Small Area Estimation Techniques Research Articles

Estimation of house prices in regions with small sample sizes

House price indexes had become important economic indicators worldwide, since movements in house prices have been closely correlated with the economic cycle. In order to compute these kind of indexes it is imperative to produce reliable estimates of the average transaction price of houses, not only at the macrolevel (e.g. national and state level), but also at the microlevel (e.g. district, municipalities or further disaggregate regional level). In Portugal, there is a rapidly growing demand of such microlevel statistics since the beginning of the recent financial and economic crisis. The Portuguese Statistical Office provides a range of invaluable data at national level; however, this data cannot be used directly to produce reliable regional-level estimates due to small sample sizes. In this paper we employ small area estimation techniques to produce design and model-based estimates of average transaction price of houses for Portuguese regions with small sample sizes. Our results show that the model-based estimates based on spatial and temporal models are more accurate than the traditional direct design-based estimates. The use of these techniques allows the production of information at disaggregated regional levels that would not be available under the traditional direct estimation approaches. Furthermore, it is even possible to produce reliable model-based estimates for geographical areas without sample. The estimates are expected to provide invaluable information to policy-analysts and decision-making.

Estimating unmet need for contraception by district within Ghana: An application of small-area estimation techniques

The importance of meeting the unmet need for contraception is nowhere more urgent than in the countries of sub-Saharan Africa, where the fertility decline is stalling and total unmet need exceeds 30 per cent among married women. In Ghana, where fertility levels vary considerably, demographic information at sub-national level is essential for building effective family planning programmes. We used small-area estimation techniques, linking data from the 2003 Ghana Demographic and Health Survey to the 2000 Ghana Population and Housing Census, to derive district-level estimates of contraceptive use and unmet need for contraception. The results show considerable variation between districts in contraceptive use and unmet need. The prevalence of contraceptive use varies from 4.1 to 41.7 per cent, while that of the use of modern methods varies from 4.0 to 34.8 per cent. The findings identify districts where family planning programmes need to be strengthened.

Estimation of the monthly unemployment rate for six domains through structural time series modelling with cointegrated trends

National statistical institutes generally apply design-based techniques like the generalized regression estimator to compile official statistics. These techniques, however, have relatively large design variances in the case of small sample sizes. In such cases, model based small area estimation techniques can be considered to improve the precision of the estimates. A multivariate structural time series model is developed and applied to obtain more precise estimates of the Dutch monthly unemployment rate for six domains. The model takes advantage of sample information from preceding time periods through an appropriate time series model and from other domains by modelling the correlation between the trend components of the time series models for the different domains. The trends of the six domains are cointegrated, which allows the use of a more parsimonious common factor model that is based on three common trends. Although the use of common factor models is a well known approach in econometrics, its application in the context of small area estimation is novel. The standard errors of the direct estimates of the monthly unemployment rates are more than halved with this approach.

Small area estimation of forest attributes in the Norwegian National Forest Inventory

The Norwegian National Forest Inventory (NNFI) provides estimates of forest parameters on national and regional scales by means of a systematic network of permanent sample plots. One of the biggest challenges for the NNFI is the interest in forest attribute information for small sub-populations such as municipalities or protected areas. Frequently, too few sampled observations are available for such small areas to allow estimates with acceptable precision. However, if an auxiliary variable exists that is correlated with the variable of interest, small area estimation (SAE) techniques may provide means to improve the precision of estimates. The study aimed at estimating the mean above-ground forest biomass for small areas with high precision and accuracy, using SAE techniques. For this purpose, the simple random sampling (SRS) estimator, the generalized regression (GREG) estimator, and the unit-level empirical best linear unbiased prediction (EBLUP) estimator were compared. Mean canopy height obtained from a photogrammetric canopy height model (CHM) was the auxiliary variable available for every population element. The small areas were 14 municipalities within a 2,184 km2 study area for which an estimate of the mean forest biomass was sought. The municipalities were between 31 and 527 km2 and contained 1–35 NNFI sample plots located within forest. The mean canopy height obtained from the CHM was found to have a strong linear correlation with forest biomass. Both the SRS estimator and the GREG estimator result in unstable estimates if they are based on too few observations. Although this is not the case for the EBLUP estimator, the estimators were only compared for municipalities with more than five sample plots. The SRS resulted in the highest standard errors in all municipalities. Whereas the GREG and EBLUP standard errors were similar for small areas with many sample plots, the EBLUP standard error was usually smaller than the GREG standard error. The difference between the EBLUP and GREG standard error increased with a decreasing number of sample plots within the small area. The EBLUP estimates of mean forest biomass within the municipalities ranged between 95.01 and 153.76 Mg ha−1, with standard errors between 8.20 and 12.84 Mg ha−1.

Is There a Metropolitan Bias? The relationship between poverty and city size in a selection of developing countries

This paper provides evidence from eight developing countries of an inverse relationship between poverty and city size. Poverty is both more widespread and deeper in very small and small towns than in large or very large cities. This basic pattern is generally robust to the choice of poverty line. The paper shows, further, that for all eight countries, a majority of the urban poor live in medium, small or very small towns. Moreover, it is shown that the greater incidence and severity of consumption poverty in smaller towns is generally compounded by similarly greater deprivation in terms of access to basic infrastructure services, such as electricity, heating gas, sewerage and solid waste disposal. We illustrate for one country – Morocco – that inequality within large cities is not driven by a severe dichotomy between slum dwellers and others. Robustness checks are performed to assess whether the findings in the paper hinge on a specific definition of “urban area”; are driven by differences in the cost of living across city-size categories; by reliance on an income-based concept of well-being; or by the application of small-area estimation techniques for estimating poverty rates at the town and city level.

Examining poverty and inequality across small areas of Islamic Republic of Iran; toolmaking for efficient welfare policies

Small area estimation techniques are frequently used in poverty mapping. For this paper, an econometric approach to small area estimation, known as the ELL method, was applied to estimate poverty and inequality indicators in small areas of the Islamic Republic of Iran. This study aims to determine patterns of poverty and inequality in small areas and household characteristics related to them in order to provide practical tools for a geographically targeted pro-poor policy. Drawbacks in the current Government welfare policy (uniform cash distribution) along with the diversity among provinces and small areas regarding scale of poverty and inequality and their correlates, as well as the level of living standards, underlines the need to utilize small area estimations as a tool for evidence-based policymaking.

Small area estimation-based prediction methods to track poverty: validation and applications

Tracking poverty is predicated on the availability of comparable consumption data and reliable price deflators. However, regular series of strictly comparable data are only rarely available. Price deflators are also often missing or disputed. In response, poverty prediction methods that track consumption correlates as opposed to consumption itself have been developed. These methods typically assume that the estimated relation between consumption and its predictors is stable over time -- an assumption that cannot usually be tested directly. This study analyzes the performance of poverty prediction models based on small area estimation techniques. Predicted poverty estimates are compared with directly observed levels in two country settings where data comparability over time is not a problem. Prediction models that employ either non-staple food or non-food expenditures or a full set of assets as predictors are found to yield poverty estimates that match observed poverty well. This offers some support to the use of such methods to approximate the evolution of poverty. Two further country examples illustrate how an application of the method employing models based on household assets can help to adjudicate between alternative price deflators.

District-level poverty estimation: a proposed method

This paper develops a method of estimating micro-level poverty in cases where data are scarce. The method is applied to estimate district-level poverty using the household level Indian national sample survey data for two states, viz., West Bengal and Madhya Pradesh. The method involves estimation of state-level poverty indices from the data formed by pooling data of all the districts (each time excluding one district) and multiplying this poverty vector with a known weight matrix to obtain the unknown district-level poverty vector. The proposed method is expected to yield reliable estimates at the district level, because the district-level estimate is now based on a much larger sample size obtained by pooling data of several districts. This method can be an alternative to the “small area estimation technique” for estimating poverty at sub-state levels in developing countries.

Disaggregate-level estimates of indebtedness in the state of Uttar Pradesh in India: an application of small-area estimation technique

The National Sample Survey Organisation (NSSO) surveys are the main source of official statistics in India, and generate a range of invaluable data at the macro level (e.g. state and national levels). However, the NSSO data cannot be used directly to produce reliable estimates at the micro level (e.g. district or further disaggregate level) due to small sample sizes. There is a rapidly growing demand of such micro-level statistics in India, as the country is moving from centralized to more decentralized planning system. In this article, we employ small-area estimation (SAE) techniques to derive model-based estimates of the proportion of indebted households at district or at other small-area levels in the state of Uttar Pradesh in India by linking data from the Debt–Investment Survey 2002–2003 of NSSO and the Population Census 2001 and the Agriculture Census 2003. Our results show that the model-based estimates are precise and representative. For many small areas, it is even not possible to produce estimates using sample data alone. The model-based estimates generated using SAE are still reliable for such areas. The estimates are expected to provide invaluable information to policy analysts and decision-makers.

Mapping poverty in rural China: how much does the environment matter?

ABSTRACTA recently developed small area estimation technique is used to geographically derive detailed estimates of consumption-based poverty and inequality in rural Shaanxi, China. These estimates may be helpful for targeting since there is wide variability in poverty rates within Shaanxi but low levels of inequality within most counties and townships. We also investigate whether including environmental variables in the equation used to predict consumption and poverty improves upon typical approaches that only use household survey and census data. Ignoring environmental variables appears likely to produce targeting errors.

Examining small area estimation techniques for public health intervention: Lessons from application to under-5 mortality data in Uganda

In Uganda, estimates of under-5 mortality are available only at national and regional levels. None exist at decentralized levels of governance or district level. Using small area statistical techniques in a Hierarchical Bayesian Framework, we applied a modeling approach to determine whether we could learn how to target health interventions to reduce under-5 mortality at the district level. Our modeling approach has an advantage over the commonly used Standardized Mortality Ratios, as it estimates the relative risk of under-5 mortality for a particular district. Using data from Uganda's Demographic and Health Survey in 2006, we were able to estimate relative risk of under-5 mortality for each district. Our findings reveal the evidence of district-to-district variations in under-5 mortality with potential spatial clustering. We believe that this information will be useful in Uganda, as interventions can be targeted at districts with higher relative risk of under-5 mortality. Discussion of these results at district level could increase funding for primary health-care activities. Our analysis also suggests the utility of small area techniques for other countries and other health problems.

ROBUST ESTIMATION OF SMALL‐AREA MEANS AND QUANTILES

SummarySmall‐area estimation techniques have typically relied on plug‐in estimation based on models containing random area effects. More recently, regression M‐quantiles have been suggested for this purpose, thus avoiding conventional Gaussian assumptions, as well as problems associated with the specification of random effects. However, the plug‐in M‐quantile estimator for the small‐area mean can be shown to be the expected value of this mean with respect to a generally biased estimator of the small‐area cumulative distribution function of the characteristic of interest. To correct this problem, we propose a general framework for robust small‐area estimation, based on representing a small‐area estimator as a functional of a predictor of this small‐area cumulative distribution function. Key advantages of this framework are that it naturally leads to integrated estimation of small‐area means and quantiles and is not restricted to M‐quantile models. We also discuss mean squared error estimation for the resulting estimators, and demonstrate the advantages of our approach through model‐based and design‐based simulations, with the latter using economic data collected in an Australian farm survey.

Small-area estimation of forest stand structure in Jalisco, Mexico

Natural resource statistics are often unavailable for small ecological or economic regions and policymakers have to rely on state-level datasets to evaluate the status of their resources (i.e., forests, rangelands, grasslands, agriculture, etc.) at the regional or local level. These resources can be evaluated using small-area estimation techniques. However, it is unknown which small area technique produces the most valid and precise results. The reliability and accuracy of two methods, synthetic and regression estimators, used in small-area analyses, were examined in this study. The two small-area analysis methods were applied to data from Jalisco’s state-wide natural resource inventory to examine how well each technique predicted selected characteristics of forest stand structure. The regression method produced the most valid and precise estimates of forest stand characteristics at multiple geographical scales. Therefore, state and local resource managers should utilize the regression method unless appropriate auxiliary information is not available.

Spline smoothing in small area trend estimation and forecasting

Semiparametric models combining both non-parametric trends and small area random effects are now currently being investigated in small area estimation (SAE). These models can prevent bias when the functional form of the relationship between the response and the covariates is unknown. Furthermore, penalized spline regression can be a good tool to incorporate non-parametric regression models into the SAE techniques, as it can be represented as a mixed effects model. A penalized spline model is considered to analyze trends in small areas and to forecast future values of the response. The prediction mean squared error (MSE) for the fitted and the predicted values, together with estimators for those quantities, are derived. The procedure is illustrated with real data consisting of average prices per squared meter of used dwellings in nine neighborhoods of the city of Vitoria, Spain, during the period 1993–2007. Dwelling prices for the next five years are also forecast. A simulation study is conducted to assess the performance of both the small area trend estimator and the prediction MSE estimators. The results confirm a good behavior of the proposed estimators in terms of bias and variability.

Semiparametric M‐quantile regression for estimating the proportion of acidic lakes in 8‐digit HUCs of the Northeastern US

AbstractBetween 1991 and 1995, the Environmental Monitoring and Assessment Program of the US Environmental Protection Agency conducted a survey of lakes in the Northeastern states of the US to determine the ecological condition of these waters. Here, to this end, we want to obtain estimates of the proportion of lakes at (high) risk of acidification or acidified already for each 8‐digit hydrologic unit code (HUC) within the region of interest. Sample sizes for the 113 HUCs are very small and 27 HUCs are not even observed. Therefore, small area estimation techniques should be invoked for the estimation of the distribution function of acid neutralizing capacity (ANC) for each HUC. The procedure is based on a semiparametric M‐quantile regression model in which ANC depends on elevation and the year of the survey linearly, and on the geographical position of the lake through an unknown smooth bivariate function estimated by low‐rank thin plate splines. Copyright © 2008 John Wiley & Sons, Ltd.

Geographic Decomposition of Inequality in Health and Wealth: Evidence from Cambodia

Health and wealth are found positively correlated, but whether the spatial inequality in health and wealth necessarily exhibits a similar pattern is unclear. We apply the small-area estimation technique to the estimation of inequality in consumption poverty and undernutrition. We develop a framework to compare the wealth and health inequality, and decompose each of the health and wealth inequality into the between-area and within-area components. We found that the sizable proportion of wealth inequality is determined by geography whereas health inequality is intrinsically a local phenomenon.

Commune-Level Estimation of Poverty Measures and its Application in Cambodia

In this study, we combined the Cambodian socioeconomic survey for 1997 and the country's population census of 1998 to produce poverty measures at the commune-level in Cambodia using the small-area estimation technique developed by Elbers, Lanjouw and Lanjouw. While there are a number of communes for which the standard errors associated with the estimates are too high, we found that they are on average small enough to be useful. We illustrate the application of poverty maps with reference to education programmes.

M-quantile models for small area estimation

Small area estimation techniques typically rely on regression models that use both covariates and random effects to explain variation between the areas. However, such models also depend on strong distributional assumptions, require a formal specification of the random part of the model and do not easily allow for outlier-robust inference. We describe a new approach to small area estimation that is based on modelling quantilelike parameters of the conditional distribution of the target variable given the covariates. This avoids the problems associated with specification of random effects, allowing inter-area differences to be characterised by area-specific M-quantile coefficients. The proposed approach is easily made robust against outlying data values and can be adapted for estimation of a wide range of area-specific parameters, including quantiles of the distribution of the target variable in the different small areas. The differences between M-quantile and random effects models are discussed and the alternative approaches to small area estimation are compared using both simulated and real data.

Nutrition Mapping in Tanzania: An Exploratory Analysis

For effective decisionmaking, policymakers and program managers often need detailed information about the welfare of the population, including knowledge about which specific areas are most affected by poverty and undernutrition. Household sample surveys are an important source of information, yet because the typical sample size is only a few thousand observations, the information is only useful for inferences at high levels of aggregation, such as the nation or large regional units. In contrast, data sources with wider coverage, such as national censuses, rarely capture detailed information on welfare levels. Recently small-area estimation techniques have been applied to the study of poverty to produce estimates of poverty, or poverty maps, for small geographic units.This paper uses household survey and unit record census data from Tanzania to explore the possibility of applying small-area estimation methods to the study of children's nutritional status as measured by anthropometry. Overall, undernutrition models have had lower explanatory power than poverty models, which has important implications for the precision of the small-area estimates. The analysis finds that applying small-area estimation techniques to anthropometric data is feasible, although the relatively low explanatory power of the regressions does limit both the degree of disaggregation possible and the power to detect significant differences in undernutrition prevalence between districts and subdistricts. In the case of Tanzania, the nutrition mapping approach reveals considerable heterogeneity in nutritional status within regions and within districts. The most striking finding is the much lower levels of undernutrition in areas classified as urban, including relatively small district centers.

Spatial clustering of rural poverty and food insecurity in Sri Lanka

We mapped poverty, with reference to a nutrition-based poverty line, to analyse its spatial clustering in Sri Lanka. We used the Divisional Secretariat poverty map, derived by combining the principal component analysis and the synthetic small area estimation technique, as the data source. Two statistically significant clusters appear. One cluster indicates that low poverty rural areas cluster around a few low poverty urban areas, where low agricultural employment and better access to roads are key characteristics. The other indicates a cluster of high poverty rural areas, where agriculture is the dominant economic activity, and where spatial clustering is associated with factors influencing agricultural production. Agricultural smallholdings are positively associated with spatial clustering of poor rural areas. In areas where water availability is low, better access to irrigation significantly reduces poverty. Finally, we discuss the use of poverty mapping for effective policy formulation and interventions for alleviating poverty and food insecurity.