Data and model cross-validation to improve accuracy of microsimulation results: Estimates for the polish household budget survey

The majority of large scale household surveys conducted by statistical offices or private survey agencies are designed to be representative of the population which the respective samples are drawn from. Due to frequent non-random survey participation this representativeness is usually less than perfect and the problems of under-representation of certain groups of the population - for example the very rich or the very poor - have been long recognized (United Nations, 2011; Schräpler, 2002; Korinek et al., 2006; Riphahn & Serfling, 2005). As we demonstrate using the example of the Polish Household Budget Surveys, if this under- or over-representation of certain groups is unaccounted for in the process of generating population grossing-up weights, the resulting population structure may differ substantially from other official statistics and administrative records. This in turn has significant consequences for the accuracy of tax and benefit simulations using microsimulation models and thus the reliability of the models for the purpose of policy analysis (Klevmarken, 2002). Because validity of any microsimulation model relies, to a large extent, on the degree of correspondence between model outcomes and administrative records, significant deviations in terms of the age or economic activity distribution, and the resulting simulation discrepancies might lead to questioning of the models’ role for policy purposes. In such cases even if model calculations for each particular household are correct, the grossed-up values are bound to be wrong.

We examine the data of the Polish Household Budget Surveys (PHBS) for years 2006–2011 from the perspective of tax and benefit microsimulation. The exercise presented in this paper serves primarily the purpose of improving consistency of microsimulation results with administrative data on aggregate tax burden and benefit expenditure. We are thus far from either questioning the general approach of the Polish Central Statistical Office (CSO) to the generation of PHBS grossing- up weights or from arguing that our approach should be applied more broadly in other applications of household micro-level data. We show, however, that a relatively simple method of data re- weighting along the lines of Gomulka (1992), Deville and Sarndal (1992) and Creedy and Tuckwell (2004), which has recently been applied widely in various types of micro-data analysis (e.g.: Brewer et al., 2009; Navicke et al., 2013; O’Donoghue and Loughrey, 2014), can significantly improve the accuracy of tax and benefit microsimulations in many dimensions. We present different approaches to weight calibration and suggest key factors which ought to be considered in the process. Since these factors can be generalized to other datasets and countries, the analysis presented here could be applied to other data used for microsimulation purposes. We extend the weight calibration criteria which are used by the Polish CSO in three stages. In the first stage, the calibration of weights is done with respect to demographic variables (e.g.: Cai, Creedy & Kalb, 2006). In the second stage we additionally include the number of recipients of main income sources, while in the third use a process of “cross-validation” where we calibrate population weights in the data with respect to a set of tax identifiers related directly to microsimulation.

The second and third stages of this exercise generate significant improvements in terms of the performance of the tax and benefit microsimulation with respect to a chosen set of key tax and benefit system parameters, but in many instances correcting the age distribution on its own also improves the accuracy of microsimulation. The re-weighting demonstrates how a careful approach to household survey data could make microsimulation models much more reliable and thus applicable for policy analysis.

The rest of the paper is organised as follows. In Section 2 we briefly describe the Polish Household Budget Survey data used for the analysis including the sampling frame of the survey and the approach of the Central Statistical Office to the computation of population weights provided with the data, referred to as “baseline” weights. Using these weights in Section 3 we present the differences in the age distributions between the baseline PHBS data and official sources on demographics as well as the correspondence of economic status information in the data and administrative statistics. The divergence between these distributions forms the principal motivation for the weight calibration in the paper. In Section 3 we also show how these underlying differences find their reflection in discrepancies of microsimulation results using a number of key tax and benefit parameters from the microsimulation model SIMPL which is applied to the PHBS data (see e.g.: Bargain et al., 2007; Morawski et al., 2008). The method of weight re-calibration, which follows Gomulka (1992) and Creedy and Tuckwell (2004) is briefly discussed in Section 4, including details on different stages of calibration and discussion of factors we consider in the process. Results of re-weighting in the form of a comparison of tax and benefit microsimulation outcomes with administrative information is presented in Section 5. Consistency of the grossed-up population structure in the data in terms of demographics, income sources and tax identifiers has substantial influence on the accuracy of microsimulation. We show that weight adjustments for income sources and tax identifiers have significant implications for the level and trends in inequality indicators in Poland. Conclusions including some words of caution regarding the methods applied in this paper follow in Section 6.

The Polish Household Budget Survey (PHBS) is an annual representative survey covering in recent years over 37,000 Polish households. The first survey was conducted in 1957 and it has been a regular source of information on income, consumption and quality of life of Polish citizens. Through the years it has undergone a number of more and less significant methodological changes, related among other things to the political and economic transition after 1989 and various forms of standardization to international procedures, but the survey continues to collect detailed information on the household structure, income sources and household expenditure. The information covered by the survey includes:

• socio-demographic composition of the household;

• life quality and housing conditions;

• durable goods and housing equipment;

• economic activity of household members;

• level and sources of individual and household-level incomes;

• detailed household expenditures.

The PHBS has changed over the years, but fieldwork procedures and the overall methodology since 2006 have seen only minor modifications (Główny Urząd Statystyczny, 2011a). In the years covered by the analysis the sample includes all households with the exception of collective dwellings such as prisons, cloisters, retirement homes or boarding schools, which in total accounted for less than 1% of the whole population in 2011. The sampling methodology since 2006 targets 3132 of different dwellings in each month, which are selected for the survey giving a total of expected 37584 dwellings each year. Due to the possibility of multiple households in one dwelling and survey interruptions (which are not replaced with reserve households), the actual number of surveyed households may slightly deviate from the target, as summarized in Table 1.

The data from the PHBS has been used in a number of studies of incomes and consumption and has long been the main data source used in the Polish microsimulation model SIMPL (see e.g.: Brzezinski & Kostro, 2010; Brzezinski, 2010; Morawski & Myck, 2010; Haan & Myck, 2012; Myck, et al., 2013). Most of the information collected in the PHBS, and in particular incomes and expenditures, covers the survey period of one month. For every quarter of the year each household being surveyed in that quarter is once again asked to fill in a questionnaire regarding durable goods present in the household, as well as rare income and expenditure (e.g. buying or selling property, buying a car, health care services) and other sources of income such as employment fringe benefits.

Table 1 gives a summary of the number of households and individuals in the PHBS in the years covered by the analysis, and the split at the household and individual level by some main characteristics. Over the years we can observe the increasing number of people with higher education and the higher (unweighted) average age of participants in the survey. The average household size fell from over three individuals per household in 2006 to 2.87 in 2011.

Validation of survey data against other sources is notoriously problematic given various definitional differences and the nature of the specific survey. Thus not only grossing-up weights of the survey data will determine discrepancies between different sources of information. In this Section we present three groups of variables from the PHBS which are set against other data sources in a validation exercise using the baseline grossing-up weights provided by the CSO (and derived along the lines outlined above). These groups are:

• demographics: age, education, residence;

• economic status: employment, self-employment, pension and unemployment benefit receipt;

• microsimulation output: aggregated tax and benefit values; the number of tax payers and benefit recipients.

The grossed up values of these variables from the PHBS together with the most appropriate counterpart information from other sources are presented in Tables 2, 3 and 4 respectively. The information used to validate the PHBS data derives principally from CSO’s Statistical Yearbooks based on alternative data sources (principally on the National Census data from 2002 and 2011 which are updated using administrative records or surveys). Administrative information on taxes, insurance contributions and benefits comes from published and online statistics of the Ministry of Finance, the Ministry of Labour and Social Policy and the Polish Social Security Institution (ZUS).²

This choice of benchmark variables is driven primarily by the reliability of the sources to which we compared them. Demographic variables are based on the National Census and are updated by current registry data while in the case of the number of taxpayers or pension and benefit recipients the aggregate information comes directly from administrative sources, i.e. institutions responsible for tax collection and benefit payments.

As we can see from Table 2, the gross population of Poland in PHBS data using the CSO baseline weights accounts for about 98–99% of the total population in the official statistics. This small discrepancy is partly driven by lack of survey coverage of collective dwellings and may result from definitional differences concerning residence status.³ Looking at the population distribution by age, however, suggests significant under and over-representation of some of the age groups. Details for the years covered by the analysis are given in Figure 1 in the form of population pyramids by 5- year age groups. The dark-coloured bars represent the PHBS population, while the lighter coloured are the census-based official statistics. In all years that we examine we find over-representation of children and under-representation of those aged 20–49 in the PHBS data relative to external statistics, both among men and women. There is also some under-representation of the oldest groups of the population.

Figure 1

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This difference in the demographic structure of the population is surprising. Some of the discrepancy among older individuals could be explained by lack of coverage of collective dwellings like hospitals or retirement homes, although the latter are not very common in Poland and lack of coverage of collective dwellings in the survey affects other age groups as well. Lower numbers among those of working age could be partly related to temporary migrations. In case of children, there is however no obvious reason for the discrepancies other than over-representation of families with children in the survey.

Table 2 suggests also that the PHBS under-represents individuals with higher education. This under-representation is as high as 21%–27% for years 2006–2010 relative to other official statistics, but falls to only about 6% in 2011. In Table 3 we can see that relative to external statistics employees are over-represented in the sample by between 10–15% and the self-employed are under- represented, in particular in more recent years of data. We return to these two issues in the discussion of the factors we consider in the re-weighting process in Section 4. The PHBS data from years prior to 2010 significantly over-represents farmers which may be caused by definitional problems in survey and administrative data, but probably reflects also the fact that weights prior to 2010 were based on the 2002 Farming Census and the structure of farming in Poland saw substantial changes since then. The data beginning with 2010, with weights based on the 2010 Farming Census and the 2011 National Census, are much closer to other administrative records on the number of farmers. In Table 3 in addition to employment status comparisons we also present the correspondence of the PHBS data with administrative records with regard to the number of recipients of the main Social Security benefits. The correspondence of these numbers to official statistics differs in different years, but the numbers are generally close. The main exception are Family Pensions, which seem to be underreported by up to 26%. The most likely reason behind it is reporting accuracy related to the precise naming of pensions, which we discuss in Section 4.

The values presented in Table 4 compare direct output from the SIMPL microsimulation model to administrative statistics on the main elements of the tax and benefit system. We present the simulated number of individuals contributing to Social Security (SSC), Health Insurance (HI) and Personal Income Tax (PIT), and the number of recipients of Family Benefits including the principal Family Allowance (FA) and four main supplements (for large families: SLF, for starting school: SSS, for child birth: SCB, and education of disabled children: SEDC). In the case of each year we use the SIMPL microsimulation model to simulate the baseline tax and benefit system which operated in that year. Within the HI and PIT categories we show the total number of contributors and additionally list the numbers by those paying contributions on permanent employment and self-employment income. For PIT we also give the numbers of recipients of the Child Tax Credit, a generous tax credit for families with children introduced in 2007.

Simulated numbers for Social Security contributions are relatively close to the official figures, with an overestimate of 6.3% in 2011. As in the case of the employment status we overestimate Health Insurance contributions for the employees (by between 10% and 21%) and underestimate them for the self-employed (by 7%–17%). The number of people paying income taxes, on the other hand, overall matches relatively well with administrative statistics. However, since we are unable to account for the details of tax deductions among the self-employed, and cannot identify clearly the specific ways people file their taxes, the number of tax payers in this category is substantially higher compared to the official statistics. Given the over-representation of children in the data it is not surprising that the model significantly overestimates the number of recipients of the Child Tax Credit as well as the means-tested Family Benefits. In the latter case the basic Family Allowance is overestimated by about 32% in 2006 and by 17% in 2011, while the supplement to large families by as much as 104% in 2006 and 40% in 2011. Some of this overestimation might reflect non-take up, but the differences between supplements suggest that while the data generally over-represents families with children, it might be over-representing households with a high number of children to a much larger extent than households with one or two children.

In the weight calibration exercise we take the age distribution as the primary source of external data with respect to which the baseline weights are adjusted. This is then supplemented with information on a number of income sources and finally with a combination of selected income sources and a small number of variables simulated in the microsimulation model. The weight calibration exercise follows the approach of Vanderhoeft (2001) and Creedy (2004) described also in Deville and Sarndal (1992).

The main principle of the approach is that it assumes validity of the “target” data to which the weights are calibrated. The calibration procedure does not change the observations themselves. Instead, it changes the household weights in such a way as to represent different aggregated population characteristics in the best possible way, taking into account a “minimum-distance” criterium which minimizes the sum of differences between the old and new weights. Having variables and observations, we have a vector x_jk, where j = 1, 2, …, m and k = 1, 2, …, n. We can then define population totals for every variable such that $t_j=\sum _{k=1}^n{d}_k{x}_{jk}$ where are the initial (baseline) weights.

The goal of the exercise is to minimise the distance w_kG(·), where G(·) is a distance function:

subjected to m calibration constraints:

where w_k are the new calibrated weights equal to w_k = g_kd_k, with g_k representing the factors by which baseline weights are adjusted, and t^′_k are the target population totals, set as targets for the calibration exercise.

Different distance functions can be used for the calibration procedure. The approach used here follows the Deville-Sarndal distance function (Deville & Sarndal, 1992), that eliminates negative weights and constrains the new weights so that they do not exceed a specified lower and upper bound, relative to the old weights. The optimization problem (1) constrained by (2) is solved numerically (for more details on properties of different distance functions see: Deville & Sarndal, 1992, Vanderhoeft, 2001 and Creedy, 2004). Calibration procedure according to the above methodology is available in Stata in the REWEIGHT package of Pacifico (2010). The Deville and Sarndal (1992) distance function allows setting the minimum and maximum factors by which new weights may differ relative to the old ones, and the package permits automatic adjustment of these values once the initial factors prove too restrictive for the iterative algorithm.

Calibration of grossing-up weights can result in substantial improvements in the accuracy of microsimulation results. Important gains in the performance of the Polish microsimulation model SIMPL appear already after correcting for the distribution of age (S1), which is probably the least controversial and arbitrary adjustment. Interestingly, in our application these changes are neutral from the point of view of the overall income distribution. More detailed re-weighting using indicators related to income sources (S2) and tax identifiers (S3) result in further overall improvement of the accuracy of microsimulation, and these significantly change the distribution of income in terms of the level of inequality and also affect the pattern of changes in inequality over time.

One should approach re-weighting of data with caution and bear in mind a set of important factors. First of all, it is important to identify the most likely reasons for the observed discrepancies between the survey data and external statistics, in particular taking into account the way the survey weights are constructed. It needs to be noted as well that the comparison will be affected not only by the representativeness of the survey but also by such factors as accuracy of external statistics, definitional correspondence between survey data and external statistics, reporting accuracy of the survey and coverage of external data. In the Polish case as far as the age distribution is concerned, we can count on reliable and directly comparable external data, and there is also little reason for definitional discrepancy or survey reporting inaccuracies. In such cases the most likely reason for discrepancies is selective survey non-response with respect to these characteristics and the fact that baseline weights do not account for it. Adjusting the weights in such cases, in particular if it also accounts for categories taken into consideration in generating the baseline weights, seems justified, and as we saw in Section 5, might bring substantial gains in the accuracy of simulation results.

When there are reasons to believe that discrepancies between survey and external data are consequences of factors other than survey representativeness, one should approach reweighting with a degree of caution. Our analysis pointed out examples of discrepancies which are most likely results of other factors we considered. These other factors affected the comparisons of the number of recipients of family pensions (survey reporting accuracy), number of people with higher education (accuracy of external statistics) and employment status (definitional correspondence).

In the third stage of re-weighting and in the additional exercise presented in Section 5.4 we used microsimulation output to re-weight the data. This approach needs to assume accuracy of the microsimulation output at the level of individual households, and we argued that one should only use it in cases when the scope for computational error is small and when the benefits of using microsimulation output outweigh the possible costs. This will for example be the case when there are problems with finding high quality external data to compare the survey to, in particular in the case of problems with the factors outlined above. For example, in our analysis in Stage 3 of re- weighting, we only used the number of contributors to Health Insurance identified in microsimulation analysis, rather than its aggregate values. From this point of view the third stage of re-weighting might be seen as a trade-off between using more directly comparable data on contributions at the cost of having to take advantage of microsimulation information. In the extension of Stage 3 we showed that using more detailed microsimulation output, in this case the aggregate value of tax advantages from joint taxation, can bring further benefits in terms of microsimulation accuracy. In such cases however, one has to be aware that any error in microsimulation might have substantial consequences for the accuracy of the model in respects other than the targeted outcome.

The final note of caution relates to the issue of the effect of re-weighting on the so called residual groups, i.e. groups of the population which are largely missing from the specified calibration targets. The best example of such groups in our case are farmers. The potential definitional discrepancies and lack of accuracy of external data which we discussed in Section 3, is the main reason why we leave them out of the calibration process, but the comparison of Stage 2 and 3 of re-weighting very clearly reflects the effects of calibrating a high number of targets (in Stage 2) on this residual group. We can see for example in Table 6 that the second stage of the calibration has a very substantial effect on the number of farmers in the data, with much less pronounced implications of using the smaller set of calibration targets under Stage 3.

Re-weighting ought to take into account a number of factors relating to the way survey data is collected and the nature of external statistics. As the exercise in this paper shows, careful approach to data re-weighting may significantly improve accuracy of microsimulation and thus make the analysis much better suited for the purpose of policy analysis. Various approaches to re-weighting are possible and some of them will have substantial consequences for the resulting distribution of income in the survey data and the implied levels and trends in inequality. Such differences in the distribution of income resulting from re-weighting in our view deserve further careful analysis.

1. 1
   Error Measures For Generalizing About Forecasting Methods: Empirical Comparisons

   1. JS Armstrong
   2. F Collopy

   (1992)

   International Journal of Forecasting 8:69–80.

   • Google Scholar
2. 2
   As SIMPL As That: Introducing a Tax-Benefit Microsimulation Model for Poland. IZA Discussion Papers 2988

   1. O Bargain
   2. L Morawski
   3. M Myck
   4. M Socha

   (2007)

   Bonn: Institute for the Study of Labor (IZA).

   • Google Scholar
3. 3
   Micro-simulating Child Poverty in Great Britain in 2010 and 2020. Working Paper 06–31

   1. M Brewer
   2. J Browne
   3. R Joyce
   4. H Sutherland

   (2009)

   National Poverty Centre.

   • Google Scholar
4. 4
   Income Affluence in Poland

   1. M Brzeziński

   (2010)

   Social Indicators Research 99:285–299.

   • Google Scholar
5. 5
   Income and consumption inequality in Poland, 1998–2008

   1. M Brzeziński
   2. K Kostro

   (2010)

   Bank i Kredyt 41:45–72.

   • Google Scholar
6. 6
   Accounting For Population Ageing In Tax Microsimulation Modelling By Survey Reweighting. Australian Economic Papers

   1. L Cai
   2. J Creedy
   3. G Kalb

   (2006)

   18–37, Accounting For Population Ageing In Tax Microsimulation Modelling By Survey Reweighting. Australian Economic Papers, 45, 1.

   • Google Scholar
7. 7
   Microeconometrics: Methods and Applications

   1. A Cameron
   2. P Trivedi

   (2005)

   Cambridge: University Press.

   • Google Scholar
8. 8
   Survey Reweighting for Tax Microsimultaion Modeling

   1. J Creedy

   (2004)

   Research on Economic Inequality 12:229–249.

   • Google Scholar
9. 9
   Reweighting Household Surveys for Tax Microsimulation Modelling: An Application to the New Zealand Household Economic Survey

   1. J Creedy
   2. I Tuckwell

   (2004)

   Australian Journal of Labour Economics 7:71–88.

   • Google Scholar
10. 10
    Calibration Estimators in Survey Sampling

    1. J-C Deville
    2. C-E Sarndal

    (1992)

    Journal of the American Statistical Association 87:376–382.

    • Google Scholar
11. 11
    Grossing-up revisited

    1. J Gomulka

    (1992)

    In: R Hancock, H Sutherland, editors. Microsimulation Models for Public Policy Analysis: New Frontiers. London: London School of Economics and Political Science. pp. 121–132.

    • Google Scholar
12. 12
    Rocznik demograficzny

    1. Główny Urząd Statystyczny

    (2006)

    Warszawa: Zakład Wydawnictw Statystycznych.

    • Google Scholar
13. 13
    Mały rocznik statystyczny Polski

    1. Główny Urząd Statystyczny

    (2006)

    Warszawa: Zakład Wydawnictw Statystycznych.

    • Google Scholar
14. 14
    Rocznik Statystyczny Rzeczpospolitej Polskiej

    1. Główny Urząd Statystyczny

    (2006)

    Warszawa: Zakład Wydawnictw Statystycznych.

    • Google Scholar
15. 15
    Ludność. Stan i struktura w przekroju terytorialnym

    1. Główny Urząd Statystyczny

    (2008)

    Warszawa: Departament Badań Demograficznych.

    • Google Scholar
16. 16
    Metodologia badania budżetów gospodarstw domowych

    1. Główny Urząd Statystyczny

    (2011a)

    Warszawa: Departament Warunków Życia.

    • Google Scholar
17. 17
    Praca nierejestrowana w Polsce w 2010 roku

    1. Główny Urząd Statystyczny

    (2011b)

    Warszawa: Departament Pracy.

    • Google Scholar
18. 18
    Wyniki wstępne Narodowego Spisu Powszechnego Ludności i Mieszkań 2011

    1. Główny Urząd Statystyczny

    (2011)

    Warszawa: Zakład Wydawnictw Statystycznych.

    • Google Scholar
19. 19
    Multi-family households in a labour supply model: a calibration method with application to Poland

    1. P Haan
    2. M Myck

    (2012)

    Applied Economics 44:2907–2919.

    • Google Scholar
20. 20
    Statistical Software Components

    1. SP Jenkins

    (1999)

    INEQDECO: Stata module to calculate inequality indices with decomposition by subgroup, Statistical Software Components, Boston College Department of Economics.

    • Google Scholar
21. 21
    Statistical inference in micro-simulation models: incorporating external information

    1. NA Klevmarken

    (2002)

    Mathematics and Computers in Simulation 59:255–265.

    • Google Scholar
22. 22
    Survey nonresponse and the distribution of income

    1. A Korinek
    2. JA Mistiaen
    3. M Ravallion

    (2006)

    The Journal of Economic Inequality 4:33–55.

    • Google Scholar
23. 23
    Budżety gospodarstw domowych w 2011 r

    1. P Łysoń

    (2012)

    Warszawa: Główny Urząd Statystyczny.

    • Google Scholar
24. 24
    Evaluating Accuracy (or Error) Measures. Working Paper 1995/18/TM, INSEAD

    1. S Makridakis
    2. M Hibon

    (1998)

    Evaluating Accuracy (or Error) Measures. Working Paper 1995/18/TM, INSEAD.

    • Google Scholar
25. 25
    Statistical Software Components

    1. A Mander

    (2007)

    RADAR: Stata module to draw radar (spider) plots, Statistical Software Components, Boston College Department of Economics.

    • Google Scholar
26. 26
    Informacja dotycząca rozliczenia podatku dochodowego od osób fizycznych

    1. Ministerstwo Finansów

    (2006)

    Warszawa: Departament Podatków Dochodowych.

    • Google Scholar
27. 27
    Preferencje podatkowe w Polsce 3

    1. Ministerstwo Finansów

    (2012)

    Warszawa: Ministerstwo Finansów.

    • Google Scholar
28. 28
    Informacja o realizacji świadczeń rodzinnych

    1. Ministerstwo Pracy i Polityki Społecznej

    (2006)

    Warszawa: Departament Polityki Rodzinnej.

    • Google Scholar
29. 29
    Model podatkowo-świadczeniowy dla Polski- SIMPL2003

    1. L Morawski
    2. O Bargain
    3. M Myck
    4. M Socha

    (2008)

    Wiadomości Statystyczne 4:30–38.

    • Google Scholar
30. 30
    ‘Klin’-ing up: Effects of Polish tax reforms on those in and on those out

    1. L Morawski
    2. M Myck

    (2010)

    Labour Economics 17:556–566.

    • Google Scholar
31. 31
    Financial support for families with children and its trade-offs: balancing redistribution and parental work incentives

    1. M Myck
    2. A Kurowska
    3. M Kundera

    (2013)

    Baltic Journal of Economics 13:59–83.

    • Google Scholar
32. 32
    Nowcasting Indicators of Poverty Risk in the European Union: A Microsimulation Approach. EUROMOD Working Papers EM11/13

    1. J Navicke
    2. O Rastrigina
    3. H Sutherland

    (2013)

    EUROMOD at the Institute for Social and Economic Research.

    • Google Scholar
33. 33
    A Simplex Method for Function Minimization

    1. JA Nelder
    2. R Mead

    (1965)

    The Computer Journal 7:308–313.

    • Google Scholar
34. 34
    Ludność: stan i struktura demograficzno-społeczna: Narodowy Spis Powszechny Ludności i Mieszkań 2011

    1. L Nowak

    (2013)

    Warszawa: Zakład Wydawnictw Statystycznych.

    • Google Scholar
35. 35
    Nowcasting in Microsimulation Models: A Methodological Survey

    1. C O’Donoghue
    2. J Loughrey

    (2014)

    Journal of Artificial Societies and Social Simulation, 17, 4.

    • Google Scholar
36. 36
    Integrating output in Euromod: an assessment of the sensitivity of multi country microsimulation results. EUROMOD Working Papers EM1/99

    1. C O’Donoghue
    2. H Sutherland
    3. F Utili

    (1999)

    EUROMOD at the Institute for Social and Economic Research.

    • Google Scholar
37. 37
    REWEIGHT: The Stata command for survey reweighting. Center for the Analysis of Public Policies (CAPP) 0079

    1. D Pacifico

    (2010)

    Universita di Modena e Reggio Emilia.

    • Google Scholar
38. 38
    Item non-response on income and wealth questions

    1. RT Riphahn
    2. O Serfling

    (2005)

    Empirical Economics 30:521–538.

    • Google Scholar
39. 39
    Respondent Behavior in Panel Studies: A Case Study for Income- Nonresponse by Means of the German Socio-Economic Panel (GSOEP). Discussion Paper 299

    1. J-P Schräpler

    (2002)

    DIW-Berlin.

    • Google Scholar
40. 40
    Canberra Group Handbook on Household Income Statistics

    1. United Nations

    (2011)

    Canberra Group Handbook on Household Income Statistics, United Nations.

    • Google Scholar
41. 41
    Generalised Calibration at Statistics Belgium: SPSS Module G-CALIB-S and Current Practices. Working Paper 3

    1. C Vanderhoeft

    (2001)

    Brussels: Statistics Belgium.

    • Google Scholar
42. 42
    Ważniejsze informacje z zakresu ubezpieczeń społecznych

    1. Zakład Ubezpieczeń Społecznych

    Warszawa: Departament Statystyki i Prognoz Aktuarialnych.

    • Google Scholar

Author details

1. Michał Myck

   Centre for Economic Analysis, Poland

   For correspondence

   mmyck@cenea.org.pl

2. Mateusz Najsztub

   Centre for Economic Analysis, Poland

   For correspondence

   mnajsztub@cenea.org.pl