How to Adjust for Nonignorable Nonresponse: Calibration, Heckit or FIML?

When a survey response mechanism depends on the variable of interest measured within the same survey and observed for only part of the sample, the situation is one of nonignorable nonresponse. Ignoring the nonresponse is likely to generate significant bias in the estimates. To solve this, one option is the joint modelling of the response mechanism and the variable of interest. Another option is to calibrate each observation with weights constructed from auxiliary data. In an application where earnings equations are estimated these approaches are compared to reference estimates based on large a Swedish register based data set without nonresponse.