The sensitivity of econometric results to alternative implementations of least squares

Abstract

This paper is concerned with a detailed study of the accuracy tradeoffs of differences in data precision and alternative approaches to the estimation of OLS models. The implications of the analysis of a variety of problems, most of which have known answers, extend far beyond OLS modeling and directly impact any empirical analysis when the matrices are at all ill conditioned or "stiff". While the focus here is on linear modeling, the findings are equally, if not more, important to nonlinear modeling. Independent of the effect of the algorithm used, the precision in which the data was initially read was found to have a major impact on accuracy, even when the data was subsequently moved to a higher precision. This finding, illustrated best with the extremely multicollinear Filippelli data set, suggests that if a data base standard is agreed upon, the precision of the data saved will be of critical importance. By the use of variable precision arithmetic software, an extended benchmark was developed for the Filippelli data and the results compared to the real*8 and real*16 QR results. Much of the software developed for this paper has been put in the public domain to be used by other researchers.