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18.1 Household size and living standards18.1.1Using the file AGGR-7 [p.319], compute the poverty headcount by using the variable EXPCAP and a poverty line of 373 FCFA. 18.1.2Then, find the poverty line which you must use with the variable TTEXP to obtain the same estimate of poverty as that obtained in question 18.1.1. 18.1.3Using for the variable EXPCAP the poverty line used in question 18.1.1, and for the variable TTEXP the poverty line found in question 18.1.2, decompose poverty across household size GSIZE using EXPCAP and TTEXP. Discuss. 18.1.4Using again the same file AGGR-7 [p.319], decompose poverty across the sex of the household head SEX by using EXPCAP and TTEXP and their associated poverty line used in questions 18.1.1 and 18.1.2. Discuss. 18.2 Aggregative weights and poverty analysis18.2.1Using the file AGGR-7 [p.319], compute total poverty in Cameroon without using the SIZE variable and by using it. Discuss. 18.2.2Using the file AGGR-7 [p.319], decompose total poverty in Cameroon according to the categories captured by GSIZE without using the SIZE variable and by using it. Discuss. 18.2.3Using the file DECB-8 [p.319], decompose total poverty in Cameroon according to the categories captured REGION without using the SIZE variable and by using it. Discuss. 18.3 Absolute and relative poverty18.3.1Using the file DECB-8 [p.319], compute the average of EXPEQ for the whole of Cameroon and for each of the two regions of REGION. 18.3.2Then, compute half of these averages for the whole of Cameroon and for each of its two regions in REGION. (These statistics are subsequently used as relative poverty thresholds in 18.3.3.) 18.3.3Finally, compute the poverty headcount for the whole of Cameroon and for each of its two regions using as poverty lines: a- a national absolute threshold of 373 FCFA; b- the national relative threshold; c- the relative thresholds for each of the two regions. Check whether using an estimate of the national relative threshold (as opposed to a known or deterministic national relative threshold) has an impact on the standard error of the national headcount. 18.4 Estimating poverty lines18.4.1Computing a food poverty line with a "FEI-inspired" method. With LINE-6 [p.319], draw a non-parametric regression of FDEQ on CALEQ for an interval of CALEQ of 0 to 4000 calories. Find the level of food expenditures that is expected to yield an intake of 2400 calories per day. 18.4.2Computing a CBN poverty line. With LINE-6 [p.319], draw a non-parametric regression of EXPEQ on FDEQ for an interval of FDEQ which includes the food poverty line estimated in 18.4.1. Find the level of total expenditures expected at a level of food expenditures equal to the food poverty line estimated in 18.4.1. 18.4.3Using the results of 18.4.1 and 18.4.2, compute the share of food expenditures in the total expenditures of those whose level of food expenditures equals the food poverty line. By dividing the food poverty threshold by this share, estimate a global poverty line. 18.4.4A second method of estimation of the share of food expenditures in total expenditures. With LINE-6, draw a non-parametric regression of FDEQ on EXPEQ for an interval of EXPEQ of 0 to 500 FCFA. Find the level of food expenditures expected at a level of total expenditures equal to the food poverty line estimated in 18.4.1. 18.4.5Using the results of 18.4.4, compute the share of food expenditures in the total expenditures of those whose level of total expenditures equals the food poverty line estimated in 18.4.1. By dividing the food poverty line by this share, estimate a second global poverty line. 18.4.6A third method for the estimation of the non-food poverty line. With LINE-6, draw a non-parametric regression of EXPEQ on FDEQ for an interval of FDEQ which includes the food poverty line estimated in 18.4.1. Find the level of total expenditures expected at a level of food expenditures equal to the food poverty line estimated in 18.4.1. 18.4.7Using the results of 18.4.6, compute the expected non-food expenditures of those whose level of total expenditures equals the food poverty line estimated in 18.4.1. By adding these expected non-food expenditures to the food poverty line, estimate a third global poverty line. 18.4.8Computation of a global poverty line according to the FEI method. With LINE-6 [p.319], draw a non-parametric regression of EXPEQ on CALEQ for an interval ranging from 0 to 4000 calories for CALEQ. Estimate the global poverty line that corresponds to 2400 calories per day. 18.5 Descriptive data analysis18.5.1Density functions. With DECB-8 [p.319], estimate the density of LEXPEQ for the whole country and for each region (by using REGION). 18.6 Decomposing poverty18.6.1With AGGR-7 [p.319], decompose poverty across SEX. Then check the calculations of the absolute and relative decompositions provided by DAD by separately calculating the poverty indices for each group in SEX. Reconstruct manually the decomposition to verify that DAD gives the correct decomposition results. 18.6.2Using DECA-7 [p.319], decompose total poverty according to the socio-economic categories AGE and EDUC. 18.6.3Using DECB-8 [p.319], decompose total poverty according to the socio-economic categories SECT, TYPE and OCCUP. 18.7 Poverty dominance18.7.1Using DECA-7 [p.319], plot the first-order dominance curves separately for those who have a primary level and a superior level of education (see variable EDUC) and for poverty lines varying between 0 and 1000 FCFA. What do these curves show? 18.7.2Using DECA-7 [p.319], plot the first-order dominance curves separately for the female-headed and for the male-headed households, for poverty lines varying between 0 and 300 FCFA. What do these curves indicate? Find the relevant "critical thresholds" and comment. 18.7.3Repeat 18.7.1 and 18.7.2 for second- and third-order dominance. 18.7.4Compute the FGT poverty index for α = 0 and for poverty lines equal to 150, 250 and 300 FCFA, separately for the female- and male-headed households. 18.7.5Repeat 18.7.4 for second- and third-order dominance. 18.7.6Using DECB-8 [p.319], draw poverty gap curves separately for the two groups identified by the variable REGION. 18.7.7Using DECA-7 [p.319], draw poverty gap curves separately for the female-headed and the male-headed households. 18.7.8Using DECB-8 [p.319], draw CPG curves separately for the two groups identified by the variable REGION. 18.7.9Using DECA-7 [p.319], draw CPG curves separately for the female-headed and the male-headed households. 18.8 Fiscal incidence, growth, equity and poverty18.8.1Use the file "CAN4"[p.321] to predict the level of taxes paid and benefits received by individuals at different gross incomes X. For this, use the window "non-parametric regression ", and choose alternatively for the x axis the "level" or the "percentile" of gross incomes. What do these regressions indicate? 18.8.2Use the file "CAN6"[p.321] to draw the Lorenz Curve for gross income (X) and net income (N) in 1990 Canada. a- What does the difference between the two Lorenz curves indicate? b- Then, draw a concentration curve for each of the three transfers B1, B2 et B3 and the tax T. What can you say about the TR- progressivity and the "equity" of the distribution of the tax and benefits? c- Would a proportional increase in the benefit B1 combined with a proportional decrease in B3 of the same absolute magnitude be good for inequality, poverty and social welfare? d- Would a proportional increase in the benefit B2 financed by a balanced-budget proportional increase in the tax T be good for inequality, poverty and social welfare? 18.8.3Use the same file "CAN6"[p.321] to check the IR- progressivity of each of the three benefits and the tax T. For this, you can draw concentration curves for X combined separately with each of the three transfers B1, B2 and B3 and the tax T. What can you say about the IR- progressivity and the "equity" of the distribution of the tax and benefits? How does it compare with the TR-progressivity results? 18.8.4Using the file "CAN4"[p.321], compute the concentration indices of each of B and T, and compare them to the Gini index of gross income X. Then, compute an estimate of TR- progressivity of the tax and benefit system in Canada. 18.8.5Compare the Lorenz curve for N with the concentration curve for N (using X as the ranking variable). What does this tell you? 18.8.6Express the total redistribution exerted by the Canadian tax and transfer system as vertical equity minus horizontal inequity (reranking), using Gini and concentration indices. 18.8.7Draw the conditional standard deviation of benefits B and taxes T at various values of gross income X. 18.8.8Draw the conditional standard deviation of net income N at various values of gross income X. What does this indicate? 18.8.9Draw the share of total taxes T paid by those at different levels of gross income X, and at different ranks of X. Compute this as the ratio of expected taxes over mean gross income µx. Do the same for total benefits B. Compare this to the share of total gross income, computed as X over µX. What does this say? 18.8.10Compute the average tax rate paid by individuals at different levels of gross income X and at different ranks of X. Estimate this as the expected tax paid at X over X. What does this say about tax progressivity in Canada? Use the file PERHE-12 [p.322] for exercises 18.8.11 to 18.8.17. 18.8.11Compare the Lorenz curve of per capita total expenditures (EXPCAP), using SIZE, and of total expenditures (TTEXP). Which type of expenditures is more equally distributed? Why? a- To understand better why, add to the graph a concentration curve of total expenditures, using per capita expenditures as the ranking variable, and WHHLD to count observations; this will indicate the concentration of total expenditures among the poorest households, ranked by per capita expenditures. b- To complete your understanding, add a concentration curve for household size, using WHHLD as the aggregating weight and EXPACP as the ranking variable; this will indicate the concentration of individuals among the poorest households, as ranked by EXPCAP. Does this help you understand the difference between the above two Lorenz curves? 18.8.12Predict the proportion of individuals who visited a public health center and a public hospital in a given month. For this, use the variables CENTRO and HOSPIT, who indicate the proportion of individuals in a household who visited these institutions. Make this prediction at different percentiles of the distribution of per capita total expenditures. 18.8.13Graph again the concentration curve of total expenditures (TTEXP) using WHHLD and EXPCAP to rank individuals. Compare it to the concentration curve among households (thus use WHHLD) of their use of health centers and public hospitals, which is given respectively by NCENTRO and NHOSPIT, and use EXPCAP to rank households. What does this suggest? 18.8.14Add to the previous graph the concentration curve of individuals in households. What does this information add to your equity judgement? 18.8.15Draw on a new graph the concentration curve of total expenditures (TTEXP) using WHHLD and EXPCAP to rank households. Compare this to the concentration curves for access to piped water (PUBWAT) and to sewerage (PUBSEW), using WHHLD as the aggregating weight to draw the curves and EXPCAP as the ranking variable. That is, find out the concentration of access to piped water and sewerage among various proportions of poorest households, and compare that to their share in total expenditures. What do you find? 18.8.16Add to your previous graph the concentration curves for the number of individuals who have piped water (NPUBWAT) and who have sewerage (NPUBSEW), using household weighting and EXPCAP as the ranking variable. How do you interpret the differences you obtain with the results of question 18.8.15? 18.8.17Redo the previous analysis of the incidence of access to piped water (PUBWAT) and to sewerage (PUBSEW), but this time use individual weighting (which is usually considered to be the best descriptive choice from a normative or ethical perspective). Thus, draw the Lorenz curve of per capita total expenditures (EXPCAP) using individual weighting, WIND. Compare this to the concentration among individuals of the access to piped water (PUBWAT) and to sewerage (PUBSEW), using WIND as the aggregating weight to draw the curves and EXPCAP as the ranking variable. That is, find out the concentration of access to piped water and sewerage among various proportions of poorest individuals, and compare that to their share of the population and of the total expenditures. Use the file PERED-16 [p.322] for exercises 18.8.18 to 18.8.22. 18.8.18Make a new graph again of the concentration curve of total expenditures (TTEXP) using WHHLD and EXPCAP to rank households. Compare it to the concentration curve of the number of children at various levels of public education, NPUBPRIM, NPUBSEC and NPUBUNIV using the same aggregating weights. Is education enrolment equitably distributed according to this? What happens to our understanding of the "picture" if we add the concentration curve for the number of children NCHILD? 18.8.19Now add the Lorenz curve of per capita total expenditures EXPCAP using NCHILD as the size variable. Compare it to the concentration curve of the enrolment of children at various levels of public education, which is given by PUBPRIM, PUBSEC and PUBUNIV, using NCHILD and EXPCAP as the ranking variable. Has your equity judgement evolved? 18.8.20Redraw the Lorenz curve of per capita total expenditures, now using WCH0612 as the aggregating weight, and compare it to the concentration curve of PUB-PRIM using the same aggregating weight. 18.8.21Redraw the Lorenz curve of per capita total expenditures now using WCH1318 as the aggregating weight, and compare it to the concentration curve of PUB-PSEC using the same aggregating weight. 18.8.22Test the hypothesis that a small increase in secondary school fees combined with a decrease in primary school fees of the same total magnitude would not change the distribution of well-being in Peru. Use the file SENESAM [p.323] to do exercises 18.8.23 to 18.8.26. 18.8.23Using EXPEQ as ranking variable, predict the proportion of children between 7 and 12 at different levels of living standards who attend primary school. Compare these results to those you obtain when you separate children into boys and girls. 18.8.24Draw the conditional standard deviation of primary school attendance separately for boys and girls at various values of EXPEQ. What does this indicate? 18.8.25Draw the conditional standard deviation of primary school attendance separately for each of the three STRATA, and this, at various values of EXPEQ. Explain what you find. 18.8.26Compare the Lorenz curve for EXPEQ with the concentration curve for EXPEQ (using TTEXP as the ranking variable). What does this suggest? Use the file ESPMEN [p.325] to do exercises 18.8.27 to 18.8.53. When needed, use EXPEQ as the variable of interest, the headcount as the poverty index, and a poverty line of 60000 FCFA per adult equivalent. 18.8.27Draw the concentration curves of FDEQ, NFDEQ, HEALTHEQ and SCHEX-PEQ for the population of individuals (i.e., setting the size variable to SIZE) and using EXPEQ as the ranking variable. How do these curves compare to the Lorenz curve for EXPEQ? 18.8.28Compare the Lorenz curves of EXPEQ and INCOMEQ. What do you find? How do you explain this? 18.8.29Compare the Lorenz curves of EXPEQ for each of the 3 values of DEPT. 18.8.30Draw the CD curve (normalized by the mean of the variables but not by the poverty lines) of FDEQ and NFDEQ for different poverty lines and for c=l. What does it tell you? 18.8.31Compute the Gini inequality index for TTEXP, EXPEQ and INCOMEQ. Do this for values of ρ equal to 1, 2 and 3. Then, draw these indices for each of these variables on a graph for ρ ranging from 1 to 5. 18.8.32Decompose inequality in EXPEQ as a sum of inequality in each of its four components, FDEQ, NFDEQ, HEALTHEQ and SCHEXPEQ. 18.8.33Draw the share of total SCHEXPEQ of those at different levels of EXPEQ, and at different ranks of EXPEQ. Compute this as the ratio of expected SCHEXPEQ conditional on some value of EXPEQ over that value of EXPEQ. over Do the same for HEALTHEQ. What do you find? 18.8.34What would the impact on poverty be if we were to transfer 1000 FCFA (per adult equivalent) to each individual in the population? 18.8.35Where, among the different DEPT, would the impact of group- targeting an equal amount to all be the greatest for the same overall budget spent by the government? Does this result depend on the choice of the poverty line? 18.8.36Where, among the different REGION, would the impact of group- targeting an equal amount to all be the greatest for the same overall budget spent by the government? 18.8.37Assume that some form of government targeting can raise everyone's EXPEQ by the same proportion in a particular area. Per FCFA of overall per capita increase in EXPEQ, for which targeted DEPT would aggregate poverty reduction be the largest? Check this for the headcount and for the average poverty gap indices. 18.8.38Assume that some form of government targeting can raise everyone's EXPEQ by the same proportion in a particular area. Per FCFA of overall per capita increase in EXPEQ, for which targeted ZONE would aggregate poverty reduction be the largest? 18.8.39Say that food prices are about to increase by about 5%, due to the removal of food subsidies. In which group within DEPT will poverty increase the most? 18.8.40Using CD curves, check whether the ZONE for which the impact of an increase in food prices will be the largest depends on the choice of the poverty line and on the choice of poverty index (focus on first-order poverty indices). 18.8.41The government wishes to determine whether increasing the price of HEALTHEQ, for the benefit of a fall in the price of SCHEXPEQ, would be good for poverty. a- Compare the distributive cost/benefit of changing the price of each of HEALTHEQ and SCHEXPEQ. b- Check whether the reform is good for poverty for ratios of MCPF ranging from 0.5 to 2.0. 18.8.42Find the impact on poverty of those within ZONE=1 of a predicted increase of 3% in expenditures EXPEQ. 18.8.43Find the impact on national poverty of a predicted increase of 3% in the expenditures EXPEQ of those within ZONE=1. Compare your results to those obtained for ZONE=2. Do this for FGT indices with α=0, 1 and 2. 18.8.44Find the impact on national poverty of a predicted increase of 3% in everyone's expenditures FDEQ. Compare your results to those for a 3% increase in everyone's NFDEQ. Do this for the FGT indices with α=0, 1 and 2. 18.8.45Per FCFA of growth in overall per capita EXPEQ, in which of ZONE=1 or ZONE=2 is growth in expenditures EXPEQ conducive to greater poverty reduction? 18.8.46Per FCFA of growth in overall per capita EXPEQ, which of growth in FDEQ or in NFDEQ leads to greater poverty reduction? Graph this for a range of poverty lines and for all poverty indices of the second-order (α=1, or s=2). 18.8.47What is the elasticity of poverty with respect to EXPEQ? Compute this for the different DEPT. 18.8.48The government wishes to determine whether increasing the price of HEALTHEQ by 5%, for the benefit of a revenue-neutral fall in the price of SCHEXPEQ, would be good for inequality reduction. Assume a ratio of MCPF=1. Find out the impact on the Lorenz curve and on the Gini coefficient. 18.8.49Say that food prices are about to increase by about 10%, due to the removal of food subsidies. What is the predicted impact on the Gini index and on L(p = 0.5)? 18.8.50Find the impact on the Gini index of inequality of a predicted increase of 3% in the expenditures EXPEQ. 18.8.51Find the impact on the Gini index and on L(p = 0.5) of a predicted increase of 3% in everyone's expenditures FDEQ. Compare your results to those for a similar 3% increase in NFDEQ. 18.8.52The government wishes to determine whether increasing the price of NFDEQ, for the benefit of a fall in the price of FDEQ, would be good for poverty. i Assess this for a ratio of the MCPF of NFDEQ over that of FDEQ equal to 1, for a range of poverty lines and for all distribution-sensitive poverty indices (second-order, α=1 or s=2). ii Up to which ratio of MCPF can we go and still declare the reform to be good for poverty? iii Are these conclusions also valid for the goal of inequality reduction? Use the file ESPSANT [p.326] to do exercises 18.8.53 to 18.8.54.. When needed, use the headcount as a poverty index and set the poverty line to 60000 FCFA per adult equivalent. 18.8.53Using EXPEQ as the ranking variable, predict the proportion of individuals at different levels of living standards whose households make use of public health services. Do this separately for the different values of SEX. 18.8.54Compute the proportion of EXPEQ that is spent on HEALTHEQ by individuals at different levels and ranks of EXPEQ. What does this suggest? Use the file SCOL [p.326] to do exercises 18.8.55 to 18.8.57. When needed, use the headcount as the poverty index and set the poverty line to 60000 FCFA per adult equivalent. 18.8.55Predict the proportion of children below 14 at different values of EXPEQ that attend primary school. Compare the results you obtain across the different values of ZONE. How do these results compare with those for attending secondary school? 18.8.56Compare the concentration curve (among children below 14) of attendance at primary school, secondary school, public primary school and public secondary school, using EXPEQ as the ranking variable. Draw this for various proportions of the poorest children. Compare this concentration curve with the Lorenz curve for EXPEQ. Discuss your results. 18.8.57Draw the concentration curves of UNI and SUP. Compare this to the Lorenz curve for EXPEQ for the same population. 18.9 Sampling designs and sampling distributions18.9.1Load the file Burkina_94 [p.327] and initialize its sampling design (SD). Do this first only by specifying the variable WEIGHT as sampling weight. a- Compute the mean of total expenditure per adult equivalent (EXEPQ) with the size variable equal to SIZE. Why does STD1 differ from STD2? What is a sufficient condition so that both standard deviations be equal? b- Now use both variables WEIGHT and STRATA to reinitialize the SD of this file. Compute, again, the mean of total expenditure per adult equivalent when the size variable is SIZE, and compare with the STD's of question a. What can be said about the impact of stratification on STD1? c- Now use variables WEIGHT, STRATA and PSU to reinitialize the SD of this file. Compute, again, the mean of total expenditure per adult equivalent when the size variable is SIZE, and compare with the STD's of questions a and b. What can you say about the impact of PSU's on STD1? d- By using the GSE variable to specify the socio-professional group, compute the mean of total expenditure per adult equivalent when the size variable is SIZE and for groups 1, 2, and 6. How does the sampling variability differ across these estimates? 18.10 Equivalence scales and statistical units18.10.1Load the file Senegal_95 [p.323] and compute the mean of total expenditure per adult equivalent (EXEPQ) after initializing the sampling design with variables STRATA, PSU and WEIGHT. 18.10.2Well-being, in a household, can be represented alternatively by: a- Total expenditure of household "EXP" b- Total expenditure per capita "EXPCAP" c- Total expenditure per adult equivalent "EXPEQ" Using the variable SIZE to set the size variable, compute the headcount and the average poverty gap indices when the poverty line equals 140000 FCFA and when the variable of interest is alternatively EXPEQ, EXPCAP and EXP. Explain why the results differ. 18.10.3When sample observations represent households, three size variables are typically used in combination with the variable of interest EXPEQ: a- 1 for all households b- The number of persons in the household (SIZE) c- The number of adult equivalents in the household (EQUI) Compute the FGT index for α = 0, 1 for every one of these three alternative definitions of the size variable and explain the difference. 18.10.4Compute the Gini and Atkinson (with ε = 0.5) indices of inequality for: a- Total expenditure when the size variable equals 1 for all households. b- Expenditure per capita when the size variable equals SIZE. c- Expenditure per equivalent adult when the size variable equals SIZE. d- Expenditure per equivalent adult when the size variable equals 1. Comment on the differences between these results. 18.11 Description of illustrative data sets18.11.1 CAMEROON_96, LINE-6, AGGR-7, DECA-7, and DECB-8The files LINE-6, AGGR-7, DECA-7, and DECB-8 are made of a sub-sample of 1000 observations drawn from a survey (the Enquête Camerounaise auprès des ménages or ECAM) on the expenditures and the incomes of households in 1996 Cameroon. The file CAMEROON-96 is made of approximately 1700 households from the same survey. The ECAM is a nationally representative survey, with sample selection using two-stage stratified random sampling. The first stage consists in the selection of 150 PSUs ("îlot") within each of the six strata, and the second stage consists in the selection of households within each PSU. Table 18.1: The distribution of households in ECAM (1996)
α Cities <50000 inhabitants. In Yaoundé and Douala, PSU's are systematically selected with equal probabilities. The number of PSU's drawn by stratum is proportional to the number of urban households found in 1987 in that stratum. In a second stage, 8 households are drawn in every PSU (with equal probabilities), using a list of households established during an enumeration of that PSU. For the other cities, at the first stage, one city is selected for every one of the ten provinces. Enumeration zones are then drawn with probability proportional to the number of households originally listed in 1987. Households are then drawn as above. In every one of the three rural strata, two PSU's were selected within the semi-urban area and 8 in the rural area. PSU's were again drawn with probability proportional to the number of households enumerated in 1987. Within each selected PSU, 21 households were systematically selected from a household list. Variables for CAMEROON-96
Variables for LINE-6, AGGR-7, DECA-7, and DECB-8
18.11.2 CAN4 and CAN6CAN4 and CAN6 contain illustrative data made of a small sub-sample of observations drawn from the Canadian surveys of Consumer Finance. They contain the following variables: Variables for CAN4 and CAN6
18.11.3 PERHE-12 and PERED-16PERHE-12 and PERED-16 contain an illustrative sample of some 3600 household observations drawn from the 1994 Peru LSMS survey. Variables for PERHE-12
Variables for PERHE-16
18.11.4 SENEGAL_95 and SENESAMSENEGAL_95 is drawn from a nationally representative survey carried out in 1995 Sénégal (the Enquête sénégalaise auprès des ménages), with sample selection using a multi-stage stratified random sampling procedure. The country was first split in five strata. The first sampling stage consisted in the selection of PSU's (enumeration areas, or Secteurs d'énumération (SE)) from a 1990 "Master Sample" list with probability proportional to the number of households in the PSU's. 396 SE were thus selected in the urban area and 204 in the rural area. Census districts were then selected within each SE. In a final stage, 15 households were systematically selected within each of the urban census districts, and similarly 24 households were systematically selected within each of the rural census districts. Table 18.2: The distribution of households in ESAM (1995)
Variables for SENEGAL.95
Variables for SENESAM
18.11.5 ESPMEN, ESPSANT and ESPSCOL These files are drawn from illustrative subsamples of Sénégal's ESP (Enquête Sénégalaise Prioritaire Variables for ESPMEN
Variables for ESPSANT
Variables for ESPSCOL
18.11.6 Burkina_94Burkina_94 is drawn from a nationally representative survey (Enquête Prioritaire) carried out in 1994 Burkina Faso with sample selection using two-stage stratified random sampling. Seven strata were formed. Five of these strata were rural and two were urban. Enumeration areas (PSU's, or zones de dénombrement) were sampled in a first stage from a list computed from the 1985 census. This first-stage sampling within strata 7 (Ougadougou-Bobo-Dioulasso) was made with equal probability and without replacement. First-stage sampling within the other 6 strata was made with probability proportional to the size (estimated from the 1985 census) of each PSU and without replacement. 20 households were then systematically sampled within each of the selected PSU's in a second stage. Variables for BURKINA_94
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