A benchmark-free approach to access the accuracy of an OLS model calculation in an econometrically uncertain world

Abstract

Although it is possible to test the calculation accuracy of a software system's implementation of OLS using sample datasets that have been extensively studied and have benchmarked answers, this approach will not help access the calculation accuracy of a user's model for which such answers are not available. Since in theory estimated residuals of an OLS model are required to be orthogonal to the right-hand-side variables, this paper investigates the impact of changes in data precision and calculation method on the software's success in achieving this goal. In attempting estimation of an OLS model the investigator must make two critical decisions. The first decision is the precision of the data used in the calculation, both how it was loaded and whether its precision was subsequently increased for the actual calculation. The second and related decision is the calculation method. To investigate these tradeoffs, two rather simple and well known data sets that do not exhibit extreme multicollinearity are used to illustrate the data precision / calculation method accuracy tradeoff.