Report No. 1586b-ZA E CLiOEY Zambia-A Basic Economic Report Annex 4: A Long-Run Projection Model November 3, 1977 Country Programs Department Eastern Africa Regional Office FOR OFFICIAL USE ONLY Document-of the YWirid Bank This document.has a-restricted-distribution.and im,avobe used-Oy recipients oniv in the performance ot their official-duties. Its.conrtentscma'inot otherw ise,be dislosed sw.ithout World'Bannk authorizaiion CURRENCY EQUIVALENTS Prior to February 1973 February 1973 to-July 1976 US$1 = K 0.7143 US$1 = K 0.643 K 1 = US$1.40 K.1 = US$1.554 SINCE JULY 1976 SDR 1 = K 0.9218 K 1 = SDR 1.0848 US$1 = K 0.8000 (July - December 1976 average) K 1 = US$1.2499 (July - December 1976 average) US$1 = K 0.7952 (January - June 1977 average) K 1 US$1.2576 (January - June 1977 average) FISCAL YEAR January 1 to December 31 FOR OFCIAL USE ONLY A.NEN- 4 A LONG-RUN PROJE-CTION MODEL TABLE OF CON=E1TS Page No. A. INTRODUCTION * ....... ........ ............................ 1 The Model - An Overview ................................ 1 Policy Variables in the Model ............................. 1 B. DESCRIPTION OF TME MODEL ..... ............ ,, 2 C. AN ALGEBRAIC FORKOTATION OF THE MODEL .................. 7 Production Functicons ..8.... ... ,,,,,.,,,,,,,,,,,,,,,,,, 8 Resource Allocaticn . ,. ,. ...... .. , ... ... ...... . ... 9 Personal Income Distribution ,,,,,,,,,,,,,,,,,,,,.,,,,, 10 Personal Consumption and Savings,,,,,,, ,,,,,,,,,,,,, 12 Private Investment: and Capital Accumulation,,.,,,,,,,.,, 13 Government Revenue: *,. . ,, . . . .. 9 . . .* *. 9 a 9 a.9 a9 *9 9.. 5 Public Expenditure: and the Budget Deficit ..,,.,.,,, ,,, 16 The Trade Balance ,,.,,,,,,,,,,,,,,, ,,,,,,.,,,,,,,,,., 17 Mligration and Demc'graphic Changes ,,,,,,*,,,,,,,,,,,,, 17 Solution Procedures ..,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, 19 D. MODEL SM!ULATIONS .....,,,,,,,.,,,,,,,,,,,,,,,,,,..,,,,, 19 This Annex was prepared by William A. McCleary in coll-aboration with Jan Gunning. Xohan Mun.asinghe and ?atrick .Momal also cocitributed to its preparation. This document has a restricted distribution and may be used by recipients only in.the performance Of their.official duties. Its conunts may not otherwise be disclsed 'without Worldl Bank authorization. ANNEX 4 A LONG-RUN PROJECTION MODEL A. INTRODUCTION The Model - An OvervLew 1. Our model for Zambia is a dynamic, dual economy model which enables us to simulate the long-run behavior of the economy for the period 1977-1992 under alte7mative sets of assumptions about the behavior of government policies and exogenous variables. Because of the importance of dualism in Zambia.-both between the urban and rural sectors and within the rural sector, the model attempts to capture the effects of various policies on the long-run development of a high-income modern sector, which consists of a mining sector and an urban goods sector (producing manufac- tures, power, services, etc.), and of a relatively lower income agricultural sector which is itself divided into a traditional subsistence sector and relatively more capii:al-intensive emergent and commercial farm sectors. Alternative sets of government policies (given the behavior of other exogenous variables) will lead to different projected growth paths for aggregate and sectoral product, income distribution, migration, employment, government budgetary balance, the balance of payments and net foreign capital require- ments. Hence our simaulation model makes explicit the different impacts of alternative policies and provides some quantitative basis for choosing between alternative dlevelopment strategies. 2. Variables :Ln the model may be computed both in constant and in current prices: (a) on the real level, the levels of physical production, consumption, imports, exports, migration and employment are determined on the basis of real incomes and relative (or real) prices (i.e., current prices of the various goods within the model deflated by the price index of one of the goods); and (b) conversion from real to current prices enables us to make projections about the government budget, the balance of payments and Zambia's capital requirements. Policy Variables in t:he Model 3. The model contains a number of exogenous variables (e.g., world price projections, population growth) and a number of policy variables which are subject to government control (e.g., domestic relative prices, the growth rate of government consumption, the allocation of government invesrment .to 'various sectors). Among the exogenous variables, the forecasted copper price is.'particularly -important since the .availability of foreign exchange and tax revenues fluctuates widdly with-small changes in copper's price; hence, we will use alternative projections,.together with the Bank's forecast, to:determine how sensitive the budget and.balance of payments outlook is to price assumptions. Among 'available government policy instruments, we ANNEX 4 -2- will pay particular attention to alternative assumptions about: (a) tariff- indirect tax-subsidy policies; (b) the growth rates of government consump- tion and government capital formation; (c) the allocation of government budgetary investment between the agricultural and urban sectors; and (d) wage policy. 4. The Government directly influences the development process through its taxation, pricing and expenditure policies. Its tariff/indirect tax and subsidy policies affect domestic relative prices and hence affect profits and investment rates in the agricultural and urban sectors, sector output, incomes received in the urban and rural areas (hence rural-urban migration) and the pattern of consumption and investment demand. Past government poli- cies have encouraged the production of industrial goods through tariffs while protecting consumers of food by setting food prices below their correspon- ding world prices (and 'subsidizing the price differential for any imports). Such policies have encouraged urban production and raised urban incomes, increased.the drain of subsidies on government budgetary resources, reduced agricultural output and stimulated rural-urban migration. We will attempt' to simulate the effects of alternative pricing policies on the Government's budget, agricultural output and the distribution of real income between the rural and urban sectors. 5. In addition, the Government affects the rate and pattern of dev- elopment by decisions about how rapidly its recurrent expenditures should grow relative to its capital expenditures and by the allocation of its development expenditures between rural and urban areas. In our model simula- tions, we will attempt to determine feasible long-run growth rates for re- current and capital expenditures as well asshow the effects on growth, em- ployment and income distribution of allowing recurrent expenditures to grow more rapidly at the expense of capital expenditures; in addition, we will attempt to show the effects of allocating increasing proportions of the development budget to the rural sector. B. DESCRIPTION OF THE MODEL 1/ 6. The model assumes that the Zambian economy produces three goods: (a) a mining good (mostly copper); (b) a rural good (highly aggregated and largely agricultural); and (c) an urban good (an even more highly aggregated good consisting of the remaining domestically produced goods and services). All three goods are assumed to be tradable and Zambia faces fixed world terms of trade; world prices are exogenously determined and may change from year to year. The world prices of the -three goods are -represented by the 1/ The model presented -here is a -combination of the standard 'TBRD macro- economic model for 'projecting the balance-of 'payments and 'foreign -capital requirements in developing countries and a -revised version of a dynamic simulation model, originally developed by Blitzer (see Development and Income Distribution in a Nal F rv- Dvnan±c Simulation Model for Zambia; IBRD: Development Research Center; January 1975). ANNEX 4 -3- World Bank's forecasi:s for the prices of copper, agricultural food products, and developed countries' manufactured exports (the IBRD Index of Inter- national Prices) respectively. Given world prices, government indirect taxes/tariffs and subsidies determine the domestic producer and consumer prices for the agricultural and urban goods. 7. The three goods are produced by five producing sectors-- a mining sector, an urban sec:or and three agricultural sectors. In order to focus on dualism within the agricultural sector, the rural economy is divided into three producing sectors: (1) traditional agriculture, consisting-of small farmers marketing only a small share of their output; (2) "emergent agriculture" which includes somewhat larger scale farmers who earn cash incomes by marketing over one-half their product; and (3) large-scale com- mercial farming whicha includes state farms and private farms, Zambian and expatriate. 8. The produci:ion of agricultural and urban goods is determined by Cobb-Douglas production functions, the parameters of which have--been estimated- using 1972 data for sectoral output and inputs of labor and capital.l/ The urban sector and commaercial farm sectors are assumed to maximize profits given wages, produce:r prices and the size of the capital stock (which is fixed in any year bui: changes from year to year because of private savings, government investment, depreciation, etc.); profit-maximizing behavior deter- mines the level of output and employment in both sectors. Emergent farmers are assumed neither to hire labor nor to seek outside employment; their numbers are the result of natural increase plus "migration" from the tra- ditional sector. Hence, given the capital stock and labor force in emergent agriculture, emergent sector agricultural output is determined. The tra- ditional sector labor force is the residual between the total agricultural labor force and the 'Labor absorbed by the emergent and commercial agricultural sectors. Given the craditional sector's capital stock and labor force, that sector's output is determined. In mining, output is assumed to grow exogenous- ly at the rate projected by the Basic Economic Mission - i.e., about 1 percent p.a. until 1983 and zero percent thereafter 2/, given the projected level of output in any year anid the assumed increased in the productivity of mining workers, the required inputs of capital, labor, and intermediate goods can be determined. While agricultural labor is assumed to'be fully employed, open unemployment is allowed for in the modern sector; urban unemployment is the difference bez:ween the urban labor force and the level of employment in the urban and mining sectors. 9. The model has seven :income -and consumption classes- five working classes -(three agriciLltural, one urban and one :mining) and two profit earning classes. Regarding ;:he distribution of 'income, it is useful to consider 1/ For data on sectoral output -and inputs of capital and labor, see Statistical Appendix, Tables, .2.02, -2.09 and 5.01 2/ See Main Report, Chapter II, para. 2.53. - 4 - ANNEX 4 wage and profit income separately. The real wages of commercial farm and urban workers are assumed to grow as rapidly as their productivity (3.5 percent p.a.). The productivity of mining workers is assumed to continue declining at the rate of about 2.5 percent p.a. leading the Government and mining companies to attempt to hold real wages in check; real wages, therefore, are assumed to remain constant. The total wage income of commercial farm, urban and mining workers is the amount of em- ployment times their respective wages. Urban and mining workers also obtain income in the form of interest on their accumulated savings; the interest rate is-assumed to be 5 percent. Traditional and emergent farmer "wage incomes".are equal to total product (since workers own the capital stock, all the returns to capital and labor accrue to them). The goverment and Zambian and foreign profit earners own capital in the commercial agri- cultural, urban and mining sectors. The remainder of the value of gross output at factor cost accrues to the owners of capital in the three sectors according to their shares of ownership. On the basis of expenditure functions, estimated on the basis of the 1972-73 urban and rural household income and expenditure survey in Zambia, the after-tax incomes of each of the seven groups can be spent on consumption (in the form of urban or agricultural goods), or saved or, in the case of expatriates consumed, saved or repatriated abroad. These expenditure relations determine the per capita consumption of agricultural and urban goods in each class as well as per capita saving; they can be summed over the population in all income classes to determine aggregate private consumption of agricultural and urban goods, aggregate private savings and foreign remittances. 10. The government derives income from mining taxes and dividends, personal and company taxes and indirect taxes. The total income tax bill- personal and company--and the direct tax bill for each income group can be determined by applying company tax rates to the returns to capital in the commercial agricultural, urban and mining sectors (with mining subject to a mineral income tax in addition to the company income tax) and income taxes to the gross personal incomes of four of the seven income classes (the three agricultural working classes are assumed to be exempt from income taxation).l/ Indirect taxes are in the form of tariffs and sales taxes on the urban good creating a differential between the world and domestic producer prices and between the domestic producer and consumer prices. In a similar fashion, the goverment pays subsidies on the importation and consumption of the agri- cultural good; .the subsidy on imports arises because domestic producer prices have been fixed at levels below world prices and a further subsidy to consump- tion because domestic consumer prices are maintained at levels below domestic -producer .prices. Govermment budgetary expenditures consist of consumption 1/ The assumption that total .incomes in-traditional and emergent agriculture and wage incomes in commercial agriculture are exempt from income taxation is justified by the well-known difficulty of enforcing direct taxation .in rural areas In developing countries -and by the fact that income per worker in these areas is too low to be subject to taxation under Zambian tax laws. - 5 - ANNEX 4 and investment of the urban good and are assumed to grow at exogenously determined rates; in our "basic case" below the exogenous growth rates are set at 3.5 percent p.a. in real terms. Because there is no link between government expenditures and net revenues, it follows that the government's budget need not be balanced in any year (in real or in nominal terms). 11. From the fcregoing, it is possible to 4etermine the foreign trade balance in real terms. All of mining output in any year is assumed exported at a fixed real price (equal to the Bank's forecast of copper.prices in current terms deflated by the Bank's Index of International Prices with 1972 = 100). Exports or imports of agricultural and urban goods result from differences between domestic supply and demand. Given the producer prices of agricultural and urban goods, the level of private demand for agricultural and urban gooas is determined by the expenditure functions of the seven income classes; savings generated in any class are assumed to lead to a demand for capital goods (which are produced by the urban sector or imported). To private demand for urban goods must be added the Government's budgetary consumption and investment expenditures which are assumed to be on the urban good. Any imbalance between production and private plus government demand for agricultural or urban goods would lead to exports or imports of that good; in all of the simulations of the Zambian economy made in this Annex, the country will continue to be a net importer of both urban and agri- cultural goods for the next decade or more. 12. Up to this point in our description of the model, we have been con- cerned with statics--the determination of sectoral output and income distribu- tion, employment and unemployment, the balance of payments and the government's budget in any year. Cver time, such magnitudes would be expected to change because of growth of the sectoral capital stocks and labor forces and tech- nological change. 13. The change in the size of the capital stocks in the agricultural and urban sectors between any two years depends upon the allocation of private savings (Zambian and expatriate) to the sector, government reinvestment of profits generated fromn its ownership of capital and the allocation of govern- ment budgetary investment and the rate of depreciation on capital in the sector. The savings of traditional and emergent farmers is reinvested entirely in those two sectors. The savings of Zambian and expatriate profit earners out of profits from capital owned in the comercial agriculture and urban sectors will be reinvested in proportion to profits they earn from the two sectors - e.g., if Zambian capitalists earn 10 percent of their profits in commercial :agriciilturxe and the remainder from investment in the urban sector, 10 percent of their-savings would'flow -to agriculture. IThe profits accruing to public enterprises in commercia.l-agriculture and thelurban sector are reinvested in those sectors. 'In addition, in our "basic case" below, 80 percent of government budgetary investment is allocatedlto the urban sector and 20 percent to the agricultural sector;-the budget allocation to the rural sector is in line wit1h past shares if due account is taken not only of agri- cultural investments but investments in roads, schools, health facilities, -6- ANNEX 4 etc. which also benefit the sector. Investment in mining is handled some- what differently than that in other sectors: the required level of net investment in any year is dictated by the exogenously given rate of growth of output and gross investment as net investment plus depreciation. Gross investment in mining is financed by the government and foreign shares in after tax profits, depreciation flows and (if necessary) borrowing. 14. In order to solve the model in any year, the total urban and agri- cultural labor forces and the number of emergent farmers must also be known. In the absence of migration, the- agricultural and urban labor force would be growing at 3 percent p.a. (i.e., the same rate as total population). The model provides for two types of "migration": (1) traditional farmer-urban migration which reduces the growth of the agricultural labor force and in- creases the growth of the urban; and (2) traditional farmer-emergent farmer migration which would leave the total -agricultural labor force unchanged. Both types of migration are dependent upon economic and social factors. The rate of rural-urban migration is postulated to be greater, the greater is the differential between urban and rural incomes and the lower is the- urban unemployment rate (i.e., a Harris-Todaro type function). Rural-rural migration does not necessarily involve physical movement but rather a trans- formation of traditional into emergent farmers through adoption of more pro- ductive techniques and the more rapid accumulation of capital. The rate of "rural-rural migration" depends not only upon the relative incomes of emergent and traditional farmers but also upon the absolute level of real incomes of traditional farmers (as the real incomes of traditional farmers become greater, their capital accumulation becomes more rapid and the possibility of market- ing surplus production becomes more attractive). 15. The above flows of income, product and expenditures have been deter- mined in real terms; that is, all prices whether domestic or world prices, have been expressed in real or relative terms in that they have been deflated by the Index of International Prices. To convert all the variables expressed in real terms to current terms, it is merely necessary to multiply each by the Index of International Prices. The resulting series of world prices reflect the Bank's forecasts for copper, exports of manufactures from the developed countries (the urban good), and agricultural goods in current prices out to 1985. 1/ These world prices are linked to domestic producer prices and consumer prices by the system of tariffs, excise taxes and sub- sidies outlined above. 16. The conversion of model from constant to current prices provides 1/ World Bank Commodity price projections do not extend beyond 1985. There- fore, we have assumed that, after that year, the world relative prices of agricultural and urban goods-remain unchanged. However, world copper prices are assumed to increase at a 1.3 percent p.a. in real terms (when deflated by the Index of International Prices), the projected long-term trend increase in the real cost of producing the world's copper. ~ 7 ~ ANNEX 4 a linkage between the real growth and structural transformation of the economy and the financial aspects of the government's budget and the balance of payments and allows a connection with the Bank's Debt Reporting System. The Government's budgetary deficit (surplus) is the difference between its revenues (net of subsidies) and its recurrent and capital expenditures, all expressed in current ,rices. A deficit would provide a demand for foreign financing additional to the (net) financing required to meet the net flow of disbursements and service payments on past accumulated debt; conversely, budgetary surpluses would reduce the required (net) foreign financing. 17. The current account balance is derived from imports and exports- in current prices, neir interest consisting of earnings on foreign exchahge reserves minus intere:.t payments on debt outstanding prior to the beginning of the projection perLod and on newly accumulated debt, and the transfers of foreigners on their earnings of wages and profits. 18. With respeci: to the capital account, we have projected World Bank - commitments for 1977-92 by using the 1977-81 lending program and assuming that the Bank's program remains constant in real terms thereafter; aid from other sources has beeni projected an the assumption that it remains at its 1975 level in real terms. Further, it is assumed that Zambia's net foreign asset holdings will increase by a fixed fraction of any increase in imports; since the level of net: foreign assets is currently negative, we have assumed this fixed fraction to be 60 percent until such assets have accumulated to a level equal to 25 percent of imports at which point the fixed fraction adjusts so as to maintain that level. Given the projected current account balance, the flows of disbursements and amortization payments from loans incurred prior to 1977 (obtained from the Bank's Debt Reporting System) and from projected new coumitments by the World Bank and other aid agencies, and the assumed build-up in net foreign assets, the model then will calculate the residual required capital inflow. We have assumed that this additional capital is available on terms similar to those that Zambia has been able to obtain in the recent past (i.e., with a grant element of about 20 percent). The behavior of the required aggregate capital inflows will be an important indicator of the underlying realism of the model: if the required flows are unrealistically large compared to past flows or result in too large a burden of debt servicing, it would be a clear indication that some of the assumptions we have made about parameter values or the behavior of the exogenous variables are unreasonable and that adjustments should be made (e.g., reductions in the assumed growth rates for government expenditures, tax increases, etc.) C. AN ALGEBRAIC FORMU{LATION OF THE MODEL 19. .In -section .13, we -described -the if orulation of 'the dynamic simula- -tion-model in general terms, -focusing-on it-s u2derlying rationale. In this section, specific algel,raic equations-wi11 be -presented with a minimum of coment. In Table l, iiectoral and.income class indices are presented 1/ 1/ The subscript t is sometimes used to denote-the time period. It always refers to the year relative to the based year (1972); e.g., for 1977, t - 5. Where the meaning is clear from the context, the time subscript is dropped. ANNEX 4 Table 1: SECTORAL AND INCOME CLASS INDICES Number Producing Sector Income Group I Traditional agriculture Workers in sector 1 2 Emergent agriculture Workers in sector 2 3 Commercial agriculture Workers in sector 3 4 Urban Workers in sector 4 5 aining Workers in sector 5 6 Zambian profit earners 7 Foreigners 8 _ Government Production Fudnctions 20. Cobb-Douglas production functions are utilized to relate inputs of labor and capital to output of agricultural and urban goods. Thus: cc xxi 4 i 1 + gi)t Li ,for i-l,...,4 (1) where XX!ty Ki'ti and Li,t refez to output, capital input, and labor inputs in sector i in year t. At is a scaling constant and gi the rate of growth in labor productivity for sector i. Since we have assumed identical produc- tion functions for all three agriculture sectors, Al - A2 - A3 ,c(1l 'C mG =dg A- ':2 " 3' 21. Wlthiu .min.In , labor, capital, and intermediate inputs vary with output leveLs. Thus: _9 ANNEX 4 5,t a1 5,t (2) L a2 x and (3) and intermediate inputs are INTMG a3,tXX5,t (4) Here, al, a2, a3 t are the coefficients of a Leontief-type production process, and g. is the annual rate of increase in the productivity of mining workers. a3 is allowed to grow according to a3t' (1.025)t a3,0 to reflect the fact that intermediate inputs are increasing relative to output due to declining ore grades and greater depths in mining 1/. Resource Allocation 22. In the shor,:-run, physical capital is fixed in each sector. Thus, the only resource allocation problem within a given year involves labor. The total supply of labor in the rural and urban sectos is also fixed in the short-run. 23. In the urbani sector, we assume that competitive forces lead pro- ducers to maximize profits. Thus, labor is hired until the value of its marginal product equal.s its fixed nominal wage: P4 _ 4 W (5) This in turn can be solved for L4 as a function of K4, W4 , and P4 Since L5 is determined through equations (2) and (3) the urban unemployment -rate can be computed residually as: 1/ See Main Report, Chapter. II, paras. 2.50 .and 2.51. - 10- ANNEX 4 u = Lu - L4 - L5 (6) L U where u is the rate of urban unemployment, and L is the total urban work force the size of which in any year is u determined by equation 26 below) 24. Within agriculture, the labor allocation works in a similar fashion. Commercial farms act as if they maximize their profits, just like firms in the urban sector. Thus, p 3x3 , W3 (7) -3 3. = L3 can then be solved for as a function of P3 , W3 , and K3 . Since we have assumed that emergent farmers neither hire outside labor nor compete themselves for jobs in commercial agriculture, L2,t is fixed in each year. Since there is no open unemployment in the rural sector, L1 is determined residually: Li = La L2 L3 (8) where La and L2 are predetermined by prior year behavior patterns (see below paras. 39 and 40). Personal Income Distribution 25. Once factor allocations and output levels are known, the consumption of per capita disposable income for each group is straightforward. For traditional and emergent agriculture, all returns to capital accrue to the farmers (or workers) themselves. Thus: C. (1 - tj) q; a Xj , for i = j = 1,2 . (9) L. Here, C: represents net per capita income, tj the average tax rate, and q. the reciprical of the dependency ratio, all for income class j. For - 11 - ANNEX 4 salaried workers, we have: C (. - t3) q3 W3 (lOa) C4 - (2. - t4) (q4 W4 + r S4,t) (lOb) c5 (1-ts) (q5 W4 + r S5,t) (lOc) where r is the fixed rate of interest (assumed to be 5 percent), Si t is the cumulative savings per capita in income class j from period 0 to the end of period t, and qj is the reciprocal of the dependency ratio in class j (hence qjWj is wage income per capita). Thus, while the savings of income classes 1 and 2 are directly reinvested in-those sectors and workers in commercial agriculture (class 3) are assumed to save nothing, workers in the urban (class 4) and mining (class 5) sectors do save, lend their savings to the Zambian profitearning class and in return are paid a fixed rate of interest. 26. Net returns to capital in sectors 3, 4, and 5 are divided between the government, foreigne3s and Zambians according to the share of the capital stock each owns in the sector. Net returns are calculated in the following manner in commercial agriculture and in the urban sector. Pri =P - Wi Li - FWi - di P4 Ki (lla) where Pri is profits,, FWj is the fdreign wage bill, di is the depreciation rate, and Ki is the real capital stock in sector i and i = 3, 4. And in the mining sector Pr5 P5 3X5 - W5 L5 - FW5 - d5P4 K5 - P4. INMrM Cllb) where P4. INEMG is intermediate inputs at current prices. - 12 - ANNEX 4 And then net profits are NPri = Pri (1 - txi) + txi P4 di Ki (llc) NFr5, Pr5 (1 - tx5) + tx5 P4 d5 K (lid) where txi is the corporate income tax rate in sector i and tx5 is the combined mineral tax and income tax rate on mining income. Net profits (after taxes), Ri1;. are divided among the owners of capital in the sectors according to: R NPr i,i (lie) i1 i i,j .i ~Ki where K is the amount of capital in sector i owned by class j and i = 3,4,5 and j = 6,7,8. Then, to obtain disposable income per head for income classes 6 and.7, we must remove taxes, the interest paid to workers for savings in classes 4 and 5, and (in the case of expatriates) foreign remittances. Thus C6 ' (1 - t6) (R3,6 + R4,6 - r N4 S4,t - r N5 S5,t)/N6 (12a) and C7 = (1 - t7) (R3,7 + R4,7 + FW3 + FW4 + FW5) (1 - REM 4N7 (12b) where the Ni are the number of persons in income classes 4,5,6, and 7 and REM is the foreign remittance rate out of after-tax'income. Personal Cousumption and Savings 27. Consumption and. savings -patterns for .each income group are determined using an extended linear expenditure system. Thus: ci=j Pi Yi,+ (1-- E ) Cj - a ,j i = a,u jndj - 1,.... '7 (13) - 13 - ANNEX 4 In (13), Ci is expenditures by a-member of class j on consumption good i;Yi j is the m:Lnimal consumption by members of group j on good i; 11 is the marginal propensity to save for group j; . and are the proportions according to which marginal income devoted to consumption is divided between agricultural and urban goods (A,j +ft,j = 1); and Pi is the consumers' price of good i. Completing the system, we have: S = - L ICj - Pa Ya,j j Pu Yu,jJ where (14) si is savings by member of group J. Total expenditures on each good are easily calculated by multiplying the average expenditures in each income group by the number in that group, Private Investment and Capital Accumulation 28. Although we. have already shown how total savings are generated, we must also allocate. savings between sectors; in other words, compute next year's capital stocks by sector of use and by ownership group. First can- sider the savings of small farmers, S1 t and S2t . The total savings in classes 1 and 2, Nl Si,t and N2 S2,t (where N. is the number of persons in the i th class), is reinvested in sectors 1 and 2, except for capital transfers associated with migration (as shown paras. 40 and 41). Thus: Ki i,t+l (1 - di) Ki,i,t + i,t i't - capital transfers, u,t for i = 1,2 (15) Here, K i,it+l is capital stock in sector i, owned by group i, available in year t+l. 29. 'Grsoup 6., Ziambian -prof itearners., dcivide .their savings and the savings loaned:to-then 'by .urban..and-mining workers between the commercial agriccultural and .urbam sectors I.n the same 'proportions as their profits accrue from the two sectors: - 14- ANNEX 4 Ki,6,t+l (1 - di) Ki,*6,t +[N4 S4,t + ;:S ,t + N6 S6, [ ~~Pu, t .rit Ki,6,t i Tri,t K,,6,tl (16a) i = 3 and Ki,7dt+l (1 di) Ki,7,t + S7,t N7,t ri't Ki,7,t l (16b) u,t z ri t Ki,7,t where ri,t is the rate of return on capital in sector i and i = 3,4. 30. Mining output is assumed to grow at an exogenous rate and the capital stock in mining must grow at the same rate. The capital stock in mining is owned by the government and foreign interests, who finance the necessary capital formation out of after-tax profits. Foreigners are assumed to be willing to maintain their share of the total capital stock by reinvesting all of their share of after-tax profits if necessary. However, if maintenance of their share in the capital stock requires an amount of investment greater than their share after-tax profits, the foreign share- holders are assumed to be unwilling to finance the excess through capital inflows from abroad; in this case, the government must increase its invest- ment in order to achieve the required growth of the capital stock. Hence, we have K5,7,t+l = (1 + gm) K5,7,t (17a) K5,8,t+l - (1 + gm) K5,8,t (17b) if R5 7,t > (gm + d5) K5,7,t or K5,7 t+1 = (1 - d5) K57t + R (17c) P4 K5,8 t+ (1 + gm) K5t - K (17d) 5,7,t < (gm + d5) K5,7,t where gm is the planned exogenous growth rate of mining - 15 - ANNEX 4 Government Revenue 31. The public sector obtains revenue through (1) its ownership of capital assets in sectors 3, 4 and 5; (2) direct taxes on personal and profit incomes; and (3) indirect taxes on consumption and imports. Government profits from its ownership of capital in commercial agriculture and the urban sector are assumed to be reinvested directly in those sectors. Hence budgetary revenue from direct sources is: Direct Revenue = R5,8 + j Nj tx Pri (18) - GCAPY + DIRTAX + PROTCA + PROTU + PROTM where yj is income per person in the j th income class, GCAPY is government after-tax capital income from mining, DIRTAX is personal income taxes (and fees, fines, etc.) paid by income classes 1...7 and PROTCA, PROTU and PROTM are profit tax revenues from commercial agriculture, the urban sector and mining. 32. In order to compute revenue from consumption taxes, we first compute the total consumption of the urban and agricultural good in physical terms, defined as Ci i Cl Ci,j N for i = a, u and then for good i, consumption tax revenue is CONTAX 'Pi - Pi) Ci (19) where and Pi are the prices of the i th good gross and net of tax repectively. 1/ 33. Revenue fromL tariffs is equal to the difference between world and domestic prices (i.e., the kwacha tariff per unit) times the difference between total domestic. consumption and investment demand (excl. government budgetary demand which is not subject to tariff) and domestic production. .1/ Note .that for agricultural goods Pi - Pi 1is negative reflecting the fact that the consumption of food -is subsidized. In the case of agri- cultural goods, equation (19) should read CONSUB 0 (Pa - Pa) Ca - 16 - ANNEX 4 To keep food prices lower, the Governaent sets the domestic producer price of agricultural goods lower than the world price and the price differential leads to a government subsidy of food imports. Hence we obtain tariff revenues from imports of the urban good T TARINC= (PU - P (C + S Nit + INTMG - XX4) (20a) u,t tariff revenues from imports of agricultural goods - TARSUB= ( a la) (Ca XX1- 2 -X3) (20b) Where TARINC and TARSUB are the tariff rWrenues and subsidies on the import of urban and agricultural goods and Pa, Pa and Pu, ;u are the domestic and world prices of agricultural and urban goods respectively. Total government revenue is the sum of equations 18, 19, 20a and 20b. Public Expenditure and the Budget Deficit 34. Government budgetary spending for consumption and investment is assumed to be exogenously determined and can readily be altered within the model to simulate the effects of alternative policies. Specifically, alter- native assumptions are made about (1) the growth rates of government budgetary consumption and investment expenditures and (2) the allocation of budgetary investment among the 3 agricultural sectors and the urban sector. Thus real government consumption 1/ and investment are assumed to be growing at the rate of 3.5 percent a year (in our "basic scenario") as in cg,t = (l.035)Cg,t-1 (21) and Ig,t = (1.035) Ig,t_l (22) Government investment at time t is allocated-among the agricultural and urban sectors as: Ig,t 1-l b GOINV'V where bl 'i - (22a) 1/ The assumed growth rate is for government recurrent expenditur.es exrlusivve of subsidies and debt servicing. 'Subsdiesiasre computed along with -other indirect taxes and are treated as negative revenues. 'Debt servicing -is handled separately in the model along with o6ther capital account tran-sactions. - 17 - ANM 4 35. The budgetary surplus or deficit in current prices can be calculated by conver-:ing government recurrent and capital expenditures from real terms to current prices (by multiplying the price index for urban goods) and sub:racting total government revenues as determined in paras. 31-33 above. The Trade Balance 36. The adjustment between domestic production and demand is through world trade. An excess of domestic demand over domestic production of the agricultural or urban good results in imports and conversely. Hence real agricultural imports are MAR1 4 Ca,j 'a - CK + XX2+X3) (23) The total demand for urban goods is the sum of the consumption demand of the seven income classes, government consumption, private and public investment in the agricultural and urban sectors, government budgetary investment in the agricultural and urban sectors, intermediate inputs into the mining sector and government and foreign investment in mining. Real imports of the urban good are the difference between total demand and domestic production, XX4, as in MURB =i Cuj N A + S N Pu + (R3,8 + R4,8YIFU + Ig + INTMG + (Gm + d5) K5,t-1 - XX4 (24) 37. Exports consist entirely of mining goods and the entire production of the mining sector is assumed to be exported. Hence real exports equal XX5. 38. The trade surplus in current prices is, therefore: XP5x5 a iMAGR - P MURB (25) with Pi denoting the world price of the i th good. Migration-and -emograohic Changes 39. The .composition and amount of prsoduction of agricultural and urban goods-varies over time -because of the increase of labor productivity, the accumulation of capita l, growth of:-the labor force and migration. The role of the first two factors have been shown above in paras. 20, 28-29, and 34. Here we will discuss the role of labor force growth and migration. Let - 18- ANNEX4 LU t be the total urban work force in year t. Growth in Lu depends on the rate of population growth as well as on rural-urban migration, Mlt. Thus: Lu,t+i (1.03) Lu,t + ML,t and (26) by symmetry, the growth in the total agricultural labor force, La, is: La,t+l ' (1.03) La,t - Ml,t . (27) Rural urban migration depends upon the ratio of expected urban income to income in traditional agriculture and the urban unemployment rate. Ml,t f (1 urban unemployment rate) W4 _ - 1) (urban unemployment rate Li Pa X, / L, 1 (28) where 01 and 42 are estimated positive parameters. 40. The number of workers in emergent farming, sector 2, depends also on population growth and the transformation rate of traditional into emergent farmers, defined as M2,t . Thus: L2,t+l (1.03) L2,t + M2,t (29) The rate of transformation, M2,t , depends on real income levels in sector 1 and 2. That is: M + (a L1t 1 + a / (Pa Xi L (30) where e11,2, and 93 are estimated parameters. 41. Finally, as part of this transformation process, the traditional farmers who become "emergent" take with them their capital stock. We assume that it is always the richer traditional farmers who engage in this process, and--thns that their average capital/labor ratio is twice the average throughout the whole traditional sector. Hence - 19 - ANNEX 4 K capital transfers - 2 ;l,t m (31) Solution Procedures 42. The model can be solved in a segmental manner starting with the base year and working forward. Once the following parameters and variables are known, equations (1) - (31) can be solved: K1 t,... ,K5,t, La,t, Lu,t, L2,t W3 t3 W4 t, W5,t, world prices,consumer prices, and producer prices. The soluiion ol these equations in turn determines the size of the sectoral capital stocks and the agricultural and urban labor forces in the following year; with these-magnitudes and exogenously given prices and real wages, the model can again be-solved in that year. And so forth. D. MODEL SIMULATION', 43. In tables 4 through 11, the results of eight model simulation runs showing the effects of alternative assumptions about key policy para- meters and exogenous variable are presented. The "basic scenario" (table 4) assumes (a) government real recurrent and capital expenditures grow at 3.5 percent p.a.; (b) the Government allocates 20 percent of its capital budget to the agricu:!tural sector and the remainder to the urban sector; and (c) the Government manipulates tariffs and subsidies on the production and consumption of agricultural and urban goods in such a manner as to keep the domestic terms oi trade unchanged. The first assumption represents a departure from past policy while the latter two are approximations of past policies. A 3.5 perc:ent growth rate for government real capital expenditures is much more rapid tILan the Government has been able to sustain in the recent past; government real capital expenditures have stagnated since 1970.1/ However, we feel that the assumption of future growth can be justified by projections for improvements in the terms of trade which will increase foreign exchange and budgetary resources and by recent government decisions to plan for steadier long-term growth in budgetary expenditures. 44. With respect to the second and third major as'sumptions of the "basic scenario", the 20 percent allocation of the capiltal budget to agri- culture is in line with past shares if due account is taken not only of agri- cultural investments but also of investment in roads, eaucation, health, etc., which also supports the sector. IBRD price forecasts project an increase in the price of agricultural goods relative to;manufactured goods (as compared with the '197.2 base year) by 1980 and 1985.' l/ Under these 1/ See Main Report, Chapter III 2/ Since IBRD projections do not extent beyond 1985, we have assumed that there is no further change in relative prices of agricultural and manufactured goods after that date. - 20 - ANNEX 4 circumstances, maintaining the domestic terms of trade constant requires growing subsidies on the import and consumption of agricultural goods. Putting the same point a slightly different way, to keep the domestic terms of trade from turning in favor of agriculture as world food prices increase relative to the world prices of manufactured goods, the Government must adopt policies which increase the differential between the domestic and world prices of agricultural goods over time. 1/ 45. In the remaining tables (5 through 11), alternative simulation runs, where the values of one or more key policy or ezogenous variables have been changed as compared with the "basic scenario", are presented. Table 2 summarizes the differences in assumptions and in results as compared with the "basic scenario"; these results are discussed more fully in the Chapter VI of the Main Report. In Table 3, the symbols for the model variables are listed, and, defined. 1/ Alternatively, the Government could maintain the domestic terms of trade unchanged by raising tariffs on -imports of the uzban good. Because Zambia has traditionally relied heavily on food subsidies, we have chosen to emphasize this policy tool. - 21 - ANNEX 4 Table 2: SUMMARY OF ALTERNATIVE SIMULIATION RUNS Major Differences from Table Number Variables Changed Basic Scenario 5 Copper prices 5 percent lower Value of exports lower and required capital inflows larger; debt service larger. 6 Copper prices 10 percent lower Value of exports lower and required capital inflow larger; debt service larger. 7 Growth of gov't real recurrent Slower growth of the agricultural expenditures (4.2 percent p.a.1 and urban sector and higher urban and of government real capital unemployment. expendituees Q percent p.a.) 8 Proportioni of government capital More rapid growth of agricultural expenditures devoted to agri- output and slower expansion of culture Uicreased from 20 to 30 food imports. Slower migration. percent during 1977-1981. Slower urban growth and higher urban unemployment. 9 Proportioln of government capital Slower agricultural growth and expenditures devoted to agri- more rapid food import expansion. culture reduced from 20 to 10 More rapid urban growth leading percent during 1977-1981. to lower urban unemployment despite a higher rate of rural- urban migration. 10 Elimination of subsidies on the Aggregate growth accelerates due import and domestic consumption to more rapid expansion of agri- of agricultural goods 1977-1981. cultural and urban sectors. Food Budgetary resources released by imports virtually stagnate. Per subsidy elimination devoted to capita incomes higher in rural miore rapid real growth 6f re- areas and lower in urban areas. current expenditures (5.5 percent Rates of rural-urban migration p.a.) and capital expenditures and urban unemployment lower. (6 percenl: p.a.) 11 ("Alternative Budgetary recurrent expenditures Faster agricultural growth com- Scenario") grow at 5.5 percent p.a. and pensates for slower urban expan- capital expenditures at 6-percent sion and aggregate growth accel- p.a. Share of budgetary capital erates.i Agricultural imports expenditure allocated_to agri- declineiand after 1990 Zambia cuiture grows,:from'20.to":30 becomes net exporter of food. Per- percent 1:977-1981. ETim.ination capita incomes in rural areas of budgetry vsubsidies ..for food -raised relative to urban areas import andl -consumption. but turban incomes per capita con- tinue to grow more rapidly than -rural -per capita incomes. Rural- urban migration and urban un- employment rates are lower. -iNNtA 4 - 22 - Table 3: LIST OF SYI2OLS - ZAMBIA LONG-RUN PROJECTION XODEL Number Neumonic Description 226 GDP Gross Domestic Product, constant value 228 TTADJ Terms of Trade adjustment factor 237 GDY Gross Domestic Income, constant value 185 M Net Imports, goods and NFS, constant value 162 X Exports of mining output, constant value 229 XTTADJ Exports of mining output, adjusted for terms of trade 238 RG Resource Gap 239 C Total (private and public) consumption, in constant prices 236 I Total (private and public) investment, in constant prices 241 GDS Gross Domestic Saving, in constant prices 242 FSY Net Factor Service Payments, in constant prices 243 NCT Net Current Transfers, in constant prices 245 GNS Gross National Savings, in constant prices 470 MAGR Imports of Agricultural Goods, in constant prices 471 MURB Imports of Urban Goods, in constant prices 298 vX1 Value added in traditional agriculture, in constant prices 299 XX2 Value added in emergent agriculture, in constant prices 300 XX3 Value added in commercial agriculture, in--constant prices 301 XX4 Value added in the urban sector, in constant prices 302 XX5 Value of output in the mining sector, in constant prices 303 Kl Capital Stock in traditional agriculture, in constant prices 304 K2 Capital Stock in emergent agriculture, in constant prices 305 K3 Capital Stock in commercial agriculture, in constant prices 306 K4 Capital Stock in the urban sector, in constant prices 307 K5 Capital Stock in mining, in constant prices 308 LI Labor force (in thousands) in traditional agriculture 309 L2 Labor force (in thousands) in emergent agriculture 310 L3 Labor force (in thousands) in co mercial agriculture 311 L4 Labor force (in thousands) employed in urban sector 312 L5 Labor forec (in thousands) employed in mining 479 UNEMP Percentage of urban labor force unemployed 480 Ml Rate of traditional farmer-urban sector migration (as a percentage of LI) 481 M2 Rate of traditional farmer-emergent farmer migration (as a percentage of LI) 164 EXPORT Exports of mining goods, current prices 187 IMPORT Net Imports of goods and NFS, current prices 208 RESBAL Resource balance, current prices 205 NETFSY Net factor service income, current values 194 NETTRN Net transfers, current values 209 CU BAL Current account balance, current values 98 DETPUB Gross disbursements on ppublic borrowing, current values 104 AMKIUB Amortization of public borrowing, curret values 109 NETPUB Net transfer on public borrowing, current values 201 CEGRES Change in reserves, current values 202 RESLEV Level of reserves, curr-ent values 276 .PROTCA Profit tax revenues from commercial .agriculture, current values - 23 - ANNEX4 Number Neumonic Description 277 PROTU Profits tax revenues from urban sector, current values 278 PROTM Profits tax revenues from mining, current values 482 PROT Total profit tax revenues, current values 279 CONTAX Consumption tax revenues, current values 280 CONSUB Consumption subsidies (food), current values 281 TARINC Tariff revenues, current values 282 TARSUB Import subsidies (food), current values 483 DIRTAX Revenues from personal income taxes, fees, fines, current values 485 GCAPY Government after-tax capital income from mining, current values . 426 GOVIN Total government revenue from taxes and mining capital income, current values 427 GCONS Government recurrent expenditures', current values 285 GINVG1 Government investment in traditional agriculture, current values 286 GINVG2 Government investment in emergent agriculture, current values 510 GINVG3 Government investment in commercial agriculture, current- values 511 GINVG4 Government investment in urban sector, current values 289 GINVG5 Government investment in mining current values 405 WPRA World price of agricultural goods 406 WPRU World price of urban goods 407 WPRM World price of copper 325 P3 Domestic producer prices of agricultural goods 326 P4 Domestic produter price of urban goods 327 P5 Domestic producer price of copper 408 CONPA Consumer price of agricultural goods 409 CONPU Consumer price of urban goods 188 XPRICE Export Price Index 189 MPRICE Import Price Index 190 TTINDX Terms of Trade Index 254 M/GDP Imports to Gross Domestic Product Ratio 255 X/GDP Exports to Gross Domestic Product Ratio 256 C/GDY _-Consui'mption-to Gross Domestic Income Ratio 257 I/GDY Investment to Gross Domestic Income Ratio 258 DS/GDY Domestic Savings to Gross Domestic Income Ratio 259 NS/GNY National Savings to Gross National Income Ratio 260 M-EIAS Elasticity of Imports with respect to GDP 261 GNS-MR Marginal Gross National Savings Rate 262 ICOR Incremental Capital-Output Ratio 263 .RESL/M Reserves to-imports rati :264 'DSRADJ Debt -service -ratio suet ,.* tr I 9S t oo', w I g. tI iti Lt 11 .,l t4 ~9 ~ # c i.t1 f I e t* Aut t tu* l o tr teu *, Oee *c et e0 tv lt'O ll o 119 s. *fi* l te I tii is io f,iu ii iis iii.rs tiiis i iit 1 f w9 Xi iiiei i,i; 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