The jacknife statistic: an application in econometrics

Quenouille has developed a procedure, later termed the jackknife by Tukey, for reducing the bias of a consistent estimator of an unknown parameter. A measure of the variance of the resulting estimator can be obtained and used to provide approximate confidence intervals and tests of significance. Thus the jackknife technique may be especially interesting when the estimator under consideration is biased but consistent and mathematically intractable distribution theory prevents the construction of exact confidence intervals.

Considerable research has been devoted to studying the jackknife technique, predominantly in the fields of biometrics, statistics and numerical analysis. So far the use of the jackknife method in econometrics has been negligible, although one very important class of econometric estimators, the simultaneous equation estimators, is biased in finite samples and, in general, has a mathematically intractable distribution.

In this thesis we investigate the application of the jackknife technique to the Two-Stage Least Squares (2SLS) structural parameter estimator in a simultaneous equation system. The bias reducing property was found to be present in the majority of cases considered in an investigation of the effects of jackknifing on the exact bias of the 2SLS estimator in a two equation model. Conditions are given for which it is unlikely that jackknifing will reduce the bias of the 2SLS estimator.

Since the exact variance of the jackknifed 2SLS estimator is unknown, an examination of the effect on the variance of 2SLS of applying the jackknife had to be made by a simulation experiment.

Whilst the 2SLS estimator always had a smaller mean square error than the jackknifed 2SLS estimator, a comparison of absolute errors rarely produced a significant difference between them.

Finally, it was observed that t statistics formed using the 2SLS estimator may not be distributed according to the Student t distribution. The actual distribution may be highly skewed and serious errors could result if the postulated theoretical distribution was used for statistical inference. In general, this feature was less noticeable for the J2SLS estimator which appeared to have a reasonably symmetric distribution, and consequently there is less likelihood of serious errors being made if the postulated theoretical distribution is used for the purpose of statistical inference.