Small Area Models for Linking Deprivation to Local Areas in Italy - - PowerPoint PPT Presentation

2nd June 2016 University of Naples “Parthenope” (Italy) Department of Management and Quantitative Studies

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Small Area Models for Linking Deprivation to Local Areas in Italy

Gennaro PUNZO

InGrid Summer School “Reaching out to hard-to-survey groups among the poor”

HIVA-KU Leuven, Leuven - Belgium, 30 May -3 June 2016

IT IS PLANNED TO PRODUCE RELIABLE INCOM OME POVERTY ESTIMATES ONLY AT A NATIONAL LEVEL OR, AT LEAST, FOR LARGE GEOGRAPHICAL DIVISIONS IT DOESN’T ALLOW TO ANALYSE THE PEOPLE’S LIVING CONDITIONS ACCORDING TO A MULTID IDIM IMENSIO IONAL AND FUZZY ZZY APPROACH

TO COMBINE THESE ASPECTS IN ORDER TO YIELD MORE RELIABLE POVERTY ESTIMATES

IN ITALY, THE SOURCE OF OFFICIAL STATISTICS ON POVERTY, PROVIDED BY ISTAT, IS THE HOUS USEHOLD BUD UDGE GET SUR URVEY (HBS)...

Poverty is considered as a latent con contin inuum uum (Lemmi et al., 1997) that is not directly observable and, in addition to the level of monetary income, it can be revealed by a variety of indicators of life-style deprivation

2nd June 2016 University of Naples “Parthenope” (Italy) Department of Management and Quantitative Studies

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Exploring POVERTY PATTERNS and DIFFERENTIALS across Italian NUTS3 regions (administrative provinces) for several dimensions of life-style deprivation

AIM OF OUR WORKS

STEPS

• JOINT

ANALYSIS OF “MONETARY” AND “SUPPLEMENTARY” DEPRIVATION ACCORDING TO A MULTIDIMENSIONAL AND FUZZY APPROACH

• MANIFEST AND LATENT DEPRIVATION MEASURES (BETTI

ET AL., 2006; BETTI AND VERMA, 2006)

• BORROWING STRENGTH ACROSS SMALL AREAS, TIME, AND SPACE:

2nd June 2016 University of Naples “Parthenope” (Italy) Department of Management and Quantitative Studies

FAY-HERRIOT MODEL (1979) RAO – YU MODEL (1992, 1994) PETRUCCI-SALVATI MODEL (2004)

EFFICIENCY GAIN

THE MAIN PROBLEM OF POVERTY ESTIMATES AT A SUB- NATIONAL LEVEL IS THEIR HIGH LEVEL OF VARIABILITY

due to the SAMPLING ERROR that increases with the decreasing size of su sub-samples in the areas (i.e., of the regions, or even at the level of smaller units, which in Italy are the PROVINCES)

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2nd June 2016 University of Naples “Parthenope” (Italy) Department of Management and Quantitative Studies

A NEW CLASS OF ESTIMATORS SMALL AREA ESTIMATION (SAE MODELS)

As a rule, a domain is regarded as small ll if the domain-specific sample is not large enough to support direct estimates of adequate precision; they are likely to produce large standard errors due to the unduly small size of the sample in the area (Ghosh & Rao, 1994)

it is necessary to use special estimators that “borrow strength” from related areas across space and/or time

• r through auxiliary information that is supposed to be

correlated to the variable of interest

What’s a Small Area?

therefore, in small areas…

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2nd June 2016 University of Naples “Parthenope” (Italy) Department of Management and Quantitative Studies

SMALL AREA ESTIMATORS

DIRECT ESTIMATORS (refer to the estimates derived from the survey data for small areas concerned) OVERESTIMATE THE VARIABILITY AMONG SMALL AREAS (It is due to the effect of the sampling error because of the smallness of the sample size available at small area level ) INDIRECT ESTIMATORS (based on models relating to the target variable to some available auxiliary variables)

UNDERESTIMATE THE TRUE VARIABILITY

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2nd June 2016 University of Naples “Parthenope” (Italy) Department of Management and Quantitative Studies

COMPOSITE ESTIMATORS weighted mixture of DIRECT and SYNTHETIC estimators of the same unknown parameter

SMALL AREA ESTIMATORS

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2nd June 2016 University of Naples “Parthenope” (Italy) Department of Management and Quantitative Studies

1) IT IS MORE LIKELY TO REFLECT THE TRUE VARIABILITY THAN EITHER OF THE TWO (DIRECT AND SYNTHETIC) 2) AS A RESULT, IT BALANCES THE POTENTIAL BIAS OF SYNTHETIC ESTIMATOR, WHICH IS CAPTURED BY THE MEAN-SQUARED ERROR, AGAINST THE HIGHER INSTABILITY OF THE DIRECT ONES

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A FOCUS ON DEPRIVATION IN ITS MULTIPLE DIMENSIONS...

FUZZY SET approach (Zadeh, 1965) TOTALLY FUZZY and RELATIVE method (Cheli-Lemmi, 1995) and, in particular,

A NEW CLASS OF MONETARY AND SUPPLEMENTARY DEPRIVATION MEASURES TREATING POVERTY AS A MATTER OF DEGREE, REPLACING THE TRADITIONAL DICHOTOMIZATION POOR/NON POOR

FUZZY MONETARY FUZZY SUPPLEMENTARY

PROPENSITY TO INCOME POVERTY PROPENSITY TO OVERALL NON-MONETARY DEPRIVATION

2nd June 2016 University of Naples “Parthenope” (Italy) Department of Management and Quantitative Studies

2 FSUP_1 Basic life-style deprivation 3 FSUP_2 Secondary life-style deprivation

SUPPLEMENTARY POVERTY MEASURES

1 FSU SUP Fuzzy Supplementary OVERALL DEPRIVATION MEASURE (NON-MONETARY)

Following Betti–Verma (2004) and aggregating 24 basic non-monetary variables: Moreover, following Nolan–Whelan (1996), Whelan et al. (2001) and Betti–Verma (2004): FIVE DIMENSION–SPECIFIC DEPRIVATION MEASURES Lack of ability to afford most basic requirements (7 items) “Enforced” absence of widely desired possession because of lack of resources (6 items)

1) Keeping the household’s principal accommodation adequately warm 2) Paying for a week’s annual holiday away from home 3) Replacing any worn-out furniture 4) Buying new rather than second hand clothes 5) Eating meat chicken or fish every second day, if the household wanted to 6) Having friends or family for a drink or meal at least one a month 7) Inability to meet payment of scheduled mortgage payments, utility bills or hire purchase instalments

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2nd June 2016 University of Naples “Parthenope” (Italy) Department of Management and Quantitative Studies 1) Car or van 2) Colour TV 3) Video recorder 4) Micro wave 5) Dishwasher 6) Telephone

4 FSUP_3 Housing Facilities 5 FSUP_4 Housing Deterioration 6 FSUP_5 Environmental problems

SUPPLEMENTARY POVERTY MEASURES

Lack of basic housing facilities (3 items) Serious problems with accommodation (3 items) Problems with the neighborhood and environment (5 items)

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2nd June 2016 University of Naples “Parthenope” (Italy) Department of Management and Quantitative Studies

FIVE DIMENSION–SPECIFIC DEPRIVATION MEASURES 1) Bath or shower 2) Indoor flushing toilet 3) Hot running water 1) Leaky roof 2) Damp walls, floors, foundation, etc. 3) Rot in window frames or floors 1) Shortage of space 2) Noise from neighbours or outside 3) Too dark/not enough light 4) Pollution, grime or other environmental problems caused by traffic or industry 5) Vandalism or crime in the area

FIRST STEP

Area Level Random Effect Model (Fay-Herriot, 1979)... considering the area random effects as INDEPENDENT

SAE MODELS: FAY-HERRIOT MODEL

In the sphere of SAE models, we choose…

UNDER THIS MODEL, THE EBLUP ESTIMATOR IS OBTAINED

EBLUP composite estimates of poverty measures at a provincial level (NUTS3) with advanced degrees of efficiency in comparison with the corresponding direct estimates

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2nd June 2016 University of Naples “Parthenope” (Italy) Department of Management and Quantitative Studies

Punzo et al. (2007; 2011)

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METHODOLOGY: SECOND STEP

In order to assess the gain, in terms of efficiency, that could be achieved by borrowing strength across BOTH SMALL AREAS AND TIME...

Survey data ECHP sample (waves 1994 – 2001)

DIRECT ESTIMATES

Auxiliary variables Istat Territorial Indicators

SYNTHETIC ESTIMATES

DATA SOURCES

RAO AND YU MODEL (1992, 1994)

as extension of the basic Fay–Herriot (1979)

2nd June 2016 University of Naples “Parthenope” (Italy) Department of Management and Quantitative Studies

AREA-LEVEL PROVINCIAL INDICATORS AS INDEPENDENT VARIABLES

1 Activity R Rate 11 Crude D Death Rate 2 Em Employment R Rate 12 Infant M Mortality R Rate 3 Unemployment R Rate 13 Marriage R Rate 4 Popu pulation D n Dens nsity 14 Crime R Rate 5 Resident nt P Popu pulation pe n per 100 inha nhabi bitant nts 15 Suic icid ides p s per 1 100.000 in inhabit itants s 6 Index of

• f T

Territor

• rial C

Con

• ncentration
• n
• f the

he R Resident nt P Popu pulation n 16 Legal al S Separ arat ation Rat ate 7 Net M Migratory R Rate 17 Divorce R Rates 8 Hosp spit italiz izatio ion R Rate 18 Gross D ss Domest stic ic Product ( (GDP) 9 Public ic H Hosp spit italiz izatio ion Rate 19 Growth En Enterprises Rate (net o

• f a

agriculture) 10 Crude B Birth Rate

AUXILIARY VARIABLES MATRIX

STEPWISE PROCEDURE...

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2nd June 2016 University of Naples “Parthenope” (Italy) Department of Management and Quantitative Studies

THIRD STEP

Spatial Area Level Random Effect Model (Petrucci–Salvati, 2004)... considering the area specific random effects SPATIALLY CORRELATED

In order to try to explain the portion of the random error unaccounted for and left over by exogenous variables (territorial indicators)...

UNDER THIS MODEL, THE SPATIAL EBLUP ESTIMATOR IS OBTAINED

SEBLUP composite estimates of poverty measures at NUTS3 level with different degrees of efficiency in comparison with the corresponding direct and EBLUP estimates

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2nd June 2016 University of Naples “Parthenope” (Italy) Department of Management and Quantitative Studies

SAE MODELS: PETRUCCI-SALVATI

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Significance levels: *** 99%; ** 95%; * 90% Source: Our elaborations on ECHP data, Italian Section (1994-2001), and Istat (2001)

POVERTY MEASURES Moran’s I Geary’s C 1 FSU SUP Overall Fuzzy Supplementary 0.1978** 0.8281** 2 FSUP_1 Basic Life-style Deprivation 0.0410 0.8909 3 FSUP_2 Secondary Life-style Deprivation 0.1872** 0.7955** 4 FSUP_3 Housing Facilities 0.1522* 0.7133* 5 FSUP_4 Housing Deterioration 0.1586** 0.7522** 6 FSUP_5 Environmental Problems 0.1502* 0.7884* 7 HCR_I _I Head Count Ratio 0.7828*** 0.2497*** 8 FM Fuzzy Monetary 0.2057** 0.7757**

Table 1 – Moran’s I and Geary’s C

DETECTING THE SPATIAL PATTERN...

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2nd June 2016 University of Naples “Parthenope” (Italy) Department of Management and Quantitative Studies

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IN ORDER TO EVALUATE THE PERFORMANCE OF THE ESTIMATION PROCESS THROUGH SMALL AREA MODELS...

IT ALLOWS TO TEST THE EXTENT TO WHICH THE MODELING MODIFIES THE DIRECT ESTIMATES

Direct Estimate (S)EBLUP Composite Estimate MSE Direct Estimate MSE (S)EBLUP Estimate

IT MEASURES THE IMPROVEMENT IN THE ACCURACY LEVEL OF THE ESTIMATES BY MODELING

1 – 0.5797 = 0.4203

2nd June 2016

1 – 0.8795 = 0.1205

Total Gain:

1 – 0.5120 = 0.4880

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REGRESSION COEFFICIENT ESTIMATES AND STANDARD ERRORS

RAO-YU MODELS HAVE ALSO BEEN ESTIMATED FOR:

2nd June 2016 University of Naples “Parthenope” (Italy) Department of Management and Quantitative Studies

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0.1 0.2 0.3 0.4 0.5

0.05 0.1 0.15 0.2 0.25 0.3 0.35

0.1 0.2 0.3

0.05 0.1 0.15 0.2 0.25 0.3 0.35

0.1 0.2 0.3

0.05 0.1 0.15 0.2 0.25 0.3 0.35

0.1 0.2

0.05 0.1 0.15 0.2 0.25 0.3 0.35

0.1 0.2 0.3 0.4 0.5

0.05 0.1 0.15 0.2 0.25 0.3 0.35

0.1 0.2 0.3 0.4 0.5

0.3 0.35 0.4 0.45 0.5 0.55 0.6

SOME DETERMINANTS OF INCOME AND LIFE-STYLE DEPRIVATION...

UNEMPLOYMENT RATE VS S HCR UNEMPLOYMENT RATE VS VS FM UNEMPLOYMENT RATE VS VS FS UNEMPLOYMENT RATE VS VS MANIFEST UNEMPLOYMENT RATE VS S LATENT ACTIVITY RATE VS VS HCR NORTH- WEST NORTH- EAST

SOUTH ISLANDS

CENTRO 2nd June 2016 University of Naples “Parthenope” (Italy) Department of Management and Quantitative Studies

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Distribution of Italian NUTS3 regions by classes of poverty intensities

Head Count Ratio Fuzzy Monetary Fuzzy Supplementary Fuzzy Manifest Fuzzy Latent

< 0.05 0.05 |– 0.10 0.10 |– 0.15 0.15 |– 0.20 0.20 |– 0.25 0.25 |– 0.30 > 0.30 6.45 30.11 26.88 4.30 3.23 7.53 21.50 0.00 3.23 44.09 35.48 12.90 4.30 0.00 0.00 1.07 41.94 40.86 16.13 0.00 0.00 36.56 53.76 9.68 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 36.56 43.01 20.43

Source: Authors’ elaborations on ECHP data, Italian Section (1994-2001), and Istat

EXPLORING POVERTY PATTERNS AND DIFFERENTIALS...

• Nearly 57% of Italian provinces shows an income poverty incidence (HCR)

between 5% and 15%, while a substantial share of provinces (32%), with a poverty incidence higher than 20%, is located in the South and Islands

• More than 92% of Italian provinces shows a FM between 10% and 25%,

while there isn’t any province with a FM higher than 30% or lower than 5%

• Almost the totality (98.93%) of Italian provinces shows a FS between 10%

and 25%, denoting lower levels of territorial disparities

2nd June 2016 University of Naples “Parthenope” (Italy) Department of Management and Quantitative Studies

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0.1 0.2 0.3 North-West North-East Center South Islands

EXPLORING POVERTY PATTERNS AND DIFFERENTIALS...

0.1 0.2 0.3 0.4 0.5 North-West North-East Center South Islands

TERRITORIAL SERIES OF POVERTY COMPOSITE ESTIMATES AT A NUTS3 LEVEL

HEAD COUNT RATIO (continuous line) VS VS FUZZY MONETARY (broken line) FUZZY MONETARY (broken line) VS VS FUZZY SUPPLEMENTARY (continuous line)

• The territorial series of HCR, substantially stable across Northern Italian

provinces, rapidly increases as we move to the Southern and Insular ones

• The territorial series of FM is quite stable across Northern provinces and

it slightly tends to increase as we move to the Southern and Insular ones

• Supplementary deprivation increases across provinces with the increasing of

income poverty

2nd June 2016 University of Naples “Parthenope” (Italy) Department of Management and Quantitative Studies

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EXPLORING POVERTY PATTERNS AND DIFFERENTIALS...

FUZZY MANIFEST (continuous line) VS S FUZZY LATENT (broken line) 0.1 0.2 0.3 0.4 North-West North-East Center South Islands

• Although both the MAN and LAT territorial series show an upward

trend for the poorer Southern provinces, the MAN always states a degree of poverty largely more severe than the LATENT one

TERRITORIAL SERIES OF POVERTY COMPOSITE ESTIMATES AT A NUTS3 LEVEL

2nd June 2016 University of Naples “Parthenope” (Italy) Department of Management and Quantitative Studies

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Distribution of Italian NUTS3 regions by classes of poverty intensities

Head Count Ratio Fuzzy Monetary Fuzzy Supplementary Fuzzy Manifest Fuzzy Latent

< 0.05 0.05 |– 0.10 0.10 |– 0.15 0.15 |– 0.20 0.20 |– 0.25 0.25 |– 0.30 > 0.30 6.45 30.11 26.88 4.30 3.23 7.53 21.50 0.00 3.23 44.09 35.48 12.90 4.30 0.00 0.00 1.07 41.94 40.86 16.13 0.00 0.00 36.56 53.76 9.68 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 36.56 43.01 20.43

Source: Authors’ elaborations on ECHP data, Italian Section (1994-2001), and Istat

EXPLORING POVERTY PATTERNS AND DIFFERENTIALS...

• No Italian province shows a MAN estimate higher than 15% so

as no province denotes a LAT estimate lower than 20%

• Although at a different level, the MAN and LAT estimates

show an adequate co-graduation degree (τ = 0.50) across Italian provinces

2nd June 2016 University of Naples “Parthenope” (Italy) Department of Management and Quantitative Studies

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CONCLUDING REMARKS

• Even though at a different level, both the monetary and the living

conditions approaches broadly confirm the distinctive territorial socio- economic gap between the North and South of Italy

• Although

the deprivation patterns are basically unchanged, the territorial distances between the Northern provinces and the Southern

• nes appear to be more marked by the conventional approach than the

fuzzy income one

• Supplementary deprivation increases across provinces with the increasing
• f the income poverty even though the living conditions seem to be more

severe than the income deprivation across Northern provinces

2nd June 2016 University of Naples “Parthenope” (Italy) Department of Management and Quantitative Studies

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CONCLUSIONS AND DEVELOPMENTS

However, EBLUP Estimators are variable-specific since they may depend on the particular poverty measure considered in the small area models

Therefore, in order to assess still further the RELATIVE PERFORMANCE

• f DIRECT, SYNTHETIC and COMPOSITE EBLUP estimators associated to

the Fay-Herriot and Rao-Yu models (or also Petrucci-Salvati)...

• SIMULATION STUDY
• A set of QUALITY INDICATORS, i.e., AARB, AARE, AEFF, ARMSE, ...

2nd June 2016 University of Naples “Parthenope” (Italy) Department of Management and Quantitative Studies

From ECHP to EU-SILC (2011 module on material deprivation with a focus on children under 16)

Remarkable GAINS IN EFFICIENCY of the poverty estimates AND the high level of STATISTICAL SIGNIFICANCE

• f some territorial indicators highlight the model adequacy

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REFERENCES

2nd June 2016 University of Naples “Parthenope” (Italy) Department of Management and Quantitative Studies

Betti G., Cheli B., Lemmi A., Verma V. (2006), On the construction of fuzzy measures for the analysis of poverty and social exclusion, Statistica & Applicazioni IV, 77–97 Punzo G. (2011), Measuring poverty and living conditions in Italy through a combined analysis at a sub-national level. Journal of Eco conomic c and S Soci cial M Mea easurem emen ent 36 (1,2), 93-118 (with Quintano C. and Castellano R.) Punzo G. (2007), Estimating poverty in the Italian provinces using small area estimation models. Metod

• dol
• loš
• ški Z

Zvezki – Advances ces in Met ethodology y and S Statistics cs 4 (1), 37-70 (with Quintano C. and Castellano R.) Punzo G. (2007), Estimating Supplementary Poverty in the Italian Provinces: A Multidimensional and Fuzzy Analysis through Small Area Models, IASS Satellite Conference on Small Area Estimation, Pisa (Italy), September 3-5 (with Quintano C., Castellano R.) Rao J.N.K. (2003), Small Area Estimation, Wiley, London Rao J.N.K. , Yu M. (1994), Small area estimation by combining time series and cross- sectional data, Canad J Statist 22 (1994), 511–528 Verma V. (1993), Sampling Errors in Household Surveys. Nation

• nal H

Hou

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• Programme. Statistical Division, United Nations, New York