On the use of sampling weights when estimating regression models with survey data

In this paper it is argued that when the population regression coefficient is of interest, the use of sampling weights can be desirable in regression models with complex survey data. A two-step ML estimator is proposed as an alternative to OLS and weighted least squares. Specification tests are given. The ML estimator does well in simulations, including several cases where it is based on a misspecified model. The specification tests are effective 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.