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Poverty measures for local comparison: statistical problems and empirical results in OECD countries Gianni Betti*, Francesca Gagliardi*, Achille Lemmi*, Mario Piacentini** and Vijay Verma* * Department of Economics and Statistics -

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This project is supported by funding under the EU Seventh Research Framework Programme – Capacities

Poverty measures for “local” comparison: statistical problems and empirical results in OECD countries

Gianni Betti, Francesca Gagliardi, Achille Lemmi*, Mario Piacentini** and Vijay Verma*

* Department of Economics and Statistics - University of Siena ** OECD, Paris Brussels, 13 March 2015

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1. Poverty estimates at local level: empirical examples

and possible solutions

2. Gain in efficiency by the cumulation approach
3. Empirical examples of regional poverty indicators

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Poverty and social exclusion indicators are an essential monitoring tool, most useful when comparable across countries. Implementing informed policies often requires statistics disaggregated to lower levels then those whom meet national needs.

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National estimates are particularly insufficient for monitoring poverty and social exclusion, as these fields require complex statistics that take into account the distribution. The correct statistics are necessarily based on intensive and relatively small-scale surveys of households and individuals.

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To introduce the problem with an empirical and real case we take in to account (with authorisation) some slides presented by Matthias Till of Statistics Austria at the OECD in Paris on November the 27th, 2012, titled: Precision gains for NUTS2 poverty estimates: preliminary findings from an Austrian exercise

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Our problem: Eratic patterns over time

2 4 6 8 10 12 14 16 18 20

Oberösterreich Salzburg Tirol Vorarlberg Niederösterreich Steiermark Burgenland Kärnten Wien

APR (2005-10)

2005 2006 2007 2008 2009 2010

Statistics Austria Eu-SILC

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AT34: a special case

Statistics Austria Eu-SILC

13 9 13 18 12 10

2 4 6 8 10 12 14 16 18 20

Vorarlberg

APR (2005-10)

2005 2006 2007 2008 2009 2010

minus 37% plus 40%

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Our problem: precision proportionate to region size

NUTS 2 n= CI AT11 247 4,7 AT34 307 3,6 AT32 440 3,0 AT21 475 4,3 AT33 584 2,6 AT22 1.014 2,4 AT13 1.219 2,4 AT31 1.233 2,2 AT12 1.287 1,8 Total 6.806 0,8

not significantly different from AT13 (Vienna) EU-SILC 2007, number of households, 95% confidence interval for Poverty Rate

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Possible solutions:

1. Relying on direct estimates

Inacceptable volatility for small regions

2. Aggregation over several years

cheap and easy but not timely and limited scope

3. Augmenting income information in LFS (using registers)

Larger (and in AT: disproportional sample design) quality concerns and unmet data requirements

4. Imputing poverty status in LFS (using models)

borrows statistical strength and can enhance understanding Unit level is most flexible and can be augmented with region covariates Overlapping core variables & micro data availability of LFS & EU- SILC Shrinkage towards the mean = bias of between region differences

5. Composite of imputed (4) and direct (1) estimates

Minimizes expected bias across regions Reduces precision gain for small regions

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This speech addresses how to improve the sampling precision for OECD regions, through the cumulation of data over rounds of regularly repeated national surveys. The reference data for our innovative proposal is the EU-SILC Statistics on Income and Living Conditions, which provides a complex and integrated design adopted by all EU countries.

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EU-SILC complexity involves a rotational panel, where a new sample of households and individuals replace each year 25% of the existing sample, and are followed for four years, offering each year a cross-sectional sample and longitudinal samples of various duration.

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Gain from cumulation over k waves - 1

In this speech we are concerned with the efficiency gain given by the use of cumulation. Hypothesis: “Suppose a person's poverty status is determined from his income within the income distribution independently for each year, and once the poverty measure has been computed for each wave in the dataset, they are averaged over the number of consecutive waves.”

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Gain from cumulation over k waves - 2

Question: “How much gain in sampling precision derives from such pooling, given that consecutive years generally present highly correlated income data?”

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Gain from cumulation over k waves - 3

Under a two waves model and a full sample

verlap, the variance of the poverty measure

can be estimated as: Alternatively, if the overlap is only partial:

        v c 1 . 2 v v

1 A

 

                  

H 2 1 A

n n . b 1 . 4 v v v

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Gain from cumulation over k waves - 4

In the case of multiple waves the correlation will be inversely proportional to distance between years, hence we can assume: From which we can derive the gain in precision averaging over K waves:

k 1 k

v c v c             

                            



  k K k k

v c K k K K v v

1 1 1

. . 2 1 . 1

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Gain from cumulation over k waves - 5

Where:

“b” is the correlation “c” is the covariance “v” is the variance “n” is the sample overlap size “ “ is the harmonic mean of different waves sizes “ ” and “ ”

nh

n1

n2

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Quantifying the gain in sampling precision from pooling over three waves - 1

So, for example, if we have a three consecutive years dataset and we want to estimate the average of the three years, we proceed as follows.

replication

We first construct a common structure of Strata and PSUs from the union of the three datasets and assign to this common structure new weights equal to the average of the weights of the three years:

( ) 1 2 3

( ) ( ) / 3

Common Average t t

w w w w w    

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Quantifying the gain in sampling precision from pooling over three waves - 2

For each year (t) and for each replication (k), we can estimate yk

(t)

where t=1,2,3 and from this, the required statistic

( ) Average t k t k t

y a y  that in our case is just

1 2 3

( ) / 3

Average k k k k

y y y y   

So the variance estimate of this measure can be easily estimated applying the variance estimation using resampling methods (JRR) as if the statistic would be a common cross sectional measure.

( ) t t t

V aV 

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(a) est 2011 (b) s.e. 2011 (c) s.e. 3 years average (d) 1-(c)/(b) AUSTRIA HCR 60% national p.l. 13.8 0.61 0.43 30% S80/S20 4.0 0.08 0.07 21% Gini 26.9 0.38 0.31 18% SPAIN HCR 60% national p.l. 22.0 0.48 0.31 35% S80/S20 6.5 0.15 0.11 28% Gini 33.8 0.30 0.24 20%

Empirical analysis: Austria and Spain

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Empirical analysis: Austria and Spain

The methodology for the estimates of s.e. of

average measures over three years confirm to perform well both at national and regional level.

In particular for both AT and ES at national level

they show a sensible reduction of the standard errors using the three year average, that is, for each index, very similar in both countries.

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HCR 60%, national p.l. S80/S20 Gini (a) s.e. 2011 (b) s.e. 3 years average (c)=(b)/(a) (a) s.e. 2011 (b) s.e. 3 years average (c)=(b)/(a) (a) s.e. 2011 (b) s.e. 3 years average (c)=(b)/(a) AT11 3.72 2.44 0.66 0.48 0.32 0.68 2.10 1.48 0.70 AT12 1.07 0.78 0.74 0.18 0.14 0.78 0.90 0.70 0.78 AT13 1.86 1.35 0.73 0.23 0.17 0.75 0.95 0.73 0.77 AT21 3.35 2.24 0.67 0.31 0.24 0.75 1.49 1.11 0.74 AT22 1.30 1.10 0.85 0.22 0.16 0.75 1.04 0.77 0.74 AT31 1.12 0.72 0.64 0.18 0.14 0.77 0.93 0.74 0.80 AT32 1.88 1.32 0.70 0.36 0.26 0.71 1.82 1.31 0.72 AT33 1.91 1.15 0.60 0.30 0.22 0.71 1.50 1.10 0.73 AT34 1.99 1.59 0.80 0.43 0.40 0.95 1.99 1.79 0.90 Mean 0.71 0.76 0.77 Median 0.70 0.75 0.74

Empirical analysis at Regional level: Austria

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References

Betti G., Gagliardi F., Lemmi A., Verma V. (2012), Sub-national

indicators of poverty and deprivation in Europe: methodology and applications, Cambridge Journal of Regions, Economy and Society, 5(1), pp. 149-162.

Piacentini, M. (2014), “Measuring Income Inequality and poverty at

the Regional Level in OECD Countries”, OECD Statistics Working Papers, 2014/03, OECD Publishing.

Verma V., Betti G. (2011), Taylor linearization sampling errors and

design effects for poverty measures and other complex statistics, Journal of Applied Statistics, 38(8), pp. 1549-1576.

Verma, V., Betti, G. and Gagliardi, F. (2010), An assessment of

survey errors in EU-SILC, Eurostat Methodologies and Working Papers, Eurostat, Luxembourg.

Verma, V., Gagliardi, F. and Ferretti, C. (2013) Cumulation of poverty

measures to meet new policy needs, in Advances in Theoretical and Applied Statistics. Torelli, N. and Pesarin, F.; Bar-Hen, Avner (Eds.) 2013, XIX, Springer.

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TÁRKI Social Research Institute Inc. (HU) Amsterdam Institute for Advanced labour Studies, Universiteit van Amsterdam (NL) The Swedish Institute for Social Research, Stockholms Universitet (SE) Fachbereich IV, Wirtschafts- und Sozialstatistik, Universität Trier (DE) Centre d’Etudis Demogràfics, Campus de la Universitat Autònoma de Barcelona (ES) Centre d’Etudes de Population, de Pauvreté et de Politiques Socio-Economiques (LU) Centre for Social Policy, Universiteit Antwerpen (BE) Institute for Social & Economic Research, University of Essex (UK) Bremen International Graduate School of Social Sciences, Universität Bremen (DE) Department of Dynamics of Organisations of Work, Centre d’Etudes de l’Emploi (FR) The Centre for European Policy Studies (BE) Dipartimento di Economica e Menagement, Università di Pisa (IT) Social Statistics Division, University of Southampton (UK) Luxembourg Income Study, asbl (LU) WageIndicator Foundation (NL) School of Social Sciences, The University of Manchester (UK)

Partners Co-ordinator

Inclusive Growth Research Infrastructure Diffusion contract no. 312691 For further information about the InGRID project, please contact inclusive.growth@kuleuven.be www.inclusivegrowth.be p/a HIVA – Research Institute for Work and Society Parkstraat 47 box 5300 3000 Leuven Belgium

Guy Van Gyes Monique Ramioul

InGRID

Poverty measures for “local” comparison: statistical problems and empirical results in OECD countries

Gianni Betti*, Francesca Gagliardi*, Achille Lemmi*, Mario Piacentini** and Vijay Verma*

Table of contents

and possible solutions

Poverty and social exclusion indicators are an essential monitoring tool, most useful when comparable across countries. Implementing informed policies often requires statistics disaggregated to lower levels then those whom meet national needs.

Our problem: Eratic patterns over time

APR (2005-10)

AT34: a special case

Our problem: precision proportionate to region size

Possible solutions:

Inacceptable volatility for small regions

cheap and easy but not timely and limited scope

Larger (and in AT: disproportional sample design) quality concerns and unmet data requirements

borrows statistical strength and can enhance understanding Unit level is most flexible and can be augmented with region covariates Overlapping core variables & micro data availability of LFS & EU- SILC Shrinkage towards the mean = bias of between region differences

Minimizes expected bias across regions Reduces precision gain for small regions

EU-SILC complexity involves a rotational panel, where a new sample of households and individuals replace each year 25% of the existing sample, and are followed for four years, offering each year a cross-sectional sample and longitudinal samples of various duration.

Gain from cumulation over k waves - 1

Gain from cumulation over k waves - 2

Question: “How much gain in sampling precision derives from such pooling, given that consecutive years generally present highly correlated income data?”

Gain from cumulation over k waves - 3

Under a two waves model and a full sample

can be estimated as: Alternatively, if the overlap is only partial:

        v c 1 . 2 v v

 

                  

n n . b 1 . 4 v v v

Gain from cumulation over k waves - 4

In the case of multiple waves the correlation will be inversely proportional to distance between years, hence we can assume: From which we can derive the gain in precision averaging over K waves:

v c v c             

                            



v c K k K K v v

. . 2 1 . 1

Gain from cumulation over k waves - 5

Where:

“b” is the correlation “c” is the covariance “v” is the variance “n” is the sample overlap size “ “ is the harmonic mean of different waves sizes “ ” and “ ”

nh

n1

n2

Quantifying the gain in sampling precision from pooling over three waves - 1

We first construct a common structure of Strata and PSUs from the union of the three datasets and assign to this common structure new weights equal to the average of the weights of the three years:

( ) ( ) / 3

w w w w w    

Quantifying the gain in sampling precision from pooling over three waves - 2

For each year (t) and for each replication (k), we can estimate yk

where t=1,2,3 and from this, the required statistic

y a y  that in our case is just

( ) / 3

y y y y   

So the variance estimate of this measure can be easily estimated applying the variance estimation using resampling methods (JRR) as if the statistic would be a common cross sectional measure.

V aV 

Empirical analysis: Austria and Spain

Empirical analysis: Austria and Spain

average measures over three years confirm to perform well both at national and regional level.

they show a sensible reduction of the standard errors using the three year average, that is, for each index, very similar in both countries.

Empirical analysis at Regional level: Austria

References

indicators of poverty and deprivation in Europe: methodology and applications, Cambridge Journal of Regions, Economy and Society, 5(1), pp. 149-162.

the Regional Level in OECD Countries”, OECD Statistics Working Papers, 2014/03, OECD Publishing.

design effects for poverty measures and other complex statistics, Journal of Applied Statistics, 38(8), pp. 1549-1576.

survey errors in EU-SILC, Eurostat Methodologies and Working Papers, Eurostat, Luxembourg.

measures to meet new policy needs, in Advances in Theoretical and Applied Statistics. Torelli, N. and Pesarin, F.; Bar-Hen, Avner (Eds.) 2013, XIX, Springer.

Thank you for your attention!

Gianni Betti, Francesca Gagliardi, Achille Lemmi*, Mario Piacentini** and Vijay Verma*