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Time series example in Koop

The differences here seem to be of order 1 percent. You could suspect
a number of things, including the published data file being published
to less precision than that used in the book numbers(also look at number
of points and see if any were added or dropped etc ). However, you may want
to judge these based on what they do to your error which they
presumably are both supposed to minimize but the calculation of which could
be subject to various roundoff errors etc. Unless minimization is done
analytically, it is of course subject to limitations of convergence or iteration
count. Plotting both fits over the data and looking at residuals may help too.
Depending on what you are really trying to do, you may want to change
your error calculation etc. 

Details of numerical results often depend on details of implementation.
This is why stats packages that are not open
source have limitations in applicability. With "real models" of course
things get even more confusing. 
( take a look at credit rating agencies results for example LOL).