MI. .±' - - - ,L. UO staff use CCICL. is nct for pi 1Di1- Ca-t : i I .The vie,s are _ /\/ IJp j those of :ihe author and not 1 - w w * _ necessarily those of Jhe Bank, I:C!T.ElRTilTONLAL BA1N1M FOR ROECO0J,STRUCTION ANTD DEVELOPI4MT wcononucs Depsrtmeint W1orking Paper No0o 8 A LIMMEAI PRlOG1iiAi2j'NDIGOIU OF THE OUTRPU.7T ANI' iPTLOYMJT POSSIBILITIES OF THE ECDONOT4Y OF JIJAPICA 1965-1975.; PRELIfltfl1IRY RFSUI.TS Oc-tober 30, 1967 FCTh F. (Wn97 WASHINGTON, D.C. 20161 ,'pplied Quantitative Research Division Prepared by: Nicholas G. Carter Introduction This paper, together with paper No. 7, was prepared as part of a project on Jamaica within the work program of the Division, which is concerned with the use of quantitative techniques as aids for country econornic analysis. The choice of Jamaica, mad.e in the consultation with the Area Department, was based on the need to include within The work program an exanple of a snmall cou-ntry. It was also felt that Jamaica was a country in which the Bank was likely to be operationally involved. The project consists of three interrelated parts; (1) a structural mode' (circulated in draft form in November, 1966) and nowr under revrision0 (2) specia) studies of problems relating to employment, wage levels, productivity and savings behavior of which this paper and paper No. 7 represent the first draft conclusions0 (Thle work on savinigs behavior will be incorporated in the revised version of the structural model). The problems of employment and wage structure were raised by the lWiestern Hemisphere Department as likely to be crucial areas for consideration in their continuing economic work on Jamaica0 The Jamaican economy has been characterized for some years by a rapid rate of population grow-th and a high level of unemployment0 In any development perspective, therefore, the question of employment opportunities is very importalnt0 This paper uses the linear programming technique to explore the structure of the Jamaican economy as it is at present, wxith particular reference to its employment possibilities, and as it may appear over the next decade0 The object is to derive a function that will represent the costs of various choices, open to the economy over the next decade, involving more or less employment possi- bilities. This function can be said to illustrate the possible "trade- off" between the maximun potential grouth in income in Jamaica and the maximum potential increase in employment. It is stressed that the results presented here are from a preliminary formulation of the model based .on imperfect statistics available here in the Bank. They should not be interpreted as quantitative predictions, but are intended to indicate possible overall patterns of the development of the structure of the economy0 The model will be applied to more up-to-date data as it becomes available through country economic work0 The calculations were performed using the Control Data "Allegro" Linear Programming system. The author wishles to thank Alfred Conrad, Edwjard Hawlcins, Atle Elsaas, and Marshall Hall for their helpful comments and criticisms; he maintains the traditional responsibility for any remaining errors0 The author also notes with appreciation the statis- tical assistance of W.L. van der Valk and Dawn Elvis. The setting of the problem During the 1950's, the Jamaican ecoionmy, while gromqing rapidly, experienced substantial emigration (mainly to the U.K.) and, at the same tile, continued to suffer from chronic unemployment0 With the advent of limitations on emmigration to the U.K. in the early 60's the employment problem became even more serious. Thus it seems that prob- ably the most important question facing the Jamaican government is whether the economy can continue to grow as it has in the past while at the same time absorbing a substantially larger number of people.into the labor force. This paper undertakes to explore the potential possibilities in terms of output and employment for the economy over the coming years up to 1975. As 1965 is the most recent year for which we have good data, we look at the entire decade 1965-75. The tentative conclusions seem to irnicate that the range of possibilities for increasing employment beyond the pattern that pertains if we simply maximize output, is very limited, and that although the employmernt problem will be serious the economy will face a more fundamental rroblem arising from a lack of foreign exchange. In many instances no conflict need be expected between the objectives of increased output and increased employment9 If the output of an economy, or even a sector, wises we expect that employment will rise also and prob- ably in proportion. Thus over a large range of possibilities maximiza- tion of one objective mill result in the maximization of the other. If, however, we introduce the concept of limited supplies of complementary factors such as foreign exchange, capital, and skilled labor, the goal of increasing output may conflict with that of reducing unemployment. - 2 - For example, investment of a limited amoult of capital in the mining industry will bring about a high increase in output with only a nominal increase in employment. On the other hand i^nvestment in agriculture may employ many more people, but tlic increases in output Will be much smaller than if the same amount had been put into mining. Thus the choice that appears before the planners, given a general scarcity of capitalg foreign exchange, and skilled labor, is whether to encourage industries with a high employment to resource ratio, or those wzith a high output to resource ratio. Certainly the former is a more popular strategy and it carries iwith it a connotation of a more equitable income distribution, but this may take place only at the cost of substantial amounts of potential output. What we w,ish to explore in this paper is the nature of the so- called "trade-off" betwreen output and employment; specifically hoaw much choice do the planmers really have and what are the costs in terms of foregone potential output of a policy of maximization of employment? Method of Approach The first problem is how to analyze the situation. Looking at the past and trying to derive some relevant overall ratios is rather difficult. In the first place the structural changes brought about first by the outmigration of labor and then by the cessation of this activity make it difficult to make any quantitative statements about the relationships of unemployment and investment over the period for which we have good data. Furthermore, looking simply at aggregates gives us no notion of the problem of choice between sectors. In addition there is a problem of identifying the connecti.on between changes in output and employment over the past and particular patterns of resource availability. Moreover there is no way of telling if a particular change was made in response to any constraint at all, What we propose to do is to treat the problem in an optimizing fashion, maximizing the two objectives (output and employment) subject to the structure of the economy and the scarcity of factors such as foreign exchange and capital.. For this purpose all that is needed from the past are the average relationships that pertain in the economy. Then, given the projections of resources for the future, we can look at the differming sectoral output patterns that result when wye shift from one objective to the other, always maintaining the resource constraints. It should be noted at this point that wle do not consider labor to be a scarce factor in this particular context0 We assume that skilled labor is necessary, but that it is not as scarce as the other factors, and thus never provides a binding constraint to the expansion of the economy0 Unskilled labor we treat as a free good in terms of opportunity costs, so that it never imposes a constraint on growth0 The approach can be illustrated by Figure I which shows the choices open to the economy between the output of goods and services and the amount of employment necessary to produce goods and services, given the resources available to the economy0 These choices can be visualised in the form of a "production possibility" curve, or frontier; the possi- bility of any choice at all between the two objectives is represerted by drawing the curve ACB sloping downwards from left to right, implying that, with all other factors given, it is only possible to obtain additional employment at the expense of a smaller Gross Domestic Product (and vice versa). It is obvious, however, that employment and output are highly complementary. To expand output aluays nocess3.t-ates some addition- al labor and an expansion of employmont -wJ11 not take place unless there is some additional output, however small, as a result0 Y FigLre I Al Output /- E 0 Employment X. In terms of the Figure I this means that the curve ACB will never be continuous over the whole range from the Y to the X axes (the sections shown as broken lines need never be considered). It will never be possi- ble to achieve high outputs with very low levels of employment, or high levels of employment with low levels of output -/ There must exist 1/ The reductio ad absurdum iwouldbe the cases where the production possi- bility curve cut the axes; a point on the Y axis, for example, would imply maximum. output, with zero employment. limits, represented. in Fig. I by the lines OA and OB, withi.u which the possible choices for the economy are contained. The line GA, for example, shows the possible expansion of output for the economy when the maximi- zation of output is the sole objecoivez a moveInent outwrards from 0 towards A involves relatively large increases in output associated -with relatively small increases in employment0 Similarly the line OB shoves the possible combinations when the maxizL.zation of employment is the sole objective. If there is no choice open the two lines OA and OB -ill coincide and there need be no conflict betueen the tuo objectiveso The argument of this paper is that there does exist for Jamaica a range of choices notionally represented by a line ACB and an attempt is made to trace out this frontier of possibilities, It is customary in the pedagogic treatment of this case to go beyond the above argument to try and establish how.r the choice might be made once the curve ACB is established. This is done by postulating a preference function for the economy show-ing the preferred combinations of output and employment at all possible combinations of the twJo; this function can then be represented by a set of community indifference curves (of which DCE in Fig. I is one such curve)0 The best position for the economy will then be a point such as C, where the production possibility curve is tangential to the highest possible community indifference curve; at C the rate at which the economr can balance the tvin objectives,given all its resources, coincides writh the relative preferences of the commun- ityo It is generally agreed that it may not be possible (even in principle) to estimate a community preference function and this Daner does not enter 6 - into that question10 It has t.he more limited aim of mapping out the shape of ACB, thus providing all the potential choices for the consideration of the authorities charged by the coinmqunity with the task of making the necessary policy decisions. The problem, therefore, is how to solve for the various points along AB. If the economy wias of one or a few sectors the solution could easily be obtained either by a classical maximization, subject to constraints, or by an exhaustive enumeration of the various possibilities. Howrevrer, if we wish to look at the probleni on a multisectoral basis (which we must in order to get the effects of differences in sectoral factor and output intensities) we must use some form of programming model. In this case we choose to make linear assumptions about the economy and thus to take advantage of the technique of linear programmingO It will be readily admitted that such a process may introduce distortions into the model as a representation of the economy, but the power of the technique over alternate methods is so great as to override most of the objections so long as we are always fully aware of the limitations of the assumptions made. In addition at a later stage of refinement, we shall relax the assumption to introduce some non-linearities. Data In order to make such a model we need certain pieces of data, fore- most of which is an input-output table. Such a table exists for Jamaica for the year 19583 and although in general a rather unsatisfactory piece of work- we have projected it forward to 1965 and have adapted it to our 1/ See Note on the input-output table in Annex 1. model. IIost of the rest of the information used comes from the industrial surveys of 1954, 1960 and 19631/ and from the national income accounts for the period 1959-65. Finally some eT;iployment data wJas taken fron, the 2/ employment surveys and fromn the cer.lus of populJation. In general there are a number of inadequacies in this data and further research on the model will initially entail the use of more up-to-date inforynation. The Model Having described the background to the model and the problem we are seeking to solve, we proceod to describe the equations that make up the system. The first consideration is the items that are maximiuzed, specif- ically olutput and employmentO If we let Z stand for some measul e of national welfare- then at maximization of the relative increase in output,- (la) Z=(Q-Qo)/Qo where Q is output in time t and Q0 is output at time zero. When we are at maximization of the relative increase in employment then (lb) Z=(L-L0)/Lo 1/ Report on a Survey of Establishments, 1954, 1960, 1963. Department of Statistics, Kingston, Jamaica. 2/ Annual Abstract of Statistics 1966, No. 25. pp. 126-131. Department of Statistics, Kingston, Jamaica. 0C.' Francis, The People of Modern Jamaicag Department of Statistics, Kingston, Janaica 1963. 3/ It should be stressed that although we are dealing in actual units, Z is an ordinal variable. We are interested in the ability to say one state is preferred to another, and do not intend any judgment as to the absolute magnitudes involved. 4/ In actual running of the model we have used consumiption instead of out- put. The difference is conceptual and computational and it does not affect the results. vhere L stands for employmerft, ard the subscrirpt as before refers to the base period. At some combinlation of the t,wo objectives, (lC) Z= a(Q-QO),/QO * b(L-LO)/LO where a + b=l, as we can normalize Z without any loss of ordinalityo Fur- thermore, we can use the fact that we only need. an ordinaJ. measure to state,l/ (1) Z=aQ + b (Qo/Lo)L which will be the objective function (the function which is maximized) in our model. As we vary "a" from 1 to 0 subject to the normalization con- straint we will in effect be moving the point C in Figure I along the cossibilities curve from A to B. The next step. is the structural equations of the economy* We have divided the economy up into twelve sectors followzing partly the input- output table and partly the availability of other data, The sectors are: 1) Sugar--this includes both the grow.-ing of canie and the manufacture of sugar, as well as the manufacture of rum. 2) Agriculture--covers the rest of agriculture including both subsistence and market production whether or not for export. 3) Mining--this is mainly the bauxite mines, but also includes gypsum and quarrying0 4) Construction--this includes all capital formation and maintenance. 5-8) Manufacturing sectors covering food,. 1/ Z= aQ/0o - a + bL/Lo-b. Since a+b=l, Z=aQ/Qo + bL/L,-l, multiplying by Qo and rearranging, ZQo+Qo=aQ:±b(Qo/Lo)L and since we are only looking for an ordinal measure and Qo is a constant, we can ignore it on the left hand side. - 9 - clothing and textiles, heavy industry., and miscellaneous0 9) utilities 10) distribution, 11) transport 12) servi.ces-including ownership of dwellings, but not including adininstit'ralbion of government3 In each. sector we state, (2a) Supply j= Demand and this relationship is stated mathematically as; (2) Xi= Ci + Ii + Ni + Ei + Gii + baijXj9 i= 100012 Where X stands for production, (gross output or deliveries from sector i), C for consumption, I for investment goods, N for inventories, E for exports, G for govern-menlt, axid the final term for the interindustry uses of the output from industry io The coefficients aij are from the input table and simply state the amount of input required from the ith industry for a unit of output in the jth industryO- Now we need to relate X (gross output) to Q (net output)o If we let Mi stand for the ratio of imports for intermediate use in the ith sector to the gross output in that sector, then (3) Qi= Xi. (1-; aji~-mi) and sulmming up, 1/ It should be made clear that the demands for goods in this model are highly structured and thus output in a particular sector is limited by this s-tructure rather than by factor availabilities, although overall output is factor determined. There are no activities, other than linear programming slacks, that allow unlimited disposals of sector output. 10 (h) Q= ELQi + Vg where V is value added in government. Both the government and the export sectors eae exogenous to the system we are considering. As a good forecast of the probable activity in these sectors we have used estimates contained, or implied, in the most recent Bank economic report (ii-154a-Decenmber 1965)1 Although most of the analysis contained therein is with regard to 1970, we have projected the trends through to 1975. VWe project government-activity to grow. at about 5.2% per annum and thus total government expenditure G is estimated to be at a level of E59,0 million in 19750 Of this E3578 million will. be value added (Vg) and about 115 millioi vill be demand for goods ard services to be purchased from the domestic economy. This demand (Gd) is broken dowm as follows; (5) Gi= giGd ifhere the coefficients gi reflect the distribution of demand in the base period; thus w-e assume that there will be no change in the nature of the government demand over the ten year period. In the case of exports, we have made detailed projections of most of the sectoral exports0 Sugar, as a result of the Common-wealth sugar agreement, is not expected to earn more than E22 million in 1975 having earned L16 million in 19650 However, this is a demand limitation, it nay very well happen that the economy will not want to export this much (or may not be able to) but we feel that it will export at least L19 million worth. Thus (in 1 million) (6) 19 - El! 22 Similarly for exports of food agr4icu.1ta-w.aI products, (7) M where F is the expected inflow on capital account (iLe. the allowable imbalance on current account). Wle have tentatively set F at £9 milli.on. The inequality of (18) is in order that foreign exchange be a constraint that binds only as long as imports try to exceed exports. If it happens that the earnings from exports plus the capital inflow are more taan desired imports then, foreign exchange is no-t a constraint on the system. We summarize the foreign exchange situation as follows0 The crucial equation is (18) and. it is in terms of the value of an increase in F (exchange without a current cost) that we will be able to determine the scarcity of foreign exchange0 Imports are in most cases fixed pro!or- tions of sectoral output and thus can only be "saved" by shifting cutput patterns. Exports are all limited by factors assumed to be related to external demand condi.ticis, however, we have included lower levels to prevent the complete removal of the export activity (as the result of the nature of the linear programming system) should such activity become too costly in terms of output and employment gained per unit of factor expenditure0 This case of export activities going to lower bounds should only occur when factors other than foreign exchange serve as the binding constraints on the system. - 1.7 - Finally the amount of employment must be related to the levels of production, (19) L=li X. where li is the omployment to production ratio for the ith industry, Here again we assume the ratio to be constant over the ten year period. Equations (1-19) complete the basic system. (A tableau of the system is shoin in Figure II; this is mainly for the purpose of arranging the information for coding on the computer, but is also useful for an overall visualization). This system has a total of 27 "activities" and a total of 49 possible const.raints. In the progran-mming framework the solution will be such that there is one constraint for each activity and such that *tho valuo of Z in oquatiocn (1) is maximizea. The basic problem is to determine levels of each of the activities at this maximum point and to find how these levels change when the coefficients of equation (1) (a and b) are varied. Results The table shows a set of preliminary results from subjecting the system described above to a linear programming process. Four separate results are shown (cases 1-h), based on different assumptions. The first three are with a marginal propensity to consume of O,85, while the fourth one uses a figure of 0.80, The first and fourth results place the emphasis entirely on increasing output, while the third emphasises only employ- menit, The second set of results is a case where equal emphasis is given to both objectives, (a=b=005). For purposes of comparison the initial LINEAR PROGRA,MNMG TABLEAU X… ----------------X12 If In L 0 C E1 E2 E3 E5 E6 E7 E3 ET Eo M R.H.S. Max b_Lo c XI~ ~~~~~~~~~~~~~~~~~~ 1.1.0 I O T10 Es,0 1.0| 1.0 1.0-c [I-A-N] I1.0 I C Matrix :I I "s ' l Xt1.0 Mimmum~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~FI Ej 10 0-__ 1.0 > Xioi~~~~~H F0 cI Minimum E_i_________ Q;_______ 10 = L Manimum EX IONN H Labor < - - - - - - - - - -~~~~ -1.1 ---- >10L Investment (~---0.2 Ki- -- -- ----> 1.0 = (0.2£:Ki XiO) Inventory Ic - - - - - - - -_-ni - --_-_-_-_-_-_-_-> -1 .0 = o Output E- - - )--- -1.0 . V Savings r b1.0 < rr+G…-…Go-Co) Eo …0eal - 0 = Foreign Exchange -1.0 F F II - 19 JAMAICA: Resultsof PCLenr Proranmdin, (all values in fOOO) Initial Growth rate - Level 1965^-75 1 2 3 4 (1965) (pa_)_ Sugar 33)710 33,682 339668 33,978 239568 307 Agriculture 57,026 59,292 59,l410 60,644 479175 2-5 Mining 54 637 51,396 49,568 54,824 35,116 4.6 Construction 97,510 97,o48 96,896 1079849 76,523 305 M4fg0.l 65,138 64;971 64.,912 66.t439 46, 978 3$5 14fg. 2 15,160 15,169 16,391 16,702 9,502 5.8 Mfg- 3 27,376 26,514 27,9295 28,882 19,197 402 Mfgo 4 13,701 139684 13,680 139958 9,93 4.0 Utilities 7,112 7,104 7,I3.6 7,288 5,257 3.3 Distribution 265,508 265,126 2614850 273o432 203,009 3.0 Transport 55,887 55,670 55,510 57,185 40O,951 3°4 Services 121$934 122,655 122,497 1242715 82,972 402 I. Fixed 72,9334 729096 72,0]. 829088 589,620 3-ii 2/ 1,4099895 194269397 19428,119 l1468;820 190279396 3.6 Output 411,897 h09,983 4t09,219 425,278 311,779 3.2 Cases: 1l Output alone maximized - marginal savings rate= 00150 2. Output and employment both maximized (equal weights)-marginal savings rate= 015. 3. Employment alone maximized marginal savings rate= 00150 4. Output alone maximized - marginal savings rate= 0.20. 1/ Growth from base period to 1975 case 4 (Savings rate = 0.20). 2/ Number of people employed. - 20 levels (1965) of the vari.ables are presented, as are the inlied aninual compound grctith rates fronm the 2.965 level to the 1975 case 4, where, with a marginal propensity to consune of 0.8, the marginal national savings rate is 020O Case h was chosen for the comparison as it represents the maximum amount of growth that can be had from the economy; the scarcity of foreign exchange binds the economy to a single solution - a shift of emphasis to employment does not change the results0 The rows of the table show the output (production) levels of each sector, as well as the level of fixed investment, employment, and output. It should be noted in this respect that the employment includes agricul- tural employment0 (However, if the model is restated so as to look only at non-agricultural employment, the results, as far as sectoral output patterns are concerned, are the sane.) We should make clear what dis- tinguishes cases 1-3 from case 40 In the first three the crucial constraint is capital, (resulting from setting the inarginaJ. savings rate at 0.15) and the segments of the curve are the result of alternate ways in which the foreign exchange earned can be used to produce greater or lesser amounts of output and employment. Case 4 is a relaxation of the savings constraint to 0.20, and we then find that foreign exchange is the crucial constraint0 In these circumstances there is only one possible optimal point. Figure III shows the transformation curve (ACB in figure I) that we have been looking for. It shows five different points representing the three presented in the table for a savings rate of 00159 and two others not presented which are in between (a=0.55, a=0.35)o As can be seen the curve is the shape that we expected, but what is surprising is how small a difference it makes whether one is at maximum employment or at EMPLOYMENT-THOUSANDS OF PERSONS -Ph cn ~~0 710(10 0 - _ _ __ _' _ M cC~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~c -4~~~~~~~~~~~~~~~~~~~~~~~~~~c co -n to zw - 22 - mafium output. The totai trade-off betvueen c.ase I. and case 3 (and thus between employment aridc output or betwreen points A and B in figure ,) is EJL7 of output lost per additional person eriroloyed, iwfhich is equivalent to an elasticity of about 2oO (i.c, for a 1% lo3s in potential ou-tput we can get a 2% increase in employment)0 However, the total difference in employment possible is only slightly over 15% Furthermore, if wre look just at the first increment (between points A and C) the "cost" of a job is only E57 and the elasticity is over 5, but the difference is only 0.5to, The reason the range of possibilities is so small is that the con- straints that bind the system to a maximum level are not too far removed from the initial level0 Thus none of the many possible grow'th paths have much latitude to change the patterns of the base period. This means that the range of possibilities, when viewed from the terminal period, show very little variation. It is interesting to look at the mechanism which causes the segments0 At all points capital and foreign exchange are scarce factors. HIowrever, as we move from A to B differenb sectoral exports as a source of foreign exchange move from their upper bounds to their lower bounds thus indicat- ing their relative profitabilities as earners of foreign exchange. An activity at a lower bo-und is an indication of a greater cost (in terms of capital) to produce the good for export than to use the same capital to make consumption and employment. Similarly at the upper bound, the model gains more from the export of the good and the use of the resulting foreign exchange to make consumption and employment than from using the capital to make these directly. At point A where the emphasis is on 3 - ou-tput and not at all on employnent, exports of 'agriculture, tMourisG1!, and food and clothing are inferior activities (they are all labor intell- sive) and are all at their lowyer levels; all other export activities- are at upper levels meaning they are favored modes of earning exchangei This situation lasts until vre move to point C where Agriculture becomes worth- while and exports of heary rmnufactures drops out. Then at point D, miniing (being not at all, labor intensive) drops out and tourism (which uses a lot of labor) becomes a worthwhile export. Point E brings heavy manufacturing back in, (as the stress is placed on anything that car enploy people) and finally to get to point D the exports of food and clothing become a good w,ay to employ people and earn foreign exchange. If we look at the overall change from A to B we find the three exports that were not favored at A(agriculture, food and clothing, ard tourism) as they are labor using, are all favored at B while the export of mining which uses very little labor has dropped out. Case 4 shows the results when we relax the savings constraint by a large amount0 This was done by dropping the marginal consumption rate down to 080, and in fact the model is only able to get to a marginal rate of 0.83, (equivalent to a marginal savings rate of 017) at which point it is constrained from saving (and thus investing and thus growing) any more by the limits of foreign exchange0 If we look at the last column of the table it can be seen that this is equivalent to a rate of growth of only 3.2% per annum, which is low compared to the rate of 5.2% (in constant prices) experienced over the period 1960-65. How-ever as mentioned above, this growth rate can be traced directly to the growth of exports which in the 60-65 period w-as 71 and in the 65-75 period will be 4%. In point of fact, the use of the optin-Z3ing process has pointed the way for a slightly more efficient uso of foreign exchange; in the past it has -taken about a 103 grouth in exports for a 1% groith in output, in t+he model this ratio has been dropped to a 1.2% in exports for every 1% in output, It is interesting to ca