SMALL AREA ESTIMATION OF UNEMPLOYMENT FOR SOUTH AFRICAN LABOUR MARKET STATISTICS. Jean-Marie Vianney Hakizimana

Transcription

1 SMALL AREA ESTIMATION OF UNEMPLOYMENT FOR SOUTH AFRICAN LABOUR MARKET STATISTICS by Jean-Mare Vanney Hakzmana A research report submtted to the Faculty of Scence, Unversty of Wtwatersrand n fulflment of the requrements for the degree of Master of Scence Supervsor: Professor Jacquelne Galpn School of Statstcs and Actuaral Scence Unversty of Wtwatersrand Johannesburg, 2011

2 Declaraton I declare that ths research report s my own, unaded work. It s beng submtted to the Faculty of Scence, Unversty of Wtwatersrand n fulflment of the requrements for the degree of Master of Scence. The report has not been submtted before for any degree or examnaton at any other Unversty. Sgnature: Name: Jean-Mare Vanney Hakzmana Date: 28 February 2011

3 Abstract The need for Offcal Statstcs to assst n the plannng and montorng of development projects s becomng more ntense, as the country shfts toward better servce delvery by local government. It s evdent that the demand for statstcs at small area level (muncpal rather than provncal) s hgh. However, the statstcs wth respect to employment status at muncpal level s lmted by the poor estmaton of unemployment n 2001 Census and by changes n boundares n local government areas. Estmates are judged to be relable only at provncal level (Stats SA, 2003) The am of ths study s to nvestgate possble methods to resolve the problem of the msclassfcaton of employment status n Census 2001 by readjustng the data wth respect to the classfcaton of people as employed, unemployed or economcally nactve, to that of Labour Force Survey of September Ths report gves an overvew of the dfferent methods of small area estmaton proposed n the lterature, and nvestgates the use of these methods to provde better estmates of employment status at a small area (muncpal) level. The applcaton of the small area estmaton methods to employment status shows that the choce of the method used s dependent on the avalable data as well as the specfcaton of the requred doman of estmaton. Ths study uses a two-stage small area model to gve estmates of unemployment at dfferent small areas of estmaton across the geographcal herarchy (.e. Dstrct Councl and Muncpalty). Even though plausble estmates of the unemployment rate were calculated for each local muncpalty, the study ponts out some lmtatons, one of whch s the poor statstcal representaton (very few people) lvng n some specfc muncpaltes (e.g. Dstrct Management Areas used for natonal parks). Another ssue s the poor classfcaton of employment status n rural areas due to poor data wth respect to economc actvtes, mostly wth respect to famly busnesses, and the non-avalablty of addtonal auxlary data at muncpal level, for the valdaton of the results. The nablty to ncorporate the tme dfference factors n the small area estmaton model s also a problem. In spte those lmtatons, the small area estmaton of unemployment n South Afrca gves the reference estmates of unemployment at muncpalty level for targeted polcy nterventon when lookng at reducng the gap between those who have jobs and those who do not. Hence, the outcome of the small area estmaton nvestgaton should assst polcy makers n ther decson-makng. In addton, the methodologcal approach used n ths report consttutes a techncal contrbuton to the knowledge of usng Small Area Estmaton technques for South Afrcan Employment statstcs.

4 Dedcaton To my nuclear famly: Albertna, my wfe Nancy, my frst daughter Nadne, my second daughter v

5 Acknowledgement The completon of ths research report would not have been possble were t not for the support of several people. Prmarly, I would lke to express my deep grattude to Prof Jacquelne Galpn, my research supervsor. She has been patent and very generous wth her tme n provdng nvaluable advce. The same apprecaton goes to Prof Paul Fatt, wth whom I started the preparaton for the proposal before hs retrement. Statstcs South Afrca has provded the data and the computer software. I am especally grateful to Mr Pal Lehohla and Prof Mbulahen Nthangen for havng allowed me to further my studes and use Statstcs South Afrca resources. I would also lke to extend my heartfelt thanks to frends who have been supportve. They have gven me moral support to persevere when over-commtments between offce work and studes were becomng dffcult to manage. I would lke to thank colleagues at work who allowed the reschedulng of some requrements so that I could be able to contnue on the path of personal development after so many years outsde school. Gong back to school followng the turbulent years of mgraton from Rwanda was not easy. Fnally, I want to thank the members of famly who have endured a reducton n famly tme. They have been patent, forgvng and understandng. They have gven me the moral and physcal support that has allowed me to persevere. v

6 Table of Contents Declaraton... Abstract... Dedcaton... v Acknowledgement... v Table of Contents... v Lst of Fgures... v Lst of Acronyms... x CHAPTER 1: INTRODUCTION The context of ths research study Statstcal nformaton for polcy makng The mportance of the labour market statstcs The need for small area estmaton Motvaton of the study Methodologcal motvaton Practcal motvaton The lmtaton of accuracy of labour force survey The poor estmaton of unemployment by 2001 Census The change n the spatal dstrbuton of the populaton n the country The lack of relevant comparatve data source at low level The objectve of the study Summary of the road map n ths research report... 6 CHAPTER 2: CONCEPTS AND METHODS Concepts and Defntons Defnton of small areas Defnton of some terms used Defnton of unemployment Addtonal defntons used n the Census and the Labour Force Survey Methods of Small Area Estmaton Statstcal notaton Drect doman estmaton Survey measurement estmaton Populaton Census Indrect Estmaton Synthetc Estmaton procedure Composte Estmaton Structure Preservng Estmaton Synthetc Regresson Area level and unt level models Area level model Unt level model Summary on methodology of Small Area Estmaton CHAPTER 3: LITERATURE SURVEY Standard approaches to Small Area Estmaton Desgn-based methods Model-based approach: mxed effects regresson Consderatons for the practcal applcaton of small area methods Desgn ssues Model selecton and valdaton v

7 3.2.3 Area level vs. unt level models Non-samplng errors Other consderatons related to model specfcaton Practcal examples of the applcaton of Small Area Estmaton methods Canadan experence Turksh experence Unted Kngdom: Offce for Natonal Statstcs (ONS) Practcal example from the Unted States of Amerca (USA) Italan experence An example appled n the Phlppnes SAE estmaton of unemployment n Iran Summary of the lterature survey CHAPTER 4: APPLICATION OF SMALL AREA ESTIMATION TO EMPLOYMENT STATUS Introducton Avalable sources of nformaton Labour Force Survey Populaton Census Geographc nformaton database Estmaton based on the mplct approach Drect estmaton Results from the Labour Force Survey (September 2001) Results from Populaton Census (October 2001) The problem of msclassfcaton Synthetc estmaton Model-based estmaton Model formulaton Dscrmnant Analyss model Multnomal Logstc model Evaluaton of the results Summary of the applcaton of Small Area Estmaton to employment status CHAPTER 5: CONCLUSIONS Summary of fndngs Lmtaton of the estmaton and future work Polcy mplcatons Bblography ANNEXURE I: ESTIMATION OF UNEMPLOYMENT RATE BY MUNICIPALITIES ANNEXURE II: Extract from Census 2001 questonnare AII.1. Census demographc questons AII.2. Census Employment related questons ANNEXURE III: Extract from LFS 4 September 2001 questonnare AIII.1. LFS demographc questons AIII.2. LFS Employment related questons v

8 Lst of Tables Table : People aged from 2001 September LFS by Provnce and economc status 32 Table : People aged from 2001 Census by Provnce and economc status 33 Table : Percentage of persons aged n LFS 2001 by Provnce and economc status 35 Table : Dstrbuton of muncpaltes by class of unemployment rate 36 Table : Group statstcs: LFS and Census 40 Table : LFS Group statstcs by employment status 40 Table : Correlatons pooled wthn groups matrces 41 Table : Group covarance of canoncal dscrmnant functons 41 Table : Egen-values 42 Table : Wlks' Lambda 42 Table : Standardzed Canoncal Dscrmnant Functon Coeffcents 43 Table : Structure Matrx 43 Table : Canoncal Dscrmnant Functon Coeffcents 43 Table : Functons at Group Centrods 44 Table : Classfcaton Results 45 Table : Outcome of the reclassfcaton of Census Table : Profle of Employment status for Census and LFS n Table : Model-Fttng Informaton 48 Table : Lkelhood Rato Tests 49 Table : Pseudo R-Square 49 Table : Parameter Estmates 51 Table : Multnomal Logstcs regresson classfcaton results 52 Table : Employment status profle comparson for Census and LFS n Table : Model based estmaton of People aged by Employment status for LFS September Table : Model based estmaton of People aged by Employment status for 2001 Census 53 Table 4.5.1: Comparson of unemployment rate for dfferent estmaton approach by Provnce 55 Table 4.5.2: Percent ARD dfference of unemployment rate between LFS 2001 (reference) and dfferent estmaton approach by Provnce 56 Table A1: Estmaton of unemployment by Muncpaltes (Census drect measure, Dscrmnant estmate and Multnomal Logstcs estmate) Lst of Fgures Fgure : Internatonal Labour Organsaton classfcaton 9 Fgure : Proporton of people aged by methods of estmaton 54 Fgure 4.5.1: Dstrbuton of muncpaltes by unemployment rates 55 v

9 Lst of Acronyms Acronym ARD BLUP CV DSE DU EA EB EBLUP GIS HLFS ILO IPF ISTAT LFS MSE OFHS ONS PES PSU RDP SAE SEE SPREE Stats SA UK UI USA Descrpton Absolute Relatve Dfference Best Lnear Unbased Predctor Coeffcent of Varaton Dual System Estmaton Dwellng Unt Enumeraton Area Emprcal Bayes Emprcal Best Lnear Unbased Predctor Geographc Informaton Systems Household Labour Force Survey Internatonal Labour Organsaton Iteratve Proportonal Fttng Italy Statstcs Labour Force Survey Mean Squared Error Oho Famly Health Survey Offce for Natonal Statstcs Post-Enumeraton Survey Prmary Samplng Unt Reconstructon and Development Programme Small Area Estmaton Survey of Employment and Earnngs Structure Preservng Regresson Estmaton Statstcs South Afrca Unted Kngdom Unemployment Insurance Unted States of Amerca x

10 CHAPTER 1: INTRODUCTION 1.1. The context of ths research study Statstcal nformaton for polcy makng Statstcs have become fundamental to the effectve functonng of a democratc socety. Central and local government use offcal statstcs to develop and montor publc polcy, make decsons, allocate resources and for other admnstratve purposes. Hence, offcal statstcs are vtal for publc polcy, for montorng the well-beng of people and for the democratc process tself. The reportng of the status of economc and socal changes n socety s a constant feature of modern socety (Holt, 2000). Wth the establshment of an all-nclusve democratcally governed state n 1994, the South Afrcan government nherted a country of gross nequtes wth hgh unemployment (Knght, 2001). Government polcy prortes were: allevatng wdespread poverty, reducng ncome dspartes and hgh unemployment and supplyng basc necesstes to poor people (Reconstructon and Development Programme [RDP] goals) The mportance of the labour market statstcs In the South Afrcan context, the measurement of poverty and nequalty uses dfferent comparatve ndcators between people as a proxy measure for the standard of lvng. In the summary report to the Offce of Deputy Presdent, May, Budlender, Mokate, Rogerson and Stavrou (1998) stated that poverty s closely correlated wth unemployment. The lack of a job culmnates n a lack of wage ncome and the reducton of basc resources. The unemployment ndcators can also be used to determne the level of socal excluson n the development of people. In response to the growng needs of montorng the labour market, Statstcs South Afrca (Stats SA) has prortsed labour force surveys snce 2000 as part of ts household surveys, n order to obtan more accurate estmates of employment and unemployment levels. Ths was because estmates of employment based on the Survey of Employment and Earnngs (SEE) may be nconsstent wth estmates based on household surveys, as the SEE covers only the formal sector. The Labour Force Survey (LFS) provdes estmates of the numbers and proportons of unemployed persons at natonal and provncal level. The data cannot provde relable or precse estmates of unemployment at the muncpal level because the sample s not drawn to be representatve at that level, and the sze of the sample s not large enough to gve precse estmates. The attempt to estmate unemployment at natonal and provncal levels usng the 2001 Census data also gave mplausble estmates of unemployment, because of shortcomngs n the desgn of the census questons on labour force status. 1

11 The need for small area estmaton The demand for small area estmates of labour market statstcs s ncreasng, partcularly for use by local government servces n ther polcy plannng. Ths growng demand from local authortes s not only at macro level, but also at the level of socal and economc dynamcs of small parts of the area of admnstraton (Gebzloudlu, Depep and Toprak, 1996). Ths s prompted by a more decentralsed approach n managng polcy and allocatng resources. In South Afrca, nformaton from Census 1996 and Census 2001 have been used n the budget allocatons per provnce. As the qualty of data mproves, the decentralsed approach s ganng momentum, partcularly at the muncpalty level. On one hand, the tradtonal approach of populaton estmaton wthn the statstcal doman of precson n regular sample surveys cannot provde suffcent data for small areas or sub-populatons of nterest for a vald and vable statstcal nference. On the other hand, due to ts prohbtve costs, the census operaton cannot be conducted frequently enough to get data for montorng pattern changes of dynamc phenomena such as employment and unemployment. However, several other methods can be used, for example, combnng some survey data wth the latest census results, frames or regsters. A number of technques have been developed for the estmaton of small area statstcs n order to respond to the growng use of small area estmates for local plannng. The technques related to Small Area Estmaton (SAE) have been well documented through the semnal works of Rao (2003a) and Longford (2005a). The SAE methods have been dentfed as the drect doman of estmaton methods (.e. survey doman estmaton), ndrect doman estmaton methods (.e. synthetc or composte estmaton), model-based methods (.e. area level or unt level models) and the Bayesan approach to SAE. The technques of SAE are a generalsaton or a combnaton of other statstcal methods, partcularly structured around the regresson framework (Marker, 1999). More detaled dscussons of the methods are gven n Chapter Motvaton of the study Methodologcal motvaton In South Afrca, populaton censuses have been the man source of nformaton at local area level. The experence wth the last two censuses conducted by Stats SA has been that t consttutes a huge logstcal exercse that had some weaknesses n terms of operatonal management. Ths has resulted n the reducton of coverage wth the net undercount calculated usng the post-enumeraton survey (PES), estmated at 8.28% (10,69% wthout removal of census erroneous ncluson) n the 1996 Census, and 17.6% n the 2001 Census. However, Stats SA has been usng almost the same conceptual defnton of labour statstcs from household based ntervews. Consequently, some demographc varables from both the census and labour force surveys gve a good bass for the development of model-based estmates. 2

12 The evaluaton of the results of Census 2001 showed a substantal dfference between the unemployment estmates from the September 2001 LFS and Census Ths prompted the SA Statstcs Councl to ssue a warnng statement regardng the hgher unemployment measured from the Census as opposed to unemployment measured from the LFS (Stats SA, 2003). The dfference mght be attrbutable n part to the probng questons ncluded n LFS but not n the Census questonnare. There s also a possblty that the dfference s due to dynamc changes that need to be adjusted from the LFS (Sept. 2001), as the LFS sample was desgned usng the samplng frame from the 1996 Census. Lastly, the dfferences mght be caused by the large undercount rate from the 2001 Census. Based on 2001 Census data, the spatal dstrbuton of the census unemployment rates for the 262 muncpaltes (shown n Annexure I) vares from 0.71 to 84.06%. It s expected that combnng the unemployment estmates from the LFS and the Census wll produce better controlled estmates at the small areas of estmaton. The focus of ths study wll be on mnmsng model errors, borrowng the strength from the LFS, makng use of spatal relatonshps of neghbourng areas (usng lattude and longtude as the x and y coordnates), takng advantage of the desgn crtera of complex samples (LFS) and lookng nto mprovement of some other classfcaton estmates. The muncpalty s currently consdered as the small area of estmaton at whch statstcal relablty s requred n South Afrcan labour statstcs Practcal motvaton The lmtaton of accuracy of labour force survey The measurement of unemployment has been ncorporated nto the household survey program snce The October Household Surveys of 1994, 1995, 1996, 1997, 1998 and 1999 provded trends and levels of unemployment measured from the household members pont of vew. It s mportant to note that some addtonal reconclaton s necessary when comparng the results from successve October household surveys and the subsequent LFSs. The questonnares used n these surveys have constantly been revewed, whle keepng to nternatonally accredted concepts and standards. These mprovements n the questonnare as well as changes n the estmates of the total populaton do, however, mean that data from the dfferent years are sometmes not completely comparable. In vew of the avalable data from the populaton census (1996 Census), the October household survey was replaced by a survey of labour statstcs, whch was seen as a prorty. The LFS was ntroduced n February 2000, to be conducted twce a year. The estmates of the survey have been made relable at least wthn a doman of estmaton such as provnce (February 2000 February 2004) and later (snce September 2004), after the revson of the sample desgn based on the 2001 Census frame, at dstrct councl level. However, the data cannot yeld relable estmates of unemployment for plannng purposes at the admnstratve target 3

13 unt of polcy mplementaton, such as the muncpalty. Other sources of data on labour market statstcs, such as the SEE, are lmted n terms of coverage, to the formal economy or large establshments. Hence, there s a growng demand to extend the measurement of unemployment by the LFS to at least the lowest level of polcy formulaton The poor estmaton of unemployment by 2001 Census Although the release of the 1996 Census gave an mproved overall profle of the demographc characterstcs of the South Afrcan populaton, the fnal estmates were subject to adjustment accordng to an undercount derved from the PES. There were also qute sgnfcant changes n the way the employment questons were phrased and sequenced over the perod 1994 to 1997 (Stats SA, 1998, p 64)., resultng n slght changes n the method of calculaton of the unemployment rate over ths perod. The 2001 Census questonnare desgn was done takng nto consderaton the formulaton of labour questons. However, the questons were lmted n terms of probng of the respondents as to the classfcaton of those economcally actve or not, and specfcally a new category ntroduced n 1997, namely those not workng, not lookng for work, but avalable for work. There are a consderable number of persons excluded from labour market partcpaton because they have abandoned the search for employment. The unemployment estmates from the 2001 Census were substantally dfferent to the estmates of September 2001 LFS (Stats SA, 2003). Some attempts to readjust the dfference suggested that varaton was due to LFS results beng calbrated to the md-year estmates for 2001 and to the huge adjustment arsng from the undercount n the 2001 Census. The Census adjustment factors were calculated wthn the homogenous classes obtaned usng an Automatc Interacton Detecton analyss wth the assumpton of smlar undercount rates wthn the same classes. However, the dfference of estmates of unemployment between Census and LFS s so large that there s a need to use auxlary nformaton from other sources to nvestgate f ths mght produce more plausble estmates. Ths study looked at possble mprovements n the measurement of unemployment usng Census nformaton corrected by the LFS and the centrod x and y (lattude and longtude) coordnates of each target geographcal area represented n the small area framework The change n the spatal dstrbuton of the populaton n the country The settlement pattern of the South Afrcan populaton has been nfluenced by many endogenous and exogenous factors varyng from poltcal nfluence to spatal demographc growth. Snce the 1996 Census, the spatal populaton dstrbuton has been measured based on the full demarcaton of the country nto small unts of data collecton called enumeraton areas (EAs). The EA has been consdered as the buldng 4

14 block of the aggregaton of the populaton nto place-names or suburbs, local government areas, Dstrct Councl and provnces. In the 2001 Census operatons, the EA groupngs and defntons were redefned based on populaton or household concentratons. Ths re-demarcaton showed that there are other spatal elements attractng people to a gven area. For nstance, nfrastructure such as schools, roads, hosptals and ndustral establshments are some of the elements attractng populaton settlement. These elements are closely correlated wth employment creaton n dfferent areas. If one generalses any value measured from an EA to a geographc coordnate pont, the pont pattern dstrbuton of the central pont of EA or muncpalty can be spatally regressed on the pont patterns of nfrastructure, n order to mprove the estmaton n the spread of the measurement of unemployment. The dstrbuton wthn the muncpalty prompts the need for spatally dstrbuted correcton factors of unemployment, n order to mplement polcy nterventon programmes such as job creaton nvestment or labour ntensve projects The lack of relevant comparatve data source at low level The need to support local government programmes n job creaton requres a statstcal tool for the estmaton of unemployment. Snce the LFS s able to gve the requred trend at natonal and provncal level, the use of auxlary varables avalable also n the census data and geographcal nformaton system data could assst n gettng a SAE of unemployment The objectve of the study The am of ths study s to brng together the nformaton on unemployment estmated by the LFS and other nformaton from census and geographcal data, n order to get an mproved spatal estmate of unemployment per target area (muncpalty or dstrct councl). Therefore, ths study wll explore methodologcal ssues arsng from a combned/ntegrated model for the estmaton of unemployment, usng LFS data together wth other soco-economc varables and census varables n a regresson. Both sources are relatvely less relable than the expected true estmate for local areas due to sample desgn lmtatons n the LFS and poor drect measurement of unemployment by the 2001 Census. A varety of SAE approaches wll be examned n ths study, wth the ntenton of assessng the most relable methodology by combnng the model fttng methods and other estmaton methods. The am s to produce enhanced estmates for the counts and rates of unemployment for each proclamed muncpalty n South Afrca (based on Local Government: Muncpal Structure Act No 117 of 1998 wth the subsequent amendment). 5

15 Though the study could use data collected over dfferent perods, the objectve s to get a feasble estmate of unemployment for small areas n 2001, usng the September 2001 LFS, the 2001 Populaton Census and the Geographc Informaton System (GIS) dentfcaton of the 2001 EAs fttng the proclamed boundares. Some of the ssues to be nvestgated are: - to assess whether t s possble to estmate the unemployment rate wthn dfferent levels of geographcal herarchy; - whether SAE methods are able to yeld estmates that are acceptable; and - whether the labour market profle (e.g. unemployment among youth versus unemployment among other age groups) s mantaned at the level of the tradtonal domans of estmaton (Natonal and Provnce). The other ssue s the varablty of estmates across data sources. The census fgures are adjusted for the undercount accordng to a dual-system-estmaton (DSE) analyss used n the PES. The adjustment factors from the 2001 PES are not relable beyond the doman of estmaton of the survey desgn: Natonal level, Urban/non-urban natonally and Provncal level (Stats SA, 2004). The PES unverse was also lmted to resdents of housng unts and workers hostels, wth the excluson of other collectve lvng quarters such as resdental hotels, homes for the aged, student resdences, tourst hotels and nsttutons (Stats SA, 2004). The master sample used for the LFS used a smlar unverse wth dentcal exclusons Summary of the road map n ths research report Ths research report comprses fve man sectons: (1) ntroducton n chapter 1, (2) overvew of the concepts and methods n chapter 2, (3) lterature survey n chapter 3, (4) applcaton of SAE to the estmaton of unemployment n chapter 4, (5) conclusons n chapter 5. The ntroducton covered the context, relevance and needs of the estmaton of unemployment statstcs for small areas for polcy plannng. The context gves an understandng of reasons motvatng ths study, both methodologcal and practcal. It s understood that the dfferent methodologes of estmaton of statstcal nformaton wthn the doman of estmaton are lmted by the samplng errors, n the case of surveys, or coverage errors n the case of the census. There are also practcal reasons that motvate the need for estmaton for small areas. These are referenced by exstng sources of nformaton for labour market statstcs. The offcal LFS has lmtatons of accuracy wthn ts doman of estmaton. Even the use of the 2001 Census has not been able to gve a better estmate of unemployment n South Afrca, most probably 6

16 due to the huge undercount and the depth of the screenng questons for the populaton n or out of the work force. The other practcal reason s the rapd change n the pattern of the spatal populaton observed n the last 10 years. There s evdence that nternal mgraton has ncreased snce 1994 (Stats SA, 2002). The analyss presented n ths report s supported by the relevant lterature. The revew attempts to cover dfferent estmaton methods, supported by a succnct dscusson of practcal experences n the estmaton of small area statstcs. Based on dfferent statstcal methods of estmaton for small areas, specal mportance s gven to ther applcaton to the labour market. The focus n terms of practcal applcaton to the South Afrca employment status profle wll be the technques of drect estmaton, synthetc estmaton and the unt level SAE methods. Further approaches are defned n Chapter 2, as background for the llustraton of experences of other countres recorded n the lterature. 7

17 CHAPTER 2: CONCEPTS AND METHODS Ths chapter gves the theoretcal foundaton of the report. In addton to the understandng of the SAE concepts, the chapter explorers the standard defntons of the terms used concernng labour market statstcs before gvng the methods and procedures of SAE Concepts and Defntons Defnton of small areas The concept of small area estmaton can be defned as a dervatve of the sample survey defnton of the doman of estmaton. In ths context, the doman s the subpopulaton of nterest, where the sample desgn should yeld drect estmates wth adequate precson assocated wth the nferred weghted populaton estmates. Ths s usually referred to as desgn-based estmaton. A doman (area) s regarded as small f the doman-specfc sample s not large enough to support drect estmates of adequate precson (Rao, 2003a). In some other nstances, SAE wll use model-asssted estmaton wth the objectve of dervng robust nferences, whch correct the data dstorton wthn the doman (small area). It s often necessary to use ndrect estmates by fortfyng the data wth good auxlary data such as a recent Census or current admnstratve records of the doman, and the determnaton of sutable models lnkng areas Defnton of some terms used The defntons gven n ths secton were taken from the statstcal release P0210 Labour Force Survey September 2001 (Stats SA, 2002) as referenced n the metadata notes on pages x, xv and xv Defnton of unemployment The offcal defnton of unemployment s referred to as the strct defnton where the characterstcs of unemployed persons are for those people wthn the economcally actve populaton who: (a) dd not work durng the seven days pror to the ntervew, (b) wanted to work and were avalable to start work wthn two weeks of the ntervew, and (c) had taken actve steps to look for work or to start some form of self-employment n the four weeks pror to the ntervew. South Afrca has been reportng, n addton to the offcal defnton, another type of defnton called the expanded defnton of unemployment that excludes crteron (c). The target group for the measurement of unemployment s all persons aged between 15 and 65 years old. Even though the Internatonal Labour Organsaton (ILO) prescrpton for the age unverse s 15 to 64 (nclusve), the upper lmt s set to 65 because ths s the most common retrement age n South Afrca. The ultmate am s to be able to classfy all persons aged between 15 and 65 nto economcally actve or nactve. 8

18 For those economcally actve, the measure of employment and unemployment s determned. Among the not economcally actve, there are those who do not want to work (e.g. pensoner) and those who mght stll want to work but are not currently able to do so (e.g. student, rasng chldren.) (Fgure ). Fgure Internatonal Labour Organsaton classfcatons All aged between 15 and 65 Economcally actve Economcally nactve In employment Unemployed Wants a job Does not want a job In the LFS, the other mportant concepts are: The workng age populaton comprses all persons aged years. The economcally actve populaton conssts of both those who are employed and those who are unemployed. The employed are those who performed work for pay, proft or famly gan n the seven days pror to the survey ntervew, or who were absent from work durng these seven days, but dd have some form of work to whch to return. The people who are out of the labour market or who are not economcally actve are those who are not avalable for work. Ths category ncludes full-tme scholars and students, full-tme homemakers, those who are retred, and those who are unable or unwllng to work. Workers nclude the self-employed, employers and employees. The formal sector ncludes all busnesses that are regstered n any way. The nformal sector conssts of those busnesses that are not regstered n any way. They are generally small n nature, and are seldom run from busness premses. Instead, they are run from homes, street pavements or other nformal arrangements. Labour market dynamcs refer to movement nto, out of, and wthn the labour market over a specfed perod of tme. 9

19 Addtonal defntons used n the Census and the Labour Force Survey A Populaton Census s the total process of collectng, processng, analysng and publshng or otherwse dssemnatng demographc, economc and socal data pertanng to all persons n a country or n a welldefned part of a country at a specfed tme. In South Afrca, the lstng unt s sometmes referred to as dwellng unt (DU). The LFS s a twce-yearly rotatng panel household survey, specfcally desgned to measure the dynamcs of employment and unemployment n the country. It also provdes nsght nto a varety of ssues related to the labour market, ncludng the level and pattern of unemployment and the ndustral and occupatonal structure of the economy. The target populaton s all persons resdng n normal households and n workers hostels. The survey does not cover nsttutons such as old age homes, hosptals, prsons and mltary barracks. The Master Sample s a mult-stage stratfed sample used by Stats SA s household surveys. The LFS overall sample sze of Prmary Samplng Unts (PSU) s The explct strata were the 53 dstrct councls and 9 Provnces. A PSU corresponds n most cases to one or two EAs. The number of PSUs was allocated usng the power allocaton method and these were sampled usng probablty proportonal to sze prncples. The measure of sze used was the number of households n a PSU, as calculated n the Census. The sampled PSUs were lsted wth the DU as the lstng unt and a systematc sample of dwellng unts per PSU was drawn. These samples of dwellng unts form clusters of ten dwellng unts. The LFS uses a rotatng panel methodology, whch gves a pcture of movements nto and out of the labour market over tme. The rotatng panel methodology nvolves vstng the same DU on a number of occasons (n ths nstance, fve at most). After the panel s establshed, a proporton of the DUs s replaced each round (n ths nstance, 20%). New DUs are added to the sample to replace those that are taken out. The advantage of ths type of desgn s that t provdes the bass for montorng changes n the work stuaton of members of the same households over tme, whle retanng the larger pcture of the overall employment stuaton n the country. It also allows for both longtudnal and cross-sectonal analyss. The dwellng unt or housng unt s a unt of accommodaton for a household, whch may consst of one structure, or more than one structure, or part of a structure. (Examples of each are a house, a group of rondavels, and a flat.) It may be vacant, or occuped by one or more than one household. A housng unt usually has a separate entrance from outsde or from a common space, as n a block of flats. A dwellng unt s any structure or part of a structure or group of structures occuped by one or more than one household; or whch s vacant or under constructon but could be lved n at the tme of the survey. The DU s the 10

20 major lstng unt for these surveys. However, f multple households are dentfed durng lstng, then each household s lsted separately. However, the lstng unt s not prmarly households, as multple households are sometmes dscovered at the tme of the survey. In workers hostels, (1) where rooms are occuped by ndvdual persons/households, then each room s treated as a DU, and (2) n the case of dormtores/communal rooms, each bed s lsted separately and treated as a DU. It s mportant to note that the dwellng unt as defned here was also the selecton unt for these surveys. A household s defned as a person, or group of persons, who occuped a common DU (or part of t) for at least four days n a week on average durng the four weeks pror to the survey ntervew. They lve together and share resources as a unt. Other explanatory phrases can be eatng from the same pot and cook and eat together. Workers hostel s a communal lvng quarter for workers, provded by a publc organsaton such as a local authorty, or a prvate organsaton such as a mnng company. These were resdental dormtores establshed for mgrant workers durng the aparthed era, and they contnue to house people workng n certan ndustres, such as the mnng ndustry. Domestc worker s a person employed to work n the household e.g. as a house cleaner, cook, gardener, drver or nanny. There are some domestc workers who lve on the property of the employer, ether n the same house or n separate domestc quarters. There are those who lve n separate dwellng unt. Usually, domestc workers have famles and responsbltes of ther own elsewhere. Thus, they are consdered as separate households Methods of Small Area Estmaton Statstcal notaton For the purpose of the dscusson of the dfferent statstcal estmaton technques, a populaton of sze N s consdered from whch a sample of sze n was drawn. The attrbute or measurement of the characterstc of nterest s represented by y, for nstance the unemployed populaton. It s assumed that there are m small geographc subdvsons (such as provnce, dstrct Councl, or muncpalty) and l soco-demographc subgroups. As a result, yhk represents the value of the characterstc of nterest y on the th k unt n the th h soco-demographc subgroup n the k=1,2,... n h. th small geographc area, where = 1,2, m, h=1,2, l and 11

21 Sncen h n, ths mples that nh represents the sample sze n the h th ( h) cross classfcaton. The notaton for the overall populaton s Nh N where Nh represents the populaton sze n the th ( h) cross classfcaton. The th stratum by h th stratum populaton s represented by n and the total measure by y. n h h Drect doman estmaton Survey measurement estmaton h k hk y N N h h, the sample sze of the Sample surveys have been used to provde relable drect estmates of totals and means (Rao, 2003a). They use data from the sample unts n the area of doman of nterest such as the whole populaton and large area. Hence, the estmate of a characterstc Y, for smple random samplng, would be gven by ^ srs Y N n l h h n k1 y hk f n 1 or zero otherwse. (2.1) h In the case where N s known, a post-stratfed estmator can be defned as ^ pst Y N n l h nh k1 y hk N y f n 1 and zero otherwse. (2.2) h A drect estmator for the mean for the small area s gven by ^ Y y 1 n l h h n k1 y hk f n 1 and zero otherwse. (2.3) The varance for f N s known where 2 y may be estmated by Var l N 2 n 2 Y k Y f and S y N h k1 N y 1 f s y sy n n N, (2.4) l n 1, 2 yk y sy n 1 h k 1 2, N 2 snce 2 s y s an unbased estmator for the populaton parameter 2 S y. If N s unknown, the varance of y may be 1 f where n estmated by 2 strata. Var y s y f n N, f t can be assumed that the f s are very smlar for all The varance of the estmator (Cochran, 1977, page 23-24). Y^ (total number) may be estmated n a smlar way to that of y (the mean) 12

22 The drect estmator s used when the sample sze for each small area s suffcently large to yeld acceptably precse estmates for that area. In the case of the LFS of September 2001, acceptably relable estmates can be obtaned at natonal and provncal level only. (The acceptably relable estmates at Dstrct Councl level were only possble after the ntroducton of the new master sample n 2003, whch s representatve at the Dstrct Councl level). There are some tradtonal ssues of sample desgn related to the number of strata requred, the constructon of strata, the sample allocaton and the selecton of probabltes, that need to be taken nto consderaton. Although the deal goal s to fnd an optmal desgn that mnmses the mean square error (MSE) of the drect estmate wthn the avalable budget, n practce a compromse s adopted where a reduced relablty n some small areas or domans wll be allowed. Whle clusterng may lead to a reducton of the survey cost, Rao (2003a) notes that the mnmsaton of clusterng s sometmes consdered n order to avod the loss n the effectve sample sze. It may also assst estmaton for domans where the sample sze can only be determned after the data s collected, such as socal-demographc domans. However, the choce of the samplng frame to use, the samplng unts and number of samplng stages have a sgnfcant mpact on the effectve sample sze. Rao (2003a) also suggests that, n cases where there are dfferent surveys measurng the same characterstc, usng dfferent stratfcatons n the samplng desgn, a better sample sze dstrbuton at the small area level can be obtaned by stratfcaton usng the ntersecton of these strata, or small strata. In addton, he suggests usng a compromse sample allocaton may be suffcent for the relablty requrements at both the small area and large area, usng only drect estmates. Here part of the sample s allocated so as to provde relable estmates at the large area level, wth the remanng sample beng allocated to mprove the estmates as small area level. It s mportant to have a knd of ntegrated survey program, so that the questons relatng to the characterstcs of measurement or varables are harmonsed across surveys, across regons or countres. The South Afrcan LFS s based on a two-stage complex sample, where the frst stage nvolves the selecton of PSUs usng the probablty proportonal to sze selecton scheme wth the number of households per PSU as a measure of sze. The second stage nvolves the systematc selecton of 10 dwellng unts from each of the selected PSUs. The number of households used as a measure of sze for selectng PSUs s obtaned from the Census 1996 lst of EAs. The overall weghts are obtaned from the desgn weghts for unt non-response and for post-stratfcaton by adjustng the weghts to conform to known populaton dstrbutons, mprove precson and to compensate for non-coverage. 13

23 The fnal estmate of the characterstc of nterest wthn the small area under a stratfed multstage samplng (wth soco-demographc varables dfferent n varous areas) s gven by Y where the overall weght s wrtten whk whk 1 * whk2.1 * whk 3. 21where ^ l h n h1 k1 w hk y hk (2.5), o w hk1 and DU. 1 1 where phk represent the probablty of selecton for the PSU p p ( PSU )* p ( DU) hk hk o whk2. 1 s the adjustment factor for non-response where o w w * hk hk2.1 hk3.21 where whk2.1 hk estmaton to whch the results are calbrated Populaton Census w hk2.1 1 Re sponse _ rate s the known margnal total n the th small area or doman of The populaton census provdes populaton counts for detaled geographcal areas of a country as well as for dfferent domans (sub-populatons) such as age, sex, martal status, populaton group, level of educaton and other demographc varables. These counts gve, n most cases, the bass for the calculaton of resource allocaton (budget for the equtable share of the muncpal nfrastructure grant). The Census requres a huge feldwork operaton where each dwellng unt n the country s vsted. In the South Afrcan Census, the method of data collecton s the applcaton of a questonnare form, where all people who were present n the country on a gven reference nght are recorded. The 2001 Census reference nght was on 9 10 October People lvng n households across the country, as well as those n hostels, hotels, hosptals and all other types of communal lvng quarters, and even the homeless, were all vsted. The total count of persons can be wrtten as P, 1,..., N (2.6) p j j hk where p j represents the counted persons n a gven household. Each person can also be assocated wth a partcular characterstc, so that y j s the number of persons n household j havng the gven characterstc Y y y y. (2.7) j j h k hk 14

24 In preparaton for the total count, the entre country s always demarcated nto EAs. The sze of each EA s such that an enumerator can vst all DUs n the EA to admnster the census questonnare to the household. Although the Census ams to have a complete enumeraton, a perfect census s mpossble due to omssons and false enumeraton. A second vst s conducted ndependently of the census, where a representatve sample of EA s s re-vsted. Ths second exercse s called a PES. The census and PES records for each household are matched and compared. The expected outcome s an estmate of the true populaton based on a dual system of estmaton calculated usng adjustment factors n order to correct the under-coverage or the over-coverage. In the 2001 South Afrcan Census, the estmate of true populaton was calculated as P ˆ Pˆ * P PES cenus_ corrected af * PCensus _ count (2.8) Pˆ matched and af 1 where af s the adjustment factor and ur s the undercount rate (Census 2001: Post- 1 ur enumeraton Survey, 2004). The dual system of estmaton assumes that there was a closed populaton wth nsgnfcant mgratory movement n the perod between the census nght and the PES vst. There s an ndependency between the Census and PES wth respect to the feldwork teams; there are almost no erroneous nclusons n ether system such as duplcaton, fabrcatons, boundary msallocaton or the ncluson of unts outsde the target unverse. In addton, t assumes that all matchng cases had been resolved, consderng that nether the sample nor the full census count s better than the other. The estmaton of the true populaton usng the dual system of estmaton s affected by some errors, as wth any other sample that ncludes samplng errors (.e. varance and bas) and non-samplng errors (.e. non-response bas, correlaton bas and matchng bas). The PES varance s obtaned by a deducton of the samplng procedure where the estmates of varance are represented by the standard error, the absolute error and the confdence ntervals from each dual system estmate. The PES samplng bas s controlled by mantanng adequate sample sze n each cell of estmaton. The PES non-response bas s a result of the refusals, non-contacts and unusable questonnares. The operatonal management of the feldwork s paramount n reducng types of error. The PES correlaton bas s observed n stuatons where the same event results n dffculty n enumeratng a group of persons n both the PES and Census. Ths arses f there s a lack of operatonal ndependence between the PES and Census under the same organzaton or dvson structure. The other bas concern, the PES matchng bas, refers to errors durng the matchng process, such as erroneous matches and erroneous non-matches. 15

25 Indrect Estmaton The ndrect estmator for the small area borrows strength from sample unts outsde the doman and/or tme perod of nterest usng a statstcal model. Ths study wll nvestgate whch ndrect methods yeld the most plausble estmates based on the avalable data: the Populaton Census, the LFS and the geographcal coordnates Synthetc Estmaton procedure A smple ndrect estmator would assume that there s the same proporton of the characterstc of nterest at the small area level as at the large area (e.g. natonal or provncal) level. Ths proporton can be wrtten as: p p where represents the dfferent small areas. Gven an unbased estmate from a sample for the large area, ths estmator can be used to derve estmates for sub-areas on the assumpton that the small areas have the same characterstcs as the larger area. Ths method s referred to as synthetc estmaton. The method assumes the avalablty of estmates from, e.g. a survey for a large subset of the populaton. In ths case, the relable estmates of the LFS were publshed n September 2001 for the whole country, provnces and demographc groups. If t s assumed that the small area of nterest s the small geographcal area (.e. muncpalty) and the relable drect estmate Y ˆ. h s avalable for each subgroup h at the large area level from the survey, the correspondng estmates can be deduced as Y ˆ phyˆ. h where small area as observed n census and h h ph N h ph represents the weghts of the subgroup h n the N 1. The varance of the synthetc estmate s based on nverse of the sample sze for the large area, and therefore t s smaller than that of the post-stratfed estmator. However, the synthetc estmates are based f the assumpton of homogenety for a gven socodemographc subgroup for both the large and small areas s not be vald (Francsco, 2003). Moreover, the structure of the populaton may have changed between the Census and the survey even though the October 2001 Census and September 2001 LFS are close together n tme Composte Estmaton The composte estmator s a weghted average of a drect estmator and an ndrect estmator (Ghosh and Rao, 1994). It s expected that the composte estmator wll balance the potental bas of the synthetc estmator aganst the nstablty of the drect estmator (Francsco, 2003). The composte estmator can be wrtten as Yˆ c w * Yˆ (1 w )* Yˆ (2.9) s 16

26 where and c Yˆ s the composte estmator for small area, Yˆ s the drect estmator, w s a selected weght wth0 w s Yˆ s the synthetc estmator There are dfferent ways of determnng the weghts. The optmal weghts suggested by Ghosh and Rao (1994) are obtaned by mnmzng the MSE of that ˆ ˆ s cov(, ) 0 c Yˆ wth respect to 2 ˆ s ˆ s MSE( Y ˆ ) Y Y V Y Y. The result s w ( ˆ s MSE Y ) ( ˆ ) ˆ s ˆ 2 V Y Y Y w under the assumpton ( Yˆ ). (2.10) The composte estmator s presented here for llustraton purposes as a method that has been used n the lterature, but wll not be nvestgated n ths study Structure Preservng Estmaton The Structure Preservng Regresson Estmaton (SPREE) s a generalzaton of the synthetc estmator, based on relable drect estmates. The parameter of nterest s a count, such as the number of unemployed persons n a small area. It assumes that the totals of N ab (as provded by the census) are known, where denotes the small area of nterest, a denotes the categores of the varable of nterest (y) and b denotes the categores of the categores of an auxlary varable x correlated wth y. SPREE uses the teratve proportonal fttng (IPF) method to adjust the cell counts M ab of the survey, to those of the N ab, usng relable survey totals of the auxlary varable N.b The SPREE method s smlar to calbraton estmaton usng the Horvtz- Thomson estmator, leadng to Ŷ w y where k k wk represents the calbrated weght subject to the k constrant wk xk X representng the total wthn a specfc doman or area of xk auxlary data or ks reference data. The above estmator (SPREE) s also presented as an llustraton of possble methods that have been appled to the measurement of unemployment n the lterature Synthetc Regresson Under the assumpton of the same populaton characterstcs for both the large and small areas, a regressonsynthetc estmator can be derved usng a vector of doman-specfc auxlary varables n the form of known totals (Rao, 2003a). Suppose that the vector of auxlary characterstc nformaton populaton totals s avalable (as n Census 2001) and that the smlar auxlary characterstcs X h of the known x h for h s are also measured n the sample s of the unverse (as n the September 2001 LFS). Ths mples that the