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11.2.4 Statistical Methods in Poverty Estimation
MEASUREMENT AND POVERTY MAPPING
UPA Package 1, Module 2
21.2.4 Statistical Methods in Poverty Estimation
POVERTY: Theory, Measurement, Policy and Administration
- Statistical Methods in Poverty Estimation -
31.2.4 Statistical Methods in Poverty Estimation
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)
41.2.4 Statistical Methods in Poverty Estimation
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
51.2.4 Statistical Methods in Poverty Estimation
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
61.2.4 Statistical Methods in Poverty Estimation
Types of Small Area Estimation Models
i ~ IID N(0, b2)
~ known positive constants
~ IID N(0, e2)
i ~ IID N(0, b2)
• Unit-level Model (Battese et al., 1988)
i i i iy x z
i i i ijy x e
• Area-level Model (Fay and Herriot, 1979)
iz
ije
71.2.4 Statistical Methods in Poverty Estimation
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
ix( 1, , )i m
iY ( )i ig Y log( )i iY ix
i
, 1, ,i i i i m x β
β 2
81.2.4 Statistical Methods in Poverty Estimation
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
i
ˆiY iY
1in
i i ie ˆˆ ( )i ig Y ie(0, )iN i
91.2.4 Statistical Methods in Poverty Estimation
Area Level Models
• Combining the sampling model with the “linking” model, we get the well-known area level mixed model of Fay and Herriot
i i i ie x β
101.2.4 Statistical Methods in Poverty Estimation
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 Ni is the number of population units in the i-th area
ijy j iijx
, 1, , , 1, ,ij ij i ij iy e j N i m x β
2(0, )i IID N 2(0, )ij ee IID N
111.2.4 Statistical Methods in Poverty Estimation
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.
iYiY
121.2.4 Statistical Methods in Poverty Estimation
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
131.2.4 Statistical Methods in Poverty Estimation
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
141.2.4 Statistical Methods in Poverty Estimation
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: 27Sex: maleM: married
2nd 3rd
0.7
0.542
owner-occupied
Age: 32Sex: maleM: married
0.7
0.823
rented
Age: 87Sex: femaleM: divorced
0.54
0.794
rented
Source: Clarke (1996)
151.2.4 Statistical Methods in Poverty Estimation
Object Representation of Household Microdata
BaselineCharacteristics
UnobservedCharacteristics
Target of Microsimulation
ComputationalObjects/ Models
MEMBERVariablesProvince-IDDistrict-IDBarangay-IDHousehold-IDMember-IDRelation to headAgeSexMarital statusEducation(Occupation)(Employment sector)(Income)MethodsGetEconomicActivityGetOccupationGetEmploymentSectorGetIncome…
HOUSEHOLDVariablesProvince-IDDistrict-IDBarangay-IDHousehold-IDHousehold sizeAge of headSex of headMarital status of headEducation of head(Economic Activity of head)(Occupation of head)(Employment sector of head)Members [Vector]Building typeRoof typeWall typeState of repairYear builtHousehold incomeHouse ownership
Land ownershipMethodsGetEconomicActivityofHeadGetOccupationofHeadGetEmploymentSectorofHeadGetIncomeofHead…
161.2.4 Statistical Methods in Poverty Estimation
Available Household Data Sets
• Detailed household and housing characteristics
• No income/employment variable• Non- response on housing variables• All households in 1990 (1,567,665
households)
1990 Census of Population and Housing (CPH)
Barangay
Description/ CoverageData SetZone System
1996 MMUTIS Land Use GIS1997 Building Footprint Data
1996 Metro Manila Urban Transportation Integration
Study (MMUTIS)
1997 Family Income and Expenditure Survey (FIES)
• Urban land use zoning map for entire Metro Manila
• Building footprints for most cities
GIS
• Selected household demographics• Member/ household income• 50,000 samples for Metro Manila
Traffic Zone
• Household demographics, some housing variables
• Detailed household incomes and expenditures
• 4,030 samples for Metro Manila
City
• Detailed household and housing characteristics
• No income/employment variable• Non- response on housing variables• All households in 1990 (1,567,665
households)
1990 Census of Population and Housing (CPH)
Barangay
Description/ CoverageData SetZone System
1996 MMUTIS Land Use GIS1997 Building Footprint Data
1996 Metro Manila Urban Transportation Integration
Study (MMUTIS)
1997 Family Income and Expenditure Survey (FIES)
• Urban land use zoning map for entire Metro Manila
• Building footprints for most cities
GIS
• Selected household demographics• Member/ household income• 50,000 samples for Metro Manila
Traffic Zone
• Household demographics, some housing variables
• Detailed household incomes and expenditures
• 4,030 samples for Metro Manila
City
171.2.4 Statistical Methods in Poverty Estimation
Different Scales of Analysis
City
Traffic Zone
Barangay
Households
181.2.4 Statistical Methods in Poverty Estimation
Spatial Microsimulation of Informal Households in Metro Manila
• Manila City (54 traffic zones, 900 barangays, 1.59 million pop. in 1990, 308,874 households)
191.2.4 Statistical Methods in Poverty Estimation
Informal Sim Structure
Initialize base householdsusing 1990 CPH data
(age, sex, marital status,and education of household
head, household size)
Assign occupation ofhousehold head based
on Monte Carlo sampling
Assign employment sectorof household head basedon Monte Carlo sampling
Compute occupation probabilities from
Occupation Choice Model
Compute employmentprobabilities from
Employment Choice Model
Estimate household incomebased on characteristics
of household head
Compute employment status probabilities and
assign employment statusby Monte Carlo sampling
Compute bias-adjustedhousehold income function
based on employment status
Compute economic activityrate of household head
Estimate permanentIncome of household
Compute housing tenure status probabilities and
assign housing tenure statusby Monte Carlo sampling
Compute bias-adjustedhousing value functionbased on tenure status
Estimate housing tenureand housing value
201.2.4 Statistical Methods in Poverty Estimation
Simulated Mean Household Incomes
Low
Low
High
Middle
Low
High
211.2.4 Statistical Methods in Poverty Estimation
Ground Truths
Smokey Mountain
Port Area, Tondo
Pandacan
Punta
221.2.4 Statistical Methods in Poverty Estimation
Simulated Housing Tenure
231.2.4 Statistical Methods in Poverty Estimation
Simulated Informal Employment
241.2.4 Statistical Methods in Poverty Estimation
Inequality Measures