The Estimation of Economic Relationships using Instrumental Variables

TLDR

Dynamic stochastic relationships generate ideal economic variables, while observed series differ due to random disturbances, and the estimation method was previously suggested by Durbin. The study aims to address the choice of instrumental variables when more instruments are available than the minimum required. The authors derive the asymptotic error‑variance matrix for coefficients under instrumental‑variable estimation and propose an estimation method based on Hotelling’s canonical‑correlation characteristic equation. The resulting estimates coincide with those obtained by maximum‑likelihood limited‑information methods.

Abstract

which the relationships are not exact, so that a set of ideal economic variables is assumed to be generated by a set of dynamic stochastic relationships, as in Koopmans [12], and the actual economic time series are assumed to differ from the ideal economic variables because of random disturbances or measurement errors. The asymptotic error variance matrix for the coefficients of one of the relationships is obtained in the case in which these relationships are estimated using instrumental variables. With this variance matrix we are able to discuss the problem of choice that arises when there are more instrumental variables available than the minimum number required to enable the method to be used. A method of estimation is derived which involves a characteristic equation already considered by Hotelling in defining the canonical correlation [10]. This method was previously suggested by Durbin [7]. The same estimates would be obtained by the maximum-likelihood limited