Peru - Education at a crossroads - challenges and opportunities for the 21st century (Vol. 2 of 2) : Background notes and appendices

Report No 19066-PE Peru Education at a Crossroads Challenges and Opportunities for the 21 st Century (In Two Volumes) Volume II Background Notes and Appendices December 30, 1999 Human Development Department Bolivia, Paraguay and Peru Country Management Unit Latin America and the Caribbean Region ocrrument of the Wd Bank  ACRONYMS AND ABBREVIATIONS ADE Areas de Desarrollo Educativo (Education Development Areas) AE Area de Ejecuci6n (Area of Execution) AFP Administraci6n de Fondo de Pensiones APP Authorized Pensionable Position CIAS Comite Interministerial de Asuntos Sociales (Inter-ministerial Committee of Social Affairs) CORDELICA Corporaci6n de Desarrollo de Lima y Callao CTAR Consejo Transitorio de Administraci6n Regional (Transitional Council of Regional Administration) DRE Director Regional de Educaci6n FONAVI Fondo Nacional de Vivienda (National Housing Fund) FONCODES Fondo Nacional de Compensaci6n y Desarrollo Social (Social Fund) GRADE Grupo de Analisis para el Desarrollo INEI Instituto Nacional de Estadistica e Informatica INFES Infraestructura Nacional para Educaci6n y Salud (National Infrastructure for Education and Health) IPSS Instituto Peruano de Seguro Social (Peruvian Institute of Social Security) IST Institutos Superiores Tecnicos (Higher Technical Institutes) ISP Institutos Superiores Pedag6gicos (Higher Institutes of Pedagogy) MECEP Proyecto para Mejoramiento de la Calidad de la Educaci6n Primaria MED Ministerio de Educaci6n (Ministry of Education) MEF Ministerio de Economia y Finanzas (Ministry of Economy and Finance) MINSA Ministerio de Salud (Ministry of Health) OECD Organization for Economic Cooperation and Development ONP Oficina de Normalizaci6n Previsional (Pension Office) PLANMED Planning Unit in MED PROMUDEH Ministerio de Promoci6n de la Mujer y del Desarollo Humano (Ministry for the Promotion of Women and Human Development) PRES Ministerio de la Presidencia (Ministry of the Presidency) USE Unidades de Servicios Educativos (Educational Service Units) UNESCO United Nations Educational, Scientific and Cultural Organization Exchange Rates (1997): Soles 2.66 = US$1 Fiscal Year: January 1 to December 31 School Year: April 1 to December 31 (180 days/year) Vice Presidents Shahid Javed Burki (through June 30, 1999) David de Ferranti (from July 1, 1999) Country Director Isabel Guerrero Lead Economist Ernesto May Sector Director Xavier Coll Education Sector Manager Jamil Salmi Lead Specialist in Human Donald Winkler Development Country Sector Leader Evangeline Javier Task Team Leader Kin Bing Wu  Peru Education at a Crossroads: Challenges and Opportunities for the 218t Century Volume 11: Background Notes and Appendices   TABLE OF CONTENTS: VOLUME II BACKGROUND NOTES 1. The Structure of Education ............................................................1 2. Income Elasticity of Demand for Education and Engel's Curve .............................3 Table 1: Determinants of Household Budget Shares ......................................................4 Table 2: Elasticity Estimates from Engel's Curves ........................................................5 3. Private and Social Returns to Public Education in Urban Peru ..............................7 Table 1: Earnings Functions Coefficients ............................................................9 Table 2: Linear Hypothesis on Regression Coefficients ............................................... 10 Table 3: Estimated Educational Premiums .......................................................... 1. I Figure 1: Earnings by Age and Educational Level, Females ........................................ 10 Figure 2: Earnings by Age and Educational Level, Males ........................................... 11 4. Determinants of Achievement ........................................................... 13 Table 1: Descriptive Statistics of Student-Level Variables Used in the HLM Model ........................................................... 1 5 Table 2: Descriptive Statistics of School-Level Variables Used in the HLM Model ........................................................... 16 Table 3: Descriptive Statistics of Department-Level Variables Used in the HLM Model ........................................................... 17 Table 4: Effects of Student Characteristics on Student Outcomes .............................. 22 Table 5: Effects of School Characteristics on School Mean ......................................... 24 Table 6: Cross-Level Effects of School Characteristics on Mathematics Achievement Slopes ........................................................... 27 Table 7: Extent to which Variation in Math Achievement Is Accounted for by Student-Level Characteristics and the Variation in True School Mean Mathematics Achievement Is Accounted for by School-Level Factors ............... 28 Table 8: Correlation Matrix ........................................................... 31 Table 9: Effects of Departmental Characteristics on the Grand Mean of Math Test Scores ........................................................... 32 Table 10: Final Three-level Model for Average Math Achievement with Interaction ........................................................... 36 Table 11: The Extent to which Mathematics Achievement is Accounted for by Student, School, and Department Level Characteristics ...................................... 40 5. Teacher Education and Professional Development .................................................. 41 Table 1: A Comparison of Old and New Pilot Curriculum in Teacher Education ........................................................... 43  APPENDICES 1. Student Enrollment Statistics ...................... 51 1.1. Enrollment in Formal and Nonformal Education (Disaggregated by Minors and Adults) in Public Institutions by Level, 1990-1997 1.2. Enrollment in Formal and Nonformal Education (Broadly Grouped) in Public Institutions by Level as Percentage of Total, 1990-1997 1.3. Enrollment in Formal and Nonformal Education (Disaggregated by Minors and Adults) in Private Institutions by Level, 1990-1997 1.4. Enrollment in Formal and Nonformal Education (Broadly Grouped) in Private Institutions by Level as Percentage of Total, 1990-1997 1.5. Total Enrollment in Formal and Nonformal Education (Disaggregated by Minors and Adults) in Public and Private Institutions, 1990-1997 1.6. Public Enrollment by Level and by Department, 1997 2. Teacher Statistics ............. 59 2.1. Teachers in Formal and Nonformal Education (Disaggregated by Minors and Adults) in Public Institutions by Level, 1990-1997 2.2. Teachers in Formal and Nonformal Education (Broadly Grouped) in Public Institutions by Level as Percentage of Total, 1990-1997 2.3. Teachers in Formnal and Nonformal Education (Disaggregated by Minors and Adults) in Private Institutions by Level, 1990-1997 2.4. Teachers in Formal and Nonformal Education (Broadly Grouped) in Private Institutions by Level as Percentage of Total, 1990-1997 2.5. Total Teachers in Formal and Nonformal Education (Disaggregated by Minors and Adults) in Public and Private Institutions by Level, 1990-1997 2.6. Teacher-to-Student Ratio in Formal and Nonformal Education (Disaggregated by Minors and Adults) in Public Institutions by Level, 1990-1997 2.7. Teacher-to-Student Ratio in Formal and Nonformal Education (Disaggregated by Minors and Adults) in Private Institutions by Level, 1990-1997 2.8. Teachers by Level and by Department, 1997 2.9. Teacher to Student Ratio by Level and by Department, 1997 2.10. Student Enrollment and Teachers in Public FPedagogical Institutes by Region, 1997 2.11. Student Enrollment and Teachers in Private Pedagogical Institutes by Region, 1997 2.12. Changes in Student Enrollment and Student to Teacher Ratios in Public Pedagogical Institutes by Region, 1997 2.13. Change in Student Enrollment and Student to Teacher Ratios in Private Pedagogical Institutes by Region, 1997 3. School Statistics ............ 75 3.1. Public Schools for Formal and Nonformnal Education (Disaggregated by Minors and Adults) by Level, 1990-1997 ii  3.2. Public Schools for Formal and Nonformal Education (Broadly Grouped) by Level as Percentage of Total, 1990-1997 3.3. Private Schools for Formal and Nonformal Education (Disaggregated by Minors and Adults) by Level, 1990-1997 3.4. Private Schools for Formal and Nonformal Education (Broadly Grouped) by Level as Percentage of Total, 1990-1997 3.5. Total Public and Private Schools for Formal and Nonformal Education (Disaggregated by Minors and Adults) by Level, 1990-1997 3.6. Total Public and Private Schools for Formal and Nonformal Education (Broadly Grouped) by Level as Percentage of Total, 1990-1997 4. Indicators of Equity and Efficiency ........................... 83 4.la. Rural Gross Enrollment Ratio by Gender, Age, and Consumption Quintile, 1997 4.1 b. Urban Gross Enrollment Ratio by Gender, Age, and Consumption Quintile, 1997 4.1 c. Rural Net Enrollment Ratio by Gender, Age, and Consumption Quintile, 1997 4. ld. Urban Net Enrollment Ratio by Gender, Age, and Consumption Quintile, 1997 4.2a. Rural Public Gross Enrollment Ratio by Gender, Age, and Consumption Quintile, 1997 4.2b. Urban Public Gross Enrollment Ratio by Gender, Age, and Consumption Quintile, 1997 4.2c. Rural Public Net Enrollment Ratio by Gender, Age, and Consumption Quintile, 1997 4.2d. Urban Public Net Enrollment Ratio by Gender, Age, and Consumption Quintile, 1997 4.3a. Rural Private Gross Enrollment Ratio by Gender, Age, and Consumption Quintile, 1997 4.3b. Urban Private Gross Enrollment Ratio by Gender, Age, and Consumption Quintile, 1997 4.3c. Rural Private Net Enrollment Ratio by Gender, Age, and Consumption Quintile, 1997 4.3d. Urban Private Net Enrollment Ratio by Gender, Age, and Consumption Quintile, 1997 4.4a. Simulation 1 - Distribution of Public Expenditure by Consumption Quintile, 1997 4.4b. Simulation 2 - Distribution of Public Expenditure by Consumption Quintile, 1997 4.4c. Simulation 3 - Distribution of Public Expenditure by Consumption Quintile, 1997 4.4d. Simulation 4 - Distribution of Public Expenditure by Consumption Quintile, 1997 4.4e. Simulation 5 - Distribution of Public Expenditure by Consumption Quintile, 1997 4.5. Water and Sanitation in Public and Private Schools by Age and Income Group, 1994 iii  4.6. Typology of Urban and Rural Schools, Based on School Characteristics, Infrastructure, Equipment and Other Resources, Principals' and Teachers' Characteristics and Perceptions, 1994 4.7. Internal Efficiency of Public Education (Primary and Secondary) in Peru (Average 1994 to 1996) 5. International Comparison of Between-School Variation in Achievement ............ 105 5.1. International Comparison: Between-School Variation in Achievement in Selected Countries 5.2. International Comparison: Between-School Variance in IEA International Studv on Reading, 1990 6. Public Expenditure on Education .........................................................111 6.1 Gross Domestic Product, Total Government Expenditure, and Total Public Expenditure on Education, 1970-1997 (Million Soles in Current Prices) 6.2 Gross Domestic Product, Total Government Expenditure, Total Public Expenditure on Education, and Tax Revenue of Central Government, 1970-1997 (Million Soles in Constant 1997 Prices) 6.3. Gross Domestic Product, Total Government Expenditure, and Total Public Expenditure on Education, 1970-1997 (Million US dollars at the 1997 Exchange Rate) 6.4. Recurrent and Capital Expenditure on Education, 1990-1997 (Constant 1997 Soles) 6.5. Public Expenditure on Education by Budgetary Entities, 1990-1997 6.6. Functional Composition of Public Expenditure on Education According to Pre- 1997 Classification, 1990-1996 6.7 Reclassified Functional Composition of Public Expenditure on Education According to the 1997 Classification, 1990-1997 6.8. Functional Composition of Public Expenditure on Education by Budgetary Entities, 1995-1997 6.9. Public Expenditure on Education by Level, 1'990-1997 6.10.Per Student Recurrent Public Expenditure by Level, 1990-1997 6.11. Recurrent public Expenditure by Level, by Function and by Department from Central Government Allocation, 1997 6.12. Recurrent Public Expenditure by Level, by Function and by Department from Own Resources, 1997 6.13. Recurrent Public Ependiture by Level, and by Department from Other Sources. 1997 6.14. Total Public Expenditure on Education by Level, and by Department from All Sources of Funding, 1997 6.15.Departmental Revenues from Central Government Allocation as a Percentage of Total, 1997 6.16. Department's Own Resrouces as a Percentage of Total, 1997 6.17. Other Resources as a Percentage of Total, 1997 6.18. Per Student Recurrent Expenditure by Level and by Department, 1997 (Soles) 6.19.Teachers Salary Scale (July 1990-August 1997) (Soles in Current Prices) iv  7. Household Expenditure on Education ....................................... 157 7.1. Average Household Expenditures on Pre-Primary Education by School Type, 1997 (Soles Per Child) 7.2. Average Household Expenditures on Primary Education by School Type, 1997 (Soles Per Student) 7.3. Average Household Expenditures on Secondary Education by School Type, 1997 (Soles Per Student) 7.4. Average Household Expenditures on Tertiary Nonuniversity Education by School Type, 1997 (Soles Per Student) 7.5. Average Household Expenditures on University Education by School Type, 1997 (Soles Per Student) 7.6. Average Household Expenditures on Education by Education Level, 1997 (Soles Per Student) 7.7. Average Household Expenditures on Education by School Type, 1997 (Soles Per Student) 7.8. Total Household Expenditures on Pre-Primary Education by School Type, 1997 (Soles) 7.9. Total Household Expenditures on Primary Education by School Type, 1997 (Soles) 7.10. Total Household Expenditures on Secondary Education by School Type, 1997 (Soles) 7.11. Total Household Expenditures on Tertiary Nonuniversity Education by School Type, 1997 (Soles) 7.12.Total Household Expenditures on University Education by School Type, 1997 (Soles) 7.13. Total Household Expenditures on Education by Education Level, 1997 (Soles) 7.14. Total Household Expenditures on Education by School Type, 1997 (Soles) 8. Population Projection ....................................... 173 8.1. Assumptions of Population Projection 8.2. Population by Single Years of Age for Selected Age Ranges and Years, 1995- 2020 8.3. Projected School-Age Population, 1995-2020 9. External Support for Education Since 1990 ....................................... 179 10. Selected Indicators for International Comparison ....................................... 189 10.1. Educational Expenditure as a Percentage of GDP for all Levels of Education Combined, by Source of Funds (1995) 10.2. Educational Expenditure as a Percentage of GDP for Primary and Secondary Education, by Source of Funds (1995) 10.3. Educational Expenditure as a Percentage of GDP for Tertiary Education, by Source of Funds (1995) 10.4.Educational Expenditure from Public and Private Sources for Educational Institutions as a Percentage of GDP by Level of Education (1995) v  10.5.Index of the Change between 1990 and 1995 in Public and Private Expenditure on Education, by Level of Education (1990=100) 10.6. Educational Expenditure on Primary and Secondary Education by Resource Category for Public and Private Institutions (1995) 10.7.Educational Expenditure on Tertiary Education by Resource Category for Public and Private Institutions (1995) vi  Background Notes   Background Note 1. The Structure of Education The existing structure of education comprises four levels: initial, primary, secondary, and tertiary. (See Appendices 1.1-1.3 for enrollment in public institutions, Appendices 1.4-1.6 for enrollment in private institutions, and Appendices 1.7-1.9 for total enrollment). Initial education is offered in daycare for those under the age of 3 and in kindergartens for those between the ages of 3 and 5. There is also a nonformal system of initial education. It is estimated that about 20 percent of those under 5 are having some form of initial education (INEI, 1997). In 1997, 522,000 children enrolled in initial education in the public system, and 147,000 in private organizations. In a recent proposal for restructuring education, one year of initial education is to be made compulsory and form part of basic education. Primary education comprises six grades, intended for the age group between 6 and 11, but also available to adults who have not received it. In 1997, about 3.7 million persons enrolled in public, formal and nonformal programs, and 491,000 in private programs. The majority of primary schools are coeducational and the program of study comprises 25 hours per week during 36 weeks per year (900 hours per annum). Secondary education is offered to the age group between 12 and 16, as well as to adults who did not have it. In 1997, about 1.6 million enrolled in public secondary schools, and 318,000 in private schools. Secondary education is organized in two cycles: the first has a common curriculum for all students in Grades 7 to 8, and the second has a diversified curriculum of three years, divided into science and humanity streams. Secondary education is offered at 36 hours per week for 38 weeks in a year (1,368 hours per annum). Tertiary education includes nonuniversity and university education. Nonuniversity institutions include teacher training institutions (institutos superieroes pedagogicos or ISPs for short), technical education institutions (institutos superiories tecnicos or ISTs), and schools for the arts. In 1997, 211,000 students attended public universities, and 129,000 private universities. Another 165,000 students enrolled in public tertiary institutions, and 139,000 in private institutions. In 1997, MED proposed major changes in the structure of the system, with the aims to improve the articulation between levels, to meet needs of a changing labor market, and to improve system efficiency and organizational flexibility. It pledged to universalize one year of initial education, improve the quality of primary education, reduce secondary education from five to four years, and introduce two years of preparatory course work (bachillerato) which will provide the transition to tertiary education or to the world of work. In other words, basic education will comprise 11 years of instruction, which includes one year of pre-school, six years of primary and four years of secondary education. 1  What is new is not only the structural change but the introduction of certifications of study at three levels: at the end of basic education, bachillerato, and tertiary nonuniversity education, respectively. Accreditable capacities of basic education will include: (a) comprehension of reading, editing, communication, and expression; (b) development of logic and mathematics; (c) management of the basics of technology and informatics; (d) facility for continuous learning and holistic reasoning; (e) creativity and imagination; (f) understanding of environment; (g) local, national, and universal culture; (h) basic work and organizational abilities; and (i) basic knowledge of an international language. Accreditable capacities of the bachillerato will include: (a) productive use of resources (time, space, skills, and technology); (b) abilities to search and select information; (c) facility for analysis, synthesis, abstraction, and systematization; (d) proficiency in an international language; (e) internediate professional competency; (i) tools for management and self-employment. Students will be certified after having had no less than 2,500 hours of studies in tertiary non-university education. The proposed bachillerato is divided into two streams: (a) scientific and technological, and (b) scientific and humanistic. The former will prepare for studies in engineering, medicine, mathematics, the sciences and accounting in universities, and technical courses in tertiary non-university education. The latter will prepare for studies in law, education, the social sciences and humanities in universities, and tourism, graphic arts, translation, catering, and public relations in other tertiary education. In each stream, there will be a core curriculum and other subjects that prepare for the world of work. The core curriculum is shared by both streams and includes science and technology, earth science, oral and written communication, economics and management, informatics, history of Peru, natural philosophy, and international language. Bachillerato can be offered by (a) secondary colleges as add-ons to their four years of secondary education, (b) universities before the beginning of undergraduate studies, (c) postsecondary institutes before the beginning of two years of tertiary education, and (d) academic institutes specialized just in offering bachillerato. This ambitious plan requires investment in infrastructure, curriculum development, and teacher training. The implementation of bachillerato is sequenced as follows. In 1997, the proposed structural change was made public; the modernization of the secondary curriculum has begun; the transitional fifth. year of secondary schooling was elaborated; and the bachillerato curriculum was proposed. Subsequently, a law was promulgated to give the structural change legal force; new curriculum and training of principals and teachers was piloted; the development and distribution of education materials in secondary education was initiated; a new administrative system was set up; and infrastructure was planned. Thereafter, a second application of transition curriculum in the fifth year of secondary was implemented; training of teachers; and equipping institutions for implementation of bachillerato with follow-up and monitoring. Full scale implementation is expected to begin in 2000, affecting 200,000 young people each year. The following year will see the first batch of graduates from bachillerato. The effort to revamp the education system is expected to come to fruition in 2007. 2  Background Note 2. Income Elasticity of Demand for Education and Engel's Curve' The share of household expenditures for education were analyzed using an Engel equation framework. The explanatory variables include the logarithm of income (here proxied by total expenditure), the logarithm of the size of the household, and a set of variables intended to capture the gender and age composition of the household (with age brackets set up to correspond to the various levels of education in Peru). The explanatory variables also include a dummy for residence in the Lima metropolitan area, and three variables indicating, respectively, the education level of the household head, whether or not the household head is male, and whether or not the household head belongs to an indigenous group. The focus of analysis in this section is the expenditure variable, but the other variables are included as "control" variables, so that the coefficient estimates reported in this section are not biased. In other words, it is important to be sure that what we call the effect of income is indeed the effect of income, and not, say, the effect mainly of the education of the household head. In addition to estimating the Engel function for expenditure, we also provide estimates for expenditures on Food, on Health, and on Other Expenditures. The object of the analysis is to compute income elasticities for each of the budget shares. It is an empirically established fact that the income elasticity for food shares is negative, because poor households need to spend larger shares on food, but an a priori judgment cannot be made about the income elasticities of the other budget shares. In particular it is important to compare the income elasticity for education with those for health. The object of the analysis is to estimate a value for b, the slope on income in the budget share regression, as well as r1, the income elasticity which tells us the percentage points by which the budget share goes up for a given percentage increase in income. The estimates from the Engel function analysis are presented in Table 1. It can be seen from the table that the average budget share for education is 0.0467 and the coefficient on log total expenditures is 0.0128. The respective values for health related expenditures are 0.0411 for the average budget share and 0.0151 for the coefficient on log total expenditures. The income effect of food has the expected negative sign and the coefficient on log total expenditure for food share is of the same order of magnitude as reported from other countries. It is of interest to note that the dummies for Lima, rural location, female head, and indigenous head of household are economically and statistically insignificant in the education share regression. Some of these dummy variables are important in the food share regression, such as the 0.1315 effect of a rural location. The lack of significance of the dumrmy variables for the education share, in contrast with the significance for food share, tells an important story about the stability of preferences for education across This analysis was undertaken by Suhas Parandeker. 3  households which vary across these measured variables. The estimates of elasticity, derived from the regression coefficients are reported in Table 2. Table 1: Determinants of Household Budget Shares Budget Shares Explanatory variables Education I Food Health Other Mean OLS Coefficient (t-value for H0 Coeff = 0) (Std Dev.) Intercept -0 1424 0.8066 -0 0970 0 4328 (-10 02) (24 078) (-6 455) (13.52) Logarithm of total household expenditure 0 0128 -0.0377 0.0151 0 0098 9 2304 (8 113) (-10.139) (9 072) (2 750) (0 7202) Logarithm of total household size 0.0187 0 001 0 0046 -0.0242 1 5189 (8.755) (0 199) (2 035) (-5.052) (0.4920) Proportion of boys aged 0-5 years -0 0179 0.1294 0 0026 -0.1142 0.0706 (-2.209) (6 769) (0 307) (-6 249) (0 1174) Proportion of boys aged 6-11 years 0.0746 0 1185 -0.0095 -0.1837 0 0660 (9 109) (6 133) (-1 091) (-9951) (0 1130) Proportion of boys aged 12-16 years 0 1120 00489 -0.0131 -0 1477 0.0483 (12 43) (2.3000) (-I 377) (-7 279) (0 1000) Proportion of boys aged 17-22 years 0 0730 0.0322 -0 0119 -0 0932 0 0505 (8 875) (I 661) (-1 367) (-5.037) (0 1064) Proportion of girls aged 0-5 years -0 0321 0.1612 0 0118 -0.1409 0 0671 (-3.970) (8 443) (1 383) (-7 724) (0.1163) Proportion of girls aged 6-11 years 0 0717 0.0728 -0.0020 -0 1425 0.0607 (8 503) (3 661) (-0.234) (-7 498) (0 1085) Proportion of girls aged 12-16 years 0.0805 0 0899 -0.0169 -0 1535 0 0470 (8.711) (4 125) (-1.728) (-7 374) (0.0944) Proportion of girls aged 17-22 years 0 0718 0 0427 -0.0081 -0 1063 0 0560 (8 419) (2 125) (-0 906) (-5.537) (0 1069) Proportion of girls aged > 22 years 0 0209 -0 0008 0.0078 -0 0279 0 2815 (3.198) (-0 054) (I 122) (-I 891) (0.1848) Dummy for residence in metropolitan Lima -0.0032 -0.0130 -0 0071 0 0234 0 2893 (-I 646) (-2 812) (-3.430) (5 286) (0.4357) Dummy for residence in rural area -0 0010 0 1315 0.0075 -0 1380 0.3481 (-0.515) (27 00) (3 436) (-29 64) (0.4852) Female head of household -0 0020 -0.0148 -0 0007 0 0175 0.1563 (-0 776) (-2 434) (-0.248) (3 008) (0.3602) Indigenous head of household 0 0022 0 0022 -0.0035 -0.0009 0.2335 (1.182) (0.493) (-1 749) (-0 219) (0 4111) Education in years of the head of household 0 0019 -0.0049 -0 0011 0 0040 7.7645 (10 15) (-10 81) (-5.208) (9 257) (4 8485) Mean value of budget share 0.0467 0 5050 0.0411 0 4072 R2 0.28 0 49 0.04 0.48 F value 91.8 233 5 8 94 220 8 Sample Size (N=3820 Households) 4  Table 2: Elasticity Estimates from Engel's Curves Expenditure Group Elasticity Education Food Health Other Budget share with respect to total expenditure 0 274 -0 0747 0 3674 0 0241 Specific expenditure with respect to total expenditure 1.274 0,9253 1.367 1 024 Budget share with respect to household size -0 6133 -0,0969 -0.0613 0 0769 Specific expenditure with respect to household size -0.6133 -0.0969 -0.0613 0 0769 The findings from the Engel's curve analysis are a mixed blessing. On the one hand, the income elasticity is a low 0.27, and education expenditures are considered to be a necessity by Peruvian households.2 This is a positive finding, as it indicates that there is a strong underlying demand for education in Peru. A high income elasticity would indicate that the item of expenditure is a luxury-households spend money on luxuries when they have the money, but simply do without it when they do not have money. The relative magnitudes are small, but the evidence also suggests that education expenditures are less responsive to changes in income as compared to expenditures on health. However, from the point of view of educational policy, the implication is that we cannot rely on general increases in income to bring about greater expenditures on education. For every doubling of household income, the budget share spent on education would go up only by a quarter. Add this finding to the fact that levels of household expenditure on education vary vastly by income level. (This fact can be seen from the Lorenz curve analysis reported in the main body of this report-the total amount spent on education by the richest quintile in Peru was more than 13 times the total amount spent on education by the poorest quintile.) The findings show the need for specific policy instruments that will address the inability of poorer households to incur additional expenditures.3 2 Mwabu's work on Kenya indicated a much higher income elasticity of education expenditures of 0.73. 3 To make sure that the conclusion was not based just on one pooled set of regressions, the regressions (not reported here) were run separately for subsamples by indigenous and nonindigenous, rural and urban, and poor and rich. Consistently, the pattern is that the income elasticities are lower for the more disadvantaged groups. 5  Engel's Curves: Formulae for Elasticity Estimates The Engel curve estimates are based on the following equation, presented as Equation (3) in the Working Paper by Germano Mwabu.4 i x i- pi 0log(x) + 17i log(N) + EYi r(n N) +. oz + 6 where w= the share of expenditure of the i th grouping of household expenditure items. i household spending for the four groups, viz., education, health, food, and other expenses. (The share is conceptually equal to pi times qi, the price times the quantity, divided by the total expenditure x, but pi and qi are not empirically observed as separate entities in the actual estimation of the Engel curve.) n, = the number of family members in the age-by-gender group j. These groups range in the reported estimation from (boys aged 0 to 5 years) to (girls aged older than 22 years). Ni= the total family size, thus (nj/N) represents the relative size of group j in the family. z = a set of control variables. These include (a) dummy for residence in metropolitan Lima, (b) dummy for residence in rural area, (c) female head of household, (d) indigenous head of household, and (e) education in years of the head of household. 6i = the error term in the regression equation, assumed to be i.i.d. normal. aj,6j, i, yi = the parameters to be estimated. The equations for elasticities follow from the above equation. Letting Si represent the elasticity of the budget share for expenditure group i, and Ei represent the elasticity of specific expenditure with respect to total expenditure, x, and household size, N, the elasticities are: a) Six= 31i/w, b) SiN 1/wi ( i-