There is practice variation in the selection of a total hip arthroplasty (THA) or a hemiarthroplasty (HA) for the treatment of displaced femoral neck fractures in elderly patients. Large data sets are needed to compare the rates of rare complications following these procedures. We sought to examine the relationship between surgery type and secondary hip surgery (revision or conversion arthroplasty) at 12 months following the index arthroplasty, and that between surgery type and dislocation at 12 months, among elderly Medicare beneficiaries who underwent THA or HA for a femoral neck fracture, taking into account the potential for selection bias. We performed a population-based, retrospective study of elderly (>65 years of age) Medicare beneficiaries who underwent THA or HA following a femoral neck fracture. Two-stage, instrumental variable regression models were applied to nationally representative Medicare medical claims data from 2017 to 2019. Of the 61,695 elderly patients who met the inclusion criteria, of whom 74.1% were female and 92.2% were non-Hispanic White, 10,268 patients (16.6%) underwent THA and 51,427 (83.4%) underwent HA. The findings from the multivariable, instrumental variable analyses indicated that treatment of displaced femoral neck fractures with THA was associated with a significantly higher risk of dislocation at 12 months compared with treatment with HA (2.9% for the THA group versus 1.9% for the HA group; p = 0.001). There was no significant difference in the likelihood of 12-month revision/conversion between THA and HA. The use of THA to treat femoral neck fractures in elderly patients is associated with a significantly higher risk of 12-month dislocation, as compared with the use of HA, although the difference may not be clinically important. A low overall rate of dislocation was found in both groups. The risk of revision/conversion at 12 months did not differ between the groups. Therapeutic Level III. See Instructions for Authors for a complete description of levels of evidence.