The Use of Polynomials to Shift Coefficients in Linear Regression Models

Abstract

Polynomials are commonly used in linear regression models to capture nonlinearities in explanatory variables. It is less common, however, that polynomials are used to shift the regression coefficients, an exception being the use of polynomially distributed lag coefficients. This note recommends the technique for a wider range of applications and suggests the Lagrangian interpolation representation as the most convenient for practitioners.