The design of a probability sample jointly determines the method used to select sampling units from the population and the estimator of the population parameter. If the sampling fraction is constant for all the units in the sample, then the unweighted sampling mean is an unbiased estimator. In the Survey on Household Income and Wealth (SHIW), units included in the sample have unequal probabilities of selection and each observation is weighted using the inverse of the proper sampling fraction (design weight) adjusted for the response mechanism (nonresponse weight) and for other factors such as imperfect coverage. In this paper we present the weighting scheme of the SHIW and assess its impact on bias and variance of selected estimators. Empirical evidences show that the increasing variability induced by using weighted estimators is compensated by the bias reduction even when performing analysis on sample domains. A set of longitudinal weights is also proposed to account for the selection process and the attrition of the SHIW panel component. These weights, giving their enhanced description of the "panel population", should be better suited to perform longitudinal analysis; nevertheless their higher variance implies that they wouldn't always be preferable in terms of mean square error.
