Regional Demand Functions for Fertilizer," Journal of Farm Economics, February 1959, pp. 90-102. _ "lhe Demand for Fertilizer: An Economic Interpretation of a Technical Change," Journal of Farm Economics, Vol. 40, lS58, pp. 591-605. _ _ "The Dern-nd for Fertilizer in 1954: An Inter-State Study," Journal of Farm Economics, Vol. 41, 1959, pp. 377-384. Hansen, L.P., and T.J. Sargent, "Formulating and Estimating Dynamic Linear Rational Expectations Models," Journal of Economic Dynamics and Control, 1980, pp. 7-46. Mitchell, D.O., "A World Grains and Soybeans Model," Division Working Paper No. 1985-77, Comodity Studies and Projection Division, World Bank. Sargent, T.J., Macroeconomic Theory, 1979, Academic Press, New York. Timmer, P.T., "The Demand for Fertilizer in Developing Countries," Stanford Rice Project, Working Paper No. 5, Food Research Institute, Stanford University, 1974. END