Information and computation in simultaneous equations estimation

The complexity and size of simultaneous equations systems necessitates great care with computations for parameter estimation. In three-stage least-squares (3SLS) large matrix inversions are required, and because of the sensitivity of many economic systems to key parameters, accuracy in estimation is important. There are many numerical techniques available which yield accurate solutions to systems of equations. We make use of Householder transformations and recursive triangulation solutions in presenting numerical algorithms for the computation of 3SLS and k-class estimates. Another numerical technique, the singular value decomposition is valuable in providing additional information in k-class estimation. The values of k for which this estimator does not exist are accurately derived, their use being demonstrated by an example.