In yesterday's Budget, George Osborne said:

Let me tell the House what HMRC say about the difference between 50p and 45p.
Their figures tell the story.
The direct cost is only ''100 million a year.

However, it is not really HMRC figures (pdf) that tell this story. The estimate that the 45p rate will cost the Exchequer only ''100m is based not so much upon the evidence of the impact of the 50p rate so much as upon a 2008 report (pdf) to the Mirrlees committee by Mike Brewer, Emmanuel Saez and Andrew Shephard.

The key thing here is the taxable income elasticity (TIE)- the extent to which people reduce their (reported) pre-tax income in response to a cut in their after-tax income. The higher is the TIE, the less a tax rise will bring in to the Treasury - and the less a tax cut will cost.

The Treasury's estimate that the cut to 45p will cost only ''100m is based upon a TIE of 0.45; it had earlier assumed a TIE of just 0.35.

This TIE is almost identical to Brewer, Saez and Shephard's estimate, of 0.46.

The HMRC report corroborates this, in that it estimates a TIE of 0.48. But given the difficulties of distinguishing between genuine long-term behavioural responses and one-off forestalling responses (pulling income forward from 2010-11 into 2009-10), this estimate adds little to BSS's work. The standard error around it is 0.33.

And even BSS's estimate is not precise. There's a SE of 0.13 points around it. This implies that there's a two-thirds chance that the TIE is between 0.33 and 0.58 - and a one-in-six chance that it is below 0.33.

If we take the TIE of 0.58, the cut in the top rate to 45p will save the Treasury almost ''1bn*. Mr Osborne was keen to point that out. What he didn't say is that if we take the lower TIE, of 0.33, then the cut in the top rate to 45p will cost the Treasury not ''100m but over ''1bn. In other words, it would be a big giveaway to the rich.

And the HMRC suggests a reason to believe a lower TIC. It says (par A.17):

There is some reason to believe that these elasticities may not be symmetric for reductions in tax rates that follow increases. This is because tax planning arrangements to mitigate the tax increase may not be unwound if the tax rate subsequently falls again, as the costs of making the arrangements have already been incurred. Individuals who have emigrated since the tax increase might not decide to return after the tax cut. Likewise, some individuals who have chosen to retire earlier in response to the tax rate may decide not to return to work if the tax rate falls. This suggests the elasticity for the rate reduction could be slightly lower than observed by HMRC for the preceding rate increase.

Now, I don't say all this to take a definite view on whether the cut in the top tax rate will or will not raise money. We just don't know.

And this is the point. The fact that Osborne was willing to take a decision based upon such flimsy evidence shows that policy-making is determined more by the interests of the rich than by the objective empirical evidence. And this, as Simon says, signals that there's a political problem which has potentially serious economic effects.

* My estimate, based on HMRC methodology described on p15 of their report.