The Estimation of Relationships with Autocorrelated Residuals by the Use of Instrumental Variables

Abstract

SUMMARY The instrumental variables method of estimating the coefficients of a linear relationship between time series which have measurement errors is applied to the case where the coefficients are functions of a set of parameters. The asymptotic error variance matrix of the estimates is obtained, asymptotic tests for the existence and identification of the suggested form of relationship are suggested, and asymptotic confidence regions are given. The general theory is then applied to the case of a relationship with an autoregressive residual, and practical computational methods are suggested.