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

11.2.4 Statistical Methods in Poverty Estimation

MEASUREMENT AND POVERTY MAPPING

UPA Package 1, Module 2


POVERTY: Theory, Measurement, Policy and Administration

- 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)


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


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


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


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


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


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


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


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


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


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


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)


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…


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


Different Scales of Analysis

City

Traffic Zone

Barangay

Households


Spatial Microsimulation of Informal Households in Metro Manila

• Manila City (54 traffic zones, 900 barangays, 1.59 million pop. in 1990, 308,874 households)


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


Simulated Mean Household Incomes

Low

Low

High

Middle

Low

High


Ground Truths

Smokey Mountain

Port Area, Tondo

Pandacan

Punta


Simulated Housing Tenure


Simulated Informal Employment


Inequality Measures

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

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