Nonignorable item nonresponse in panel data

To estimate unknown population parameters based on panel data having nonignorable item nonresponse, we propose an innovative data grouping approach according to the number of observed components in the multivariate outcome $ \boldsymbol {y} $ y when the joint distribution of $ \boldsymbol {y} $ y and associated covariate $ \boldsymbol {x} $ x is nonparametric and the nonresponse probability conditional on $ \boldsymbol {y} $ y and $ \boldsymbol {x} $ x has a parametric form. To deal with the identifiability issue, we utilise a nonresponse instrument $ \boldsymbol {z} $ z, an auxiliary variable related to $ \boldsymbol {y} $ y but not related to the nonresponse probability conditional on $ \boldsymbol {y} $ y and $ \boldsymbol {x} $ x. We apply a modified generalised method of moments to obtain estimators of the parameters in the nonresponse probability, and a generalised regression estimation to utilise covariate information for efficient estimation of population parameters. Consistency and asymptotic normality of the proposed estimators of the population parameters are established. Simulation and real data results are presented.