1. 1.2.4 Statistical Methods in Poverty Estimation 1 MEASUREMENT AND POVERTY MAPPING UPA Package 1, Module 2

2. 1.2.4 Statistical Methods in Poverty Estimation 2 POVERTY: Theory, Measurement, Policy and Administration - Statistical Methods in Poverty Estimation -

3. 1.2.4 Statistical Methods in Poverty Estimation 3 Small Area Estimation Background Small area estimation has received a lot of attention in recent years due to growing demand for reliable small area estimators Traditional area-specific direct estimators do not provide adequate precision because sample sizes in small areas are seldom large enough Sample surveys are used to provide estimates not only for the total population but also for a variety of subpopulations (domains)

4. 1.2.4 Statistical Methods in Poverty Estimation 4 Small Area Estimation Background “Direct” estimators, based only on the domain-specific sample data, are typically used to estimate parameters for large domains But sample sizes in small domains, particularly small geographic areas, are rarely large enough to provide direct estimates for specific small domains

5. 1.2.4 Statistical Methods in Poverty Estimation 5 Small Area Models It is now generally accepted that when indirect estimators are to be used they should be based on explicit model that related the small areas of interest through supplementary data such as last census data and current administrative data An advantage of the model approach is that it permits validation of models from the sample data Small area models may be broadly classified into two types: area level and unit level

6. 1.2.4 Statistical Methods in Poverty Estimation 6 Types of Small Area Estimation Models  i ~ IID N(0,  b 2 ) ~ known positive constants ~ IID N(0,  e 2 )  i ~ IID N(0,  b 2 ) Unit-level Model (Battese et al., 1988) Area-level Model (Fay and Herriot, 1979)

7. 1.2.4 Statistical Methods in Poverty Estimation 7 Area Level Models Sampling model Area-specific auxiliary data,, are assumed to be available for the sampled areas as well as the non- sampled areas A basic area level model assumes that the population small area mean or some suitable function, such as, is related to through a linear model with random area effects, where is the p-vector regression parameters and the ’s are uncorrelated with mean zero and variance

8. 1.2.4 Statistical Methods in Poverty Estimation 8 Area Level Models Normality of the is also often assumed The model also holds for non-sampled areas It is also possible to partition the areas into groups and assume separate models of the same form across groups Linking model We assume that direct estimators of are available whenever the area sample size. It is also customary to assume that where and the sampling errors are independent with known

9. 1.2.4 Statistical Methods in Poverty Estimation 9 Area Level Models Combining the sampling model with the “linking” model, we get the well-known area level mixed model of Fay and Herriot

10. 1.2.4 Statistical Methods in Poverty Estimation 10 Unit Level Models A basic unit level population model assumes that the unit y- values, associated with the units in the areas, are related to the auxiliary variables through a one-way nested error regression model where are independent of and N i is the number of population units in the i-th area

11. 1.2.4 Statistical Methods in Poverty Estimation 11 Unit Level Models The parameters of interest are the total or the means The above model is appropriate for continuous variables y. To handle count or categorical (e.g. binary) y variables, generalized linear mixed models with random small area effects, are often used.

12. 1.2.4 Statistical Methods in Poverty Estimation 12 Spatial Microsimulation Approach Developed by Guy Orcutt in 1957 ‘A new kind of socio-economic system’ Directly concerned with microunits such as persons, households, or firms Models lifecycle by the use of conditional probabilities One major objective in spatial microsimulation is the estimation of microdata

13. 1.2.4 Statistical Methods in Poverty Estimation 13 Spatial Microsimulation Approach Spatial microsimulation is increasingly applied in the quantitative analysis of economic and social policy problems (Clarke, 1996) –Tax benefit incidence –Income –Housing –Water consumption –Transportation –Health

14. 1.2.4 Statistical Methods in Poverty Estimation 14 Example of Spatial Microsimulation Steps 1. Age,sex, and marital status (M) of hh head 2. Probability of hh head of given age, sex, and M being an owner- occupier 3. Random number (computer generated) 4. Tenure assigned to hh on the basis of random sampling 5. Next hh (keep repeating until a tenure type has been allocated to every hh) Head of household (hh) 1st Age: 27 Sex: male M: married 2nd3rd 0.7 0.542 owner-occupied Age: 32 Sex: male M: married 0.7 0.823 rented Age: 87 Sex: female M: divorced 0.54 0.794 rented Source: Clarke (1996)

15. 1.2.4 Statistical Methods in Poverty Estimation 15 Object Representation of Household Microdata Baseline Characteristics Unobserved Characteristics Target of Microsimulation Computational Objects/ Models

16. 1.2.4 Statistical Methods in Poverty Estimation 16 Available Household Data Sets

17. 1.2.4 Statistical Methods in Poverty Estimation 17 Different Scales of Analysis City Traffic Zone Barangay Households

18. 1.2.4 Statistical Methods in Poverty Estimation 18 Spatial Microsimulation of Informal Households in Metro Manila Manila City (54 traffic zones, 900 barangays, 1.59 million pop. in 1990, 308,874 households)

19. 1.2.4 Statistical Methods in Poverty Estimation 19 Informal Sim Structure Initialize base households using 1990 CPH data (age, sex, marital status, and education of household head, household size) Assign occupation of household head based on Monte Carlo sampling Assign employment sector of household head based on Monte Carlo sampling Compute occupation probabilities from Occupation Choice Model Compute employment probabilities from Employment Choice Model Estimate household income based on characteristics of household head Compute employment status probabilities and assign employment status by Monte Carlo sampling Compute bias-adjusted household income function based on employment status Compute economic activity rate of household head Estimate permanent Income of household Compute housing tenure status probabilities and assign housing tenure status by Monte Carlo sampling Compute bias-adjusted housing value function based on tenure status Estimate housing tenure and housing value

20. 1.2.4 Statistical Methods in Poverty Estimation 20 Simulated Mean Household Incomes Low High Middle Low High

21. 1.2.4 Statistical Methods in Poverty Estimation 21 Ground Truths Smokey Mountain Port Area, Tondo Pandacan Punta

22. 1.2.4 Statistical Methods in Poverty Estimation 22 Simulated Housing Tenure

23. 1.2.4 Statistical Methods in Poverty Estimation 23 Simulated Informal Employment

24. 1.2.4 Statistical Methods in Poverty Estimation 24 Inequality Measures