Properties of the Correlation Matrix Implied by a Recursive Path Model using the Finite Iterative Method

Abstract

The present paper announces and demonstrates some useful properties of the impliedcorrelation matrix built by the Finite Iterative Method (Elhadri and Hanafi,2015, 2016; Elhadri et al., 2019) The most important property is that the impliedcorrelation matrix is affine for each of its parameters. In other words, the firstderivative with respect to each parameter does not depend on this parameter. Moreover,two properties affirm that the first and the second derivatives can be builtiteratively using the previous property. The final property shows that the secondderivatives with respect to every pair ofparameters in the same structural equationare null. These properties are very important in the sense that they can be used toconstruct a new computational approach to estimate recursive model parameters.These findings can be exploited in the estimation stage implementation, especiallyin the computation of the Newton Raphson algorithm to make the first and the secondderivatives of the discrepancy function more explicit and simplistic.