Estimating Regression Models Using Survey Sample Weights

Economists often work with microdata taken from surveys using complex sampling designs. Each redord includes a weight variable represnting the reciprocal of its probability of getting into the sample. When should these weights be used? If they be used, what is the best way to use them? In this paper it is argued that using the weights can be desirable in regression models when the population regression coefficient is of interest. A two-step maximum likelihood estimator is proposed as an alternative to OLS and weighted least squares. Tests for selection bias and misspecification are given. The ML estimator does well in simulations, including several cases where it is based on a misspecification model. Selection bias and misspecification tests are shown tobe successful as pretests in selecting the best estimator. As an example, the methods are used to estimate the returns to education using data from the Canadian Survey of Consumer Finances.