World Bank Reprint Series: Number Forty-one Bela Balassa he Income i istribution Parameter in -roject .ppraisal Reprinted from Economic Progress, Private Values, and Public Policy (North-Holland, 1977) The most recent editions of Catalog of Publications, describing the fuli range of World Bank publications, and World Bank Research Program, describing each of the continuing research programs of the Bank, are avail- able without charge from: The World Bank, Publications Unit, 1818 H Street, N.W., Washington, D.C. 20433 U.S.A. WORLD BANK BOOKS ABOUT DEVELOPMENT Research Publications The Mining Industry and the Developing Countries by Rex Bosson and Bension Varon, published by Oxford University Press, 1977 Patterns in Household Demand and Saving by Constantino Lluch, Alan Powell, and Ross Williams, published by Oxford University Press, 1977 Unskilled Labor for Development: Its Economic Cost by Orville McDiarmid, published by The Johns Hopkins University Press, 1977 Electricity Economics: Essays and Case Studies by Ralph Turvey and Dennis Anderson, published by The Johns Hopkins University Press, 1977 Housing for Low Income Urban Families: Economics and Policy in the Develop- Ing World by Orville F. Grimes, Jr., published by The Johns Hopkins University Press, 1976 Village Water Supply: Economics and Policy in the Developing World by Robert Saunders and Jeremy Warford, published by The Johns Hopkins University Press, 1976 Economic Analysis of Projects by Lyn Squire and Herman G. van der Tak, published by The Johns Hopkins University Press, 1975 The Design of Rural Development: Lessons from Africa by Uma Lele, published by The Johns Hopkins University Press, 1975 Economy-Wide Models and Development Planning edited by Charles R. Biitzer, Peter B. Clark, and Lance Taylor, published by Oxford University Press, 1975 Patterns of Development, 1950-1970 by Hollis Chenery and Moises Syrquin with Hazel Elkington, published by Oxford University Press, 1975 A System of International Comparisons of Gross Product and Purchasing Power by Irving B. Kravis, Zoltan Kenessey, Alan Heston, and Robert Summers, Published by The Johns Hopkins University Press, 1975 Country Economic Reports Chad. Development Potential and Constraints by Richard Westebbe and others, distributed by The Johns Hopkins University Press, 1974 Economic Growth of Colombia: Problems and Prospects by Dragoslav Avramovic and others, published by The Johns Hopkins University Press, 1972 Kenya: Into the Second Decade by John Burrows and others, published by The Johns Hopkins University Press, 1975 Korea: Problems and Issues in a Rapidly Growing Economy by Parvez Hasan, published by The Johns Hopk; )s University Press, 1976 Lesotho: A Development Challsnge by Willem Maane, distributed by The Johns Hopkins University Press, 1975 Nigeria: Options for Long-Term Development by Wouter Tims and others, published by The lohns Hopkins University Press, 1974 (continued on inside back cover) Chapter 10 The Inconme Distributional Parameter in Project Appraisal Bela BALASSA* 1. Recent concern with the distribution of incomes in developing countries has led to recommendations in project evaluation manuals prepared for international institutions to introduce income distributional considera- tions in the appraisal of investment projects undertaken by these coun- tries. The Manual of Industrial Project Analysis in Developing Countries, prepared for the OECD Development Center by I. M. D. Little and J. A. Mirrlees, called for "attaching different weights to the consumption of different income groups" [Little-Mirrlees (1969, p. 42)]. In the revised volume, Project Appraisal and Planning for Developing Countries, it has been proposed that "these weights give expression to the objectives of the government" [Little-Mirrlees (1974, p. 234)]. Little indication is given, however, as to how these weights are to be determined on the grounds that: "In a book primarily concerned with practical applications, it would not be right to develop a theory of welfare weights in great detail" (ibid). The UNIDO Guidelines for Project Evaluation, prepared by Partha Dasgupta, Stephen Marglin and Amartya Sen, put forward a rationale for the introduction of income distributional considerations in project ap- praisal in the following terms: "given the concern with mitigating ine- qualities professed by most of the developing countries, disregard of the distribution of benefits and costs from a project can be justified only if it is assumed that the desired distribution of consumption is to be achieved independently of the mix of public investment" [Dasgupta et al. (1972, p. 76)]. It is claimed that such is not the case in developing countries as "Political, institutional, and administrative obstacles prevent taxation of the rich to the point necessary to reduce consumption inequalities substantially. And, the other side of the coin is the widespread objection *This paper was written as part of a consultant arrangement with the World Bank. For helpful comments and suggestions, the author is indebted to his colleagues and especially to Messrs Graham Pyatt and Lyn Squire. 218 Bela Balassa to increasing the consumption of the poor through direct subsidies" (ibid). Dasgupia et al. further suggested that income distributionai ;onsidera- tions be introduced in project appraisal by weighting the consumption increments accuring to people in various income groups that result from the project's implementation (p. 77).' These weights are to "directly reflect political value judgments" (p. 139). They are to be derived on the basis of choices made by policy-makers in regard to particular projects and their possible variants. According to the authors of the UNIDO Guidelines, "Eventually, a consistent pattern of weighting would, it is hoped, emerge from a large number of choices" (p. 144). The proposed World Bank Guidelincs on Ezconovnnic Analysis of Pro- jects, written by H. G. van der Tak and L. Squire, also express the view that "if the government is unable to secure a desired redisLribution of income through taxation, it can use the allocation of investment resources as an alternative method of redistributing income" [van der Tak and Squire (1975, p. 17)]. The use of distributional weights is recommended for this purpose when "Value judgments by the government determine the weights to be given .. . to benefits for different classes of inco-le recipients. .." (p. 26). Distributional weights are to be derived from a utility function where the marginal utility of consumption (Ut) is taken to depend on the initial level of consumption (c) and the parameter of the utility function (n). In the formulation chosen, Uc = C , (1) this parameter is the (social) elasticity of the marginal utility of consump- tion, while the utility function itself is supposed to express the govern- ment's preferences. Thus, "the higher n the more egalitarian the government's objectives, since the higher n the higher the rate of diminishing marginal utility" (p. 63), It is added that: "For most governments n would probably center around 1. Values close to zero or two, although possible, may be considered extrtme" (ibid).2 Within this range, it is recommended that the project analyst consider values between 0.5 and 1.5 for n (p. 103). Little 'The UNIDO Guidelines also consider introducing regional distribution weights (pp. 77, 78-82) and government pricing policy (pp. 82-84) but these will not be discussed in what follows. 2Setting the elasticity of the marginal utility of consumpuion equal to I would mean that a weight twice (one-half) of the averagc was ass,igned to a marginal increment of consumption accruing to an individual who had one-half (twice) tNl average consumption level. The assigned weight would be four times (one-fourth) the average if n was set at 2, while equating n to zero would mean that increments in consumption were valued equally regardless of the recipient's existing level of zonsumption. frcome distributional parameter in project appraisal 219 justification is given, however, for the choice of the proposed range of values. While the UNIDfl Guidelines call for deriving income distributional weights on the basi, 4' government preferences as revealedJ by choices of projects and project variants, according to the Bank Guidelines "if an international agency such as the World Bank conducts the analysis, it must try to arrive at an understanding with the government about [its socioeconomic goals] before the analysis is undertaken" (p. 27). It is further added that "if views diverge - with respect to the desired distribu- tion of the gains from development, for example - tie agency should analyze the proposed project relative to both its objectives and those of the government and satisfy itself that the project meets the objectives of both" (ibid). Thus, all three project evaluation manuals call for the use of income distributional weights in project appraisal, to be derived from a social welfare function expressing governmental preferences and/or the prefer- ences of international institutions. In so doing, they disregard private preferences that are reflected in the individual valuation of the utility of consumption. A different approach is followed in this paper. We will take the private valuation of the utility of consumption as the basis for deriving the social elasticity of the marginal utility of consumption. The relationship between the social and the private elasticity of the marginal utility of consumption is derived below. Assume that each individual has the same isoelastic utility function u(i) and that the social welfare function is expressed aw: W = W[u(c1), U(C2),. ., u(cM)], (2) with W, > 0 for all i. The social elasticity 'f the marginal utility of consumption (n) can now be written as3 a log a - - a log(W,u') (3) a log a. 8d, J a log c, a log u', a log W, a log c, a log c, a log u ' c,W, u'W a logc, W, The first term on the right-hand side of equation (3) will be the private 'The formula was originally derived by Anand (1973): the simplified derivation used here has been suggested to me by Graham Pyatt. 22(1 Bela Balassa elasticity of the marginal utility of conisumption (w), while the second term will provide an adjustment factor for deriving the social elasticity of the marginal utility of consumption from the private elasticity. As Anand (1973) shows, this term can be rewritten as the product of the elatsticity of the marginal social welfare functioni with respect to individual i's utility and the income elasticity of inidividual i's utility function. Having defined the social welfare function used in the paper, questions relating to the empirical measurement ot the private elasticity of the marginal utility of consumption and the choice of adjustment factors for deriving the social elasticity will need to be considered. Section 2 of the paper provides an introduction to the measurement of the private elasticity of the marginal utility of consumption, taking as a point of departure a paper by William Fellner. In Section 3. empirical results derived in a within-country and an inter-country context will be pre- sented. This will be followed by a discussion of the limitations of the results (Section 4). In turn, in Section 5, comments will be offered on the choice of adjustment factors for deriving the '.ocia! elasticity of the marginal utility of consumption. Finally, Section 6 will examine the issue of introducing income distributional considerations in project appraisal in general terms. 2. As Fellner reports (1967, pp. 42-43), Irving Fisher first put forward the proposition that the cardinal measurability of marginal utility depends on the independence (non-complementarity) of wants [Fisher (1892)]. The theoretical analysis underlying this proposition was further developed by Fisher himself (1927) and by Frisch (1959), who utilized the concept of the elasticity of the marginal utility of consumption or, in his terminology, the "money flexibility", in deriving a scheme for computing direct and cross demand elasticities.4 The first numerical estimates of the elasticity of the marginal utility of income were also made by Frisch (1932). The work of Fisher and Frisch was subsequently extended to the von Neumann-Morgen';tcrn framework by William Fel3ner who also estimated the elasticity of the marginal utility of income fronm consumption data of U.S. cities (1967). In the Fisher-Frisch tradition, Fellner has established the measurahility of the elasticity of the marginal utility of consumption (income) on the 'The assumption of want independence was earlier made by Iligou (1910) in suggesting a method to derive price elasticities from income ela%ficitics. Income distributional parameter in project appraisal 221 assumption that the individual utility function is separable into at least two additive terms, representing groups of co'-nmodities (x), u -u,(xl) + u2(X2). (4) This permits interpreting "observable marginal rates of substitution as ratios of marginal utilities, on the assumption that if the quantity of one good is held constant and that of another is varied, then the marginal utility of the first of these goods remains unchanged" [Fellner (1967, p. 46)]. Expressing the first-order condition of utility maximization as (a3u/xi)/pi = A, (5) we can determine the increase in income necessary to induce the consumer to buy the same quantity of xi at a higher price. With au lax, being the same for the identical level of consumption of xi in the low price-low income as well as in the high price-high income situation, Fellner suggests that, for the small income range in which we observe x to be constant, the ratio of the ith commodity's income elasticity (E,) to its compensated own price elasticity (e,) will provide an estimate of the. elasticity of the marginal utility of income. Fellner's formula provides an approximation to the true elasticity of the marginal utility of income, which has been derived from a general model of utility maximization by Frisch (1958, p. 187),6 W = Ei ( l-a,E,) = E(l(- aE) (6) e;i - ajEi ei The difference between the results obtained with the two formulas tends to be small. Thus, Nicholas Stern has shown that Fellner's estimates of the elasticity of the marginal utility of income for the United States exceeds the true elasticity by 15 percent (1973). The difference between the results will be the smaller, the smaller is the budget share of commodity i. Fellner's estimate of the elasticity of the marginal utility of income was based on data on incomes and on the coinsumption and relative price of food in a cross-section of American cities. In turn, several authors made estimates in the framework of a linear expenditure system (LES) and other models with additive specifications.7 In the course of research sIn the equations, p refers to prices and A is the marginal utility of income. 'In equation (6) a, refers to the budget share of the ith commodity and C,, is its uncompensated own price elasticity. To express the elasticity of the marginal utility of income with a positive sign as in (3) we here followed Feliner in multiplying the compensated own price elasticity (the denominator of Frisch's original expression) by - L 'For references, see Brown and Deaton (1972). 222 Bela Balassa undertaken at the World Bank Development Research Center, the LES system was extended by Lluch (1973) to allow for the consumption-saving decision, and the elasticity of the marginal utility of income and consump- tion was estimated by Lluch and Williams (1975a, 1975b) in the framework of the extended LES system. Equation (7) shows the relationship between the elasticity of the marginal utility of income (y) and that of consumption (w) in the framework of the extended LES. here ,IL is the marginal propensity to consume [Lluch-Williams (1975a, p. 12)], 'y - ,11(1 + W) - l. (7) In the following, we will briefly review available estimates of the elasticity of the marginal utility of consumption, which is the relevant concept for project appraisal. 3. Frisch conjectured that the elasticity of the marginal utility of consump- tion (money flexibility) is negatively related to per capita incomes.' In his view [Frisch (1958, p. 189)], "we may perhaps assume that in most cases the money flexibility has values of the order of magnitude given below, w = 10 for an extremely poor and apathetic part of the population; w = 4 for the slightly better off but still poor part of the population with a fairly pronounced desire to become better off; w = 2 for the middle income bracket, 'the median part' of the population; w = 0.7 for the better off part of the population. w = 0.1 for the rich part of the population with ambitions toward 'conspicuous consumption'." Frisch further added that: "It would be a very promising research project to determine w for differant countries and for different types of population. A universal 'atlas' of the values of w should be constructed. It would serve an extremely useful purpose in demand analysis" (ibid). Estimates based on U.S. data have led Fellner (1967, p. 73) to conclude that the elasticity of the marginal utility of income is constant over a wide range of incomes in the United States at a level of about 1.5 Other 'Recall that we express the elasticity of the marginal utility of consumption with a positive sign while Frisch and econometric studies used a negative sign. Income distributional parameter in project appraisal 223 authors, utilizing various forms of additive utility functions, have ob- tained estimates clustering around 2 [Brown-Denton (1972, p. 1206)], and results reached by the so-called "Australian" [Hoa (1968)] and "Rotter- dam" [Theil-Brooks (1970)] models have not provided evidence of a definite relationship between the elasticity of the marginal utility of income (consumption) and per capita incomes in a within-country con- text. In turn, the application of the Extended Linear Expenditure System (ELES) to Korean data has given ambiguous results. Dividing Korean urban consumers in two groups, with incomes below and above 4000 won a year in 1970, Lluch and Williams (1975b, table 4) estimated the elasticity of the marginal utility of consumption at 3.1 in the first case and 1.9 in the second. How ver, the estimated elasticity is higher for urban than for rural households in Korea (6.8 and 5.3, respectively), although average incomes are twvo-fifths higher for the former than for the latter. Estimates for particular countries thus do not validate Frisch's conjec- ture about a negative relationship between the elasticity of the marginal utility of consumption and per capita incomes in a within-country context. Brown and Denton (1972, p. 1206) extend this conclusion to inter-country relationships, suggesting the universal constancy of the elasticity of the marginal utility of consumption. This generalization is, however, con- tradicted by results of Lluch and Williams and Janvry, Bieri, and Nunez. Lluch and Williams (1975a) estimated the elasticity of the marginal utility of consumption for fourteen countries chosen on the basis of data availability,9 utilizing the extended LES system. Estimation was done by the use of equation (8). where v denotes total consumption expenditures per head, and IV = V ( v - 2 piT) (8) is the "subsistence quantity" of the ith commodity (i.e., the amount of the ith commodity consumed at the subsistence level). Because of uncertainty as regards the level of commodity aggregation at which the additivity assumption is appropriate, for each country estimates were made at four levels of commodity aggregation (8, 4, 2, and 1 commodities)."' The statistical signihcance of the results tends to be the 'United States, Sweden, West Germany. Au%tralia. United Kingdom, Israel, Italy, Ireland, Greece, South Africa. Jamaica, Taiwan, Thailand, and South Korea. '"In the following discussion, the I-commodity aggregation scheme has been disregarded as this corresponds to the simple Keynesian consumption function. 224 Bela Balassa highest at the 8-commodity level and declines as the level of commodity aggregation increases" [Liuch-Williams (1975a, table 2)]. Lluch and Williarns further utilized the mean estimates for the fourteen countries under study to test Frisch's hypothesis that the elasticity of the marginal utility of consumption is negatively related to per capita incomes in an inter-country framework. According to the results at the three levels of commodity aggregation, this elasticity tends to decline by about one-third of one percentage point as per capita incomes increase by one percent. Selecting for each country the estimate with the highest level of statistical significance Lluch and Williams obtain, in a weighted regres- sion,'2 the results shown by'3 log w = 1.565 - 0.358 log x. (5.49) (3.51) (9) For an "average" country with incomes per head of $3000 in 1970 prices, the elasticity of the marginal utility of consumption is shown to be 2.1 while the corresponding elasticities for countries with per capita incomes of $1000, -5600, $300, and $100 are estimated at 3.1, 4.0, 4.8 and 7.0. A greater degree of progression was found by Janvry et al, (1972), who regressed LES estimates of the elasticity of the marginal utility of consumption for the United States, Norway, Argentina, Peru and Israel on per capita incomes. For countries with per capita incomes of $3000, $1000, $500, $300, and $100, the estimates derived from log w = 1.759- 0.513 log x, R2 = 0.538, (3.92) (2.42) (9a) are 1.0, 1.7, 2.4, 3.1, and 5.5. 'Out of fourteen countries. the results are significant at the 5% level in twelve cases under the 8-commodity aggregation scheme and eleven cases each under the 4-commodity and the 2-commodity aggregation schemes. The number of significant results increases to fourteen in the 8-commodity aggregation scheme if a 10% level of significance is utilized [Lluch-Williams (1975a, table 2)), "The regression equations estimated by combining country results obtained at the 8-, 4- and 2-commodity aggregation, respectively, are 8 commodity log w = 1.338 -0.302 log x, R 0.276, (3.18) (2.14) 4 commodity log iv = 1.645 - 0.409 log x. R' = 0.518, (4.84) (2.90) 2 commodity log w = 1.284 - 0.304 log x, Rl = 0.300. (3.22) (2.27) In the equations x refers to per capita incomes measured in IJ.S. dollars at the official exchange rate; t-values are shown in parentheses. "The variables have been w eighted by the standard error of the dependent variable. Income distributional parameter in project appraisal 225 The Lluch-Williams results can be judged superior to the estimates by Janvry et al. This is because Lluch and Williams have used data for a substantial number of countries that also exhibited large income dis- parities; they have applied the same model to the data of all the countries; and they have employed statistical tests to choose among results pertain- ing to different degrees of commodity aggregation. In turn, the Janvry- Bieri-Nunez study combines results for a smaller group of countries that exhibit lesser variations in income, and the estimates were made employ- ing a variety of methods which did not permit making a choice on the basis of degrees of statistical significance. 4. The Lluch-Williams, as well as the Janvry-Bieri-Nunez, results provide empirical support for Frisch's conjecture, according to which the elastic- ity of the marginal utility of consumption is negatively correlated with incomes in a inter-country context. The results are, however, subject to qualifications as regards the methodology employed and the applicability of the estimates to developing countries. The measurement of the elasticity of the marginal utility of consump- tion necessitates an, essentially arbitrary, normalization of the utility function. In the cited studies, normalization has been accomplished by assuming additivity in utilities derived from particular product groups. Fellner suggests that the error committed thereby may not be substantial; thus, in a two-commodity group model, "we would be making excessive allowance for complementarities if we reduced our estimate [of 1.51 by 30%" [Fellner (1967, pp. 65-66)]. However, as Squire has noted (!975), in the framework of the linear expenditure system the elasticity cf the marginal utility of consumption cannot be estimated if the additivity assumptions underlying the Stone-Geary formulation of individual iltility functions are not made. It should further be recalled that, in the ELES formulation. the elasticity of the marginal utility of consumption equals consumptior. ner head divided by the difference between actual and subsistence consump- tion. Since, by definition, subsistence consumption cannot exceed actual consumption, the values of the elasticity will have a lower bound of 1. The elasticity values are thus constrained within certain limits by construc- tion, excluding values hypothesized by Frisch for high-income groups. At the same time, this formulation implies a declining elasticity of the marginal utility of consumption at higher-income levels, since the share of subsistence consumption in the total tends to fall as income rises. Further questions arise as regards the application of the inter-country 226 Bela Balassa results to developing countries. To begin with, while the inclusion of countries with wide differences in income levels ensured a relatively low standard error in the Lluch-Williams regressions, the large devia- tions between observed and estimated values for the middle-income countries reduce the applicability of the results to any particular country. Also, differences in the economic structure and in the distribution of incomes in the mixed group of developed and developing countries for which estimates were made may conflict with the assumption of homogeneity in the pattern of consumption. The heterogeneity of the developing country group in regard to resource endowment, climatic conditions, customs and habits, and political as well as sociological factors, too, limits the applicability of the results to individual developil.. countries. Furthermore, the group of countries included in the Lluch-Williams study does not comprise developing countries with a per capita income below $140 in 1970 prices. This excludes some of the largest developing countries, such as India, Indonesia, and Pakistan, which account for three-fifths of the population of the developing world. At the same time, extrapolation outside the range of observations involves a forecasting error which increases more than proportionately as we move away from this range. Finally, the use of exchange rates to convert national income data expressed in terms of domestic currencies into U.S. dollars imparts a systematic bias to the inter-country relationship between the elasticity of the marginal utility of consumption and per capita incomes. This will be apparent if we consider that productivity tends to increase less rapidly in the production of non-traded goods (services) than in the production of traded goods (agricultural and manufactured products), leading to a rise in the relative price of services at higher-income levels. Now, as purchasing power parities express average differences in the prices of traded and non-traded goods while only traded goods enter into the determination of exchange rates, the ratio of purchasing power parities to exchange rates will be positively correlated with differences in income levels. Correspondingly, the conversion of data at exchange rates will sys- tematically understate per capita incomes in low-incomc countries, aned the degree of understatement will be negatively correlated with incomes per head. Taking the United States as the benchmark of comparisons, in 1960 the degree of understatement was 10%. for Canada and Sweden, 20 to 30% for the United Kingdom, Norway. Belgium. Germany, and Denmark. 40 to 50% for France. Italy, and the Netherlands, and 65% for Japan[Balassa (1964, p. 588)]. The extent of understatement increases Income distribh7tional parameter in project appraisal 227 further in the developing countries, but the lack of a sufficient number of observations and the error possibili. 'es involved in extrapolating the relationships obtained for developed countries do not permit us to estimate this quantitatively at low income levels [Balassa (1973)]. Given the systematic bias in per capita income figures, their range will be substantially smaller than estimated through conversion at exchange rates. Consequently, appropriately adjusted income data will inicrease the slope of the regression line between the elasticity of the marginal utility of consumption and per capita incomes, 5. The preceding sections focused on the estimation of the private elasticity of the marginal utility of consumption that expresses valuation by individual consumers. The next question concerns the relationship be- tween this elasticity and the social elasticity of the marginal utility of consumption. It will be discussed below by making use of equations (2) and (3). The social welfare function shown in (2) will be strictly concave (W,, < 0) or a straight line (Wii = 0), depending on whether it it utilitarian or egalitarian. In the first case, social welfare is taken to be independent of the distribution of individual utilities; in the second case, the social welfare function expresses an aversion to inequality in utility levels, with diminishing marginal rate of substitution of one person's utility for another's. The social elasticity of the marginal utility of consumption (n) will equal the private elasticity (wv), if a utilitarian social welfare function is adopted which involves setting W,,, and hence the second term of equation (3), to zero. In turn, the social elasticity of the marginal utility of consumption will exceed the private elasticity, if we employ an egalitarian social welfare function as negative values for W1, will make the second term of equation (3) positive. Reformulating equation (2) in an additive form under the assumption that the social welfare function is separable in individual utilities, Anand (1973) has derived the relationship between n and w under alternative assumptions as to the values taken by w. Equation (10) shows the relationship for the case when w exceeds 1, n = w + m(w - 1). (10) 228 Bela Balassa In the equation, m reflects the de.gree of social aversion to inequalities in individual utilities.'4 The same relationship was derived independently by Stern who has obtained a value of 4 for the social marginal utility of consumption by assuming that both w and m equal 2. The value chosen for m is said to reflect an a priori judgment as to the range of social elasticity of the marginal utility of income, as well as the view that "we should add something for the egalitarian position" to estimates of w [Stern (1973)]. The choice of m thus requires a value judgment and we are led back to the question of how a social welfare function could be derived. 6. Arrow (1963) has shown the impossibility of deriving a social welfare function from individual preferences, The project evaluation manuals implicitly or explicitly substitute the government's preferences for the social welfare function. In this they appear to follow those who regard the government as the depository of the "will of the people". Such a view has been put forward in regard to a system of representa- tive government, which is not the case in many developing countries where one-party systems and military governments continue in power without the benefit of popular elections, It further endows the govern- ment, irrespective of how it came into power, with attributes of rational- ity. In particular, it is implicitly assumed that, in overruling private preferences, a government's actions will conform to what may be regarded as the well-considered interests of the community. The proponents of introducing government preferences in project evaluation also assume that governments are monolithic and that a welfare function can be derived either from government actions with regard to projects (UNIDO Guidelines) or from government pronounce- ments (Bank Guidelines). Yet not even totalitarian governments are monolithic; they represent instead a conglomeration of interest groups, with continuing shifts in their power position. Also, there is rarely a single project-evaluating agency; rather, decisions on projects are taken by different ministries depending on the sector concerned and often by regional or local authorities. If we consider the decentralization of decision-making on projects and "It should be emphasized that these results depend on the assumed form of the social welfare function. As Squire shows (1975), if the welfare function is written as W= W[F(u(c,)), F(u(c)),. . ., F(u(cj ))], utilitarianism does not necessarily imply that n equals w, nor does an aversion to inequality necessarily imply that n exceeds w. Instcone distributional ptirameter in project appraisal 229 changes in relative powei positioins over time, it will appear to be a rather futile exercise to derive uA elfare weights from historical decisions taken in regard to investment projects. At the same time, deriving a social welfare function from public pronouncements nas the failing that such pro- nouncements are frequently different from the actions taken. Thus, we often find publicly expressed concern with income distribution accom- panied by actions that benefit special groups which are close to the government in power. This fact may reflect differences as between intentions and realization as well as the misstating of intentions for political purposes. Furthermore, the distinction made in project evaluation manuals be- tween intrinsically political objectives-reducing income inequalities- and political constraints-supposedly impeding the realization of these objectives-involves an ambiguity. The problem is put essentially in black-and-white terms, with the objectives being regarded as desirable and the constraints undesirable. This may reflect a rather naive view of the decision-making process or give expression to value judgments on the part of outsiders. The proposed use of project appraisal as a substitute for tax- expenditure policies also involves an ambiguity. Should political con- straints not permit the choice of "appropriate" tax and expenditure measures, the question arises if these constraints would be inoperative in project appraisal. Were this assumed to be the case on the grounds that the complexity of project appraisal permits concealing the use of income distributional measures that would be directly apparent if they were incorporated in the government budget, one might not sufficiently ap- preciate the perspicacity of those affected. Alternatively, the use of income distributional weights in project evaluation may provide a conve- nient excuse for not proceeding with fiscal policies. In this connection, note that in a mixed economy only some of the investment projects are evaluated by an international or governmental authority, often covering but a very small part of economic activity. This fact will limit the practical importance of introducing income distribu- tional considerations in project appraisal. In the partial equilibrium framework used by project evaluation manuals, it also gives rise to the familiar problem,, of the second-best. Second-best considerations will apply even if we limit our attention to public projects. Thus, the introduction of income distributional considera- tions may lead to the choice of a project with a lower increment of output, expressed in terms of income distributional weights, by reason of its effects on relative prices. In the case when producers are the "rich" and consumers the "poor" and supply is completely inelastic, a project whose output faces less elastic demand may then be favored over the one facing 230 Bela Balassa more elastic demand because the increment in intra-marginal transfer inherent in the fall of prices on existing consumption exceeds the loss in output, . In view of the possibility of a loss in output, valued by using income distributional weights, one would need to consider alternative ways of improving the distribution of income, which may be less costly to the national economy. Such alternatives are, however, excluded by assump- tion, since project evaluation manuals generally take fiscal policies as given. In judging the appropriateness of using income distributional weights in project appraisal, one would further need to consider possible effects on entrepreneurial risk-taking and on savings. The former is disregarded in project appraisal manuals while savings effects are considered by assum- ing fixed marginal propensities for individual income recipients and excluding possible changes in saving propensities that may result from the introduction of income distributional considerations in project evaluation. More generally, the quetion needs to be raised if actions taken to reduce income inequalities necessarily improve the lot of the poor in the long run. The validity of this proposition cannot be taken for granted. Thus, we find that countries, such as Argentina and Uruguay in Latin America and Sri Lanka and India in Asia, which adopted egalitarian policies have experienced low rates of economic growth and very slow improvements, if any, in the living standards of the poor. The experience of these countries may be contrasted with that of Hong Kong and Singapore, and subsequently Korea and Taiwan. whose policies oriented towards rapid economic growth have brought substantial in- creases in the income levels of the poor. In Korea, for example, it has been shown that during the 1964-1970 period the per capita incomes of the poor, whether defined as the lowest decile or the lowest four deciles of the population, increased by 58 percent, i.e., at the same rate as average incomes [Adelman-Robinson (forthcoming)]. Thus, tlere are situations when policies aimed at improving income distribution may be damaging for the group they are supposed to serve. This is not to say, however, that one should accept the existing distribu- tion of incomes as given. Rather, one would need to search for methods that can improve income distribution at least cost in terms of a loss in output. The taxation of luxury goods, with the proceeds used to benefit the poor, may be more appropriate for this purpose than the introduction of income distributional weights in project appraisal."6 "I am indebted to Marcelo Selowsky on this point. "On the merits of luxury taxes for reducing income inequalities, see Fellner (1960). Incomte di.stributional parami?eter in project appraisal 231 To begin with. Iluxury taxes do not have adverse effects on entrep- reneurial risk-taking and savings. Also, they reduce conspicuous con- sumption with its unfavorable effects in the form of consumer exter- nalities and limit the flow of domestic resources into the production of luxuries. At the same time, in the event that reliance is based on luxury taxes, one would not neecl to apply a complicated system of taxes and subsidies which is unavoidable in the event that income distributional considerations are introduced in project appraisal since shadow prices will diverge from market prices as a restult. It follows that the introduction of distributional considerations in project appraisal must be preceded by a study of alternative policy instruments, with attention given to their effects on efficiency, savings, and risk-taking.' This suggests the need to place the project appraisal process in the general framework of public decision-making rather than in isolation as the project evaluation manuals tend to do. Finally, questions arise concerning the choice of income distributional weights in project appraisal and in policy making in general. Given the arbitrariness of leriving a social welfare function, it is suggested here that reliance be placed on the private evaluation of the elasticity of the marginal utility of consumption. This, in turn calls for further research to improve available estimates of this elasticity. 7. References Adelman, 1. and S. Robinson, forthcoming, A wage and price endogenous general equilib- rium model of a developing country: Factors affecting the distribution of income in the short run. Anand, S., 1973, Distributional weights in project analysis, mimeo. (International Bank for Reconstruction and Development, W;oshington, DC). Arrow, K., 1963, Social choice and individual values, Cowles Foundation Monograph 12 (Wiley, New York). Balassa, B., 1973, Just how misleading are official exchange rate conversions?, Comment, Economic Journal, Dec. Balassa, B,. 1975, The purchasing-power parity doctrine: A reappraisal, Journal of Political Economy, Dec. Barten, A. 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Fisher, I., 1972, A statistical method of measuring marginal utility and the justice of the progressive income tax, in: Economic essays contributed in honor of John Bates Clark. Frisch, R., 1932, New methods of measuring marginal utility, Beitrage zur Okonomischen Theorie no. 3 (J. C. B. Mohr, Tiibingen). Frisch, R., 1959, A complete scheme for computing all direct and cross demand elasticities in a model with many sectors, Econometrica, April. Hoa, T. V., 1968, Inter-regional elasticities and aggregative bias: A study of consumer demand in Australia, Australian Economic Papers. Janvry, A. de, J. Bieri and A. Nunez, 1972, Estimation of demand parameters under consumer budgeting: An application to Argentina, American Journal of Agricultural Economics, Aug. Little, I. M. D. and J. A. Mirrlees, 1974, Project appraisal and planning for developing countries (Heinemann Educational Books, London). Little, I. M. D. and J. A. Mirrlees, 1965, Manual of industrial project analysis in developing countries, vol. II- Social cost benefit analysis (Development Center of the Organisation for Economic Cooperation and Development (OECD), Paris). Lluch, C., 1973, The extended linear expenditure system, European Economic Review, April, pp. 21-32. Lluch, C. and R. Williams, 1975a, International patterns in the elasticity of the marginal utility of income and expenditure, Development Research Center Discussion Paper no. 1 1 (IBRD, Washington, DC). Lluch, C. and R. Williams, 1975b, Dualism in demand and savings patterns: The case of Korea, Economic Record, March. Pigou, A. C., 1970, A method of determining the numerical values of elasticities of demand, Economic Journal. Sen, A., 1973, On economic inequality (Clarendon Press, Oxford). Squire, L., 1975, Social welfare functions and the private elasticity of the marginal utility of income, mimeo. (IBRD, Washington, DC). Stern, N., 1973, Welfare weights and the elasticity of the marginal valuation of income, mimeo. (St. Catherine College). Tak, H. G. van der and L. Squire, 1975, Economic analysis of projects, Published for the World Bank (Johns Hopkins University Press, Baltimore, MD). Theil, H. and R. B. Brooks, 1970, How does the marginal utility of income change when real income changes?, European Economic Review, Winter. Reprinted with permission from Economic Progress, Private Values, and Public Policy, ed. Bela Balassa and Richard Nelson (Amsterdam: North-Holland, 1977), pages 217-232. The Philippines: Priorities and Prospects for Development by Russell Cheetham, Edward Hawkins, and others, distributed by The Johns Hopkins University Press, 1976 Senegal: Tradition, Diversification, and Economic Development by Heinz Bachmann and others, distributed by The Johns Hopkins University Press, 1974 Turkey: Prospects and Problems of an Expanding Economy by Edmond Asfour and others, distributed by The Johns Hopkins University Press, 1975 Yugoslavia: Development with Decentralization by Vinod Dubey and others, published by The Johns Hopkins University Press, 1975 World Bank Staff Occasional Papers Coffee, Tea, and Cocoa: Market Prospects and Development Lending by Shamsher Singh and others, published by The Johns Hopkins University Press, 1977 Malnutrition and Poverty: Magnitude and Policy Options by Shlomo Reutlinger and Marcelo Selowsky, published by The Johns Hopkins University Press, 1976 Economic Evaluation of Vocational Training Programs by Manuel Zymelman, published by The Johns Hopkins University Press, 1976 A Development Model for the Agricultural Sector of Portugal by Alvin C. Egbert and Hyung M. Kim, published by The Johns Hopkins University Press, 1975 The Future for Hard Fibers and Competition from Synthetics by Enzo R. Grilli, dis- tributed by The Johns Hopkins University Press, 1975 Public Expenditures on Education and Income Distribution in Colombia by Jean- Pierre Jallade, distributed by The Johns Hopkins University Press, 1974 Tropical Hardwood Trade in the Asia-Pacific Region by Kenji Takeuchi, dis- tributed by The Johns Hopkins University Press, 1974 Methods of Project Analysis: A Review by Dec-pak Lai, distributed by The Johns Hopkins University Press, 1974 Other Publications World Tables 1976, published by The Johns .' pkins University Press, 1976 The Tropics and Economic Development: A Provocative Inquiry into the Poverty of Nations by Andrew Kamarck, published by The Johns Hopkins University Press, 1976 Size Distribution of Income: A Compilation of Data by Shail Jain, distributed by The Johns Hopkins University Press, 1975 Redistribution with Growth by Hollis Chenery, Montek S. Ahluwalia, C.L.G. Bell, John H. Duloy, and Richard Jolly, published by Oxford University Press, 1974 THE WORLD BANK Headquarters 1818 H Street, N.W. Washington, D.C. 20433 U.S.A. European Office 66, avenue d'Ilna 75116 Paris, France Tokyo Office Kokusai Building 1-1 Marunouchi 3-chome Chiyoda-ku, Tokyo 1 00, Japan World Bank reprints No. 28. Norman L. Hicks, "A Model of Trade and Growth for the Developing World," European Economic Review No. 29. V. V. Bhatt, "On Technology Policy and its Institutional Frame," World Devel- opment No. 30. Bela Balassa and Ardy Stoutjesdijk, "Economic Integration among Develop- ing Countries," Journal of Common Market Studies (also available in Spanish as published in El Trimestre Econ6mico) No. 31. Constantino Lluch and Ross Williams, "Cross Country Demand and Savings Patterns: An Application of the Extended Linear Expenditure System," The Review of Economics and Statistics No. 32. Marcelo Selowsky, "A Note on Preschool-Age Investment in Human Capital in Developing Countries," Economic Development and Cultural Change No. 33. Shankar Acharya, "Fiscal Financial Intervention, Factor Prices and Factor Propositions: A Review of Issues," Bangladesh Development Studies No. 34. Shlomo Reutlinger, "A Simulation Model for Evalutating Worldwide Buffer Stocks of Wheat," American Journal of Agricultural Economics No. 35. John Sinimons, "Retention of Cognitive Skills Acquired in Primary School," Comparat'.te Education Review No. 36. Montek S. Ahluwalia, "Inequality, Poverty, and Development," Journal of De- velopment Economics No. 37. P.B.R. Hazell and P. L. Scandizzo, "Farmers' Expectations, Risk Aversion, and Market Equilibrium under Risk," American Journal of Agricultural Economics No. 38. Graham Pyatt, "On the Interpretation and Disaggregation of Gini Coeffi- cients," The Economic Journal No. 39. Shamsher Singh, "The International Dialogue on Commodities," Resources Policy No. 40. Gary Kutcher and P. L. Scandizzo, "A Partial Analysis of the Sharetenancy Relationships of Northeast Brazil," Journal of Development Economics No. 41. Bela Balassa, "The Income Distributional Parameter in Project Appraisal," Economic Progress, Private Values and Public Policy (North-Holland)