st: comparing differences in Kendall's tau or Spearman's coefficient using somersd

["Chong, Qi Lin Andrew" <qchong@middlebury.edu>]

Hi all,

I have generated efficiency scores for a cost stochastic frontier with two different definitions of bank output. (So by one definition a bank might seem to have generated more output than the other) The scores are bounded from 1 to infinity, and a half-normal distribution has been assumed for them in the original stochastic frontier (and a normal distribution for the errors). A score of say 1.25 indicates a firm incurs 25% more costs than the most efficient firm it can be compared to.

I have scores for 2003, 2004, 2005, 2006 for a unbalanced sample of banks. I test the correlation in rankings between each pair of years (2003-2004, 2004-2005, 2005-2006) under the two different definitions.

Using Kendall's tau, the idea is if I get 0.85 for Definition 1 and 0.86 for Definition 2, is there a way I can test whether this difference is statistically significant?

I have read the somersd manual quite carefully, by Dr. Roger Newson, which describes how "we can define confidence limits for differences between two Kendall's t's and Somer's Ds, and these are informative, because a larger Kendall's t or Somer's D cannot be secondary to a smaller one." This seems similar to what I'm trying to do, but I am unsure how to implement this.

Also, the scores have been generated from a specific stochastic process and have a distribution assumed for them. So I am unclear whether the assumptions hold under the different methods to be proposed, as the data is of a rather unique nature.

I am a bit new to statistics in general, so a bit more detail would be much appreciated. The Definition 1 efficiency rates are effa03 effa04 and the Definition 2 rates are effb03 effb04. If anyone could outline the steps/commands to take with these variables, I would appreciate that very much. Again, the question is to test whether the difference between Kendall's tau under Definition 1 and 2 is statistically significant - whether the different definitions yield a statistically significant difference in rankings.

Thank you!

Andrew



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