The samples used in econometric studies are not always sets of randomly drawn observations from the populations of interest. In many studies sampling has a complex design involving clustering and stratification. In stratification, the population is divided into subpopulations or strata based on exogenous or endogenous variables and then a random sample of unit observations or clusters is drawn from each stratum. Clusters are contiguous groups of units existing within a stratum. Reducing the cost of sampling or operational convenience might be reasons for applying stratification and clustering. On the other hand, particular interest in a small subpopulation may cause oversampling that justifies non-random sampling scheme.This dissertation consists of three essays addressing estimation and inference in cross section and panel data models with non-random samples. In general, ignoring sampling design could produce inconsistent estimators and also inconsistent estimators for their standard errors. In the first essay a multi-stage sampling design including standard stratification and clustering stages at first and variable probability sampling in the final stage is considered. The problem is studied under M-estimators framework. Under a set of regularity conditions the usual weighting estimators are consistent and have asymptotic normal distributions. In cases that stratifications in the first or the second or in the both stages are exogenous dropping the corresponding weights are allowed; we still have consistent estimators. The second essay contributes to the subject of non-random sampling by studyingefficiency in panel data models when data set comes from stratified samples. The goal in this chapter is to obtain more efficient estimators by considering correlation within panels in models with stratified structure. We do not try to find the efficiency bound in this kind of models. Our attempt is to increase efficiency in compare with pooled models that ignore correlations within panels.The paper takes into account correlation within each panel and in eachstratum under a GMM based framework. Theoretical development shows that byconsidering correlation within the panels in each stratum and adding themtogether with appropriate weights, finding more efficient estimators is possible. Likegeneralized estimating equations (GEE) we are able to consider the specificform for correlation for panels in each stratum. Monte Carlo results confirm that the new GMM estimators that is called weighted and unweighted GLS are more efficient than their competitors OLS and weighted OLS that simply overlook the correlation within the panels. Incase of endogenous stratification, weighted GLS and in case of exogenousstratification unweighted GLS is doing better than the rest. For a specificsample size, this efficiency gain depends on what form is chosen forcorrelation and how strong or weak it is. We applied results to study determinants of inequality in the U.S. and estimation results show that efficiency gain in compare with POLS or weighted POLS is substantial.The subject of the third essay is model selection problem. In complex samples involving stratification and clustering, the assumption that observations are distributed independently and identically is not held anymore and therefore the Vuong's (1989) model selection tests are not applicable directly. In order to generalize Vuong's results to estimators other than MLE, we study the problem under M- estimator framework that contains many estimators including but not limited to linear and non-linear least squares, MLE, and QMLE. The theoretical results show that for two nonnested competing models, the asymptotic property of the weighted tests statistics are not a function of the competing estimators but observations and has normal distribution. An interesting finding is that even in case of exogenous stratification, we cannot drop weights in the tests statistics since for nonnested tests both competing models should be misspecified under the null. We also apply results in two empirical studies.
Read
