The Numerical Reliability of Econometric Software

Abstract

Numerous examples show that some econometric software packages contain serious flaws, and that users cannot safely assume that their software is accurate. A brief survey of the fundamentals of computer arithmetic discusses the sources of numerical error and emphasizes that computer arithmetic is not at all like pencil-and-paper arithmetic. Both users and developers of econometrics software should first pay attention to accuracy, and only later consider user-friendliness. Details are provided for assessing the accuracy of basic estimation routines, statistical distributions, and random number generators. More accuracy benchmarks are needed, especially for specialized econometric procedures.

Verifying the Solution from a Nonlinear Solver: A Case Study

“…As part of our continuing investigation into the reliability of econometric software (McCullough and Vinod, 1999;McCullough, 2000b;Vinod, 2001), our original goal was to replicate each article in an issue of this journal using the author's software package. Porting the code to other software packages might have enabled us to determine the extent to which econometric results are software-dependent.…”

Multivariate Location-Scale Mixtures of Normals and Mean-Variance-Skewness Portfolio Allocation

“…Unfortunately, such numerical derivatives are sometimes unstable, and moreover, their values may be rather sensitive to the size of the finite increments used. Fortunately, it is possible to obtain analytical expressions for the score vector of our model, which should considerably improve the accuracy of the resulting estimates (McCullough and Vinod, 1999). Moreover, a fast and numerically reliable procedure for the computation of the score for any value of φ is of paramount importance in the implementation of the score-based indirect estimation procedures introduced by Gallant and Tauchen (1996).…”

On the importance of verifying forecasting results

“…This is not true because there is a dichotomy between the use of output and the calculation of output. As McCullough and Vinod (1999) argues, while reporting 10 digits of a solution is not necessary, all intermediate calculations should be done with as many digits as possible. What makes oating point calculations problematic is how small errors can accumulate after successive operations.…”