A C T A U N I V E R S I T A T I S L O D Z I E N S I S FOLIA OECONOMICA 182, 2004
Czesław D om ański*
A P P L IC A T IO N O F S M A L L A R E A S T A T IS T IC S F O R IN T E R N A T IO N A L C O M P A R IS O N S
S m all is beau tifu l
1. In trod u ction
S tatistics is the science that has great applicability and this fact is o f great significance for research relating to both econom ic and social life. Any organised com m unity cannot exist w ithout a suitable system o f gathering inform ation as well as system o f handling inform ation on a scale o f the entire country, isolated com m unities, distinguished com m unities or distinguished populations. T his results in dem and for data gathering m ethods and inference on the ground o f them. C osts o f conducting em pirical statistical investigation are usually rather high. T hat is why we are looking for m ethods that would give an opportunity o f m aking full use o f the gathered inform ation. The problem appears in the case o f analyses relating to subpopulations having data obtained for the entire population with the representative method. T he branch o f statistics called small area statistics is the one that deals with the problem s m entioned above. In the world econom y perm anent territorial changes take place. T he process can cause additional difficulties in continuing statistical investigation in, for exam ple, countries o f the form er Soviet Union. A sim ilar situation takes place in particular countries. It seems that small area statistics will be able to solve the problem o f lack o f data for past periods.
T hese problem s have becom e m ore and m ore popular recently both am ong statisticians and statistical data users. They result from the lim itation o f financial means and tim e for conducting investigation, as well as refusal o f participating in research, incorrect answ ers, or the quality o f statistical data.
Small area statistics provides methods of using data gathered for the entire population in com plete research (censuses, current registration) and fragm entary research (usually representative) to infer about phenom ena occurring in subpopulations. T he m ethodology relating to estim ation o f small area param eters in case o f different sam ple sam pling schemes and procedures o f data obtaining has been m ainly developed. The conception o f fragm entary investigation of finite populations with the representative method presented by Neyman (1934) is primary.
The concept o f “small area statistics” was developed in the 1970-ies o f the form er century but problem s that it includes had been engaged in much earlier when the fragm entary statistical surveys had begun to be undertaken. In Poland we can num ber inform ation gathering and handling fo r tax purposes in the 16lh century, the first census in 1789, representative surveys relating to school-age children and num ber o f men o f military age which were m ade on the ground of data originating from the census taking place in 1921 am ong fragm entary statistical surveys (see: K ordos 1993). The essential developm ent of m ethodology o f small area statistics can be observed for about thirty years. Published papers refer m ainly to statistical inform ation m aking and problem s o f distribution param eters o f subpopulation estim ation.
G enerally, in small area statistics we can m ake an assum ption that relations occurring betw een considered quantities or m easures for the entire population are retained in distinguished subpopulations that is small areas.
T o estim ate num erical characteristics o f investigated phenom ena in small area we can use not only data originated from censuses, i. e. current registration but also inform ation obtained by representative m ethod as a result o f suitable sam ples sam pling.
Surveys in which m ethods o f small area statistics are used can often be related to dem ographic phenom ena. In many countries birth and death registrations are run. H ow ever, the problem arises from determ ining regional size o f m igration. T he basis o f estim ating the level o f the phenom enon method on the particular area is an assum ption that the proportion o f m igration levels in the entire population and distinguished subpopulation (the population inhabiting distinguished area) is the same as proportion o f the num ber o f school-age children in the entire population and this subpopulation (see: Dol 1991).
A nother m ethod o f migration size estim ation for distinguished subpopulation uses the difference betw een the real num ber o f school-age children (obtained from suitable registrations) and the num ber o f school-age children estim ated on the ground o f life duration table for a suitable age group. Know ing the m igration level in subpopulation we can estim ate the am ount o f population in subpopulation.
A nother m ethod uses the estim ation o f num ber o f households in subpopulation and average num ber o f people per household for the entire
population to estim ate the am ount o f population in this subpopulation. The difference betw een the num bers o f households obtained on the ground o f the last census m ade before the investigated period m ultiplied by the average num ber of people in a household is the quantity which is used for estim ating m igration level and then the num ber o f people in subpopulation in a particular period.
M ethods o f small area statistics can be used in different fields o f socio-econom ic life (see for exam ple Falorsi and others (1993), Platek (1993), Falorsi and others (1999), Fay, H erriot (1979), Dom ański, Pruska (1998, 1999), Gam bio, Dick (1999), G am bio and others (1998), G ołata (1996, 1997, 2002), Kordos (1997, 1999), Kordos, Paradysz (1999), W itkow ska (1999), W itkow ski (1992), Rao (2002). T he subject literature is very wide and it is hard to present the most im portant publications even in general profile. H ow ever, the above list shows that Polish scientists have made a great contribution in this branch of science. K ordos (1994, 1997, 1999, 2002) presented achievem ents on this scale most widely. In recent years the m ost significant m om ents for the developm ent o f this branch o f science were three international conferences, w hich took place in turn: in O ttaw a in 1985, in W arsaw in 1992 and Riga in 1999. In 2000 The International C onsortium o f “Small Area S tatistics” was created within T he Fifth Fram ew ork Project in which statisticians from seven countries took part. They cam e from Finland (R isto Lehtonem ), Spain (C arlos B allano Fernandez), Norw ay (Li-C hun Zhang), Poland (Jan K ordos) Sw eden (Sixten Lundström ), G reat Britain (Patrick Heady and K erry Ellis from T he U nited N ations, and Ray C ham bers from Southham pton U niversity, N. T. Longford from M edical Statistics D epartm ent, Harvey G oldstein from Education Institute) and Italy (Stefano Falorsi). The organizers assum ed that partners taking part in consortium should:
a) understand w hat problem s o f small area estim ation ate to be solved, b) know basic m ethods o f small area estim ation,
c) have basic data sets on the ground o f which these m ethods could be sim ulated.
T he general purpose o f the research schem e is to provide European countries (and EU as a w hole) with estim ation m ethods directed at small areas that would enable to obtain solid estim ations o f these areas.
M ore specific purposes were form ulated as follows:
1. D evelopm ent and im provem ent o f suitable statistical m ethods which are directed at small area estim ation and the estim ation o f their practical aptitude.
2. D evelopm ent or im provem ent o f adm inistering data system s used with small area estim ation.
3. Investigation o f conditions for these m ethods application in each interested European country.
2. B asic issu es u f sm all area statistics
Small area statistics as a branch o f statistics deals with m ethods o f using statistical inform ation obtained for the entire population (based on representative research o f population, censuses, current registration and other auxiliary data) for inferring about investigated features in distinguished subpopulations which are called small areas, fields or dom ains.
One o f small area classifications was proposed in the paper o f Purcell and Kish (1979). They distinguish four kinds of small areas:
- main small area (if its population totals at least 1 0% o f entire population size)
-s e c o n d a ry small area (if its population totals from 1% to 1 0% o f the population size)
- mini small area (the area which has the size o f the order from 0,0 1% to 1% o f the population size),
- rare small area (if the num ber o f its elem ents is sm aller than 0,0 1% o f the population size).
The requisition for inform ation and statistical m ethods for small area is notified both by the governm ent (because o f distribution problem s and detecting regions o f characteristics which differ much from the countryw ide indexes) and self-governm ent as well as individual businessm en w ho are interested in local econom ic situation for planning and adm inistrative purposes.
A huge interest in small area statistics results from, am ong others, the need of:
- obtaining statistical data for suitable geographical levels in sections, - w orking out program m es o f regional, econom ic and social developm ent, as well as their realization estim ation,
- m onitoring various phenom ena and processes for distinguished subpopulations (for exam ple districts, com m unities and pen sion ers’ households).
Statistical inform ation gathering on regional scale, when the requisition for the data appears, is very expensive. That is why the problem o f possibility o f using data gathered for nation-w ide research purposes in regional research arises. It is o f particular im portance in case o f data gathered using the representative m ethod. That is because the representative m ethod for the entire population does not have to provide representative inform ation for distinguished subpopulations, or there is too little inform ation for small area to use in the process o f various econom ic decision making.
Small area statistics research concentrates m ainly on such construction of estim ators or functional characteristics o f investigated variables distributions which are to provide precise estim ations o f these distributions param eters. New possibilities o f increasing the size of the sam ple referring to sm all area or
increasing the representativeness of the sam ple are created by sim ulation m ethods.
M ethodological papers about small areas refer to developing procedures o f gathering reliable data (special sam ple sam pling schem es, obtaining extra inform ation) and statistical inference m ethods for subpopulations. T he average and global value are param eters which are estim ated m ost often. M uch attention is paid to error analysis o f estim ators. The sam ple for small area is m ade by elem ents o f sam ple sam pled from the entire population, which pertain to small area. F eatures o f estim ators for sam ples specified in this way generally differ from those, w hich are sam pled from the entire population.
3. S h ort ch a ra cteristics o f con stru ctio n o f sm all area estim ator
D istribution o f investigated characteristic in a given population can be characterized by various methods. M ost often we estim ate chosen param eters and precision estim ation o f the estim ation. In order to do that we can use direct or indirect m ethods (see: Schaible and Casady 1994, Dom ański and Pruska 2001) .
D irect estim ation is the estim ation o f small area param eters on the basis o f random sam ple w hose elem ents are units pertaining to sam ple sam pled from the entire population and small area, or on the basis o f sam ple sam pled specially from small area. If we use inform ation referring to other subpopulations or the entire population in the inference process, we talk about indirect estim ation. It is aim ed at increasing estim ation efficiency.
On the ground o f K oros’s paper (1999) we can give the follow ing classification of indirect estim ation methods.
-e s tim a tio n based on data from another small area but com ing from the same period in which a given small area is investigated,
- e s tim a tio n using investigated variable value from a given small area but from another period than the analysed one,
-e s tim a tio n based on variable values from another small area than investigated one, and another period than considered one,
- estim ation based on data from other sources.
E stim ators w hose values result from transform ation o f only values o f investigated variable observed in a sample are called com m on ones. If we use additional inform ation (for exam ple about auxiliary variables) w hile estim ators constructing the special nam es, which are typical o f given statistics (for exam ple quotient or regressive estim ator), will be assum ed.
W ithin indirect estim ators we can distinguish synthetic estim ators class. They are constructed by assum ption that population structure does not differ much from small area structure. One o f the possible approaches is the division o f population, which contains H small areas to G separable layers, how ever distinguished populations and layers are not separable. C onstructing synthetic estim ators we often assum e that G layers in a small area have the same num erical characteristics as G analogous layers in the entire population, for exam ple in particular layers the relation o f global values o f tw o characteristics in the entire population is the sam e as the one in distinguished small areas.
M ethods o f indirect estim ators for small area construction are to lead to increasing their efficiency in com parison with direct estim ators. W e also consider estim ators which are linear com bination or more com plex functions o f other estim ators. W e should also notice that statistics’ characteristics are influenced by sam ple sam pling scheme.
Small area estim ation issues concentrate m ainly on estim ation o f global value, average and obtained estim ations precision. W e can distinguish a few main types o f estim ators o f global value for small area (see: Falorsi and others (1999)). In case o f dependent sam ple sam pling the follow ing estim ators belong to them:
1) Com m on estim ator:
T ^ h K'
Тн. = — 1 у п ( 1)
nh 16
where: N h and nh - num ber o f elem ents, adequately from /?-th sm all area and the entire population belonging to /i-th small area.
2) Q uotient estim ator:
A (2)
A h.
where: X h - global value in h-th small area, X h - global value estim ator in Л-th small area, qŤh defined by the form ula (1).
where: J h - global value estim ator adequately in A group o f small areas and in
h-th small area.
4) C om plex estim ator:
=
qf h.+ a -n „ )Á ,
(4)
where: w(l is a constant from (0 ; l ) ,
5) Sam ple size-dependent estim ator:
«1 mplJ'h. = a h q^h. + ^ ~ a h > (5)
where: a h = 1 if n ’h > N ‘h = N h / N , and at the sam e tim e nh = n h l n , and otherw ise a h = n h /N*h (n- population sam ple size).
Em pirical Best L inear Predictors (EB LU P) m ake another group o f small area estim ators.
O ne o f them is the estim ator o f the follow ing form:
e n ifjf h. = r , A + ü - r , , ) x J > (6)
where: ß is B LU E estim ator that is Best L inear U nbiased E stim ator o f param eter ß which occurs in model:
f h = X hß + vh,+eh_, (7)
in which vh is such a random com ponent that E (vh ) = 0 and D 2(vh ) = cr2 and eh stands for error resulting from using estim ator Th and at the sam e time E ( eh 17),) - 0 , D ~ ( eh^Th ) = cr2 . The average y h in form ula (7) stands for the
relation o f variance cr2 estim ation and the sum o f variances cr; and 0 7
estim ations.
In given form ulas sizes N b occur. If they are not known they should be estim ated.
(8) D epending on the sam ple sam pling schem e and inform ation about auxiliary variables it is possible to construct other average and global value estim ators. In each o f those issues their variance estim ation and distribution form defining becom es a big problem . Estim ation precision issues are analysed in various papers. V ery often these are sim ulation investigations. Dehnel (1997) in his paper presented results which indicated bigger precision o f regressive estim ators in com parison with direct and quotient estim ators.
The com parison o f estim ators (1) and (6) precision on the ground o f em pirical data using M onte C arlo m ethods and individual dependent sam pling was presented in the paper o f Falorsi and others (1991). A ccording to the presented results com plex estim ator (4) had the best precision m easured, am ong others, by m eans o f the follow ing measure:
- the average o f relative radical o f mean square error:
where H A stands for the num ber o f small areas belonging to distinguished small areas set, L - the num ber of sam ples for which param eter Th value was estim ated, tTh - the estim ator o f param eter Th distinguished on the ground of l-th sam ple I = 1,..., I .
In the discussed investigation com plex estim ator (4) had a bigger bias than estim ators (1), (2) and (5).
Estim ation o f estim ators’ variances for small area can be developed by sim plified m ethods for exam ple by M ahalanobin m ethod or jackk nife method (see: for exam ple B racha 1998, Domański, Pruska 2001).
We should em phasise here that estim ation o f estim ators’ variances, used in small area statistics, is the problem which is being continually discussed and updated.
4. E xa m p les o f in tern atio n a l solu tion s
(9)
In the USA billions o f dollars are annually divided betw een states, sm aller com m unities and, in particular, adm inistrative units o f the low er level - counties w hose num ber totals 3143, depending on their econom ic and social
characteristics. T he criteria o f division o f som e o f funds depend on the population num ber o f a particular county, income or the poverty size. The C ensus O ffice o f the USA usually provides indispensable data. D ata are based on inform ation obtained from censuses, which take place every 10 years. Up till now the size o f these funds has been defined m ainly on the ground o f inform ation obtained from census data. In the USA it is already a traditional source o f d elin ing o f incom e and poverty estim ates on the local scale. Estim ates refer to the follow ing param eters:
- size o f incom e m edian in households, - num ber o f people living below poverty limit,
- num ber o f school-age children (age 5 -1 7 ) living in poor fam ilies - num ber o f people over the age o f 18 living below poverty limit.
As the econom ic conditions o f particular regions have been changing fundam entally betw een census periods, it was necessary to develop m ethods allow ing to obtain m ore current data. W e can illustrate it by the follow ing numbers: in the years from 1989 (the reference year for incom e data obtained from the census in 1990) to 1993 the median o f househo ld s’ incom e decreased by 7% , the num ber o f people below poverty limit increased by 25% , num ber of school-age children living in poor families increased by 24% . M oreover, w hat is also very im portant the changes are not uniform in case o f a particular region. R esearch results o f the C urrent Population Survey (C PS) disclosed 52% increase in the num ber o f the poor in Florida and 44% increase in C alifornia, but only 4% in Texas and 7% in Illinois. Considerable diversification o f these param eters can also occur in districts.
To obtain m ore current data about poverty for states and districts it was necessary to use the representative survey results, which is CPS. H ow ever, the way o f obtaining estim ates on the local scale is different for the census and for CPS surveys. W hat is also different is the precision o f the obtained estim ations. This is caused by various reasons.
D eveloped statistical model links data com ing from various sources including:
- m arch C PS survey in which incom e data are obtained, - food stam ps program m e data,
- tax sets data, and
- population size estim ation for investigated districts.
F our m odels, w hich allow defining quantities connected w ith describing poverty on the scale o f a particular district, w ere outlined. T he quantities are as follows:
a) global num ber o f people living below poverty level, b) num ber o f school-age children living below poverty level,
c) num ber o f people under the age o f 18 living below poverty level, and d) size o f incom e median.
W e showed only the general treatm ent o f size estim ation o f school-age children poverty according to the Am erican counties. R esearch team is still working so the final report has not been published yet. H ow ever, we can com e to som e conclusions on the ground o f prelim inary reports. W e can see that various data sources w ere used here, obtained from both statistical surveys and adm inistrative records. W hen using the term “small area” we understand the area for which, in som e circum stances, we are not able to estim ate dem anded param eters estim ations w hich could be regarded as reliable ones. F or exam ple, we can regard provinces o f small num ber o f investigated households on the ground o f w hich we can obtain unreliable estim ations as small areas.
Kordos, K ubacki (1999) presented the application o f the A m erican approach to the estim ation o f poverty level for small areas in Poland.
How ever, we cannot directly apply the A m erican approach to estim ate poverty level according to new districts. In Poland we have access to com pletely different data sources. In our census we do not obtain inform ation about the income from considerable fraction o f households taking part in it. Instead we have household budget surveys and life conditions surveys in which population income data are gathered. Kordos and Kubacki propose solving the issue in a few stages. In the first one it would be necessary to use accessible data sources from statistical surveys and adm inistrative records and try to estim ate the poverty size for 49 form er provinces. For most of these provinces the estim ated precision o f the poverty level on the ground o f households’ budgets survey is very low. W e can also estim ate poverty size for 10 m acro-regions for which households budget surveys were estim ated. It would be experim ental research work. E xperience from the work could be used in further stages w hich are aim ed at estim ating the poverty level for districts, and next, for 16 new provinces.
From the previous investigations o f household budget and po pulatio n’s living conditions w hich took place in 1996 we are not able to estim ate poverty size for form er provinces. T he estim ation precision for m ost o f provinces is very low. That is why the estim ations do not have very big cognitive value. H ow ever, we can try to m ake them using small area statistics m ethods.
In the quoted paper authors presented approach based on the m odel which can be used to obtain estim ations o f num ber and frictions o f poor households, for exam ple in 1996. T he estim ation for province procedure uses two regression m odels w hich estim ate poverty level - the previous provinces m odel (D W ) and the 10 m acro-regions m odel (M R) according to which household budget surveys (BG D ) are developed.
Estim ation procedure in 1996 contains:
1) creating and using DW model for 49 provinces aim ed at obtaining prelim inary estim ations o f the num ber o f households living below poverty level (GUS, 1997). T he estim ations for previous provinces contain:
- using data obtained from adm inistrative records and other sources which are accessible for all previous provinces and using them as predicted variable,
-d e f in in g and estim ating regression equation referring to predicted variables in relation to dependent variable which is estim ated as logarithm o f the num ber o f poor households in 1996 from household budget surveys for particular provinces,
- obtaining estim ation o f the num ber o f poor households for 49 provinces using estim ated regression coefficient from equation and predicted variables. For previous provinces w hich contained households in sam ple o f household budget survey, estim ations from the model are linked in som e way with estim ations obtained from B G D surveys for these provinces ( that is estim ations obtained from the model for a given province and surveys (B G D ));
2) building and using m acro-regional model MR to obtain estim ations o f the num ber o f poor households according to m acro-regions. E stim ation procedure for m acro-regions is sim ilar to DW model for previous provinces although M R model differs from DW model in a few places:
3) correcting initial estim ations o f the num ber o f poor households obtained from DW model (step 1) for the sake o f com patibility o f a given m acro-region (step 2). In this way we obtain final estim ations o f the num ber o f households living in poverty in 1996 for provinces o f a given m acro-region;
4) obtaining estim ations for m acro-regions in 1996 o f general num ber o f households using dem ographic data. W e can use estim ations from steps 3 and 4 to calculate fraction o f poor households for previous provinces w hich can be useful in scientific research and socio-econom ic policy.
The equation o f previous provinces uses, as predicted variables, estim ations from records:
• individual taxes,
• people getting social welfare, • registered jobless,
• the num ber o f pensioners o f Social Insurance E stablishm ent, • The level o f PKB (G D P) from the nearest year.
T he num ber o f the poor is estim ated from the household budget surveys in 1996. T he equation is as follows:
y, = a + ß xxu + ß 2x2i + /З3*3(. + ß 4x4l + ß 5x5i + Uj +
«?,-where:
y t - logarithm (the num ber o f poor households in DW i),
xu - logarithm (the num ber o f people in tax registers o f total incom e o f
specific value in province DW i ),
*3, - logarithm (the estim ation o f num ber o f households in DW i ),
x 4i - logarithm (the num ber o f pensioners in DW i ),
x si - logarithm (the num ber o f the jobless registered in DW i ), x6l - logarithm (PKB level estim ated for DW i ),
ut - the model error for DW i ,
et - the random error o f dependent variable for DW i .
A nother exam ple o f the application o f small area statistics for international com parisons is labour market. It can be analysed on the scale o f the entire population (for exam ple for particular country or particular groups o f countries) or distinguished subpopulations. In the second case m ethods o f small area statistics can be used to estim ate sizes characterizing labour m arket, such as:
- num ber o f occupationally active people, - num ber o f the jobless,
- num ber o f people looking for a jo b because o f losing one, resigning from a jo b , intending to take a jo b after a break or intending to take a jo b for the first time.
T hese sizes can be regarded as global values o f suitable variables and estim ated by using estim ators presented in the paper o f D om ański, Pruska (2001) if the sam ple sam pling runs according to schem e o f lam inar, individual, dependent sam pling. If the survey is run on the ground o f inform ation gathered by m eans o f m ultistage sam ple sam pling m ethods, global value estim ators form ulas have different form and become more com plex (see: for exam ple, Russo, Falorsi 1999; Bracha 1998;G olata 1996).
It is a good idea to use m ethods o f small area statistics for survey of unem ploym ent phenom enon on the regional scale considering possibility o f using data gathered in the entire population surveys (both in representative surveys and com plete ones, for exam ple current registration o f people looking for a job). Small area statistics m ethods allow to avoid m aking special survey in order to gather needed information.
T he analysis o f unem ploym ent was presented using the exam ple o f three macro-regions: W arsaw , Łódź, Lublin. M ethods, which we used, can be applied analogously in other regional unem ploym ent surveys, for exam ple in particular UE countries or, in the future, in specified regions o f M onetary Union.
Population o f people at the age o f 15 and more, according to international standards, is divided to three categories; the em ployed, the jo bless, the occupationally passive. The em ployed and the jo b less m ake a group of occupationally active people and all the rest o f population is subsum ed into the group o f occupationally passive ones. Unem ploym ent m eter stands for the so
called unem ploym ent rate, which qualifies the unem ployed share in the num ber o f occupationally active people.
Econom ic activity analyses o f population are m ade system atically and in various aspects in many countries. T hese types o f investigations are also conducted in Poland (see: Kałaska, W itkowski 1993), for exam ple on the ground o f current register, in Em ploym ent O ffices and special questionnaire. One o f them is Survey o f Econom ic Activity o f Population (B A EL) m ade four times a year since 1992 (in February, M ay, August and N ovem ber). Inform ation is gathered on the ground o f tw o-stage sam pling sam ple in which the first-stage elem ents are sam pled with stratification according to provinces. At the same time provinces are divided to rural layer and from 2 to 5 urban layers. The second-stage sam pling layer contains flats. All inhabitants o f sam pled flat pertain to the sam ple.
A ccording to definition accepted in BAEL em ployed people are those who w orked or did not work in an investigated week but w ere em ployed by som e em ployer.
A ccording to B A EL, the jobless are people aged 15 or more who do not work but expect to start working in next 30 days or fulfil three conditions:
- in investigated week period were not em ployed,
- were actively looking for a jo b , that is took an action aim ed at finding a jo b during four weeks previous to the survey,
- were able to take a jo b in investigated week as well as in the follow ing one.
In our exam ple we accepted a little different definition o f the jobless. A m ong ones we num ber people w ho regard them selves as those w ho are looking for a jo b but expect to take one. The rem aining ideas (the occupationally active, the em ployed and the occupationally passive) are conform able to version given above. H ow ever, we m ust rem em ber that changing the definition o f the jobless causes the change o f the occupationally active group size. Introduced m odifications w ere caused by intention o f m aking a survey that differs from BAEL analyses, result o f which is published in Poland by C entral Statistical Office. A lthough in our investigation we use statistical data gathered in BAEL, our results give a little different unem ploym ent estim ation than analyses based on the definition accepted by BAEL.
W e used data gathered in BAEL survey in N ovem ber 1996 and N ovem ber 1998.
In order to determ ine estim ations o f global value o f som e variables characterizing labour m arket in considered m acro-regions we used direct estim ator (5). It m eans that we applied estim ators corresponding to single stratiform sam pling (layers stand for provinces which pertain to particular m acro-region, and auxiliary variable stands for dem ographic variable).
C z e s la w D o m a ń s k i
ZASTOSOWANIE STATYSTYKI MAŁYCH OBSZARÓW DO PORÓWNAŃ MIĘDZYNARODOWYCH
Statystyka jest nauką mającą ogromne zastosow anie, zarówno w życiu społecznym , jak i ekonom icznym , jednak nie często dysponujemy pełnymi informacjami zbiorow ości generalnej, zachodzi w ięc potrzeba stosow ania metod wnioskow ania statystycznego. K oszty prowadzenia badań statystycznych są na o g ó ł w ysokie, stąd statystyka małych obszarów w ychodzi naprzeciw potrzebom, co w ięcej, dynam iczne zmiany, w tym terytorialne, zachodzące w św iecie uniem ożliw iają prowadzenie ciągłych badań statystycznych. Artykuł zawiera propozycje stosowania metod statystyki małych obszarów w porównaniach m iędzynarodowych na przykładzie badania sfery ubóstwa i bezrobocia w ujęciu regionalnym ze szczególnym uw zględnieniem badań m ikrospisów prowadzonych w USA i w Polsce.
