A sample selection model for unit and item nonresponse in cross-sectional surveys

We consider a general sample selection model where unit and item nonresponse simultaneously affect a regression relationship of interest, and both types of nonresponse are potentially correlated. We estimate both parametric and semiparametric specifications of the model. The parametric specification assumes that the errors in the latent regression equations follow a trivariate Gaussian distribution. The semiparametric specification avoids distributional assumptions about the underlying regression errors. In our empirical application, we estimate Engel curves for consumption expenditure using data from the first wave of SHARE (Survey on Health, Aging and Retirement in Europe).