Int. Statistical Inst.: Proc. 58th Worl Statistical Congress, 2011, Dublin (Session CPS016) p.4218 A Fay Herriot Moel for Estimating the Proportion of Househols in Poverty in Brazilian Municipalities Quintaes, Viviane, Hansen, Nícia, Silva, Denise e Pessoa, Djalma Brazilian Institute of Geography an Statistics - IBGE, Coorination of Methos an Quality - COMEQ Avenia República o Chile, 500, 10º floor Rio e Janeiro (20031-170), Brazil E-mail: viviane.quintaes@ibge.gov.br, nicia.brenolin@ibge.gov.br, enise.silva@ibge.gov.br Silva, Pero Brazilian Institute of Geography an Statistics - IBGE, National School of Statistical Sciences - ENCE Rua Anré Cavalcanti, 106 Rio e Janeiro (20231-050), Brazil E-mail: pero-luis.silva@ibge.gov.br Introuction The National Statistical Institutes face the challenge of proucing comprehensive, accurate an reliable information uner financial an time constraints. The pressure for reucing sample sizes an responent buren prompte the nee for the use of methos to prouce small area statistics from combine ata sources. Small area estimation covers a variety of methos use to prouce survey-base estimates for geographical areas or omains of stuy in which the sample sizes are too small to provie reliable irect estimates. Thus, small areas or omains are those for which the sample is very small, common in stuies that are esigne to prouce accurate estimates at national, regional or state level. The estimation methoology implemente in this paper is base on the use of a regression moel with ranom effects that relates the sample estimates to auxiliary ata obtaine from census an aministrative recors available for the small areas (or omains) of interest. The resulting preicte values provie estimates, calle moel-base estimates, for the small areas base on the moel. This work is part of a project aiming at eveloping small area estimation moels an proceures to allow publication of statistical outputs for areas or omains that are not currently consiere for publication ue to the low precision of the estimates (or lack of sample observations in some of these areas or omains). IBGE has alreay publishe a first set of poverty estimates base on the so-calle Worl Bank Metho (Elbers, Lanjouw, an Lanjouw, 2002). The focus of this work is to test some well-known small area estimation moels that have been use successfully by other National Statistical Institutes (such as SAIPE1 from US Bureau of Census) an compare results with those obtaine uner the Worl Bank Metho. 1 Small Area Income an Poverty Estimates (http://www.census.gov//i/www/saipe/). 1
Int. Statistical Inst.: Proc. 58th Worl Statistical Congress, 2011, Dublin (Session CPS016) p.4219 The Fay-Herriot Moel The moel propose by Fay-Herriot (FH) is a linear moel with ranom area effects an it was evelope to preict per capita income for areas in the Unite States with population of fewer than 1000 persons. This moel is useful in cases where the auxiliary ata are available at the area level or when is not possible to link the information of the sample units with census ata an aministrative recors. It links the parameter of interest Y in the area to the auxiliary variables [ ] t = x 1 K xp θ g( Y ) an i.i.. ( 2 ~ N 0 ) t x through the linear moel: θ = xβ + u with = 1, L, D where = u σ. The ranom effect u aims at capturing the variation between, areas not explaine by the auxiliary information. Inferences about the small areas are mae base on assumption that the population moel applies to the q < D areas. In aition to this, the moel ˆ θ = θ + e with = 1, L, q an ˆ θ g(ŷ ) inicates how the sample estimates Ŷ are relate to inep. 2 the unknown population value an sampling error ~ N( 0 ) = e σ. Combining sampling an, t population moels we obtain ˆ θ = x β + u + e with = 1, L, q. Moel estimation is carrie out using ata from sample areas an the moel-base estimates ~ t for the small areas are given by ˆ ~ t θ = x β + û or by the synthetic estimator θ x β ˆ when there is no sample in a specific area. More information about the FH estimator an its corresponing mean square error can be foun in Rao (2003). A Moel for Estimating the Proportion of Househols in Poverty D = The survey ata use in this stuy comes from the Brazilian Family Expeniture Survey - Pesquisa e Orçamentos Familiares - POF 2002-2003 (POF, IBGE, 2004) an the auxiliary information was obtaine from: the 2000 Demographic Census, an inquiry that collects aministrative ata from Brazilian municipalities ( Pesquisa e Informações Básicas Municipais - 2002 (MUNIC, IBGE, 2005), the School Census - Censo Escolar 2003 (INEP, 2004) an from a system of municipal evelopment inicators maintaine by an association of Rio e Janeiro enterprises - Sistema Firjan IFDM 2000 (2000). The atabase contains estimates of the proportion of househols in poverty for the municipalities of Minas Gerais (MG) state calculate base on the househol per capita income. The sample sizes are small (from 6 to 75 househols2) an 75% of the sample municipalities have less than 21 househols in the sample. Besies, the survey was not esigne to provie accurate estimates for municipalities an in only 151 from the 853 municipalities of MG there are househols in the sample. The auxiliary variables are available for all municipalities in the state of interest an the moel fitte with survey ata allows the estimation of a poverty measure for those municipalities that o not have any sample househol, assuming that the statistical moel that links the estimates with the auxiliary information is also vali in this case. Although, in general, the small area moelbase estimates are more precise than the irect sample estimates, they are subjecte to bias. The 2 Belo Horizonte (Minas Gerais capital city) has a sample size of 336 househols. 2
Int. Statistical Inst.: Proc. 58th Worl Statistical Congress, 2011, Dublin (Session CPS016) p.4220 selection of an appropriate moel is vital in the estimation process. In this paper, the response is the estimate proportion of househols in poverty calculate base on the househol income. A househol is consiere in poverty when its per capita income is below a poverty line3. Results an Discussion Table 1 presents the selecte variables inclue in the moel an the estimates of βˆ obtaine by the FH estimator. The moel selection proceure was carrie out fitting a single level linear moel (without area ranom effects (because the atabase only containe recors at municipal level). For the final single area level, an R 2 = 0,47 was obtaine. The FH estimator, however, incorporates the ranom area effect (municipality). Table 1: Estimates of the fitte moel Coefficient Estimates Covariates FH moel Intercept -0,035 FIRJAN inex: employment an income -0,215 2000 Demographic Census 2000 Covariates Log of Proportion of Househols with no Bathroom 0,934 Log of Proportion of Househols Serve by Urban Sanitation 0,407 Log of Proportion of Househols with income between 5 an 10 Brazilian Minimum Wages 4-0,990 Failure Rate in Junior School5 0,007 Figure 1 isplays the scatterplot of the irect survey estimates against the moel-base estimates obtaine by FH metho for the 151 municipalities of Minas Gerais in which there are some sample househols. The graphic that shows the line y = x (in re) constitutes a bias iagnostic base on the assumption that the irect estimates of the small areas values are unbiase. Although the irect estimates are very variable, they are nevertheless Unbiase, thus a plot of irect estimates (on the y axis) an moel-base estimates (on the x axis) shoul isplay irect estimates ranomly scattere about the moel estimates. From Figure 1, it can be note that the irect estimates are ranomly istribute aroun the moel-base FH estimates an they are close to the line in re inicating no evience of bias. 3 The evelopment of an absolute poverty line followe the steps: (1) conversion the amount of foo acquire by househols in terms of energy (kcal) using tables of foo composition, (2) estimation of per capita househol energy consumption, (3) calculation of nutritional requirements following the FAO / WHO / UN recommenations, (4) efinition of the reference group, (5) calculation of the foo poverty line, (6) calculation of the poverty line. 4 Minimum Wage Value in 2011: US$ 330. 5 For 6-14 years ol chilren. 3
Int. Statistical Inst.: Proc. 58th Worl Statistical Congress, 2011, Dublin (Session CPS016) p.4221 Figure 1: Estimates of proportion of househols in poverty by municipalities of Minas Gerais (151 municipalities that have sample in the Family Expeniture Survey 2002/2003). Direct estimates obtaine from Family Expeniture Survey FH estimates Figure 2 shows the synthetic estimates obtaine by FH metho for the proportion of househols in poverty for the municipalities of MG. Vale o Jequitinhonha, a well known region with high incience of poverty in the north of the state is among the arkest areas of the map. This region is known to have low socioeconomic inexes. Figure 2: Moel base estimates for the proportion of househols in poverty for Municipalities in Minas Gerais Brazil. Estimates obtaine by FH metho (synthetic estimator). 4
Int. Statistical Inst.: Proc. 58th Worl Statistical Congress, 2011, Dublin (Session CPS016) p.4222 Due to the lack of sample in many municipalities, it is noteworthy that synthetic estimator was use in 702 of them consequently affecting the quality of the estimates. It woul, therefore, be interesting to consier the use of ifferent geographical bounaries to efine the areas of interest in a future work. In aition, these results are being compare to those obtaine base on the Worl Bank methoology an confience intervals for the estimates will be prouce. Concluing Remarks The results of this stuy emonstrate the feasibility of proucing small area estimates base on sample surveys of IBGE. However, there is the nee for a careful evaluation of the efinition of areas of interest, since the lack of sample in several municipalities imposes the use of synthetic estimators. It is important to mention that the process of choosing the auxiliary variables is crucial, since the small area estimation methos are mainly base on the evelopment of a regression moel. Thus the availability an choice of auxiliary ata have a irect effect on the quality of the estimates. REFERENCES Elbers, C., Lanjouw, J.O. an Lanjow, P. Micro-level estimation of welfare. Policy Research Working Paper n. 2911. Worl Bank, Washington, 2002. Fay, R.E. an Herriot, R.A. Estimates of income for small places: an application of James-Stein proceures to census ata. Journal of the American Statistical Association. V. 74, p. 269-277, 1979. IBGE. Mapa e pobreza e esigualae: municípios brasileiros 2003. Rio e Janeiro, 2008. IBGE. Perfil os municípios brasileiros: pesquisa e informações básicas municipais gestão pública 2002. Rio e Janeiro, 2005. 120 p. Instituto Nacional e Estuos e Pesquisas Eucacionais Anísio Teixeira. Sinopse estatística a eucação básica: censo escolar 2003. Brasília, 2004. IPEA/IBGE (Instituto e Pesquisa Econômica Aplicaa / Funação Instituto Brasileiro e Geografia e Estatística). Dimensionano a pobreza no Brasil: uma proposta metoológica (in press). National Statistical Service. A guie to small area estimation. Austrália, 2006. Available at: < http://www.nss.gov.au/nss/home.nsf/pages/small+areas +Estimates?OpenDocument > Pessoa, D.G.C., Corrêa, S. an Quintaes, V.C.C. (2010). Comparação e Estimaores a Proporção e Domicílios Pobres em Minas Gerais Obtios por Estimação Direta, Moelo e Fay-Herriot e Métoo ELL. Rio e Janeiro: IBGE, Coorenação e Métoos e Qualiae, 6 p. Rao, J.R.K. Small Area Estimation. New York: Wiley, 2003. Sistema FIRJAN Feeração as Inústrias o Estao o Rio e Janeiro. Ínice FIRJAN e esenvolvimento municipal 2000. Available at: http://www.firjan.org.br >. 5
Int. Statistical Inst.: Proc. 58th Worl Statistical Congress, 2011, Dublin (Session CPS016) p.4223 ABSTRACT The Brazilian Institute of Geography an Statistics (IBGE) faces the challenge of proucing comprehensive, accurate an reliable information uner financial an time constraints. The pressure for reucing sample sizes an responent buren reveals increases the nee for methos to prouce small area statistics from combine ata sources. Small area estimation covers a variety of methos use to prouce survey-base estimates for geographical areas or omains of stuy in which the sample sizes are too small to provie reliable irect estimates. This work presents a first attempt to implement an area level Fay-Herriot moel to estimate the proportion of househols in poverty for municipalities of Minas Gerais state combining survey ata from the Family Expeniture Survey with Census an aministrative ata. This work is part of a project aiming at eveloping small area estimation moels an proceures to allow publication of statistical outputs for areas or omains that are not currently consiere for publication ue to the low precision of the estimates (or lack of sample observations in some of these areas or omains). IBGE has alreay publishe a first set of poverty estimates base on the so-calle Worl Bank Metho (Elbers, Lanjouw, an Lanjouw, 2002). The focus of this work is to test some wellknown small area estimation moels that have been use successfully by other National Statistical Institutes an compare results with those obtaine uner the Worl Bank Metho. The paper escribes the steps taken for eveloping this area level moel. Results obtaine so far prove the feasibility of the area level approach an the vital role of goo quality auxiliary ata but also inicate the nee to revise the choice of target areas for estimation in orer to avoi the use of synthetic estimator to obtain estimates for large numbers of areas with no sample observations. Key-wors: Fay-Herriot moel, small area estimation, poverty, Brazilian Family Expeniture Survey 6