Abstract
Policy measures to combat low literacy are often targeted at municipalities or regions with low levels of literacy. However, current surveys on literacy do not contain enough observations at this level to allow for reliable estimates when using only direct estimation techniques. To provide more reliable results at a detailed regional level, alternative methods must be used.
The aim of this article is to obtain literacy estimates at the municipality level using model-based small area estimation techniques in a hierarchical Bayesian framework. To do so, we link Dutch Labour Force Survey data to the most recent literacy survey available, that of the Programme for the International Assessment of Adult Competencies (PIAAC). We estimate the average literacy score, as well as the percentage of people with a low literacy level. Variance estimators for our small area predictions explicitly account for the imputation uncertainty in the PIAAC estimates. The proposed estimation method improves the precision of the area estimates, making it possible to break down the national figures by municipality.
References
1.
Arima, S., W.R. Bell, G.S. Datta, C. Franco, and B. Liseo. 2017. “Multivariate Fay-Herriot Bayesian estimation of small area means under functional measurement error.” Journal of the Royal Statistical Society, Series A 180: 1191–1209 DOI: https://doi.org/10.1111/rssa.12321.
2.
Battese, G.E., R.M. Harter, and W.A. Fuller. 1988. “An Error-Components Model for Prediction of County Crop Areas Using Survey and Satellite Data.” Journal of the American Statistical Association 401: 28 – 36. DOI: https://doi.org/10.1080/01621459.1988.10478561.
3.
Boonstra, H.J. 2015. Package ‘hbsae’ (version 1.0). Available at: https://cran.r-project.org/web/packages/hbsae/hbsae.pdf (accessed December 2015).
4.
Boonstra, H.J., J.A. van den Brakel, B. Buelens, S. Krieg, and M. Smeets. 2008. “Towards small area estimation at Statistics Netherlands.” METRON International Journal of Statistics LXVI: 21–49. Available at: https://EconPapers.repec.org/RePEc:mtn:ancoec:080102 (accessed April 2020).
5.
Buisman, M., J. Allen, D. Fouarge, W. Houtkoop, and R. van der Velden. 2013. PIAAC: Kernvaardigheden voor werk en leven. Resultaten van de Nederlandse survey 2012 , Den Bosch/Maastricht: ECBO/ROA.
6.
Casas-Cordero, C., J. Encina, and P. Lahiri. 2016. “Poverty mapping for the Chilean Comunas.” In Analysis of Poverty Data by Small Area Estimation , edited by M. Pratesi, 379–403. Hoboken: Wiley. DOI: https://doi.org/10.1111/j.1467-9787.2007.00538.x
7.
Coulombe, S. and J.F. Tremblay. 2007. “Skills, Education, and Canadian Provincial Disparity.” Journal of Regional Science 47: 965–991. DOI: https://doi.org/10.2307/2669921.
8.
Datta, G., P. Lahiri, T. Maiti, and K. Lu. 1999. “Hierarchical Bayes Estimation of Unemployment Rates for the States of the U.S.” Journal of the American Statistical Association 448: 1074–1082.
9.
Elbers, C., J.O. Lanjouw, and P. Lanjouw. 2003. “Micro estimation of poverty and inequality.” Econometrica 71: 355 – 364. DOI: https://doi.org/10.1111/1468-0262.00399.
10.
Fay, R.E. and R.A. Herriot. 1979. “Estimates of income for small places: An application of James-Stein procedures to census data.” Journal of the American Statistical Association 366: 269–277. DOI: https://doi.org/10.2307/2286322.
11.
Ganzeboom, H.B.G., P.M. de Graaf, and D.J. Treiman. 1992. “A Standard International Socio-Economic Index of Occupational Status.” Social Science Research 21: 1–56. DOI: https://doi.org/10.1016/0049-089X(92)90017-B.
12.
Gibson, A. and P. Hewson. 2012. “2011 Skills for Life Survey: Small Area Estimation Technical Report.” BIS Research Report 81C. Available at: https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/36077/12-1318-2011-skills-for-life-small-area-estimation-technical.pdf (accessed November 2018).
13.
Hanushek, E.A. and L. Woessmann. 2008. “The Role of Cognitive Skills in Economic Development.” Journal of Economic Literature 46: 607–668. DOI: https://doi.org/10.3386/w15949.
14.
Hanushek, E.A. and L. Woessmann. 2011. The Economics of International Differences in Educational Achievement. In Handbook of the Economics of Education , Vol. 3: 89–200. Amsterdam: North Holland.
15.
Hastie, T., R. Tibshirani, and J. Friedman. 2001. The elements of statistical learning . Springer: New York.
16.
Hodges, J.S. and D.J. Sargent. 2001. “Counting degrees of freedom in hierarchical and other richly parameterized models.” Biometrika 88: 367–379. DOI: https://doi.org/10.1093/biomet/88.2.367.
17.
Johnson, E.G. and K.F. Rust. 1992. “Sampling and Weighting in the National Assessment.” Journal of Educational and Behavioral Statistics 17: 111–129. DOI: https://doi.org/10.2307/1165165.
18.
Lohr, S. and N. Prasad. 2003. “Small Area Estimation with Auxiliary Survey Data.” The Canadian Journal of Statistics 31: 383–396. DOI: https://doi.org/10.2307/3315852.
19.
McHenry, P. 2014. “The Geographic Distribution of Human Capital: Measurement of Contributing Mechanisms.” Journal of Regional Science 54: 215–248. DOI: https://doi.org/10.1111/jors.12067.
20.
National Research Council. 2000. “Small Area Estimates of School-Age Children in Poverty: Evaluation of current methodology.” Committee on National Statisitcs , edited by C.F. Citro and G. Kalton. Washington, DC: National Academy Press.
21.
OECD. 2013a. OECD skills outlook 2013: first results from the survey of adult skills . Paris: OECD Publishing. DOI: https://doi.org/10.1787/9789264204256-en.
22.
OECD. 2013b. The Survey of Adult Skills – Reader’s Companion . Paris: OECD Publishing. DOI: https://doi.org/10.1787/9789264204027-en.
23.
OECD. 2013c. Technical Report of the Survey of Adult Skills (PIAAC) . Available at: http://www.oecd.org/site/piaac/publications.htm (accessed December 2015).
24.
Pokropek, A. and M. Jakubowski. 2013. Package ‘PIAAC tools’ (version 4.3). Available at: https://ideas.repec.org/c/boc/bocode/s457728.html (accessed September 2016).
25.
Pfeffermann, D. 2013. “New Important Developments in Small Area Estimation.” Statistical Science 28: 40–68. DOI: https://doi.org/10.1214/12-STS395.
26.
PricewaterhouseCoopers. 2013. Laaggeletterdheid in Nederland kent aanzienlijke maatschappelijke kosten. Internal Rapport, PWC, Amsterdam.
27.
Rao, J.N.K. and I. Molina. 2015. Small Area Estimation, Second Edition . New York: John Wiley and Sons.
28.
Rubin, D.B. 1996. “Multiple Imputation After 18 þ Years.” Journal of the American Statistical Association 434: 473–489. DOI: https://doi.org/10.2307/2291635.
29.
Särndal, C.E., B. Swensson, and J. Wretman. 1992. Model Assisted Survey Sampling . New York: Springer Verlag.
30.
Schmid, T., F. Bruckschen, N. Salvati, and T. Zbiranski. 2017. “Constructing sociodemographic indicators for national statistical institutes by using mobile phone data: estimating literacy rates in Senegal.” Journal of the Royal Statistical Society Series A (Statistics in Society) 180: 1163–1190. DOI: https://doi.org/10.1111/rssa.12305Y.
31.
Statistics Netherlands. 2010. “Methoden en definities Enquête Beroepsbevolking 2010.” Available at: https://www.cbs.nl/nl-nl/onze-diensten/methoden/onderzoeksomschrijvingen/aanvullende%20onderzoeksbeschrijvingen/enquete-beroepsbevolking-uitgebreideonderzoeksbeschrijving-2010 (accessed March 2018).
32.
Statistics Netherlands. 2011. “Methoden en definities Enquête Beroepsbevolking 2011.” Available at: https://www.cbs.nl/nl-nl/onze-diensten/methoden/onderzoeksomschrijvingen/aanvullende%20onderzoeksbeschrijvingen/enquete-beroepsbevolking-uitgebreideonderzoeksbeschrijving-2011 (accessed March 2018).
33.
Statistics Netherlands. 2012. “Methoden en definities Enquête Beroepsbevolking 2012.” Available at: https://www.cbs.nl/nl-nl/onze-diensten/methoden/onderzoeksomschrijvingen/aanvullende%20onderzoeksbeschrijvingen/enquete-beroepsbevolking-uitgebreideonderzoeksbeschrijving-2012 (accessed March 2018).
34.
Taylor, J., G. Moon, and L. Twigg. 2016. “Using geocoded survey data to improve the accuracy of multilevel small area synthetic.” Social Science Research 56: 108–116. DOI: https://doi.org/10.1016/j.ssresearch.2015.12.006.
35.
Thao, L.T.P. and R. Geskus. 2019. “A comparison of model selection methods for prediction in the presence of multiply imputed data.” Biometrical Journal 61: 343–356. DOI: https://doi.org/10.1002/bimj.201700232.
36.
Tighe, E., D. Livert, M. Barnett, and L. Saxe. 2010. “Cross-Survey Analysis to estimate low-incidence religious groups.” Sociological Methods & Research 39: 56–82. DOI: https://doi.org/10.1177/0049124110366237.
37.
Vaida, F. and S. Blanchard. 2005. “Conditional Akaike information for mixed effect models.” Biometrika 92: 351–370. DOI: https://doi.org/10.1093/biomet/92.2.351.
38.
Van den Brakel, J.A. and B. Buelens. 2015. “Covariate selection for small area estimation in repeated sample surveys.” Survey Methodology and Statistics in Transition , Special issue on Small Area Estimation, Vol.16: 523–540. DOI: https://doi.org/10.21307/stattrans-2015-031.
39.
Van den Brakel, J.A. and S. Krieg. 2015. “Dealing with small sample sizes, rotation group bias and discontinuities in a rotating panel design.” Survey Methodology 41: 267 – 296. Available at: https://www150.statcan.gc.ca/n1/pub/12-001-x/2015002/article/14231-eng.pdf (accessed April 2020).
40.
Van der Velden, R. and I. Bijlsma. 2018. “Effective skill: a new theoretical perspective on the relation between skills, skill use, mismatches and wages.” Oxford Economic Papers , Advance articles. DOI: https://doi.org/10.1093/oep/gpy028.
41.
World Bank. 2002. “How Low Can You Go? Combining Census and Survey Data for Mapping Poverty in South Africa.” Journal of African Economies 11: 169–200. DOI: https://doi.org/10.1093/jae/11.2.169.
42.
Yamamoto, K. 2014. Using PIAAC Data for Producing Regional Estimates . Working Paper, Educational Testing Service, Princeton.
43.
Ybarra, L.M.R. and S.L. Lohr. 2008. “Small area estimation when auxiliary information is measured with error.” Biometrika 95: 919–931. DOI: https:///doi.org/10.1093/biomet/asn048.
44.
You, Y., J.N.K. Rao, and P. Dick. 2004. “Benchmarking Hierarchical Bayes Small Area Estimators in the Canadian Census Undercoverage Estimation.” Statistics in Transition 6: 631–640. Available at: https://www.semanticscholar.org/paper/BENCHMARKING-HIERARCHICAL-BAYES-SMALL-AREA-IN-THE-You-Rao/efaafa565aa134-fe0943f03bbad15278eb228e3a (accessed April 2020).
45.
You, Y., J. Rao, and J. Gambino. 2003. “Model-based unemployment rate estimation for the Canadian Labour Force Survey: A Hierarchical Bayes approach.” Survey Methodology 29: 25–32. Available at: https://www150.statcan.gc.ca/n1/en/catalogue/12-001-X20030016602 (accessed April 2020).