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Estimating Costs of Achieving Global Goals

Estimates of the costs of achieving intermediate or long-term global development goals are subject to uncertainties that go well beyond those in applied economic contexts, and exceed the level that is tolerable. It therefore seems inappropriate that such estimates should be relied on heavily to determine global resource mobilisation targets and priorities for action for lengthy planning horizons. Consequently, an alternative planning and resource allocation framework that is flexible and learning-oriented is needed. In this note, we explore one important class of reasons for uncertainties concerning the validity of recent estimates of the intermediate or long-term cost of achieving global goals, which stem from the unknown nature of the "development production function" and its (dual) cost function.

NOTESfebruary 9, 2008 EPW Economic & Political Weekly68Estimating Costs of Achieving Global GoalsSanjay Reddy, Antoine HeutyEstimates of the costs of achieving intermediate or long-term global development goals are subject to uncertainties that go well beyond those in applied economic contexts, and exceed the level that is tolerable. It therefore seems inappropriate that such estimates should be relied on heavily to determine global resource mobilisation targets and priorities for action for lengthy planning horizons. Consequently, an alternative planning and resource allocation framework that is flexible and learning-oriented is needed. In this note, we explore one important class of reasons for uncertainties concerning the validity of recent estimates of the intermediate or long-term cost of achieving global goals, which stem from the unknown nature of the “development production function” and its (dual) cost function. In recent years, there has been consider-ableinterest in intermediate or long-term global development goals, most notably the Millennium Development Goals (or MDGs).1 Various estimates have been produced of the cost of achieving these goals, by the World Bank, United Nations, and the Millennium Project, directed by Jeffrey Sachs. Such cost esti-mates are thought necessary to facilitate the raising of adequate resources and the allocation of the available resources among different ends and interventions. Unfortunately, estimates of the costs of achieving intermediate or long-term global development goals are subject to uncer-tainties that go well beyond those which are accustomed in applied economic con-texts and exceed the level that is tolerable. It therefore seems inappropriate that such estimates should be relied on as much as they have in determining global resource mobilisation targets and priori-ties for action. These uncertainties point to the requirement for a flexible and learning-oriented planning and resource allocation framework of the kind de-scribed in Reddy and Heuty (2005). An alternative framework of this kind would periodically reassess the resource re-quirements of attaining development goals on the basis of current information and cumulated experience and redeploy resources accordingly. In this paper, we explore one important class of reasons for uncertainties con-cerning the validity of recent estimates of the intermediate or long-term cost of achieving global goals, which stem from the unknown nature of the “develop-ment production function” and its dual cost function. We use data from the influential Com-mission on Macroeconomics and Health to explore the impact of erroneous assump-tions. Although the case we examine is specific, the lessons that may be drawn from it are general.1 Development GoalsA subtle but profound obstacle to produc-ing estimates of the cost of achieving indi-vidual development goals is that this con-cept is not well-defined. The reason is that, as has been widely recognised, the distinct development goals are likely to be “jointly produced”. The interventions that help promote a given development goal are likely to very often also promote other development goals. To take just one exam-ple, better nutrition may promote both the ability of children to learn and to survive. In such circumstances, it is not feasible, unambiguously, to identify the cost of achieving the goals associated with edu-cation and with good health. The reason is that it is not possible to unambiguously identify the share of the cost of an inter-vention (serving as a joint input to more than one development goal) that should be attributed to each of the goals. Only thecost of achieving development goals jointly can, properly speaking, be identified. The cost of achieving individual devel-opment goals can be specified by arbitrar-ily attributing the cost (or a share of the cost) of a particular input to a specific de-velopment goal. However, under this ap-proach (which, for example, is that taken by theUN Millennium Project in its recent estimates of the cost of achieving the MDGs2) the presumed cost of achieving the development goals jointly (i e, the sum to-tal of the costs attributed to each develop-ment goal) will not equal the true cost of achieving the development goals jointly. All of the existing efforts to estimate the total global cost of achieving development goals, which have simply added estimates of the presumed costs of achieving indi-vidual development goals are invalid.3 Efforts to identify the cost of achiev-ing development goals jointly require an adequate understanding of the joint pro-duction function for development goals. However, the requirements for under-standing the causal pathways by which development goals are interrelated can be immense and can severely strain the limits of existing knowledge. Problems in Sanjay Reddy (sr793@columbia.edu) is at the department of economics, Barnard College, Columbia University and Antoine Heuty (antoine.heuty@undp.org) is at the United Nations Development Programme.
NOTESEconomic & Political Weekly EPW february 9, 200869theestimation of costs that arise due to the presence of joint production, which are conveniently ignored in many em-pirical economic analyses, cannot be ignored in the context of development goals in view of thehighlyinterdependent causalprocesses that are likely to underlie aggregatesocialand economic achieve-ments in developingcountries.2 Uncertain Unit CostsExisting methodologies for estimating the cost of achieving major development goals (for instance those related to education and to health) rely on the generalisation of unit cost estimates derived from rather limited evidence. A major issue concerns the accuracy of these unit cost estimates. Often, it is not made clear whether they refer to average or marginal costs, and what is their source (for example, national average data or on a specific local observa-tion that has been generalised). Estimates of marginal costs are based on assumptions regarding counterfactuals (for instance, concerning what factors of production are fixed and what factors of production are flexible in the short run). These can be specified in many different ways. The methodologies used are rarely made clear and may well be mutually incompatible.Generalisation of unit cost estimates across countries is invariably done (for instance, by Kumaranayake, Kurowski and Conteh (2001) in their report for the Commission on Macroeconomics and Health and by recent country studies con-cerning the cost of achieving the MDGs on the part of the World Bank and the UN Millennium Project)by using general purchas-ingpower parity (PPP) conversion factors, which may be based on poor underlying infor-mation in poor countries as mask consid-erable diversity of relative prices across different types of commodities. The re-sulting estimates of the cost of expanding development achievements could be po-tentially quite incorrect. It can be shown that the relative costs of the components of healthcare (such as drugs or the servic-es of physicians) across countries can be widely divergent from the relative costs of general consumption .Table 1, which draws on the data exam-ined more fully in Reddy and Heuty (2004), demonstrates that the relative price structure across different components of health expenditure is widely divergent even among poorer countries. It may easily be checked that these divergences exist even between pairs of countries in thesameregion. This suggests that the use of general consumption PPPs (or even existing disaggregatedPPPs) to predict overall costs of achieving health improve-ments in poor countries may lead to non-negligible errors. It has been widely noted that existing PPPs are based on data drawn from price points in major cities (and often from capital cities alone). As a result, they are unlikely to accurately reflect the costs of purchasing goods and services in small towns and in rural areas, in which both the level and structure of prices are like-ly to be different, in ways that vary from country to country. Thisisanadditional reason that estimates of unit and total costs based on these PPPs are unlikely to be especially accurate. Quite apart from the difficulties involved in generalising cost estimates across countries, recent country studies from differentsources have made unit cost Table 1: Correlation between PPP for All Consumption and for Components of Healthcare(for poor countries)Drugs MedicalTherapeuticHospitalCare Physicians’ Dentists’ Nurses’ SuppliesAppliancesServicesServicesServices0.943861 0.940963330.441764840.642953120.645680340.600786940.94344501Source: Reddy and Heuty (2004).SAMEEKSHA TRUST BOOKS1857Essays from Economic and Political WeeklyA compilation of essays that were first published in the EPW in a special issue in May 2007. Held together with an introduction by Sekhar Bandyopadhyay, the essays – that range in theme and subject from historiography and military engagements, to the dalit viranganas idealised in traditional songs and the “unconventional protagonists” in mutiny novels – converge on one common goal: to enrich the existing national debates on the 1857 Uprising.The volume has 18 essays by well known historians who include Biswamoy Pati, Dipesh Chakrabarty, Peter Robb and Michael Fisher.The articles are grouped under five sections:‘Then and Now’,‘Sepoys and Soldiers’,‘The Margins’,‘Fictional Representations’ and ‘The Arts and 1857’.Pp viii + 364 2008 Rs 295Available fromOrient Longman LtdMumbai Chennai New Delhi Kolkata Bangalore Bhubaneshwar Ernakulam Guwahati Jaipur LucknowPatna Chandigarh Hyderabad Contact: info@orientlongman.com
NOTESfebruary 9, 2008 EPW Economic & Political Weekly72Table A3: Comparison between Linear and Non-linear Costs: Dis/Economies of Scale (Figures are in ‘000 000 000 US$) LinearNon-linear Beta0.000 0.001 0.005 0.01 0.05 0.1Scenario 2007A Tuberculosis Treatment 0.40 0.400 0.400 0.402 0.403 0.417 0.435 Malaria Diagnosis 1.20 1.200 1.202 1.212 1.224 1.324 1.464 Prevention 0.30 0.300 0.301 0.304 0.307 0.338 0.381 HIV/AIDS Care of OI 1.60 1.600 1.603 1.614 1.628 1.745 1.907 HAART 1.00 1.000 1.001 1.006 1.012 1.063 1.132 Scenario 2007B Tuberculosis Treatment 0.50 0.500 0.501 0.504 0.509 0.547 0.600 Malaria Diagnosis 2.00 2.000 2.005 2.024 2.048 2.254 2.546 Prevention 0.50 0.500 0.501 0.507 0.515 0.578 0.669 HIV/AIDS Care of OI 2.80 2.800 2.807 2.834 2.868 3.161 3.577 HAART 5.00 5.000 5.014 5.070 5.141 5.754 6.636 Scenario 2015 Tuberculosis Treatment 0.90 0.900 0.902 0.910 0.921 1.009 1.133 Malaria Diagnosis 3.40 3.400 3.409 3.446 3.492 3.889 4.459 Prevention 1.00 1.000 1.003 1.016 1.033 1.176 1.386 HIV/AIDS Care of OI 6.40 6.400 6.420 6.500 6.601 7.480 8.762 HAART 8.00 8.000 8.025 8.127 8.257 9.380 11.023 Delta = O, beta varies.Table A4: Comparison between Linear and Non-linear Costs: Dis/Economies of Scale (Figures are in ‘000 000 000 US$) LinearNon-linear Beta 0.000 - 0.001 -0.005 - 0.01 - 0.05 - 0.1Scenario 2007A Tuberculosis Treatment 0.40 0.400 0.400 0.398 0.397 0.385 0.372 Malaria Diagnosis 1.20 1.200 1.198 1.188 1.177 1.090 0.993 Prevention 0.30 0.300 0.299 0.297 0.293 0.267 0.239 HIV/AIDS Care of OI 1.60 1.600 1.597 1.586 1.573 1.471 1.356 HAART 1.00 1.000 0.999 0.994 0.988 0.943 0.892 Scenario 2007B Tuberculosis Treatment 0.50 0.500 0.499 0.496 0.491 0.458 0.421 Malaria Diagnosis 2.00 2.000 1.995 1.976 1.953 1.779 1.587 Prevention 0.50 0.500 0.499 0.493 0.486 0.434 0.377 HIV/AIDS Care of OI 2.80 2.800 2.793 2.767 2.734 2.486 2.214 HAART 5.00 5.000 4.986 4.931 4.863 4.356 3.805 Scenario 2015 Tuberculosis Treatment 0.90 0.900 0.898 0.890 0.880 0.805 0.722 Malaria Diagnosis 3.40 3.400 3.391 3.355 3.311 2.980 2.619 Prevention 1.00 1.000 0.997 0.984 0.968 0.852 0.729 HIV/AIDS Care of OI 6.40 6.400 6.380 6.302 6.205 5.490 4.722 HAART 8.00 8.000 7.975 7.875 7.752 6.840 5.864 Delta = O, beta varies.β = 0, the cost function becomes linear = cx and there are no economies of scale.It is assumed that the unit cost, c,identified by theCME background paper is correct for the last (observed) unit (1 per cent) of the cover-age. For the next unit (1 per cent) of coverage cproduced, we have: MC = —— (β + 1) xβ = cxβ. β + 1 At the first additional unit produced, x=1, (1 per cent additional coverage of the intervention), theMC is exactly c (the unit cost). A positive value of βimplies rising marginal costs, and a negativevalueofβimplies falling marginal costs. A value of zero implies constant marginal costs, in line with the linearity as-sumption of the background paper.A value of 0.5 (the maximum value considered here) implies that the one-hundredth unit costs 10 times as much to produce as does the first. A value of -0.5 (the minimum value con-sidered in the esti-mates) implies that the one-hundredth unit costs one-tenth as much to produce as Table A5: Comparison between Linear and Non-linear costs: Dis/Economies of Scale (Figures are in ‘000 000 000 US$) LinearNon-linear Beta 0.15 0.20 0.30 0.40 0.50Scenario 2007A Tuberculosis Treatment 0.40 0.455 0.477 0.527 0.585 0.653 Malaria Diagnosis 1.20 1.623 1.802 2.233 2.783 3.487 Prevention 0.30 0.430 0.487 0.627 0.813 1.058 HIV/AIDS Care of OI 1.60 2.089 2.292 2.773 3.376 4.131 HAART 1.00 1.209 1.293 1.487 1.720 2.000 Scenario 2007B Tuberculosis Treatment 0.50 0.659 0.725 0.884 1.083 1.333 Malaria Diagnosis 2.00 2.882 3.268 4.225 5.494 7.180 Prevention 0.50 0.777 0.904 1.229 1.680 2.309 HIV/AIDS Care of OI 2.80 4.055 4.607 5.975 7.796 10.224 HAART 5.00 7.670 8.881 11.969 16.226 22.111 Scenario 2015 Tuberculosis Treatment 0.90 1.276 1.439 1.840 2.366 3.059 Malaria Diagnosis 3.40 5.122 5.895 7.850 10.514 14.155 Prevention 1.00 1.637 1.938 2.728 3.863 5.497 HIV/AIDS Care of OI 6.40 10.285 12.096 16.814 23.513 33.049 HAART 8.00 12.981 15.316 21.429 30.160 42.667 Delta = O, beta varies.Table A6: Comparison between Linear and Non-linear Costs, Dis/Economies of Scope (Figures are in‘000 000 000 US$) Non-linearScenario 2007A Delta -0.1 -0.05 -0.01 -0.005-0.001 1.6241.6121.6021.6011.600Total linear costs: $ 1.6 B Delta 0.001 0.005 0.01 0.05 0.1 1.6001.5991.5981.5881.576Scenario 2007B Delta -0.1 -0.05 -0.01-0.005-0.001 2.5782.5392.5082.5042.501Total linear costs: $ 2.5 B Delta 0.001 0.005 0.01 0.05 0.1 2.4992.4962.4922.4612.422Scenario 2015 Delta -0.1 -0.05 -0.01-0.005-0.001 4.509 4.4044.3214.3104.302Total linear costs: $ 4.3 B Delta 0.001 0.005 0.01 0.05 0.1 4.2984.2904.2794.196 4.091Beta = O, delta varies. Two interventions: tuberculosis treatment and malaria diagnosis.andso are unit costsof providing the health interventions defined. First Exercise: (Dis)economies of Scale cxβ+ 1Nonlinear cost: =——– ;β∈R,β≠ 1 where x β + 1is the increase in coverage of the intervention, c is the initial unit cost, and β is a parameter. For does the first. A value of 0.2 impliesthat the one-hundredth unit costs 2.5 times as muchtopro-duce as does the first. A value of -0.2 implies that the one-hundredth unit costs less to produce than does the first unit by a factor of2.5.Avalue of 0.1 implies that the one-hundredth unit costs 1.6 times as much to produce as does the first. A value of -0.1 implies that the one-hun-dredth unit costs less to produce than does the first unit by a factor of 1.6.Economies of scale in service delivery may exist due to phenomena such as, for instance, informational externalities and fixed costs of health infrastructure development. Dis-economies of scale in service delivery may exist due to, for instance, increasing difficulty in reach-ing underserved (for example geographically and socially marginalised) populations.Second Exercise: (Dis)economies of ScopeWhat is the cost of achieving the development goals concomitantly? Are there spillovers be-tween interventions? Are there economies or diseconomies of scope? Table A2: Implied Annual Unit Costs(in 2002 US$) Disease Year2007A 2007B 2015Tuberculosis Treatment 6,66,66,667 3,12,50,000 3,46,15,385 Malaria Diagnosis 6,31,57,895 6,89,65,517 8,71,79,487 Prevention 1,07,14,286 1,04,16,667 1,47,05,882 HIV/AIDS Care of OI 10,66,66,667 9,33,33,333 10,66,66,667 HAART 11,11,11,111 11,36,36,364 12,50,00,000 Source: Kumaranayake, Kurowski and Conteh (2001).
NOTESEconomic & Political Weekly EPW february 9, 200873Table A8: Comparison between Linear and Nonlinear Costs, Dis/Economies of Scope (Figures are in ‘000 000 000 US$) Non-linear Scenario 2007A Delta -0.15 -0.25 -0.35 -0.4 -0.45 1.6361.6601.6841.6951.707Total linear costs: $ 1.6 B Delta -0.5 -0.55 -0.6 -0.65 -0.7 1.7191.7311.7431.7551.767Scenario 2007B Delta -0.15 -0.25 -0.35 -0.4 -0.45 2.6172.6952.7742.8132.852Total linear costs: $ 2.5 B Delta -0.5 -0.55 -0.6 -0.65 -0.7 2.8912.9302.9693.0083.047Scenario 2015 Delta -0.15 -0.25 -0.35 -0.4 -0.45 4.613 4.822 5.031 5.135 5.239Total linear costs: $ 4.3 B Delta -0.5 -0.55 -0.6 -0.65 -0.7 5.344 5.448 5.552 5.657 5.761Beta = O, delta varies. Two interventions: tuberculosis treatment and malaria diagnosis.Table A7: Comparison between Linear and Non-linear Costs, Dis/Economies of Scope (Figures are in‘000 000 000 US$) Non-linearScenario 2007A Delta 0.15 0.25 0.35 0.40 0.45 1.5641.5401.5161.5051.493Total linear costs: $ 1.6 B Delta 0.50 0.55 0.60 0.65 0.70 1.4811.4691.4571.4451.433Scenario 2007B Delta 0.15 0.25 0.35 0.40 0.45 2.3832.3052.2262.1872.148Total linear costs: $ 2.5 B Delta 0.50 0.55 0.60 0.65 0.70 2.1092.0702.0311.9921.953Scenario 2015 Delta 0.15 0.25 0.35 0.40 0.45 3.987 3.778 3.569 3.465 3.361Total linear costs: $ 4.3 B Delta 0.50 0.55 0.60 0.65 0.70 3.256 3.152 3.0482.943 2.839Beta = O, delta varies. Two interventions: tuberculosis treatment and malaria diagnosis.An Example Involving Two Goals:Take tuberculosis treatment and malaria diagnosis, and denote the interventions by x and y.In general, let the total cost function identi-fying the minimum cost of providing a given level of outputs (jointly) be represented by TC(x,y), where x and y denote the improve-ments in intervention coverage to be attained (by 2007 or 2015). c1xβ1+ 1 y c2yβ2+ 1 xTC(x,y) =——–(1 – δ1——)+ ——– (1 – δ2 ——), β1 + 1 ymax β2 + 1 xmaxwhereβ∈R,β≠ -1,δ∈[-1, 1]. Theδparameters will generate economies/diseconomies of scope. Ymax and Xmax are defined as follows: ymax = 100 – ybaseline, and similarly xmax = 100 – xbaseline (the coverage extensions which are required to attain complete cover-age, beginning at the empirical baseline).In what follows, assume that δ1 = δ2 = δ and β1 = β2 = β for simplicity.δ = 0 means that there are no economies of scope. Note that δ>0 yields economies of scope and δ<0 yields dis-economies of scope. An interpretation of delta is that it corre-sponds to the percentage decrease (or in-crease, depending on the sign of delta) in the total cost of producing both outputs to the maximum extent feasible (i e, covering the population entirely with both interventions) that arises as a result of the existence of econ-omies (diseconomies) of scope.6 For example, a value for delta of 0.5 implies that the total cost of covering the entire population is 50 per cent lower (due to the presence of econo-mies of scope, or complementarities) than it would have been if there had not been any complementarities. Economies of scope may exist in the health sector due to the presence, for instance, of posi-tive spillovers in diagnosis. Diseconomies of scope may exist due to the presence, for instance, of “congestion effects” or crowding out in the uti-lisation of health service infrastructure. In the exercises below, we have tried to use what we believe to be plausible values of both beta and delta. In particular, we consider maxi-mum values of β= 0.5, and δ = 1 and minimum values of β= -0.5, and δ = -1. The assumption that δ = -1, which suggests that the total cost of achieving both goals completely is zero, is not as implausible ex ante as it may first appear. One reason it is not implausible is that the cost con-cept employed by Kumaranayake, Kurowski and Conteh (2001) is that of “incremental expendi-ture” above and beyond existing health expendi-tures. A second reason is that complete coverage of the population by the diagnostic, preventative and treatment interventions considered entails substantial decreased disease prevalence (in-deed possibly to zero). Such substantial decreas-es in disease prevalence will entail substantial reductions in costs actually incurred. Table A9: Comparison between Linear and Non-linear Costs, Dis/Economies of Scale and of Scope Delta Positive (economies of scope), (figures are in ‘000 000 000 US$) Non-linear Delta0.00 0.15 0.40 0.70 1.00 Beta Scenario2015 Total linear costs: $4.3B 0.000 4.300 3.987 3.465 2.839 2.213 0.001 4.311 3.997 3.474 2.846 2.218 0.005 4.356 4.039 3.510 2.876 2.242 Diseconomies of scale 0.01 4.413 4.091 3.556 2.913 2.271 0.054.8984.541 3.948 3.235 2.522 0.1 5.592 5.185 4.508 3.694 2.881 0.2 7.334 6.802 5.914 4.849 3.784 0.517.21515.97013.89411.4048.913Scenario2015 Total linear costs: $4.3B 0.000 4.300 3.987 3.465 2.839 2.213 -0.001 4.245 3.977 3.456 2.832 2.207 -0.005 4.245 3.936 3.421 2.802 2.184 Economies of scale - 0.01 4.191 3.886 3.377 2.767 2.156 -0.053.785 3.509 3.049 2.498 1.946 -0.1 3.341 3.097 2.691 2.204 1.717 -0.22.629 2.437 2.117 1.733 1.349 -0.51.442 1.336 1.160 0.948 0.737Beta, delta varies.Table A10: Comparison between Linear and Non-linear Costs, Dis/Economies of Scale and of Scope Delta Negative (diseconomies of scope), (figures are in ‘000 000 000 US$) Non-linear Delta 0.00 -0.15 -0.40 -0.70 -1.00 BetaScenario2015 Total linear costs: $4.3B 0.000 4.300 4.613 5.135 5.761 6.387 0.001 4.311 4.625 5.148 5.776 6.404 0.005 4.356 4.673 5.202 5.836 6.470 Diseconomies of scale 0.01 4.413 4.734 5.269 5.912 6.554 0.054.8985.2545.8486.5617.274 0.1 5.592 5.998 6.676 7.489 8.302 0.2 7.334 7.867 8.755 9.820 10.885 0.517.21518.46020.53523.02625.516Scenario2015 Total linear costs: $4.3B 0.000 4.300 4.613 5.135 5.761 6.387 -0.001 4.245 4.601 5.122 5.746 6.371 -0.005 4.245 4.554 5.069 5.687 6.306 Economies of scale - 0.01 4.191 4.496 5.005 5.615 6.225 -0.05 3.785 4.061 4.520 5.072 5.623 -0.1 3.341 3.585 3.991 4.478 4.965 -0.22.629 2.821 3.141 3.525 3.909 -0.51.442 1.548 1.724 1.935 2.147Beta, delta varies.

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