The Investigation of Parameter Drift by Expanded Regressions: Generalities, and a ‘Family-Planning’ Example

Abstract

A functional relationship ‘drifts' across a ‘context’ if it holds with different parameter values at different points of an external environment referred to as context. The focus in this paper is upon the analysis of contextual parametric drift. The technique proposed for such analyses involves embedding an ‘initial model’ into a more complex ‘terminal model’ that incorporates the specification of an hypothesized drift. Hypotheses testing upon, and the estimation of, the terminal model can reveal the occurrence of drift and also can provide a mathematical portrait of it. If parametric drift does occur, any point in the context is associated with an ‘expected’ initial model on which hypothesis testing can be carried out and confidence regions obtained. The investigation of parametric drift by expanded regressions is demonstrated by an illustrative example concerned with the effectiveness of family-planning policies on the decline of fertility in the contemporary less-developed countries.