Job assignment with multivariate skills and the Peter Principle

•I analyze a model of job assignment with and without slot constraints.•Workers have many skills about which the employer can learn through task assignment.•With slot constraints, employers are more likely to reallocate workers internally.•They may do so even if the worker is likely to be less productive in his new job.•This can be interpreted as a version of the Peter Principle.

This paper analyzes the job assignment problem faced by a firm when workers' skills are distributed along several dimensions and jobs require different skills to varying extent. I derive optimal assignment rules with and without slot constraints, and show that under certain circumstances workers may get promoted although they are expected to be less productive in their new job than in their old job. This can be interpreted as a version of the Peter Principle which states that workers get promoted up to their level of incompetence.