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  • 1. Official data and poverty indicators: small area estimates in local governance Monica Pratesi, Stefano Marchetti, Caterina Giusti, Nicola Salvati Department of Statistics and Mathematics Applied to Economics, University of Pisa SISVSP 2012 Rome, 19-20 April 2012 M. Pratesi (DSMAE, Pisa) Official data and poverty indicators 19-20 April 2012 1 / 25
  • 2. Structure of the Presentation1 Motivation2 Poverty indicators and SAE methods3 Oversampling and Small Area Estimation: A Comparison4 Application of small area M-quantile models to poverty mapping in Tuscany5 Concluding remarks M. Pratesi (DSMAE, Pisa) Official data and poverty indicators 19-20 April 2012 2 / 25
  • 3. Part I MotivationM. Pratesi (DSMAE, Pisa) Official data and poverty indicators 19-20 April 2012 3 / 25
  • 4. MotivationMotivation Problem: to estimate some key statistics for poverty at the small area level to drive local governance We focus on small area estimation of Laeken poverty indicators, such as head count ratio and poverty gapProposed methodologyUsing M-quantile models to estimate poverty indicators and to provide also anestimator of the corresponding mean squared errorsOpportunityComparing model-based estimates with direct estimates computed with anEU-SILC oversampling of households M. Pratesi (DSMAE, Pisa) Official data and poverty indicators 19-20 April 2012 4 / 25
  • 5. MotivationMotivation Available data to measure poverty and living conditions in Italy come mainly from sample surveys, such as the Survey on Income and Living Conditions (EU-SILC) However, EU-SILC data can be used to produce accurate estimates only at the NUTS 2 level (that is, regional level) To satisfy the increasing demand from official and private institutions of statistical estimates on poverty and living conditions referring to smaller domains (LAU 1 and LAU 2 levels, that is Provinces and Municipalities), there is the need to resort to small area methodologies We focus on the estimation of poverty measures at the small area level. For this purpose we use data coming from the EU-SILC survey 2008 and from the Population Census 2001 M. Pratesi (DSMAE, Pisa) Official data and poverty indicators 19-20 April 2012 5 / 25
  • 6. Part II Poverty indicators and SAE methodsM. Pratesi (DSMAE, Pisa) Official data and poverty indicators 19-20 April 2012 6 / 25
  • 7. Poverty indicators and SAE methodsPoverty MeasuresDenoting by t the poverty line and by y a measure of welfare, the Foster et al.(1984) poverty measures (FGT) for a small area d can be defined as −1 Zd (α, t) = Nd zjd (α, t) + zkd (α, t) . j∈sd k∈rdwhere for a generic unit i in area d t − yid α zid (α, t) = I(yid t) i = 1, . . . , Nd t zjd (α, t) is known for j ∈ sd zkd (α, t) is unknown for k ∈ rd and should be predictedSetting α = 0 defines the Head Count Ratio whereas setting α = 1 defines thePoverty Gap. M. Pratesi (DSMAE, Pisa) Official data and poverty indicators 19-20 April 2012 7 / 25
  • 8. Poverty indicators and SAE methodsPoverty Measures The HCR indicator is a widely used measure of poverty because of its ease of construction and interpretation, since it counts the number of individuals with income below the poverty line. At the same time this indicator also assumes that all poor individuals are in the same situation. For example, the easiest way of reducing the headcount index is by targeting benefits to people just below the poverty line because they are the ones who are cheapest to move across the line. Hence, policies based on the headcount index might be sub-optimal. For this reason we also obtain estimates of the PG indicator. The PG can be interpreted as the average shortfall of poor people. It shows how much would have to be transferred in mean to the poor to bring their expenditure up to the poverty line. M. Pratesi (DSMAE, Pisa) Official data and poverty indicators 19-20 April 2012 8 / 25
  • 9. Poverty indicators and SAE methodsM-quantile models With regression models we model the mean of the variable of interest (y ) given the covariates (x) A more complete picture is offered, however, by modeling not only the mean of (y ) given (x) but also other quantiles. Examples include the median, the 25th, 75th percentiles. This is known as quantile regression An M-quantile regression model for quantile q Qq = xT β ψ (q) jdMain features of these models No hypothesis of normal distribution Robust methods (influence function of the M-quantile regression) M. Pratesi (DSMAE, Pisa) Official data and poverty indicators 19-20 April 2012 9 / 25
  • 10. Poverty indicators and SAE methodsUsing M-quantile models to measure area effectsCentral Idea: Area effects can be described by estimating an area specific q value ˆ(θd ) for each area (group) of a hierarchical dataset (Chambers & Tzavidis 2006) Estimate the area specific target parameter by fitting an M-quantile model ˆ for each area at θd ˆ jd ˆ ˆ yjd = xT β ψ (θd ) Mixed effects model use random effects to capture the dissimilarity between domains. M-quantile models attempt to capture this dissimilarity via the ˆ domain-specific M-quantile coefficients θd M. Pratesi (DSMAE, Pisa) Official data and poverty indicators 19-20 April 2012 10 / 25
  • 11. Poverty indicators and SAE methodsSAE Poverty Measures EstimatorsUsing a smearing-type predictor that follow the same idea of the Chambers andDunstan (1986) distribution function estimator we can predict the zkd (α, t) values −1 t − ykjd ˆ α zkd (α, t) = nd ˆ I(ˆkjd y t) k ∈ rd , j ∈ sd t j∈sd ˆ ykjd = xT β ψ (θd ) + ejd ˆ kd ˆ ejd = yjd − xT β ψ (θd ) jdFinally, the small area estimator of FGT poverty measures is ˆ −1 Zd (α, t) = Nd zjd (α, t) + zkd (α, t) . ˆ j∈sd k∈rd M. Pratesi (DSMAE, Pisa) Official data and poverty indicators 19-20 April 2012 11 / 25
  • 12. Poverty indicators and SAE methodsA Mean Squared Error Estimator of the Poverty MeasuresEstimatorsTo estimate the mean squared error of the M-quantile poverty estimators we canuse the bootstrap proposed by Tzavidis et al. (2010) and Marchetti et al. (2012). Let b = (1, . . . , B), where B is the number of bootstrap populations Let r = (1, . . . , R), where R is the number of bootstrap samples Let Ω = (yk , xk ), k ∈ (1, . . . , N), be the target population By ·∗ we denote bootstrap quantities ˆ Zd (α, t) denotes the FGT poverty measures estimator of the small area d Let y be the study variable that is known only for sampled units and let x be the vector of auxiliary variables that is known for all the population units Let s = (1, . . . , n) be a within area simple random sample of the finite population Ω = {1, . . . , N} M. Pratesi (DSMAE, Pisa) Official data and poverty indicators 19-20 April 2012 12 / 25
  • 13. Poverty indicators and SAE methodsA Mean Squared Error Estimator of the Poverty MeasuresEstimator ˆ ˆ Fit the M-quantile regression model on sample s, yjd = xT β ψ (θd ) ˆ jd Compute the residuals, yjd − yjd = ejd ˆ Generate B bootstrap populations of dimension N, Ω∗b ∗ ˆ ˆ ∗ 1 ykd = xT β ψ (θd ) + ekd , k = (1, . . . , N) kd ∗ 2 ekd are obtained by sampling with replacement residuals ejd 3 residuals can be sampled from the empirical distribution function or from a smoothed distribution function 4 we can consider all the residuals (ej , j = 1, . . . , n), that is the unconditional approach or only area residuals (ejd , j = 1, . . . , nd ), that is the conditional approach. From every bootstrap population draw R samples of size n without replacement M. Pratesi (DSMAE, Pisa) Official data and poverty indicators 19-20 April 2012 13 / 25
  • 14. Poverty indicators and SAE methodsA Mean Squared Error Estimator of the Poverty MeasuresEstimator Using the B bootstrap populations and from the R samples drawn from every bootstrap population we can estimate the mean squared error of the FGT estimatorBiasˆ ˆ B R ˆE Z (α, t)∗ − Z (α, t)∗ = B −1 b=1 R −1 r =1 Z (α, t)∗br − Z (α, t)∗bVariance 2 ˆVar Z (α, t)∗ − Z (α, t)∗ = B −1 B R −1 R ˆ ¯ ˆ Z (α, t)∗br − Z (α, t)∗br b=1 r =1where Z (α, t)∗b is the FGT of the bth bootstrap population ˆ Z (α, t)∗br is the FGT estimate for Z (α, t)∗b estimated using the r th sample drown from the bth bootstrap population ¯ ˆ R ˆ Z (α, t)∗br = R −1 r =1 Z (α, t)∗br M. Pratesi (DSMAE, Pisa) Official data and poverty indicators 19-20 April 2012 14 / 25
  • 15. Part IIIPoverty Mapping in the Province of Pisa: Oversampling vs. Small Area Estimation M. Pratesi (DSMAE, Pisa) Official data and poverty indicators 19-20 April 2012 15 / 25
  • 16. Oversampling and Small Area Estimation: A ComparisonOversampling and Small Area Estimation: A ComparisonWhen direct estimates are unreliable there are two possible solutions: Increase the sample size in the domains of interest in such a way that direct estimates became reliable (oversampling solution) Use small area methods (small area solution)In order to make a comparison between these alternatives we can take theopportunity to use data referring to an EU-SILC 2008 oversampling of householdsfor the Province of Pisa - side result of the SAMPLE project(www.sample-project.eu). Sample size for the province of Pisa EU-SILC 2008: 149 households Sample size for the province of Pisa Oversample: 675 households (that include the 149 household of the EU-SILC survey)REMARK: Oversample has been managed by the ISTAT who warrantees the highquality of the data M. Pratesi (DSMAE, Pisa) Official data and poverty indicators 19-20 April 2012 16 / 25
  • 17. Oversampling and Small Area Estimation: A ComparisonSAE methods for poverty indicators in Tuscany Provinces Data on the equivalised income in 2007 are available from the EU-SILC survey 2008 for 1495 households in the 10 Tuscany Provinces To better compare the living conditions in these areas we estimate the indicators considering the gender of the head of the household A set of explanatory variables is available for each unit in the population from the Population Census 2001 We employ an M-quantile model to estimate Head Count Ratio (HCR) and Poverty Gap (PG) for the Provinces by gender of the head of the household (HH), for a total of 20 areas National poverty line: 9310.74 Euros (equivalised household income) M. Pratesi (DSMAE, Pisa) Official data and poverty indicators 19-20 April 2012 17 / 25
  • 18. Oversampling and Small Area Estimation: A ComparisonModel Specifications The selection of covariates to fit the small area models relies on prior studies of poverty assessment The following covariates have been selected: household size (integer value) ownership of dwelling (owner/tenant) age of the head of the household (integer value) years of education of the head of the household (integer value) working position of the head of the household (employed / unemployed in the previous week) M. Pratesi (DSMAE, Pisa) Official data and poverty indicators 19-20 April 2012 18 / 25
  • 19. Oversampling and Small Area Estimation: A ComparisonOversampling and Small Area Estimation: A ComparisonWe estimate the Head Count Ratio (HCR) and the Poverty Gap (HCR) in theProvince of Pisa considering the gender of the Head of the Household (HH) using: Direct estimators based on the EU-SILC survey data Direct estimators based on the Oversampling data M-quantile small are estimators based on the EU-SILC survey dataTable: Direct estimates (without and with oversampling) and MQ/CD estimates of the HCRand PG with corresponding estimated Root Mean Squared Errors (in brackets) and number ofsampled households (h) in the Province of Pisa, by gender of the Head of the Household (HH). Estimates HH gender h HCR % PG % Direct estimate Female 44 9.88 (4.28) 4.48 (2.56) Male 105 6.62 (2.24) 2.25 (0.91) MQ/CD estimates Female 44 20.72 (3.13) 8.64 (2.00) Male 105 9.02 (1.63) 2.91 (0.74) Direct estimates Female 193 23.57 (4.92) 6.64 (2.77) (with oversampling) Male 482 8.21 (1.61) 2.40 (0.60) M. Pratesi (DSMAE, Pisa) Official data and poverty indicators 19-20 April 2012 19 / 25
  • 20. Part IVApplication of small area M-quantile models to poverty mapping in Tuscany M. Pratesi (DSMAE, Pisa) Official data and poverty indicators 19-20 April 2012 20 / 25
  • 21. Application of small area M-quantile models to poverty mapping in TuscanyEstimates of the HCR at small area level in Tuscany MS MS LU LU PT PO PT PO FI FI AR AR PI PI LI LI SI SI GR GR 8.48 10.17 16.76 24.04 31.63 Figure: Provinces by gender of the HH: males (left) and females (right) M. Pratesi (DSMAE, Pisa) Official data and poverty indicators 19-20 April 2012 21 / 25
  • 22. Application of small area M-quantile models to poverty mapping in TuscanyEstimates of the PG at small area level in Tuscany MS MS LU LU PT PO PT PO FI FI AR AR PI PI LI LI SI SI GR GR 2.69 3.31 6.37 10.39 15.05 Figure: Provinces by gender of the HH: males (left) and females (right) M. Pratesi (DSMAE, Pisa) Official data and poverty indicators 19-20 April 2012 22 / 25
  • 23. Part V Concluding remarksM. Pratesi (DSMAE, Pisa) Official data and poverty indicators 19-20 April 2012 23 / 25
  • 24. Concluding remarksConcluding remarks and ongoing researchMain results Focus on the poverty indicators small area estimators Small area methods play a crucial role in providing poverty measures for local governance Small area estimates are very close to the oversampling estimate and they are (almost) costlessOngoing and future research Consider non-monetary measures of poverty (Cheli and Lemmi, 1995) Enhance the fitting of the models, considering non parametric models and spatial models Compare with alternative methods Take into account the survey weights M. Pratesi (DSMAE, Pisa) Official data and poverty indicators 19-20 April 2012 24 / 25
  • 25. Concluding remarksEssential bibliography Breckling, J. and Chambers, R. (1988). M -quantiles. Biometrika, 75, 761–771. Chambers, R. and Dunstan, R. (1986). Estimating distribution function from survey data, Biometrika. 73, 597–604. Chambers, R. and Tzavidis, N. (2006). M-quantile models for small area estimation. Biometrika, 93, 255–268. Chambers, R., Chandra, H. and Tzavidis, N. (2007). On robust mean squared error estimation for linear predictors for domains. CCSR Working paper 2007-10, University of Manchester. Cheli B. and Lemmi, A. (1995). A Totally Fuzzy and Relative Approach to the Multidimensional Analysis of Poverty. Economic Notes, 24, 115-134. Foster, J., Greer, J. and Thorbecke, E. (1984) A class of decomposable poverty measures. Econometrica, 52, 761-766. Giusti C., Pratesi M., Salvati N. (2009). Estimation of poverty indicators: a comparison of small area methods at LAU1-2 level in Tuscany, Abstract Book, NTTS - Conferences on New Techniques and Technologies for Statistics, Brussels, 18-20 Febbraio 2009. Hall, P. and Maiti, T. (2006). On parametric bootstrap methods for small area prediction. Journal of the Royal Statistical Society: Series B, 68, 2, 221–238. Marchetti, S., Tzavidis, N. and Pratesi, P. (2012). Non-parametric bootstrap mean squared error estimation for image-quantile estimators of small area averages, quantiles and poverty indicators. Computational Statistical and Data Analysis, doi:10.1016/j.csda.2012.01.023 Lombardia M.J., Gonzalez-Manteiga W. and Prada-Sanchez J.M. (2003). Bootstrapping the Chambers-Dunstan estimate of finite population distribution function. Journal of Statistical Planning and Inference, 116, 367-388. Royall, R. and Cumberland, W.G. (1978). Variance Estimation in Finite Population Sampling. Journal of the American Statistical Association, 73, 351-358. Tzavidis N., Marchetti S. and Chambers R. (2010). Robust estimation of small area means and quantiles. Australian and New Zealand Journal of Statistics, 52, 2, 167–186. Tzavidis, N., Salvati, N., Pratesi, M. and Chambers, R. (2007). M-quantile models for poverty mapping. Statistical Methods & Applications, 17, 393-411. M. Pratesi (DSMAE, Pisa) Official data and poverty indicators 19-20 April 2012 25 / 25

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