Project 2008/s Methodological studies and quality assessment of EU-SILC

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1 Università degli Studi di Siena Project 2008/s Methodological studies and quality assessment of EU-SILC Report SILC March 2009 SAS programs for variance estimation of the measures required for Final Quality Report Project Director Prof. Giulio GHELLINI Research Directors Prof. Vijay VERMA Prof. Gianni BETTI Università degli Studi di Siena c/o Dipartimento di Metodi Quantitativi, Piazza S. Francesco 8, Siena (Italy)

2 Report SILC March 2009 SAS programs for variance estimation of the measures required for Final Quality Report Table of contents 1. Introduction General framework for variance estimation programs Scope of the programs included in this set Description of Macros Macros for the calculation of the means of the income components Macro jrr Macro Kish Step-by-step description of the program Quick Guide Example...12 ANNEX I: SAS codes...13 ANNEX II: Illustrative output...25 ANNEX III: Technical note on JRR procedure for estimating variance and design effect...27 ANNEX IV: Requirements concerning the reporting of sampling errors

3 1. Introduction This document lists the SAS programs for variance estimation of the measures specified in the EU-SILC regulations and technical guidelines for the Final Quality Report to be produced by countries. As specified in the existing guidelines, these measures are all cross-sectional in nature. A list of the measures involved is provided below in Annex IV: Requirements concerning the reporting of sampling errors. The variance estimation method employed in the programs is the Jackknife Repeated Replication (JRR). This is the method adopted by Eurostat for the computation of sampling errors. A brief outline of the approach is provided below in Annex III: Technical note on JRR procedure for estimating variance and design effect. Sections 2 describes the general framework for variance estimation programs developed for application by countries if they chose to use the JRR approach. The various programs will be divided into sets for the purpose of their development and presentation. The first set deals with the variables list for sampling error computation in the Final Quality Report guidelines. Section 3 describes the scope of the programs included in the set covered in this report. The central part of this report is Section 4 which describes the fundamental SAS macros which the program code is divided into, along with a listing of the actual SAS coded in Annex I. The first group of macro contains 32 macros and concerns the calculation of the means of the income components and is divided into three parts dealing with H, P and R files, respectively. The second set Macro JRR implements the Jackkinfe Repeated Replications (JRR) methodology. The third set Macro Kish calculates the quantity Kish_Jrr described in Annex III as the part of the design effect ( deft ) which arises from variation in sample weights. The SAS code, along with the illustrative data set and results, which accompany this report are being provided separately. Section 5 provides a step-by-step description of the program, and Section 6a quick guide for the user. Finally, Section 7 provides an illustrative example, and the output for this illustration is listed in Annex II. More detailed results with commentary, meant for inclusion the quality reports, will be provided in subsequent documents. Related reports Issues concerning the specification of sampling error measures required for the EU-SILC Final Quality Reports prepared by countries are discussed in the following report by the University of Siena Team: Report SILC.01 (18 March 2009): Required tables on sampling errors in EU-SILC Final Quality Report (FQR) 3

4 2 General framework for variance estimation programs As noted, the method adopted by Eurostat for the computation of sampling errors is Jackknife Repeated Replication (JRR). Where applicable, the JRR approach is quite straightforward technically. Apart from specifying the sample structure and defining appropriate computational units for the purpose, the method merely involves repeated computation of the estimates (for which sampling errors are required) over different (often numerous) sample replications; variance of any statistic is estimated simply from variability in the estimate itself across the replications. The form of the final variance estimation formula does not depend on the particular statistic involved or on details of the sample design. Eurostat has been developing SAS routines and macros for the computation of sampling errors and design effects using the JRR approach for all the indicators as specified for the EU-SILC Intermediate and Final Quality Reports to be produced be countries, and to the extent possible also for other measures of income sources and distribution, poverty, inequality etc. which may be of interest in analysis and reporting of the survey results. The objective of programs is to encourage and facilitate routine computation of sampling errors for these statistics by countries. There are two main tasks involved in the computation of sampling error. (1) The first task is the development of efficient and accurate computer programs (in our case SAS routines) for the computation of each statistic for which sampling errors are required. This computation does not depend on the structure of the sample, apart from the sample base (i.e., the analysis units to be included in the computation) and the sample weight of each unit. While these routines are specific to each statistic of interest, they apply unchanged for any national survey, independent of its sample structure. The variance computational task involves repeated estimation of the statistic over a large number of full-scale replications of the sample, the construction these replications being the objective of the second task. (2) The second task is the specification of the replications to be used in the estimation of sampling errors. These are defined in terms of structure of the sample, specifically the strata and the primary sampling units in the sample. This task is essentially independent of the particular statistic involved, thus being the same for any statistic. However, it has to be performed separately for each country, taking into account the specific sample structure. (3) The above two aspects are linked through one or more datasets of specified content and structure. The datasets specify the sample of units on which the computations are performed, and for each unit all the substantive variables involved and also a small set of variables defining the sample structure. The sample structure variables are the output of task (2), and at a minimum include the following: Computational stratum Computational PSU Sample weight of the unit Computational stratum and PSU are defined from the type of units actually involved in the sample (at the time the unit was first selected into the sample), but possibly after some redefinition based on statistical considerations. (4) A source of variation in programs (1) can arise from differences in the type of statistic involved. The following are some examples. 4

5 (i) Mostly, cross-sectional and normal longitudinal variables (such as persistent poverty rates) can be treated in exactly the same way. However, estimating sampling errors of measures of net change and averages has some special features making the programs in set (1) a little different from those for normal cross-sectional and longitudinal measures. (ii) Two types of measures for subpopulations need to be distinguished. Computations for ordinary means or proportions for subclasses are no different from those for the full sample: the only difference being in the dataset (3) involved. Units not belonging to the subpopulation of interest can be simply disregarded in the computations. However, some measures for subpopulations are more complex in the sense that the total sample is also involved in their construction. An example is the poverty rate for children (subpopulation), but with the poverty line defined on the basis of income distribution of the whole population. Such measures involve some differences in the structure of the programs under (1). (iii) At least in principle, the JRR procedure can be used to incorporate or to identify separately the effect on sampling error of various data adjustment and estimation steps, such as imputation, calibration or smoothing etc. Essentially, this involves reapplying the step concerned before computing the estimate in each replication. This again requires adjustments to the structure of the variance estimation programs under (1). (2) Specification of sample structure (country-specific) (0) Original data files (UDB files H, R, P, ) (3) Standardised datasets (files H, R, P, ) (1) JRR variance estimation programs (variable-specific) (4) Variations in structure of the program for special types of statistics, e.g.: (i) measures of net changes and averages (ii) special subpopulation statistics (iii) incorporating effect of imputation, calibration, etc. 5

6 3. Scope of the programs included in this set The programs described in this first set concern (1), namely variance estimation programs for the specified set of variables required for in the Final Quality Report. These variables are all of a cross-sectional type, but are required for both cross-sectional and various longitudinal sample bases. The programs assume as input standardised datasets (files H, R, P, ), with the sample structure variables (computational stratum, computational PSU, and sample weight of each unit). These standard programs apply for all countries. In each case several runs using different datasets may be involved as follows. The variables included are grouped according to three types of data files (H, R, and P), which can be run separately or as a single run with three data sets. There are up to four sample basis of interest for the Final Quality Report (cross-sectional sample, and longitudinal samples of 2, 3 and 4 year duration). The computations may be repeated by replacing two actual sample structure variables (computational stratum and PSU) by those constructed by randomising the order of units in the sample (as explained in the Annex). This provides estimates of design effects. The numerical illustrations included with this report are confined to four countries which in fact used simple random samples (apart from the presence of unequal sample weights), for which the sample structure is therefore know to us. Furthermore the illustrations are confined to the (full) cross-sectional sample for 2006; similar computations will be performed shortly for the two longitudinal sample of two ( ) and three ( ) year duration. In these random samples of elements, design effect arises simply from the variation in sample weights. 6

7 4. Description of Macros In this section a brief description of the main macros that user can find at the very beginning of the program is provided. These macros can be divided in three classes: macros for the calculation of the means of the income components required in the Final Quality Report, one macro for the estimation of the variances of these measures with the Jackknife Repeated Replication methodology and one macro for the estimation of the Kish factor. 4.1 Macros for the calculation of the means of the income components These macros can be divided into three groups: (a) Macros for components of income from the H file; (b) Macros for components of income from the P file; (c) Macros for components of income from the R file. (a) These are 32 macros. Macros from 1 to 27 calculate the means of the following households income components. %macro stat_1; hy010 total household gross income; %macro stat_2; hy020 total disposable household income; %macro stat_3; hy022 Total disposable household income before social transfers other than old-age and survivors benefits; %macro stat_4; hy023 Total disposable household income including old-age and survivors benefits; %macro stat_5; hy040n income from rental of property or land net; %macro stat_6; hy040g income from rental of property or land gross; %macro stat_7; hy050n Family/child related allowances net; %macro stat_8; hy050g Family/child related allowances gross; %macro stat_9; hy060n Social exclusion not elsewhere classified net; %macro stat_10; hy060g Social exclusion not elsewhere classified gross; %macro stat_11; hy070n Housing allowances; %macro stat_12; hy070g Housing allowances; %macro stat_13; hy080n Regular inter-household cash transfer received; %macro stat_14; hy080g Regular inter-household cash transfer received; %macro stat_15; hy090n Interest, dividends, profit from capital investments; %macro stat_16; hy090g Interest, dividends, profit from capital investments; %macro stat_17; hy100n Interest repayments on mortgage; %macro stat_18; hy100g Interest repayments on mortgage; %macro stat_19; hy110n Income received by people aged under 16; %macro stat_20; hy110g Income received by people aged under 16; %macro stat_21; hy120n Income received by people aged under 16; %macro stat_22; hy120g Income received by people aged under 16; %macro stat_23; hy130n Regular inter-household cash transfer paid; %macro stat_24; hy130g Regular inter-household cash transfer paid; %macro stat_25; hy140n Tax on Income and Social Contributions; %macro stat_26; hy140g Tax on Income and Social Contributions; %macro stat_27; hy145n Repayments/receipts for tax adjustment. 7

8 Then macros from 28 to 32 calculate the mean of the equivalised disposable income by household size. %macro stat_28; mean equivalised disposable income for household size equal to 1; %macro stat_29; mean equivalised disposable income for household size equal to 2; %macro stat_30; mean equivalised disposable income for household size equal to 3; %macro stat_31; mean equivalised disposable income for household size equal or greater than 4; %macro stat_32; mean equivalised disposable income for all household. (b) These are 25 macros and calculate the means of the following personal income components. %macro stat_33; py010n Employee cash or near cash income; %macro stat_34; py010g Employee cash or near cash income; %macro stat_35; py020n non-cash employee income; %macro stat_36; py020g non-cash employee income; %macro stat_37; py035n Contributions to individual private pension plans; %macro stat_38; py035g Contributions to individual private pension plans; %macro stat_39; py050n Cash benefits or losses from self-employment; %macro stat_40; py050g Cash benefits or losses from self-employment; %macro stat_41; py070n Value of goods produced by own consumption; %macro stat_42; py070g Value of goods produced by own consumption; %macro stat_43; py080n Pension from individual private plans; %macro stat_44; py080g Pension from individual private plans; %macro stat_45; py090n Unemployment benefits; %macro stat_46; py090g Unemployment benefits; %macro stat_47; py100n Old-age benefits; %macro stat_48; py100g Old-age benefits; %macro stat_49; py110n Survivor' benefits; %macro stat_50; py110g Survivor' benefits; %macro stat_51; py120n Sickness benefits; %macro stat_52; py120g Sickness benefits; %macro stat_53; py130n Disability benefits; %macro stat_54; py130g Disability benefits; %macro stat_55; py140n Education related allowances; %macro stat_56; py140g Education related allowances; %macro stat_57; py200g Gross monthly earnings of employees. (c) These are 9 macros that calculate the mean of the equivalised disposable income by age or by gender groups for all individuals in the R file. %macro stat_58; mean equivalised disposable income for individuals aged less then 25 (class age=1); %macro stat_59; mean equivalised disposable income for individuals aged between 25 and 34 (class age=2); %macro stat_60; mean equivalised disposable income for individuals aged between 35 and 44 (class age=3); %macro stat_61; mean equivalised disposable income for individuals aged between 45 and 54 (class age=4); %macro stat_62; mean equivalised disposable income for individuals aged between 55 and 64 (class age=5); 8

9 %macro stat_63; mean equivalised disposable income for individuals aged equal or greater then 65 (class age=6); %macro stat_64; mean equivalised disposable income for males (rb090=1); %macro stat_65; mean equivalised disposable income for females (rb090=2); %macro stat_66; mean equivalised disposable income for all individuals in R file. 4.2 Macro jrr This macro implements the Jackkinfe Repeated Replications (JRR) methodology. It implements the so called JRR variable (see annex for details). In order to estimate the standard errors, the measures are estimated inside the replications. In fact, inside this macro there is the computation of the %stat_&k. Inside the replications we also reallocate the weights. Once a PSU is deleted, its weights are assigned to the other PSUs in the same stratum of the PSU deleted, so that the total sum of the weights doesn t change (see formula [4] in annex for details). 4.3 Macro Kish This macro calculates the quantity Kish_Jrr described in Annex III as the correlation between the weights and the statistic implemented. 9

10 5. Step-by-step description of the program In this section we give a brief description step by step of the program for the estimation of the measures estimates, standard errors and design effect. A. The program start with the preparation of the datasets to be used with all the necessary variables. Three datasets can be used: one from H file, one from P file and one from R file. B. Then there is the macro %macro choose_options in which the user should specify the number of PSUs of the dataset and two numbers corresponding to the statistic number with which the program should start and end. Presently, all or a valid range (only consecutive measures) or a single measure can be chosen. In order to have estimates for measures from stat_1 to stat_10, one should choose 1 as first measure to estimate and 10 as the last one. For a single measure one should mention the number of the measure as both first and last index. The latter case means the macro will be run once for the measure, whereas in former case (a range of measures) the macro will run sequentially from the beginning of the range to end, once for each measure. Only consecutive measures can be chosen. Details about the place where these numbers have to be inserted are in next section. C. In next step there is a macro called %macro cycle. This macro repeats the same steps for each measure required in B. First it assigns the appropriate dataset for the measure required. Then variables that are necessary in order to rescale the weights are added to the dataset. Finally the estimate of the measure, its standard error and Kish factor are calculated. D. Point C is repeated for each measure chosen. E. Finally the program put the results for all the measures selected all together in an output dataset. 10

11 6. Quick Guide For the running of the program, user should create a directory with the files to be used in the program. Then from SAS should be created a library called silc06 that refers to the previous directory where the dataset is present. First of all you have to prepare three data sets (H, P and R files) for a given country, each of which should contain the following variables: The structure of the data for the data set: stratum = the stratum where the observation is located; psu = the primary selection unit (PSU) where the observation is located; ah = number of PSUs per stratum. The H file should contain also the household cross-sectional weights DB090. These three data sets should be named: H file: h ; P file: p ; R file: r. Then the user need to insert into the program the following: 1. Insert, at the end of the program inside %choose_options all necessaries information. %choose_options(a, b, c); where a = number of PSU in the dataset; b = first measure chosen; c = last measure chosen; (b and c can range from 1 to 66; b should be always chosen smaller than c (or equal to) ; e.g. b=10 and c=20 will run measures from 10 th to 20 th ) 11

12 7. Example At the end of this document, we provide as example of the output of the program, results obtained using data of EU-SILC cross-sectional dataset for year 2006 for Austria. As structure of the dataset for this country, that is a simple random sample, we have constructed a structure with 200 PSUs and 1 Stratum. Below we report the Sas code of the program, adapted for this analysis and the output achieved. 12

13 ANNEX I: SAS codes /*MACROS;*/ %macro stat_1; *hy010 total household gross income; proc means data=working mean noprint; var hy010; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hy010-est;z=hy010;run; %macro stat_2; *hy020 total disposable household income; proc means data=working mean noprint; var hy020; output out=est mean=est; weight wj; by country;run; data JRR; merge working est;by country;subpop_i=1;y=hy020-est;z=hy020;run; %macro stat_3; *hy022 Total disposable household income before social transfers other than old-age and survivors benefits; proc means data=working mean noprint; var hy022; output out=est mean=est; weight wj; by country;run; data JRR; merge working est;by country;subpop_i=1;y=hy022-est;z=hy022;run; %macro stat_4; *hy023 Total disposable household income including old-age and survivors benefits; proc means data=working mean noprint noprint; var hy023; output out=est mean=est; weight wj;by country; run; data JRR; merge working est;by country;subpop_i=1;y=hy023-est;z=hy023;run; %macro stat_5; *hy040n income from rental of property or land net; data working; set working; where hy040n ne 0; run; proc means data=working mean noprint; var hy040n; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hy040nest;z=hy040n;run; %macro stat_6; *hy040g income from rental of property or land gross; data working; set working; where hy040g ne 0; run; proc means data=working mean noprint; var hy040g; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hy040gest;z=hy040g;run; %macro stat_7; *hy050n Family/child related allowances net; data working; set working; where hy050n ne 0; run; proc means data=working mean noprint; var hy050n; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hy050nest;z=hy050n;run; %macro stat_8; *hy050g Family/child related allowances gross; data working; set working; where hy050g ne 0; run; proc means data=working mean noprint; var hy050g; output out=est mean=est; 13

14 data JRR; merge working est;by country;subpop_i=1;y=hy050gest;z=hy050g;run; %macro stat_9; *hy060n Social exclusion not elsewhere classified net; data working;set working; where hy060n ne 0; run; proc means data=working mean noprint; var hy060n; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hy060nest;z=hy060n;run; %macro stat_10; *hy060g Social exclusion not elsewhere classified gross; data working;set working; where hy060g ne 0; run; proc means data=working mean noprint; var hy060g; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hy060gest;z=hy060g;run; %macro stat_11; *hy070n Housing allowances; data working;set working; where hy070n ne 0; run; proc means data=working mean noprint; var hy070n; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hy070nest;z=hy070n;run; %macro stat_12; *hy070g Housing allowances; data working;set working; where hy070g ne 0; run; proc means data=working mean noprint; var hy070g; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hy070gest;z=hy070g;run; %macro stat_13; *hy080n Regular inter-household cash transfer received; data working;set working; where hy080n ne 0; run; proc means data=working mean noprint; var hy080n; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hy080nest;z=hy080n;run; %macro stat_14; *hy080g Regular inter-household cash transfer received; data working;set working; where hy080g ne 0; run; proc means data=working mean noprint; var hy080g; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hy080gest;z=hy080g;run; %macro stat_15; *hy090n Interst, dividends, profit fron capital investments; data working;set working; where hy090n ne 0; run; proc means data=working mean noprint; var hy090n; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hy090nest;z=hy090n;run; 14

15 %macro stat_16; *hy090n Interest, dividends, profit from capital investments; data working;set working; where hy090g ne 0; run; proc means data=working mean noprint; var hy090g; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hy090gest;z=hy090g;run; %macro stat_17; *hy100n Interest repayments on mortgage; data working;set working; where hy100n ne 0; run; proc means data=working mean noprint; var hy100n; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hy100nest;z=hy100n;run; %macro stat_18; *hy100g Interest repayments on mortgage; data working;set working; where hy100g ne 0; run; proc means data=working mean noprint; var hy100g; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hy100gest;z=hy100g;run; %macro stat_19; *hy110n Income received by people aged under 16; data working;set working; where hy110n ne 0; run; proc means data=working mean noprint; var hy110n; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hy110nest;z=hy110n;run; %macro stat_20; *hy110g Income received by people aged under 16; data working;set working; where hy110g ne 0; run; proc means data=working mean noprint; var hy110g; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hy110gest;z=hy110g;run; %macro stat_21; *hy120n Income received by people aged under 16; data working;set working; where hy120n ne 0; run; proc means data=working mean noprint; var hy120n; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hy120nest;z=hy120n;run; %macro stat_22; *hy120g Income received by people aged under 16; data working;set working; where hy120g ne 0; run; proc means data=working mean noprint; var hy120g; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hy120gest;z=hy120g;run; %macro stat_23; *hy130n Regular inter-household cash transfer paid; data working;set working; where hy130n ne 0; run; proc means data=working mean noprint; var hy130n; output out=est mean=est; 15

16 data JRR; merge working est;by country;subpop_i=1;y=hy130nest;z=hy130n;run; %macro stat_24; *hy130g Regular inter-household cash transfer paid; data working;set working; where hy130g ne 0; run; proc means data=working mean noprint; var hy130g; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hy130gest;z=hy130g;run; %macro stat_25; *hy140n Tax on Income and Social Contributions; data working;set working; where hy140n ne 0; run; proc means data=working mean noprint; var hy140n; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hy140nest;z=hy140n;run; %macro stat_26; *hy140g Tax on Income and Social Contributions; data working;set working; where hy140g ne 0; run; proc means data=working mean noprint; var hy140g; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hy140gest;z=hy140g;run; %macro stat_27; *hy145n Repayments/receipts for tax adjustment; data working;set working; where hy145n ne 0; run; proc means data=working mean noprint; var hy145n; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hy145nest;z=hy145n;run; %macro stat_28; *mean eqinc hhs=1; data working; set working; where hhs_size eq 1; run; proc means data=working mean noprint; var hx090; output out=est mean=est; weight wj; by country;run; data JRR; merge working est;by country;subpop_i=1;y=hx090-est;z=hx090;run; %macro stat_29; *mean eqinc hhs=2; data working; set working; where hhs_size eq 2; run; proc means data=working mean noprint; var hx090; output out=est mean=est; weight wj; by country;run; data JRR; merge working est;by country;subpop_i=1;y=hx090-est;z=hx090;run; %macro stat_30; *mean eqinc hhs=3; data working; set working; where hhs_size eq 3; run; proc means data=working mean noprint; var hx090; output out=est mean=est; weight wj; by country;run; data JRR; merge working est;by country;subpop_i=1;y=hx090-est;z=hx090;run; %macro stat_31; *mean eqinc hhs=4; data working; set working; where hhs_size eq 4; run; proc means data=working mean noprint; var hx090; output out=est mean=est; weight wj; by country;run; 16

17 data JRR; merge working est;by country;subpop_i=1;y=hx090-est;z=hx090;run; %macro stat_32; *mean eqinc all hhs; proc means data=working mean noprint; var hx090; output out=est mean=est; weight wj; by country;run; data JRR; merge working est;by country;subpop_i=1;y=hx090-est;z=hx090;run; %macro stat_33; *py010n Employee cash or near cash income; data working;set working; where py010n ne 0; run; proc means data=working mean noprint; var py010n; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=py010nest;z=py010n;run; %macro stat_34; *py010g Employee cash or near cash income; data working;set working; where py010g ne 0; run; proc means data=working mean noprint; var py010g; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=py010gest;z=py010g;run; %macro stat_35; *py020n non-cash employee income; data working;set working; where py020n ne 0; run; proc means data=working mean noprint; var py020n; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=py020nest;z=py020n;run; %macro stat_36; *py020g non-cash employee income; data working;set working; where py020g ne 0; run; proc means data=working mean noprint; var py020g; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=py020gest;z=py020g;run; %macro stat_37; *py035n Contributions to individual private pension plans; data working;set working; where py035n ne 0; run; proc means data=working mean noprint; var py035n; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=py035nest;z=py035n;run; %macro stat_38; *py035g Contributions to individual private pension plans; data working;set working; where py035g ne 0; run; proc means data=working mean noprint; var py035g; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=py035gest;z=py035g;run; %macro stat_39; *py050n Cash benefits or losses from self-employment; data working;set working; where py050n ne 0; run; proc means data=working mean noprint; var py050n; output out=est mean=est; 17

18 data JRR; merge working est;by country;subpop_i=1;y=py050nest;z=py050n;run; %macro stat_40; *py050g Cash benefits or losses from self-employment; data working;set working; where py050g ne 0; run; proc means data=working mean noprint; var py050g; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=py050gest;z=py050g;run; %macro stat_41; *py070n Value of goods produced by own consumption; data working;set working; where py070n ne 0; run; proc means data=working mean noprint; var py070n; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=py070nest;z=py070n;run; %macro stat_42; *py070g Value of goods produced by own consumption; data working;set working; where py070g ne 0; run; proc means data=working mean noprint; var py070g; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=py070gest;z=py070g;run; %macro stat_43; *py080n Pension from individual private plans; data working;set working; where py080n ne 0; run; proc means data=working mean noprint; var py080n; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=py080nest;z=py080n;run; %macro stat_44; *py080g Pension from individual private plans; data working;set working; where py080g ne 0; run; proc means data=working mean noprint; var py080g; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=py080gest;z=py080g;run; %macro stat_45; *py090n Unemployment benefits; data working;set working; where py090n ne 0; run; proc means data=working mean noprint; var py090n; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=py090nest;z=py090n;run; %macro stat_46; *py090g Unemployment benefits; data working;set working; where py090g ne 0; run; proc means data=working mean noprint; var py090g; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=py090gest;z=py090g;run; %macro stat_47; *py100n Old-age benefits; 18

19 data working;set working; where py100n ne 0; run; proc means data=working mean noprint; var py100n; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=py100nest;z=py100n;run; %macro stat_48; *py100g Old-age benefits; data working;set working; where py100g ne 0; run; proc means data=working mean noprint; var py100g; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=py100gest;z=py100g;run; %macro stat_49; *py110n Survivor' benefits; data working;set working; where py110n ne 0; run; proc means data=working mean noprint; var py110n; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=py110nest;z=py110n;run; %macro stat_50; *py110g Survivor' benefits; data working;set working; where py110g ne 0; run; proc means data=working mean noprint; var py110g; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=py110gest;z=py110g;run; %macro stat_51; *py120n Sickness benefits; data working;set working; where py120n ne 0; run; proc means data=working mean noprint; var py120n; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=py120nest;z=py120n;run; %macro stat_52; *py120g Sickness benefits; data working;set working; where py120g ne 0; run; proc means data=working mean noprint; var py120g; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=py120gest;z=py120g;run; %macro stat_53; *py130n Disability benefits; data working;set working; where py130n ne 0; run; proc means data=working mean noprint; var py130n; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=py130nest;z=py130n;run; %macro stat_54; *py130g Disability benefits; data working;set working; where py130g ne 0; run; proc means data=working mean noprint; var py130g; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=py130gest;z=py130g;run; 19

20 %macro stat_55; *py140n Education related allowances; data working;set working; where py140n ne 0; run; proc means data=working mean noprint; var py140n; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=py140nest;z=py140n;run; %macro stat_56; *py140g Education related allowances; data working;set working; where py140g ne 0; run; proc means data=working mean noprint; var py140g; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=py140gest;z=py140g;run; %macro stat_57; *py200g Gross monthly earnings of employees; data working;set working; where py200g ne 0; run; proc means data=working mean noprint; var py200g; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=py200gest;z=py200g;run; %macro stat_58; *mean eqinc class age=1; data working; set working; where age_class eq 1; run; proc means data=working mean noprint; var hx090; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hx090-est;z=hx090;run; %macro stat_59; *mean eqinc class age=2; data working; set working; where age_class eq 2; run; proc means data=working mean noprint; var hx090; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hx090-est;z=hx090;run; %macro stat_60; *mean eqinc class age=3; data working; set working; where age_class eq 3; run; proc means data=working mean noprint; var hx090; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hx090-est;z=hx090;run; %macro stat_61; *mean eqinc class age=4; data working; set working; where age_class eq 4; run; proc means data=working mean noprint; var hx090; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hx090-est;z=hx090;run; %macro stat_62; *mean eqinc class age=5; data working; set working; where age_class eq 5; run; proc means data=working mean noprint; var hx090; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hx090-est;z=hx090;run; 20

21 %macro stat_63; *mean eqinc class age=6; data working; set working; where age_class eq 6; run; proc means data=working mean noprint; var hx090; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hx090-est;z=hx090;run; %macro stat_64; *mean eqinc rb090=1; data working; set working; where rb090 eq 1; run; proc means data=working mean noprint; var hx090; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hx090-est;z=hx090;run; %macro stat_65; *mean eqinc rb090=2; data working; set working; where rb090 eq 2; run; proc means data=working mean noprint; var hx090; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hx090-est;z=hx090;run; %macro stat_66; *mean eqinc all R; proc means data=working mean noprint; var hx090; output out=est mean=est; data JRR; merge working est;by country;subpop_i=1;y=hx090-est;z=hx090;run; %macro jrr (local);* JRR variable; %do i=1 %to &local; ; proc univariate data=working3 noprint; output out=str_notuse mean=stratum mean=w_i; var stratum w_c;where psu eq &i;run; data str_notuse;set str_notuse;pr=1;run; data working4;merge working3 str_notuse;by stratum;run; data working;set working4;where psu ne &i;if pr eq 1 then wj=wj_old*w_h/(w_h-w_i);else wj=wj_old;run; proc univariate data=working4 noprint;output out=info mean=country mean=ah mean=psu mean=stratum; var country ah psu stratum;where psu eq &i;run; %stat_&k; proc univariate data=jrr noprint; output out=est mean=est;var z;weight wj;where subpop_i eq 1;by country;run; data est; set est (keep= est country);run; data replicate; merge info est;by country;run; data h;set h replicate;run; %end; %macro Kish(local,index); proc univariate data=kish_input noprint;output out=ymean mean=ybar;var y;weight wj;by country;run; proc univariate data=kish_input noprint;output out=wmean mean=wbar;var wj;by country;run; data work;merge kish_input ymean wmean;by country; if &local eq 1 then zj_2=(y-ybar)**2;else zj_2=1; wjz_2=(wj/wbar)*zj_2;wj_2z_2=((wj/wbar)**2)*zj_2;run; proc univariate data=work noprint;output out=sums sum=wjz_2_sum sum=wj_2z_2_sum n=n; var wjz_2 wj_2z_2;by country;run; data kish_output (keep=kish index);set sums;se_srs=sqrt(wjz_2_sum/(n*(n- 1)));index=&index; 21

22 se_wt=sqrt(wj_2z_2_sum/(n*(n-1)));kish=se_wt/se_srs;run; ***********PROGRAM***************************************************; /*FOR MEASURES FROM H FILES: STAT 1--32;*/ data h; set silc06.h; if hx040 eq 1 then hhs_size=1; if hx040 eq 2 then hhs_size=2; if hx040 eq 3 then hhs_size=3; if hx040 ge 4 then hhs_size=4; run; data original_h; set h; country=1; rename hb030=hid; rename db090=wt; run; /*FOR MEASURES FROM P FILES: STAT ;*/ data original_p; set silc06.p ; country=1; rename px030=pid; rename pb040=wt; run; /*FOR MEASURES FROM R FILES: STAT ;*/ data original_r; set silc06.r; if rx020 lt 25 then age_class=1; if (25 le rx020 le 34) then age_class=2; if (35 le rx020 le 44) then age_class=3; if (45 le rx020 le 54) then age_class=4; if (55 le rx020 le 64) then age_class=5; if (rx020 ge 65) then age_class=6; country=1; rename rb050=wt; rename rb030=pid; run; %macro choose_options(psu,index1,index2); data stat;set stat0;run; data kish;set kish0;run; %macro cycle (ciclo); %do k=&index1 %to &ciclo; title 'cycle' &k; %if &k le 32 %then %do; data working_pop_1;set original_h;run; %end; %if ((&k ge 33)and(&k le 57)) %then %do; data working_pop_1;set original_p;run; %end; %if &k ge 58 %then %do; data working_pop_1;set original_r;run; %end; data working_pop; set working_pop_1;wj=wt;run; proc means data=working_pop noprint; output out=sum_w sum=sum_w;by country;var wj;run; data working_pop; merge working_pop sum_w;by country;wj=(wt)/sum_w;run; proc sort data=working_pop;by stratum;run; proc univariate data=working_pop noprint;output out=weight_str sum=w_h;var wj;by stratum;run; proc sort data=working_pop;by psu;run; proc univariate data=working_pop noprint; output out=weight_notuse sum=w_c;var wj;by psu;run; proc sort data=working_pop;by stratum;run; data working2;merge working_pop weight_str;by stratum;run; proc sort data=working2;by psu;run; data working3;merge working2 weight_notuse;by psu;wj_old=wj;run; 22

23 data h;set h0;run; %jrr(&psu); data h;set h;where country ne 0;run; data working;set working_pop;run; %stat_&k; data kish_input;set jrr;run; %kish(1,&k); data kish;set kish kish_output;where index gt 0;run; proc univariate data=jrr noprint; output out=est mean=est n=n;var z;weight wj;where subpop_i eq 1;by country;run; proc univariate data=h noprint;output out=jks mean= ah; var ah; by stratum;run; proc sort data=h;by country stratum;run; proc univariate data=h noprint;output out=jkm sum= yhsum_stat;var est;by country stratum;run; proc sort data=jkm;by stratum;run; proc sort data=jks;by stratum;run; data jk;merge jkm jks;by stratum;run; data jk;set jk;yh_stat=yhsum_stat/ah;run; proc sort data=h;by stratum;run; proc sort data=jk;by stratum;run; data prova;merge h jk;by stratum;factor=(ah-1)/ah;run; data jk2;set prova;statdif2=(est-yh_stat)**2;run; proc univariate data=jk2 noprint;output out=var_stat sum=stat_v;var statdif2;weight factor;by country;run; data se_stat; set var_stat;stat_se=stat_v**0.5;run; data stat_act (keep= est stat_se n index);merge est se_stat;by country;index=&k;run; data stat;set stat stat_act;run; proc freq data=stat_act;table index;run; %end; %cycle(&index2); data JRR;set stat;where index ne 0;run; data output(keep=index est stat_se n kish);merge jrr kish;by index;run; data h0;input country ah psu stratum est;cards; ;run; data stat0;input est stat_se index;cards; ;run; data kish0;input kish index;cards; 0 0 ;run; %choose_options(200,32,33); *********************CHANGE NUMBERS HERE*********************; data Jrr_results (drop=index);set output; if index eq 1 then Measure='mean HY010 if index eq 2 then Measure='mean HY020'; if index eq 3 then Measure='mean HY022'; if index eq 4 then Measure='mean HY023'; if index eq 5 then Measure='mean HY040n'; if index eq 6 then Measure='mean HY040g'; if index eq 7 then Measure='mean HY050n'; if index eq 8 then Measure='mean HY050g'; if index eq 9 then Measure='mean HY060n'; if index eq 10 then Measure='mean HY060g'; '; 23

24 if index eq 11 then Measure='mean HY070n'; if index eq 12 then Measure='mean HY070g'; if index eq 13 then Measure='mean HY080n'; if index eq 14 then Measure='mean HY080g'; if index eq 15 then Measure='mean HY090n'; if index eq 16 then Measure='mean HY090g'; if index eq 17 then Measure='mean HY100n'; if index eq 18 then Measure='mean HY100g'; if index eq 19 then Measure='mean HY110n'; if index eq 20 then Measure='mean HY110g'; if index eq 21 then Measure='mean HY120n'; if index eq 22 then Measure='mean HY120g'; if index eq 23 then Measure='mean HY130n'; if index eq 24 then Measure='mean HY130g'; if index eq 25 then Measure='mean HY140n'; if index eq 26 then Measure='mean HY140g'; if index eq 27 then Measure='mean HY145n'; if index eq 28 then Measure='mean eqinc hhs=1'; if index eq 29 then Measure='mean eqinc hhs=2'; if index eq 30 then Measure='mean eqinc hhs=3'; if index eq 31 then Measure='mean eqinc hhs=4'; if index eq 32 then Measure='mean eqinc all hhs'; if index eq 33 then Measure='mean PY010n'; if index eq 34 then Measure='mean PY010g'; if index eq 35 then Measure='mean PY020n'; if index eq 36 then Measure='mean PY020g'; if index eq 37 then Measure='mean PY035n'; if index eq 38 then Measure='mean PY035g'; if index eq 39 then Measure='mean PY050n'; if index eq 40 then Measure='mean PY050g'; if index eq 41 then Measure='mean PY070n'; if index eq 42 then Measure='mean PY070g'; if index eq 43 then Measure='mean PY080n'; if index eq 44 then Measure='mean PY080g'; if index eq 45 then Measure='mean PY090n'; if index eq 46 then Measure='mean PY090g'; if index eq 47 then Measure='mean PY100n'; if index eq 48 then Measure='mean PY100g'; if index eq 49 then Measure='mean PY110n'; if index eq 50 then Measure='mean PY110g'; if index eq 51 then Measure='mean PY120n'; if index eq 52 then Measure='mean PY120g'; if index eq 53 then Measure='mean PY130n'; if index eq 54 then Measure='mean PY130g'; if index eq 55 then Measure='mean PY140n'; if index eq 56 then Measure='mean PY140g'; if index eq 57 then Measure='mean PY200g'; if index eq 58 then Measure='mean eqinc class age=1'; if index eq 59 then Measure='mean eqinc class age=2'; if index eq 60 then Measure='mean eqinc class age=3'; if index eq 61 then Measure='mean eqinc class age=4'; if index eq 62 then Measure='mean eqinc class age=5'; if index eq 63 then Measure='mean eqinc class age=6'; if index eq 64 then Measure='mean eqinc rb090=1'; if index eq 65 then Measure='mean eqinc rb090=2'; if index eq 66 then Measure='mean eqinc all R'; run; 24

25 ANNEX II: Illustrative output est stat_se n kish Measure mean HY mean HY mean HY mean HY mean HY040n mean HY040g mean HY050n mean HY050g mean HY060n mean HY060g mean HY070n mean HY070g mean HY080n mean HY080g mean HY090n mean HY090g mean HY100n mean HY100g mean HY110n mean HY110g mean HY120n mean HY120g mean HY130n mean HY130g mean HY140n mean HY140g mean HY145n mean eqinc hhs= mean eqinc hhs= mean eqinc hhs= mean eqinc hhs= mean eqinc all h mean PY010n 25

26 mean PY010g mean PY020n mean PY020g mean PY035n mean PY035g mean PY050n mean PY050g mean PY070n mean PY070g mean PY080n mean PY080g mean PY090n mean PY090g mean PY100n mean PY100g mean PY110n mean PY110g mean PY120n mean PY120g mean PY130n mean PY130g mean PY140n mean PY140g mean PY200g mean eqinc class age= mean eqinc class age= mean eqinc class age= mean eqinc class age= mean eqinc class age= mean eqinc class age= mean eqinc rb090= mean eqinc rb090= mean eqinc all R 26

27 ANNEX III: Technical note on JRR procedure for estimating variance and design effect Jackknife Repeated Replication (JRR) for variance estimation The Jackknife Repeated Replication (JRR) is one of a class of methods for estimating sampling errors from comparisons among sample replications which are generated through repeated sampling of the same parent sample. Each replication needs to be a representative sample in itself and to reflect the full complexity of the parent sample. The basic model of the JRR may be summarised as follows. Consider a design in which two or more primary units have been selected independently from each stratum in the population. Within each primary sampling unit (PSU), sub-sampling of any complexity may be involved, including weighting of the ultimate units. In the standard version, each JRR replication can be formed by eliminating one sample PSU from a particular stratum at a time, and increasing the weights of the remaining sample PSUs in that stratum appropriately so as to obtain an alternative but equally valid estimate to that obtained from the full sample. Briefly, the standard JRR involves the following. Let y be a full-sample estimate of any complexity, and y (hi) be the estimate produced using the same procedure after eliminating primary unit i in the stratum h and increasing the weight of the remaining ( a h 1) units in the stratum by an appropriate factor g h. Let y (h) be the simple average of the y (hi) over a h values of i in h. The variance of y is then estimated as: ah 1 2 (1 f h ) ( y hi) y( h) ) var( y ) = (. [1] h ah i A possible variation may be replacing y (h), the simple average of the y (hi) over the a h replication created from h, by the full-sample estimate of y. ah 1 2 (1 f h ) ( y hi) y) var( y ) = (. [2] h ah i Concerning the re-weighting the of units in a stratum after dropping one unit, normally the factor g is taken as: h ah g h =. [3] a 1 h However, a different form of g h can be used for practical reasons: g w h h = [4] wh whi where w h = w hi, w = i hi w hij j, the sum of sample weights of ultimate units j in the primary selection i. This form retains the total weight of the included sample cases unchanged across the replications created the same total as that for the full-sample. With sample weights scaled such that their sum is equal (or proportional) to some external more 27