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We show how to use a smoothed empirical likelihood approach to conduct efficient semiparametric inference in models characterized as conditional moment equalities when data are collected by variable probability sampling. Results from a simulation experiment suggest that the smoothed empirical likelihood based estimator can estimate the model parameters very well in small to moderately sized stratified samples.

We extend Vuong’s (1989) model-selection statistic to allow for complex survey samples. As a further extension, we use an M-estimation setting so that the tests apply to general estimation problems – such as linear and nonlinear least squares, Poisson regression and fractional response models, to name just a few – and not only to maximum likelihood settings. With stratified sampling, we show how the difference in objective functions should be weighted in order to obtain a suitable test statistic. Interestingly, the weights are needed in computing the model-selection statistic even in cases where stratification is appropriately exogenous, in which case the usual unweighted estimators for the parameters are consistent. With cluster samples and panel data, we show how to combine the weighted objective function with a cluster-robust variance estimator in order to expand the scope of the model-selection tests. A small simulation study shows that the weighted test is promising.

Standard stratified sampling (SSS) is a popular non-random sampling scheme. Maximum likelihood estimator (MLE) is inconsistent if some sampled strata depend on the response variable Y (‘endogenous samples’) or if some Y-dependent strata are not sampled at all (‘truncated sample’ – a missing data problem). Various versions of MLE have appeared in the literature, and this paper reviews practical likelihood-based estimators for endogenous or truncated samples in SSS. Also a new estimator ‘Estimated-EX MLE’ is introduced using an extra random sample on X (not on Y) to estimate the distribution EX of X. As information on Y may be hard to get, this estimator's data demand is weaker than an extra random sample on Y in some other estimators. The estimator can greatly improve the efficiency of ‘Fixed-X MLE’ which conditions on X, even if the extra sample size is small. In fact, Estimated-EX MLE does not estimate the full FX as it needs only a sample average using the extra sample. Estimated-EX MLE can be almost as efficient as the ‘Known-FX MLE’. A small-scale simulation study is provided to illustrate these points.

Educational achievement as measured by students’ performance in international tests is receiving scant attention in the educational research. The launch of these tests helped the educational community to better understand the factors underlying students’ achievement and guided the policy makers in their policies. However, Middle East and North African (MENA) countries were underrepresented in these discussions mainly because of data scarcity. Fortunately, Trends in International Mathematics and Science Study (TIMSS) 2007 data provides data for 15 MENA countries for students at the eighth grade and for many MENA countries; this is the first time that such data is available. This chapter aims to present estimates of students’ family background over mathematics and science scores. The results show that students with abundant home resources perform better than those with less home resources. Moreover, expatriate students in Gulf countries perform better than natives.

A common approach to dealing with missing data is to estimate the model on the common subset of data, by necessity throwing away potentially useful data. We derive a new probit type estimator for models with missing covariate data where the dependent variable is binary. For the benchmark case of conditional multinormality we show that our estimator is efficient and provide exact formulae for its asymptotic variance. Simulation results show that our estimator outperforms popular alternatives and is robust to departures from the parametric assumptions adopted in the benchmark case. We illustrate our estimator by examining the portfolio allocation decision of Italian households.

Applied econometric analysis is often performed using data collected from large-scale surveys. These surveys use complex sampling plans in order to reduce costs and increase the estimation efficiency for subgroups of the population. These sampling plans result in unequal inclusion probabilities across units in the population. The purpose of this paper is to derive the asymptotic properties of a design-based nonparametric regression estimator under a combined inference framework. The nonparametric regression estimator considered is the local constant estimator. This work contributes to the literature in two ways. First, it derives the asymptotic properties for the multivariate mixed-data case, including the asymptotic normality of the estimator. Second, I use least squares cross-validation for selecting the bandwidths for both continuous and discrete variables. I run Monte Carlo simulations designed to assess the finite-sample performance of the design-based local constant estimator versus the traditional local constant estimator for three sampling methods, namely, simple random sampling, exogenous stratification and endogenous stratification. Simulation results show that the estimator is consistent and that efficiency gains can be achieved by weighting observations by the inverse of their inclusion probabilities if the sampling is endogenous.