Reply to comment by glenn gotz on “the dynamics of job separation: The case of federal employees”

Abstract

The comment by Glenn Gotz discusses the advantages of a dynamic programming model under uncertainty relative to our model. We have no major disagreement with Gotz on what those advantages are. However, the advantages of our model relative to a programming model could be more clearly brought out, particularly the advantages of computation that largely motivated our model choice. In this short reply we would like to clarify the differences between the two models in behavioural assumptions and in computational difficulty, and to delineate for the practitioner the trade-offs that must be faced by any analyst. Since the trade-offs we discuss are present in all discrete dynamic programming models under uncertainty, not just in our application, our discussion should be useful to a fairly wide audience. To begin we shall state concisely a simple genetic optimal stopping model of the type discussed by Gotz but using slightly different notation to be more consistent with that in the programming literature. In the simplest optimal stopping program the agent (the individual in our case) begins in a particular state (working for the Federal government, for example) and must choose when to change to an alternative state (e.g. to leave the government). It is assumed that the individual cannot return if he leaves, although allowing that possibility would not change the nature of the trade-offs we discuss below. We also assume a finite horizon. Letting L denote the choice to leave and S the choice to stay, the values of leaving and staying, respectively, can be written as follows: