Consider this an addendum to my last post.
The decay in the VAT return is assumed to be linear, but the range of data is really too small to say for certain. The data could just as easily be an exponential decay. Exponential decay obeys the relationship that the gradient of the function is proportional to the local value of the function. Over short spans it can also look linear. However, it never quite goes to zero.
A curve fit of the data with both an assumed linear gradient and exponential gradient is shown below. The linear fit represents a conservative approximation, while the exponential decay represents an optimistic approximation. We would therefore expect the actual response to fall within the bounds of the two approximations. What this tells us is that the maximum %GDP we can get with VAT is between 11% and 13%.
This is actually a fairly important finding.
All of the arguments associated with use of a sales related revenue assume a constant relationship between revenue and tax rate. The data tells us otherwise. More importantly, we have bounded the maximum value obtained with this method at a much lower level than would be required by a stand-alone tax.
What this means is that a variety of tax mechanisms may be required to reach the higher revenue levels required in our current economy.
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