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X0Í ÍX0Í Í2443|7    X І #x6X@X@# The Consequences of Rapid Population Growth on Human Resource Development: The Case of Education Allen C. Kelley* Duke University  #wd6X@@#August 1994. This paper was presented to the Australian International Development Assistance Bureau on April 7, 1994. The Inquiry Proceedings will appear in Dennis A. Ahlburg, Allen C. Kelley and Karen Oppenheim Mason, The Impacts of Population Growth in Developing Countries (Berlin: SpringerVerlag), 1995. *James B. Duke Professor of Economics, and Associate Director, Center for Demographic Studies, Duke University. We gratefully acknowledge the financial support of the Australian International Development Assistance Bureau; the editorial and manuscriptpreparation assistance of Ms. Gail McKinnis; the research assistance of Anarudh K. Agarwal and Joel Moody; and comments of Dennis Ahlburg, Jere R. Behrman, Robert Cassen, Susan Cochrane, Deborah S. DeGraff, Elizabeth King, Cynthia B. Lloyd, Andrew Mason, Mark Montgomery, Eva Mueller, Richard Sabot, Robert M. Schmidt, JeePeng Tan, Robert J. Willis and Dennis Yang. The usual caveats apply.  Copyright 1995 1.0The Problem The consequences of rapid population growth on human resource development have attracted considerable concern amongst analysts and policy makers. Theories have highlighted the adverse impact on economic growth of diverting resources from productivityenhancing machines and factories toward education and human capital, hypothesized to have lower rates of return.IThe classic assessment is provided in Coale and Hoover (1958) in a model that has had enormous impact. According to political scientist and policy analyst Phyllis T. Piotrow, the CoaleHoover thesis "...eventually provided the justification for birth control as a part of U.S. foreign policy" (1973, p. 15). While the Coale and Hoover study incorporated the extreme assumption of education as a consumption good, the emphasis on the relative productivity of physical capital dominated the literature of the 60s and 70s. In the 80s increased emphasis on the investment returns to human capital emerged. However, few quantitative macroeconomic models incorporate this notion formally, in spite of the reasonably high returns to human capital that have been estimated in many studies (Psacharopoulos [1981, 1985]).I Empirical studies have documented the potentially high costs of schooling required just to sustain educational standards. Expanding the coverage and levels of education would seem to represent a daunting task for many Third World countries.(Studies by Gavin Jones (1971, 1975, 1976, 1990) and others he cites are in this tradition. He appropriately cautions readers that his projections of high education costs in the face of population pressures represent hypothetical possibilities and not actual outcomes. ( While such predictions are at first glance plausible, they represent an overstatement of the economicgrowth costs of, and an understatement of the capacity of countries to respond to, population growth. On analytical grounds, it is not obvious that either the public or the private sectors will finance education costs exclusively or even primarily at the expense of more productive growthrelated expenditures. Government financing may come all or in part from increased efficiencies within the education sector or from a diversion of resources from sectors whose impact on economic growth is low; similarly, household financing may occur all or in part at the expense of lowpriority consumption, or by expanding household income through more work. Whether these financing costs of education are empirically important is not clear; indeed, the real impacts on economic growth or welfare can be small or they can be large.Mason (1993) describes some of the complexities of assessing the welfare impacts of children. "When a woman bears a child, per capita income declines because a given household income must be spread over more members. This is not to say that the parents or the siblings or other relatives of the new member are worse off.... Indeed, if the new child was 'wanted,' those who chose to bear the child are unquestionably better off given any reasonable measure of welfare. But, it is not possible to demonstrate that siblings are better off and the material resources available to any one child will be reduced" (pp. 270271).ċ While it is easy to advance hypothetical scenarios on possible economicgrowth costs of supporting youthrelated expenditures, the actual response of governments and households to population pressures is complex and uncertain; it can only be ascertained with reference to data. In this paper we assemble evidence on the ways in which Third World countries over the period 19601990 have responded in the provision and use of educational services in the face of population pressures. We take up three questions. First, have population pressures significantly constrained the pace of human capital growth in education? To gain empirical perspective, we examine for Third World countries the economywide trends in the "quantity" of education provided, as measured by enrollment rates and by the growth of attainment levels (years of schooling completed), and the "quality" of services offered, as measured by studentteacher ratios. Second, have education expenditures associated with population growth "crowded out" other areas of investment? To gain empirical perspective, we assess the impact of population growth on economywide expenditure shares on education, controlling for the stage of economic development. Third, have large families deterred schooling enrollments and attainment; and how have families underwritten the costs of schooling? To gain empirical perspective, we summarize econometric findings from some 36 studies using householdlevel data on 20 countries.  1.1 Overview of Results We will provide evidence that on average, Third World countries have been surprisingly successful in expanding educational opportunities in the face of significant population pressures, and that the costs of this effort have not been particularly growthinhibiting. While this impressive "widening" of educational opportunitiesan expansion of enrollments to a larger share of schoolaged studentsmay have been financed partially (but by no means totally) by reductions in the "deepening" of the education receivedlowered expenditures or teachers per pupil, the net impact of this quantityquality tradeoff on educational achievements (e.g., exam scores) is highly uncertain. Indeed, changes in class sizes to finance expanding educational opportunities seem to have been relatively unimportant. Contrary to expectations, across countries and over three decades of experience, there may have been a small improvement, not a deterioration, in class sizesa result largely insensitive to demographic pressures. Moreover, there appears to be little or no evidence that the financing of education has systematically diverted funds from more productive investments in physical capital.If investments in human capital have higher returns than investments in physical capital, or even if the returns are lower but there are constraints on capital markets that deter the channeling of funds to physical capital, then it is theoretically possible that an expansion of the investment "vehicle" (children) associated with humancapital investments can contribute to the level as well as the productivity of overall growthenhancing investment. These results must be viewed with caution. None of the research studies ideally addresses the relevant question. Thus, while slower population growth hypothetically "could" have eased the strains on the education sector and "could" have provided released educationwidening resources to undertake desirable educationdeepening and other spending, there are few if any studies that are able to demonstrate what slower population growth "would" have accomplished. As a result, strong conclusions should not be drawn either from the notable successes observed in educational advancement by most Third World countries in the face of rapid population growth, or from hypothetical calculations that illustrate potential, but not actual, outcomes associated with a lower population growth rate scenario. With this in mind, it is instructive to go below national aggregates and consider the impacts on children's educational attainments (years of schooling completed) at the level of the household. Based on many research studies, we find that more often than not, large families do not have a statistically significant impact on educational attainment, as revealed in regression models that account for a wide variety of factors potentially influencing educational outcomes. Where a statistically significant result is revealed, it is usually negative, but the size of the impact is typically quite small. Moreover, in around onethird of the models the impact is positive. Lamentably, most empirical studies also incorporate a bias of undetermined size that exaggerates the estimated negative impacts of family size on educational attainment. Indeed, if parents determine family size in part in response to the prospective costs of educating their children, then virtually all microeconomic studies are misspecified and the results are difficult to interpret. Evidence drawn from appropriately specified and estimated models using microeconomic data is too small to permit any generalizations. There is also considerable evidence of biases in the distribution of education within the family according to gender and, to a lesser extent, birth order, the way in which such biases are related to family size is not well established. Indeed, the prevailing evidence suggests that gender bias is deeply rooted in culture, and that the independent impact of family size #wd6X@@#per se#wd6X@@# in accentuating or attenuating gender bias is relatively unimportant. These various results must be qualified and viewed in context. The total amount of human capital (education) produced by households does indeed increase in large families. How this is financed is relevant. Research tends to show that family financial saving is little impacted by family size, and thus investmentdiversion impacts are plausibly small.See Hammer (1986), National Research Council (1986), Mason (1987). There is recent evidence that this may have changed in the 1980s (Kelley and Schmidt [1994]).ļ As a result, reductions in consumption within the family in favor of investments in children's education (humancapital saving) could enhance economic growth. However, if reduced consumption cuts into family health, growthenhancing impacts can be offset, all or in part. Moreover, most studies do not expose particularly well the impacts on the distribution of human capital resources within families that may be altered by family size. In short, even within the family, tradeoffs between education and other allocations of time and money are complex and difficult to assess. One should therefore be cautious in drawing strong conclusions from findings that show small negative or positive impacts of family size on educational attainments, since this is but one part of a complex picture.Two final qualifications must be emphasized. First, at the macroeconomic level, the data are often poorly measured and they incorporate biases of undetermined magnitude. This is true of all social statistics which tend to be inordinately subjected to political influences. Second, while it may be possible to determine whether the impacts of population pressures exert "small" or "large" impacts on educational inputs (e.g., costs per student), whether these impacts are notable on relevant educational outputs (e.g., achievement scores) is highly subjective since the educationalproduction function is so ill defined. For example, a 2% increase in per student expenditures resulting from an easing of population pressures may seem tiny in terms of "input" growth; but, in the poorest countries, it may well determine whether the school has basic supplies such as books, chalk, and paper. In sum, given the "fuzziness" of the education production function, one should treat evidence from aggregate relationships with a heavy dose of caution.  1.2 Implications Where does this review of educational achievements in the Third World in the face of population pressures leave us? Unfortunately, with an inconclusive assessment which, in an area dominated by strong opinions, may itself represent an interesting finding. While the investmentdiversion formulation has not been confirmed empirically, the challenge to this interpretation must still be considered as suggestive. Surely some investment diversion took place, but such a mechanism for financing schooling in response to population pressures has been neither the exclusive nor even the most important response; indeed, if investmentdiversion has occurred, it has been sufficiently small that it has not been picked up in the broad crosscountry studies. Governments, like households, face many alternatives in adjusting to demographic change. The results showing substantial improvements in enrollment rates and average years completed per pupil also raise a fundamental issue concerning the impact of demographic change on capital formation. In particular, the classification of spending on items such as schooling as "unproductive" and spending on physical capital as "productive" is inappropriate because it downplays the value of literacy, numeracy, and other schoolacquired skills as determinants of income growth. The greatest flaw in the literature that assesses the impact of rapid population growth on development is the failure to take into account, or to weight heavily enough, "feedbacks" in response to population pressures. In areas as diverse as natural resource use and economywide saving, these feedbacks have been shown to be pervasive and important.QSee National Research Council (1986) and Kelley (1993).Q This now appears to be the case in education provision. Shortrun resourceshallowing characterizations of the impacts of rapid population growth that hypothesize little or no tradeoffs in consumption and/or production can be wide of the mark. In fact, businesses, households, and governments respond to population pressures in ways that expand resources, including reallocations that improve overall efficiency of resource use. For example, and in direct response to population pressures, governments may reallocate education resources toward basic and away from tertiary education, doubleshift schools to obtain higher use of capital, modify studentteacher ratios and resource use in ways that appear to be cost effective, and costshare at more advanced education levels where the benefits of additional education accrue primarily to the student.fFor example, Korea has maintained high studentteacher ratios to provide qualitative improvements resulting in greater retention and efficiency; Thailand has multiple higher education options, from high to low cost (and relative quality) offerings; the Philippines has extensive private financing, especially at postprimary levels.f As a result, while impacts of population growth in the short run are often negative, over the longer run positive feedbacks attenuate, and in some cases offset, the shortrun impacts. In the case of education, while some resourceshallowing impacts are found at the household level, the importance of this on educational attainment, properly measured, is uncertain. What is clear is that the widening of educational opportunities during periods of rapid population growth has been impressive, if not extraordinary, at the economywide level; and that levels of education per student have risen notably. While some reductions in educational quality per student in a given grade level have likely occurred, we would speculate that the growth of the qualityadjusted perstudent human capital stock in the face of population pressures has been impressive indeed. 2.0 Trends in Schooling Outcomes: The EconomyWide Perspective As noted above, two broad hypotheses have characterized the literature describing economywide responses by the education sector to the pressures of rapid population growth. The first, the "investmentdiversion" argument found in several economicdemographic models, shows population growth shifting (mainly governmental) spending away from growthenhancing forms such as physicalcapital investment, and toward allegedly less productive forms such as schooling.In most models, spending on education is classified as consumption (Coale and Hoover [1958]; McFarland, Bennett, and Brown [1973]; Rodgers, W)ry and Hopkins [1976]; Anker and Knowles [1983]. The World Development Report 1984 presents a variant of the investmentdiversion hypothesis, speculating that the schooling requirements of an expanding population (capital widening) diverts resources from quality improvements (capital deepening) in education (World Bank [1984], p. 85). See also Gavin W. Jones (1971, 1975, 1976). An alternative perspective that highlights the productivity of human capital is provided by Birdsall and Sabot (1993). They conclude that, with appropriate government policies, Asian countries expanded human capital investments in ways that simultaneously reduced population growth and reinforced both the pace and an equitable distribution of production.ĕ The second, the "humancapital constraint" argument, predicts difficulty in even maintaining existing educational achievements; notably widening the coverage of education, and/or deepening schooling achievements (e.g., advancing attainment levels per student) would appear to represent an unattainable outcome in the face of higher priority areas of development spending, shortages of teachers, and the like. In this section we examine these hypotheses in light of trends in schooling over the period since 1960. We first explore enrollment and schoolingattainment trends to gain some perspective into the widening/deepening issues.Education data are subject to considerable error and biases and must, as a result, be used with great care. See Behrman and Rosenzweig (1993, 1994).į We next examine the results of one study of these tradeoffs for the 1970s, considering in particular the matter of possible investment diversion; and we update these results to the 1980s.  2.1` ` ` Trends in Schooling Outcomes: 19601990 What has been the record of educational investments in the Third World since 1960? In terms of the quantity of educational outcomes, this question can be addressed in part by examining enrollment ratesa measure of the flow of educational activity during a period of time, and by changes in average achievement levels (e.g., years of schooling completed)a measure of the growth of the stock of education over time. Both measures must be qualified by changes that may be occurring in the quality of education. The latter is sometimes measured (quite imperfectly) by students per teacher or by expenditures per student, data we will examine in the next two sections. Enrollment Rates. The top panels of figure 1 present gross enrollment rates for primary and secondary education for a group of 67 developing countries over the period 19601990 by region; the bottom panels provide changes in these rates for each fiveyear period.Gross enrollment rates represent school enrollments divided by the number of students whose ages correspond to the schooling level. These rates can exceed 100% due to various delays in completing an education level. The rates, typically representing beginning school year attendance, can notably overstate enrollments due to the existence of dropouts. For more detailed analyses, see Behrman and Rosenzweig (1993, 1994). The underlying data are presented in table 1.While trends in some of these indexes are provided for various country groupings and periods elsewhere, our empirical contributions here are to 1) update the estimates to 1990 using recently released UNESCO data, 2) assemble regional and other categorizations using a common country grouping that permits comparison with findings in other studies, and 3) utilize the recently available Barro and Lee (1993) measure of educational attainment. For both primary and secondary education, the record is impressive and clear. There has been a surprisingly large expansion of enrollments over this period. Primary enrollment ratios are presently around 100% in both Asia and Latin America. While enrollment ratios are lower in Africa, the overall growth of enrollments in this region was especially rapid over the 1960s and 70s, as seen in the third panel: enrollment rates rose from 40% to 70% in just two decades, an amazing pace by historical standards.Williamson (1993), pp. 147151. Part of the somewhat astonishing success in Africa results from the colonial legacy of an exceptionally high value attributed to education. Thus, while progress has been impressive, this has not been without cost. There is abundant evidence of households making substantial sacrifices to insure the educational outcomes of children.ĉ In the 1980s Africa has struggled to maintain its advancing pace of educational participation; indeed, small reversals have taken place. Whether the previous trend will be reestablished depends in substantial part on a reversal of blank page for figure 1 Table 1  Gross Enrollment Rates by Level and Region, 19601990    Level   Change  | dd888888 dd888888 | *^^*Date/ PeriodAfricaAsiaLatin America AfricaAsiaLatin America**܃܃܃܃**܃܃Primary܃܃**܃܃܃܃܃܃**196039.967.585.3܃܃܃**196549.677.091.49.79.56.1**197051.881.794.92.24.73.5**197560.686.896.98.85.12.0**198071.691.6100.711.04.83.8**198572.395.9102.60.74.31.9**199069.398.5100.7ܩ3.02.6ܩ2.0 **Secondaryă | dd88(8 dd88(8 | **19603.515.617.8܃܃܃**19655.521.822.82.16.35.0**19707.827.628.52.25.85.8**197511.733.236.83.95.68.3**198016.838.542.45.15.35.6**198520.544.145.23.75.62.9**199021.848.148.41.34.03.2 Source: UNESCO, Statistical Yearbook, various years. See appendix table B. largely exogenous events that have plagued this region in the 1980sthe impacts of severe droughts, falling terms of trade, and reduced exports arising from OECDinduced recession. Declining fertility, just beginning in Africa, will be facilitating as well. Secondary enrollment rates in all regions also increased impressively over the entire period. The lower growth in Africa in the earlier decades is attributable in part to the lower initial conditions in this region (i.e., fewer students qualified for secondary schools). Still, by the mid 1970s the growth of secondary enrollment rates in Africa was equal to the rates in Asia and Central/Latin America, and not until the late 1980s did this region's pace begin to fall behind. Attainment Levels. In terms of the impact on economywide economic growth, possibly a better measure of educational progress relates to changes in the average educational attainment (years of schooling completed) of adults. This represents a bottomline measure that takes into account the age distribution of the population, as well as the impact of those entering (leaving) the workforce with relatively high (low) education levels. Table 2 presents levels and changes in average attainment by region over the period 19601985. Over the entire 25year period, average attainment doubled in Africa and Asia, and increased by 80% in Latin America. Africa, of course, began from a lower level and thus, in terms of absolute change, advanced relatively slowly (1.2 years) by comparison with Latin America (1.8 years) and Asia (2.0 years). In each region, including Africa, the pace of change has increased over time. Table 2 Z Z Educational Attainment of Adults (25+) by Region: 19601985  X   Date/ Africa Asia Latin Period Amer.   <!301960 B41.18 By4y1.92 B2.91 1965B41.28By4y2.19B3.11 1970B41.48By4y2.53B3.33 1975B41.67By4y2.86B3.74 1980B42.01By4y3.27B4.22 1985B42.36By4y3.91B4.66  Source: Barro and Lee (1993). Average years of education completed, population 25 years and older. Country coverage is provided in appendix table B.   X` hp x (#%'0*,.8135@8:t@ Bangladesh 159 49 11 1.8 4.4 33 54 60 .. 18 .. 5.2 China 273 33 25 0.2 7.8 69 89 118 24 39 0.6 1.7 India 259 44 10 1.6 4.4 43 73 92 26 41 8.6 9.0 Indonesia 470 46 8 1.8 6.1 74 80 118 16 42 2.4 6.5 Korea 2,040 31 40 0.8 7.4 92 103 96 42 75 10.3 31.6 Malaysia 1,860 41 27 0.8 6.3 74 87 99 34 53 2.8 6.0 Myanmar 184 47 7 2.4 5.8 .. 83 107 21 23 2.1 5.4 Nepal 142 49 7 2.7 3.1 26 22 82 10 25 2.3 4.6 Papua N.G. 621 50 6 2.6 1.5 45 52 70 8 13 2.5 2.0 Philippines 581 47 11 2.1 2.5 86 108 106 46 65 18.4 38.0 Sri Lanka 374 36 27 0.1 4.9 87 99 103 47 63 1.3 4.6 Thailand 712 41 27 0.6 5.8 91 83 97 17 30 3.4 19.6  Regional Ave. 640 43 14 1.3 5.0 65 78 96 26 41 5.0 11.2 Rapid Dep. Decl. 1051 36 29 0.2 6.4 83 92 103 33 52 3.7 12.7 Mod. Dep. Decl. 367 47 10 1.8 4.4 59 79 94 29 42 9.8 14.7 Slow Dep. Decl. 315 49 7 2.6 3.5 36 52 86 13 20 2.3 4.0 ,4 <DL!T$&)\+- 0d247l9;>t@ Average Public Spending Share of Government Unit Operating Costs Grade on Education  Education Spending on   as % of GDP/N  Country Attainment as % of GDP Prim. Sec. Tert. Oth. Prim. Sec. Tert.  (13) (14) (15) (16) (17) (18) (19) (20) (21)   Bangladesh 3.9 1.5 49 34 15 2 6.4 30.0 284.6 China 5.1 3.3 41 42 18 0 6.7 22.6 199.2 India 4.8 3.0 27 47 19 6 6.0 17.3 231.1 Indonesia 7.3 3.7 62 27 9 2 12.6 23.3 91.1 Korea 11.4 3.4 57 34 9 0 16.5 23.4 70.6 Malaysia 9.2 6.0 36 34 26 4 14.1 21.3 190.3 Myanmar 7.0 1.8 .. .. .. .. .. .. .. Nepal 3.6 1.8 41 21 35 3 9.0 13.5 249.0 Papua N.G. 4.3 6.9 45 18 28 10 29.0 65.0 1050.0 Philippines 10.2 1.8 64 16 20 0 5.8 8.6 50.0 Sri Lanka 9.5 2.8 43 41 16 0 6.1 9.3 83.3 Thailand 7.0 3.6 58 24 12 6 15.5 15.3 39.9  Regional Ave. 6.9 3.3 48 31 19 3 11.6 22.7 230.8 Rapid Dep. Decl. 8.4 3.8 47 35 16 2 11.8 18.4 116.7 Mod. Dep. Decl. 6.6 2.5 51 31 16 3 7.7 19.8 164.2 Slow Dep. Decl. 5.0 3.5 43 20 32 7 19.0 39.3 649.5     X  X ^Table 5 (continued)   Teacher Costs Pupils per Fees as % of Share Enrollment per GDP/N Teacher Unit Costs Private in Total Country Prim. Sec. Prim. Sec. Tert. Sec. Tert. Sec. Tert.  (22) (23) (24) (25) (26) (27) (28) (29) (30)   Bangladesh 2.2 .. 47.0 26.2 15.9 4.0 0.1 93.0 58.7 China 1.6 2.8 24.9 17.2 5.2 3.2 0.3 0.0 0.0 India 2.9 3.1 57.6 20.2 15.7 11.6 4.5 .. 57.6 Indonesia 2.5 3.2 25.3 15.3 14.0 27.4 18.9 49.7 58.3 Korea 5.0 5.5 38.3 34.3 42.2 34.2 45.9 39.9 66.1 Malaysia 2.4 3.1 24.1 22.1 11.4 4.0 5.8 1.7 11.0 Myanmar .. .. 46.4 28.5 30.3 .. .. .. 0.0 Nepal 2.8 5.0 35.5 27.5 13.2 40.7 10.4 10.4 23.8 Papua N.G. 6.8 10.0 31.0 25.4 7.7 39.8 0.0 .. 6.3 Philippines 1.6 1.7 30.9 32.2 16.0 9.3 15.3 42.4 83.2 Sri Lanka 1.6 2.1 31.7 26.1 10.7 3.1 3.4 2.4 0.0 Thailand 2.5 2.9 19.3 19.6 8.3 18.3 5.0 20.0 6.4  Regional Ave. 2.9 3.9 34.3 24.6 15.9 17.8 10.0 28.8 31.0 Rapid Dep. Decl. 2.6 3.3 27.7 23.9 15.6 12.6 12.1 12.8 16.7 Mod. Dep. Decl. 2.3 2.7 40.2 23.5 15.4 13.1 9.7 61.7 64.5 Slow Dep. Decl. 4.8 7.5 37.6 27.1 17.1 40.3 5.2 10.0     Note: Data from Tan and Mingat (1992): Cols. 1, 6 and 13, p. 106; cols. 2 and 3, p. 19; cols. 45, p. 20; cols. 712, p. 15; col. 14, p. 17; cols. 1518, p. 27; cols. 1921, p. 29; cols. 2225, p. 34; col. 26, p. 37; cols. 27 and 28, p. 40, and cols. 29 and 30, p. 18. Regional averages were calculated for those countries for which data were available; the countries were divided into three groups: those whose youth dependencyrate decline since 1970 has been 1) rapid (China, Korea, Malaysia, Sri Lanka, Thailand), 2) moderate (Bangladesh, India, Indonesia, Philippines), or 3) slow (Myanmar, Nepal, Papua New Guinea). 3'   have experienced rapid demographic transformations to 2.6% in those where the transformation has yet to begin (col. 4). One indicator of the capacity of countries to invest in schooling is provided by comparing the growth of the schoolaged population with the growth of income (cols. 4 and 5). By this measure, and in spite of rapid population growth, the Asian region had substantial capacity to advance its educational programming over the last decade. Indeed, the average economic growth rate of 5.0% notably outpaced the growth of schoolaged children of 1.3%, providing plenty of resourcesa growth dividend of 3.7%with which to widen and/or deepen educational opportunities without diverting resources from other areas in the economy.Birdsall and Sabot (1993) have emphasized the importance of economic growth in East Asia in accounting for exceptional educational advances in recent decades.ĸ This growth dividend gap varied from a whopping 6.2% in countries experiencing rapid demographic transformation to only .9% in the relatively poor countries of the region. (The gap was negative in Nepal and Papua New Guinea.) It is important to note that most of the variation in the size of the growthdividend gap is determined by variations in aggregate economic, and not population, growth. This comparison underscores and quantifies, in a simple way, the obvious importance of economic growth in accommodating the requirements of a rapidly expanding population. Educational achievements in Asia have been impressive. Universal primary enrollment has been reached in most countries, and this goal is rapidly becoming a reality in even the poorest countries of the region (cols. 78). Secondary enrollments have risen substantially as well: from 26% in 1970 to 41% in only 15 years (cols. 910). The regionwide average educational attainment of 7 years is also high, although variation around this average is considerablefrom 5 years in the poor countries to in excess of 10 in the most prosperous (col. 13). Possibly the most interesting data in table 5 relate to the structure of financing and costs. There is substantial variability in the unit cost of providing education. On average, secondary and tertiary costs are, respectively, double and 20times those of primary education. The determinants of costs vary from place to place. In Korea and Papua New Guinea, teachers are relatively expensive (cols. 2223); in Indonesia and Thailand, class sizes are quite small (cols. 2426). Interestingly, class size (especially above the primary level) does not appear to be strongly related either to income per capita or to demographic pressures. CLASS These results are corroborated by regressions (see appendix table C) that examine the determinants of studentteacher ratios for LDCs in 1985. Higher studentteacher ratios are found in lower income, and more urban, countries. Neither the rate of population growth nor the size of the schooling cohort has an independent impact on the ratios. These results control for region (Asia, Latin America, Africa), and they hold both for primary and secondary education. These results should be considered as preliminary, since they have not been subjected to sensitivity analysis with respect to observations of unusual influence, alternative data samples, periods of analysis, and the like. Clearly the classsize measure of "education quality" must be used with great caution. Contrasts in the patterns and strategies of education provision can be illustrated by comparing Korea and Thailand, both countries well along in the demographic transition.We refer here to that phase of the "Demographic Transition" where death rates are fairly low and declining, and birth rates are declining quite significantly as well. On the one hand, Thailand appears to be lagging in the spread of educational services: years of schooling attained is below the average of the region, and secondary enrollments are relatively low. On the other hand, schooling expenditures (especially at the primary level) are high, and class sizes are small. In contrast, in Korea, held by some observers as exemplifying success in Asian education (the output statistics are supportive), a different structure emerges. Class sizes have been amongst the largest in the region, and emphasis has been placed on the spread of educational services (secondary and tertiary enrollments are high) and possibly teacher quality (teacher salaries are amongst the highest in the region). These types of comparisons confirm the judgment of Tan and Mingat that, in assessing schooling in the region, allocations within the education sector are likely to be as important as, or even more important than, the total amount of resources devoted to education. Indeed, on average Asian countries spend about the same share of their GDP on education as do countries in Africa and Latin America, in spite of higher incomes and lower demographic pressures in the region.&Evidence for the 1980s above (table 3) shows that Africa's commitment to public education is relatively strong if one controls for the level of per capita income, urbanization, and demographic structure. This is consistent with Schultz' (1987) findings for the 1970s.& But there is considerable variation: for example, the shares are around 2% in Bangladesh, Nepal and the Philippines, and around 6% in Malaysia and Papua New Guinea (col. 14). In only the first three countries do the authors feel confident that there is notable underinvestment in education, and that increases in spending should represent a priority. For many, if not most, of the remaining countries, progress in the education sector should focus largely on efficiencyraising strategies. "The explanation is simple: outcomes are determined as much by the efficiency with which resources are used as by the aggregate amount of resources available" (p. 6). Tan and Mingat are somewhat critical of some aspects of Asian education; in particular, in a sizeable number of countries, there is: 1) poor performance in retention, especially at the primary level;They note that 91 percent of the population enters grade 1, but only 62% reaches the end of primary schooling. In countries like Bangladesh, Bhutan, India, Lao PDR and Nepal, the survival rates are around 40% or less. To resolve this problem they note that, while in some countries (e.g., Bangladesh and India) some increase in expenditures per student would help, "...throwing more money at schools does not in itself insure against low cohort survival rates,..." (p. 7).  2) a decided bias toward higher education at the expense of primary education;This bias is strongest in some of the countries least able to afford it: Bangladesh, India, and Papua New Guinea.Č 3) the existence of numerous opportunities for improving the efficiency of school provision that are not taken up; and 4) a tendency to reinforce social inequities through high public subsidies to relatively welloff students attending universities, where the cost of education per student can be upwards of 50 times that of the cost of educating a primary student, with no correspondingly high rate of return.Hughes et al. (1986, pp. 97100, 111112) provide a similar assessment for the Pacific Island developing countries, citing numerous areas where restructuring of the education system could result in more efficient use of educational resources. For a more recent assessment, see Ahlburg (1993), who notes for this region that "Educational outcomes are not in line with the percentage of budget spent on it" (p. 35).ĸ "Thus, for most Asian countries improvement will result largely from promoting the efficient use of resources rather than expanding the overall resource envelope" (pp. 67).They illustrate the importance of government policies by noting that enrollment ratios in the Philippines far exceed those in Bangladesh (both with relatively low spending levels on public education), and enrollment rates in Malaysia exceed those in Papua New Guinea (both with relatively high spending levels on public education). Differential roles of the private sector, also influenced by government policy, enter importantly into these comparisons. These findings may extend beyond Asia. A regression model is presented that attempts to explain gradelevel attainment for some 82 countries in the mid 1980s.CTan and Mingat (1992), table 2.21, p. 23.C While gradelevel attainment (years of schooling) is reduced by high dependency rates, surprisingly the share of GDP that governments devote to education does not influence attainment. This result, coupled with several studies showing no direct impact of demography on the share of GDP devoted to education, suggests that the impact of population growth on attainment likely operates mainly through resource allocations within the education sector.Such a conclusion must be guarded since the statistical results, to date, do not account simultaneously for the possibility of mutually interacting relationships, and thus may be unreliable. This is consistent with the Tan and Mingat conclusion that "relatively large gaps in public spending on education account for only modest disparities in the volume of human capital formation" (p. 22). If one accepts this assessment, what are the implications on the possible impacts of reduced population growth? While, on the one hand, Tan and Mingat observe that lower population growth has the potential to provide substantial released resources for both expanding and upgrading the education sector, on the other hand, they provide little evidence that such an outcome would be in the offing. Indeed, for a number of Asian countries Tan and Mingat are not optimistic that infusions of even moderate additional resources from any source would appreciably enhance educational outcomes unless policy changes are made to improve the productivity of resource use. Their results also raise a relevant and intriguing question: will governments be more, or less, likely to make politically difficult but "enlightened" policy changes with respect to the education sector under the pressures of rapid demographic change? While the latter can constrain options, it can also serve as a catalyst for change. For example, rapid population growth may "force" unpopular policy changes such as shifting resources from tertiary to basic education or imposing higher fees at more advanced levels of education;Based on an analysis of data from the Demographic and Health Survey for Kenya, Kelley and Nobbe (1990) argue that a combination of population pressures and fiscal restraint in the 1980s has resulted in the government implementing a policy of expanded costsharing for some social services, including education. Without passing normative judgment on the appropriateness of such a policy, the impact is clear. It raised the costs of children to parents who, in response, had smaller families. These populationinduced policychanges may well have been the triggering device that initiated the next phase of the Kenyan demographic transition. See also Lillard and Willis (1994), and Jones (1990).  alternatively, demographic pressures may constrain viable options for change. While clearly one would not advocate high fertility as a means to encourage improved government policy making, one should not ignore the potential impacts of demographic pressures on government policies. At the least, such feedbacks, still highly speculative given a lack of a robust theory of government "behavior," could well modify assessments of the consequences of population growth on the education sector. These politicaleconomy issues are relatively unexplored but, in our judgment, they are central to assessing the consequences of rapid population growth. As we have noted elsewhere,(Kelley (1988).( a major impact of population growth has been to reveal the consequences of bad policies sooner and more dramatically; as such, population growth "exacerbates" some problems, but may not be their most important cause. As a result, it may represent misplaced emphasis to confront such problems with population policies because, without a change in economic and sectoral policies, slower population growth may simply postpone the day of reckoning when the adverse consequences of poor public policies are tallied. On the other hand, the most defendable strategy is likely to be one that advances an appropriate balance between sectoral and population policies, taking into account the fact that the impacts of population policies will typically be gradual and slow in realization. The eitheror choice between, say, policies that improve education provision versus policies to reduce population growth (e.g., voluntary family planning programs), should be eschewed: the two policies are intertwined and often mutually reinforcing. This position is nicely summarized by Srinivasan (1987) with respect to food shortages caused in large part by bad government policies, although he cautions:   The cause of eliminating starvation...will be illserved if, instead of analyzing avoidable policy failure, policy makers turn their attention to attempts at changing an admittedly slowacting process such as the interaction between population growth and the food economy. This is not to deny the modest improvements... resulting from an exogenous reduction in the rate of population growth; rather it is to point out that the payoff to the correction of policy failures is likely to be much more rapid and perhaps greater (p. 25).   At any rate, whether or not policies that reduce population growth rates will facilitate educational advancement in Asia, it is likely that alternative policies will have much stronger impacts and be faster acting. This simply argues for a broad perspective in assessing combinations of education and population policies that will carry out a common set of goals such as advancing the qualityadjusted level of educational attainment in the region. This analysis also exposes the difficulties of assessing public policies in general. While direct interventions almost always have much larger and fasteracting impacts on targeted goals, population policies, having seemingly relatively small impacts on several sectors, can still be costeffective economically, especially if the costs of intervention are low and the sectoral impacts interact in positive ways. Virtuous Circles: Human Capital, Growth, and Equity in East Asia, by Nancy Birdsall and Richard Sabot (1993), examines the impacts of the extraordinary expansion of education in the relatively successful countries of East Asia. The authors observe that the development strategy of simultaneously promoting education and skill/laborintensive production has resulted in three mutually reinforcing trends: a rapid pace of economic growth, a relatively equitable distribution of income and wealth, and a reduced rate of population growth. In accounting for East Asia's remarkable achievements in education, Birdsall and Sabot, like Tan and Mingat, downplay the importance of the overall share of GDP allocated to education. Instead, five other factors are highlighted: 1) rapid overall economic growth (largely the result of an exportoriented, skill/laborintensive production strategy); 2) a strong commitment to basic (as distinct from higher) education; 3) government policies that equalize the distribution of income and wealth (especially land); 4) a high investment in the quality of basic education, resulting in fairly high expenditures per student at the primary level; and 5) an early demographic transition.They do not rank the various factors, but they examine in some detail the potentially favorable impacts of reduced population growth, emphasizing the adverse qualityquantity tradeoffs necessitated by relatively rapid rates of population growth in an environment where the overall expenditure share is relatively fixed. Considerable detail is provided on the nature of these tradeoffs for East Asia. How can we reconcile the relatively higher predicted favorable impacts of reduced population growth on educational outcomes as assessed by Birdsall and Sabot, and the less optimistic prediction implied by the results of Tan and Mingat? The answer appears to lie largely in the different country samples. In those countries in which government economic policies are relatively sound and the education sector is quite efficientthe BirdsallSabot EastAsian sampleincremental expenditures on education enabled by reduced population growth rates will enjoy relatively high rates of return. Indeed, they emphasize that "The efficient utilization of educated workers is also a necessity. Some nations squandered their [human] capital which, at great sacrifice, they had accumulated" (p. 3) (emphasis ours). This is in contrast to the TanMingat sample which, in addition to the "miracle" countries, includes a sizeable group of Asian nations saddled with arguably questionable economic policies and inefficient education sectors. As a result, released resources deriving from reduced population growth, if used to expand but replicate inefficient budgetary allocations, could have disappointing impacts on educational outcomes.`Tan and Mingat (1992, table 5.3) compile an index of the relative degree of emphasis on higher education for the mid 1980s in Asia. The index focuses on 1) unit costs, 2) coverage, and 3) costliness to the government. In order, countries with the largest highereducation bias are Bangladesh, India, and Papua New Guinea. ` It is this latter group of relatively poorperforming countries that is most relevant to Australia's area of interest in terms of foreignaid support. Sadly, it appears that the mutual interaction of poor government policies, rapid population growth, and poverty can for these countries result in vicious rather virtuous circles of change.According to Tan and Mingat's classifications, Asian virtuous countries include, for example, Indonesia, Korea, and Taiwan; those with relatively inefficient education structures include Bangladesh, India, Malaysia, and Papua New Guinea.֌This analysis highlights the sensitivity of assessments of the impact of population growth rate reductions to the specific way in which the question is framed. Reduced rates of population growth do indeed release funds that could be used to productive end: improvements in the quality and scope of educational services, and a host of other options. But these funds could, and often are, squandered, as both Birdsall and Sabot, and Tan and Mingat, have observed. Whether population growth rate reductions would have favorable impacts can only be surmised, but assessing this impact depends very significantly on an assessment of government policies more generally. Unfortunately, with few exceptions, the evidence for those countries in which Australia is most likely to allocate its programming efforts are the very countries plagued with relatively inefficient macroeconomic and sectoral public policies which, until corrected, will greatly diminish the potential for positive impacts of population growth rate reductions generally, and in the education sector in particular. This argues for a consideration of policy packages that address issues of sectoral resource allocation in those areas where population programming is anticipated to yield its greatest returns, and the consideration of conditionalities that will increase the potential efficacy of aid spending. 5.0Educational Outcomes within the Household While trends in schooling enrollments, attainment, and financing are useful for assessing economywide impacts of population pressures on educational provision and economic growth, the underlying impacts of these pressures are in large part manifested within families and households, whose responses can be not only subtle and important to welfare, but also masked by aggregate statistics. In this section we take up the question: what has been the impact of sibsize (numbers of brothers and sisters) on the level and distribution of education within the family or household?_Throughout we loosely use "sibsize," "number of children," and "family size" interchangeably, a correspondence that is not strictly accurate. Most studies we have examined focus on sibsize. Those using number of children predominantly represent sibsize. The impact of number of adults is typically controlled for directly._  5.1 Theory Social and economic theories describing possible impacts of sibsize on the consumption and distribution of education are abundant. Hypotheses vary from family size having a deterring to a stimulating impact, and from the financing of education being broadly shared by family members to being assessed disproportionately to particular children. None of the predictions is compelling on analytical grounds. Indeed, the impact of sibsize on family commitments of "resources"money and time, including especially the time of childrento children's education is sufficiently complex that the underlying relationships can only be determined from the data.GIn addition to the direct impacts of family size on education, two indirect impacts, downplayed (but possibly important) in this study, include impacts on IQ (or mental age) and health. An IQ linkage with birth order, based in part on a study of Dutch males (Belmont and Marolla [1973]), is often assessed to be negative. These results are not without challenge (Retherford and Sewell [1991]). Lloyd (1994a) assesses the linkages between health and education to be empirically strong. See also Lloyd and Montgomery in this volume, and World Bank (1993).G Two examples, relating first to the impacts of family size on intrafamily resource commitments to education, and second to the impacts of family size on the intrafamily production function of education and other activities, suffice to establish this proposition. Resource Commitments. In terms of the impact of family size on the household's resource commitments to education, and in a simple model which assumes that 1) the family's time and monetary allocations to various household activities are relatively fixed and 2) the family's total resources are fixed (more precisely, unrelated to family size), additional children impose incremental burdens and cause a reduction in the amount of resources allocated to the education of each child. This is sometimes called the "resourcedilution" effect.QThis framework is elaborated in detail by Blake (1989).Q Whether such an effect is important depends on the strength of the two key assumptions. For example, contrary to the simple model, parents may elect to maintain perchild educational expenditures, financing them from saving, from time and money devoted to themselves, or from expenditures on or by children in areas other than education.Most household expenditure studies focus on the size and not the distribution of the costs of children. Based on household data for the Philippines and Thailand and on Engle and Rothbarth equivalence scales, Bauer and Mason (1993) conclude that children assume the bulk of the total (not just educational) financial costs accruing from larger household size.ā Parents in larger families may also elect to work more and longer, and children may contribute directly both to market and to nonmarket (home) activities. Either of these modifications of the simple resourcedilution model is sufficient to reduce or eliminate negative resourceallocation impacts of increased family size on educational outcomes within the household. While it is certain that some adjustments to attenuate resourcedilution impacts of family size take place, the key issue is whether these responses are quantitatively important. Production Function. In terms of the impact of family size on the household's production function of education and other activities, again the hypotheses offered in the literature are numerous and varied.By "production function" we mean the amount of "factors" such as time and money that households use, and the ways they combine these factors, to produce various outcomes such as children's educational achievements. Empirical studies are required to ferret out the impacts. Several examples establish this proposition. First, large families plausibly exert a positive impact on the educational outcomes of siblings through economies of scale: older siblings may assist younger siblings in their studies, and there may be some sharing of educational supplies. Second, large families may result in middle children receiving relatively less education than their siblings. While more resources may be available from child labor in larger families, and while large families may enjoy efficiencies resulting from greater division of labor in household production, credit constraints may deter families from their desired allocation of resources to education.3Parish and Willis (1993).3 Thus middle children may be disadvantaged since the share of total resources potentially available to education declines with family sizea pattern advantaging the older children; and the expansion of household resources from the contributions of child labor increases with family sizea pattern advantaging the younger children. Timing of these offsetting trends works to the disadvantage of middle children in large families unless resources can be made available from credit or other means (e.g., government subsidies, extended family expenditures, or loans).This does not imply that middle children necessarily lose in wealth distribution overall, but only that some education expenditures may not be available while they are growing up. Should parents so elect, alternative wealth transfers can be made at a later date to compensate middle children for this inequity. Thus, the impact of sibsize on overall lifetime wealth distribution may turn out to be less than the form of that distribution. Third, large families may positively contribute to education, other things equal, to the extent that there are diminishing returns to child labor in activities that compete with education. Finally, large families may amplify or mitigate gender effects in the allocation of educational resources. Most gender biases are strongly culturally based and/or are related to differential returns to education by gender that are independent of family size. On the other hand, the opportunities to discriminate may vary by family size: in small families, more resources may be available to enable discrimination; in large families, there are greater opportunities for genderspecific division of labor in home and market production. The impact of family size per se can only be determined from the data.xRigorous empirical tests of this relationship are rare. See below, footnote  TEST75 .x Endogenous Fertility. The analysis of household allocations to education is made more complex by the possibility that the family size choice depends in part on the resources parents plan to invest in each child. In one commonlyemployed economic model of this decision, parents strive to allocate the same amount of resources (quality) to each of their children.ZBecker and Lewis (1973), Becker and Tomes (1976), Willis (1973).Z As a result, any increase in the cost of quality (e.g., education)a necessary result of increased family sizecan induce parents to seek a smaller family size. Such a possibility qualifies the interpretation of empirical studies that relate child quality (education enrollments and attainment) to family size but that fail to take into account the reverse feedback of the costs of child quality on the familysize decision.Models of such a process assume a capacity of parents to finance children's education, e.g., a credit market. Parish and Willis (1993) emphasize that the lack of such credit in part accounts for some apparent birthorder inequities in educational outcomes. Mueller (1984a) argues that the BeckerLewis framework applies to relatively advanced areas, and is largely inapplicable to poor and rural developing countries.Ľ Elizabeth King's (1987) survey of the literature is explicit in this regard:   ...given that family size and child quality are simultaneously determined choices, it is erroneous to interpret the negative association between family size and the child's physical health or intellectual performance as evidence of causality (p. 397).   Summary. Theory suggests that the direction of the impact of family size on educational outcomes is ambiguous: it can be positive, negative, or zero, and it can be associated with several alternative allocations of education by gender and birth order. It is more likely to be negative where intrahousehold resource allocations are inflexible, where children contribute little to economic output, where the options for parents to expand their income is low, and where the family size choice itself is largely unrelated to child investments and quality. The impact is more likely to be positive where the above conditions are relatively unimportant, and where positive impacts of scale economies and division of labor within the household, and diminishing returns to child labor in competing activities, are large.This ambiguity of the quantityquality tradeoff is emphasized by Mueller (1984a), who predicts a positive relationship "(a) under a regime of natural fertility, (b) if the opportunity cost of school attendance is seen as being lower in large than in small families, (c) if the net rates of return to parents from educating their children are perceived as being positive, and (d) if siblings and relatives share in the cost of children's education" (p. 139). Finally, adverse distributional consequences associated with family size are likely to be largest where credit institutions (markets, government subsidies, extended family relations) are limited.In the Asian context, and referring to table 5, this would include, for example, Bangladesh, India, Myanmar, Nepal, Papua New Guinea.ğ We turn, then, to the data.  5.2 Empirical Findings Data Base. The data for our analysis represent 36 studies that use household or familylevel survey data from Third World countries to examine the impacts of sibsize on various education outcomes. The results are summarized in appendix table A. Most of the studies use multivariant analysis whereby the impact of sibsize is at least conceptually isolated from the impact of intervening variables. The lattermainly parents' education and occupation, economic status, and locationvary from study to study, but on the whole provide adequate controls. Measures of educational outcomes include whether a child is enrolled, is a dropout, has completed a specified grade level, and/or has ever attended school, as well as years of schooling attained and parents' monetary expenditures on education. Unfortunately, there are seldom any measures of schooling quality, a notable shortcoming of this literature. The statistical techniques depend on whether the dependent variable, such as the child's years of schooling attained, is continuous (in which case ordinary or twostage least squares regression analysis is typically used), or dichotomous, such as whether or not a child is currently attending school (in which case probit or logit analysis is typically used). Most of the studies possess adequate sample size. The country coverage is extensive: five from Africa (Botswana, C=te d'Ivoire, Egypt, Ghana [three studies] and Kenya), four from Central/South America (Brazil, Colombia, Guatemala and Nicaragua [two studies]), and the rest from South and East Asia. Within this latter group there is reasonable representation by level of development (Bangladesh [two studies], India, Indonesia, Nepal and Pakistan versus Korea, Malaysia [three studies], Philippines [three studies], Taiwan [two studies] and Thailand). Several studies provide a temporal dimension by comparing familysize impacts in a given country at earlier versus later stages of development.For example, Hermalin et al. (1982) on Thailand, Jamison and Lockheed (1987) on Nepal, and Parish and Willis (1993) on Taiwan.Ę Pitfalls. The empirical literature on the impacts of family size on educational outcomes possesses five significant deficiencies. First, in most studies the impact of family size is hypothesized to be linear. This effectively assumes that there is a fixed impact of additional children on educational outcomes that is invariant to the size of the family; i.e., scale economies are excluded by assumption. These models assume that the impact is the same for an increase in family size from 2 to 3 as it is from 7 to 8. There are strong theoretical reasons to question such an hypothesis and to embrace an empirical research strategy that admits more flexibility in the underlying relationships (e.g., through the use of binary variables for family size). In those few studies where this has been done (or at least reported), notable nonlinearities are revealed. One must, as a result, be cautious in interpreting the various correlations since there is a tendency by researchers to generalize over the entire range of family size, a procedure appropriate only if the relationship is in fact linear.#An example of the importance of the implied linearity hypothesis is provided by Sathar and Lloyd (1993, p. 28), who emphasize the quantitative importance of family size impacts on urban children's school enrollment in Pakistan. They observe that a reduction from 6 children to 1 child will increase the likelihood of enrollment by around 17 percentage points. Quite apart from the somewhat extreme counterfactual, if a nonlinear relationship in family size in fact prevaileda possibility ruled out by assumption in their formulationa reduction from 6 to, say, 2 children could result in a much smaller or negligible impact, or even a 25 percentage point change. Such a finding is not implausible. See, for example, Shavit and Pierce (1991), and the following footnote.# If nonlinearities are present, the interpretation of estimated linear correlations can be quite misleading.LConsider an example. Shavit and Pierce (1991) provide a study that admits a nonlinear family size/schoolingattainment relationship for Israel. For Ashkenazi families, the impact on years of schooling attained of 1, 2, 3, 4, and 5 children, by comparison with families with 6 or more children, is, in years, .833, .900, 1.011, .910, and .589 (the last parameter estimate is not statistically different from zero). Thus, an only child would receive .833 more years education than the average of six or more children. Note, however, that the differential impact of family size within the range of 15 children is likely zero! (It may even be positive between 4 and 5 children, although a test to assess this possibility was not provided.) This result, which we find to be the key finding of their study, is downplayed by the authors. The specific overall negative impact, which the authors highlight, derives mainly from comparing very large families of six or more children with families with only one child. Clearly the nonlinearity in the impact of family size is highly significant for Ashkenazi Jews, and the interpretation of the overall relationship is dependent on revealing such a nonlinearity. For example, by focusing on a linear relationshipthe pervasive emphasis in the literature and in this article, one might conclude that reducing family size from 4 to 1 child would be beneficial to educational attainment. That conclusion would be wrong. Focusing alternatively on the actual, nonlinear relationship revealed in the data, one should instead conclude that reducing family size from 4 children to 1 child would have no impact on educational attainment. This point can be made even stronger. The only impact is that of having some children (irrespective of number), versus having none.L Second, several studies have revealed differential allocations of educational outcomes by gender and by birth order. Such distributional results are indeed relevant, and they can be important. However, many studies attribute these distributional impacts in part to family size. While on the one hand there are reasons to entertain such an hypothesis, it is not appropriate to assume such a connection without empirical test. Tests that reveal differential impacts by gender of family size on educational outcomes are rare.NFor an exception, see Lloyd and GageBrandon (1992).N As a result, one must be cautious, at this stage, in attributing these distributional impacts to family size or population growth, #wd6X@@#per se#wd6X@@#. We emphasize that the focus of this paper is on the impacts of family size (and thus population growth) on educational outcomes; we are thus interested in distributional impacts relating to education mainly if these are established empirically to be connected to, and importantly influenced by, family size. Third, there is a pervasive tendency in this literature to equate the statistical significance of a variable with a sizeable quantitative impact. Most often, where sibsize impacts are significant statistically, the quantitative size of the impacts is modest or small. Even more often, sufficient data are not provided to assess the quantitative impacts, which are alleged but not demonstrated to be notable. Fourth, there is a tendency to generalize to country experience the impacts of statistically significant results obtained for (sometimes small) subsets of the student population. Those subsets affected, either positively or negatively, must be viewed within the context of the entire student population. When this is done, the quantitative assessment of familysize impacts is often notably attenuated. Finally, most studies assume that the family size decision is unrelated to parents' preferences with respect to the amount of resources (time and money) they wish to invest in each child's education. This extreme assumption is at variance with most theories of household behavior, and it results in estimates that exaggerate a possible negative impact of sibsize on schooling. More fundamentally, based on the new home economics model where "child services" are demanded, we find that both schooling (quality) and numbers of children (quantity) are generally related to the same determining variables (income, assets, etc.). As a result, it is extremely difficult to identify the separate impacts of these determinants on schooling and, correspondingly, the relationship of schooling to the demand for child quantity. The empirical literature, described in this section, therefore represents reducedform representations that are not easily interpreted in terms of their analytical underpinnings.  5.3. The Findings Appendix table A, our data base for assessing the impacts of family size on educational outcomes, supports the following generalizations.  An absence of a statistically significant association between sibsize and educational attainment constitutes the most representative finding. While we place no weight on the signs of these findings, some analysts do. (In these regressions, the signs on the impact of sibsize on educational attainment are more often than not positive.)Cynthia Lloyd's (1994b) recent assessments are confirming. Table 3 on educational attainments lists signs (and significance) of sibsize coefficients found in some twenty studies. Over half of the coefficients show no impact. (I tabulate an insignificant positive or negative sign as "no impact." Positives dominate negatives, but this is unimportant/irrelevant.) Of the significant impacts, negatives dominate positives 2:1. Thus, around 35% of all estimated parameters show a negative impact; the rest are positive or zero. The same general results are supported by the somewhat larger and overlapping set of studies summarized in appendix table A. Since parameter counting is fraught with methodological pitfalls, I have elected to provide qualitative assessments in table A. Still, Lloyd's confirming results, an armslength rendering of one dimension of table A, are useful methodologically.Ģ  The overall impact of family size on schooling enrollments and years attained is mixed, although when statistically significant, a small negative impact is the most representative result. In terms of table A, four studies report overall impacts that cannot be distinguished from zero, and five report positive impacts. In around half of those studies that show negative impacts, either positive or nonsignificant findings are reported as well, and/or the negative impacts, while statistically significant, are quantitatively small. Eva Mueller's (1984a) review of the earlier literature arrives at a similar mixedresult conclusion. Her reading finds evidence consistent with: (1) a positive relationship in Sierra Leone (Snyder [1974]), Botswana (Chernichovsky [1981] and Mueller [1984b]), rural Kenya (Anker and Knowles [1982]), Malaysia (DeTray [1982]), and tropical Africa (Caldwell et al. [1982]); (2) a negative relationship in rural South India (Caldwell et al. [1982]), Java and Nepal (Nag et al. [1978]), Guatemala (Clark [1979]), and central Thailand (Ron and Schutjer [1982]); and (3) no relationship in the Philippines (King and Lillard [1983]), South Indian villages (Caldwell et al. [1982]), and urban Kenya (Anker and Knowles [1982]).CSeveral of Mueller's net assessments are based on somewhat indirect connections. Her assessment of the King and Lillard study is too conclusive since sibsize #wd6X@@#per se#wd6X@@# was not considered, although being an only child was.C Her review is also consistent with DeLancey's (1990) for Africa, where on average a positive relationship is found.This study surveys the impact of family size on a abroad spectrum of household allocations, including saving and expenditureshousing, medical, clothing, and education. Drawing on many of the studies cited in our own paper, she concludes that there is considerable evidence of a positive relationship between fertility and education due to "'sibling chains of assistance' or of family's ability, with greater number of children, to obtain the needed labor and still send some children to school" (p. 127). Finally, the mixedresult (but negativeleaning) finding is consistent with a recent review by Lloyd (1994a) who concludes: "[M]easures of children's educational participation or progress in school ...were found to be usually, but not always, negatively associated with numbers of siblings" (p. 185). Assessing the overall size of the impacts can be tricky and is, of necessity, somewhat arbitrary. Generally we classify a quantitative impact as "small" if a change in family size by one (say from 6 to 5 children) results in less than a 2.5% change in the educationaloutcome variable. Often the impact is smaller than this. For example, in those studies examining educational attainment (years completed) and for which sufficient data are available, a reduction of one child typically increases attainment by around .10 to .15 years, or by around 4 to 6 weeks of the child's lifetime of formal education. In most of the studies, this represents around a 23% change in the attainment variable (see, for example, Lloyd and GageBrandon [1992] on Ghana, Chernichovsky and Meesook [1985] on Indonesia, Chernichovsky [1985] on Botswana, Jamison and Lockheed [1987] on Nepal, and Parish and Willis [1993] on Taiwan). In other studies where the impact of family size appears to fall primarily in a small subset of the population, we also attribute the impact to be small unless the quantitative impact is itself very large. For example, in Ghana (Lloyd and GageBrandon [1992]) the negative impacts of family size are found mainly for girls, most conclusively for those in the father rather than the motherbased sample, and then only for older girls (1217, and not those 611) with younger (not older) siblings. Our assessments also tend to balance qualitatively the apparent importance of the variable under consideration. For example, and again with reference to the Ghana study, we attach somewhat greater weight to the attainment and dropout measures than to the everenrolled measure where, interestingly, the impact of family size, where statistically significant, is typically positive. Most of the studies yield statistically biased estimates of the impact of sibsize. Correcting for this bias would likely both reduce the number of, and weaken the (small), negative impacts that have been revealed in the literature.5 In simple models of jointly determined fertility and schooling, the direction of the bias depends on the degree of sensitivity of family size to education costs, and of schooling to family size. For many reasons this sensitivity will plausibly be small in lowincome countries, in rural areas, and where education levels are themselves low. In these cases, the bias will be negative. It will be less negative, or could even be positive, at higher levels of development. This is seen as follows. Define S = a0 + a1F + a2X1 + es, and F = b0 + b1S + b2X2 + ef where S and F are endogenous schooling and fertility, respectively; X1 and X2 are vectors of exogenous variables; and es and ef are "nice" in every way except for the presence of simultaneity. The OLS estimator, a1, is biased upward (downward) when F and es are positively (negatively) correlated. With respect to this correlation, the reduced form equation for F includes a term for es: F = [b1/1a1b1]es ... In terms of our model, a1 and b1 are both posited as negative, so the numerator is negative. If the denominator is positive, the OLS estimate of a1 is biased downward. Since the product of (a1 x b1) is positive, the telling factor is whether this product is larger or smaller than one. If it is less (greater) than unity, the OLS estimate of a1 is biased downward (upward). It is most likely to be less than unity in the circumstances noted in the previous paragraph. If families are not in "equilibrium," i.e., they obtain more or fewer children than they "want," the above analysis must be augmented by considerations of additional bias. Mark Montgomery (in correspondence) has worked out this bias for several cases, and finds it to depend on the correlation between unwanted fertility and family size. (His modeling uses an errorsinvariables approach that assumes F [equilibrium family size] to be a noisy measure of unwanted fertility.) If positive, the estimated parameters in the schooling equation are biased toward zero: i.e., "one should be cautious in drawing strong conclusions from a set of studies having weak positive or negative results." On the other hand, if unwanted fertility and family size are not positively correlated (they are likely weakly correlated at high and low family sizes, with a correlation of uncertain magnitude in mid ranges), then the direction of the bias is also uncertain.5 Indeed, the conclusion above suggesting a "small net negative impact" of sibsize on educational attainment could well be modified to a largely "mixed" impact. All but four studies assume that parents determine family size without regard to the costs of educating their children. This premise is analytically implausible and at variance with the results of a large empirical literature. For the present survey, the relevant issues are: 1)whether failure to account for this jointness of decision makingthe impact of planned schooling investments on the family size decisionhas a quantitatively important effect on estimates of sibsize impacts on educational attainment; and 2) when and where such biases are likely to be important. Answering the latter question may assist in explaining the "patterns" of sibsize effects, described below and documented in table A. Limited evidence suggests that statistical biases resulting from failure to account for jointness in decision making may be relevant. First, for Nicaragua, Wolfe and Behrman (1984) find that the negative impact disappears when jointness is reckoned, and that the size of the estimated effect is cut in half.In their model the OLS coefficient (tstatistic) on standardized fertility is .064 (4.0); and in the simultaneous equation model, it is .036 (.5).Į Second, for Pakistan, Indonesia, and the Philippines, in regressions where jointness is modeled, King et al. (1986) fail to uncover any negative statistically significant sibsize impacts; many coefficients are statistically insignificant, and six show positive impacts of family size on educational attainment. Their results are in contrast to several studies using other data for these countries, most of which show some small, negative impacts.For Pakistan, see Cochrane et al. (1988), Sathar (1993), and Sathar and Lloyd (1993); for the Philippines, see Paqueo (1985), and DeGraff et al. (1993); for Indonesia, see Chernichovsky and Meesook (1985). Based on the results of King et al. and others, these several studies abstracting from family size choice likely overestimate the negative impacts of sibsize. Since in all cases the estimated (negative) impacts are judged to be small, one could justify reclassifying them toward, or into, the "littleornonotableimpact" category.The King et al. sample applied to households at an earlier period of development, a factor that would increase the negative bias visavis that likely in studies using data applying to more recent periods. See footnote  LLOYD67  below. Finally, in several studies where positive impacts of sibsize have been identified, jointness is explicitly modeled. Possibly the most interesting implication of accounting for jointness (family size endogeneity) relates to our attempts to identify and explain apparent systematic patterns, noted below, of when sibsize appears to matter. It seems to be least important in lowincome countries where fertility rates are yet to decline, and particularly in Africa. One might speculate that these are areas where the family size decision is substantially unaffected by childinvestment decisions. After all, both the return to and the costs of education may be low in these settings. Since the highest cost of education to the family is typically the foregone wages of mothers during child rearing, and of children when attending school, the prospect of rising wages and improved employment opportunities can notably affect the family size decision. Thus, as countries and labor markets develop economically, the endogeneity of family size becomes increasingly important: parents become more sensitive to choosing between more children and fewer children who receive more education.One should not conclude that high fertility is sufficient to identify such countries. For example, Kenya, with one of the highest TFRs in the world, experienced in the 1980s notable reductions in fertility, plausibly triggered by a jump in the costs of education. Parents' perception of the  high value of education, and a shifting of some education costs to households directly, resulted in great pressure to constrain family size (Kelley and Nobbe [1990]). An excellent discussion of these issues of household modeling, as they apply to Africa in particular, is provided by Montgomery and Kouam) (1993). Observing the lack of a negative relationship between child schooling and fertility, they emphasize the importance of African institutionssibling chains of support, child fostering, withinhousehold division of child rearing responsibilitiesas weakening the quantityquality tradeoffs between child numbers and education investments there (p. 10). They emphasize the importance of perceived high values of education, and in particular a labor market that provides premia for education skills of children, as important to conditioning important quantityquality tradeoffs. See also Caldwell and Caldwell (1987), Ainsworth (1990, 1992), and Gomes (1984).֌It follows that the statistical bias problem resulting from failure to account for jointness in family size choice may become less important over time and at higher levels of per capita income and wages, although it may still be negative. Within the context of interpreting the 31 studies in table A that fail to account for family size endogeneity, we would expect the bias to decrease across countries with economic development, and over time within a country. Having said this, we should caution against overestimating the quantitative size of the (negative) bias based on the large number of seemingly misspecified studies. For many of the countries examined, even some presently well along in the development process, the relevant family size decisions were made decades ago at earlier stages of development when plausibly the importance of child education costs in the family size decision was less. LLOYD I am grateful to Cynthia B. Lloyd for pointing this out, and to a preview of her forthcoming tabulations (Lloyd [1994b]).ġ  The impact of family size appears to be greatest in comparing relatively large with relatively small families; within the small and large family sizes, the impact may be small . This conclusion must be guarded since most studies do not explore directly the impacts of additional children by the size of the family (they typically impose a linear functionalform restriction). In those that do, it is found that the impact between two and four or five children is small, and that a negative impact emerges thereafter.YSee, for example, Birdsall (1980) and Shavit and Pierce (1991).Y Additionally, large families occur most prevalently at early stages of the demographic transition and development, where the impact of family size is often found to be very small.4Lloyd (1994a) points out that "some level of development is required before family size can have an impact on child investment" (p. 186). This conclusion is buttressed by Desai's (1993) study of the impact of family size on children's nutritional status in 15 developing countries.4 Together these findings tentatively suggest a possible break in the family size impact at around 45 children, with a relatively flat portion between 14 and 5+ children. The negative impact of large families appears to be least in countries that are relatively poor and/or at early stages of the demographic transition, and in Africa .This is consistent with Lloyd's (1994a, p. 186) review of the evidence. She concludes that a negative relationship is more likely to be found in urban than rural settings, and in the more developed countries of Southeast Asia and Latin America than in South Asia and subSaharan Africa. She also concludes that the negative impacts will be larger for countries in the midst of the decliningfertility stage of the demographic transition. Below we modify this interpretation to admit the possibility that such a theoretical hypothesis carries modeling requirements seldom evaluated in the empirical literature. Lamentably, two dozen studies provide estimated impacts that are statistically biased, often downwardtoward showing negative impacts of family size. Three of the seven African studies show small positive impacts, two show a small negative impact, and two are mixed. At an earlier stage of Taiwanese development, the impact appeared to be negligible; in a later stage, a small negative impact is uncovered (Hermalin et al. [1982]). Similar differential impacts by generation have been found for Nicaragua (Behrman and Wolfe [1987], Taiwan (Parish and Willis [1993]), and Peninsular Malaysia (Shreeniwas [1993]), although in the latter study the impact emerged for Chinese and Indian families but not for the numerically dominant Malays, and the impact was quantitatively small.sInterpreting the Malay results is complicated by government policies favoring this group.s  The impact of family size on the distribution of education benefits by gender is mixed and difficult to interpret . Consider the mixed results. Of the studies we have surveyed in table A that are statistically able to provide a rigorous assessment of gender impacts,MThese are typically multiple regression studies that include a gender variable on pooled data. Excluded are four studies that run the regressions separately by gender, but do not test either for overall gender differences or, more importantly, for whether individual parameters are statistically different.M seven show boys to be advantaged, five show girls to be advantaged, and five basically fail to uncover any gender impacts.tIn the multivariate studies statistically isolating the impact of gender: boys are advantaged in Thailand, as reported by Cochrane and Jamison (1982); in Kenya, by Gomes (1984); in Indonesia, by Chernichovsky and Meesook (1985); in Nepal, by Jamison and Lockheed (1987); in Ghana, separately by Glewwe and Jacoby (1992) and Lavy (1992); in Taiwan, by Parish and Willis (1993); and in C=te d'Ivoire, by Montgomery and Kouam) (1993). Girls are advantaged in Nicaragua, as reported by Wolfe and Behrman (1984); in Botswana, by Chernichovsky (1985); and in the Philippines, separately by Paqueo (1985) and DeGraff et al. (1993) . Mixed gender impacts are found in the Philippines by Herrin (1992) and in Brazil by Psacharopoulos and Arriagada (1989). Statistically insignificant results are found for Thailand (5 out of 6 regressions), by Cochrane and Jamison (1982); for the Philippines (Bicol region), by King and Lillard (1983); for Nicaragua, by Wolfe and Behrman (1984); for the Philippines, by Bauer, et al. (1992); for Bangladesh, by Foster and Roy (1993); and for Taiwan by Lillard and Willis (1994).t In these studies, a total of 62 fundamentally different regressions (i.e., different dependent variables or sample stratifications such as urban/rural) are run: 21 show boys to be advantaged, 13 show girls to be advantaged, and the rest fail to uncover a gender impact. Of the 36 studies, 30 use multiple regression analysis. Of these, 7 do not take up gender. Of the remaining, 15 include gender terms in pooled data; 8 run the models separately by gender, but do not provide tests to assess whether observed differences in specific (or often combined) parameters are statistically different. Of the remaining studies that do not use multiple regression or multivariate analysis, 3 do not take up gender issues; the 4 remaining conclude that boys are advantaged.  Combining these results with the remaining studies that use statistical techniques less suited to isolating gender impacts, but nonetheless useful in providing relevant evidence, we find that boys are typically, but by no means exclusively, advantaged in education provision; and that, when gender impacts are revealed, the quantitatively largest differences almost always favor boys. Consider the difficulty of interpretation. First, unfortunately those studies that have emphasized gender have typically not been ideally set up to test or isolate gender impacts directly or rigorously, or they do not rely on multivariate statistical analysis that permits controlling for other influences. While these studies are usually rich in plausible hypotheses and relevant qualitative background, they are less convincing in their analysis of data which are often available, but not ideally used, to test the advanced hypotheses. Second, the key hypothesis we wish to examinewhether gender differences vary systematically by family sizeis almost never evaluated directly or explicitly. This may come as a surprise, given the strength of conclusions by some observers. Lloyd (1994a), for example, is unequivocal in her assessment:   In most parts of the world, parents with more children tend to discriminate against their female children in the allocation of schooling and other forms of investments more than parents with fewer children... (p. 196).   Our own reading of the literature is quite different. While there is abundant evidence of gender impacts, we have found only one study (Lloyd and GageBrandon [1992]), based on LDC household data, that reports results that test the above specific hypothesis directly and rigorously;hSuch a test could be provided in regressions, for example, that include terms that not only admit gender effects (for any reason) but include, in addition, an interaction term between gender and the size of the family. An excellent summary of the hypotheses linking gender discrimination and family size is provided by Lloyd (1994a).h TEST  if such studies exist, they are few in number, and it is unlikely that they are able to support the global generality of the hypothesized empirical relationship. Finally, we find family size impacts to be quantitatively small and, in contrast, gender impactsalmost always estimated in models that hypothesize gender to be independent of family sizeto be quantitatively large. Indeed, it is not uncommon in studies that include estimated parameters for both gender and sibsize to reveal that being of the opposite sex has an impact on educational outcomes that is five to twenty times the value of being from a family with one (or even two or three) fewer siblings.See, for example, Wolfe and Behrman (1984) on Nicaragua; Chernichovsky (1985) on Botswana; Montgomery and Kouam) (1993) on C=te d'Ivoire.ĩ Hypotheses that account for gender impacts are abundantalmost to the point of gender being characterized as representing a pervasive impact. Gender impacts are hypothesized to vary by rural and urban locations, by parents' education, by family wealth, by school availability, by ethnic background, by religion, etc. Such a perspective is consistent with the oftnoted and plausible observation that gender bias is deeply rooted in culture. However, to isolate the share of this deeprooted and pervasive influence that is in turn attributable to a relatively weak variable such as family size, especially since the latter likely manifests its impact in a nonlinear way, is problematical both analytically and econometrically. Thus, while the empirical literature is conclusive on the existence of strong gender impacts on education (most often favoring boys), there is little or no reported evidence that rigorously associates this gender impact as notably related to family size, #wd6X@@#per se#wd6X@@#.Most of the studies in appendix table A that explicitly examine gender do not associate gender impacts with family size. Those that do are about equally divided in assessing the impact. DeGraff et al.'s study (1993) of children's time use in the Philippines concludes that the education of male children is most likely to be negatively influenced by larger families (p. 321). A study of Maharashtra in India by Jejeebhoy (1993) concludes that gender impacts may be smaller in larger families since in small families resources are more available to enable discrimination. Her analysis "...raises the alarming possibility that with the increasing prevalence of small families, gender disparities in outcomes for children will widen" (p. 446). In contrast, Sathar and Lloyd (1993) and Sathar (1993) attribute a notable portion of educational distribution against girls in Pakistan to family size interactions, and Lloyd and GageBrandon (1992) note a similar correlation in Ghana.  Middle children may be disadvantaged in larger families . There are very few studies that confront this issue directly, although a few studies provide some information consistent with this hypothesis.`Parish and Willis (1993), Lloyd and GageBrandon (1992), Gomes (1984).`֌  Й 5.4 Bottom Line  Evidence on the impact of family size on educational outcomes is mixed, showing no convincingly consistent and strong impact, one way or the other .These results represent the impact on "average" sibling years of schooling completed. Averages, however, may mask distributional impacts occurring within the household, and related to family size. Very little evidence is available on these issues. The majority of the models fail to uncover a statistically significant impact. However, when a statistically significant impact is revealed, more often than not large families deter educational participation and attainment of children. On the other hand, this finding must be qualified. First, the quantitative size of the impacts is typically small, especially when account is taken of the relative size of the subsets of the child population affected. Second, a number of studies show the impact to be positive. Finally, almost all studies are statistically biased, many toward showing a negative impact of large families. Indeed, two dozen studies fail to account for the likelihood that parents take the future costs of educating their children into account in determining the size of family they can afford. Evidence on the impact of family size on educational outcomes by gender is inconclusive. Most studies do not consider such gender impacts. Those that do find mixed results, and most are not particularly successful in sorting out gender from other impacts. (This is not to deny the existence of welldocumented gender impacts; it is to question the strength of their association with family size.) From a policy perspective that focuses on the impact of international contributions to family planning, in the short to intermediate run it is unlikely that moderate reductions in family size from high existing levels in the relatively poor countriesthe targets of family planning efforts supported by expatriate fundingwill have a notable impact on educational outcomes.aThis analysis underscores the importance of obtaining a reasonably precise estimate of where the breakpoint of the familysize impact occurs. If it is substantially at the zero/positive number of children point, then family planning will be of limited use since most couples will be unwilling to reduce their families to zero.a These are the very countries found in household studies to be relatively insensitive to family size impacts on education and where the estimated negative impacts of family size are most likely exaggerated due to methodological difficulties; this is especially true of Africa (where the impacts may even be contrary). If concern is with an upgrading of the education of children over the next decade or two, the return to policies and programs that directly impact the education sector plausibly represents the most promising strategy. On the other hand, this conclusion, while relevant, represents an excessively narrow framework within which to evaluate family planning programs. A broader perspective is appropriate. Such a perspective would support a strategy of developing humanresource policy packages that would in addition include maternal and child health (especially emphasizing mortality reduction, immunization, and nutrition supplements), and education. Within such a package, voluntary family planning can be justified even where the demonstrated impacts on specific sectors appear to be somewhat small and seemingly untargeted. In evaluating population programs where the impacts are diffused, it is important to reckon the sum of the individual impacts. Moreover, for human resource investments in general, it is important to account for the impacts of interactions between various investment outcomes. We have little hard evidence about the quantitative importance of these synergies, but the direction of the impacts is usually clear. For example, healthy children are a prerequisite to realizing high returns from education, and high returns are in turn necessary for parents to perceive the benefits of smaller numbers of, but healthier and more educated, children. Lamentably, social science research is unable to offer much precision to the design of "optimal" human resource aidassistance packages. However, research has demonstrated that a broadbased, humanresources perspective and approach appears to be justified methodologically, and advantageous operationally. '3    X jjTable A Summary of Econometric Studies on the Impact of Sibsize on Educational Outcomes in the Third World   Study Data Stat. Impact of Impact on Results (Bottomline in Bold) Technique   00Carol Anne Maxwell Clark (1979) on GUATEMALA ă h ddx8  ddx8  h "mm"348 children 714 rural/semiruralProbit# siblings Community chars. Family SESAttendance Ever attended No impact . VVNancy Birdsall (1980) on COLOMBIA ă h ddx8  ddx8  h "bb"1967/68 family budget survey 1,433 urban HHsOLS 2SLQ# siblings Parents' educ. Income Migration status City Age of wifeTotal expend. on educ. Share expend. on educ. Enrollment Negative impact on perchild educational expenditures up to 4 children; relatively smaller impact thereafter . Smaller impact when endogeneity of family size is taken into account. Mark R. Rosenzweig and Kenneth I. Wolpin (1980) on INDIA ă h ddx8  ddx8  h ""Rural incomes survey 1969, 1971 2,939 HHsOLS Control with twins Family size Cons. durable expendituresAttainment Negative impact . Somewhat weaker impact in the twins sample. Table A (continued) Summary of Econometric Studies on the Impact of Sibsize on Educational Outcomes in the Third World   Study Data Stat. Impact of Impact on Results (Bottomline in Bold) Technique   Susan H. Cochrane and Dean T. Jamison (1982) on THAILAND ă h ddx8  ddx8  h "WW"400 rural HHs 3 generationsOLSYounger siblings Age Parents' educ. & aspirations Land ownership Innate ability Distance from school Water avail.Attainment Participation Literacy Numeracy Younger siblings have little impact on attainment and participation of most children . No impact on attainment of children 513; sizable negative impact on young adults (1425); i.e., a reduction by one sibling increases attainment by .35 years, or 6% of average attainment. Similar pattern for participation.  Albert Hermalin, Judith A. Seltzer and ChingHsiang Lin (1982) on TAIWAN ă h ddx8  ddx8  h "bb"Married Women aged 2039 1973 urban & ruralOLSSibship size Sex Father's educ. & work status Mother's ageAttainment No overall impact . Negative impact emerging with younger women, but quantitative size is small. (A reduction by one sibling increases average educational attainment around 2.2%).  Melba Gomes (1984) on KENYA ă h ddx8  ddx8  h "WW"2 sets: 1 rural 1 urban wage earners 1,802 children & parentsOLSFamily size Birth order Land size Father's occupa tion & job experience Tribe Parental age & educ.Attainment Small positive impact . Reduction by one sibling decreases attainment by .1 years. (Average attainment data are not provided.) Table A (continued) Summary of Econometric Studies on the Impact of Sibsize on Educational Outcomes in the Third World   Study Data Stat. Impact of Impact on Results (Bottomline in Bold) Technique   Barbara L. Wolfe and Jere R. Behrman (1984) on NICARAGUA ă h ddx8  ddx8  h ""197778 Survey Children 827 central urban 653 other urban 595 ruralOLS 2SLQChild age/sex Mother's expen diture Mother's age when child born Parental schooling Marital status Male preference Standardized fertilityAttainment (no. years above age 5) No impact in preferred model where schooling decisions are simultaneously determined with fertility. OLS models show negative fertility impact, but these are biased downward. Rural boys receive less schooling than rural girls. Dov Chernichovsky (1985) on BOTSWANA ă h ddx8  ddx8  h ""1974 Rural survey 2,043 childrenOLSChildren 714 Acres & cattle owned Income Educ. of HH head # elderly Baby present Sex of HH headEnrollment Attainment Small positive impact on enrollment and attainment. An increase by one child aged 714 increases years completed by .1 year. (Average attainment is 3.4 years.) Girls are more likely to be enrolled, to stay longer, and to achieve higher schooling levels. Girls attain .2 years more schooling than boys.  Table A (continued) Summary of Econometric Studies on the Impact of Sibsize on Educational Outcomes in the Third World   Study Data Stat. Impact of Impact on Results (Bottomline in Bold) Technique   Dov Chernichovsky and Oey A. Meesook (1985) on INDONESIA ă h ddx8  ddx8  h ""National Socio economic Survey 1978 6,000 HHsOLSHH size HH expenditure Child's age & sex Parents' educ. School locationEnrollment Attainment by child age Impacts mixed: some positive, some negative; all very small . No impact on attendance of children aged 1315; positive impact on persons aged 1618, 1926. Negative impact on schooling completed of children aged 1012, 1315; no impact on persons aged 1618; positive impact on persons aged 1915. A change in HH size by one leads to .05 years change in schooling completed. (Sample averages not presented.) Boys advantaged in attendance. No gender impact on schooling completed of children 1015; boys aged 16+ advantaged. 00Vincente B. Paqueo (1985) on the PHILIPPINES ă h ddx8  ddx8  h "bb"3907 children aged 713 urban and rural 1982 School Matching Survey Bicol RegionOLSAge, HH assets Parents' educ. Attitudes Health Interest rate # siblingsAttainment Very small negative impact . Reduction in siblings (average 5.5/family) by 1 reduces years of schooling by .02, or .67%. Girls attain .22 (or 5.8%) more years than boys. Table A (continued)  Summary of Econometric Studies on the Impact of Sibsize on Educational Outcomes in the Third World   Study Data Stat. Impact of Impact on Results (Bottomline in Bold) Technique    Elizabeth M. King, Jane R. Peterson, Sri Moertiningsih, Lita J. Domingoand Sabiha Hasaan Syed (1986) on INDONESIA, PAKISTAN and PHILIPPINES  h ddx8  ddx8  h "  "Asian Marriage Surveys 197980 Two adult generations Middleclass urban, urban poor, rural 4,352, 4,787 and 6,224 in Pakistan, Indonesia, and Philippines, resp.Maximum likeli hood, vari ance compo nents model with sibsize endog.Cohort Age Sibsize (pred.) Parents' educ. & occupation Land ownership Mother's age at marriageAttainment (yrs. completed) Small positive impacts . Most estimates (12 out of 18) are not statistically significant. Where significant, impact is always positive, a result occurring in all three samples. Positive impacts were more likely in female samples (4 out of 6 estimates). Jere R. Behrman and Barbara L. Wolfe (1987) on NICARAGUA ă h ddx8  ddx8  h "  "702 adult sisters across two generations 197778OLS# siblings Parents' educ. Age Income Grandparents' educ. School supplyAttainment boys & girls 613 Negative impact . In 4 out of 6 models, impact was not statistically significant at 95%; 2 out of 6 at 90%. Low schooling levels. Dean T. Jamison and Marlaine E. Lockheed (1987) on NEPAL ă h ddx8  ddx8  h ""795 rural HHs 1977/78 children 616OLS ProbitCaste Parents' educ., age, sex Modernity score School avail.Participation Completed at least 1 yr.  Indeterminant . Presence of small children slightly decreased girls' chances to participate in schoolthe only family size variable investigated. Girls less likely to attend school.Table A (continued) Summary of Econometric Studies on the Impact of Sibsize on Educational Outcomes in the Third World   Study Data Stat. Impact of Impact on Results (Bottomline in Bold) Technique   Mark R. Rosenzweig and T. Paul Schultz (1987) on MALAYSIA ă h ddx8  ddx8  h "WW"1,262 HHs national 1976OLS 2SLQEstimated fecundity Mother's educ. and age Father's earnings Indirectly family planning, desired family sizeCompleted and/or expected attainment Negative impact of estimated fecundity . This study attempts to disentangle biological and demand factors contributing to fertility variation.  Susan H. Cochrane, Kalpana Mehra and Ibrahim Taha Osheba (1988) on EGYPT ă h ddx8  ddx8  h "LL"1990 Egyptian Fertility Survey 2,277 children urban & rural National SampleLogit TabularAges of children & parents Rural & urban location Family income Parents' education & education aspirations for children Assets Distance from schoolParents' edu cational aspirations for children Ever attended Currently attending Attainment Small negative impact on participation (3 out of 16 cases); no impact in rural areas. Results invariant to sex. Small negative impact on attainment in urban areas; no impact in rural areas. (Overall impact around .1 year/sibling.) Table A (continued)  Summary of Econometric Studies on the Impact of Sibsize on Educational Outcomes in the Third World   Study Data Stat. Impact of Impact on Results (Bottomline in Bold) Technique    George Psacharopoulos and Ana Maria Arriagada (1989) on BRAZIL ă h ddx8  ddx8  h ""1,761 HHs National 714yearold childrenOLS Logit TobitChild age/sex Parents' educ. Parents' occupation Family income Dwelling attributes RegionEnrollment Attainment Dropout Small overall negative impact . Enrollments negatively impacted by younger, but not (statistically) by schoolaged children; attainment negatively impacted by younger and older children; probability of dropout not impacted (statistically) by either. If male, less likely to participate, attain, and drop out.  Susan Cochrane, Valerie Kozel and Harold Alderman (1990) on PAKISTAN ă h ddx8  ddx8  h "  "Urban, lowincome neighborhoods 1000 HHs Pakistan Insti tute of Devel opment Eco nomics SurveyLogit# children, by age Age of parents HH educationParticipation Negative impact on females of children aged 04 years; no impact on males. No impact on males or females of siblings aged 1014 years. \\Shaikh I. Hossain (1990) on BANGLADESH ă h ddx8  ddx8  h ""1,382 currently married women 1979802SLQ# siblings Parents' educ., income, occupa tion, age, birth control use, childhood location School avail.Attendance (standar dized) Positive impact of child numbers on attendance . Table A (continued) Summary of Econometric Studies on the Impact of Sibsize on Educational Outcomes in the Third World   Study Data Stat. Impact of Impact on Results (Bottomline in Bold) Technique     John Knodel, Napaporn Havanon and Werasit Sittitrai (1990) on THAILAND ă h ddx8  ddx8  h "LL"2 rural villages Survey data Focus group discussionsDifferences in gross & adjusted means of various subsamplesFamily size Age Wealth Stage in demo. transition Educ. support by other than parents Parents' educ. attainment & preferences Income sourceActual & pre dicted sec ondary at tendance, assessed by parents Negative impact . Yossi Shavit and Jennifer L. Pierce (1991) on ISRAEL ă h ddx8  ddx8  h "  "1,736 Ashkenazi & Oriental Jewish men, 1980/81 931 Moslem men, 1987/88OLSSibsize Parents' educ. Father's occupa tion & religi osity Attainment Transition to higher levels Small mixed impacts: positive and negative, varying by family size . Ashkenazis: no impact over 14 children range; only 6+ families (few in number) have negative impact. Orientals: little or no differential impact over 411 children range; large families, negative impact visavis families with 13 children. Moslems: positive impact of larger families, especially over 12 children; little or no differential impact between 311 children. Too much variability to compute "average" impact, positive or negative. No gender impacts considered. Table A (continued) Summary of Econometric Studies on the Impact of Sibsize on Educational Outcomes in the Third World   Study Data Stat. Impact of Impact on Results (Bottomline in Bold) Technique    John Bauer, Dante Canlas, Maria Theresa Fernandez and Andrew Mason (1992) DDon the PHILIPPINES ă h ddx8  ddx8  h "  "8,838 HHs nationalLogitSiblings by age and sex Parents' educ. Head's occupation Family income Location (region, urban)Enrollment, secondary & tertiary Small negative impact . No (negative) impact of older (younger) siblings on enrollments. No sexspecific impacts. 00Paul Glewwe and Hanan Jacoby (1992) on GHANA ă h ddx8  ddx8  h ""Children com pleted primary & entering middle school 1399 children Living standards survey 198788Ordered Probit OLSLocation Age and sex Parents' educ. Religion & ethnicity Siblings Per capital expenditures Land ownership School attributesAttainment (years) Late starting Mathematics achievement Reading achievement Small negative impact on attainment; no statistically significant impact on late starting, mathematics or reading achievement. Table A (continued)  Summary of Econometric Studies on the Impact of Sibsize on Educational Outcomes in the Third World   Study Data Stat. Impact of Impact on Results (Bottomline in Bold) Technique   Alejandro N. Herrin (1992) on the PHILIPPINES ă h ddx8  ddx8  h "bb"500 HHs Misamis Oriental province ruralOLS LogitChild age/sex Siblings Mother's educ. Wages of child and father Distance to schoolEnrollment Attainment Modest negative impact . No (negative) impact on enrollments and attainment of children 712 (1317). If male 712 (1317), less (more) likely to participate. Victor Lavy (1992) on GHANA ă h ddx8  ddx8  h ""1800 Rural HHs 1987 living stan dards surveyLogit OLSSex and age Siblings Land ownership Income per capita Parents' educ. Distance from school Community attributes School attributesEnrollment Ever attended Attainment (years) Small positive impact on everattended school, and attainment; no impact on enrollment . Table A (continued) Summary of Econometric Studies on the Impact of Sibsize on Educational Outcomes in the Third World   Study Data Stat. Impact of Impact on Results (Bottomline in Bold) Technique    Cynthia B. Lloyd and Anastasia J. GageBrandon (1992) on GHANA ă h ddx8  ddx8  h "  "Living standards survey 1987/88 3,200 HHs Urban & rural Children by: 1) sex, 2) # older or younger sibs., 3) ages 611 or 1217, 4) link ed to biologi cal mother or fatherLogit OLSSibsize (older or younger) Father or mother based sample Ages of children Sex of children Parental ages & marital status Consumption per adult equiva lent Urban or rural Studentteacher ratio Proportion of teachers trainedEver enrolled Dropout Attainment Small negative impact . Most regression combinations show no significant impact; remaining positive and negative impacts are roughly offsetting. Only consistent finding relates to dropouts and attainment of older girls with younger siblings. Dropout impact is small (.03% increased dropout per additional sibling); attainment impact proportion is also small (.15 less years per additional younger sibling  2.5% of average attainment). Attainment uninfluenced and enrollments advantaged by older siblings. Those affected are a small share of total student population. $$Alaka Malwade Basu (1993) on INDIA ă h ddx8  ddx8  h ""NCAER survey of Uttar Pradesh and Tamil Nadu Lower socio economic classMultiple clas sifica tionFamily size Age Father's educ. Mother's occupa tionParental edu cational aspirations Enrollment No impact on educational aspirations. Negative impact on enrollments that varies by region . (Insignificant impact in Uttar Pradesh; moderate negative impact in Tamil Nadu.) Table A (continued) Summary of Econometric Studies on the Impact of Sibsize on Educational Outcomes in the Third World   Study Data Stat. Impact of Impact on Results (Bottomline in Bold) Technique   Andrew D. Foster and Nikhil Roy (1993) on BANGLADESH ă h ddx8  ddx8  h ""5,052 HHs rural 1990OLS TobitChildren, by age Parents' educ. Parents' age Land owned Village attributesAttainment Modest overall net impact . Young children (ls. 8 years) have negative impact on attainment; older children (8 and older) have no statistically significant impact. No differences by sex. Deborah S. DeGraff, Richard E. Bilsborrow, and Alejandro N. Herrin (1993) on the PHILIPPINES ă h ddx8  ddx8  h "WW"2,679 children from Bicol region (urban & rural) 1983ProbitSiblings by age & sex Sex Age Mother's age & educ. Land holdings Degree urban Enrollment Small negative impact . Older (younger) siblings have (no) statistically significant negative impact on enrollments; small negative impacts are greatest for males. Shireen J. Jejeebhoy (1993) on INDIA ă h ddx8  ddx8  h "bb"198384 1,149 HHs Rural MaharashtraTabularParents' educ. Women's ownership of durables Work statusParental educational aspirations Attainment Enrollment Completion Likely small overall negative impact . Children from smaller families are advantaged; discrimination in favor of boys is invariant to family size; attainment of girls is possibly advantaged in larger families. Table A (continued)  Summary of Econometric Studies on the Impact of Sibsize on Educational Outcomes in the Third World   Study Data Stat. Impact of Impact on Results (Bottomline in Bold) Technique   Andrew Mason (1993) on SOUTH KOREA and THAILAND ă h ddx8  ddx8  h ""1981 Socioeco nomic survey, Thailand 1983 Income & Ex penditure sur vey, S. KoreaLogit OLSAge & sex of children HH disposable income Enrollment Family expen ditures on education Mixed impact on Thai and S. Korean enrollments . In Thailand, older children help (larger quantitative impact, and more likely statistically significant); younger children hurt. Overall impacts about offsetting, likely negative on average. Approximately the same pattern for Korea. Here, older girls have a positive impact on enrollments; older boys do not. Perchild expenditures on education are negatively affected. Mark R. Montgomery and Aka Kouam) (1993) on C<TE D'IVOIRE ă h ddx8  ddx8  h "WW"Living Standards Survey 198587 4,310 women 8,175 childrenOLS Probit Ordered probitFertility Mother's educ. Consumption per adult Residence Ethnicity Age School location & amenitiesCumulative schooling Enrollment Projected completed schooling Impact is positive in rural, negative in urban areas . Table A (continued)  Summary of Econometric Studies on the Impact of Sibsize on Educational Outcomes in the Third World   Study Data Stat. Impact of Impact on Results (Bottomline in Bold) Technique    William L. Parish and Robert J. Willis (1993) on TAIWAN ă h ddx8  ddx8  h "  "Women/family survey, ages 2560 1989 2,897 HHsOLSSiblings by sex & birth order Parents' educ. & occupation, incomeAttainment  Small mixed impacts: positive and negative, varying by gender and over time . For 32 comparisons, 20 are statistically insignificant; 8 show a negative, and 4 a positive, impact. A change by one sibling increases or decreases average attainment by around 2.5%. Overall negative impact reduces this net impact to around .6% of average attainment. Negative impact of sibsize increases over time as family size declines and income increases, a puzzling result. Samesex siblings hurt, older sisters always help, and crosssex siblings are neutral to educational attainment. VVZeba A. Sathar (1993) on PAKISTAN ă h ddx8  ddx8  h ""125 HHs in five villages 1990Multiple clas sifica tion OLSOlder & younger siblings Age Parents' educ. Land size holding HH income Village Attendance Attainment Attainment impact is negligible; enrollment impact is negative and small . For both boys and girls, attainment is unaffected by siblings. Impact of number of older (younger) siblings on enrollment for girls (boys) is negative; no impact of number of younger (older) siblings on enrollment for boys (girls). Table A (continued) Summary of Econometric Studies on the Impact of Sibsize on Educational Outcomes in the Third World   Study Data Stat. Impact of Impact on Results (Bottomline in Bold) Technique   Zeba A. Sathar and Cynthia B. Lloyd (1993) on PAKISTAN  h ddx8  ddx8  h ""Integrated HH survey 1991 4,711 HHsLogit OLSSibling # & posi tion Child's age Mother's educ. Father's literacy # adults HH income Land size School proximityPrimary en rollment Primary com pletion Parental expend. on educ. Small negative impact . Enrollment impact is very small (86% unaffected; urban girls disadvantaged). Impact on completion is small (rural children72% of totalunaffected; urban children, negative impact with one less sibling increasing the chance of completing primary school by .025). Impact on total educational expenditure is small (rural boys are unaffected; rural girls experience a small negative impact; there is a larger negative impact in urban areas with 28% of children).  Sudha Shreeniwas (1993) on PENINSULAR MALAYSIA ă h ddx8  ddx8  h ""1976 family life survey 1,165 ever married women Younger & older generationsOLS# siblings Parents' educ. Father's job Mother's work Urban or rural residence Gender Birth cohort order Attainment Impact is negligible . Amongst older generation, there is no impact. Amongst younger generation, there is a small negative impact in Chinese and Indian families, and no impact amongst numerically dominant Malays. Table A (continued) Summary of Econometric Studies on the Impact of Sibsize on Educational Outcomes in the Third World   Study Data Stat. Impact of Impact on Results (Bottomline in Bold) Technique   <<Lee A. Lillard and Robert J. Willis (1994) on MALAYSIA ă h ddx8  ddx8  h ""4,794 HHs nationalProbitSiblings by sex Parents' educ. Father's occup. Place of residence Race and policyAttainment  Small negative impact . Negative impact of boys' older brothers and girls' younger sisters on attainment; no impact of other combinations.   3' Table B  Country Samples for Third World Education Indicators   Region Enroll. Attain E/GDP Data StudentTeacher Ratios Country Ratio ment IMFcons IMFbud UNESCO Primary Secondary   ` h! Algeria` ` ` Afr xxhhhxx!!!x Argentina ` ` ` L.A. xxxxhhhx Bangladesh` ` ` Asia xxxhhhxx Benin` ` ` Afr xx Bolivia` ` ` L.A. xxxxhhhxx Brazil` ` ` L.A. xxxxhhhxx Burundi` ` ` Afr xhhhx Cameroon` ` ` Afr xxxxhhhxx Cent.Afr.` ` ` Afr xxhhhxx Chad` ` ` Afr xhhhx Chile` ` ` L.A. xxxxhhhx Colombia` ` ` L.A. xxhhhxx!!!x Costa Rica` ` ` L.A. xxxxhhhxx Cote d'Iv` ` ` Afr xhhhxx Dom.Repub.` ` ` L.A. xxxxhhhx Ecuador` ` ` L.A. xxxhhhxx Egypt` ` ` Afr xxxxhhhx!!!x El Salvador` ` ` L.A. xxxhhhxx Ethiopia` ` ` Afr xxxhhhxx!!!x Ghana` ` ` Afr xxxhhhxx!!!x Guatemala` ` ` L.A. xxxxhhhxx Haiti` ` ` L.A. xxhhhxx Honduras` ` ` L.A. xxhhhx Hong Kong` ` ` Asia xxhhhxx India` ` ` Asia xxxxhhhxx!!!x Indonesia` ` ` Asia xxxxhhhxx!!!x Iran` ` ` Asia xxhhhx Jamaica` ` ` L.A. xxhhhxx Kenya` ` ` Afr xxxhhhxx!!!x Korea Rep.` ` ` Asia xxxxhhhxx!!!x Madagascar` ` ` Afr xhhhxx Malawi` ` ` Afr xxxhhhxx!!!x Malaysia` ` ` Asia xxxhhhxx Mauritania` ` ` Afr x Mexico` ` ` L.A. xxxxhhhxx Morocco` ` ` Afr xxxhhhxx Myanmar` ` ` Asia xx Nepal` ` ` Asia xxxxhhhxx Nicaragua` ` ` L.A. xxhhhxx Niger` ` ` Afr xxhhhxx!!!x Nigeria` ` ` Afr xxhhhxx Pakistan` ` ` Asia xxxxhhhxx!!!x Panama` ` ` L.A. xxxxhhhxx!!!x Pap.New Gn.` ` ` Asia xxx Paraguay` ` ` L.A. xxxxhhhxx Peru` ` ` L.A. xxxhhhxx Philippines` ` ` Asia xxxhhhxx Rwanda` ` ` Afr xxhhhx Senegal` ` ` Afr xx Sier. Leon.` ` ` Afr xxxhhhxx!!!x Singapore` ` ` Asia xxhhhxx!!!x Somalia` ` ` Afr xhhhx 66Table B (continued)   Region Enroll. Attain E/GDP Data StudentTeacher Ratios Country Ratio ment IMFcons IMFbud UNESCO Primary Secondary   ` h! Sri Lanka` ` ` Asia xxxxhhhx Sudan` ` ` Afr xxhhhxx!!!x Syria` ` ` Asia xxxxhhhxx!!!x Tanzania` ` ` Afr xxxxhhhxx!!!x Thailand` ` ` Asia xxxxhhhxx!!!x Togo` ` ` Afr xxxxhhhxx Tunisia` ` ` Asia xxxxhhhxx Turkey` ` ` Asia xxxxhhhxx!!!x Uganda` ` ` Afr xxxhhhxx!!!x Uruguay` ` ` L.A. xxxxhhhxx Venezuela` ` ` L.A. xxxxhhhxx Zaire` ` ` Afr xxxxhhhx Zambia` ` ` Afr xxhhhxx!!!x Zimbabwe` ` ` Afr xxxxhhhx   The LDC sample is taken from Kelley/Schmidt (1994) and represents all countries exceeding 1 million people in 1960 with complete data on GDP, saving and population over the entire period as available in Summers and Heston (1993), excluding countries classified as DCs (Australia, Canada, Israel, Japan, New Zealand, South Africa, United States, and Western Europe). Table C  Determinants of StudentTeacher Ratios: LDCs in 1985   Primary Secondary   X p!3333   Constant B  36.66 B  38.04 B 34.46 BD33.70 Bh22.54 BL28.53 Bp 24.64 B4!#4!26.52 B  (5.59)B  (2.22)B (4.21)BD(6.68)Bh(2.95)BL(1.18)Bp (2.57)B4!#4!(0.85) ln(Y/N)B, , 14.36BD D 14.11Bh h16.31BD16.65Bphp11.65BL10.47Bp 10.98B # 10.23 B, , (4.78)BD D (4.77)Bh h(4.53)BD(4.63)Bphp(3.51)BL(3.27)Bp (2.65)B # (2.33) UrbanizationB  0.22B  0.22B0 00.31BTDT0.37B8h80.36B\L\0.31Btp t0.37B!#!0.32 B  (2.12)B  (1.97)B (2.72)BD(2.88)Bh(2.94)BL(2.22)Bp (2.80)B4!#4!(1.91) N515/NBX X B  0.14B BTDT0.52BhBL0.44Bp B4!#4!0.38 BX X BD D (0.25)B BD(0.86)BhBL(0.57)Bp B # (0.39) NgrB  0.98BppB 1.15BDBh2.88BLBp 3.46 B, , (0.5)BppBh h(0.55)BDBphp(1.17)BLBp (1.24) AsiaBX X BppB0 03.91BTDT6.25BhBLBp 1.43B4!#4!0.14 BX X BppB (0.87)BD(1.4)BhBLBp (0.26)B # (0.02) Lat.Amer.BX X BppB 3.35BD2.54BhBLBp 5.92B4!#4!2.95 BX X BppBh h(0.78)BD(0.66)BhBLBp (0.77)B # (0.39) R2B  0.44B  0.44B0 00.50BTDT0.50B8h80.40B\L\0.36Btp t0.42B!#!0.37 Obsv. 48 48 48 48 23 23 23 23   Data Source: See tables 1 and 4. **BIBLIOGRAPHY Ahlburg, Dennis A. 1988. 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