Poverty measures for local comparison: statistical problems and - PowerPoint PPT Presentation

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

Table of contents 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 2 2 www.inclusivegrowth.be www.inclusivegrowth.be 2

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. 3 3 www.inclusivegrowth.be www.inclusivegrowth.be 3

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. 4 4 www.inclusivegrowth.be www.inclusivegrowth.be 4

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 5 5 www.inclusivegrowth.be www.inclusivegrowth.be 5

Our problem: Eratic patterns over time APR (2005-10) 2005 2006 2007 2008 2009 2010 20 18 16 14 12 10 8 6 4 2 0 Oberösterreich Salzburg Tirol Vorarlberg Niederösterreich Steiermark Burgenland Kärnten Wien 6 6 www.inclusivegrowth.be www.inclusivegrowth.be Statistics Austria Eu-SILC 6

AT34: a special case APR (2005-10) 2005 2006 2007 2008 2009 2010 20 18 18 plus 40% 16 minus 37% 14 13 13 12 12 10 9 10 8 6 4 2 0 Vorarlberg 7 7 www.inclusivegrowth.be www.inclusivegrowth.be Statistics Austria Eu-SILC 7

Our problem: precision proportionate to region size NUTS 2 n= CI 247 4,7 AT11 307 3,6 AT34 not significantly different from AT13 (Vienna) 440 3,0 AT32 475 4,3 AT21 584 2,6 AT33 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 EU-SILC 2007, number of households, 95% confidence interval for Poverty Rate 8 8 www.inclusivegrowth.be www.inclusivegrowth.be 8

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 9 9 www.inclusivegrowth.be www.inclusivegrowth.be 9

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. 10 10 www.inclusivegrowth.be www.inclusivegrowth.be 10

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. 11 11 www.inclusivegrowth.be www.inclusivegrowth.be 11

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. ” 12 12 www.inclusivegrowth.be www.inclusivegrowth.be 12

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 ? ” 13 13 www.inclusivegrowth.be www.inclusivegrowth.be 13

Gain from cumulation over k waves - 3 Under a two waves model and a full sample overlap, the variance of the poverty measure can be estimated as:    c v    1 v . 1 A   2 v Alternatively, if the overlap is only partial:        v v n       1 2 v . 1 b .     A   4 n   H 14 14 www.inclusivegrowth.be www.inclusivegrowth.be 14

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: k     c c      k 1     v v From which we can derive the gain in precision averaging over K waves:    k       v 1  K k c            K 1 k 1 . 1 2 . .    k 1       v K K v   15 15 www.inclusivegrowth.be www.inclusivegrowth.be 15

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 “ ” n h n 1 n 2 16 16 www.inclusivegrowth.be www.inclusivegrowth.be 16

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. k 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:     ( Common ) Average w ( w ) ( w w w ) / 3 t t 1 2 3 17 www.inclusivegrowth.be www.inclusivegrowth.be 17

Quantifying the gain in sampling precision from pooling over three waves - 2 (t) For each year ( t ) and for each replication ( k ), we can estimate y k where t=1,2,3 and from this, the required statistic   Average ( ) t y a y k t k t that in our case is just    Average 1 2 3 ( ) / 3 y y y y k k k k   ( ) t So the variance estimate of this measure V aV t t can be easily estimated applying the variance estimation using resampling methods (JRR) as if the statistic would be a common cross sectional measure. 18 www.inclusivegrowth.be www.inclusivegrowth.be 18

Empirical analysis: Austria and Spain (a) (c) est (b) s.e. 3 years (d) 2011 s.e. 2011 average 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% 19 www.inclusivegrowth.be www.inclusivegrowth.be 19

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. 20 www.inclusivegrowth.be www.inclusivegrowth.be 20

Empirical analysis at Regional level: Austria HCR 60%, national p.l. S80/S20 Gini (b) s.e. 3 (b) s.e. 3 (b) s.e. 3 (a) s.e. years (a) s.e. years (a) s.e. years 2011 average (c)=(b)/(a) 2011 average (c)=(b)/(a) 2011 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 21 www.inclusivegrowth.be www.inclusivegrowth.be 21